Subgroups — #31720234

Order 17152.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573612	C₂	1	1	yes	maximal, characteristic
2	#22569158	C₂	1	1	yes	maximal, characteristic, complemented
3	#22569157	C₂	1	2	yes	maximal, complemented
4	#22569156	C₂	1	1	yes	maximal, characteristic, complemented
5	#22569155	C₂	1	1	yes	maximal, characteristic, complemented
6	#22569155	C₂	1	1	yes	maximal, characteristic, complemented
7	#22569154	C₂	1	2	yes	maximal, complemented
8	#22569154	C₂	1	2	yes	maximal, complemented
9	#22569153	C₂	1	1	yes	maximal, characteristic, complemented
10	#22569153	C₂	1	1	yes	maximal, characteristic, complemented
11	#22569152	C₂	1	1	yes	maximal, characteristic, complemented
12	#22569151	C₂	1	2	yes	maximal, complemented
13	#22569145	C₂	1	2	yes	maximal, complemented
14	#22569145	C₂	1	2	yes	maximal, complemented
15	#22569140	C₂	1	2	yes	maximal, complemented
16	#22569138	C₂	1	2	yes	maximal, complemented
17	#22568770	C₂	1	1	yes	maximal, characteristic
18	C₂×#16863421	C₂	1	1	yes	maximal, characteristic
19	#424×D₆₇	C₂	1	1	yes	maximal, characteristic
20	#22568626	C₂	1	1	yes	maximal, characteristic
21	#22568625	C₂	1	1	yes	maximal, characteristic
22	#405×D₆₇	C₂	1	1	yes	maximal, characteristic
23	C₆₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#11761611	C₂²	1	1	yes	characteristic
25	C₂×M₁₆×D₆₇	C₂²	1	1	yes	characteristic
26	C₂×M₁₆×D₆₇	C₂²	1	1	yes	characteristic
27	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
28	#16864026	C₄	1	1	yes	characteristic
29	#16864026	C₄	1	1	yes	characteristic
30	#16864026	C₄	1	1	yes	characteristic
31	#16864026	C₄	1	1	yes	characteristic
32	#16864025	C₄	1	2	yes	—
33	#16864025	C₄	1	2	yes	—
34	#16864023	C₄	1	1	yes	characteristic
35	#16864023	C₄	1	1	yes	characteristic
36	#16864023	C₄	1	1	yes	characteristic
37	#16864023	C₄	1	1	yes	characteristic
38	#16864021	C₄	1	2	yes	—
39	#16864021	C₄	1	2	yes	—
40	#16863953	C₂²	1	1	yes	characteristic
41	#16863950	C₂²	1	2	yes	—
42	#16863950	C₂²	1	2	yes	—
43	#16863950	C₂²	1	2	yes	—
44	#16863950	C₂²	1	2	yes	—
45	#16863949	C₂²	1	1	yes	characteristic
46	#16863949	C₂²	1	1	yes	characteristic
47	C₂×#14524000	C₂²	1	1	yes	characteristic
48	#117×D₆₇	C₂²	1	1	yes	characteristic
49	#117×D₆₇	C₂²	1	1	yes	characteristic
50	#16863527	C₂²	1	2	yes	complemented
51	#16863527	C₂²	1	2	yes	complemented
52	#16863527	C₂²	1	2	yes	complemented
53	#16863526	C₂²	1	2	yes	complemented
54	#16863526	C₂²	1	2	yes	complemented
55	#16863526	C₂²	1	2	yes	complemented
56	#16863525	C₂²	1	2	yes	complemented
57	#16863525	C₂²	1	2	yes	complemented
58	#16863525	C₂²	1	2	yes	complemented
59	#16863525	C₂²	1	2	yes	complemented
60	#16863525	C₂²	1	2	yes	complemented
61	#16863525	C₂²	1	2	yes	complemented
62	#16863524	C₂²	1	2	yes	complemented
63	#16863524	C₂²	1	2	yes	complemented
64	#16863524	C₂²	1	2	yes	complemented
65	#16863524	C₂²	1	2	yes	complemented
66	#16863524	C₂²	1	2	yes	complemented
67	#16863524	C₂²	1	2	yes	complemented
68	#16863523	C₂²	1	2	yes	complemented
69	#16863523	C₂²	1	2	yes	complemented
70	#16863523	C₂²	1	2	yes	complemented
71	Q₈×C₆₇⋊C₈	C₂²	1	2	yes	complemented
72	C₈×Dic₁₃₄	C₂²	1	2	yes	complemented
73	C₈×Dic₁₃₄	C₂²	1	2	yes	complemented
74	C₈×Dic₁₃₄	C₂²	1	2	yes	complemented
75	#16863520	C₂²	1	2	yes	complemented
76	#16863520	C₂²	1	2	yes	complemented
77	#16863520	C₂²	1	2	yes	complemented
78	#16863424	C₂²	1	1	yes	characteristic
79	#16863424	C₂²	1	1	yes	characteristic
80	#16863423	C₂²	1	1	yes	characteristic
81	#16863423	C₂²	1	1	yes	characteristic
82	#16863422	C₂²	1	1	yes	characteristic
83	#16863422	C₂²	1	1	yes	characteristic
84	#16863421	C₂²	1	2	yes	—
85	#16863421	C₂²	1	2	yes	—
86	#16863421	C₂²	1	1	yes	characteristic
87	#16863421	C₂²	1	1	yes	characteristic
88	#16863421	C₂²	1	1	yes	characteristic
89	#16863421	C₂²	1	1	yes	characteristic
90	#16863421	C₂²	1	1	yes	characteristic
91	#16863421	C₂²	1	1	yes	characteristic
92	#16863421	C₂²	1	1	yes	characteristic
93	#16863421	C₂²	1	1	yes	characteristic
94	#16863421	C₂²	1	2	yes	—
95	#16863421	C₂²	1	2	yes	—
96	#16863418	C₂²	1	2	yes	—
97	#16863418	C₂²	1	2	yes	—
98	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
99	C₂×Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic
100	C₂×Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic
101	C₄⋊C₈×D₆₇	C₂²	1	2	yes	—
102	C₄⋊C₈×D₆₇	C₂²	1	2	yes	—
103	#16863354	C₂²	1	1	yes	characteristic
104	#16863354	C₂²	1	1	yes	characteristic
105	#16863353	C₂²	1	2	yes	—
106	#16863353	C₂²	1	2	yes	—
107	#16863353	C₂²	1	2	yes	—
108	#16863353	C₂²	1	2	yes	—
109	#16863352	C₂²	1	1	yes	characteristic
110	#16863352	C₂²	1	1	yes	characteristic
111	#16863351	C₂²	1	1	yes	characteristic
112	#16863351	C₂²	1	1	yes	characteristic
113	#16863350	C₂²	1	2	yes	—
114	#16863350	C₂²	1	2	yes	—
115	#16863350	C₂²	1	2	yes	—
116	#16863350	C₂²	1	2	yes	—
117	C₄×#11761612	C₂²	1	1	yes	characteristic
118	#16863348	C₂²	1	2	yes	—
119	M₁₆×Dic₆₇	C₂²	1	1	yes	characteristic
120	M₁₆×Dic₆₇	C₂²	1	1	yes	characteristic
121	C₄×#11761611	C₂²	1	2	yes	—
122	#97×D₆₇	C₂²	1	2	yes	—
123	C₄×C₈×D₆₇	C₂²	1	2	yes	—
124	#533×C₆₇	C₂²	1	1	yes	characteristic
125	#446×C₆₇	C₂²	1	2	yes	complemented
126	#446×C₆₇	C₂²	1	2	yes	complemented
127	#446×C₆₇	C₂²	1	2	yes	complemented
128	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
129	#424×C₆₇	C₂²	1	1	yes	characteristic
130	#424×C₆₇	C₂²	1	1	yes	characteristic
131	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
132	#405×C₆₇	C₂²	1	1	yes	characteristic
133	#405×C₆₇	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
135	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
136	C₂×#11761612	C₂³	1	1	yes	characteristic
137	C₂×#11761612	C₂³	1	1	yes	characteristic
138	C₂×#11761611	—	2	4	no	—
139	C₂×#11761611	C₂³	1	1	yes	characteristic
140	C₂×#11761611	C₂³	1	1	yes	characteristic
141	C₂×#11761611	C₂³	1	1	yes	characteristic
142	C₂×#11761611	C₂³	1	2	yes	—
143	C₂×#11761611	C₂³	1	1	yes	characteristic
144	C₂×#11761611	C₂³	1	2	yes	—
145	M₁₆×D₆₇	—	2	4	no	—
146	M₁₆×D₆₇	Q₈	1	8	yes	complemented
147	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
148	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₆₇	—	2	4	no	—
150	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₆₇	C₂³	1	2	yes	—
154	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₆₇	C₂³	1	2	yes	—
156	#14524043	C₂×C₄	1	1	yes	characteristic
157	#14524043	C₂×C₄	1	1	yes	characteristic
158	#14524042	C₂×C₄	1	1	yes	characteristic
159	#14524042	C₂×C₄	1	1	yes	characteristic
160	#14524042	C₂×C₄	1	1	yes	characteristic
161	#14524042	C₂×C₄	1	1	yes	characteristic
162	#14524042	C₂×C₄	1	2	yes	—
163	#14524042	C₂×C₄	1	2	yes	—
164	#14524042	C₂×C₄	1	2	yes	—
165	#14524042	C₂×C₄	1	2	yes	—
166	#14524041	C₂×C₄	1	2	yes	—
167	#14524041	C₂×C₄	1	2	yes	—
168	#14524041	C₂×C₄	1	2	yes	—
169	#14524041	C₂×C₄	1	2	yes	—
170	#14524035	C₂×C₄	1	1	yes	characteristic
171	#14524035	C₂×C₄	1	1	yes	characteristic
172	#14524034	C₂×C₄	1	1	yes	characteristic
173	#14524034	C₂×C₄	1	1	yes	characteristic
174	#14524034	C₂×C₄	1	1	yes	characteristic
175	#14524034	C₂×C₄	1	1	yes	characteristic
176	#14524033	C₂×C₄	1	2	yes	—
177	#14524033	C₂×C₄	1	2	yes	—
178	#14524033	C₂×C₄	1	2	yes	—
179	#14524033	C₂×C₄	1	2	yes	—
180	#14524033	C₂×C₄	1	2	yes	—
181	#14524033	C₂×C₄	1	2	yes	—
182	#14524033	C₂×C₄	1	2	yes	—
183	#14524033	C₂×C₄	1	2	yes	—
184	#14524023	C₂×C₄	1	2	yes	—
185	#14524023	C₂×C₄	1	2	yes	—
186	#14524023	C₂×C₄	1	2	yes	—
187	#14524023	C₂×C₄	1	2	yes	—
188	#14524022	C₂×C₄	1	2	yes	—
189	#14524022	C₂×C₄	1	2	yes	—
190	#14524021	C₂×C₄	1	2	yes	—
191	#14524021	C₂×C₄	1	2	yes	—
192	#14524021	C₂×C₄	1	2	yes	—
193	#14524021	C₂×C₄	1	2	yes	—
194	#14524021	C₂×C₄	1	2	yes	—
195	#14524021	C₂×C₄	1	2	yes	—
196	#14524021	C₂×C₄	1	2	yes	—
197	#14524021	C₂×C₄	1	2	yes	—
198	#14524020	C₂×C₄	1	2	yes	—
199	#14524020	C₂×C₄	1	2	yes	—
200	#14524020	C₂×C₄	1	2	yes	—
201	#14524020	C₂×C₄	1	2	yes	—
202	#14524019	C₂×C₄	1	2	yes	—
203	#14524019	C₂×C₄	1	2	yes	—
204	#14524019	C₂×C₄	1	2	yes	—
205	#14524019	C₂×C₄	1	2	yes	—
206	C₄×Dic₁₃₄	C₂³	1	2	yes	—
207	C₄×Dic₁₃₄	C₂³	1	2	yes	—
208	C₄×Dic₁₃₄	C₂³	1	2	yes	—
209	C₄×Dic₁₃₄	C₂³	1	2	yes	—
210	C₄×Dic₁₃₄	C₂³	1	2	yes	—
211	C₄×Dic₁₃₄	C₂³	1	2	yes	—
212	#14524002	C₂³	1	1	yes	characteristic
213	#14524002	C₂³	1	1	yes	characteristic
214	#14524001	C₂×C₄	1	1	yes	characteristic
215	#14524001	C₂×C₄	1	1	yes	characteristic
216	#14524001	C₂×C₄	1	1	yes	characteristic
217	#14524001	C₂×C₄	1	1	yes	characteristic
218	#14524000	C₂×C₄	1	1	yes	characteristic
219	#14524000	C₂×C₄	1	1	yes	characteristic
220	#14524000	C₂×C₄	1	1	yes	characteristic
221	#14524000	C₂×C₄	1	1	yes	characteristic
222	#14524000	C₂³	1	2	yes	—
223	#14524000	C₂³	1	2	yes	—
224	#14524000	C₂³	1	1	yes	characteristic
225	#14524000	C₂³	1	1	yes	characteristic
226	#14524000	C₂³	1	1	yes	characteristic
227	#14524000	C₂³	1	1	yes	characteristic
228	#14523999	C₂×C₄	1	2	yes	—
229	#14523999	C₂×C₄	1	2	yes	—
230	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
231	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
232	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
233	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
234	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
235	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
236	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
237	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
238	C₂²⋊C₄×D₆₇	C₂×C₄	1	2	yes	—
239	C₂²⋊C₄×D₆₇	C₂×C₄	1	2	yes	—
240	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
241	C₄²×D₆₇	C₂³	1	2	yes	—
242	C₄²×D₆₇	C₂³	1	2	yes	—
243	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
244	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
245	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
246	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
247	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
248	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
249	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
250	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
251	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
252	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
253	Dic₆₇⋊C₈	C₂³	1	2	yes	—
254	Dic₆₇⋊C₈	C₂³	1	2	yes	—
255	Dic₆₇⋊C₈	C₂³	1	2	yes	—
256	Dic₆₇⋊C₈	C₂³	1	2	yes	—
257	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
258	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
259	Dic₆₇⋊C₈	C₂³	1	2	yes	—
260	Dic₆₇⋊C₈	C₂³	1	2	yes	—
261	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
262	Dic₆₇⋊C₈	C₂³	1	2	yes	—
263	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
264	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
265	Dic₆₇⋊C₈	C₂³	1	2	yes	—
266	Dic₆₇⋊C₈	C₂³	1	1	yes	characteristic
267	#14523954	C₂³	1	2	yes	—
268	#14523954	C₂³	1	2	yes	—
269	#14523954	C₂³	1	2	yes	—
270	#14523953	C₂³	1	2	yes	—
271	#14523953	C₂³	1	2	yes	—
272	#14523953	C₂³	1	2	yes	—
273	#14523953	C₂³	1	2	yes	—
274	#14523953	C₂³	1	2	yes	—
275	#14523953	C₂³	1	2	yes	—
276	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
277	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
278	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
279	C₈×Dic₆₇	C₂³	1	2	yes	—
280	C₈×Dic₆₇	C₂³	1	2	yes	—
281	C₈×Dic₆₇	C₂³	1	2	yes	—
282	C₈×Dic₆₇	C₂³	1	2	yes	—
283	C₈×Dic₆₇	C₂³	1	2	yes	—
284	C₈×Dic₆₇	C₂³	1	2	yes	—
285	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
286	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
287	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
288	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
289	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
290	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
291	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
292	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
293	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
294	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
295	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
296	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
297	#117×C₆₇	C₂³	1	1	yes	characteristic
298	#117×C₆₇	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
302	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
303	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
304	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
305	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
306	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
307	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
308	#97×C₆₇	C₂³	1	2	yes	—
309	#97×C₆₇	C₂³	1	2	yes	—
310	#97×C₆₇	C₂³	1	2	yes	—
311	C₄×C₈×C₆₇	C₂³	1	2	yes	—
312	C₄×C₈×C₆₇	C₂³	1	2	yes	—
313	C₄×C₈×C₆₇	C₂³	1	2	yes	—
314	C₂³×D₆₇	C₂²×C₄	1	1	yes	characteristic
315	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
316	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
317	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
318	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
319	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
320	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
321	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
322	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
323	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
324	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
325	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
326	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
327	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
328	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
329	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
330	C₂×C₄×D₆₇	C₂×Q₈	1	4	yes	—
331	C₂×C₄×D₆₇	#41	1	4	yes	—
332	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
333	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
334	#11761612	—	2	2	no	—
335	#11761612	C₂×Q₈	1	4	yes	—
336	#11761611	—	2	4	no	—
337	#11761611	—	2	2	no	—
338	#11761611	—	2	2	no	—
339	#11761611	—	2	2	no	—
340	#11761611	—	2	2	no	—
341	#11761611	C₂×Q₈	1	8	yes	—
342	C₂×C₆₇⋊C₈	—	2	2	no	—
343	C₂×C₆₇⋊C₈	—	2	2	no	—
344	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
345	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
346	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
347	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
348	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
349	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
350	C₈×D₆₇	—	2	2	no	—
351	C₈×D₆₇	—	2	2	no	—
352	C₈×D₆₇	—	2	2	no	—
353	C₈×D₆₇	—	2	2	no	—
354	C₈×D₆₇	—	2	4	no	—
355	C₈×D₆₇	C₂×Q₈	1	8	yes	—
356	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
357	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
358	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
359	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
360	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
361	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
362	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
363	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
364	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
365	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
366	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
367	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
368	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
369	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
370	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
371	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
372	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
373	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
374	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
375	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
376	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
377	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
378	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
379	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
380	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
381	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
382	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
383	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
384	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
385	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
386	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
387	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
388	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
389	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
390	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
391	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
392	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
393	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
394	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
395	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
396	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
397	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
398	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
399	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
400	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
401	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
402	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
403	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
404	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
405	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
406	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
407	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
408	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
409	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
410	C₄×Dic₆₇	C₂⁴	1	2	yes	—
411	C₄×Dic₆₇	C₂⁴	1	2	yes	—
412	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
413	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
414	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
415	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
416	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
417	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
418	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	M₁₆×C₆₇	—	2	2	no	—
420	M₁₆×C₆₇	C₂×Q₈	1	4	yes	—
421	C₂×C₈×C₆₇	—	2	2	no	—
422	C₂×C₈×C₆₇	—	2	2	no	—
423	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
427	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
428	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
429	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
430	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
431	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
432	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
433	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
434	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
435	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
436	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
437	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
438	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
441	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
442	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
443	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
444	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
445	C₄²×C₆₇	C₂⁴	1	2	yes	—
446	C₄²×C₆₇	C₂⁴	1	2	yes	—
447	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
448	C₂²×D₆₇	—	4	1	no	—
449	C₂²×D₆₇	—	4	1	no	—
450	C₂²×D₆₇	C₄×Q₈	1	4	yes	—
451	C₂²×D₆₇	C₂³×C₄	1	1	yes	characteristic
452	C₂²×D₆₇	C₂³×C₄	1	1	yes	characteristic
453	Q₈×C₆₇	—	4	2	no	—
454	Q₈×C₆₇	—	4	2	no	—
455	C₂×C₄×C₆₇	—	4	1	no	—
456	C₂×C₄×C₆₇	—	4	1	no	—
457	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
458	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
459	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
460	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
461	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
462	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
463	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
466	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
467	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
468	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
469	C₂×Dic₆₇	—	4	1	no	—
470	C₂×Dic₆₇	—	4	1	no	—
471	C₂×Dic₆₇	C₄×Q₈	1	4	yes	—
472	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
473	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
474	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
475	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
476	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
477	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
478	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
479	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
480	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
481	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
482	C₄×D₆₇	—	4	2	no	—
483	C₄×D₆₇	—	4	2	no	—
484	C₄×D₆₇	—	4	2	no	—
485	C₄×D₆₇	—	4	2	no	—
486	C₄×D₆₇	C₄×Q₈	1	4	yes	—
487	C₄×D₆₇	C₄×Q₈	1	4	yes	—
488	C₄×D₆₇	C₂²×Q₈	1	2	yes	—
489	C₄×D₆₇	C₂²×Q₈	1	2	yes	—
490	C₄×D₆₇	C₂×#41	1	2	yes	—
491	C₄×D₆₇	C₂×#41	1	2	yes	—
492	Dic₁₃₄	—	4	2	no	—
493	Dic₁₃₄	—	4	2	no	—
494	Dic₁₃₄	—	4	2	no	—
495	Dic₁₃₄	—	4	2	no	—
496	Dic₁₃₄	—	4	2	no	—
497	Dic₁₃₄	—	4	2	no	—
498	C₈×C₆₇	—	2	1	no	—
499	C₈×C₆₇	—	2	1	no	—
500	C₈×C₆₇	—	2	1	no	—
501	C₈×C₆₇	—	2	1	no	—
502	C₈×C₆₇	—	2	2	no	—
503	C₈×C₆₇	C₂²×Q₈	1	4	yes	—
504	C₆₇⋊C₈	—	2	1	no	—
505	C₆₇⋊C₈	—	2	1	no	—
506	C₆₇⋊C₈	—	2	2	no	—
507	C₆₇⋊C₈	—	2	1	no	—
508	C₆₇⋊C₈	—	2	1	no	—
509	C₆₇⋊C₈	C₂²×Q₈	1	4	yes	—
510	C₂²×C₆₇	—	2	1	no	—
511	C₂²×C₆₇	—	2	1	no	—
512	C₂²×C₆₇	C₂×C₄×Q₈	1	2	yes	—
513	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
514	C₂×D₆₇	—	2	1	no	—
515	C₂×D₆₇	—	2	1	no	—
516	C₂×D₆₇	—	2	1	no	—
517	C₂×D₆₇	—	2	1	no	—
518	C₂×D₆₇	—	4	4	no	—
519	C₂×D₆₇	C₂×C₄×Q₈	1	2	yes	—
520	C₂×D₆₇	C₂×C₄×Q₈	1	2	yes	—
521	C₄×C₆₇	—	2	1	no	—
522	C₄×C₆₇	—	2	1	no	—
523	C₄×C₆₇	—	2	2	no	—
524	C₄×C₆₇	—	2	2	no	—
525	C₄×C₆₇	—	2	2	no	—
526	C₄×C₆₇	—	2	2	no	—
527	C₄×C₆₇	—	2	1	no	—
528	C₄×C₆₇	—	2	1	no	—
529	C₄×C₆₇	C₂×C₄×Q₈	1	2	yes	—
530	C₄×C₆₇	C₂³×Q₈	1	1	yes	characteristic
531	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
532	Dic₆₇	—	2	2	no	—
533	Dic₆₇	—	2	2	no	—
534	Dic₆₇	—	2	2	no	—
535	Dic₆₇	—	2	2	no	—
536	Dic₆₇	—	2	1	no	—
537	Dic₆₇	—	2	1	no	—
538	Dic₆₇	—	2	1	no	—
539	Dic₆₇	—	2	1	no	—
540	Dic₆₇	C₂×C₄×Q₈	1	2	yes	—
541	Dic₆₇	C₂×C₄×Q₈	1	2	yes	—
542	#60193	—	67	1	no	maximal, Sylow
543	C₂×C₆₇	—	2	2	no	—
544	C₂×C₆₇	C₂²×C₄×Q₈	1	1	yes	characteristic
545	C₂×C₆₇	#3573	1	1	yes	characteristic
546	C₂×C₆₇	#3573	1	1	yes	characteristic
547	D₆₇	—	2	2	no	—
548	D₆₇	—	2	2	no	—
549	#3458	—	67	1	no	—
550	#2962	—	67	2	no	—
551	#2962	—	67	2	no	—
552	#2962	—	67	2	no	—
553	#2962	—	67	2	no	—
554	#2962	—	67	1	no	—
555	#2962	—	67	1	no	—
556	#2962	—	67	1	no	—
557	#2962	—	67	1	no	—
558	#2962	—	67	1	no	—
559	#2962	—	67	1	no	—
560	#2962	—	67	1	no	—
561	#2962	D₆₇	1	1	yes	characteristic, complemented
562	#2961	—	67	2	no	—
563	#2961	—	67	2	no	—
564	#2960	—	67	2	no	—
565	#2960	—	67	2	no	—
566	#2905	—	67	1	no	—
567	C₂×#424	—	67	1	no	—
568	C₂×#424	—	67	1	no	—
569	#2873	—	67	1	no	—
570	#2873	—	67	1	no	—
571	C₂×#405	—	67	1	no	—
572	C₆₇	#60193	1	1	yes	characteristic, complemented, Sylow
573	C₂²×M₁₆	—	67	1	no	—
574	C₂²×M₁₆	—	67	1	no	—
575	C₂²×M₁₆	—	67	1	no	—
576	C₂³×C₈	—	67	1	no	—
577	#544	—	67	1	no	—
578	#544	—	67	1	no	—
579	#544	—	67	1	no	—
580	#544	—	67	1	no	—
581	#544	—	67	1	no	—
582	#544	—	67	1	no	—
583	#544	—	67	1	no	—
584	#544	—	67	1	no	—
585	#544	—	67	2	no	—
586	#544	—	67	2	no	—
587	#543	—	67	2	no	—
588	#543	—	67	2	no	—
589	#533	—	67	2	no	—
590	#533	—	67	2	no	—
591	#533	—	67	2	no	—
592	#533	—	67	2	no	—
593	#533	—	67	1	no	—
594	#533	—	67	1	no	—
595	#533	—	67	1	no	—
596	#533	C₂×D₆₇	1	1	yes	characteristic
597	C₂×#117	—	67	1	no	—
598	C₂×#117	—	67	1	no	—
599	C₂×#117	—	67	1	no	—
600	#446	—	67	2	no	—
601	#446	—	67	2	no	—
602	#446	—	67	2	no	—
603	#446	—	67	2	no	—
604	#446	—	67	2	no	—
605	#446	—	67	2	no	—
606	#446	—	67	2	no	—
607	#446	—	67	2	no	—
608	#446	—	67	2	no	—
609	#446	—	67	2	no	—
610	#446	—	67	2	no	—
611	#446	—	67	2	no	—
612	#446	—	67	2	no	—
613	#446	—	67	2	no	—
614	#446	—	67	2	no	—
615	#446	—	67	2	no	—
616	#446	—	67	2	no	—
617	#446	—	67	2	no	—
618	#446	—	67	2	no	—
619	#446	—	67	2	no	—
620	#446	—	67	2	no	—
621	#446	C₂×D₆₇	1	2	yes	complemented
622	#446	C₂×D₆₇	1	2	yes	complemented
623	#446	C₂×D₆₇	1	2	yes	complemented
624	C₈×Q₈	—	67	2	no	—
625	C₈×Q₈	—	67	2	no	—
626	C₈×Q₈	—	67	2	no	—
627	C₈×Q₈	—	67	2	no	—
628	C₈×Q₈	—	67	2	no	—
629	C₈×Q₈	—	67	2	no	—
630	C₈×Q₈	—	67	2	no	—
631	C₈×Q₈	C₂×D₆₇	1	2	yes	complemented
632	#424	—	67	1	no	—
633	#424	—	67	1	no	—
634	#424	—	67	1	no	—
635	#424	—	67	1	no	—
636	#424	—	67	1	no	—
637	#424	—	67	1	no	—
638	#424	—	67	2	no	—
639	#424	—	67	1	no	—
640	#424	—	67	1	no	—
641	#424	—	67	2	no	—
642	#424	—	67	1	no	—
643	#424	—	67	1	no	—
644	#424	—	67	1	no	—
645	#424	—	67	1	no	—
646	#424	—	67	1	no	—
647	#424	—	67	1	no	—
648	#424	—	67	2	no	—
649	#424	—	67	2	no	—
650	#424	C₂×D₆₇	1	1	yes	characteristic
651	#424	C₂×D₆₇	1	1	yes	characteristic
652	#423	—	67	2	no	—
653	#423	—	67	2	no	—
654	C₂×C₄⋊C₈	—	67	1	no	—
655	C₂×C₄⋊C₈	—	67	1	no	—
656	C₂×C₄⋊C₈	—	67	1	no	—
657	C₂×C₄⋊C₈	—	67	2	no	—
658	C₂×C₄⋊C₈	—	67	2	no	—
659	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
660	#405	—	67	1	no	—
661	#405	—	67	1	no	—
662	#405	—	67	1	no	—
663	#405	—	67	1	no	—
664	#405	—	67	1	no	—
665	#405	—	67	1	no	—
666	#405	—	67	2	no	—
667	#405	—	67	2	no	—
668	#405	—	67	2	no	—
669	#405	—	67	2	no	—
670	#405	—	67	2	no	—
671	#405	—	67	2	no	—
672	#405	—	67	2	no	—
673	#405	—	67	2	no	—
674	#405	C₂×D₆₇	1	1	yes	characteristic
675	#405	C₂×D₆₇	1	1	yes	characteristic
676	C₄×M₁₆	—	67	1	no	—
677	C₄×M₁₆	—	67	1	no	—
678	C₄×M₁₆	—	67	1	no	—
679	C₄×M₁₆	—	67	2	no	—
680	C₄×M₁₆	—	67	2	no	—
681	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic
682	C₂×#97	—	67	2	no	—
683	C₂×C₄×C₈	—	67	2	no	—
684	C₂³×C₄	—	67	1	no	—
685	C₂×M₁₆	—	67	1	no	—
686	C₂×M₁₆	—	67	8	no	—
687	C₂×M₁₆	—	67	1	no	—
688	C₂×M₁₆	—	67	2	no	—
689	C₂×M₁₆	—	67	1	no	—
690	C₂×M₁₆	—	67	1	no	—
691	C₂×M₁₆	—	67	1	no	—
692	C₂×M₁₆	—	67	2	no	—
693	C₂×M₁₆	—	67	1	no	—
694	C₂×M₁₆	—	134	4	no	—
695	C₂×M₁₆	—	134	4	no	—
696	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
697	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
698	C₂²×C₈	—	67	2	no	—
699	C₂²×C₈	—	67	1	no	—
700	C₂²×C₈	—	67	1	no	—
701	C₂²×C₈	—	67	1	no	—
702	C₂²×C₈	—	67	1	no	—
703	C₂²×C₈	—	67	1	no	—
704	C₂²×C₈	—	67	1	no	—
705	C₂²×C₈	—	67	2	no	—
706	C₂²×C₈	—	134	4	no	—
707	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
708	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
709	C₄⋊Q₈	—	67	2	no	—
710	C₄⋊Q₈	—	67	2	no	—
711	C₄⋊Q₈	—	67	2	no	—
712	C₄⋊Q₈	—	67	2	no	—
713	C₄⋊Q₈	—	67	2	no	—
714	C₄⋊Q₈	—	67	2	no	—
715	C₄⋊Q₈	—	67	2	no	—
716	C₄⋊Q₈	—	67	2	no	—
717	C₄⋊Q₈	—	67	1	no	—
718	C₄⋊Q₈	—	67	1	no	—
719	C₄⋊Q₈	—	67	1	no	—
720	C₄⋊Q₈	—	67	1	no	—
721	C₄⋊Q₈	—	67	1	no	—
722	C₄⋊Q₈	—	67	1	no	—
723	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
724	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
725	#125	—	67	2	no	—
726	#125	—	67	2	no	—
727	#125	—	67	2	no	—
728	#125	—	67	2	no	—
729	#125	—	67	2	no	—
730	#125	—	67	2	no	—
731	#125	—	67	2	no	—
732	#125	—	67	2	no	—
733	#125	—	67	1	no	—
734	#125	—	67	1	no	—
735	#125	—	67	1	no	—
736	#125	—	67	1	no	—
737	#125	—	67	1	no	—
738	#125	—	67	1	no	—
739	#125	C₄×D₆₇	1	1	yes	characteristic
740	#125	C₄×D₆₇	1	1	yes	characteristic
741	C₂²⋊Q₈	—	67	2	no	—
742	C₂²⋊Q₈	—	67	2	no	—
743	C₂²⋊Q₈	—	67	2	no	—
744	C₂²⋊Q₈	—	67	2	no	—
745	C₂²⋊Q₈	—	67	2	no	—
746	C₂²⋊Q₈	—	67	2	no	—
747	C₂²⋊Q₈	—	67	2	no	—
748	C₂²⋊Q₈	—	67	2	no	—
749	C₂²⋊Q₈	—	67	2	no	—
750	C₂²⋊Q₈	—	67	2	no	—
751	C₂²⋊Q₈	—	67	2	no	—
752	C₂²⋊Q₈	—	67	2	no	—
753	C₂²⋊Q₈	—	67	2	no	—
754	C₂²⋊Q₈	—	67	2	no	—
755	C₂²⋊Q₈	—	67	2	no	—
756	C₂²⋊Q₈	—	67	2	no	—
757	C₂²⋊Q₈	—	67	2	no	—
758	C₂²⋊Q₈	—	67	2	no	—
759	C₂²⋊Q₈	—	67	2	no	—
760	C₂²⋊Q₈	—	67	2	no	—
761	C₂²⋊Q₈	—	67	2	no	—
762	C₂²⋊Q₈	—	67	2	no	—
763	C₂²⋊Q₈	C₄×D₆₇	1	2	yes	—
764	C₂²⋊Q₈	C₄×D₆₇	1	2	yes	—
765	C₄×Q₈	—	67	2	no	—
766	C₄×Q₈	—	67	2	no	—
767	C₄×Q₈	—	67	2	no	—
768	C₄×Q₈	—	67	2	no	—
769	C₄×Q₈	—	67	2	no	—
770	C₄×Q₈	—	67	2	no	—
771	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
772	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
773	#117	—	67	1	no	—
774	#117	—	67	1	no	—
775	#117	—	67	1	no	—
776	#117	—	67	1	no	—
777	#117	—	67	1	no	—
778	#117	—	67	1	no	—
779	#117	—	67	2	no	—
780	#117	—	67	2	no	—
781	#117	—	67	1	no	—
782	#117	—	67	1	no	—
783	#117	—	67	1	no	—
784	#117	—	67	1	no	—
785	#117	—	67	1	no	—
786	#117	—	67	1	no	—
787	#117	—	67	2	no	—
788	#117	—	67	2	no	—
789	#117	—	67	1	no	—
790	#117	—	67	1	no	—
791	#117	C₂²×D₆₇	1	1	yes	characteristic
792	#117	C₂²×D₆₇	1	1	yes	characteristic
793	C₂×C₄⋊C₄	—	67	1	no	—
794	C₂×C₄⋊C₄	—	67	1	no	—
795	C₂×C₄⋊C₄	—	67	1	no	—
796	C₂×C₄⋊C₄	—	67	1	no	—
797	C₂×C₄⋊C₄	—	67	1	no	—
798	C₂×C₄⋊C₄	—	67	1	no	—
799	C₂×C₂²⋊C₄	—	67	1	no	—
800	C₂×C₂²⋊C₄	—	67	1	no	—
801	C₂×C₂²⋊C₄	—	67	2	no	—
802	C₂×C₂²⋊C₄	—	67	2	no	—
803	C₂×C₄²	—	67	1	no	—
804	C₂×C₄²	—	67	2	no	—
805	C₂×C₄²	—	67	2	no	—
806	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
807	C₄⋊C₈	—	67	1	no	—
808	C₄⋊C₈	—	67	2	no	—
809	C₄⋊C₈	—	67	1	no	—
810	C₄⋊C₈	—	67	1	no	—
811	C₄⋊C₈	—	67	2	no	—
812	C₄⋊C₈	—	67	1	no	—
813	C₄⋊C₈	—	67	1	no	—
814	C₄⋊C₈	—	67	2	no	—
815	C₄⋊C₈	—	67	1	no	—
816	C₄⋊C₈	—	67	1	no	—
817	C₄⋊C₈	—	67	2	no	—
818	C₄⋊C₈	—	67	1	no	—
819	C₄⋊C₈	—	67	2	no	—
820	C₄⋊C₈	—	67	2	no	—
821	C₄⋊C₈	—	67	2	no	—
822	C₄⋊C₈	—	67	2	no	—
823	C₄⋊C₈	—	67	1	no	—
824	C₄⋊C₈	—	67	2	no	—
825	C₄⋊C₈	—	67	1	no	—
826	C₄⋊C₈	—	67	1	no	—
827	C₄⋊C₈	—	67	2	no	—
828	C₄⋊C₈	—	67	1	no	—
829	C₄⋊C₈	—	67	2	no	—
830	C₄⋊C₈	—	67	2	no	—
831	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
832	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
833	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
834	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
835	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
836	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
837	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
838	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
839	#97	—	67	2	no	—
840	#97	—	67	2	no	—
841	#97	—	67	2	no	—
842	#97	—	67	2	no	—
843	#97	—	67	2	no	—
844	#97	—	67	2	no	—
845	#97	—	67	2	no	—
846	#97	—	67	2	no	—
847	#97	—	67	2	no	—
848	#97	C₂²×D₆₇	1	2	yes	—
849	#97	C₂²×D₆₇	1	2	yes	—
850	#97	C₂²×D₆₇	1	2	yes	—
851	C₄×C₈	—	67	2	no	—
852	C₄×C₈	—	67	2	no	—
853	C₄×C₈	—	67	2	no	—
854	C₄×C₈	—	67	2	no	—
855	C₄×C₈	—	67	2	no	—
856	C₄×C₈	—	67	2	no	—
857	C₄×C₈	—	67	2	no	—
858	C₄×C₈	—	67	2	no	—
859	C₄×C₈	—	67	2	no	—
860	C₄×C₈	C₂²×D₆₇	1	2	yes	—
861	C₄×C₈	C₂²×D₆₇	1	2	yes	—
862	C₄×C₈	C₂²×D₆₇	1	2	yes	—
863	C₂⁴	—	67	1	no	—
864	C₂×Q₈	—	67	2	no	—
865	C₂×Q₈	—	67	2	no	—
866	C₂×Q₈	—	67	2	no	—
867	C₂×Q₈	—	67	2	no	—
868	C₂×Q₈	—	67	2	no	—
869	C₂×Q₈	—	67	2	no	—
870	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
871	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
872	C₂²×C₄	—	67	1	no	—
873	C₂²×C₄	—	67	1	no	—
874	C₂²×C₄	—	67	2	no	—
875	C₂²×C₄	—	67	2	no	—
876	C₂²×C₄	—	67	2	no	—
877	C₂²×C₄	—	67	2	no	—
878	C₂²×C₄	—	67	1	no	—
879	C₂²×C₄	—	67	1	no	—
880	C₂²×C₄	—	67	1	no	—
881	C₂²×C₄	—	67	4	no	—
882	C₂²×C₄	—	67	4	no	—
883	C₂²×C₄	—	67	1	no	—
884	C₂²×C₄	—	67	1	no	—
885	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
886	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
887	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
888	M₁₆	—	2	2	no	—
889	M₁₆	—	67	4	no	—
890	M₁₆	—	67	8	no	—
891	M₁₆	—	134	2	no	—
892	M₁₆	—	134	2	no	—
893	M₁₆	—	134	2	no	—
894	M₁₆	—	134	2	no	—
895	M₁₆	—	134	4	no	—
896	M₁₆	—	134	2	no	—
897	M₁₆	Q₈×D₆₇	1	4	yes	—
898	C₂×C₈	—	2	2	no	—
899	C₂×C₈	—	2	2	no	—
900	C₂×C₈	—	67	2	no	—
901	C₂×C₈	—	67	8	no	—
902	C₂×C₈	—	67	1	no	—
903	C₂×C₈	—	67	1	no	—
904	C₂×C₈	—	67	2	no	—
905	C₂×C₈	—	67	1	no	—
906	C₂×C₈	—	67	1	no	—
907	C₂×C₈	—	134	2	no	—
908	C₂×C₈	—	134	2	no	—
909	C₂×C₈	—	134	2	no	—
910	C₂×C₈	—	134	2	no	—
911	C₂×C₈	—	134	4	no	—
912	C₂×C₈	—	134	2	no	—
913	C₂×C₈	—	134	2	no	—
914	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
915	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
916	C₂×C₈	C₂³×D₆₇	1	2	yes	—
917	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
918	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
919	C₂×C₈	C₂³×D₆₇	1	2	yes	—
920	C₄⋊C₄	—	67	2	no	—
921	C₄⋊C₄	—	67	2	no	—
922	C₄⋊C₄	—	67	2	no	—
923	C₄⋊C₄	—	67	2	no	—
924	C₄⋊C₄	—	67	1	no	—
925	C₄⋊C₄	—	67	1	no	—
926	C₄⋊C₄	—	67	1	no	—
927	C₄⋊C₄	—	67	1	no	—
928	C₄⋊C₄	—	67	1	no	—
929	C₄⋊C₄	—	67	1	no	—
930	C₄⋊C₄	—	67	1	no	—
931	C₄⋊C₄	—	67	1	no	—
932	C₄⋊C₄	—	67	1	no	—
933	C₄⋊C₄	—	67	1	no	—
934	C₄⋊C₄	—	67	1	no	—
935	C₄⋊C₄	—	67	1	no	—
936	C₄⋊C₄	—	67	2	no	—
937	C₄⋊C₄	—	67	2	no	—
938	C₄⋊C₄	—	67	2	no	—
939	C₄⋊C₄	—	67	2	no	—
940	C₄⋊C₄	—	67	2	no	—
941	C₄⋊C₄	—	67	2	no	—
942	C₄⋊C₄	—	67	2	no	—
943	C₄⋊C₄	—	67	2	no	—
944	C₄⋊C₄	—	67	2	no	—
945	C₄⋊C₄	—	67	2	no	—
946	C₄⋊C₄	—	67	2	no	—
947	C₄⋊C₄	—	67	2	no	—
948	C₄⋊C₄	—	67	2	no	—
949	C₄⋊C₄	—	67	2	no	—
950	C₄⋊C₄	—	67	2	no	—
951	C₄⋊C₄	—	67	2	no	—
952	C₄⋊C₄	—	67	2	no	—
953	C₄⋊C₄	—	67	2	no	—
954	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
955	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
956	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
957	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
958	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
959	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
960	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
961	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
962	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
963	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
964	C₂²⋊C₄	—	67	2	no	—
965	C₂²⋊C₄	—	67	2	no	—
966	C₂²⋊C₄	—	67	2	no	—
967	C₂²⋊C₄	—	67	2	no	—
968	C₂²⋊C₄	—	67	2	no	—
969	C₂²⋊C₄	—	67	2	no	—
970	C₂²⋊C₄	—	67	1	no	—
971	C₂²⋊C₄	—	67	1	no	—
972	C₂²⋊C₄	—	67	1	no	—
973	C₂²⋊C₄	—	67	1	no	—
974	C₂²⋊C₄	—	67	1	no	—
975	C₂²⋊C₄	—	67	1	no	—
976	C₂²⋊C₄	—	67	1	no	—
977	C₂²⋊C₄	—	67	1	no	—
978	C₂²⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
979	C₂²⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
980	C₄²	—	67	2	no	—
981	C₄²	—	67	2	no	—
982	C₄²	—	67	2	no	—
983	C₄²	—	67	2	no	—
984	C₄²	—	67	1	no	—
985	C₄²	—	67	1	no	—
986	C₄²	—	67	2	no	—
987	C₄²	—	67	1	no	—
988	C₄²	—	67	1	no	—
989	C₄²	—	67	2	no	—
990	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
991	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
992	C₄²	C₂³×D₆₇	1	1	yes	characteristic
993	C₄²	C₂³×D₆₇	1	2	yes	—
994	C₄²	C₂³×D₆₇	1	2	yes	—
995	C₄²	C₂³×D₆₇	1	1	yes	characteristic
996	C₂³	—	268	1	no	—
997	C₂³	—	268	1	no	—
998	C₂³	—	67	4	no	—
999	C₂³	—	67	1	no	—
1000	C₂³	—	67	1	no	—
1001	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
1002	Q₈	—	4	2	no	—
1003	Q₈	—	4	2	no	—
1004	Q₈	—	268	2	no	—
1005	Q₈	—	268	2	no	—
1006	Q₈	—	268	2	no	—
1007	Q₈	—	268	2	no	—
1008	Q₈	—	268	2	no	—
1009	Q₈	—	268	2	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	268	2	no	—
1013	C₂×C₄	—	268	2	no	—
1014	C₂×C₄	—	268	2	no	—
1015	C₂×C₄	—	268	2	no	—
1016	C₂×C₄	—	268	1	no	—
1017	C₂×C₄	—	268	1	no	—
1018	C₂×C₄	—	67	4	no	—
1019	C₂×C₄	—	67	1	no	—
1020	C₂×C₄	—	67	1	no	—
1021	C₂×C₄	—	67	4	no	—
1022	C₂×C₄	—	67	4	no	—
1023	C₂×C₄	—	67	2	no	—
1024	C₂×C₄	—	67	2	no	—
1025	C₂×C₄	—	67	2	no	—
1026	C₂×C₄	—	67	2	no	—
1027	C₂×C₄	—	67	2	no	—
1028	C₂×C₄	—	67	2	no	—
1029	C₂×C₄	—	67	1	no	—
1030	C₂×C₄	—	67	1	no	—
1031	C₂×C₄	—	67	2	no	—
1032	C₂×C₄	—	67	2	no	—
1033	C₂×C₄	—	67	1	no	—
1034	C₂×C₄	—	67	1	no	—
1035	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1036	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1037	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1038	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1039	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1040	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1041	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1042	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1043	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1044	C₂×C₄	C₂×Q₈×D₆₇	1	2	yes	—
1045	C₂×C₄	#41×D₆₇	1	2	yes	—
1046	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	1	no	—
1050	C₈	—	2	1	no	—
1051	C₈	—	2	2	no	—
1052	C₈	—	67	4	no	—
1053	C₈	—	134	1	no	—
1054	C₈	—	134	1	no	—
1055	C₈	—	134	2	no	—
1056	C₈	—	134	1	no	—
1057	C₈	—	134	1	no	—
1058	C₈	C₂×Q₈×D₆₇	1	4	yes	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	268	4	no	—
1062	C₂²	—	67	2	no	—
1063	C₂²	—	67	2	no	—
1064	C₂²	—	134	1	no	—
1065	C₂²	—	134	1	no	—
1066	C₂²	—	134	1	no	—
1067	C₂²	—	134	1	no	—
1068	C₂²	C₄×Q₈×D₆₇	1	2	yes	—
1069	C₂²	C₂³×C₄×D₆₇	1	1	yes	characteristic
1070	C₄	—	2	1	no	—
1071	C₄	—	2	1	no	—
1072	C₄	—	2	2	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	67	2	no	—
1079	C₄	—	67	2	no	—
1080	C₄	—	134	2	no	—
1081	C₄	—	134	2	no	—
1082	C₄	—	134	1	no	—
1083	C₄	—	134	1	no	—
1084	C₄	—	134	2	no	—
1085	C₄	—	134	2	no	—
1086	C₄	—	134	1	no	—
1087	C₄	—	134	1	no	—
1088	C₄	C₄×Q₈×D₆₇	1	2	yes	—
1089	C₄	C₂²×Q₈×D₆₇	1	1	yes	characteristic
1090	C₄	C₂×#41×D₆₇	1	1	yes	characteristic
1091	C₂	—	2	2	no	—
1092	C₂	—	134	2	no	—
1093	C₂	—	134	2	no	—
1094	C₂	C₂×C₄×Q₈×D₆₇	1	1	yes	characteristic
1095	C₂	#22574920	1	1	yes	characteristic
1096	C₂	#22574922	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁴×C₄
Fitting	C₆₇×#2962	C₂
prime radical	C₂³×D₆₇	C₂²×C₄
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	#2962	D₆₇
hypocenter	C₆₇	#60193
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ #2962

Complements

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

N	H ≅ G/N	type
2. #22569158	C₂	semidirect
3. #22569157	C₂	semidirect
4. #22569156	C₂	semidirect
5. #22569155	C₂	semidirect
6. #22569155	C₂	semidirect
7. #22569154	C₂	semidirect
8. #22569154	C₂	semidirect
9. #22569153	C₂	semidirect
10. #22569153	C₂	semidirect
11. #22569152	C₂	semidirect
12. #22569151	C₂	semidirect
13. #22569145	C₂	semidirect
14. #22569145	C₂	semidirect
15. #22569140	C₂	semidirect
16. #22569138	C₂	semidirect
23. C₆₇×#2962	C₂	semidirect
50. #16863527	C₂²	semidirect
51. #16863527	C₂²	semidirect
52. #16863527	C₂²	semidirect
53. #16863526	C₂²	semidirect
54. #16863526	C₂²	semidirect
55. #16863526	C₂²	semidirect
56. #16863525	C₂²	semidirect
57. #16863525	C₂²	semidirect
58. #16863525	C₂²	semidirect
59. #16863525	C₂²	semidirect
60. #16863525	C₂²	semidirect
61. #16863525	C₂²	semidirect
62. #16863524	C₂²	semidirect
63. #16863524	C₂²	semidirect
64. #16863524	C₂²	semidirect
65. #16863524	C₂²	semidirect
66. #16863524	C₂²	semidirect
67. #16863524	C₂²	semidirect
68. #16863523	C₂²	semidirect
69. #16863523	C₂²	semidirect
70. #16863523	C₂²	semidirect
71. Q₈×C₆₇⋊C₈	C₂²	semidirect
72. C₈×Dic₁₃₄	C₂²	semidirect
73. C₈×Dic₁₃₄	C₂²	semidirect
74. C₈×Dic₁₃₄	C₂²	semidirect
75. #16863520	C₂²	semidirect
76. #16863520	C₂²	semidirect
77. #16863520	C₂²	semidirect
125. #446×C₆₇	C₂²	semidirect
126. #446×C₆₇	C₂²	semidirect
127. #446×C₆₇	C₂²	semidirect
128. C₈×Q₈×C₆₇	C₂²	semidirect
146. M₁₆×D₆₇	Q₈	semidirect
561. #2962	D₆₇	semidirect
572. C₆₇	#60193	semidirect
621. #446	C₂×D₆₇	semidirect
622. #446	C₂×D₆₇	semidirect
623. #446	C₂×D₆₇	semidirect
631. C₈×Q₈	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22573612	2
#22569158	2
#22569157	2
#22569156	2
#22569155	2
#22569154	2
#22569153	2
#22569152	2
#22569151	2
#22569145	2
#22569140	2
#22569138	2
#22568770	2
C₂×#16863421	2
#424×D₆₇	2
#22568626	2
#22568625	2
#405×D₆₇	2
C₆₇×#2962	2
#60193	67