Subgroups — C₆₇×#61599 #30740850

Order 17152.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3329	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3325	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3313	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3311	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3305	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3303	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3284	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3276	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3271	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3268	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3214	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3197	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3191	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3005	C₂	1	2	yes	maximal, complemented
22	C₆₇×#3002	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	2	yes	—
25	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
27	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
28	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
29	#559×C₆₇	—	2	2	no	—
30	#556×C₆₇	C₂²	1	2	yes	complemented
31	#555×C₆₇	C₂²	1	1	yes	characteristic
32	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#553×C₆₇	—	2	1	no	—
34	#553×C₆₇	—	2	1	no	—
35	#550×C₆₇	C₂²	1	1	yes	characteristic
36	#550×C₆₇	C₂²	1	2	yes	complemented
37	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	#548×C₆₇	C₂²	1	2	yes	—
39	#547×C₆₇	—	2	1	no	—
40	#547×C₆₇	C₂²	1	1	yes	characteristic
41	#547×C₆₇	C₂²	1	1	yes	characteristic
42	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#546×C₆₇	—	2	2	no	—
44	#546×C₆₇	C₂²	1	2	yes	—
45	D₄²×C₆₇	—	2	1	no	—
46	D₄²×C₆₇	C₂²	1	1	yes	characteristic
47	#538×C₆₇	—	2	2	no	—
48	#535×C₆₇	—	2	1	no	—
49	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#532×C₆₇	—	2	1	no	—
51	#532×C₆₇	C₂²	1	1	yes	characteristic
52	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#525×C₆₇	—	2	2	no	—
54	#525×C₆₇	C₂²	1	2	yes	—
55	#525×C₆₇	C₂²	1	2	yes	complemented
56	#525×C₆₇	C₂²	1	2	yes	complemented
57	#520×C₆₇	—	2	1	no	—
58	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₆₇	—	2	1	no	—
60	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
61	#496×C₆₇	C₂²	1	2	yes	complemented
62	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#489×C₆₇	C₂²	1	2	yes	complemented
65	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#485×C₆₇	C₂²	1	2	yes	complemented
68	#485×C₆₇	C₂²	1	2	yes	complemented
69	#485×C₆₇	C₂²	1	2	yes	complemented
70	#482×C₆₇	C₂²	1	2	yes	complemented
71	#482×C₆₇	C₂²	1	2	yes	complemented
72	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#470×C₆₇	C₂²	1	2	yes	complemented
79	#469×C₆₇	C₂²	1	2	yes	complemented
80	#468×C₆₇	C₂²	1	2	yes	complemented
81	#468×C₆₇	C₂²	1	2	yes	complemented
82	#467×C₆₇	C₂²	1	2	yes	complemented
83	#466×C₆₇	C₂²	1	2	yes	complemented
84	#465×C₆₇	C₂²	1	2	yes	complemented
85	#465×C₆₇	C₂²	1	2	yes	complemented
86	#464×C₆₇	C₂²	1	2	yes	complemented
87	#464×C₆₇	C₂²	1	2	yes	complemented
88	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#452×C₆₇	C₂²	1	2	yes	—
97	#452×C₆₇	C₂²	1	2	yes	complemented
98	#452×C₆₇	C₂²	1	2	yes	complemented
99	#452×C₆₇	C₂²	1	2	yes	complemented
100	#452×C₆₇	C₂²	1	2	yes	complemented
101	#452×C₆₇	C₂²	1	2	yes	complemented
102	#452×C₆₇	C₂²	1	2	yes	complemented
103	#451×C₆₇	C₂²	1	2	yes	complemented
104	#450×C₆₇	C₂²	1	2	yes	complemented
105	#449×C₆₇	C₂²	1	1	yes	characteristic
106	#449×C₆₇	C₂²	1	1	yes	characteristic
107	#449×C₆₇	C₂²	1	2	yes	complemented
108	#449×C₆₇	C₂²	1	2	yes	complemented
109	#449×C₆₇	C₂²	1	2	yes	complemented
110	#449×C₆₇	C₂²	1	2	yes	complemented
111	#449×C₆₇	C₂²	1	2	yes	complemented
112	#449×C₆₇	C₂²	1	2	yes	complemented
113	#448×C₆₇	C₂²	1	2	yes	complemented
114	#447×C₆₇	C₂²	1	2	yes	complemented
115	#441×C₆₇	C₂²	1	2	yes	complemented
116	#440×C₆₇	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#436×C₆₇	C₂²	1	1	yes	characteristic
122	#436×C₆₇	C₂²	1	1	yes	characteristic
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	#435×C₆₇	C₂²	1	2	yes	complemented
125	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#419×C₆₇	C₂²	1	2	yes	complemented
130	#418×C₆₇	C₂²	1	2	yes	complemented
131	#416×C₆₇	C₂²	1	2	yes	complemented
132	#416×C₆₇	C₂²	1	2	yes	complemented
133	#407×C₆₇	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₇	—	2	1	no	—
136	C₂×#41×C₆₇	—	2	2	no	—
137	C₂×#41×C₆₇	—	2	2	no	—
138	C₂×#41×C₆₇	—	4	4	no	—
139	C₂×#41×C₆₇	—	4	4	no	—
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	2	yes	—
142	C₂×#41×C₆₇	C₂³	1	2	yes	—
143	C₂×#41×C₆₇	C₂³	1	2	yes	—
144	C₂×#41×C₆₇	C₂³	1	2	yes	—
145	C₂×#41×C₆₇	C₂³	1	2	yes	—
146	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
147	C₂²×D₄×C₆₇	—	2	2	no	—
148	C₂²×D₄×C₆₇	—	2	1	no	—
149	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
150	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
151	C₂³×C₄×C₆₇	—	2	2	no	—
152	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
153	#137×C₆₇	—	4	4	no	—
154	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
155	#135×C₆₇	—	4	4	no	—
156	#135×C₆₇	—	4	4	no	—
157	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
167	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×D₈×C₆₇	C₂³	1	2	yes	—
170	C₂×D₈×C₆₇	C₂³	1	2	yes	—
171	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
172	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
173	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
174	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
175	C₄⋊Q₈×C₆₇	—	2	1	no	—
176	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
177	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
178	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
180	#127×C₆₇	—	2	1	no	—
181	#127×C₆₇	—	2	2	no	—
182	#127×C₆₇	C₂³	1	1	yes	characteristic
183	#127×C₆₇	C₂³	1	1	yes	characteristic
184	#126×C₆₇	—	2	2	no	—
185	#126×C₆₇	—	2	2	no	—
186	#125×C₆₇	—	2	1	no	—
187	#124×C₆₇	—	2	2	no	—
188	#124×C₆₇	—	2	2	no	—
189	#124×C₆₇	—	2	2	no	—
190	#124×C₆₇	—	2	2	no	—
191	#124×C₆₇	—	2	1	no	—
192	#124×C₆₇	C₂³	1	2	yes	—
193	#123×C₆₇	—	2	2	no	—
194	#123×C₆₇	—	2	2	no	—
195	#123×C₆₇	—	2	2	no	—
196	#123×C₆₇	—	2	2	no	—
197	#123×C₆₇	—	2	2	no	—
198	#123×C₆₇	—	2	2	no	—
199	#123×C₆₇	—	2	2	no	—
200	C₂²⋊Q₈×C₆₇	—	2	1	no	—
201	C₂²⋊Q₈×C₆₇	—	2	2	no	—
202	C₂²⋊Q₈×C₆₇	—	2	2	no	—
203	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
205	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
208	#121×C₆₇	—	2	2	no	—
209	#121×C₆₇	—	2	1	no	—
210	#121×C₆₇	—	2	1	no	—
211	#121×C₆₇	—	2	1	no	—
212	#121×C₆₇	—	2	1	no	—
213	#121×C₆₇	—	2	1	no	—
214	#121×C₆₇	—	2	1	no	—
215	#121×C₆₇	—	2	1	no	—
216	#121×C₆₇	—	2	1	no	—
217	#121×C₆₇	—	2	1	no	—
218	#121×C₆₇	—	2	2	no	—
219	#121×C₆₇	—	2	2	no	—
220	#121×C₆₇	—	2	2	no	—
221	#121×C₆₇	—	2	2	no	—
222	#121×C₆₇	C₂³	1	2	yes	—
223	#121×C₆₇	C₂³	1	1	yes	characteristic
224	#121×C₆₇	C₂³	1	1	yes	characteristic
225	#121×C₆₇	C₂³	1	2	yes	—
226	#121×C₆₇	C₂³	1	2	yes	—
227	#121×C₆₇	C₂³	1	2	yes	—
228	#120×C₆₇	—	2	2	no	—
229	#120×C₆₇	—	2	2	no	—
230	#120×C₆₇	—	2	2	no	—
231	#120×C₆₇	—	2	2	no	—
232	#120×C₆₇	—	2	2	no	—
233	C₄×Q₈×C₆₇	—	2	2	no	—
234	C₄×Q₈×C₆₇	—	2	1	no	—
235	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
238	C₄×D₄×C₆₇	—	2	1	no	—
239	C₄×D₄×C₆₇	—	2	2	no	—
240	C₄×D₄×C₆₇	—	2	1	no	—
241	C₄×D₄×C₆₇	—	2	1	no	—
242	C₄×D₄×C₆₇	—	2	2	no	—
243	C₄×D₄×C₆₇	—	2	2	no	—
244	C₄×D₄×C₆₇	—	2	2	no	—
245	C₄×D₄×C₆₇	—	2	2	no	—
246	C₄×D₄×C₆₇	—	2	2	no	—
247	C₄×D₄×C₆₇	—	2	1	no	—
248	C₄×D₄×C₆₇	—	2	2	no	—
249	C₄×D₄×C₆₇	—	2	2	no	—
250	C₄×D₄×C₆₇	—	2	1	no	—
251	C₄×D₄×C₆₇	—	2	1	no	—
252	C₄×D₄×C₆₇	—	2	1	no	—
253	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
254	C₄×D₄×C₆₇	D₄	1	2	yes	—
255	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
256	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₆₇	C₂³	1	2	yes	—
262	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
263	#117×C₆₇	—	2	1	no	—
264	#117×C₆₇	—	2	1	no	—
265	#117×C₆₇	—	2	1	no	—
266	#117×C₆₇	—	2	1	no	—
267	#117×C₆₇	C₂³	1	1	yes	characteristic
268	#117×C₆₇	C₂³	1	2	yes	—
269	#117×C₆₇	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
272	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
276	C₂×C₄²×C₆₇	—	2	1	no	—
277	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
278	#107×C₆₇	C₂³	1	2	yes	—
279	#107×C₆₇	C₂³	1	1	yes	characteristic
280	#107×C₆₇	C₂³	1	1	yes	characteristic
281	#106×C₆₇	C₂³	1	1	yes	characteristic
282	#106×C₆₇	C₂³	1	2	yes	—
283	#106×C₆₇	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
288	#103×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	1	yes	characteristic
291	#103×C₆₇	C₂³	1	1	yes	characteristic
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	2	yes	—
297	#102×C₆₇	C₂³	1	1	yes	characteristic
298	#102×C₆₇	C₂³	1	1	yes	characteristic
299	#102×C₆₇	C₂³	1	1	yes	characteristic
300	#102×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	2	yes	—
305	#102×C₆₇	C₂³	1	1	yes	characteristic
306	#102×C₆₇	C₂³	1	1	yes	characteristic
307	#102×C₆₇	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
315	#97×C₆₇	C₂³	1	2	yes	—
316	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
318	C₂⁴×C₆₇	—	2	2	no	—
319	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
320	#41×C₆₇	—	2	2	no	—
321	#41×C₆₇	—	2	2	no	—
322	#41×C₆₇	—	2	4	no	—
323	#41×C₆₇	—	2	4	no	—
324	#41×C₆₇	—	4	2	no	—
325	#41×C₆₇	—	4	2	no	—
326	#41×C₆₇	—	4	2	no	—
327	#41×C₆₇	—	4	2	no	—
328	#41×C₆₇	—	4	4	no	—
329	#41×C₆₇	—	4	8	no	—
330	#41×C₆₇	—	4	2	no	—
331	#41×C₆₇	—	4	2	no	—
332	#41×C₆₇	—	4	2	no	—
333	#41×C₆₇	—	4	2	no	—
334	#41×C₆₇	—	4	8	no	—
335	C₂×Q₈×C₆₇	—	2	1	no	—
336	C₂×Q₈×C₆₇	—	2	2	no	—
337	C₂×Q₈×C₆₇	—	2	1	no	—
338	C₂×Q₈×C₆₇	—	2	4	no	—
339	C₂×Q₈×C₆₇	—	4	2	no	—
340	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
341	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
342	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₆₇	—	2	1	no	—
344	C₂×D₄×C₆₇	—	2	4	no	—
345	C₂×D₄×C₆₇	—	2	2	no	—
346	C₂×D₄×C₆₇	—	2	1	no	—
347	C₂×D₄×C₆₇	—	2	1	no	—
348	C₂×D₄×C₆₇	—	2	2	no	—
349	C₂×D₄×C₆₇	—	2	2	no	—
350	C₂×D₄×C₆₇	—	2	2	no	—
351	C₂×D₄×C₆₇	—	2	2	no	—
352	C₂×D₄×C₆₇	—	2	2	no	—
353	C₂×D₄×C₆₇	—	2	2	no	—
354	C₂×D₄×C₆₇	—	2	2	no	—
355	C₂×D₄×C₆₇	—	2	2	no	—
356	C₂×D₄×C₆₇	—	2	1	no	—
357	C₂×D₄×C₆₇	—	2	1	no	—
358	C₂×D₄×C₆₇	—	2	2	no	—
359	C₂×D₄×C₆₇	—	2	1	no	—
360	C₂×D₄×C₆₇	—	2	1	no	—
361	C₂×D₄×C₆₇	—	4	2	no	—
362	C₂×D₄×C₆₇	—	4	2	no	—
363	C₂×D₄×C₆₇	—	4	4	no	—
364	C₂×D₄×C₆₇	—	4	8	no	—
365	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
369	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
370	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₆₇	—	2	1	no	—
373	C₂²×C₄×C₆₇	—	2	2	no	—
374	C₂²×C₄×C₆₇	—	2	1	no	—
375	C₂²×C₄×C₆₇	—	2	2	no	—
376	C₂²×C₄×C₆₇	—	2	1	no	—
377	C₂²×C₄×C₆₇	—	2	1	no	—
378	C₂²×C₄×C₆₇	—	2	2	no	—
379	C₂²×C₄×C₆₇	—	2	2	no	—
380	C₂²×C₄×C₆₇	—	2	1	no	—
381	C₂²×C₄×C₆₇	—	2	2	no	—
382	C₂²×C₄×C₆₇	—	2	2	no	—
383	C₂²×C₄×C₆₇	—	4	2	no	—
384	C₂²×C₄×C₆₇	—	4	2	no	—
385	C₂²×C₄×C₆₇	—	4	8	no	—
386	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
389	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
390	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
391	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
393	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
394	Q₁₆×C₆₇	—	2	4	no	—
395	Q₁₆×C₆₇	—	4	2	no	—
396	Q₁₆×C₆₇	—	4	2	no	—
397	SD₁₆×C₆₇	—	2	2	no	—
398	SD₁₆×C₆₇	—	2	2	no	—
399	SD₁₆×C₆₇	—	2	4	no	—
400	SD₁₆×C₆₇	—	4	2	no	—
401	SD₁₆×C₆₇	—	4	2	no	—
402	SD₁₆×C₆₇	—	4	2	no	—
403	SD₁₆×C₆₇	—	4	2	no	—
404	D₈×C₆₇	—	2	2	no	—
405	D₈×C₆₇	—	2	2	no	—
406	D₈×C₆₇	—	4	2	no	—
407	D₈×C₆₇	—	4	2	no	—
408	M₁₆×C₆₇	—	4	2	no	—
409	M₁₆×C₆₇	—	4	2	no	—
410	C₂×C₈×C₆₇	—	4	2	no	—
411	C₂×C₈×C₆₇	—	4	2	no	—
412	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
416	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
417	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₆₇	—	2	1	no	—
419	C₄⋊C₄×C₆₇	—	2	1	no	—
420	C₄⋊C₄×C₆₇	—	2	2	no	—
421	C₄⋊C₄×C₆₇	—	2	2	no	—
422	C₄⋊C₄×C₆₇	—	2	2	no	—
423	C₄⋊C₄×C₆₇	—	2	1	no	—
424	C₄⋊C₄×C₆₇	—	2	1	no	—
425	C₄⋊C₄×C₆₇	—	2	1	no	—
426	C₄⋊C₄×C₆₇	—	2	2	no	—
427	C₄⋊C₄×C₆₇	—	2	1	no	—
428	C₄⋊C₄×C₆₇	—	2	2	no	—
429	C₄⋊C₄×C₆₇	—	2	1	no	—
430	C₄⋊C₄×C₆₇	—	2	1	no	—
431	C₄⋊C₄×C₆₇	—	2	2	no	—
432	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
433	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
435	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄×C₆₇	—	2	2	no	—
441	C₂²⋊C₄×C₆₇	—	2	2	no	—
442	C₂²⋊C₄×C₆₇	—	2	1	no	—
443	C₂²⋊C₄×C₆₇	—	2	2	no	—
444	C₂²⋊C₄×C₆₇	—	2	2	no	—
445	C₂²⋊C₄×C₆₇	—	2	2	no	—
446	C₂²⋊C₄×C₆₇	—	2	2	no	—
447	C₂²⋊C₄×C₆₇	—	2	2	no	—
448	C₂²⋊C₄×C₆₇	—	2	2	no	—
449	C₂²⋊C₄×C₆₇	—	2	2	no	—
450	C₂²⋊C₄×C₆₇	—	2	2	no	—
451	C₂²⋊C₄×C₆₇	—	2	2	no	—
452	C₂²⋊C₄×C₆₇	—	2	1	no	—
453	C₂²⋊C₄×C₆₇	—	2	1	no	—
454	C₂²⋊C₄×C₆₇	—	2	1	no	—
455	C₂²⋊C₄×C₆₇	—	2	1	no	—
456	C₂²⋊C₄×C₆₇	—	2	2	no	—
457	C₂²⋊C₄×C₆₇	—	2	2	no	—
458	C₂²⋊C₄×C₆₇	—	2	1	no	—
459	C₂²⋊C₄×C₆₇	—	2	1	no	—
460	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
464	C₄²×C₆₇	—	2	1	no	—
465	C₄²×C₆₇	—	2	1	no	—
466	C₄²×C₆₇	—	2	1	no	—
467	C₄²×C₆₇	—	2	2	no	—
468	C₄²×C₆₇	—	2	2	no	—
469	C₄²×C₆₇	—	2	2	no	—
470	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
473	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
474	C₂³×C₆₇	—	2	1	no	—
475	C₂³×C₆₇	—	2	1	no	—
476	C₂³×C₆₇	—	2	1	no	—
477	C₂³×C₆₇	—	2	2	no	—
478	C₂³×C₆₇	—	4	2	no	—
479	C₂³×C₆₇	—	4	2	no	—
480	C₂³×C₆₇	—	4	2	no	—
481	C₂³×C₆₇	—	4	4	no	—
482	C₂³×C₆₇	—	4	4	no	—
483	C₂³×C₆₇	—	8	2	no	—
484	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
485	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
486	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
487	Q₈×C₆₇	—	2	1	no	—
488	Q₈×C₆₇	—	2	2	no	—
489	Q₈×C₆₇	—	2	2	no	—
490	Q₈×C₆₇	—	2	2	no	—
491	Q₈×C₆₇	—	2	2	no	—
492	Q₈×C₆₇	—	4	4	no	—
493	Q₈×C₆₇	—	4	2	no	—
494	Q₈×C₆₇	—	8	1	no	—
495	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
496	D₄×C₆₇	—	2	4	no	—
497	D₄×C₆₇	—	2	2	no	—
498	D₄×C₆₇	—	2	2	no	—
499	D₄×C₆₇	—	2	1	no	—
500	D₄×C₆₇	—	2	1	no	—
501	D₄×C₆₇	—	2	1	no	—
502	D₄×C₆₇	—	2	1	no	—
503	D₄×C₆₇	—	2	2	no	—
504	D₄×C₆₇	—	2	2	no	—
505	D₄×C₆₇	—	2	1	no	—
506	D₄×C₆₇	—	4	2	no	—
507	D₄×C₆₇	—	4	4	no	—
508	D₄×C₆₇	—	4	4	no	—
509	D₄×C₆₇	—	4	2	no	—
510	D₄×C₆₇	—	4	4	no	—
511	D₄×C₆₇	—	4	4	no	—
512	D₄×C₆₇	—	4	4	no	—
513	D₄×C₆₇	—	4	2	no	—
514	D₄×C₆₇	—	4	2	no	—
515	D₄×C₆₇	—	4	2	no	—
516	D₄×C₆₇	—	8	1	no	—
517	D₄×C₆₇	—	8	1	no	—
518	D₄×C₆₇	—	8	2	no	—
519	D₄×C₆₇	—	8	2	no	—
520	D₄×C₆₇	—	8	2	no	—
521	D₄×C₆₇	—	8	2	no	—
522	D₄×C₆₇	—	8	2	no	—
523	D₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
524	C₂×C₄×C₆₇	—	2	4	no	—
525	C₂×C₄×C₆₇	—	2	1	no	—
526	C₂×C₄×C₆₇	—	2	2	no	—
527	C₂×C₄×C₆₇	—	2	2	no	—
528	C₂×C₄×C₆₇	—	2	2	no	—
529	C₂×C₄×C₆₇	—	2	2	no	—
530	C₂×C₄×C₆₇	—	2	2	no	—
531	C₂×C₄×C₆₇	—	2	1	no	—
532	C₂×C₄×C₆₇	—	2	1	no	—
533	C₂×C₄×C₆₇	—	2	2	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	2	1	no	—
536	C₂×C₄×C₆₇	—	2	1	no	—
537	C₂×C₄×C₆₇	—	2	1	no	—
538	C₂×C₄×C₆₇	—	2	2	no	—
539	C₂×C₄×C₆₇	—	2	2	no	—
540	C₂×C₄×C₆₇	—	4	2	no	—
541	C₂×C₄×C₆₇	—	4	2	no	—
542	C₂×C₄×C₆₇	—	4	2	no	—
543	C₂×C₄×C₆₇	—	4	1	no	—
544	C₂×C₄×C₆₇	—	4	4	no	—
545	C₂×C₄×C₆₇	—	4	4	no	—
546	C₂×C₄×C₆₇	—	4	4	no	—
547	C₂×C₄×C₆₇	—	4	4	no	—
548	C₂×C₄×C₆₇	—	4	2	no	—
549	C₂×C₄×C₆₇	—	4	2	no	—
550	C₂×C₄×C₆₇	—	4	2	no	—
551	C₂×C₄×C₆₇	—	8	1	no	—
552	C₂×C₄×C₆₇	—	8	2	no	—
553	C₂×C₄×C₆₇	—	8	2	no	—
554	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
558	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
559	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
562	C₈×C₆₇	—	2	1	no	—
563	C₈×C₆₇	—	2	1	no	—
564	C₈×C₆₇	—	2	2	no	—
565	C₈×C₆₇	—	2	2	no	—
566	C₈×C₆₇	—	2	1	no	—
567	C₈×C₆₇	—	2	1	no	—
568	C₂²×C₆₇	—	2	1	no	—
569	C₂²×C₆₇	—	2	2	no	—
570	C₂²×C₆₇	—	2	2	no	—
571	C₂²×C₆₇	—	2	2	no	—
572	C₂²×C₆₇	—	2	1	no	—
573	C₂²×C₆₇	—	2	2	no	—
574	C₂²×C₆₇	—	2	2	no	—
575	C₂²×C₆₇	—	2	1	no	—
576	C₂²×C₆₇	—	2	2	no	—
577	C₂²×C₆₇	—	2	2	no	—
578	C₂²×C₆₇	—	4	1	no	—
579	C₂²×C₆₇	—	4	1	no	—
580	C₂²×C₆₇	—	4	1	no	—
581	C₂²×C₆₇	—	4	1	no	—
582	C₂²×C₆₇	—	4	2	no	—
583	C₂²×C₆₇	—	4	2	no	—
584	C₂²×C₆₇	—	4	1	no	—
585	C₂²×C₆₇	—	4	1	no	—
586	C₂²×C₆₇	—	4	1	no	—
587	C₂²×C₆₇	—	4	1	no	—
588	C₂²×C₆₇	—	4	2	no	—
589	C₂²×C₆₇	—	8	4	no	—
590	C₂²×C₆₇	—	8	8	no	—
591	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
592	C₄×C₆₇	—	2	1	no	—
593	C₄×C₆₇	—	2	1	no	—
594	C₄×C₆₇	—	2	1	no	—
595	C₄×C₆₇	—	2	2	no	—
596	C₄×C₆₇	—	2	2	no	—
597	C₄×C₆₇	—	2	2	no	—
598	C₄×C₆₇	—	2	1	no	—
599	C₄×C₆₇	—	4	1	no	—
600	C₄×C₆₇	—	4	2	no	—
601	C₄×C₆₇	—	4	2	no	—
602	C₄×C₆₇	—	4	2	no	—
603	C₄×C₆₇	—	4	1	no	—
604	C₄×C₆₇	—	4	1	no	—
605	C₄×C₆₇	—	4	1	no	—
606	C₄×C₆₇	#575	1	2	yes	—
607	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
608	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
609	#61599	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
610	C₂×C₆₇	—	4	2	no	—
611	C₂×C₆₇	—	4	1	no	—
612	C₂×C₆₇	—	4	2	no	—
613	C₂×C₆₇	—	4	2	no	—
614	C₂×C₆₇	—	8	1	no	—
615	C₂×C₆₇	—	8	1	no	—
616	C₂×C₆₇	—	8	2	no	—
617	C₂×C₆₇	#3484	1	1	yes	characteristic
618	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
619	C₂×C₆₇	#3584	1	1	yes	characteristic
620	#3506	C₂×C₆₇	1	1	yes	characteristic, complemented
621	D₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
622	#3329	C₂×C₆₇	1	1	yes	characteristic, complemented
623	#3325	C₂×C₆₇	1	1	yes	characteristic, complemented
624	#3313	C₂×C₆₇	1	2	yes	complemented
625	#3311	C₂×C₆₇	1	2	yes	complemented
626	#3305	C₂×C₆₇	1	1	yes	characteristic, complemented
627	#3303	C₂×C₆₇	1	1	yes	characteristic, complemented
628	#3284	C₂×C₆₇	1	1	yes	characteristic, complemented
629	#3283	C₂×C₆₇	1	1	yes	characteristic, complemented
630	#3276	C₂×C₆₇	1	1	yes	characteristic, complemented
631	#3272	C₂×C₆₇	1	1	yes	characteristic, complemented
632	#3271	C₂×C₆₇	1	2	yes	complemented
633	#3268	C₂×C₆₇	1	2	yes	complemented
634	#3214	C₂×C₆₇	1	1	yes	characteristic, complemented
635	#3210	C₂×C₆₇	1	1	yes	characteristic, complemented
636	#3197	C₂×C₆₇	1	2	yes	complemented
637	#3191	C₂×C₆₇	1	2	yes	complemented
638	#3116	C₂×C₆₇	1	1	yes	characteristic, complemented
639	#3106	C₂×C₆₇	1	1	yes	characteristic, complemented
640	#3005	C₂×C₆₇	1	2	yes	complemented
641	#3002	C₂×C₆₇	1	2	yes	complemented
642	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
643	C₆₇	#61599	1	1	yes	characteristic, direct product factor, Sylow
644	C₂²×#41	C₂²×C₆₇	1	2	yes	—
645	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
646	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
647	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
648	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
649	#559	—	2	2	no	—
650	#556	C₂²×C₆₇	1	2	yes	complemented
651	#555	C₂²×C₆₇	1	1	yes	characteristic
652	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
653	#553	—	2	1	no	—
654	#553	—	2	1	no	—
655	#550	C₂²×C₆₇	1	1	yes	characteristic
656	#550	C₂²×C₆₇	1	2	yes	complemented
657	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
658	#548	C₂²×C₆₇	1	2	yes	—
659	#547	—	2	1	no	—
660	#547	C₂²×C₆₇	1	1	yes	characteristic
661	#547	C₂²×C₆₇	1	1	yes	characteristic
662	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
663	#546	—	2	2	no	—
664	#546	C₂²×C₆₇	1	2	yes	—
665	D₄²	—	2	1	no	—
666	D₄²	C₂²×C₆₇	1	1	yes	characteristic
667	#538	—	2	2	no	—
668	#535	—	2	1	no	—
669	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
670	#532	—	2	1	no	—
671	#532	C₂²×C₆₇	1	1	yes	characteristic
672	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
673	#525	—	2	2	no	—
674	#525	C₂²×C₆₇	1	2	yes	—
675	#525	C₂²×C₆₇	1	2	yes	complemented
676	#525	C₂²×C₆₇	1	2	yes	complemented
677	#520	—	2	1	no	—
678	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
679	C₂×C₄×D₄	—	2	1	no	—
680	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
681	#496	C₂²×C₆₇	1	2	yes	complemented
682	#494	C₂²×C₆₇	1	1	yes	characteristic, complemented
683	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
684	#489	C₂²×C₆₇	1	2	yes	complemented
685	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
686	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	#485	C₂²×C₆₇	1	2	yes	complemented
688	#485	C₂²×C₆₇	1	2	yes	complemented
689	#485	C₂²×C₆₇	1	2	yes	complemented
690	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
691	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
692	#482	C₂²×C₆₇	1	2	yes	complemented
693	#482	C₂²×C₆₇	1	2	yes	complemented
694	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
695	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
696	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
697	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
698	#470	C₂²×C₆₇	1	2	yes	complemented
699	#469	C₂²×C₆₇	1	2	yes	complemented
700	#468	C₂²×C₆₇	1	2	yes	complemented
701	#468	C₂²×C₆₇	1	2	yes	complemented
702	#467	C₂²×C₆₇	1	2	yes	complemented
703	#466	C₂²×C₆₇	1	2	yes	complemented
704	#465	C₂²×C₆₇	1	2	yes	complemented
705	#465	C₂²×C₆₇	1	2	yes	complemented
706	#464	C₂²×C₆₇	1	2	yes	complemented
707	#464	C₂²×C₆₇	1	2	yes	complemented
708	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
709	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
712	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
713	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
714	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
715	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
716	#452	C₂²×C₆₇	1	2	yes	—
717	#452	C₂²×C₆₇	1	2	yes	complemented
718	#452	C₂²×C₆₇	1	2	yes	complemented
719	#452	C₂²×C₆₇	1	2	yes	complemented
720	#452	C₂²×C₆₇	1	2	yes	complemented
721	#452	C₂²×C₆₇	1	2	yes	complemented
722	#452	C₂²×C₆₇	1	2	yes	complemented
723	#451	C₂²×C₆₇	1	2	yes	complemented
724	#450	C₂²×C₆₇	1	2	yes	complemented
725	#449	C₂²×C₆₇	1	1	yes	characteristic
726	#449	C₂²×C₆₇	1	1	yes	characteristic
727	#449	C₂²×C₆₇	1	2	yes	complemented
728	#449	C₂²×C₆₇	1	2	yes	complemented
729	#449	C₂²×C₆₇	1	2	yes	complemented
730	#449	C₂²×C₆₇	1	2	yes	complemented
731	#449	C₂²×C₆₇	1	2	yes	complemented
732	#449	C₂²×C₆₇	1	2	yes	complemented
733	#448	C₂²×C₆₇	1	2	yes	complemented
734	#447	C₂²×C₆₇	1	2	yes	complemented
735	#441	C₂²×C₆₇	1	2	yes	complemented
736	#440	C₂²×C₆₇	1	2	yes	complemented
737	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
738	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
739	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
740	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
741	#436	C₂²×C₆₇	1	1	yes	characteristic
742	#436	C₂²×C₆₇	1	1	yes	characteristic
743	#435	C₂²×C₆₇	1	2	yes	complemented
744	#435	C₂²×C₆₇	1	2	yes	complemented
745	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
746	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
747	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
748	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
749	#419	C₂²×C₆₇	1	2	yes	complemented
750	#418	C₂²×C₆₇	1	2	yes	complemented
751	#416	C₂²×C₆₇	1	2	yes	complemented
752	#416	C₂²×C₆₇	1	2	yes	complemented
753	#407	C₂²×C₆₇	1	2	yes	complemented
754	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
755	C₂×#41	—	2	1	no	—
756	C₂×#41	—	2	2	no	—
757	C₂×#41	—	2	2	no	—
758	C₂×#41	—	4	4	no	—
759	C₂×#41	—	4	4	no	—
760	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
761	C₂×#41	C₂³×C₆₇	1	2	yes	—
762	C₂×#41	C₂³×C₆₇	1	2	yes	—
763	C₂×#41	C₂³×C₆₇	1	2	yes	—
764	C₂×#41	C₂³×C₆₇	1	2	yes	—
765	C₂×#41	C₂³×C₆₇	1	2	yes	—
766	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
767	C₂²×D₄	—	2	2	no	—
768	C₂²×D₄	—	2	1	no	—
769	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
770	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
771	C₂³×C₄	—	2	2	no	—
772	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
773	#137	—	4	4	no	—
774	AGL(1,ℤ/8)	—	4	4	no	—
775	#135	—	4	4	no	—
776	#135	—	4	4	no	—
777	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
778	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
779	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
781	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
782	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
783	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
785	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
786	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
787	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
788	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
789	C₂×D₈	C₂³×C₆₇	1	2	yes	—
790	C₂×D₈	C₂³×C₆₇	1	2	yes	—
791	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
792	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
793	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
794	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
795	C₄⋊Q₈	—	2	1	no	—
796	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
797	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
798	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
799	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
800	#127	—	2	1	no	—
801	#127	—	2	2	no	—
802	#127	C₂³×C₆₇	1	1	yes	characteristic
803	#127	C₂³×C₆₇	1	1	yes	characteristic
804	#126	—	2	2	no	—
805	#126	—	2	2	no	—
806	#125	—	2	1	no	—
807	#124	—	2	2	no	—
808	#124	—	2	2	no	—
809	#124	—	2	2	no	—
810	#124	—	2	2	no	—
811	#124	—	2	1	no	—
812	#124	C₂³×C₆₇	1	2	yes	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	—	2	2	no	—
823	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
824	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
827	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
828	#121	—	2	2	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	1	no	—
833	#121	—	2	1	no	—
834	#121	—	2	1	no	—
835	#121	—	2	1	no	—
836	#121	—	2	1	no	—
837	#121	—	2	1	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	—	2	2	no	—
842	#121	C₂³×C₆₇	1	2	yes	—
843	#121	C₂³×C₆₇	1	2	yes	—
844	#121	C₂³×C₆₇	1	1	yes	characteristic
845	#121	C₂³×C₆₇	1	1	yes	characteristic
846	#121	C₂³×C₆₇	1	2	yes	—
847	#121	C₂³×C₆₇	1	2	yes	—
848	#120	—	2	2	no	—
849	#120	—	2	2	no	—
850	#120	—	2	2	no	—
851	#120	—	2	2	no	—
852	#120	—	2	2	no	—
853	C₄×Q₈	—	2	2	no	—
854	C₄×Q₈	—	2	1	no	—
855	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
856	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
857	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	2	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
874	C₄×D₄	D₄×C₆₇	1	2	yes	—
875	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
876	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
877	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
878	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
879	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
880	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
881	C₄×D₄	C₂³×C₆₇	1	2	yes	—
882	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
883	#117	—	2	1	no	—
884	#117	—	2	1	no	—
885	#117	—	2	1	no	—
886	#117	—	2	1	no	—
887	#117	C₂³×C₆₇	1	1	yes	characteristic
888	#117	C₂³×C₆₇	1	2	yes	—
889	#117	C₂³×C₆₇	1	2	yes	—
890	C₂×C₄⋊C₄	—	2	1	no	—
891	C₂×C₄⋊C₄	—	2	1	no	—
892	C₂×C₄⋊C₄	—	2	1	no	—
893	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
894	C₂×C₂²⋊C₄	—	2	2	no	—
895	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
896	C₂×C₄²	—	2	1	no	—
897	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
898	#107	C₂³×C₆₇	1	1	yes	characteristic
899	#107	C₂³×C₆₇	1	1	yes	characteristic
900	#107	C₂³×C₆₇	1	2	yes	—
901	#106	C₂³×C₆₇	1	1	yes	characteristic
902	#106	C₂³×C₆₇	1	1	yes	characteristic
903	#106	C₂³×C₆₇	1	2	yes	—
904	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
905	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
906	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
907	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
908	#103	C₂³×C₆₇	1	1	yes	characteristic
909	#103	C₂³×C₆₇	1	2	yes	—
910	#103	C₂³×C₆₇	1	2	yes	—
911	#103	C₂³×C₆₇	1	2	yes	—
912	#103	C₂³×C₆₇	1	1	yes	characteristic
913	#103	C₂³×C₆₇	1	2	yes	—
914	#103	C₂³×C₆₇	1	2	yes	—
915	#103	C₂³×C₆₇	1	2	yes	—
916	#103	C₂³×C₆₇	1	2	yes	—
917	#102	C₂³×C₆₇	1	1	yes	characteristic
918	#102	C₂³×C₆₇	1	2	yes	—
919	#102	C₂³×C₆₇	1	2	yes	—
920	#102	C₂³×C₆₇	1	2	yes	—
921	#102	C₂³×C₆₇	1	1	yes	characteristic
922	#102	C₂³×C₆₇	1	2	yes	—
923	#102	C₂³×C₆₇	1	2	yes	—
924	#102	C₂³×C₆₇	1	1	yes	characteristic
925	#102	C₂³×C₆₇	1	1	yes	characteristic
926	#102	C₂³×C₆₇	1	1	yes	characteristic
927	#102	C₂³×C₆₇	1	1	yes	characteristic
928	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
929	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
930	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
931	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
932	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
933	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
934	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
935	#97	C₂³×C₆₇	1	2	yes	—
936	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
937	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
938	C₂⁴	—	2	2	no	—
939	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
940	#41	—	2	2	no	—
941	#41	—	2	2	no	—
942	#41	—	2	4	no	—
943	#41	—	2	4	no	—
944	#41	—	4	2	no	—
945	#41	—	4	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	8	no	—
949	#41	—	4	4	no	—
950	#41	—	4	2	no	—
951	#41	—	4	2	no	—
952	#41	—	4	2	no	—
953	#41	—	4	2	no	—
954	#41	—	4	8	no	—
955	C₂×Q₈	—	2	1	no	—
956	C₂×Q₈	—	2	2	no	—
957	C₂×Q₈	—	2	1	no	—
958	C₂×Q₈	—	2	4	no	—
959	C₂×Q₈	—	4	2	no	—
960	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
961	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
962	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	4	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	2	1	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	4	2	no	—
982	C₂×D₄	—	4	2	no	—
983	C₂×D₄	—	4	8	no	—
984	C₂×D₄	—	4	4	no	—
985	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
986	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
987	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
988	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
989	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
990	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
991	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	4	2	no	—
1004	C₂²×C₄	—	4	2	no	—
1005	C₂²×C₄	—	4	8	no	—
1006	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1007	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
1009	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
1010	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
1011	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1013	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1014	Q₁₆	—	2	4	no	—
1015	Q₁₆	—	4	2	no	—
1016	Q₁₆	—	4	2	no	—
1017	SD₁₆	—	2	2	no	—
1018	SD₁₆	—	2	2	no	—
1019	SD₁₆	—	2	4	no	—
1020	SD₁₆	—	4	2	no	—
1021	SD₁₆	—	4	2	no	—
1022	SD₁₆	—	4	2	no	—
1023	SD₁₆	—	4	2	no	—
1024	D₈	—	2	2	no	—
1025	D₈	—	2	2	no	—
1026	D₈	—	4	2	no	—
1027	D₈	—	4	2	no	—
1028	M₁₆	—	4	2	no	—
1029	M₁₆	—	4	2	no	—
1030	C₂×C₈	—	4	2	no	—
1031	C₂×C₈	—	4	2	no	—
1032	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1033	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1034	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1035	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1036	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1037	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1053	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1054	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1055	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1056	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1057	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1058	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1059	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1081	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1082	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1083	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1084	C₄²	—	2	1	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	—	2	1	no	—
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	2	no	—
1089	C₄²	—	2	2	no	—
1090	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1091	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1092	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1093	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1094	C₂³	—	2	1	no	—
1095	C₂³	—	2	1	no	—
1096	C₂³	—	2	1	no	—
1097	C₂³	—	2	2	no	—
1098	C₂³	—	4	2	no	—
1099	C₂³	—	4	2	no	—
1100	C₂³	—	4	2	no	—
1101	C₂³	—	4	4	no	—
1102	C₂³	—	4	4	no	—
1103	C₂³	—	8	2	no	—
1104	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1105	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1106	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1107	Q₈	—	2	1	no	—
1108	Q₈	—	2	2	no	—
1109	Q₈	—	2	2	no	—
1110	Q₈	—	2	2	no	—
1111	Q₈	—	2	2	no	—
1112	Q₈	—	4	4	no	—
1113	Q₈	—	4	2	no	—
1114	Q₈	—	8	1	no	—
1115	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1116	D₄	—	2	4	no	—
1117	D₄	—	2	2	no	—
1118	D₄	—	2	2	no	—
1119	D₄	—	2	1	no	—
1120	D₄	—	2	1	no	—
1121	D₄	—	2	1	no	—
1122	D₄	—	2	1	no	—
1123	D₄	—	2	2	no	—
1124	D₄	—	2	2	no	—
1125	D₄	—	2	1	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	4	no	—
1128	D₄	—	4	4	no	—
1129	D₄	—	4	2	no	—
1130	D₄	—	4	4	no	—
1131	D₄	—	4	4	no	—
1132	D₄	—	4	4	no	—
1133	D₄	—	4	2	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	8	1	no	—
1137	D₄	—	8	1	no	—
1138	D₄	—	8	2	no	—
1139	D₄	—	8	2	no	—
1140	D₄	—	8	2	no	—
1141	D₄	—	8	2	no	—
1142	D₄	—	8	2	no	—
1143	D₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1144	C₂×C₄	—	2	4	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	4	2	no	—
1161	C₂×C₄	—	4	2	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	4	no	—
1165	C₂×C₄	—	4	4	no	—
1166	C₂×C₄	—	4	4	no	—
1167	C₂×C₄	—	4	4	no	—
1168	C₂×C₄	—	4	2	no	—
1169	C₂×C₄	—	4	2	no	—
1170	C₂×C₄	—	4	2	no	—
1171	C₂×C₄	—	8	2	no	—
1172	C₂×C₄	—	8	2	no	—
1173	C₂×C₄	—	8	1	no	—
1174	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1175	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1176	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1177	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1178	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1179	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1180	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1181	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1182	C₈	—	2	1	no	—
1183	C₈	—	2	1	no	—
1184	C₈	—	2	2	no	—
1185	C₈	—	2	2	no	—
1186	C₈	—	2	1	no	—
1187	C₈	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	2	2	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	2	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	2	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	2	no	—
1206	C₂²	—	4	2	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	8	4	no	—
1210	C₂²	—	8	8	no	—
1211	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1212	C₄	—	2	1	no	—
1213	C₄	—	2	1	no	—
1214	C₄	—	2	1	no	—
1215	C₄	—	2	1	no	—
1216	C₄	—	2	2	no	—
1217	C₄	—	2	2	no	—
1218	C₄	—	2	2	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	2	no	—
1224	C₄	—	4	2	no	—
1225	C₄	—	4	2	no	—
1226	C₄	#575×C₆₇	1	2	yes	—
1227	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1228	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1229	C₂	—	4	2	no	—
1230	C₂	—	4	1	no	—
1231	C₂	—	4	2	no	—
1232	C₂	—	4	2	no	—
1233	C₂	—	8	2	no	—
1234	C₂	—	8	1	no	—
1235	C₂	—	8	1	no	—
1236	C₂	C₆₇×#3484	1	1	yes	characteristic
1237	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
1238	C₂	C₆₇×#3584	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×#3506	C₂	semidirect
2. D₄×#41×C₆₇	C₂	semidirect
3. C₆₇×#3329	C₂	semidirect
4. C₆₇×#3325	C₂	semidirect
5. C₆₇×#3313	C₂	semidirect
6. C₆₇×#3311	C₂	semidirect
7. C₆₇×#3305	C₂	semidirect
8. C₆₇×#3303	C₂	semidirect
9. C₆₇×#3284	C₂	semidirect
10. C₆₇×#3283	C₂	semidirect
11. C₆₇×#3276	C₂	semidirect
12. C₆₇×#3272	C₂	semidirect
13. C₆₇×#3271	C₂	semidirect
14. C₆₇×#3268	C₂	semidirect
15. C₆₇×#3214	C₂	semidirect
16. C₆₇×#3210	C₂	semidirect
17. C₆₇×#3197	C₂	semidirect
18. C₆₇×#3191	C₂	semidirect
19. C₆₇×#3116	C₂	semidirect
20. C₆₇×#3106	C₂	semidirect
21. C₆₇×#3005	C₂	semidirect
22. C₆₇×#3002	C₂	semidirect
23. C₆₇×#2974	C₂	semidirect
25. C₂×#137×C₆₇	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
27. C₂×#135×C₆₇	C₂²	semidirect
28. C₂×#135×C₆₇	C₂²	semidirect
30. #556×C₆₇	C₂²	semidirect
32. #555×C₆₇	C₂²	semidirect
36. #550×C₆₇	C₂²	semidirect
42. #547×C₆₇	C₂²	semidirect
49. #533×C₆₇	C₂²	semidirect
52. #532×C₆₇	C₂²	semidirect
55. #525×C₆₇	C₂²	semidirect
56. #525×C₆₇	C₂²	semidirect
61. #496×C₆₇	C₂²	semidirect
62. #494×C₆₇	C₂²	semidirect
63. #492×C₆₇	C₂²	semidirect
64. #489×C₆₇	C₂²	semidirect
65. #487×C₆₇	C₂²	semidirect
66. #486×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
68. #485×C₆₇	C₂²	semidirect
69. #485×C₆₇	C₂²	semidirect
70. #482×C₆₇	C₂²	semidirect
71. #482×C₆₇	C₂²	semidirect
72. #482×C₆₇	C₂²	semidirect
73. #482×C₆₇	C₂²	semidirect
74. #477×C₆₇	C₂²	semidirect
75. #477×C₆₇	C₂²	semidirect
76. #476×C₆₇	C₂²	semidirect
77. #476×C₆₇	C₂²	semidirect
78. #470×C₆₇	C₂²	semidirect
79. #469×C₆₇	C₂²	semidirect
80. #468×C₆₇	C₂²	semidirect
81. #468×C₆₇	C₂²	semidirect
82. #467×C₆₇	C₂²	semidirect
83. #466×C₆₇	C₂²	semidirect
84. #465×C₆₇	C₂²	semidirect
85. #465×C₆₇	C₂²	semidirect
86. #464×C₆₇	C₂²	semidirect
87. #464×C₆₇	C₂²	semidirect
88. #462×C₆₇	C₂²	semidirect
89. #461×C₆₇	C₂²	semidirect
90. #461×C₆₇	C₂²	semidirect
91. #461×C₆₇	C₂²	semidirect
92. #460×C₆₇	C₂²	semidirect
93. #459×C₆₇	C₂²	semidirect
94. #459×C₆₇	C₂²	semidirect
95. #459×C₆₇	C₂²	semidirect
97. #452×C₆₇	C₂²	semidirect
98. #452×C₆₇	C₂²	semidirect
99. #452×C₆₇	C₂²	semidirect
100. #452×C₆₇	C₂²	semidirect
101. #452×C₆₇	C₂²	semidirect
102. #452×C₆₇	C₂²	semidirect
103. #451×C₆₇	C₂²	semidirect
104. #450×C₆₇	C₂²	semidirect
107. #449×C₆₇	C₂²	semidirect
108. #449×C₆₇	C₂²	semidirect
109. #449×C₆₇	C₂²	semidirect
110. #449×C₆₇	C₂²	semidirect
111. #449×C₆₇	C₂²	semidirect
112. #449×C₆₇	C₂²	semidirect
113. #448×C₆₇	C₂²	semidirect
114. #447×C₆₇	C₂²	semidirect
115. #441×C₆₇	C₂²	semidirect
116. #440×C₆₇	C₂²	semidirect
117. C₄×SD₁₆×C₆₇	C₂²	semidirect
118. C₄×SD₁₆×C₆₇	C₂²	semidirect
119. C₄×D₈×C₆₇	C₂²	semidirect
120. C₄×D₈×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. #435×C₆₇	C₂²	semidirect
125. C₈×D₄×C₆₇	C₂²	semidirect
126. C₈×D₄×C₆₇	C₂²	semidirect
127. #432×C₆₇	C₂²	semidirect
128. #431×C₆₇	C₂²	semidirect
129. #419×C₆₇	C₂²	semidirect
130. #418×C₆₇	C₂²	semidirect
131. #416×C₆₇	C₂²	semidirect
132. #416×C₆₇	C₂²	semidirect
133. #407×C₆₇	C₂²	semidirect
134. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
609. #61599	C₆₇	direct (N × H)
620. #3506	C₂×C₆₇	semidirect
621. D₄×#41	C₂×C₆₇	semidirect
622. #3329	C₂×C₆₇	semidirect
623. #3325	C₂×C₆₇	semidirect
624. #3313	C₂×C₆₇	semidirect
625. #3311	C₂×C₆₇	semidirect
626. #3305	C₂×C₆₇	semidirect
627. #3303	C₂×C₆₇	semidirect
628. #3284	C₂×C₆₇	semidirect
629. #3283	C₂×C₆₇	semidirect
630. #3276	C₂×C₆₇	semidirect
631. #3272	C₂×C₆₇	semidirect
632. #3271	C₂×C₆₇	semidirect
633. #3268	C₂×C₆₇	semidirect
634. #3214	C₂×C₆₇	semidirect
635. #3210	C₂×C₆₇	semidirect
636. #3197	C₂×C₆₇	semidirect
637. #3191	C₂×C₆₇	semidirect
638. #3116	C₂×C₆₇	semidirect
639. #3106	C₂×C₆₇	semidirect
640. #3005	C₂×C₆₇	semidirect
641. #3002	C₂×C₆₇	semidirect
642. #2974	C₂×C₆₇	semidirect
643. C₆₇	#61599	direct (N × H)
645. C₂×#137	C₂²×C₆₇	semidirect
646. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
647. C₂×#135	C₂²×C₆₇	semidirect
648. C₂×#135	C₂²×C₆₇	semidirect
650. #556	C₂²×C₆₇	semidirect
652. #555	C₂²×C₆₇	semidirect
656. #550	C₂²×C₆₇	semidirect
662. #547	C₂²×C₆₇	semidirect
669. #533	C₂²×C₆₇	semidirect
672. #532	C₂²×C₆₇	semidirect
675. #525	C₂²×C₆₇	semidirect
676. #525	C₂²×C₆₇	semidirect
681. #496	C₂²×C₆₇	semidirect
682. #494	C₂²×C₆₇	semidirect
683. #492	C₂²×C₆₇	semidirect
684. #489	C₂²×C₆₇	semidirect
685. #487	C₂²×C₆₇	semidirect
686. #486	C₂²×C₆₇	semidirect
687. #485	C₂²×C₆₇	semidirect
688. #485	C₂²×C₆₇	semidirect
689. #485	C₂²×C₆₇	semidirect
690. #482	C₂²×C₆₇	semidirect
691. #482	C₂²×C₆₇	semidirect
692. #482	C₂²×C₆₇	semidirect
693. #482	C₂²×C₆₇	semidirect
694. #477	C₂²×C₆₇	semidirect
695. #477	C₂²×C₆₇	semidirect
696. #476	C₂²×C₆₇	semidirect
697. #476	C₂²×C₆₇	semidirect
698. #470	C₂²×C₆₇	semidirect
699. #469	C₂²×C₆₇	semidirect
700. #468	C₂²×C₆₇	semidirect
701. #468	C₂²×C₆₇	semidirect
702. #467	C₂²×C₆₇	semidirect
703. #466	C₂²×C₆₇	semidirect
704. #465	C₂²×C₆₇	semidirect
705. #465	C₂²×C₆₇	semidirect
706. #464	C₂²×C₆₇	semidirect
707. #464	C₂²×C₆₇	semidirect
708. #462	C₂²×C₆₇	semidirect
709. #461	C₂²×C₆₇	semidirect
710. #461	C₂²×C₆₇	semidirect
711. #461	C₂²×C₆₇	semidirect
712. #460	C₂²×C₆₇	semidirect
713. #459	C₂²×C₆₇	semidirect
714. #459	C₂²×C₆₇	semidirect
715. #459	C₂²×C₆₇	semidirect
717. #452	C₂²×C₆₇	semidirect
718. #452	C₂²×C₆₇	semidirect
719. #452	C₂²×C₆₇	semidirect
720. #452	C₂²×C₆₇	semidirect
721. #452	C₂²×C₆₇	semidirect
722. #452	C₂²×C₆₇	semidirect
723. #451	C₂²×C₆₇	semidirect
724. #450	C₂²×C₆₇	semidirect
727. #449	C₂²×C₆₇	semidirect
728. #449	C₂²×C₆₇	semidirect
729. #449	C₂²×C₆₇	semidirect
730. #449	C₂²×C₆₇	semidirect
731. #449	C₂²×C₆₇	semidirect
732. #449	C₂²×C₆₇	semidirect
733. #448	C₂²×C₆₇	semidirect
734. #447	C₂²×C₆₇	semidirect
735. #441	C₂²×C₆₇	semidirect
736. #440	C₂²×C₆₇	semidirect
737. C₄×SD₁₆	C₂²×C₆₇	semidirect
738. C₄×SD₁₆	C₂²×C₆₇	semidirect
739. C₄×D₈	C₂²×C₆₇	semidirect
740. C₄×D₈	C₂²×C₆₇	semidirect
743. #435	C₂²×C₆₇	semidirect
744. #435	C₂²×C₆₇	semidirect
745. C₈×D₄	C₂²×C₆₇	semidirect
746. C₈×D₄	C₂²×C₆₇	semidirect
747. #432	C₂²×C₆₇	semidirect
748. #431	C₂²×C₆₇	semidirect
749. #419	C₂²×C₆₇	semidirect
750. #418	C₂²×C₆₇	semidirect
751. #416	C₂²×C₆₇	semidirect
752. #416	C₂²×C₆₇	semidirect
753. #407	C₂²×C₆₇	semidirect
754. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3506	2
D₄×#41×C₆₇	2
C₆₇×#3329	2
C₆₇×#3325	2
C₆₇×#3313	2
C₆₇×#3311	2
C₆₇×#3305	2
C₆₇×#3303	2
C₆₇×#3284	2
C₆₇×#3283	2
C₆₇×#3276	2
C₆₇×#3272	2
C₆₇×#3271	2
C₆₇×#3268	2
C₆₇×#3214	2
C₆₇×#3210	2
C₆₇×#3197	2
C₆₇×#3191	2
C₆₇×#3116	2
C₆₇×#3106	2
C₆₇×#3005	2
C₆₇×#3002	2
C₆₇×#2974	2
#61599	67

Subgroups — C67×#61599 #30740850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61599 #30740850