Subgroups — C₆₇×#61156 #30740407

Order 17152.

2254 conjugacy classes of subgroups.

The subgroup lattice has 1424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3323	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3322	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3319	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3314	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3311	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3306	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3297	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3296	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3095	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3040	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3005	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3003	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#418×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#556×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#553×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	#553×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#552×C₆₇	—	2	1	no	—
37	#552×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#552×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#551×C₆₇	—	2	1	no	—
40	#551×C₆₇	—	2	1	no	—
41	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#546×C₆₇	—	2	1	no	—
43	#546×C₆₇	—	2	1	no	—
44	#546×C₆₇	—	2	1	no	—
45	#546×C₆₇	—	2	1	no	—
46	#546×C₆₇	—	2	1	no	—
47	#546×C₆₇	C₂²	1	2	yes	—
48	#546×C₆₇	C₂²	1	2	yes	—
49	#546×C₆₇	C₂²	1	2	yes	—
50	#546×C₆₇	C₂²	1	2	yes	—
51	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#529×C₆₇	—	2	1	no	—
53	#529×C₆₇	—	2	1	no	—
54	#529×C₆₇	—	2	1	no	—
55	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
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
60	C₂×#121×C₆₇	—	2	1	no	—
61	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×#120×C₆₇	—	2	1	no	—
63	C₄×#41×C₆₇	—	2	1	no	—
64	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
66	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
67	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
68	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
70	#489×C₆₇	C₂²	1	2	yes	complemented
71	#489×C₆₇	C₂²	1	2	yes	complemented
72	#488×C₆₇	C₂²	1	2	yes	complemented
73	#488×C₆₇	C₂²	1	2	yes	complemented
74	#485×C₆₇	C₂²	1	2	yes	complemented
75	#485×C₆₇	C₂²	1	2	yes	complemented
76	#484×C₆₇	C₂²	1	2	yes	complemented
77	#483×C₆₇	C₂²	1	2	yes	complemented
78	#482×C₆₇	C₂²	1	2	yes	complemented
79	#482×C₆₇	C₂²	1	2	yes	complemented
80	#481×C₆₇	C₂²	1	2	yes	complemented
81	#480×C₆₇	C₂²	1	2	yes	complemented
82	#478×C₆₇	C₂²	1	2	yes	complemented
83	#478×C₆₇	C₂²	1	2	yes	complemented
84	#476×C₆₇	C₂²	1	2	yes	complemented
85	#474×C₆₇	C₂²	1	2	yes	complemented
86	#470×C₆₇	C₂²	1	2	yes	complemented
87	#469×C₆₇	C₂²	1	2	yes	complemented
88	#468×C₆₇	C₂²	1	2	yes	complemented
89	#468×C₆₇	C₂²	1	2	yes	complemented
90	#467×C₆₇	C₂²	1	2	yes	complemented
91	#466×C₆₇	C₂²	1	2	yes	complemented
92	#465×C₆₇	C₂²	1	2	yes	complemented
93	#465×C₆₇	C₂²	1	2	yes	complemented
94	#464×C₆₇	C₂²	1	2	yes	complemented
95	#464×C₆₇	C₂²	1	2	yes	complemented
96	#463×C₆₇	C₂²	1	2	yes	complemented
97	#463×C₆₇	C₂²	1	2	yes	complemented
98	#452×C₆₇	C₂²	1	2	yes	complemented
99	#452×C₆₇	C₂²	1	2	yes	complemented
100	#450×C₆₇	C₂²	1	2	yes	complemented
101	#450×C₆₇	C₂²	1	2	yes	complemented
102	#449×C₆₇	C₂²	1	2	yes	complemented
103	#449×C₆₇	C₂²	1	2	yes	complemented
104	#447×C₆₇	C₂²	1	2	yes	complemented
105	#447×C₆₇	C₂²	1	2	yes	complemented
106	#442×C₆₇	C₂²	1	2	yes	complemented
107	#440×C₆₇	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
109	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
110	#436×C₆₇	C₂²	1	2	yes	complemented
111	#435×C₆₇	C₂²	1	2	yes	complemented
112	#435×C₆₇	C₂²	1	2	yes	complemented
113	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
114	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#418×C₆₇	C₂²	1	1	yes	characteristic
122	#418×C₆₇	C₂²	1	1	yes	characteristic
123	#418×C₆₇	C₂²	1	1	yes	characteristic
124	#418×C₆₇	C₂²	1	1	yes	characteristic
125	#418×C₆₇	C₂²	1	1	yes	characteristic
126	#418×C₆₇	C₂²	1	1	yes	characteristic
127	#418×C₆₇	C₂²	1	2	yes	complemented
128	#418×C₆₇	C₂²	1	2	yes	complemented
129	#417×C₆₇	C₂²	1	2	yes	complemented
130	#417×C₆₇	C₂²	1	2	yes	complemented
131	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	#416×C₆₇	C₂²	1	2	yes	complemented
133	#416×C₆₇	C₂²	1	2	yes	complemented
134	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
135	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
136	#407×C₆₇	C₂²	1	1	yes	characteristic
137	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
138	C₄×M₁₆×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	—	2	4	no	—
144	C₂×#41×C₆₇	—	4	2	no	—
145	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×#41×C₆₇	C₂³	1	2	yes	—
147	C₂×#41×C₆₇	C₂³	1	2	yes	—
148	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₆₇	—	2	4	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	—	4	2	no	—
156	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
157	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
158	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
159	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
160	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
161	C₂³×C₄×C₆₇	—	2	1	no	—
162	C₂³×C₄×C₆₇	—	2	1	no	—
163	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
165	#137×C₆₇	—	4	2	no	—
166	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
167	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
168	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	complemented
169	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
170	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
171	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
172	C₂×D₈×C₆₇	C₂³	1	2	yes	—
173	C₂×D₈×C₆₇	C₂³	1	2	yes	—
174	C₂×M₁₆×C₆₇	—	4	2	no	—
175	C₂×M₁₆×C₆₇	—	4	2	no	—
176	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
181	C₂×M₁₆×C₆₇	C₂³	1	2	yes	complemented
182	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
183	C₂²×C₈×C₆₇	C₂³	1	2	yes	complemented
184	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
185	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
186	#126×C₆₇	—	2	1	no	—
187	#126×C₆₇	—	2	1	no	—
188	#126×C₆₇	—	2	1	no	—
189	#126×C₆₇	—	2	1	no	—
190	#126×C₆₇	—	2	1	no	—
191	#126×C₆₇	—	2	1	no	—
192	#125×C₆₇	—	2	1	no	—
193	#125×C₆₇	—	2	1	no	—
194	#125×C₆₇	—	2	1	no	—
195	#125×C₆₇	C₂³	1	1	yes	characteristic, complemented
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	#123×C₆₇	—	2	1	no	—
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	—	2	1	no	—
221	C₂²⋊Q₈×C₆₇	—	2	1	no	—
222	C₂²⋊Q₈×C₆₇	—	2	1	no	—
223	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
224	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
226	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
227	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
228	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
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	2	no	—
235	#121×C₆₇	—	2	2	no	—
236	#121×C₆₇	—	2	2	no	—
237	#121×C₆₇	—	2	2	no	—
238	#121×C₆₇	C₂³	1	1	yes	characteristic
239	#121×C₆₇	C₂³	1	2	yes	—
240	#121×C₆₇	C₂³	1	1	yes	characteristic
241	#121×C₆₇	C₂³	1	2	yes	—
242	#121×C₆₇	C₂³	1	1	yes	characteristic, complemented
243	#121×C₆₇	C₂³	1	1	yes	characteristic, complemented
244	#120×C₆₇	—	2	1	no	—
245	#120×C₆₇	—	2	1	no	—
246	#120×C₆₇	—	2	2	no	—
247	#120×C₆₇	—	2	2	no	—
248	#120×C₆₇	—	2	2	no	—
249	#120×C₆₇	—	2	2	no	—
250	C₄×Q₈×C₆₇	—	2	1	no	—
251	C₄×Q₈×C₆₇	—	2	1	no	—
252	C₄×Q₈×C₆₇	—	2	1	no	—
253	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
254	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
255	C₄×D₄×C₆₇	—	2	1	no	—
256	C₄×D₄×C₆₇	—	2	1	no	—
257	C₄×D₄×C₆₇	—	2	1	no	—
258	C₄×D₄×C₆₇	—	2	1	no	—
259	C₄×D₄×C₆₇	—	2	1	no	—
260	C₄×D₄×C₆₇	—	2	1	no	—
261	C₄×D₄×C₆₇	—	2	1	no	—
262	C₄×D₄×C₆₇	—	2	1	no	—
263	C₄×D₄×C₆₇	—	2	1	no	—
264	C₄×D₄×C₆₇	—	2	1	no	—
265	C₄×D₄×C₆₇	—	2	1	no	—
266	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
267	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
268	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
269	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
270	C₄×D₄×C₆₇	C₂³	1	2	yes	—
271	C₄×D₄×C₆₇	C₂³	1	2	yes	—
272	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
273	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
274	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
275	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
277	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
278	#117×C₆₇	—	2	1	no	—
279	#117×C₆₇	—	2	1	no	—
280	#117×C₆₇	—	2	1	no	—
281	#117×C₆₇	—	2	1	no	—
282	#117×C₆₇	—	2	1	no	—
283	#117×C₆₇	—	2	1	no	—
284	#117×C₆₇	—	2	1	no	—
285	#117×C₆₇	—	2	1	no	—
286	#117×C₆₇	C₂³	1	1	yes	characteristic
287	#117×C₆₇	C₂³	1	1	yes	characteristic
288	#117×C₆₇	C₂³	1	1	yes	characteristic
289	#117×C₆₇	C₂³	1	1	yes	characteristic
290	#117×C₆₇	C₂³	1	1	yes	characteristic
291	#117×C₆₇	C₂³	1	1	yes	characteristic, complemented
292	#117×C₆₇	C₂³	1	1	yes	characteristic, complemented
293	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
294	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
296	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
297	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
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	D₄	1	1	yes	characteristic
312	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
313	C₂×C₄²×C₆₇	—	2	1	no	—
314	C₂×C₄²×C₆₇	—	2	1	no	—
315	C₂×C₄²×C₆₇	—	2	1	no	—
316	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
317	#107×C₆₇	C₂³	1	2	yes	complemented
318	#107×C₆₇	C₂³	1	2	yes	complemented
319	#107×C₆₇	C₂³	1	2	yes	complemented
320	#106×C₆₇	C₂³	1	2	yes	complemented
321	#106×C₆₇	C₂³	1	2	yes	complemented
322	#106×C₆₇	C₂³	1	2	yes	complemented
323	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
324	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
325	#103×C₆₇	C₂³	1	2	yes	complemented
326	#103×C₆₇	C₂³	1	2	yes	complemented
327	#103×C₆₇	C₂³	1	2	yes	complemented
328	#103×C₆₇	C₂³	1	2	yes	complemented
329	#103×C₆₇	C₂³	1	2	yes	complemented
330	#103×C₆₇	C₂³	1	2	yes	complemented
331	#103×C₆₇	C₂³	1	2	yes	complemented
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	—
336	#102×C₆₇	C₂³	1	2	yes	—
337	#102×C₆₇	C₂³	1	2	yes	—
338	#102×C₆₇	C₂³	1	2	yes	—
339	#102×C₆₇	C₂³	1	2	yes	—
340	#102×C₆₇	C₂³	1	2	yes	—
341	#102×C₆₇	C₂³	1	2	yes	—
342	#102×C₆₇	C₂³	1	2	yes	—
343	#102×C₆₇	C₂³	1	2	yes	—
344	#102×C₆₇	C₂³	1	2	yes	complemented
345	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
346	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
347	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	complemented
348	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	complemented
349	#97×C₆₇	C₂³	1	2	yes	complemented
350	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
351	C₂⁴×C₆₇	—	2	1	no	—
352	C₂⁴×C₆₇	—	2	1	no	—
353	C₂⁴×C₆₇	—	2	2	no	—
354	C₂⁴×C₆₇	—	2	2	no	—
355	C₂⁴×C₆₇	—	4	4	no	—
356	C₂⁴×C₆₇	—	4	4	no	—
357	C₂⁴×C₆₇	—	8	2	no	—
358	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
359	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
360	#41×C₆₇	—	2	4	no	—
361	#41×C₆₇	—	2	4	no	—
362	#41×C₆₇	—	2	2	no	—
363	#41×C₆₇	—	2	2	no	—
364	#41×C₆₇	—	4	2	no	—
365	#41×C₆₇	—	4	2	no	—
366	#41×C₆₇	—	4	4	no	—
367	#41×C₆₇	—	4	4	no	—
368	#41×C₆₇	—	4	4	no	—
369	C₂×Q₈×C₆₇	—	2	1	no	—
370	C₂×Q₈×C₆₇	—	2	1	no	—
371	C₂×Q₈×C₆₇	—	2	1	no	—
372	C₂×Q₈×C₆₇	—	2	2	no	—
373	C₂×Q₈×C₆₇	—	2	2	no	—
374	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
375	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂×D₄×C₆₇	—	2	4	no	—
377	C₂×D₄×C₆₇	—	2	4	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	1	no	—
384	C₂×D₄×C₆₇	—	2	1	no	—
385	C₂×D₄×C₆₇	—	2	2	no	—
386	C₂×D₄×C₆₇	—	2	2	no	—
387	C₂×D₄×C₆₇	—	2	1	no	—
388	C₂×D₄×C₆₇	—	2	2	no	—
389	C₂×D₄×C₆₇	—	2	2	no	—
390	C₂×D₄×C₆₇	—	2	1	no	—
391	C₂×D₄×C₆₇	—	2	2	no	—
392	C₂×D₄×C₆₇	—	2	2	no	—
393	C₂×D₄×C₆₇	—	2	2	no	—
394	C₂×D₄×C₆₇	—	4	2	no	—
395	C₂×D₄×C₆₇	—	4	2	no	—
396	C₂×D₄×C₆₇	—	4	4	no	—
397	C₂×D₄×C₆₇	—	4	4	no	—
398	C₂×D₄×C₆₇	—	4	4	no	—
399	C₂×D₄×C₆₇	—	4	2	no	—
400	C₂×D₄×C₆₇	—	4	4	no	—
401	C₂×D₄×C₆₇	—	8	2	no	—
402	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
403	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
404	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
405	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
406	C₂×D₄×C₆₇	#41	1	4	yes	complemented
407	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
408	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
410	C₂²×C₄×C₆₇	—	2	2	no	—
411	C₂²×C₄×C₆₇	—	2	2	no	—
412	C₂²×C₄×C₆₇	—	2	2	no	—
413	C₂²×C₄×C₆₇	—	2	2	no	—
414	C₂²×C₄×C₆₇	—	2	1	no	—
415	C₂²×C₄×C₆₇	—	2	1	no	—
416	C₂²×C₄×C₆₇	—	2	1	no	—
417	C₂²×C₄×C₆₇	—	2	1	no	—
418	C₂²×C₄×C₆₇	—	2	1	no	—
419	C₂²×C₄×C₆₇	—	2	1	no	—
420	C₂²×C₄×C₆₇	—	2	1	no	—
421	C₂²×C₄×C₆₇	—	2	1	no	—
422	C₂²×C₄×C₆₇	—	2	2	no	—
423	C₂²×C₄×C₆₇	—	2	2	no	—
424	C₂²×C₄×C₆₇	—	2	1	no	—
425	C₂²×C₄×C₆₇	—	2	2	no	—
426	C₂²×C₄×C₆₇	—	2	2	no	—
427	C₂²×C₄×C₆₇	—	4	4	no	—
428	C₂²×C₄×C₆₇	—	8	2	no	—
429	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
430	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
431	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
432	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
433	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
434	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
435	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
436	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
437	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
440	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
442	Q₁₆×C₆₇	—	4	2	no	—
443	SD₁₆×C₆₇	—	2	4	no	—
444	SD₁₆×C₆₇	—	4	2	no	—
445	SD₁₆×C₆₇	—	4	2	no	—
446	D₈×C₆₇	—	2	4	no	—
447	D₈×C₆₇	—	4	2	no	—
448	M₁₆×C₆₇	—	2	2	no	—
449	M₁₆×C₆₇	—	2	2	no	—
450	M₁₆×C₆₇	—	2	2	no	—
451	M₁₆×C₆₇	—	2	2	no	—
452	M₁₆×C₆₇	—	4	2	no	—
453	M₁₆×C₆₇	—	4	2	no	—
454	C₂×C₈×C₆₇	—	4	2	no	—
455	C₂×C₈×C₆₇	—	4	2	no	—
456	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
457	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
458	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
459	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
460	C₄⋊C₄×C₆₇	—	2	2	no	—
461	C₄⋊C₄×C₆₇	—	2	2	no	—
462	C₄⋊C₄×C₆₇	—	2	1	no	—
463	C₄⋊C₄×C₆₇	—	2	1	no	—
464	C₄⋊C₄×C₆₇	—	2	1	no	—
465	C₄⋊C₄×C₆₇	—	2	1	no	—
466	C₄⋊C₄×C₆₇	—	2	1	no	—
467	C₄⋊C₄×C₆₇	—	2	1	no	—
468	C₄⋊C₄×C₆₇	—	2	1	no	—
469	C₄⋊C₄×C₆₇	—	2	1	no	—
470	C₄⋊C₄×C₆₇	—	2	1	no	—
471	C₄⋊C₄×C₆₇	—	2	1	no	—
472	C₄⋊C₄×C₆₇	—	2	1	no	—
473	C₄⋊C₄×C₆₇	—	2	1	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	C₂×D₄	1	1	yes	characteristic
480	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
481	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
482	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
483	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
484	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
485	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
486	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
487	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
488	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
489	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
490	C₂²⋊C₄×C₆₇	—	2	2	no	—
491	C₂²⋊C₄×C₆₇	—	2	2	no	—
492	C₂²⋊C₄×C₆₇	—	2	1	no	—
493	C₂²⋊C₄×C₆₇	—	2	1	no	—
494	C₂²⋊C₄×C₆₇	—	2	1	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	1	no	—
501	C₂²⋊C₄×C₆₇	—	2	1	no	—
502	C₂²⋊C₄×C₆₇	—	2	1	no	—
503	C₂²⋊C₄×C₆₇	—	2	2	no	—
504	C₂²⋊C₄×C₆₇	—	2	2	no	—
505	C₂²⋊C₄×C₆₇	—	2	2	no	—
506	C₂²⋊C₄×C₆₇	—	2	2	no	—
507	C₂²⋊C₄×C₆₇	—	2	2	no	—
508	C₂²⋊C₄×C₆₇	—	2	2	no	—
509	C₂²⋊C₄×C₆₇	—	2	2	no	—
510	C₂²⋊C₄×C₆₇	—	2	2	no	—
511	C₂²⋊C₄×C₆₇	—	2	1	no	—
512	C₂²⋊C₄×C₆₇	—	2	1	no	—
513	C₂²⋊C₄×C₆₇	—	2	1	no	—
514	C₂²⋊C₄×C₆₇	—	2	1	no	—
515	C₂²⋊C₄×C₆₇	—	2	1	no	—
516	C₂²⋊C₄×C₆₇	—	2	1	no	—
517	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
518	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
519	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
520	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
521	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₆₇	—	2	1	no	—
526	C₄²×C₆₇	—	2	1	no	—
527	C₄²×C₆₇	—	2	1	no	—
528	C₄²×C₆₇	—	2	1	no	—
529	C₄²×C₆₇	—	2	1	no	—
530	C₄²×C₆₇	—	2	1	no	—
531	C₄²×C₆₇	—	2	1	no	—
532	C₄²×C₆₇	—	2	1	no	—
533	C₄²×C₆₇	—	2	1	no	—
534	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
535	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
536	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
537	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
538	C₂³×C₆₇	—	2	2	no	—
539	C₂³×C₆₇	—	2	4	no	—
540	C₂³×C₆₇	—	2	2	no	—
541	C₂³×C₆₇	—	2	2	no	—
542	C₂³×C₆₇	—	2	2	no	—
543	C₂³×C₆₇	—	2	1	no	—
544	C₂³×C₆₇	—	2	2	no	—
545	C₂³×C₆₇	—	4	1	no	—
546	C₂³×C₆₇	—	4	1	no	—
547	C₂³×C₆₇	—	4	1	no	—
548	C₂³×C₆₇	—	4	4	no	—
549	C₂³×C₆₇	—	4	4	no	—
550	C₂³×C₆₇	—	4	2	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	4	no	—
557	C₂³×C₆₇	—	8	2	no	—
558	C₂³×C₆₇	—	8	2	no	—
559	C₂³×C₆₇	—	8	16	no	—
560	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
561	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
562	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
563	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
564	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
565	Q₈×C₆₇	—	2	1	no	—
566	Q₈×C₆₇	—	2	2	no	—
567	Q₈×C₆₇	—	2	1	no	—
568	Q₈×C₆₇	—	2	2	no	—
569	Q₈×C₆₇	—	4	2	no	—
570	Q₈×C₆₇	—	4	2	no	—
571	Q₈×C₆₇	—	8	1	no	—
572	D₄×C₆₇	—	2	2	no	—
573	D₄×C₆₇	—	2	2	no	—
574	D₄×C₆₇	—	2	4	no	—
575	D₄×C₆₇	—	2	1	no	—
576	D₄×C₆₇	—	2	2	no	—
577	D₄×C₆₇	—	2	2	no	—
578	D₄×C₆₇	—	2	1	no	—
579	D₄×C₆₇	—	2	2	no	—
580	D₄×C₆₇	—	4	1	no	—
581	D₄×C₆₇	—	4	1	no	—
582	D₄×C₆₇	—	4	4	no	—
583	D₄×C₆₇	—	4	4	no	—
584	D₄×C₆₇	—	4	4	no	—
585	D₄×C₆₇	—	4	4	no	—
586	D₄×C₆₇	—	4	2	no	—
587	D₄×C₆₇	—	4	2	no	—
588	D₄×C₆₇	—	4	2	no	—
589	D₄×C₆₇	—	4	2	no	—
590	D₄×C₆₇	—	8	1	no	—
591	D₄×C₆₇	—	8	1	no	—
592	D₄×C₆₇	—	8	2	no	—
593	D₄×C₆₇	—	8	2	no	—
594	D₄×C₆₇	C₂×#41	1	4	yes	—
595	C₂×C₄×C₆₇	—	2	2	no	—
596	C₂×C₄×C₆₇	—	2	2	no	—
597	C₂×C₄×C₆₇	—	2	2	no	—
598	C₂×C₄×C₆₇	—	2	2	no	—
599	C₂×C₄×C₆₇	—	2	2	no	—
600	C₂×C₄×C₆₇	—	2	2	no	—
601	C₂×C₄×C₆₇	—	2	1	no	—
602	C₂×C₄×C₆₇	—	2	1	no	—
603	C₂×C₄×C₆₇	—	2	1	no	—
604	C₂×C₄×C₆₇	—	2	1	no	—
605	C₂×C₄×C₆₇	—	2	1	no	—
606	C₂×C₄×C₆₇	—	2	1	no	—
607	C₂×C₄×C₆₇	—	2	1	no	—
608	C₂×C₄×C₆₇	—	2	1	no	—
609	C₂×C₄×C₆₇	—	2	1	no	—
610	C₂×C₄×C₆₇	—	2	1	no	—
611	C₂×C₄×C₆₇	—	2	1	no	—
612	C₂×C₄×C₆₇	—	2	1	no	—
613	C₂×C₄×C₆₇	—	2	1	no	—
614	C₂×C₄×C₆₇	—	2	1	no	—
615	C₂×C₄×C₆₇	—	2	1	no	—
616	C₂×C₄×C₆₇	—	2	2	no	—
617	C₂×C₄×C₆₇	—	2	2	no	—
618	C₂×C₄×C₆₇	—	4	1	no	—
619	C₂×C₄×C₆₇	—	4	1	no	—
620	C₂×C₄×C₆₇	—	4	4	no	—
621	C₂×C₄×C₆₇	—	4	4	no	—
622	C₂×C₄×C₆₇	—	4	2	no	—
623	C₂×C₄×C₆₇	—	4	2	no	—
624	C₂×C₄×C₆₇	—	4	2	no	—
625	C₂×C₄×C₆₇	—	4	2	no	—
626	C₂×C₄×C₆₇	—	4	2	no	—
627	C₂×C₄×C₆₇	—	4	2	no	—
628	C₂×C₄×C₆₇	—	8	1	no	—
629	C₂×C₄×C₆₇	—	8	2	no	—
630	C₂×C₄×C₆₇	—	8	2	no	—
631	C₂×C₄×C₆₇	—	8	1	no	—
632	C₂×C₄×C₆₇	—	8	1	no	—
633	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
634	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
635	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
636	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
637	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
638	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
639	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
640	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
641	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
642	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
643	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
644	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
645	C₈×C₆₇	—	2	2	no	—
646	C₈×C₆₇	—	2	2	no	—
647	C₈×C₆₇	—	2	2	no	—
648	C₈×C₆₇	—	2	2	no	—
649	C₂²×C₆₇	—	2	1	no	—
650	C₂²×C₆₇	—	2	1	no	—
651	C₂²×C₆₇	—	2	1	no	—
652	C₂²×C₆₇	—	2	1	no	—
653	C₂²×C₆₇	—	2	1	no	—
654	C₂²×C₆₇	—	2	1	no	—
655	C₂²×C₆₇	—	2	1	no	—
656	C₂²×C₆₇	—	2	1	no	—
657	C₂²×C₆₇	—	2	1	no	—
658	C₂²×C₆₇	—	2	1	no	—
659	C₂²×C₆₇	—	2	4	no	—
660	C₂²×C₆₇	—	2	1	no	—
661	C₂²×C₆₇	—	2	1	no	—
662	C₂²×C₆₇	—	2	1	no	—
663	C₂²×C₆₇	—	4	4	no	—
664	C₂²×C₆₇	—	4	8	no	—
665	C₂²×C₆₇	—	4	2	no	—
666	C₂²×C₆₇	—	4	2	no	—
667	C₂²×C₆₇	—	4	1	no	—
668	C₂²×C₆₇	—	4	2	no	—
669	C₂²×C₆₇	—	4	1	no	—
670	C₂²×C₆₇	—	4	2	no	—
671	C₂²×C₆₇	—	4	1	no	—
672	C₂²×C₆₇	—	4	2	no	—
673	C₂²×C₆₇	—	8	2	no	—
674	C₂²×C₆₇	—	8	8	no	—
675	C₂²×C₆₇	—	8	4	no	—
676	C₂²×C₆₇	—	8	8	no	—
677	C₂²×C₆₇	#546	1	2	yes	—
678	C₂²×C₆₇	#575	1	2	yes	—
679	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
680	C₄×C₆₇	—	2	1	no	—
681	C₄×C₆₇	—	2	1	no	—
682	C₄×C₆₇	—	2	1	no	—
683	C₄×C₆₇	—	2	1	no	—
684	C₄×C₆₇	—	2	1	no	—
685	C₄×C₆₇	—	2	1	no	—
686	C₄×C₆₇	—	2	1	no	—
687	C₄×C₆₇	—	2	1	no	—
688	C₄×C₆₇	—	4	2	no	—
689	C₄×C₆₇	—	4	1	no	—
690	C₄×C₆₇	—	4	1	no	—
691	C₄×C₆₇	—	4	1	no	—
692	C₄×C₆₇	—	4	2	no	—
693	C₄×C₆₇	—	4	1	no	—
694	C₄×C₆₇	—	4	1	no	—
695	C₄×C₆₇	—	4	1	no	—
696	C₄×C₆₇	—	4	1	no	—
697	C₄×C₆₇	#546	1	2	yes	—
698	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
699	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
700	#61156	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
701	C₂×C₆₇	—	2	2	no	—
702	C₂×C₆₇	—	2	2	no	—
703	C₂×C₆₇	—	4	1	no	—
704	C₂×C₆₇	—	4	1	no	—
705	C₂×C₆₇	—	4	1	no	—
706	C₂×C₆₇	—	4	4	no	—
707	C₂×C₆₇	—	8	1	no	—
708	C₂×C₆₇	—	8	2	no	—
709	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
710	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
711	C₂×C₆₇	#3585	1	1	yes	characteristic
712	#3475	C₂×C₆₇	1	1	yes	characteristic, complemented
713	C₂×#546	C₂×C₆₇	1	1	yes	characteristic, complemented
714	#3323	C₂×C₆₇	1	2	yes	complemented
715	#3322	C₂×C₆₇	1	2	yes	complemented
716	#3319	C₂×C₆₇	1	2	yes	complemented
717	#3314	C₂×C₆₇	1	2	yes	complemented
718	#3311	C₂×C₆₇	1	2	yes	complemented
719	#3306	C₂×C₆₇	1	2	yes	complemented
720	#3297	C₂×C₆₇	1	2	yes	complemented
721	#3296	C₂×C₆₇	1	2	yes	complemented
722	#3140	C₂×C₆₇	1	1	yes	characteristic, complemented
723	#3095	C₂×C₆₇	1	1	yes	characteristic, complemented
724	#3094	C₂×C₆₇	1	1	yes	characteristic, complemented
725	#3077	C₂×C₆₇	1	1	yes	characteristic, complemented
726	#3056	C₂×C₆₇	1	1	yes	characteristic, complemented
727	#3055	C₂×C₆₇	1	1	yes	characteristic, complemented
728	#3040	C₂×C₆₇	1	1	yes	characteristic, complemented
729	#3005	C₂×C₆₇	1	1	yes	characteristic, complemented
730	#3003	C₂×C₆₇	1	1	yes	characteristic, complemented
731	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
732	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
733	#2896	C₂×C₆₇	1	1	yes	characteristic, complemented
734	C₂×#418	C₂×C₆₇	1	1	yes	characteristic, complemented
735	C₆₇	#61156	1	1	yes	characteristic, direct product factor, Sylow
736	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
737	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
738	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
739	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
740	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
741	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
742	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
743	#556	C₂²×C₆₇	1	1	yes	characteristic, complemented
744	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
745	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
746	#553	C₂²×C₆₇	1	1	yes	characteristic, complemented
747	#553	C₂²×C₆₇	1	1	yes	characteristic, complemented
748	#552	—	2	1	no	—
749	#552	C₂²×C₆₇	1	1	yes	characteristic, complemented
750	#552	C₂²×C₆₇	1	1	yes	characteristic, complemented
751	#551	—	2	1	no	—
752	#551	—	2	1	no	—
753	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
754	#546	—	2	1	no	—
755	#546	—	2	1	no	—
756	#546	—	2	1	no	—
757	#546	—	2	1	no	—
758	#546	—	2	1	no	—
759	#546	C₂²×C₆₇	1	2	yes	—
760	#546	C₂²×C₆₇	1	2	yes	—
761	#546	C₂²×C₆₇	1	2	yes	—
762	#546	C₂²×C₆₇	1	2	yes	—
763	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
764	#529	—	2	1	no	—
765	#529	—	2	1	no	—
766	#529	—	2	1	no	—
767	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
768	#525	C₂²×C₆₇	1	1	yes	characteristic
769	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
770	C₂×#123	—	2	1	no	—
771	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
772	C₂×#121	—	2	1	no	—
773	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
774	C₂×#120	—	2	1	no	—
775	C₄×#41	—	2	1	no	—
776	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
777	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
778	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
779	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
780	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
781	C₂²×C₂²⋊C₄	—	2	1	no	—
782	#489	C₂²×C₆₇	1	2	yes	complemented
783	#489	C₂²×C₆₇	1	2	yes	complemented
784	#488	C₂²×C₆₇	1	2	yes	complemented
785	#488	C₂²×C₆₇	1	2	yes	complemented
786	#485	C₂²×C₆₇	1	2	yes	complemented
787	#485	C₂²×C₆₇	1	2	yes	complemented
788	#484	C₂²×C₆₇	1	2	yes	complemented
789	#483	C₂²×C₆₇	1	2	yes	complemented
790	#482	C₂²×C₆₇	1	2	yes	complemented
791	#482	C₂²×C₆₇	1	2	yes	complemented
792	#481	C₂²×C₆₇	1	2	yes	complemented
793	#480	C₂²×C₆₇	1	2	yes	complemented
794	#478	C₂²×C₆₇	1	2	yes	complemented
795	#478	C₂²×C₆₇	1	2	yes	complemented
796	#476	C₂²×C₆₇	1	2	yes	complemented
797	#474	C₂²×C₆₇	1	2	yes	complemented
798	#470	C₂²×C₆₇	1	2	yes	complemented
799	#469	C₂²×C₆₇	1	2	yes	complemented
800	#468	C₂²×C₆₇	1	2	yes	complemented
801	#468	C₂²×C₆₇	1	2	yes	complemented
802	#467	C₂²×C₆₇	1	2	yes	complemented
803	#466	C₂²×C₆₇	1	2	yes	complemented
804	#465	C₂²×C₆₇	1	2	yes	complemented
805	#465	C₂²×C₆₇	1	2	yes	complemented
806	#464	C₂²×C₆₇	1	2	yes	complemented
807	#464	C₂²×C₆₇	1	2	yes	complemented
808	#463	C₂²×C₆₇	1	2	yes	complemented
809	#463	C₂²×C₆₇	1	2	yes	complemented
810	#452	C₂²×C₆₇	1	2	yes	complemented
811	#452	C₂²×C₆₇	1	2	yes	complemented
812	#450	C₂²×C₆₇	1	2	yes	complemented
813	#450	C₂²×C₆₇	1	2	yes	complemented
814	#449	C₂²×C₆₇	1	2	yes	complemented
815	#449	C₂²×C₆₇	1	2	yes	complemented
816	#447	C₂²×C₆₇	1	2	yes	complemented
817	#447	C₂²×C₆₇	1	2	yes	complemented
818	#442	C₂²×C₆₇	1	2	yes	complemented
819	#440	C₂²×C₆₇	1	2	yes	complemented
820	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
821	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
822	#436	C₂²×C₆₇	1	2	yes	complemented
823	#435	C₂²×C₆₇	1	2	yes	complemented
824	#435	C₂²×C₆₇	1	2	yes	complemented
825	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
826	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
827	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
828	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
829	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
830	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
831	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
832	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
833	#418	C₂²×C₆₇	1	1	yes	characteristic
834	#418	C₂²×C₆₇	1	1	yes	characteristic
835	#418	C₂²×C₆₇	1	1	yes	characteristic
836	#418	C₂²×C₆₇	1	1	yes	characteristic
837	#418	C₂²×C₆₇	1	1	yes	characteristic
838	#418	C₂²×C₆₇	1	1	yes	characteristic
839	#418	C₂²×C₆₇	1	2	yes	complemented
840	#418	C₂²×C₆₇	1	2	yes	complemented
841	#417	C₂²×C₆₇	1	2	yes	complemented
842	#417	C₂²×C₆₇	1	2	yes	complemented
843	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
844	#416	C₂²×C₆₇	1	2	yes	complemented
845	#416	C₂²×C₆₇	1	2	yes	complemented
846	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
847	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
848	#407	C₂²×C₆₇	1	1	yes	characteristic
849	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
850	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
851	C₂⁵	—	2	1	no	—
852	C₂×#41	—	2	1	no	—
853	C₂×#41	—	2	1	no	—
854	C₂×#41	—	2	1	no	—
855	C₂×#41	—	2	4	no	—
856	C₂×#41	—	4	2	no	—
857	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
858	C₂×#41	C₂³×C₆₇	1	2	yes	—
859	C₂×#41	C₂³×C₆₇	1	2	yes	—
860	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
861	C₂²×D₄	—	2	4	no	—
862	C₂²×D₄	—	2	1	no	—
863	C₂²×D₄	—	2	1	no	—
864	C₂²×D₄	—	2	1	no	—
865	C₂²×D₄	—	2	1	no	—
866	C₂²×D₄	—	2	1	no	—
867	C₂²×D₄	—	4	2	no	—
868	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
869	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
870	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
871	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
872	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
873	C₂³×C₄	—	2	1	no	—
874	C₂³×C₄	—	2	1	no	—
875	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
876	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
877	#137	—	4	2	no	—
878	AGL(1,ℤ/8)	—	2	4	no	—
879	AGL(1,ℤ/8)	—	4	2	no	—
880	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	complemented
881	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
882	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
883	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
884	C₂×D₈	C₂³×C₆₇	1	2	yes	—
885	C₂×D₈	C₂³×C₆₇	1	2	yes	—
886	C₂×M₁₆	—	4	2	no	—
887	C₂×M₁₆	—	4	2	no	—
888	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
889	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
890	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
891	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
892	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
893	C₂×M₁₆	C₂³×C₆₇	1	2	yes	complemented
894	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
895	C₂²×C₈	C₂³×C₆₇	1	2	yes	complemented
896	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
897	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
898	#126	—	2	1	no	—
899	#126	—	2	1	no	—
900	#126	—	2	1	no	—
901	#126	—	2	1	no	—
902	#126	—	2	1	no	—
903	#126	—	2	1	no	—
904	#125	—	2	1	no	—
905	#125	—	2	1	no	—
906	#125	—	2	1	no	—
907	#125	C₂³×C₆₇	1	1	yes	characteristic, complemented
908	#125	C₂³×C₆₇	1	1	yes	characteristic, complemented
909	#124	—	2	1	no	—
910	#124	—	2	1	no	—
911	#124	—	2	1	no	—
912	#124	—	2	1	no	—
913	#124	—	2	1	no	—
914	#124	C₂³×C₆₇	1	2	yes	—
915	#124	C₂³×C₆₇	1	2	yes	—
916	#123	—	2	1	no	—
917	#123	—	2	1	no	—
918	#123	—	2	1	no	—
919	#123	—	2	1	no	—
920	#123	—	2	2	no	—
921	#123	—	2	2	no	—
922	#123	—	2	2	no	—
923	#123	—	2	2	no	—
924	#123	—	2	1	no	—
925	#123	—	2	1	no	—
926	#123	—	2	1	no	—
927	#123	—	2	1	no	—
928	C₂²⋊Q₈	—	2	1	no	—
929	C₂²⋊Q₈	—	2	1	no	—
930	C₂²⋊Q₈	—	2	1	no	—
931	C₂²⋊Q₈	—	2	1	no	—
932	C₂²⋊Q₈	—	2	1	no	—
933	C₂²⋊Q₈	—	2	1	no	—
934	C₂²⋊Q₈	—	2	1	no	—
935	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
936	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
937	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
938	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
939	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
940	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
941	#121	—	2	1	no	—
942	#121	—	2	1	no	—
943	#121	—	2	1	no	—
944	#121	—	2	1	no	—
945	#121	—	2	1	no	—
946	#121	—	2	2	no	—
947	#121	—	2	2	no	—
948	#121	—	2	2	no	—
949	#121	—	2	2	no	—
950	#121	C₂³×C₆₇	1	2	yes	—
951	#121	C₂³×C₆₇	1	2	yes	—
952	#121	C₂³×C₆₇	1	1	yes	characteristic
953	#121	C₂³×C₆₇	1	1	yes	characteristic
954	#121	C₂³×C₆₇	1	1	yes	characteristic, complemented
955	#121	C₂³×C₆₇	1	1	yes	characteristic, complemented
956	#120	—	2	1	no	—
957	#120	—	2	1	no	—
958	#120	—	2	2	no	—
959	#120	—	2	2	no	—
960	#120	—	2	2	no	—
961	#120	—	2	2	no	—
962	C₄×Q₈	—	2	1	no	—
963	C₄×Q₈	—	2	1	no	—
964	C₄×Q₈	—	2	1	no	—
965	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
966	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
967	C₄×D₄	—	2	1	no	—
968	C₄×D₄	—	2	1	no	—
969	C₄×D₄	—	2	1	no	—
970	C₄×D₄	—	2	1	no	—
971	C₄×D₄	—	2	1	no	—
972	C₄×D₄	—	2	1	no	—
973	C₄×D₄	—	2	1	no	—
974	C₄×D₄	—	2	1	no	—
975	C₄×D₄	—	2	1	no	—
976	C₄×D₄	—	2	1	no	—
977	C₄×D₄	—	2	1	no	—
978	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
979	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
980	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
981	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
982	C₄×D₄	C₂³×C₆₇	1	2	yes	—
983	C₄×D₄	C₂³×C₆₇	1	2	yes	—
984	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
985	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
986	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
987	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
988	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
989	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
990	#117	—	2	1	no	—
991	#117	—	2	1	no	—
992	#117	—	2	1	no	—
993	#117	—	2	1	no	—
994	#117	—	2	1	no	—
995	#117	—	2	1	no	—
996	#117	—	2	1	no	—
997	#117	—	2	1	no	—
998	#117	C₂³×C₆₇	1	1	yes	characteristic
999	#117	C₂³×C₆₇	1	1	yes	characteristic
1000	#117	C₂³×C₆₇	1	1	yes	characteristic
1001	#117	C₂³×C₆₇	1	1	yes	characteristic
1002	#117	C₂³×C₆₇	1	1	yes	characteristic
1003	#117	C₂³×C₆₇	1	1	yes	characteristic, complemented
1004	#117	C₂³×C₆₇	1	1	yes	characteristic, complemented
1005	C₂×C₄⋊C₄	—	2	1	no	—
1006	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
1007	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1008	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1009	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1010	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
1011	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
1012	C₂×C₂²⋊C₄	—	2	1	no	—
1013	C₂×C₂²⋊C₄	—	2	1	no	—
1014	C₂×C₂²⋊C₄	—	2	1	no	—
1015	C₂×C₂²⋊C₄	—	2	1	no	—
1016	C₂×C₂²⋊C₄	—	2	1	no	—
1017	C₂×C₂²⋊C₄	—	2	1	no	—
1018	C₂×C₂²⋊C₄	—	2	1	no	—
1019	C₂×C₂²⋊C₄	—	2	2	no	—
1020	C₂×C₂²⋊C₄	—	2	2	no	—
1021	C₂×C₂²⋊C₄	—	2	2	no	—
1022	C₂×C₂²⋊C₄	—	2	2	no	—
1023	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
1024	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
1025	C₂×C₄²	—	2	1	no	—
1026	C₂×C₄²	—	2	1	no	—
1027	C₂×C₄²	—	2	1	no	—
1028	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1029	#107	C₂³×C₆₇	1	2	yes	complemented
1030	#107	C₂³×C₆₇	1	2	yes	complemented
1031	#107	C₂³×C₆₇	1	2	yes	complemented
1032	#106	C₂³×C₆₇	1	2	yes	complemented
1033	#106	C₂³×C₆₇	1	2	yes	complemented
1034	#106	C₂³×C₆₇	1	2	yes	complemented
1035	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1036	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1037	#103	C₂³×C₆₇	1	2	yes	complemented
1038	#103	C₂³×C₆₇	1	2	yes	complemented
1039	#103	C₂³×C₆₇	1	2	yes	complemented
1040	#103	C₂³×C₆₇	1	2	yes	complemented
1041	#103	C₂³×C₆₇	1	2	yes	complemented
1042	#103	C₂³×C₆₇	1	2	yes	complemented
1043	#103	C₂³×C₆₇	1	2	yes	complemented
1044	#102	C₂³×C₆₇	1	2	yes	—
1045	#102	C₂³×C₆₇	1	2	yes	—
1046	#102	C₂³×C₆₇	1	2	yes	—
1047	#102	C₂³×C₆₇	1	2	yes	—
1048	#102	C₂³×C₆₇	1	2	yes	—
1049	#102	C₂³×C₆₇	1	2	yes	—
1050	#102	C₂³×C₆₇	1	2	yes	—
1051	#102	C₂³×C₆₇	1	2	yes	—
1052	#102	C₂³×C₆₇	1	2	yes	—
1053	#102	C₂³×C₆₇	1	2	yes	—
1054	#102	C₂³×C₆₇	1	2	yes	—
1055	#102	C₂³×C₆₇	1	2	yes	—
1056	#102	C₂³×C₆₇	1	2	yes	complemented
1057	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1058	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1059	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1060	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1061	#97	C₂³×C₆₇	1	2	yes	complemented
1062	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
1063	C₂⁴	—	2	1	no	—
1064	C₂⁴	—	2	1	no	—
1065	C₂⁴	—	2	2	no	—
1066	C₂⁴	—	2	2	no	—
1067	C₂⁴	—	4	4	no	—
1068	C₂⁴	—	4	4	no	—
1069	C₂⁴	—	8	2	no	—
1070	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1071	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1072	#41	—	2	4	no	—
1073	#41	—	2	4	no	—
1074	#41	—	2	2	no	—
1075	#41	—	2	2	no	—
1076	#41	—	4	2	no	—
1077	#41	—	4	2	no	—
1078	#41	—	4	4	no	—
1079	#41	—	4	4	no	—
1080	#41	—	4	4	no	—
1081	C₂×Q₈	—	2	1	no	—
1082	C₂×Q₈	—	2	1	no	—
1083	C₂×Q₈	—	2	1	no	—
1084	C₂×Q₈	—	2	2	no	—
1085	C₂×Q₈	—	2	2	no	—
1086	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1087	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1088	C₂×D₄	—	2	4	no	—
1089	C₂×D₄	—	2	4	no	—
1090	C₂×D₄	—	2	1	no	—
1091	C₂×D₄	—	2	1	no	—
1092	C₂×D₄	—	2	1	no	—
1093	C₂×D₄	—	2	2	no	—
1094	C₂×D₄	—	2	2	no	—
1095	C₂×D₄	—	2	1	no	—
1096	C₂×D₄	—	2	1	no	—
1097	C₂×D₄	—	2	2	no	—
1098	C₂×D₄	—	2	2	no	—
1099	C₂×D₄	—	2	1	no	—
1100	C₂×D₄	—	2	2	no	—
1101	C₂×D₄	—	2	2	no	—
1102	C₂×D₄	—	2	1	no	—
1103	C₂×D₄	—	2	2	no	—
1104	C₂×D₄	—	2	2	no	—
1105	C₂×D₄	—	2	2	no	—
1106	C₂×D₄	—	4	2	no	—
1107	C₂×D₄	—	4	2	no	—
1108	C₂×D₄	—	4	4	no	—
1109	C₂×D₄	—	4	4	no	—
1110	C₂×D₄	—	4	4	no	—
1111	C₂×D₄	—	4	2	no	—
1112	C₂×D₄	—	4	4	no	—
1113	C₂×D₄	—	8	2	no	—
1114	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1115	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1116	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1117	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1118	C₂×D₄	#41×C₆₇	1	4	yes	complemented
1119	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1120	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1121	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1122	C₂²×C₄	—	2	2	no	—
1123	C₂²×C₄	—	2	2	no	—
1124	C₂²×C₄	—	2	2	no	—
1125	C₂²×C₄	—	2	2	no	—
1126	C₂²×C₄	—	2	1	no	—
1127	C₂²×C₄	—	2	1	no	—
1128	C₂²×C₄	—	2	1	no	—
1129	C₂²×C₄	—	2	1	no	—
1130	C₂²×C₄	—	2	1	no	—
1131	C₂²×C₄	—	2	1	no	—
1132	C₂²×C₄	—	2	1	no	—
1133	C₂²×C₄	—	2	1	no	—
1134	C₂²×C₄	—	2	2	no	—
1135	C₂²×C₄	—	2	2	no	—
1136	C₂²×C₄	—	2	1	no	—
1137	C₂²×C₄	—	2	2	no	—
1138	C₂²×C₄	—	2	2	no	—
1139	C₂²×C₄	—	4	4	no	—
1140	C₂²×C₄	—	8	2	no	—
1141	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1142	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1143	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1144	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1145	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1146	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1147	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1148	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1149	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1150	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1151	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1152	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1153	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1154	Q₁₆	—	4	2	no	—
1155	SD₁₆	—	2	4	no	—
1156	SD₁₆	—	4	2	no	—
1157	SD₁₆	—	4	2	no	—
1158	D₈	—	2	4	no	—
1159	D₈	—	4	2	no	—
1160	M₁₆	—	2	2	no	—
1161	M₁₆	—	2	2	no	—
1162	M₁₆	—	2	2	no	—
1163	M₁₆	—	2	2	no	—
1164	M₁₆	—	4	2	no	—
1165	M₁₆	—	4	2	no	—
1166	C₂×C₈	—	4	2	no	—
1167	C₂×C₈	—	4	2	no	—
1168	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1169	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1170	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1171	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1172	C₄⋊C₄	—	2	2	no	—
1173	C₄⋊C₄	—	2	2	no	—
1174	C₄⋊C₄	—	2	1	no	—
1175	C₄⋊C₄	—	2	1	no	—
1176	C₄⋊C₄	—	2	1	no	—
1177	C₄⋊C₄	—	2	1	no	—
1178	C₄⋊C₄	—	2	1	no	—
1179	C₄⋊C₄	—	2	1	no	—
1180	C₄⋊C₄	—	2	1	no	—
1181	C₄⋊C₄	—	2	1	no	—
1182	C₄⋊C₄	—	2	1	no	—
1183	C₄⋊C₄	—	2	1	no	—
1184	C₄⋊C₄	—	2	1	no	—
1185	C₄⋊C₄	—	2	1	no	—
1186	C₄⋊C₄	—	2	1	no	—
1187	C₄⋊C₄	—	2	1	no	—
1188	C₄⋊C₄	—	2	1	no	—
1189	C₄⋊C₄	—	2	1	no	—
1190	C₄⋊C₄	—	2	1	no	—
1191	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1192	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1193	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1194	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1195	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1196	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1197	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1198	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1199	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1200	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1201	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1202	C₂²⋊C₄	—	2	2	no	—
1203	C₂²⋊C₄	—	2	2	no	—
1204	C₂²⋊C₄	—	2	1	no	—
1205	C₂²⋊C₄	—	2	1	no	—
1206	C₂²⋊C₄	—	2	1	no	—
1207	C₂²⋊C₄	—	2	1	no	—
1208	C₂²⋊C₄	—	2	1	no	—
1209	C₂²⋊C₄	—	2	1	no	—
1210	C₂²⋊C₄	—	2	1	no	—
1211	C₂²⋊C₄	—	2	1	no	—
1212	C₂²⋊C₄	—	2	1	no	—
1213	C₂²⋊C₄	—	2	1	no	—
1214	C₂²⋊C₄	—	2	1	no	—
1215	C₂²⋊C₄	—	2	2	no	—
1216	C₂²⋊C₄	—	2	2	no	—
1217	C₂²⋊C₄	—	2	2	no	—
1218	C₂²⋊C₄	—	2	2	no	—
1219	C₂²⋊C₄	—	2	2	no	—
1220	C₂²⋊C₄	—	2	2	no	—
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	1	no	—
1229	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1230	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1231	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1232	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1233	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1234	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1235	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1236	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1237	C₄²	—	2	1	no	—
1238	C₄²	—	2	1	no	—
1239	C₄²	—	2	1	no	—
1240	C₄²	—	2	1	no	—
1241	C₄²	—	2	1	no	—
1242	C₄²	—	2	1	no	—
1243	C₄²	—	2	1	no	—
1244	C₄²	—	2	1	no	—
1245	C₄²	—	2	1	no	—
1246	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1247	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1248	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1249	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1250	C₂³	—	2	2	no	—
1251	C₂³	—	2	4	no	—
1252	C₂³	—	2	2	no	—
1253	C₂³	—	2	2	no	—
1254	C₂³	—	2	2	no	—
1255	C₂³	—	2	1	no	—
1256	C₂³	—	2	2	no	—
1257	C₂³	—	4	1	no	—
1258	C₂³	—	4	1	no	—
1259	C₂³	—	4	1	no	—
1260	C₂³	—	4	4	no	—
1261	C₂³	—	4	4	no	—
1262	C₂³	—	4	2	no	—
1263	C₂³	—	4	2	no	—
1264	C₂³	—	4	2	no	—
1265	C₂³	—	4	2	no	—
1266	C₂³	—	4	4	no	—
1267	C₂³	—	4	2	no	—
1268	C₂³	—	4	4	no	—
1269	C₂³	—	8	2	no	—
1270	C₂³	—	8	2	no	—
1271	C₂³	—	8	16	no	—
1272	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1273	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1274	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1275	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1276	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1277	Q₈	—	2	1	no	—
1278	Q₈	—	2	2	no	—
1279	Q₈	—	2	1	no	—
1280	Q₈	—	2	2	no	—
1281	Q₈	—	4	2	no	—
1282	Q₈	—	4	2	no	—
1283	Q₈	—	8	1	no	—
1284	D₄	—	2	2	no	—
1285	D₄	—	2	2	no	—
1286	D₄	—	2	4	no	—
1287	D₄	—	2	1	no	—
1288	D₄	—	2	2	no	—
1289	D₄	—	2	2	no	—
1290	D₄	—	2	1	no	—
1291	D₄	—	2	2	no	—
1292	D₄	—	4	1	no	—
1293	D₄	—	4	1	no	—
1294	D₄	—	4	4	no	—
1295	D₄	—	4	4	no	—
1296	D₄	—	4	4	no	—
1297	D₄	—	4	4	no	—
1298	D₄	—	4	2	no	—
1299	D₄	—	4	2	no	—
1300	D₄	—	4	2	no	—
1301	D₄	—	4	2	no	—
1302	D₄	—	8	2	no	—
1303	D₄	—	8	2	no	—
1304	D₄	—	8	1	no	—
1305	D₄	—	8	1	no	—
1306	D₄	C₂×#41×C₆₇	1	4	yes	—
1307	C₂×C₄	—	2	2	no	—
1308	C₂×C₄	—	2	2	no	—
1309	C₂×C₄	—	2	2	no	—
1310	C₂×C₄	—	2	2	no	—
1311	C₂×C₄	—	2	2	no	—
1312	C₂×C₄	—	2	2	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	2	no	—
1329	C₂×C₄	—	2	2	no	—
1330	C₂×C₄	—	4	1	no	—
1331	C₂×C₄	—	4	1	no	—
1332	C₂×C₄	—	4	4	no	—
1333	C₂×C₄	—	4	4	no	—
1334	C₂×C₄	—	4	2	no	—
1335	C₂×C₄	—	4	2	no	—
1336	C₂×C₄	—	4	2	no	—
1337	C₂×C₄	—	4	2	no	—
1338	C₂×C₄	—	4	2	no	—
1339	C₂×C₄	—	4	2	no	—
1340	C₂×C₄	—	8	2	no	—
1341	C₂×C₄	—	8	2	no	—
1342	C₂×C₄	—	8	1	no	—
1343	C₂×C₄	—	8	1	no	—
1344	C₂×C₄	—	8	1	no	—
1345	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1346	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1347	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1348	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1349	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1350	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1351	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1352	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1353	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1354	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1355	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1356	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1357	C₈	—	2	2	no	—
1358	C₈	—	2	2	no	—
1359	C₈	—	2	2	no	—
1360	C₈	—	2	2	no	—
1361	C₂²	—	2	1	no	—
1362	C₂²	—	2	1	no	—
1363	C₂²	—	2	1	no	—
1364	C₂²	—	2	1	no	—
1365	C₂²	—	2	1	no	—
1366	C₂²	—	2	1	no	—
1367	C₂²	—	2	1	no	—
1368	C₂²	—	2	1	no	—
1369	C₂²	—	2	1	no	—
1370	C₂²	—	2	1	no	—
1371	C₂²	—	2	1	no	—
1372	C₂²	—	2	1	no	—
1373	C₂²	—	2	1	no	—
1374	C₂²	—	2	4	no	—
1375	C₂²	—	4	4	no	—
1376	C₂²	—	4	8	no	—
1377	C₂²	—	4	2	no	—
1378	C₂²	—	4	2	no	—
1379	C₂²	—	4	1	no	—
1380	C₂²	—	4	2	no	—
1381	C₂²	—	4	1	no	—
1382	C₂²	—	4	2	no	—
1383	C₂²	—	4	1	no	—
1384	C₂²	—	4	2	no	—
1385	C₂²	—	8	2	no	—
1386	C₂²	—	8	8	no	—
1387	C₂²	—	8	4	no	—
1388	C₂²	—	8	8	no	—
1389	C₂²	#546×C₆₇	1	2	yes	—
1390	C₂²	#575×C₆₇	1	2	yes	—
1391	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1392	C₄	—	2	1	no	—
1393	C₄	—	2	1	no	—
1394	C₄	—	2	1	no	—
1395	C₄	—	2	1	no	—
1396	C₄	—	2	1	no	—
1397	C₄	—	2	1	no	—
1398	C₄	—	2	1	no	—
1399	C₄	—	2	1	no	—
1400	C₄	—	4	1	no	—
1401	C₄	—	4	1	no	—
1402	C₄	—	4	1	no	—
1403	C₄	—	4	2	no	—
1404	C₄	—	4	1	no	—
1405	C₄	—	4	1	no	—
1406	C₄	—	4	1	no	—
1407	C₄	—	4	2	no	—
1408	C₄	—	4	1	no	—
1409	C₄	#546×C₆₇	1	2	yes	—
1410	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1411	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1412	C₂	—	2	2	no	—
1413	C₂	—	2	2	no	—
1414	C₂	—	4	1	no	—
1415	C₂	—	4	1	no	—
1416	C₂	—	4	1	no	—
1417	C₂	—	4	4	no	—
1418	C₂	—	8	2	no	—
1419	C₂	—	8	1	no	—
1420	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1421	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
1422	C₂	C₆₇×#3585	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×#3475	C₂	semidirect
2. C₂×#546×C₆₇	C₂	semidirect
3. C₆₇×#3323	C₂	semidirect
4. C₆₇×#3322	C₂	semidirect
5. C₆₇×#3319	C₂	semidirect
6. C₆₇×#3314	C₂	semidirect
7. C₆₇×#3311	C₂	semidirect
8. C₆₇×#3306	C₂	semidirect
9. C₆₇×#3297	C₂	semidirect
10. C₆₇×#3296	C₂	semidirect
11. C₆₇×#3140	C₂	semidirect
12. C₆₇×#3095	C₂	semidirect
13. C₆₇×#3094	C₂	semidirect
14. C₆₇×#3077	C₂	semidirect
15. C₆₇×#3056	C₂	semidirect
16. C₆₇×#3055	C₂	semidirect
17. C₆₇×#3040	C₂	semidirect
18. C₆₇×#3005	C₂	semidirect
19. C₆₇×#3003	C₂	semidirect
20. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
21. D₄×M₁₆×C₆₇	C₂	semidirect
22. C₆₇×#2896	C₂	semidirect
23. C₂×#418×C₆₇	C₂	semidirect
26. C₂×#137×C₆₇	C₂²	semidirect
30. C₂²×M₁₆×C₆₇	C₂²	semidirect
31. #556×C₆₇	C₂²	semidirect
32. #555×C₆₇	C₂²	semidirect
33. #554×C₆₇	C₂²	semidirect
34. #553×C₆₇	C₂²	semidirect
35. #553×C₆₇	C₂²	semidirect
37. #552×C₆₇	C₂²	semidirect
38. #552×C₆₇	C₂²	semidirect
41. #547×C₆₇	C₂²	semidirect
51. #533×C₆₇	C₂²	semidirect
57. #525×C₆₇	C₂²	semidirect
64. C₄×#41×C₆₇	C₂²	semidirect
68. C₂×#117×C₆₇	C₂²	semidirect
70. #489×C₆₇	C₂²	semidirect
71. #489×C₆₇	C₂²	semidirect
72. #488×C₆₇	C₂²	semidirect
73. #488×C₆₇	C₂²	semidirect
74. #485×C₆₇	C₂²	semidirect
75. #485×C₆₇	C₂²	semidirect
76. #484×C₆₇	C₂²	semidirect
77. #483×C₆₇	C₂²	semidirect
78. #482×C₆₇	C₂²	semidirect
79. #482×C₆₇	C₂²	semidirect
80. #481×C₆₇	C₂²	semidirect
81. #480×C₆₇	C₂²	semidirect
82. #478×C₆₇	C₂²	semidirect
83. #478×C₆₇	C₂²	semidirect
84. #476×C₆₇	C₂²	semidirect
85. #474×C₆₇	C₂²	semidirect
86. #470×C₆₇	C₂²	semidirect
87. #469×C₆₇	C₂²	semidirect
88. #468×C₆₇	C₂²	semidirect
89. #468×C₆₇	C₂²	semidirect
90. #467×C₆₇	C₂²	semidirect
91. #466×C₆₇	C₂²	semidirect
92. #465×C₆₇	C₂²	semidirect
93. #465×C₆₇	C₂²	semidirect
94. #464×C₆₇	C₂²	semidirect
95. #464×C₆₇	C₂²	semidirect
96. #463×C₆₇	C₂²	semidirect
97. #463×C₆₇	C₂²	semidirect
98. #452×C₆₇	C₂²	semidirect
99. #452×C₆₇	C₂²	semidirect
100. #450×C₆₇	C₂²	semidirect
101. #450×C₆₇	C₂²	semidirect
102. #449×C₆₇	C₂²	semidirect
103. #449×C₆₇	C₂²	semidirect
104. #447×C₆₇	C₂²	semidirect
105. #447×C₆₇	C₂²	semidirect
106. #442×C₆₇	C₂²	semidirect
107. #440×C₆₇	C₂²	semidirect
108. C₄×SD₁₆×C₆₇	C₂²	semidirect
109. C₄×D₈×C₆₇	C₂²	semidirect
110. #436×C₆₇	C₂²	semidirect
111. #435×C₆₇	C₂²	semidirect
112. #435×C₆₇	C₂²	semidirect
113. C₈×D₄×C₆₇	C₂²	semidirect
114. #428×C₆₇	C₂²	semidirect
115. #428×C₆₇	C₂²	semidirect
116. #428×C₆₇	C₂²	semidirect
117. #423×C₆₇	C₂²	semidirect
118. #419×C₆₇	C₂²	semidirect
119. #419×C₆₇	C₂²	semidirect
120. #419×C₆₇	C₂²	semidirect
127. #418×C₆₇	C₂²	semidirect
128. #418×C₆₇	C₂²	semidirect
129. #417×C₆₇	C₂²	semidirect
130. #417×C₆₇	C₂²	semidirect
131. #417×C₆₇	C₂²	semidirect
132. #416×C₆₇	C₂²	semidirect
133. #416×C₆₇	C₂²	semidirect
134. C₂×#102×C₆₇	C₂²	semidirect
135. C₂×#102×C₆₇	C₂²	semidirect
137. #407×C₆₇	C₂²	semidirect
138. C₄×M₁₆×C₆₇	C₂²	semidirect
168. C₂×Q₁₆×C₆₇	C₂³	semidirect
171. C₂×SD₁₆×C₆₇	C₂³	semidirect
181. C₂×M₁₆×C₆₇	C₂³	semidirect
183. C₂²×C₈×C₆₇	C₂³	semidirect
184. C₄⋊Q₈×C₆₇	C₂³	semidirect
185. C₄⋊Q₈×C₆₇	C₂³	semidirect
195. #125×C₆₇	C₂³	semidirect
196. #125×C₆₇	C₂³	semidirect
227. C₂²⋊Q₈×C₆₇	C₂³	semidirect
228. C₂²⋊Q₈×C₆₇	C₂³	semidirect
242. #121×C₆₇	C₂³	semidirect
243. #121×C₆₇	C₂³	semidirect
253. C₄×Q₈×C₆₇	C₂³	semidirect
254. C₄×Q₈×C₆₇	C₂³	semidirect
276. C₄×D₄×C₆₇	C₂³	semidirect
277. C₄×D₄×C₆₇	C₂³	semidirect
291. #117×C₆₇	C₂³	semidirect
292. #117×C₆₇	C₂³	semidirect
298. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
299. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
317. #107×C₆₇	C₂³	semidirect
318. #107×C₆₇	C₂³	semidirect
319. #107×C₆₇	C₂³	semidirect
320. #106×C₆₇	C₂³	semidirect
321. #106×C₆₇	C₂³	semidirect
322. #106×C₆₇	C₂³	semidirect
323. C₄⋊C₈×C₆₇	C₂³	semidirect
324. C₄⋊C₈×C₆₇	C₂³	semidirect
325. #103×C₆₇	C₂³	semidirect
326. #103×C₆₇	C₂³	semidirect
327. #103×C₆₇	C₂³	semidirect
328. #103×C₆₇	C₂³	semidirect
329. #103×C₆₇	C₂³	semidirect
330. #103×C₆₇	C₂³	semidirect
331. #103×C₆₇	C₂³	semidirect
344. #102×C₆₇	C₂³	semidirect
347. C₂²⋊C₈×C₆₇	C₂³	semidirect
348. C₂²⋊C₈×C₆₇	C₂³	semidirect
349. #97×C₆₇	C₂³	semidirect
350. C₄×C₈×C₆₇	C₂³	semidirect
406. C₂×D₄×C₆₇	#41	semidirect
700. #61156	C₆₇	direct (N × H)
712. #3475	C₂×C₆₇	semidirect
713. C₂×#546	C₂×C₆₇	semidirect
714. #3323	C₂×C₆₇	semidirect
715. #3322	C₂×C₆₇	semidirect
716. #3319	C₂×C₆₇	semidirect
717. #3314	C₂×C₆₇	semidirect
718. #3311	C₂×C₆₇	semidirect
719. #3306	C₂×C₆₇	semidirect
720. #3297	C₂×C₆₇	semidirect
721. #3296	C₂×C₆₇	semidirect
722. #3140	C₂×C₆₇	semidirect
723. #3095	C₂×C₆₇	semidirect
724. #3094	C₂×C₆₇	semidirect
725. #3077	C₂×C₆₇	semidirect
726. #3056	C₂×C₆₇	semidirect
727. #3055	C₂×C₆₇	semidirect
728. #3040	C₂×C₆₇	semidirect
729. #3005	C₂×C₆₇	semidirect
730. #3003	C₂×C₆₇	semidirect
731. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
732. D₄×M₁₆	C₂×C₆₇	semidirect
733. #2896	C₂×C₆₇	semidirect
734. C₂×#418	C₂×C₆₇	semidirect
735. C₆₇	#61156	direct (N × H)
738. C₂×#137	C₂²×C₆₇	semidirect
742. C₂²×M₁₆	C₂²×C₆₇	semidirect
743. #556	C₂²×C₆₇	semidirect
744. #555	C₂²×C₆₇	semidirect
745. #554	C₂²×C₆₇	semidirect
746. #553	C₂²×C₆₇	semidirect
747. #553	C₂²×C₆₇	semidirect
749. #552	C₂²×C₆₇	semidirect
750. #552	C₂²×C₆₇	semidirect
753. #547	C₂²×C₆₇	semidirect
763. #533	C₂²×C₆₇	semidirect
769. #525	C₂²×C₆₇	semidirect
776. C₄×#41	C₂²×C₆₇	semidirect
780. C₂×#117	C₂²×C₆₇	semidirect
782. #489	C₂²×C₆₇	semidirect
783. #489	C₂²×C₆₇	semidirect
784. #488	C₂²×C₆₇	semidirect
785. #488	C₂²×C₆₇	semidirect
786. #485	C₂²×C₆₇	semidirect
787. #485	C₂²×C₆₇	semidirect
788. #484	C₂²×C₆₇	semidirect
789. #483	C₂²×C₆₇	semidirect
790. #482	C₂²×C₆₇	semidirect
791. #482	C₂²×C₆₇	semidirect
792. #481	C₂²×C₆₇	semidirect
793. #480	C₂²×C₆₇	semidirect
794. #478	C₂²×C₆₇	semidirect
795. #478	C₂²×C₆₇	semidirect
796. #476	C₂²×C₆₇	semidirect
797. #474	C₂²×C₆₇	semidirect
798. #470	C₂²×C₆₇	semidirect
799. #469	C₂²×C₆₇	semidirect
800. #468	C₂²×C₆₇	semidirect
801. #468	C₂²×C₆₇	semidirect
802. #467	C₂²×C₆₇	semidirect
803. #466	C₂²×C₆₇	semidirect
804. #465	C₂²×C₆₇	semidirect
805. #465	C₂²×C₆₇	semidirect
806. #464	C₂²×C₆₇	semidirect
807. #464	C₂²×C₆₇	semidirect
808. #463	C₂²×C₆₇	semidirect
809. #463	C₂²×C₆₇	semidirect
810. #452	C₂²×C₆₇	semidirect
811. #452	C₂²×C₆₇	semidirect
812. #450	C₂²×C₆₇	semidirect
813. #450	C₂²×C₆₇	semidirect
814. #449	C₂²×C₆₇	semidirect
815. #449	C₂²×C₆₇	semidirect
816. #447	C₂²×C₆₇	semidirect
817. #447	C₂²×C₆₇	semidirect
818. #442	C₂²×C₆₇	semidirect
819. #440	C₂²×C₆₇	semidirect
820. C₄×SD₁₆	C₂²×C₆₇	semidirect
821. C₄×D₈	C₂²×C₆₇	semidirect
822. #436	C₂²×C₆₇	semidirect
823. #435	C₂²×C₆₇	semidirect
824. #435	C₂²×C₆₇	semidirect
825. C₈×D₄	C₂²×C₆₇	semidirect
826. #428	C₂²×C₆₇	semidirect
827. #428	C₂²×C₆₇	semidirect
828. #428	C₂²×C₆₇	semidirect
829. #423	C₂²×C₆₇	semidirect
830. #419	C₂²×C₆₇	semidirect
831. #419	C₂²×C₆₇	semidirect
832. #419	C₂²×C₆₇	semidirect
839. #418	C₂²×C₆₇	semidirect
840. #418	C₂²×C₆₇	semidirect
841. #417	C₂²×C₆₇	semidirect
842. #417	C₂²×C₆₇	semidirect
843. #417	C₂²×C₆₇	semidirect
844. #416	C₂²×C₆₇	semidirect
845. #416	C₂²×C₆₇	semidirect
846. C₂×#102	C₂²×C₆₇	semidirect
847. C₂×#102	C₂²×C₆₇	semidirect
849. #407	C₂²×C₆₇	semidirect
850. C₄×M₁₆	C₂²×C₆₇	semidirect
880. C₂×Q₁₆	C₂³×C₆₇	semidirect
883. C₂×SD₁₆	C₂³×C₆₇	semidirect
893. C₂×M₁₆	C₂³×C₆₇	semidirect
895. C₂²×C₈	C₂³×C₆₇	semidirect
896. C₄⋊Q₈	C₂³×C₆₇	semidirect
897. C₄⋊Q₈	C₂³×C₆₇	semidirect
907. #125	C₂³×C₆₇	semidirect
908. #125	C₂³×C₆₇	semidirect
939. C₂²⋊Q₈	C₂³×C₆₇	semidirect
940. C₂²⋊Q₈	C₂³×C₆₇	semidirect
954. #121	C₂³×C₆₇	semidirect
955. #121	C₂³×C₆₇	semidirect
965. C₄×Q₈	C₂³×C₆₇	semidirect
966. C₄×Q₈	C₂³×C₆₇	semidirect
988. C₄×D₄	C₂³×C₆₇	semidirect
989. C₄×D₄	C₂³×C₆₇	semidirect
1003. #117	C₂³×C₆₇	semidirect
1004. #117	C₂³×C₆₇	semidirect
1010. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
1011. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
1029. #107	C₂³×C₆₇	semidirect
1030. #107	C₂³×C₆₇	semidirect
1031. #107	C₂³×C₆₇	semidirect
1032. #106	C₂³×C₆₇	semidirect
1033. #106	C₂³×C₆₇	semidirect
1034. #106	C₂³×C₆₇	semidirect
1035. C₄⋊C₈	C₂³×C₆₇	semidirect
1036. C₄⋊C₈	C₂³×C₆₇	semidirect
1037. #103	C₂³×C₆₇	semidirect
1038. #103	C₂³×C₆₇	semidirect
1039. #103	C₂³×C₆₇	semidirect
1040. #103	C₂³×C₆₇	semidirect
1041. #103	C₂³×C₆₇	semidirect
1042. #103	C₂³×C₆₇	semidirect
1043. #103	C₂³×C₆₇	semidirect
1056. #102	C₂³×C₆₇	semidirect
1059. C₂²⋊C₈	C₂³×C₆₇	semidirect
1060. C₂²⋊C₈	C₂³×C₆₇	semidirect
1061. #97	C₂³×C₆₇	semidirect
1062. C₄×C₈	C₂³×C₆₇	semidirect
1118. C₂×D₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3475	2
C₂×#546×C₆₇	2
C₆₇×#3323	2
C₆₇×#3322	2
C₆₇×#3319	2
C₆₇×#3314	2
C₆₇×#3311	2
C₆₇×#3306	2
C₆₇×#3297	2
C₆₇×#3296	2
C₆₇×#3140	2
C₆₇×#3095	2
C₆₇×#3094	2
C₆₇×#3077	2
C₆₇×#3056	2
C₆₇×#3055	2
C₆₇×#3040	2
C₆₇×#3005	2
C₆₇×#3003	2
C₄×AGL(1,ℤ/8)×C₆₇	2
D₄×M₁₆×C₆₇	2
C₆₇×#2896	2
C₂×#418×C₆₇	2
#61156	67

Subgroups — C67×#61156 #30740407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61156 #30740407