Subgroups — C₆₇×#61592 #30740843

Order 17152.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3322	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3319	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3314	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3297	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3280	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3273	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3268	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3264	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3213	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3211	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3194	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3193	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3190	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3186	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3006	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3003	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#447×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
27	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
28	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
29	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
30	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	#553×C₆₇	—	2	1	no	—
33	#553×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#553×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	#550×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#546×C₆₇	—	2	1	no	—
37	#546×C₆₇	—	2	1	no	—
38	#546×C₆₇	—	2	1	no	—
39	#546×C₆₇	—	2	1	no	—
40	#546×C₆₇	—	2	1	no	—
41	#546×C₆₇	—	2	1	no	—
42	#546×C₆₇	C₂²	1	2	yes	—
43	#546×C₆₇	C₂²	1	2	yes	complemented
44	#546×C₆₇	C₂²	1	2	yes	complemented
45	#546×C₆₇	C₂²	1	2	yes	complemented
46	#546×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#546×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	D₄²×C₆₇	—	2	1	no	—
49	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#540×C₆₇	—	2	1	no	—
51	#538×C₆₇	—	2	1	no	—
52	#538×C₆₇	—	2	1	no	—
53	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#529×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#525×C₆₇	C₂²	1	1	yes	characteristic
57	#525×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	C₂×#123×C₆₇	—	2	1	no	—
59	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	C₂×#121×C₆₇	—	2	1	no	—
61	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	C₂×#120×C₆₇	—	2	1	no	—
65	#518×C₆₇	—	2	1	no	—
66	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
67	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
69	#496×C₆₇	C₂²	1	2	yes	complemented
70	#495×C₆₇	C₂²	1	2	yes	complemented
71	#489×C₆₇	C₂²	1	2	yes	complemented
72	#488×C₆₇	C₂²	1	2	yes	complemented
73	#485×C₆₇	C₂²	1	2	yes	complemented
74	#484×C₆₇	C₂²	1	2	yes	complemented
75	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#482×C₆₇	C₂²	1	2	yes	complemented
77	#480×C₆₇	C₂²	1	2	yes	complemented
78	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#478×C₆₇	C₂²	1	2	yes	complemented
82	#474×C₆₇	C₂²	1	2	yes	complemented
83	#469×C₆₇	C₂²	1	2	yes	complemented
84	#468×C₆₇	C₂²	1	2	yes	complemented
85	#468×C₆₇	C₂²	1	2	yes	complemented
86	#468×C₆₇	C₂²	1	2	yes	complemented
87	#467×C₆₇	C₂²	1	2	yes	complemented
88	#466×C₆₇	C₂²	1	2	yes	complemented
89	#466×C₆₇	C₂²	1	2	yes	complemented
90	#465×C₆₇	C₂²	1	2	yes	complemented
91	#464×C₆₇	C₂²	1	2	yes	complemented
92	#463×C₆₇	C₂²	1	2	yes	complemented
93	#463×C₆₇	C₂²	1	2	yes	complemented
94	#463×C₆₇	C₂²	1	2	yes	complemented
95	#463×C₆₇	C₂²	1	2	yes	complemented
96	#459×C₆₇	C₂²	1	2	yes	complemented
97	#452×C₆₇	C₂²	1	2	yes	complemented
98	#452×C₆₇	C₂²	1	2	yes	complemented
99	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#450×C₆₇	C₂²	1	2	yes	complemented
101	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#450×C₆₇	C₂²	1	2	yes	complemented
104	#449×C₆₇	C₂²	1	2	yes	complemented
105	#449×C₆₇	C₂²	1	2	yes	complemented
106	#449×C₆₇	C₂²	1	2	yes	complemented
107	#449×C₆₇	C₂²	1	2	yes	complemented
108	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#447×C₆₇	C₂²	1	1	yes	characteristic
112	#447×C₆₇	C₂²	1	1	yes	characteristic
113	#447×C₆₇	C₂²	1	2	yes	complemented
114	#447×C₆₇	C₂²	1	2	yes	complemented
115	#447×C₆₇	C₂²	1	2	yes	complemented
116	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	#447×C₆₇	C₂²	1	2	yes	complemented
121	#442×C₆₇	C₂²	1	2	yes	complemented
122	#440×C₆₇	C₂²	1	2	yes	complemented
123	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
124	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
125	#436×C₆₇	C₂²	1	2	yes	complemented
126	#435×C₆₇	C₂²	1	2	yes	complemented
127	#435×C₆₇	C₂²	1	2	yes	complemented
128	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
129	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	#418×C₆₇	C₂²	1	2	yes	complemented
132	#417×C₆₇	C₂²	1	2	yes	complemented
133	#416×C₆₇	C₂²	1	2	yes	complemented
134	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
135	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
136	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
138	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
139	C₂⁵×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	—	2	1	no	—
142	C₂×#41×C₆₇	—	2	1	no	—
143	C₂×#41×C₆₇	—	4	4	no	—
144	C₂×#41×C₆₇	C₂³	1	2	yes	—
145	C₂×#41×C₆₇	C₂³	1	2	yes	—
146	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic, complemented
148	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₆₇	—	2	1	no	—
150	C₂²×D₄×C₆₇	—	2	1	no	—
151	C₂²×D₄×C₆₇	—	2	1	no	—
152	C₂²×D₄×C₆₇	—	2	1	no	—
153	C₂²×D₄×C₆₇	—	2	1	no	—
154	C₂²×D₄×C₆₇	—	2	1	no	—
155	C₂²×D₄×C₆₇	—	2	1	no	—
156	C₂²×D₄×C₆₇	—	2	1	no	—
157	C₂²×D₄×C₆₇	—	4	4	no	—
158	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
159	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
161	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
162	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
165	C₂³×C₄×C₆₇	—	2	1	no	—
166	C₂³×C₄×C₆₇	—	2	1	no	—
167	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
169	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
170	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
171	#135×C₆₇	—	4	4	no	—
172	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	complemented
173	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
174	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
175	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
176	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
177	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
178	C₂×D₈×C₆₇	—	4	4	no	—
179	C₂×D₈×C₆₇	C₂³	1	2	yes	—
180	C₂×D₈×C₆₇	C₂³	1	2	yes	—
181	C₂×D₈×C₆₇	C₂³	1	2	yes	—
182	C₂×D₈×C₆₇	C₂³	1	2	yes	—
183	C₂×D₈×C₆₇	C₂³	1	2	yes	—
184	C₂×D₈×C₆₇	C₂³	1	2	yes	—
185	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
186	C₂×M₁₆×C₆₇	C₂³	1	2	yes	complemented
187	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
188	C₂²×C₈×C₆₇	C₂³	1	2	yes	complemented
189	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
190	#127×C₆₇	—	2	1	no	—
191	#127×C₆₇	C₂³	1	1	yes	characteristic, complemented
192	#126×C₆₇	—	2	1	no	—
193	#126×C₆₇	—	2	1	no	—
194	#126×C₆₇	—	2	1	no	—
195	#125×C₆₇	—	2	1	no	—
196	#125×C₆₇	C₂³	1	1	yes	characteristic, complemented
197	#124×C₆₇	—	2	1	no	—
198	#124×C₆₇	—	2	1	no	—
199	#124×C₆₇	—	2	1	no	—
200	#124×C₆₇	—	2	1	no	—
201	#124×C₆₇	—	2	1	no	—
202	#124×C₆₇	C₂³	1	2	yes	—
203	#124×C₆₇	C₂³	1	2	yes	—
204	#124×C₆₇	C₂³	1	1	yes	characteristic, complemented
205	#123×C₆₇	—	2	1	no	—
206	#123×C₆₇	—	2	1	no	—
207	#123×C₆₇	—	2	1	no	—
208	#123×C₆₇	—	2	2	no	—
209	#123×C₆₇	—	2	2	no	—
210	#123×C₆₇	—	2	2	no	—
211	#123×C₆₇	—	2	2	no	—
212	#123×C₆₇	—	2	1	no	—
213	#123×C₆₇	—	2	1	no	—
214	#123×C₆₇	—	2	1	no	—
215	#123×C₆₇	—	2	1	no	—
216	C₂²⋊Q₈×C₆₇	—	2	1	no	—
217	C₂²⋊Q₈×C₆₇	—	2	1	no	—
218	C₂²⋊Q₈×C₆₇	—	2	1	no	—
219	C₂²⋊Q₈×C₆₇	—	2	1	no	—
220	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
221	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
222	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
223	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
225	#121×C₆₇	—	2	1	no	—
226	#121×C₆₇	—	2	1	no	—
227	#121×C₆₇	—	2	1	no	—
228	#121×C₆₇	—	2	1	no	—
229	#121×C₆₇	—	2	1	no	—
230	#121×C₆₇	—	2	1	no	—
231	#121×C₆₇	—	2	1	no	—
232	#121×C₆₇	—	2	1	no	—
233	#121×C₆₇	—	2	1	no	—
234	#121×C₆₇	—	2	1	no	—
235	#121×C₆₇	—	2	1	no	—
236	#121×C₆₇	—	2	2	no	—
237	#121×C₆₇	—	2	2	no	—
238	#121×C₆₇	—	2	2	no	—
239	#121×C₆₇	—	2	2	no	—
240	#121×C₆₇	—	2	1	no	—
241	#121×C₆₇	—	2	1	no	—
242	#121×C₆₇	—	2	1	no	—
243	#121×C₆₇	—	2	1	no	—
244	#121×C₆₇	C₂³	1	1	yes	characteristic
245	#121×C₆₇	C₂³	1	1	yes	characteristic
246	#121×C₆₇	C₂³	1	1	yes	characteristic
247	#121×C₆₇	C₂³	1	2	yes	—
248	#121×C₆₇	C₂³	1	1	yes	characteristic
249	#121×C₆₇	C₂³	1	1	yes	characteristic
250	#121×C₆₇	C₂³	1	1	yes	characteristic
251	#121×C₆₇	C₂³	1	2	yes	—
252	#121×C₆₇	C₂³	1	1	yes	characteristic, complemented
253	#121×C₆₇	C₂³	1	1	yes	characteristic, complemented
254	#121×C₆₇	C₂³	1	1	yes	characteristic, complemented
255	#120×C₆₇	—	2	1	no	—
256	#120×C₆₇	—	2	1	no	—
257	#120×C₆₇	—	2	2	no	—
258	#120×C₆₇	—	2	2	no	—
259	#120×C₆₇	—	2	2	no	—
260	#120×C₆₇	—	2	2	no	—
261	#120×C₆₇	—	2	1	no	—
262	#120×C₆₇	—	2	1	no	—
263	#120×C₆₇	—	2	1	no	—
264	#120×C₆₇	—	2	1	no	—
265	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
266	C₄×D₄×C₆₇	—	2	1	no	—
267	C₄×D₄×C₆₇	—	2	1	no	—
268	C₄×D₄×C₆₇	—	2	1	no	—
269	C₄×D₄×C₆₇	—	2	1	no	—
270	C₄×D₄×C₆₇	—	2	1	no	—
271	C₄×D₄×C₆₇	—	2	1	no	—
272	C₄×D₄×C₆₇	—	2	1	no	—
273	C₄×D₄×C₆₇	—	2	1	no	—
274	C₄×D₄×C₆₇	—	2	1	no	—
275	C₄×D₄×C₆₇	—	2	1	no	—
276	C₄×D₄×C₆₇	—	2	1	no	—
277	C₄×D₄×C₆₇	—	2	1	no	—
278	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
279	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
280	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
281	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
282	C₄×D₄×C₆₇	C₂³	1	2	yes	—
283	C₄×D₄×C₆₇	C₂³	1	2	yes	—
284	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
285	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
289	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
290	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
291	#117×C₆₇	—	2	1	no	—
292	#117×C₆₇	—	2	1	no	—
293	#117×C₆₇	C₂³	1	1	yes	characteristic
294	#117×C₆₇	C₂³	1	1	yes	characteristic, complemented
295	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
296	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
297	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
300	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
301	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
302	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
303	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
304	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
305	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
306	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
307	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
308	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
309	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
310	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
312	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
313	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
314	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
315	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
316	#107×C₆₇	C₂³	1	2	yes	complemented
317	#107×C₆₇	C₂³	1	2	yes	complemented
318	#107×C₆₇	C₂³	1	2	yes	complemented
319	#106×C₆₇	C₂³	1	2	yes	complemented
320	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
321	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
322	#103×C₆₇	C₂³	1	2	yes	complemented
323	#103×C₆₇	C₂³	1	2	yes	complemented
324	#103×C₆₇	C₂³	1	2	yes	complemented
325	#103×C₆₇	C₂³	1	2	yes	complemented
326	#103×C₆₇	C₂³	1	2	yes	complemented
327	#102×C₆₇	C₂³	1	2	yes	—
328	#102×C₆₇	C₂³	1	2	yes	—
329	#102×C₆₇	C₂³	1	2	yes	—
330	#102×C₆₇	C₂³	1	2	yes	—
331	#102×C₆₇	C₂³	1	2	yes	—
332	#102×C₆₇	C₂³	1	2	yes	—
333	#102×C₆₇	C₂³	1	2	yes	—
334	#102×C₆₇	C₂³	1	2	yes	—
335	#102×C₆₇	C₂³	1	2	yes	complemented
336	#102×C₆₇	C₂³	1	2	yes	complemented
337	#102×C₆₇	C₂³	1	2	yes	complemented
338	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
339	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
340	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
341	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
342	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
343	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
344	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	complemented
345	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	complemented
346	#97×C₆₇	C₂³	1	2	yes	complemented
347	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
348	C₂⁴×C₆₇	—	2	1	no	—
349	C₂⁴×C₆₇	—	2	1	no	—
350	C₂⁴×C₆₇	—	2	2	no	—
351	C₂⁴×C₆₇	—	2	2	no	—
352	C₂⁴×C₆₇	—	2	1	no	—
353	C₂⁴×C₆₇	—	2	1	no	—
354	C₂⁴×C₆₇	—	4	4	no	—
355	C₂⁴×C₆₇	—	4	4	no	—
356	C₂⁴×C₆₇	—	8	2	no	—
357	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
358	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
359	#41×C₆₇	—	2	4	no	—
360	#41×C₆₇	—	2	4	no	—
361	#41×C₆₇	—	4	2	no	—
362	#41×C₆₇	—	4	2	no	—
363	#41×C₆₇	—	4	2	no	—
364	#41×C₆₇	—	4	2	no	—
365	#41×C₆₇	—	4	4	no	—
366	#41×C₆₇	—	4	4	no	—
367	#41×C₆₇	—	8	2	no	—
368	C₂×Q₈×C₆₇	—	2	1	no	—
369	C₂×Q₈×C₆₇	—	2	1	no	—
370	C₂×Q₈×C₆₇	—	4	2	no	—
371	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
372	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₆₇	—	2	4	no	—
374	C₂×D₄×C₆₇	—	2	4	no	—
375	C₂×D₄×C₆₇	—	2	4	no	—
376	C₂×D₄×C₆₇	—	2	1	no	—
377	C₂×D₄×C₆₇	—	2	1	no	—
378	C₂×D₄×C₆₇	—	2	1	no	—
379	C₂×D₄×C₆₇	—	2	1	no	—
380	C₂×D₄×C₆₇	—	2	1	no	—
381	C₂×D₄×C₆₇	—	2	2	no	—
382	C₂×D₄×C₆₇	—	2	2	no	—
383	C₂×D₄×C₆₇	—	2	2	no	—
384	C₂×D₄×C₆₇	—	2	2	no	—
385	C₂×D₄×C₆₇	—	2	1	no	—
386	C₂×D₄×C₆₇	—	2	1	no	—
387	C₂×D₄×C₆₇	—	2	1	no	—
388	C₂×D₄×C₆₇	—	2	1	no	—
389	C₂×D₄×C₆₇	—	2	1	no	—
390	C₂×D₄×C₆₇	—	2	1	no	—
391	C₂×D₄×C₆₇	—	2	1	no	—
392	C₂×D₄×C₆₇	—	2	1	no	—
393	C₂×D₄×C₆₇	—	2	2	no	—
394	C₂×D₄×C₆₇	—	2	2	no	—
395	C₂×D₄×C₆₇	—	2	1	no	—
396	C₂×D₄×C₆₇	—	2	1	no	—
397	C₂×D₄×C₆₇	—	2	1	no	—
398	C₂×D₄×C₆₇	—	2	1	no	—
399	C₂×D₄×C₆₇	—	4	2	no	—
400	C₂×D₄×C₆₇	—	4	2	no	—
401	C₂×D₄×C₆₇	—	4	2	no	—
402	C₂×D₄×C₆₇	—	4	2	no	—
403	C₂×D₄×C₆₇	—	4	2	no	—
404	C₂×D₄×C₆₇	—	4	2	no	—
405	C₂×D₄×C₆₇	—	4	4	no	—
406	C₂×D₄×C₆₇	—	4	4	no	—
407	C₂×D₄×C₆₇	—	4	4	no	—
408	C₂×D₄×C₆₇	—	4	4	no	—
409	C₂×D₄×C₆₇	—	4	4	no	—
410	C₂×D₄×C₆₇	—	8	2	no	—
411	C₂×D₄×C₆₇	—	8	2	no	—
412	C₂×D₄×C₆₇	—	8	2	no	—
413	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
414	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
415	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
416	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
417	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
418	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
420	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
421	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
422	C₂²×C₄×C₆₇	—	2	1	no	—
423	C₂²×C₄×C₆₇	—	2	1	no	—
424	C₂²×C₄×C₆₇	—	2	1	no	—
425	C₂²×C₄×C₆₇	—	2	1	no	—
426	C₂²×C₄×C₆₇	—	2	2	no	—
427	C₂²×C₄×C₆₇	—	2	2	no	—
428	C₂²×C₄×C₆₇	—	2	1	no	—
429	C₂²×C₄×C₆₇	—	2	2	no	—
430	C₂²×C₄×C₆₇	—	2	2	no	—
431	C₂²×C₄×C₆₇	—	2	1	no	—
432	C₂²×C₄×C₆₇	—	2	1	no	—
433	C₂²×C₄×C₆₇	—	2	1	no	—
434	C₂²×C₄×C₆₇	—	2	1	no	—
435	C₂²×C₄×C₆₇	—	4	2	no	—
436	C₂²×C₄×C₆₇	—	4	2	no	—
437	C₂²×C₄×C₆₇	—	4	4	no	—
438	C₂²×C₄×C₆₇	—	8	2	no	—
439	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
440	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
441	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
442	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
443	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
444	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
445	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
447	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
452	Q₁₆×C₆₇	—	4	2	no	—
453	SD₁₆×C₆₇	—	2	4	no	—
454	SD₁₆×C₆₇	—	4	2	no	—
455	SD₁₆×C₆₇	—	4	2	no	—
456	SD₁₆×C₆₇	—	4	2	no	—
457	SD₁₆×C₆₇	—	4	2	no	—
458	D₈×C₆₇	—	2	4	no	—
459	D₈×C₆₇	—	2	4	no	—
460	D₈×C₆₇	—	2	4	no	—
461	D₈×C₆₇	—	4	2	no	—
462	D₈×C₆₇	—	4	2	no	—
463	D₈×C₆₇	—	4	2	no	—
464	M₁₆×C₆₇	—	4	2	no	—
465	M₁₆×C₆₇	—	4	2	no	—
466	C₂×C₈×C₆₇	—	4	2	no	—
467	C₂×C₈×C₆₇	—	4	2	no	—
468	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
469	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
470	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
471	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
472	C₄⋊C₄×C₆₇	—	2	2	no	—
473	C₄⋊C₄×C₆₇	—	2	2	no	—
474	C₄⋊C₄×C₆₇	—	2	1	no	—
475	C₄⋊C₄×C₆₇	—	2	1	no	—
476	C₄⋊C₄×C₆₇	—	2	1	no	—
477	C₄⋊C₄×C₆₇	—	2	1	no	—
478	C₄⋊C₄×C₆₇	—	2	1	no	—
479	C₄⋊C₄×C₆₇	—	2	1	no	—
480	C₄⋊C₄×C₆₇	—	2	1	no	—
481	C₄⋊C₄×C₆₇	—	2	1	no	—
482	C₄⋊C₄×C₆₇	—	2	1	no	—
483	C₄⋊C₄×C₆₇	—	2	1	no	—
484	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
485	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
486	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
487	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
488	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
489	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
490	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
491	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
492	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
493	C₂²⋊C₄×C₆₇	—	2	2	no	—
494	C₂²⋊C₄×C₆₇	—	2	2	no	—
495	C₂²⋊C₄×C₆₇	—	2	1	no	—
496	C₂²⋊C₄×C₆₇	—	2	1	no	—
497	C₂²⋊C₄×C₆₇	—	2	1	no	—
498	C₂²⋊C₄×C₆₇	—	2	1	no	—
499	C₂²⋊C₄×C₆₇	—	2	1	no	—
500	C₂²⋊C₄×C₆₇	—	2	2	no	—
501	C₂²⋊C₄×C₆₇	—	2	2	no	—
502	C₂²⋊C₄×C₆₇	—	2	2	no	—
503	C₂²⋊C₄×C₆₇	—	2	2	no	—
504	C₂²⋊C₄×C₆₇	—	2	1	no	—
505	C₂²⋊C₄×C₆₇	—	2	1	no	—
506	C₂²⋊C₄×C₆₇	—	2	1	no	—
507	C₂²⋊C₄×C₆₇	—	2	1	no	—
508	C₂²⋊C₄×C₆₇	—	2	1	no	—
509	C₂²⋊C₄×C₆₇	—	2	1	no	—
510	C₂²⋊C₄×C₆₇	—	2	1	no	—
511	C₂²⋊C₄×C₆₇	—	2	1	no	—
512	C₂²⋊C₄×C₆₇	—	2	2	no	—
513	C₂²⋊C₄×C₆₇	—	2	2	no	—
514	C₂²⋊C₄×C₆₇	—	2	2	no	—
515	C₂²⋊C₄×C₆₇	—	2	2	no	—
516	C₂²⋊C₄×C₆₇	—	2	1	no	—
517	C₂²⋊C₄×C₆₇	—	2	1	no	—
518	C₂²⋊C₄×C₆₇	—	2	1	no	—
519	C₂²⋊C₄×C₆₇	—	2	1	no	—
520	C₂²⋊C₄×C₆₇	—	2	1	no	—
521	C₂²⋊C₄×C₆₇	—	2	1	no	—
522	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
523	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
524	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
525	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
526	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
527	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
528	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
529	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
530	C₄²×C₆₇	—	2	1	no	—
531	C₄²×C₆₇	—	2	1	no	—
532	C₄²×C₆₇	—	2	1	no	—
533	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
534	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
535	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
536	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
537	C₂³×C₆₇	—	2	4	no	—
538	C₂³×C₆₇	—	2	2	no	—
539	C₂³×C₆₇	—	2	2	no	—
540	C₂³×C₆₇	—	2	2	no	—
541	C₂³×C₆₇	—	2	2	no	—
542	C₂³×C₆₇	—	2	1	no	—
543	C₂³×C₆₇	—	2	2	no	—
544	C₂³×C₆₇	—	2	1	no	—
545	C₂³×C₆₇	—	2	1	no	—
546	C₂³×C₆₇	—	4	1	no	—
547	C₂³×C₆₇	—	4	1	no	—
548	C₂³×C₆₇	—	4	1	no	—
549	C₂³×C₆₇	—	4	4	no	—
550	C₂³×C₆₇	—	4	4	no	—
551	C₂³×C₆₇	—	4	2	no	—
552	C₂³×C₆₇	—	4	2	no	—
553	C₂³×C₆₇	—	4	2	no	—
554	C₂³×C₆₇	—	4	4	no	—
555	C₂³×C₆₇	—	4	2	no	—
556	C₂³×C₆₇	—	4	2	no	—
557	C₂³×C₆₇	—	4	4	no	—
558	C₂³×C₆₇	—	4	2	no	—
559	C₂³×C₆₇	—	4	2	no	—
560	C₂³×C₆₇	—	8	2	no	—
561	C₂³×C₆₇	—	8	2	no	—
562	C₂³×C₆₇	—	8	1	no	—
563	C₂³×C₆₇	—	8	1	no	—
564	C₂³×C₆₇	—	8	1	no	—
565	C₂³×C₆₇	—	8	1	no	—
566	C₂³×C₆₇	—	8	16	no	—
567	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
568	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
569	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
570	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
571	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
572	Q₈×C₆₇	—	2	2	no	—
573	Q₈×C₆₇	—	2	2	no	—
574	Q₈×C₆₇	—	2	2	no	—
575	Q₈×C₆₇	—	4	2	no	—
576	Q₈×C₆₇	—	8	1	no	—
577	D₄×C₆₇	—	2	4	no	—
578	D₄×C₆₇	—	2	2	no	—
579	D₄×C₆₇	—	2	2	no	—
580	D₄×C₆₇	—	2	2	no	—
581	D₄×C₆₇	—	2	2	no	—
582	D₄×C₆₇	—	2	2	no	—
583	D₄×C₆₇	—	2	2	no	—
584	D₄×C₆₇	—	2	2	no	—
585	D₄×C₆₇	—	2	2	no	—
586	D₄×C₆₇	—	4	1	no	—
587	D₄×C₆₇	—	4	1	no	—
588	D₄×C₆₇	—	4	4	no	—
589	D₄×C₆₇	—	4	4	no	—
590	D₄×C₆₇	—	4	2	no	—
591	D₄×C₆₇	—	4	2	no	—
592	D₄×C₆₇	—	4	4	no	—
593	D₄×C₆₇	—	4	4	no	—
594	D₄×C₆₇	—	4	2	no	—
595	D₄×C₆₇	—	4	2	no	—
596	D₄×C₆₇	—	4	2	no	—
597	D₄×C₆₇	—	4	2	no	—
598	D₄×C₆₇	—	4	2	no	—
599	D₄×C₆₇	—	8	1	no	—
600	D₄×C₆₇	—	8	1	no	—
601	D₄×C₆₇	—	8	1	no	—
602	D₄×C₆₇	—	8	2	no	—
603	D₄×C₆₇	—	8	2	no	—
604	D₄×C₆₇	—	8	1	no	—
605	D₄×C₆₇	—	8	1	no	—
606	D₄×C₆₇	—	8	1	no	—
607	D₄×C₆₇	—	8	1	no	—
608	D₄×C₆₇	—	8	1	no	—
609	D₄×C₆₇	—	8	1	no	—
610	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
611	C₂×C₄×C₆₇	—	2	2	no	—
612	C₂×C₄×C₆₇	—	2	2	no	—
613	C₂×C₄×C₆₇	—	2	2	no	—
614	C₂×C₄×C₆₇	—	2	2	no	—
615	C₂×C₄×C₆₇	—	2	2	no	—
616	C₂×C₄×C₆₇	—	2	2	no	—
617	C₂×C₄×C₆₇	—	2	1	no	—
618	C₂×C₄×C₆₇	—	2	1	no	—
619	C₂×C₄×C₆₇	—	2	1	no	—
620	C₂×C₄×C₆₇	—	2	1	no	—
621	C₂×C₄×C₆₇	—	2	1	no	—
622	C₂×C₄×C₆₇	—	2	2	no	—
623	C₂×C₄×C₆₇	—	2	2	no	—
624	C₂×C₄×C₆₇	—	4	1	no	—
625	C₂×C₄×C₆₇	—	4	1	no	—
626	C₂×C₄×C₆₇	—	4	1	no	—
627	C₂×C₄×C₆₇	—	4	1	no	—
628	C₂×C₄×C₆₇	—	4	1	no	—
629	C₂×C₄×C₆₇	—	4	1	no	—
630	C₂×C₄×C₆₇	—	4	1	no	—
631	C₂×C₄×C₆₇	—	4	4	no	—
632	C₂×C₄×C₆₇	—	4	4	no	—
633	C₂×C₄×C₆₇	—	4	2	no	—
634	C₂×C₄×C₆₇	—	4	2	no	—
635	C₂×C₄×C₆₇	—	4	2	no	—
636	C₂×C₄×C₆₇	—	8	2	no	—
637	C₂×C₄×C₆₇	—	8	2	no	—
638	C₂×C₄×C₆₇	—	8	1	no	—
639	C₂×C₄×C₆₇	—	8	1	no	—
640	C₂×C₄×C₆₇	—	8	1	no	—
641	C₂×C₄×C₆₇	—	8	1	no	—
642	C₂×C₄×C₆₇	—	8	1	no	—
643	C₂×C₄×C₆₇	—	8	1	no	—
644	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
645	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
646	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
647	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
648	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
649	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
650	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
651	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
652	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
653	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
654	C₈×C₆₇	—	2	2	no	—
655	C₈×C₆₇	—	2	2	no	—
656	C₈×C₆₇	—	2	2	no	—
657	C₈×C₆₇	—	2	2	no	—
658	C₂²×C₆₇	—	2	1	no	—
659	C₂²×C₆₇	—	2	1	no	—
660	C₂²×C₆₇	—	2	1	no	—
661	C₂²×C₆₇	—	2	1	no	—
662	C₂²×C₆₇	—	2	1	no	—
663	C₂²×C₆₇	—	2	1	no	—
664	C₂²×C₆₇	—	2	1	no	—
665	C₂²×C₆₇	—	2	4	no	—
666	C₂²×C₆₇	—	2	1	no	—
667	C₂²×C₆₇	—	2	1	no	—
668	C₂²×C₆₇	—	2	1	no	—
669	C₂²×C₆₇	—	2	1	no	—
670	C₂²×C₆₇	—	2	1	no	—
671	C₂²×C₆₇	—	2	1	no	—
672	C₂²×C₆₇	—	4	4	no	—
673	C₂²×C₆₇	—	4	8	no	—
674	C₂²×C₆₇	—	4	2	no	—
675	C₂²×C₆₇	—	4	2	no	—
676	C₂²×C₆₇	—	4	1	no	—
677	C₂²×C₆₇	—	4	1	no	—
678	C₂²×C₆₇	—	4	2	no	—
679	C₂²×C₆₇	—	4	1	no	—
680	C₂²×C₆₇	—	4	1	no	—
681	C₂²×C₆₇	—	4	1	no	—
682	C₂²×C₆₇	—	4	1	no	—
683	C₂²×C₆₇	—	4	2	no	—
684	C₂²×C₆₇	—	4	1	no	—
685	C₂²×C₆₇	—	4	1	no	—
686	C₂²×C₆₇	—	4	1	no	—
687	C₂²×C₆₇	—	4	2	no	—
688	C₂²×C₆₇	—	8	2	no	—
689	C₂²×C₆₇	—	8	8	no	—
690	C₂²×C₆₇	—	8	4	no	—
691	C₂²×C₆₇	—	8	8	no	—
692	C₂²×C₆₇	—	16	2	no	—
693	C₂²×C₆₇	—	16	2	no	—
694	C₂²×C₆₇	#575	1	2	yes	—
695	C₂²×C₆₇	#576	1	2	yes	—
696	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
697	C₄×C₆₇	—	2	1	no	—
698	C₄×C₆₇	—	2	1	no	—
699	C₄×C₆₇	—	2	1	no	—
700	C₄×C₆₇	—	2	1	no	—
701	C₄×C₆₇	—	2	1	no	—
702	C₄×C₆₇	—	2	1	no	—
703	C₄×C₆₇	—	2	1	no	—
704	C₄×C₆₇	—	2	1	no	—
705	C₄×C₆₇	—	2	1	no	—
706	C₄×C₆₇	—	4	2	no	—
707	C₄×C₆₇	—	4	1	no	—
708	C₄×C₆₇	—	4	1	no	—
709	C₄×C₆₇	—	4	2	no	—
710	C₄×C₆₇	—	4	1	no	—
711	C₄×C₆₇	—	4	1	no	—
712	C₄×C₆₇	—	4	1	no	—
713	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
714	#61592	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
715	C₂×C₆₇	—	2	2	no	—
716	C₂×C₆₇	—	2	2	no	—
717	C₂×C₆₇	—	4	1	no	—
718	C₂×C₆₇	—	4	1	no	—
719	C₂×C₆₇	—	4	1	no	—
720	C₂×C₆₇	—	4	4	no	—
721	C₂×C₆₇	—	8	2	no	—
722	C₂×C₆₇	—	8	1	no	—
723	C₂×C₆₇	—	8	1	no	—
724	C₂×C₆₇	—	8	1	no	—
725	C₂×C₆₇	#3484	1	1	yes	characteristic
726	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
727	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
728	#3519	C₂×C₆₇	1	1	yes	characteristic, complemented
729	C₂×#546	C₂×C₆₇	1	1	yes	characteristic, complemented
730	#3322	C₂×C₆₇	1	2	yes	complemented
731	#3319	C₂×C₆₇	1	2	yes	complemented
732	#3314	C₂×C₆₇	1	2	yes	complemented
733	#3297	C₂×C₆₇	1	2	yes	complemented
734	#3280	C₂×C₆₇	1	2	yes	complemented
735	#3273	C₂×C₆₇	1	2	yes	complemented
736	#3268	C₂×C₆₇	1	2	yes	complemented
737	#3264	C₂×C₆₇	1	2	yes	complemented
738	#3213	C₂×C₆₇	1	1	yes	characteristic, complemented
739	#3211	C₂×C₆₇	1	1	yes	characteristic, complemented
740	#3194	C₂×C₆₇	1	1	yes	characteristic, complemented
741	#3193	C₂×C₆₇	1	1	yes	characteristic, complemented
742	#3190	C₂×C₆₇	1	1	yes	characteristic, complemented
743	#3186	C₂×C₆₇	1	1	yes	characteristic, complemented
744	#3114	C₂×C₆₇	1	1	yes	characteristic, complemented
745	#3100	C₂×C₆₇	1	1	yes	characteristic, complemented
746	#3006	C₂×C₆₇	1	1	yes	characteristic, complemented
747	#3003	C₂×C₆₇	1	1	yes	characteristic, complemented
748	#3002	C₂×C₆₇	1	1	yes	characteristic, complemented
749	C₂×#447	C₂×C₆₇	1	1	yes	characteristic, complemented
750	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
751	C₆₇	#61592	1	1	yes	characteristic, direct product factor, Sylow
752	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
753	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
754	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
755	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
756	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
757	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
758	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
759	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
760	#553	—	2	1	no	—
761	#553	C₂²×C₆₇	1	1	yes	characteristic, complemented
762	#553	C₂²×C₆₇	1	1	yes	characteristic, complemented
763	#550	C₂²×C₆₇	1	1	yes	characteristic, complemented
764	#546	—	2	1	no	—
765	#546	—	2	1	no	—
766	#546	—	2	1	no	—
767	#546	—	2	1	no	—
768	#546	—	2	1	no	—
769	#546	—	2	1	no	—
770	#546	C₂²×C₆₇	1	2	yes	—
771	#546	C₂²×C₆₇	1	2	yes	complemented
772	#546	C₂²×C₆₇	1	2	yes	complemented
773	#546	C₂²×C₆₇	1	2	yes	complemented
774	#546	C₂²×C₆₇	1	1	yes	characteristic, complemented
775	#546	C₂²×C₆₇	1	1	yes	characteristic, complemented
776	D₄²	—	2	1	no	—
777	D₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
778	#540	—	2	1	no	—
779	#538	—	2	1	no	—
780	#538	—	2	1	no	—
781	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
782	#529	C₂²×C₆₇	1	1	yes	characteristic, complemented
783	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
784	#525	C₂²×C₆₇	1	1	yes	characteristic
785	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
786	C₂×#123	—	2	1	no	—
787	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
788	C₂×#121	—	2	1	no	—
789	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
790	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
791	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
792	C₂×#120	—	2	1	no	—
793	#518	—	2	1	no	—
794	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
795	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
796	C₂²×C₂²⋊C₄	—	2	1	no	—
797	#496	C₂²×C₆₇	1	2	yes	complemented
798	#495	C₂²×C₆₇	1	2	yes	complemented
799	#489	C₂²×C₆₇	1	2	yes	complemented
800	#488	C₂²×C₆₇	1	2	yes	complemented
801	#485	C₂²×C₆₇	1	2	yes	complemented
802	#484	C₂²×C₆₇	1	2	yes	complemented
803	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
804	#482	C₂²×C₆₇	1	2	yes	complemented
805	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
806	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
807	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
808	#480	C₂²×C₆₇	1	2	yes	complemented
809	#478	C₂²×C₆₇	1	2	yes	complemented
810	#474	C₂²×C₆₇	1	2	yes	complemented
811	#469	C₂²×C₆₇	1	2	yes	complemented
812	#468	C₂²×C₆₇	1	2	yes	complemented
813	#468	C₂²×C₆₇	1	2	yes	complemented
814	#468	C₂²×C₆₇	1	2	yes	complemented
815	#467	C₂²×C₆₇	1	2	yes	complemented
816	#466	C₂²×C₆₇	1	2	yes	complemented
817	#466	C₂²×C₆₇	1	2	yes	complemented
818	#465	C₂²×C₆₇	1	2	yes	complemented
819	#464	C₂²×C₆₇	1	2	yes	complemented
820	#463	C₂²×C₆₇	1	2	yes	complemented
821	#463	C₂²×C₆₇	1	2	yes	complemented
822	#463	C₂²×C₆₇	1	2	yes	complemented
823	#463	C₂²×C₆₇	1	2	yes	complemented
824	#459	C₂²×C₆₇	1	2	yes	complemented
825	#452	C₂²×C₆₇	1	2	yes	complemented
826	#452	C₂²×C₆₇	1	2	yes	complemented
827	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
828	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
829	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
830	#450	C₂²×C₆₇	1	2	yes	complemented
831	#450	C₂²×C₆₇	1	2	yes	complemented
832	#449	C₂²×C₆₇	1	2	yes	complemented
833	#449	C₂²×C₆₇	1	2	yes	complemented
834	#449	C₂²×C₆₇	1	2	yes	complemented
835	#449	C₂²×C₆₇	1	2	yes	complemented
836	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
837	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
838	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
839	#447	C₂²×C₆₇	1	1	yes	characteristic
840	#447	C₂²×C₆₇	1	1	yes	characteristic
841	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
842	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
843	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
844	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
845	#447	C₂²×C₆₇	1	2	yes	complemented
846	#447	C₂²×C₆₇	1	2	yes	complemented
847	#447	C₂²×C₆₇	1	2	yes	complemented
848	#447	C₂²×C₆₇	1	2	yes	complemented
849	#442	C₂²×C₆₇	1	2	yes	complemented
850	#440	C₂²×C₆₇	1	2	yes	complemented
851	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
852	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
853	#436	C₂²×C₆₇	1	2	yes	complemented
854	#435	C₂²×C₆₇	1	2	yes	complemented
855	#435	C₂²×C₆₇	1	2	yes	complemented
856	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
857	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
858	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
859	#418	C₂²×C₆₇	1	2	yes	complemented
860	#417	C₂²×C₆₇	1	2	yes	complemented
861	#416	C₂²×C₆₇	1	2	yes	complemented
862	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
863	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
864	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
865	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
866	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
867	C₂⁵	—	2	1	no	—
868	C₂×#41	—	2	1	no	—
869	C₂×#41	—	2	1	no	—
870	C₂×#41	—	2	1	no	—
871	C₂×#41	—	4	4	no	—
872	C₂×#41	C₂³×C₆₇	1	2	yes	—
873	C₂×#41	C₂³×C₆₇	1	2	yes	—
874	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
875	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic, complemented
876	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
877	C₂²×D₄	—	2	1	no	—
878	C₂²×D₄	—	2	1	no	—
879	C₂²×D₄	—	2	1	no	—
880	C₂²×D₄	—	2	1	no	—
881	C₂²×D₄	—	2	1	no	—
882	C₂²×D₄	—	2	1	no	—
883	C₂²×D₄	—	2	1	no	—
884	C₂²×D₄	—	2	1	no	—
885	C₂²×D₄	—	4	4	no	—
886	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
887	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
888	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
889	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
890	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
891	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
892	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
893	C₂³×C₄	—	2	1	no	—
894	C₂³×C₄	—	2	1	no	—
895	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
896	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
897	AGL(1,ℤ/8)	—	4	4	no	—
898	AGL(1,ℤ/8)	—	4	4	no	—
899	#135	—	4	4	no	—
900	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	complemented
901	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
902	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
903	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
904	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
905	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
906	C₂×D₈	—	4	4	no	—
907	C₂×D₈	C₂³×C₆₇	1	2	yes	—
908	C₂×D₈	C₂³×C₆₇	1	2	yes	—
909	C₂×D₈	C₂³×C₆₇	1	2	yes	—
910	C₂×D₈	C₂³×C₆₇	1	2	yes	—
911	C₂×D₈	C₂³×C₆₇	1	2	yes	—
912	C₂×D₈	C₂³×C₆₇	1	2	yes	—
913	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
914	C₂×M₁₆	C₂³×C₆₇	1	2	yes	complemented
915	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
916	C₂²×C₈	C₂³×C₆₇	1	2	yes	complemented
917	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
918	#127	—	2	1	no	—
919	#127	C₂³×C₆₇	1	1	yes	characteristic, complemented
920	#126	—	2	1	no	—
921	#126	—	2	1	no	—
922	#126	—	2	1	no	—
923	#125	—	2	1	no	—
924	#125	C₂³×C₆₇	1	1	yes	characteristic, complemented
925	#124	—	2	1	no	—
926	#124	—	2	1	no	—
927	#124	—	2	1	no	—
928	#124	—	2	1	no	—
929	#124	—	2	1	no	—
930	#124	C₂³×C₆₇	1	2	yes	—
931	#124	C₂³×C₆₇	1	2	yes	—
932	#124	C₂³×C₆₇	1	1	yes	characteristic, complemented
933	#123	—	2	1	no	—
934	#123	—	2	1	no	—
935	#123	—	2	1	no	—
936	#123	—	2	2	no	—
937	#123	—	2	2	no	—
938	#123	—	2	2	no	—
939	#123	—	2	2	no	—
940	#123	—	2	1	no	—
941	#123	—	2	1	no	—
942	#123	—	2	1	no	—
943	#123	—	2	1	no	—
944	C₂²⋊Q₈	—	2	1	no	—
945	C₂²⋊Q₈	—	2	1	no	—
946	C₂²⋊Q₈	—	2	1	no	—
947	C₂²⋊Q₈	—	2	1	no	—
948	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
949	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
950	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
951	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
952	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
953	#121	—	2	1	no	—
954	#121	—	2	1	no	—
955	#121	—	2	1	no	—
956	#121	—	2	1	no	—
957	#121	—	2	1	no	—
958	#121	—	2	1	no	—
959	#121	—	2	1	no	—
960	#121	—	2	1	no	—
961	#121	—	2	1	no	—
962	#121	—	2	1	no	—
963	#121	—	2	1	no	—
964	#121	—	2	2	no	—
965	#121	—	2	2	no	—
966	#121	—	2	2	no	—
967	#121	—	2	2	no	—
968	#121	—	2	1	no	—
969	#121	—	2	1	no	—
970	#121	—	2	1	no	—
971	#121	—	2	1	no	—
972	#121	C₂³×C₆₇	1	1	yes	characteristic
973	#121	C₂³×C₆₇	1	1	yes	characteristic
974	#121	C₂³×C₆₇	1	1	yes	characteristic
975	#121	C₂³×C₆₇	1	1	yes	characteristic
976	#121	C₂³×C₆₇	1	1	yes	characteristic
977	#121	C₂³×C₆₇	1	2	yes	—
978	#121	C₂³×C₆₇	1	2	yes	—
979	#121	C₂³×C₆₇	1	1	yes	characteristic
980	#121	C₂³×C₆₇	1	1	yes	characteristic, complemented
981	#121	C₂³×C₆₇	1	1	yes	characteristic, complemented
982	#121	C₂³×C₆₇	1	1	yes	characteristic, complemented
983	#120	—	2	1	no	—
984	#120	—	2	1	no	—
985	#120	—	2	2	no	—
986	#120	—	2	2	no	—
987	#120	—	2	2	no	—
988	#120	—	2	2	no	—
989	#120	—	2	1	no	—
990	#120	—	2	1	no	—
991	#120	—	2	1	no	—
992	#120	—	2	1	no	—
993	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
994	C₄×D₄	—	2	1	no	—
995	C₄×D₄	—	2	1	no	—
996	C₄×D₄	—	2	1	no	—
997	C₄×D₄	—	2	1	no	—
998	C₄×D₄	—	2	1	no	—
999	C₄×D₄	—	2	1	no	—
1000	C₄×D₄	—	2	1	no	—
1001	C₄×D₄	—	2	1	no	—
1002	C₄×D₄	—	2	1	no	—
1003	C₄×D₄	—	2	1	no	—
1004	C₄×D₄	—	2	1	no	—
1005	C₄×D₄	—	2	1	no	—
1006	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
1007	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
1008	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
1009	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
1010	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1011	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1012	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
1013	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
1014	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
1015	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
1016	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
1017	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
1018	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
1019	#117	—	2	1	no	—
1020	#117	—	2	1	no	—
1021	#117	C₂³×C₆₇	1	1	yes	characteristic
1022	#117	C₂³×C₆₇	1	1	yes	characteristic, complemented
1023	C₂×C₄⋊C₄	—	2	1	no	—
1024	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
1025	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1026	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1027	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
1028	C₂×C₂²⋊C₄	—	2	1	no	—
1029	C₂×C₂²⋊C₄	—	2	1	no	—
1030	C₂×C₂²⋊C₄	—	2	1	no	—
1031	C₂×C₂²⋊C₄	—	2	1	no	—
1032	C₂×C₂²⋊C₄	—	2	1	no	—
1033	C₂×C₂²⋊C₄	—	2	1	no	—
1034	C₂×C₂²⋊C₄	—	2	1	no	—
1035	C₂×C₂²⋊C₄	—	2	2	no	—
1036	C₂×C₂²⋊C₄	—	2	2	no	—
1037	C₂×C₂²⋊C₄	—	2	2	no	—
1038	C₂×C₂²⋊C₄	—	2	2	no	—
1039	C₂×C₂²⋊C₄	—	2	1	no	—
1040	C₂×C₂²⋊C₄	—	2	1	no	—
1041	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
1042	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
1043	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1044	#107	C₂³×C₆₇	1	2	yes	complemented
1045	#107	C₂³×C₆₇	1	2	yes	complemented
1046	#107	C₂³×C₆₇	1	2	yes	complemented
1047	#106	C₂³×C₆₇	1	2	yes	complemented
1048	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1049	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1050	#103	C₂³×C₆₇	1	2	yes	complemented
1051	#103	C₂³×C₆₇	1	2	yes	complemented
1052	#103	C₂³×C₆₇	1	2	yes	complemented
1053	#103	C₂³×C₆₇	1	2	yes	complemented
1054	#103	C₂³×C₆₇	1	2	yes	complemented
1055	#102	C₂³×C₆₇	1	2	yes	—
1056	#102	C₂³×C₆₇	1	2	yes	—
1057	#102	C₂³×C₆₇	1	2	yes	—
1058	#102	C₂³×C₆₇	1	2	yes	—
1059	#102	C₂³×C₆₇	1	2	yes	—
1060	#102	C₂³×C₆₇	1	2	yes	—
1061	#102	C₂³×C₆₇	1	2	yes	—
1062	#102	C₂³×C₆₇	1	2	yes	—
1063	#102	C₂³×C₆₇	1	2	yes	complemented
1064	#102	C₂³×C₆₇	1	2	yes	complemented
1065	#102	C₂³×C₆₇	1	2	yes	complemented
1066	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1067	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1068	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1069	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1070	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1071	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1072	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1073	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1074	#97	C₂³×C₆₇	1	2	yes	complemented
1075	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
1076	C₂⁴	—	2	1	no	—
1077	C₂⁴	—	2	1	no	—
1078	C₂⁴	—	2	2	no	—
1079	C₂⁴	—	2	2	no	—
1080	C₂⁴	—	2	1	no	—
1081	C₂⁴	—	2	1	no	—
1082	C₂⁴	—	4	4	no	—
1083	C₂⁴	—	4	4	no	—
1084	C₂⁴	—	8	2	no	—
1085	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1086	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1087	#41	—	2	4	no	—
1088	#41	—	2	4	no	—
1089	#41	—	4	2	no	—
1090	#41	—	4	2	no	—
1091	#41	—	4	2	no	—
1092	#41	—	4	2	no	—
1093	#41	—	4	4	no	—
1094	#41	—	4	4	no	—
1095	#41	—	8	2	no	—
1096	C₂×Q₈	—	2	1	no	—
1097	C₂×Q₈	—	2	1	no	—
1098	C₂×Q₈	—	4	2	no	—
1099	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1100	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1101	C₂×D₄	—	2	4	no	—
1102	C₂×D₄	—	2	4	no	—
1103	C₂×D₄	—	2	4	no	—
1104	C₂×D₄	—	2	1	no	—
1105	C₂×D₄	—	2	1	no	—
1106	C₂×D₄	—	2	1	no	—
1107	C₂×D₄	—	2	1	no	—
1108	C₂×D₄	—	2	1	no	—
1109	C₂×D₄	—	2	2	no	—
1110	C₂×D₄	—	2	2	no	—
1111	C₂×D₄	—	2	2	no	—
1112	C₂×D₄	—	2	2	no	—
1113	C₂×D₄	—	2	1	no	—
1114	C₂×D₄	—	2	1	no	—
1115	C₂×D₄	—	2	1	no	—
1116	C₂×D₄	—	2	1	no	—
1117	C₂×D₄	—	2	1	no	—
1118	C₂×D₄	—	2	1	no	—
1119	C₂×D₄	—	2	1	no	—
1120	C₂×D₄	—	2	1	no	—
1121	C₂×D₄	—	2	2	no	—
1122	C₂×D₄	—	2	2	no	—
1123	C₂×D₄	—	2	1	no	—
1124	C₂×D₄	—	2	1	no	—
1125	C₂×D₄	—	2	1	no	—
1126	C₂×D₄	—	2	1	no	—
1127	C₂×D₄	—	4	2	no	—
1128	C₂×D₄	—	4	2	no	—
1129	C₂×D₄	—	4	2	no	—
1130	C₂×D₄	—	4	2	no	—
1131	C₂×D₄	—	4	2	no	—
1132	C₂×D₄	—	4	2	no	—
1133	C₂×D₄	—	4	4	no	—
1134	C₂×D₄	—	4	4	no	—
1135	C₂×D₄	—	4	4	no	—
1136	C₂×D₄	—	4	4	no	—
1137	C₂×D₄	—	4	4	no	—
1138	C₂×D₄	—	8	2	no	—
1139	C₂×D₄	—	8	2	no	—
1140	C₂×D₄	—	8	2	no	—
1141	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1142	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1143	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1144	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1145	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1146	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1147	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1148	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1149	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1150	C₂²×C₄	—	2	1	no	—
1151	C₂²×C₄	—	2	1	no	—
1152	C₂²×C₄	—	2	1	no	—
1153	C₂²×C₄	—	2	1	no	—
1154	C₂²×C₄	—	2	2	no	—
1155	C₂²×C₄	—	2	2	no	—
1156	C₂²×C₄	—	2	1	no	—
1157	C₂²×C₄	—	2	2	no	—
1158	C₂²×C₄	—	2	2	no	—
1159	C₂²×C₄	—	2	1	no	—
1160	C₂²×C₄	—	2	1	no	—
1161	C₂²×C₄	—	2	1	no	—
1162	C₂²×C₄	—	2	1	no	—
1163	C₂²×C₄	—	4	2	no	—
1164	C₂²×C₄	—	4	2	no	—
1165	C₂²×C₄	—	4	4	no	—
1166	C₂²×C₄	—	8	2	no	—
1167	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1168	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1169	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1170	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1171	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1172	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1173	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1174	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1175	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1176	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1177	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1178	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1179	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1180	Q₁₆	—	4	2	no	—
1181	SD₁₆	—	2	4	no	—
1182	SD₁₆	—	4	2	no	—
1183	SD₁₆	—	4	2	no	—
1184	SD₁₆	—	4	2	no	—
1185	SD₁₆	—	4	2	no	—
1186	D₈	—	2	4	no	—
1187	D₈	—	2	4	no	—
1188	D₈	—	2	4	no	—
1189	D₈	—	4	2	no	—
1190	D₈	—	4	2	no	—
1191	D₈	—	4	2	no	—
1192	M₁₆	—	4	2	no	—
1193	M₁₆	—	4	2	no	—
1194	C₂×C₈	—	4	2	no	—
1195	C₂×C₈	—	4	2	no	—
1196	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1197	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1198	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1199	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1200	C₄⋊C₄	—	2	2	no	—
1201	C₄⋊C₄	—	2	2	no	—
1202	C₄⋊C₄	—	2	1	no	—
1203	C₄⋊C₄	—	2	1	no	—
1204	C₄⋊C₄	—	2	1	no	—
1205	C₄⋊C₄	—	2	1	no	—
1206	C₄⋊C₄	—	2	1	no	—
1207	C₄⋊C₄	—	2	1	no	—
1208	C₄⋊C₄	—	2	1	no	—
1209	C₄⋊C₄	—	2	1	no	—
1210	C₄⋊C₄	—	2	1	no	—
1211	C₄⋊C₄	—	2	1	no	—
1212	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1213	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1214	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1215	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1216	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1217	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1218	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1219	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1220	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1221	C₂²⋊C₄	—	2	2	no	—
1222	C₂²⋊C₄	—	2	2	no	—
1223	C₂²⋊C₄	—	2	1	no	—
1224	C₂²⋊C₄	—	2	1	no	—
1225	C₂²⋊C₄	—	2	1	no	—
1226	C₂²⋊C₄	—	2	1	no	—
1227	C₂²⋊C₄	—	2	1	no	—
1228	C₂²⋊C₄	—	2	2	no	—
1229	C₂²⋊C₄	—	2	2	no	—
1230	C₂²⋊C₄	—	2	2	no	—
1231	C₂²⋊C₄	—	2	2	no	—
1232	C₂²⋊C₄	—	2	1	no	—
1233	C₂²⋊C₄	—	2	1	no	—
1234	C₂²⋊C₄	—	2	1	no	—
1235	C₂²⋊C₄	—	2	1	no	—
1236	C₂²⋊C₄	—	2	1	no	—
1237	C₂²⋊C₄	—	2	1	no	—
1238	C₂²⋊C₄	—	2	1	no	—
1239	C₂²⋊C₄	—	2	1	no	—
1240	C₂²⋊C₄	—	2	2	no	—
1241	C₂²⋊C₄	—	2	2	no	—
1242	C₂²⋊C₄	—	2	2	no	—
1243	C₂²⋊C₄	—	2	2	no	—
1244	C₂²⋊C₄	—	2	1	no	—
1245	C₂²⋊C₄	—	2	1	no	—
1246	C₂²⋊C₄	—	2	1	no	—
1247	C₂²⋊C₄	—	2	1	no	—
1248	C₂²⋊C₄	—	2	1	no	—
1249	C₂²⋊C₄	—	2	1	no	—
1250	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1251	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1252	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1253	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1254	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1255	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1256	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1257	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1258	C₄²	—	2	1	no	—
1259	C₄²	—	2	1	no	—
1260	C₄²	—	2	1	no	—
1261	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1262	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1263	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1264	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1265	C₂³	—	2	4	no	—
1266	C₂³	—	2	2	no	—
1267	C₂³	—	2	2	no	—
1268	C₂³	—	2	2	no	—
1269	C₂³	—	2	2	no	—
1270	C₂³	—	2	1	no	—
1271	C₂³	—	2	2	no	—
1272	C₂³	—	2	1	no	—
1273	C₂³	—	2	1	no	—
1274	C₂³	—	4	1	no	—
1275	C₂³	—	4	1	no	—
1276	C₂³	—	4	1	no	—
1277	C₂³	—	4	4	no	—
1278	C₂³	—	4	4	no	—
1279	C₂³	—	4	2	no	—
1280	C₂³	—	4	2	no	—
1281	C₂³	—	4	2	no	—
1282	C₂³	—	4	4	no	—
1283	C₂³	—	4	2	no	—
1284	C₂³	—	4	2	no	—
1285	C₂³	—	4	4	no	—
1286	C₂³	—	4	2	no	—
1287	C₂³	—	4	2	no	—
1288	C₂³	—	8	2	no	—
1289	C₂³	—	8	2	no	—
1290	C₂³	—	8	1	no	—
1291	C₂³	—	8	1	no	—
1292	C₂³	—	8	1	no	—
1293	C₂³	—	8	1	no	—
1294	C₂³	—	8	16	no	—
1295	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1296	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1297	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1298	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1299	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1300	Q₈	—	2	2	no	—
1301	Q₈	—	2	2	no	—
1302	Q₈	—	2	2	no	—
1303	Q₈	—	4	2	no	—
1304	Q₈	—	8	1	no	—
1305	D₄	—	2	4	no	—
1306	D₄	—	2	2	no	—
1307	D₄	—	2	2	no	—
1308	D₄	—	2	2	no	—
1309	D₄	—	2	2	no	—
1310	D₄	—	2	2	no	—
1311	D₄	—	2	2	no	—
1312	D₄	—	2	2	no	—
1313	D₄	—	2	2	no	—
1314	D₄	—	4	1	no	—
1315	D₄	—	4	1	no	—
1316	D₄	—	4	4	no	—
1317	D₄	—	4	4	no	—
1318	D₄	—	4	2	no	—
1319	D₄	—	4	2	no	—
1320	D₄	—	4	4	no	—
1321	D₄	—	4	4	no	—
1322	D₄	—	4	2	no	—
1323	D₄	—	4	2	no	—
1324	D₄	—	4	2	no	—
1325	D₄	—	4	2	no	—
1326	D₄	—	4	2	no	—
1327	D₄	—	8	1	no	—
1328	D₄	—	8	1	no	—
1329	D₄	—	8	1	no	—
1330	D₄	—	8	2	no	—
1331	D₄	—	8	2	no	—
1332	D₄	—	8	1	no	—
1333	D₄	—	8	1	no	—
1334	D₄	—	8	1	no	—
1335	D₄	—	8	1	no	—
1336	D₄	—	8	1	no	—
1337	D₄	—	8	1	no	—
1338	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
1339	C₂×C₄	—	2	2	no	—
1340	C₂×C₄	—	2	2	no	—
1341	C₂×C₄	—	2	2	no	—
1342	C₂×C₄	—	2	2	no	—
1343	C₂×C₄	—	2	2	no	—
1344	C₂×C₄	—	2	2	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	2	no	—
1351	C₂×C₄	—	2	2	no	—
1352	C₂×C₄	—	4	1	no	—
1353	C₂×C₄	—	4	1	no	—
1354	C₂×C₄	—	4	1	no	—
1355	C₂×C₄	—	4	1	no	—
1356	C₂×C₄	—	4	1	no	—
1357	C₂×C₄	—	4	1	no	—
1358	C₂×C₄	—	4	1	no	—
1359	C₂×C₄	—	4	4	no	—
1360	C₂×C₄	—	4	4	no	—
1361	C₂×C₄	—	4	2	no	—
1362	C₂×C₄	—	4	2	no	—
1363	C₂×C₄	—	4	2	no	—
1364	C₂×C₄	—	8	2	no	—
1365	C₂×C₄	—	8	2	no	—
1366	C₂×C₄	—	8	1	no	—
1367	C₂×C₄	—	8	1	no	—
1368	C₂×C₄	—	8	1	no	—
1369	C₂×C₄	—	8	1	no	—
1370	C₂×C₄	—	8	1	no	—
1371	C₂×C₄	—	8	1	no	—
1372	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1373	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1374	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1375	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1376	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1377	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1378	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1379	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1380	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1381	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1382	C₈	—	2	2	no	—
1383	C₈	—	2	2	no	—
1384	C₈	—	2	2	no	—
1385	C₈	—	2	2	no	—
1386	C₂²	—	2	1	no	—
1387	C₂²	—	2	1	no	—
1388	C₂²	—	2	1	no	—
1389	C₂²	—	2	1	no	—
1390	C₂²	—	2	1	no	—
1391	C₂²	—	2	1	no	—
1392	C₂²	—	2	1	no	—
1393	C₂²	—	2	1	no	—
1394	C₂²	—	2	1	no	—
1395	C₂²	—	2	1	no	—
1396	C₂²	—	2	1	no	—
1397	C₂²	—	2	1	no	—
1398	C₂²	—	2	1	no	—
1399	C₂²	—	2	4	no	—
1400	C₂²	—	4	4	no	—
1401	C₂²	—	4	8	no	—
1402	C₂²	—	4	2	no	—
1403	C₂²	—	4	2	no	—
1404	C₂²	—	4	1	no	—
1405	C₂²	—	4	1	no	—
1406	C₂²	—	4	1	no	—
1407	C₂²	—	4	2	no	—
1408	C₂²	—	4	1	no	—
1409	C₂²	—	4	1	no	—
1410	C₂²	—	4	1	no	—
1411	C₂²	—	4	2	no	—
1412	C₂²	—	4	1	no	—
1413	C₂²	—	4	1	no	—
1414	C₂²	—	4	2	no	—
1415	C₂²	—	4	1	no	—
1416	C₂²	—	8	2	no	—
1417	C₂²	—	8	8	no	—
1418	C₂²	—	8	4	no	—
1419	C₂²	—	8	8	no	—
1420	C₂²	—	16	2	no	—
1421	C₂²	—	16	2	no	—
1422	C₂²	#575×C₆₇	1	2	yes	—
1423	C₂²	#576×C₆₇	1	2	yes	—
1424	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1425	C₄	—	2	1	no	—
1426	C₄	—	2	1	no	—
1427	C₄	—	2	1	no	—
1428	C₄	—	2	1	no	—
1429	C₄	—	2	1	no	—
1430	C₄	—	2	1	no	—
1431	C₄	—	2	1	no	—
1432	C₄	—	2	1	no	—
1433	C₄	—	2	1	no	—
1434	C₄	—	4	1	no	—
1435	C₄	—	4	2	no	—
1436	C₄	—	4	1	no	—
1437	C₄	—	4	1	no	—
1438	C₄	—	4	1	no	—
1439	C₄	—	4	2	no	—
1440	C₄	—	4	1	no	—
1441	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1442	C₂	—	2	2	no	—
1443	C₂	—	2	2	no	—
1444	C₂	—	4	1	no	—
1445	C₂	—	4	1	no	—
1446	C₂	—	4	1	no	—
1447	C₂	—	4	4	no	—
1448	C₂	—	8	2	no	—
1449	C₂	—	8	1	no	—
1450	C₂	—	8	1	no	—
1451	C₂	—	8	1	no	—
1452	C₂	C₆₇×#3484	1	1	yes	characteristic
1453	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
1454	C₂	C₂×#576×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₆₇×#3519	C₂	semidirect
2. C₂×#546×C₆₇	C₂	semidirect
3. C₆₇×#3322	C₂	semidirect
4. C₆₇×#3319	C₂	semidirect
5. C₆₇×#3314	C₂	semidirect
6. C₆₇×#3297	C₂	semidirect
7. C₆₇×#3280	C₂	semidirect
8. C₆₇×#3273	C₂	semidirect
9. C₆₇×#3268	C₂	semidirect
10. C₆₇×#3264	C₂	semidirect
11. C₆₇×#3213	C₂	semidirect
12. C₆₇×#3211	C₂	semidirect
13. C₆₇×#3194	C₂	semidirect
14. C₆₇×#3193	C₂	semidirect
15. C₆₇×#3190	C₂	semidirect
16. C₆₇×#3186	C₂	semidirect
17. C₆₇×#3114	C₂	semidirect
18. C₆₇×#3100	C₂	semidirect
19. C₆₇×#3006	C₂	semidirect
20. C₆₇×#3003	C₂	semidirect
21. C₆₇×#3002	C₂	semidirect
22. C₂×#447×C₆₇	C₂	semidirect
23. C₆₇×#2974	C₂	semidirect
24. C₂²×#41×C₆₇	C₂²	semidirect
25. C₂³×D₄×C₆₇	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
28. C₂×#135×C₆₇	C₂²	semidirect
29. C₂²×D₈×C₆₇	C₂²	semidirect
30. #555×C₆₇	C₂²	semidirect
31. #554×C₆₇	C₂²	semidirect
33. #553×C₆₇	C₂²	semidirect
34. #553×C₆₇	C₂²	semidirect
35. #550×C₆₇	C₂²	semidirect
43. #546×C₆₇	C₂²	semidirect
44. #546×C₆₇	C₂²	semidirect
45. #546×C₆₇	C₂²	semidirect
46. #546×C₆₇	C₂²	semidirect
47. #546×C₆₇	C₂²	semidirect
49. D₄²×C₆₇	C₂²	semidirect
53. #532×C₆₇	C₂²	semidirect
54. #529×C₆₇	C₂²	semidirect
55. C₂×#124×C₆₇	C₂²	semidirect
57. #525×C₆₇	C₂²	semidirect
59. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
62. C₂×#121×C₆₇	C₂²	semidirect
63. C₂×#121×C₆₇	C₂²	semidirect
67. C₂×C₄×D₄×C₆₇	C₂²	semidirect
69. #496×C₆₇	C₂²	semidirect
70. #495×C₆₇	C₂²	semidirect
71. #489×C₆₇	C₂²	semidirect
72. #488×C₆₇	C₂²	semidirect
73. #485×C₆₇	C₂²	semidirect
74. #484×C₆₇	C₂²	semidirect
75. #483×C₆₇	C₂²	semidirect
76. #482×C₆₇	C₂²	semidirect
77. #480×C₆₇	C₂²	semidirect
78. #480×C₆₇	C₂²	semidirect
79. #480×C₆₇	C₂²	semidirect
80. #480×C₆₇	C₂²	semidirect
81. #478×C₆₇	C₂²	semidirect
82. #474×C₆₇	C₂²	semidirect
83. #469×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #468×C₆₇	C₂²	semidirect
86. #468×C₆₇	C₂²	semidirect
87. #467×C₆₇	C₂²	semidirect
88. #466×C₆₇	C₂²	semidirect
89. #466×C₆₇	C₂²	semidirect
90. #465×C₆₇	C₂²	semidirect
91. #464×C₆₇	C₂²	semidirect
92. #463×C₆₇	C₂²	semidirect
93. #463×C₆₇	C₂²	semidirect
94. #463×C₆₇	C₂²	semidirect
95. #463×C₆₇	C₂²	semidirect
96. #459×C₆₇	C₂²	semidirect
97. #452×C₆₇	C₂²	semidirect
98. #452×C₆₇	C₂²	semidirect
99. #451×C₆₇	C₂²	semidirect
100. #450×C₆₇	C₂²	semidirect
101. #450×C₆₇	C₂²	semidirect
102. #450×C₆₇	C₂²	semidirect
103. #450×C₆₇	C₂²	semidirect
104. #449×C₆₇	C₂²	semidirect
105. #449×C₆₇	C₂²	semidirect
106. #449×C₆₇	C₂²	semidirect
107. #449×C₆₇	C₂²	semidirect
108. #448×C₆₇	C₂²	semidirect
109. #448×C₆₇	C₂²	semidirect
110. #448×C₆₇	C₂²	semidirect
113. #447×C₆₇	C₂²	semidirect
114. #447×C₆₇	C₂²	semidirect
115. #447×C₆₇	C₂²	semidirect
116. #447×C₆₇	C₂²	semidirect
117. #447×C₆₇	C₂²	semidirect
118. #447×C₆₇	C₂²	semidirect
119. #447×C₆₇	C₂²	semidirect
120. #447×C₆₇	C₂²	semidirect
121. #442×C₆₇	C₂²	semidirect
122. #440×C₆₇	C₂²	semidirect
123. C₄×D₈×C₆₇	C₂²	semidirect
124. C₄×D₈×C₆₇	C₂²	semidirect
125. #436×C₆₇	C₂²	semidirect
126. #435×C₆₇	C₂²	semidirect
127. #435×C₆₇	C₂²	semidirect
128. C₈×D₄×C₆₇	C₂²	semidirect
129. #432×C₆₇	C₂²	semidirect
130. #431×C₆₇	C₂²	semidirect
131. #418×C₆₇	C₂²	semidirect
132. #417×C₆₇	C₂²	semidirect
133. #416×C₆₇	C₂²	semidirect
134. C₂×#102×C₆₇	C₂²	semidirect
135. #407×C₆₇	C₂²	semidirect
136. #407×C₆₇	C₂²	semidirect
137. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
138. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
147. C₂×#41×C₆₇	C₂³	semidirect
164. C₂²×D₄×C₆₇	C₂³	semidirect
172. C₂×Q₁₆×C₆₇	C₂³	semidirect
175. C₂×SD₁₆×C₆₇	C₂³	semidirect
176. C₂×SD₁₆×C₆₇	C₂³	semidirect
177. C₂×SD₁₆×C₆₇	C₂³	semidirect
186. C₂×M₁₆×C₆₇	C₂³	semidirect
188. C₂²×C₈×C₆₇	C₂³	semidirect
189. C₄⋊Q₈×C₆₇	C₂³	semidirect
191. #127×C₆₇	C₂³	semidirect
196. #125×C₆₇	C₂³	semidirect
204. #124×C₆₇	C₂³	semidirect
224. C₂²⋊Q₈×C₆₇	C₂³	semidirect
252. #121×C₆₇	C₂³	semidirect
253. #121×C₆₇	C₂³	semidirect
254. #121×C₆₇	C₂³	semidirect
265. C₄×Q₈×C₆₇	C₂³	semidirect
288. C₄×D₄×C₆₇	C₂³	semidirect
289. C₄×D₄×C₆₇	C₂³	semidirect
290. C₄×D₄×C₆₇	C₂³	semidirect
294. #117×C₆₇	C₂³	semidirect
299. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
316. #107×C₆₇	C₂³	semidirect
317. #107×C₆₇	C₂³	semidirect
318. #107×C₆₇	C₂³	semidirect
319. #106×C₆₇	C₂³	semidirect
320. C₄⋊C₈×C₆₇	C₂³	semidirect
321. C₄⋊C₈×C₆₇	C₂³	semidirect
322. #103×C₆₇	C₂³	semidirect
323. #103×C₆₇	C₂³	semidirect
324. #103×C₆₇	C₂³	semidirect
325. #103×C₆₇	C₂³	semidirect
326. #103×C₆₇	C₂³	semidirect
335. #102×C₆₇	C₂³	semidirect
336. #102×C₆₇	C₂³	semidirect
337. #102×C₆₇	C₂³	semidirect
344. C₂²⋊C₈×C₆₇	C₂³	semidirect
345. C₂²⋊C₈×C₆₇	C₂³	semidirect
346. #97×C₆₇	C₂³	semidirect
347. C₄×C₈×C₆₇	C₂³	semidirect
714. #61592	C₆₇	direct (N × H)
728. #3519	C₂×C₆₇	semidirect
729. C₂×#546	C₂×C₆₇	semidirect
730. #3322	C₂×C₆₇	semidirect
731. #3319	C₂×C₆₇	semidirect
732. #3314	C₂×C₆₇	semidirect
733. #3297	C₂×C₆₇	semidirect
734. #3280	C₂×C₆₇	semidirect
735. #3273	C₂×C₆₇	semidirect
736. #3268	C₂×C₆₇	semidirect
737. #3264	C₂×C₆₇	semidirect
738. #3213	C₂×C₆₇	semidirect
739. #3211	C₂×C₆₇	semidirect
740. #3194	C₂×C₆₇	semidirect
741. #3193	C₂×C₆₇	semidirect
742. #3190	C₂×C₆₇	semidirect
743. #3186	C₂×C₆₇	semidirect
744. #3114	C₂×C₆₇	semidirect
745. #3100	C₂×C₆₇	semidirect
746. #3006	C₂×C₆₇	semidirect
747. #3003	C₂×C₆₇	semidirect
748. #3002	C₂×C₆₇	semidirect
749. C₂×#447	C₂×C₆₇	semidirect
750. #2974	C₂×C₆₇	semidirect
751. C₆₇	#61592	direct (N × H)
752. C₂²×#41	C₂²×C₆₇	semidirect
753. C₂³×D₄	C₂²×C₆₇	semidirect
754. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
755. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
756. C₂×#135	C₂²×C₆₇	semidirect
757. C₂²×D₈	C₂²×C₆₇	semidirect
758. #555	C₂²×C₆₇	semidirect
759. #554	C₂²×C₆₇	semidirect
761. #553	C₂²×C₆₇	semidirect
762. #553	C₂²×C₆₇	semidirect
763. #550	C₂²×C₆₇	semidirect
771. #546	C₂²×C₆₇	semidirect
772. #546	C₂²×C₆₇	semidirect
773. #546	C₂²×C₆₇	semidirect
774. #546	C₂²×C₆₇	semidirect
775. #546	C₂²×C₆₇	semidirect
777. D₄²	C₂²×C₆₇	semidirect
781. #532	C₂²×C₆₇	semidirect
782. #529	C₂²×C₆₇	semidirect
783. C₂×#124	C₂²×C₆₇	semidirect
785. #525	C₂²×C₆₇	semidirect
787. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
790. C₂×#121	C₂²×C₆₇	semidirect
791. C₂×#121	C₂²×C₆₇	semidirect
795. C₂×C₄×D₄	C₂²×C₆₇	semidirect
797. #496	C₂²×C₆₇	semidirect
798. #495	C₂²×C₆₇	semidirect
799. #489	C₂²×C₆₇	semidirect
800. #488	C₂²×C₆₇	semidirect
801. #485	C₂²×C₆₇	semidirect
802. #484	C₂²×C₆₇	semidirect
803. #483	C₂²×C₆₇	semidirect
804. #482	C₂²×C₆₇	semidirect
805. #480	C₂²×C₆₇	semidirect
806. #480	C₂²×C₆₇	semidirect
807. #480	C₂²×C₆₇	semidirect
808. #480	C₂²×C₆₇	semidirect
809. #478	C₂²×C₆₇	semidirect
810. #474	C₂²×C₆₇	semidirect
811. #469	C₂²×C₆₇	semidirect
812. #468	C₂²×C₆₇	semidirect
813. #468	C₂²×C₆₇	semidirect
814. #468	C₂²×C₆₇	semidirect
815. #467	C₂²×C₆₇	semidirect
816. #466	C₂²×C₆₇	semidirect
817. #466	C₂²×C₆₇	semidirect
818. #465	C₂²×C₆₇	semidirect
819. #464	C₂²×C₆₇	semidirect
820. #463	C₂²×C₆₇	semidirect
821. #463	C₂²×C₆₇	semidirect
822. #463	C₂²×C₆₇	semidirect
823. #463	C₂²×C₆₇	semidirect
824. #459	C₂²×C₆₇	semidirect
825. #452	C₂²×C₆₇	semidirect
826. #452	C₂²×C₆₇	semidirect
827. #451	C₂²×C₆₇	semidirect
828. #450	C₂²×C₆₇	semidirect
829. #450	C₂²×C₆₇	semidirect
830. #450	C₂²×C₆₇	semidirect
831. #450	C₂²×C₆₇	semidirect
832. #449	C₂²×C₆₇	semidirect
833. #449	C₂²×C₆₇	semidirect
834. #449	C₂²×C₆₇	semidirect
835. #449	C₂²×C₆₇	semidirect
836. #448	C₂²×C₆₇	semidirect
837. #448	C₂²×C₆₇	semidirect
838. #448	C₂²×C₆₇	semidirect
841. #447	C₂²×C₆₇	semidirect
842. #447	C₂²×C₆₇	semidirect
843. #447	C₂²×C₆₇	semidirect
844. #447	C₂²×C₆₇	semidirect
845. #447	C₂²×C₆₇	semidirect
846. #447	C₂²×C₆₇	semidirect
847. #447	C₂²×C₆₇	semidirect
848. #447	C₂²×C₆₇	semidirect
849. #442	C₂²×C₆₇	semidirect
850. #440	C₂²×C₆₇	semidirect
851. C₄×D₈	C₂²×C₆₇	semidirect
852. C₄×D₈	C₂²×C₆₇	semidirect
853. #436	C₂²×C₆₇	semidirect
854. #435	C₂²×C₆₇	semidirect
855. #435	C₂²×C₆₇	semidirect
856. C₈×D₄	C₂²×C₆₇	semidirect
857. #432	C₂²×C₆₇	semidirect
858. #431	C₂²×C₆₇	semidirect
859. #418	C₂²×C₆₇	semidirect
860. #417	C₂²×C₆₇	semidirect
861. #416	C₂²×C₆₇	semidirect
862. C₂×#102	C₂²×C₆₇	semidirect
863. #407	C₂²×C₆₇	semidirect
864. #407	C₂²×C₆₇	semidirect
865. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
866. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
875. C₂×#41	C₂³×C₆₇	semidirect
892. C₂²×D₄	C₂³×C₆₇	semidirect
900. C₂×Q₁₆	C₂³×C₆₇	semidirect
903. C₂×SD₁₆	C₂³×C₆₇	semidirect
904. C₂×SD₁₆	C₂³×C₆₇	semidirect
905. C₂×SD₁₆	C₂³×C₆₇	semidirect
914. C₂×M₁₆	C₂³×C₆₇	semidirect
916. C₂²×C₈	C₂³×C₆₇	semidirect
917. C₄⋊Q₈	C₂³×C₆₇	semidirect
919. #127	C₂³×C₆₇	semidirect
924. #125	C₂³×C₆₇	semidirect
932. #124	C₂³×C₆₇	semidirect
952. C₂²⋊Q₈	C₂³×C₆₇	semidirect
980. #121	C₂³×C₆₇	semidirect
981. #121	C₂³×C₆₇	semidirect
982. #121	C₂³×C₆₇	semidirect
993. C₄×Q₈	C₂³×C₆₇	semidirect
1016. C₄×D₄	C₂³×C₆₇	semidirect
1017. C₄×D₄	C₂³×C₆₇	semidirect
1018. C₄×D₄	C₂³×C₆₇	semidirect
1022. #117	C₂³×C₆₇	semidirect
1027. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
1044. #107	C₂³×C₆₇	semidirect
1045. #107	C₂³×C₆₇	semidirect
1046. #107	C₂³×C₆₇	semidirect
1047. #106	C₂³×C₆₇	semidirect
1048. C₄⋊C₈	C₂³×C₆₇	semidirect
1049. C₄⋊C₈	C₂³×C₆₇	semidirect
1050. #103	C₂³×C₆₇	semidirect
1051. #103	C₂³×C₆₇	semidirect
1052. #103	C₂³×C₆₇	semidirect
1053. #103	C₂³×C₆₇	semidirect
1054. #103	C₂³×C₆₇	semidirect
1063. #102	C₂³×C₆₇	semidirect
1064. #102	C₂³×C₆₇	semidirect
1065. #102	C₂³×C₆₇	semidirect
1072. C₂²⋊C₈	C₂³×C₆₇	semidirect
1073. C₂²⋊C₈	C₂³×C₆₇	semidirect
1074. #97	C₂³×C₆₇	semidirect
1075. C₄×C₈	C₂³×C₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₇×#3519	2
C₂×#546×C₆₇	2
C₆₇×#3322	2
C₆₇×#3319	2
C₆₇×#3314	2
C₆₇×#3297	2
C₆₇×#3280	2
C₆₇×#3273	2
C₆₇×#3268	2
C₆₇×#3264	2
C₆₇×#3213	2
C₆₇×#3211	2
C₆₇×#3194	2
C₆₇×#3193	2
C₆₇×#3190	2
C₆₇×#3186	2
C₆₇×#3114	2
C₆₇×#3100	2
C₆₇×#3006	2
C₆₇×#3003	2
C₆₇×#3002	2
C₂×#447×C₆₇	2
C₆₇×#2974	2
#61592	67

Subgroups — C67×#61592 #30740843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61592 #30740843