Subgroups — #31725499

Order 17152.

1798 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573613	C₂	1	1	yes	maximal, characteristic
2	#544×D₆₇	C₂	1	1	yes	maximal, characteristic
3	#22570760	C₂	1	2	yes	maximal, complemented
4	#22570757	C₂	1	2	yes	maximal, complemented
5	#22570754	C₂	1	2	yes	maximal, complemented
6	#22570752	C₂	1	2	yes	maximal, complemented
7	#22570747	C₂	1	1	yes	maximal, characteristic, complemented
8	#22570745	C₂	1	1	yes	maximal, characteristic, complemented
9	#22570744	C₂	1	2	yes	maximal, complemented
10	#22570743	C₂	1	1	yes	maximal, characteristic, complemented
11	#22570742	C₂	1	2	yes	maximal, complemented
12	#22570741	C₂	1	1	yes	maximal, characteristic, complemented
13	#22570740	C₂	1	1	yes	maximal, characteristic, complemented
14	#22570739	C₂	1	1	yes	maximal, characteristic, complemented
15	#22570738	C₂	1	2	yes	maximal, complemented
16	#22570736	C₂	1	2	yes	maximal, complemented
17	#22570735	C₂	1	1	yes	maximal, characteristic, complemented
18	#22568797	C₂	1	1	yes	maximal, characteristic
19	#22568796	C₂	1	1	yes	maximal, characteristic
20	C₂×#16863437	C₂	1	1	yes	maximal, characteristic
21	#428×D₆₇	C₂	1	1	yes	maximal, characteristic
22	#22568625	C₂	1	1	yes	maximal, characteristic
23	C₆₇×#3164	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	#16864027	C₂²	1	1	yes	characteristic
27	#16864027	C₂²	1	1	yes	characteristic
28	#16864026	—	2	1	no	—
29	#16864026	—	2	1	no	—
30	#16864026	C₂²	1	2	yes	—
31	#16864026	C₂²	1	2	yes	—
32	#16864025	—	2	2	no	—
33	#16864024	C₂²	1	1	yes	characteristic
34	#16864024	C₂²	1	1	yes	characteristic
35	#16864024	C₂²	1	1	yes	characteristic
36	#16864024	C₂²	1	1	yes	characteristic
37	#16864023	—	2	1	no	—
38	#16864023	—	2	1	no	—
39	#16864023	C₂²	1	2	yes	—
40	#16864023	C₂²	1	2	yes	—
41	#16864021	—	2	2	no	—
42	#16863952	—	2	1	no	—
43	#16863952	C₂²	1	2	yes	—
44	#16863951	—	2	1	no	—
45	#16863951	C₂²	1	2	yes	—
46	#16863948	—	2	2	no	—
47	C₄⋊Q₈×D₆₇	—	2	1	no	—
48	C₄⋊Q₈×D₆₇	C₂²	1	2	yes	—
49	#125×D₆₇	—	2	1	no	—
50	#125×D₆₇	C₂²	1	2	yes	—
51	C₂²⋊Q₈×D₆₇	—	2	2	no	—
52	C₂×#14524001	C₂²	1	1	yes	characteristic
53	#117×D₆₇	C₂²	1	1	yes	characteristic
54	#117×D₆₇	C₂²	1	1	yes	characteristic
55	#117×D₆₇	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
57	#16863806	C₂²	1	2	yes	complemented
58	#16863806	C₂²	1	2	yes	complemented
59	#16863805	C₂²	1	2	yes	complemented
60	#16863805	C₂²	1	2	yes	complemented
61	#16863804	C₂²	1	2	yes	complemented
62	#16863804	C₂²	1	2	yes	complemented
63	#16863804	C₂²	1	2	yes	complemented
64	#16863804	C₂²	1	2	yes	complemented
65	#16863804	C₂²	1	2	yes	complemented
66	#16863804	C₂²	1	2	yes	complemented
67	#16863803	C₂²	1	2	yes	complemented
68	#16863803	C₂²	1	2	yes	complemented
69	#16863802	C₂²	1	2	yes	complemented
70	#16863802	C₂²	1	2	yes	complemented
71	#16863800	C₂²	1	2	yes	complemented
72	#16863800	C₂²	1	2	yes	complemented
73	#16863799	C₂²	1	2	yes	complemented
74	#16863798	C₂²	1	2	yes	complemented
75	#16863797	C₂²	1	2	yes	complemented
76	#16863797	C₂²	1	2	yes	complemented
77	#16863796	C₂²	1	2	yes	complemented
78	#16863796	C₂²	1	2	yes	complemented
79	#16863795	C₂²	1	2	yes	complemented
80	#16863795	C₂²	1	2	yes	complemented
81	#16863794	C₂²	1	2	yes	complemented
82	#16863793	C₂²	1	2	yes	complemented
83	#16863793	C₂²	1	2	yes	complemented
84	#16863792	C₂²	1	2	yes	complemented
85	#16863439	C₂²	1	1	yes	characteristic
86	#16863439	C₂²	1	1	yes	characteristic
87	#16863438	C₂²	1	1	yes	characteristic
88	#16863438	C₂²	1	1	yes	characteristic
89	#16863437	C₂²	1	1	yes	characteristic
90	#16863437	C₂²	1	2	yes	—
91	#16863437	C₂²	1	2	yes	—
92	#16863437	C₂²	1	2	yes	—
93	#16863437	C₂²	1	2	yes	—
94	#16863437	C₂²	1	1	yes	characteristic
95	#16863437	C₂²	1	2	yes	—
96	#16863437	C₂²	1	2	yes	—
97	#16863437	C₂²	1	1	yes	characteristic
98	#16863437	C₂²	1	1	yes	characteristic
99	#16863436	C₂²	1	1	yes	characteristic
100	#16863436	C₂²	1	1	yes	characteristic
101	#16863435	C₂²	1	1	yes	characteristic
102	#16863435	C₂²	1	2	yes	—
103	#16863435	C₂²	1	2	yes	—
104	#16863435	C₂²	1	1	yes	characteristic
105	#16863435	C₂²	1	1	yes	characteristic
106	#16863435	C₂²	1	1	yes	characteristic
107	#16863434	C₂²	1	1	yes	characteristic
108	#16863433	C₂²	1	2	yes	—
109	#16863432	C₂²	1	1	yes	characteristic
110	#16863432	C₂²	1	1	yes	characteristic
111	#16863431	C₂²	1	2	yes	—
112	C₂×#14523976	C₂²	1	1	yes	characteristic
113	#107×D₆₇	C₂²	1	2	yes	—
114	C₂×#14523975	C₂²	1	1	yes	characteristic
115	C₂×#14523974	C₂²	1	1	yes	characteristic
116	#106×D₆₇	C₂²	1	2	yes	—
117	#16863354	C₂²	1	1	yes	characteristic
118	#16863353	C₂²	1	2	yes	—
119	#16863352	C₂²	1	1	yes	characteristic
120	#16863351	C₂²	1	1	yes	characteristic
121	#16863350	C₂²	1	2	yes	—
122	#16863348	C₂²	1	2	yes	—
123	C₄×#11761611	C₂²	1	2	yes	—
124	#544×C₆₇	C₂²	1	1	yes	characteristic
125	#544×C₆₇	C₂²	1	1	yes	characteristic
126	#501×C₆₇	C₂²	1	2	yes	complemented
127	#501×C₆₇	C₂²	1	2	yes	complemented
128	#500×C₆₇	C₂²	1	2	yes	complemented
129	#499×C₆₇	C₂²	1	2	yes	complemented
130	#428×C₆₇	C₂²	1	1	yes	characteristic
131	#428×C₆₇	C₂²	1	1	yes	characteristic
132	#427×C₆₇	C₂²	1	1	yes	characteristic
133	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
134	#405×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×Q₈×D₆₇	—	2	2	no	—
136	C₂²×C₄×D₆₇	—	2	1	no	—
137	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
138	C₂×#11761612	C₂³	1	1	yes	characteristic
139	C₂×#11761611	Q₈	1	8	yes	complemented
140	C₂×#11761611	C₂³	1	1	yes	characteristic
141	C₂×#11761611	C₂³	1	2	yes	—
142	C₂×#11761611	C₂³	1	1	yes	characteristic
143	C₂×#11761611	C₂³	1	1	yes	characteristic
144	C₂×#11761611	C₂³	1	1	yes	characteristic
145	M₁₆×D₆₇	Q₈	1	8	yes	complemented
146	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
147	C₂×C₈×D₆₇	C₂³	1	2	yes	—
148	#14524043	—	2	1	no	—
149	#14524043	—	2	1	no	—
150	#14524043	C₂³	1	2	yes	—
151	#14524043	C₂³	1	2	yes	—
152	#14524042	—	2	1	no	—
153	#14524042	—	2	1	no	—
154	#14524042	—	2	2	no	—
155	#14524042	—	2	2	no	—
156	#14524042	—	2	2	no	—
157	#14524042	—	2	1	no	—
158	#14524042	—	2	1	no	—
159	#14524042	C₂³	1	2	yes	—
160	#14524042	C₂³	1	2	yes	—
161	#14524042	C₂³	1	2	yes	—
162	#14524042	C₂³	1	2	yes	—
163	#14524041	—	2	2	no	—
164	#14524041	—	2	2	no	—
165	#14524041	—	2	2	no	—
166	#14524035	—	2	1	no	—
167	#14524035	—	2	1	no	—
168	#14524035	C₂³	1	2	yes	—
169	#14524035	C₂³	1	2	yes	—
170	#14524034	—	2	1	no	—
171	#14524034	—	2	1	no	—
172	#14524034	—	2	1	no	—
173	#14524034	—	2	1	no	—
174	#14524034	C₂³	1	2	yes	—
175	#14524034	C₂³	1	2	yes	—
176	#14524034	C₂³	1	2	yes	—
177	#14524034	C₂³	1	2	yes	—
178	#14524033	—	2	2	no	—
179	#14524033	—	2	2	no	—
180	#14524033	—	2	2	no	—
181	#14524033	—	2	2	no	—
182	#14524033	—	2	2	no	—
183	#14524033	—	2	2	no	—
184	#14524023	—	2	2	no	—
185	#14524023	—	2	2	no	—
186	#14524023	—	2	2	no	—
187	#14524022	—	2	2	no	—
188	#14524022	—	2	2	no	—
189	#14524021	—	2	2	no	—
190	#14524021	—	2	2	no	—
191	#14524021	—	2	2	no	—
192	#14524021	—	2	2	no	—
193	#14524021	—	2	2	no	—
194	#14524021	—	2	2	no	—
195	#14524020	—	2	2	no	—
196	#14524020	—	2	2	no	—
197	#14524020	—	2	2	no	—
198	#14524020	—	2	2	no	—
199	#14524019	—	2	2	no	—
200	#14524019	—	2	2	no	—
201	#14524019	—	2	2	no	—
202	Q₈×Dic₆₇	—	2	2	no	—
203	#14524008	—	2	2	no	—
204	#14524008	—	2	2	no	—
205	#14524008	—	2	2	no	—
206	#14524002	C₂³	1	1	yes	characteristic
207	#14524002	C₂³	1	1	yes	characteristic
208	#14524002	C₂³	1	1	yes	characteristic
209	#14524001	—	2	1	no	—
210	#14524001	—	2	1	no	—
211	#14524001	D₄	1	1	yes	characteristic
212	#14524001	D₄	1	1	yes	characteristic
213	#14524001	C₂³	1	1	yes	characteristic
214	#14524001	C₂³	1	2	yes	—
215	#14524001	C₂³	1	1	yes	characteristic
216	#14524001	C₂³	1	1	yes	characteristic
217	#14524001	C₂³	1	1	yes	characteristic
218	#14524001	C₂³	1	2	yes	—
219	#14524000	—	2	1	no	—
220	#14524000	—	2	1	no	—
221	#14524000	C₂³	1	2	yes	—
222	#14523999	—	2	1	no	—
223	#14523999	—	2	1	no	—
224	#14523999	D₄	1	2	yes	—
225	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
227	C₂×Dic₆₇⋊C₄	—	2	1	no	—
228	C₄⋊C₄×D₆₇	—	2	1	no	—
229	C₄⋊C₄×D₆₇	—	2	1	no	—
230	C₄⋊C₄×D₆₇	—	2	2	no	—
231	C₄⋊C₄×D₆₇	—	2	2	no	—
232	C₄⋊C₄×D₆₇	—	2	2	no	—
233	C₄⋊C₄×D₆₇	D₄	1	1	yes	characteristic
234	C₄⋊C₄×D₆₇	D₄	1	1	yes	characteristic
235	C₄⋊C₄×D₆₇	C₂³	1	1	yes	characteristic
236	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
237	C₄⋊C₄×D₆₇	C₂³	1	1	yes	characteristic
238	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
239	C₄⋊C₄×D₆₇	C₂³	1	1	yes	characteristic
240	C₄⋊C₄×D₆₇	C₂³	1	1	yes	characteristic
241	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
242	C₂²⋊C₄×D₆₇	—	2	1	no	—
243	C₂²⋊C₄×D₆₇	—	2	1	no	—
244	C₂²⋊C₄×D₆₇	D₄	1	2	yes	—
245	C₂×C₄×Dic₆₇	—	2	1	no	—
246	C₄²×D₆₇	—	2	1	no	—
247	C₄²×D₆₇	—	2	1	no	—
248	C₄²×D₆₇	C₂³	1	2	yes	—
249	#14523977	C₂³	1	1	yes	characteristic
250	#14523977	C₂³	1	2	yes	—
251	#14523977	C₂³	1	2	yes	—
252	#14523977	C₂³	1	1	yes	characteristic
253	#14523976	C₂³	1	1	yes	characteristic
254	#14523976	C₂³	1	2	yes	—
255	#14523976	C₂³	1	2	yes	—
256	#14523976	C₂³	1	2	yes	—
257	#14523976	C₂³	1	1	yes	characteristic
258	#14523976	C₂³	1	2	yes	—
259	#14523976	C₂³	1	2	yes	—
260	#14523976	C₂³	1	1	yes	characteristic
261	#14523976	C₂³	1	2	yes	—
262	#14523976	C₂³	1	1	yes	characteristic
263	#14523975	C₂³	1	2	yes	—
264	#14523975	C₂³	1	2	yes	—
265	#14523975	C₂³	1	1	yes	characteristic
266	#14523975	C₂³	1	2	yes	—
267	#14523975	C₂³	1	2	yes	—
268	#14523975	C₂³	1	1	yes	characteristic
269	#14523974	C₂³	1	1	yes	characteristic
270	#14523974	C₂³	1	2	yes	—
271	#14523974	C₂³	1	2	yes	—
272	#14523974	C₂³	1	2	yes	—
273	#14523974	C₂³	1	1	yes	characteristic
274	#14523974	C₂³	1	2	yes	—
275	#14523974	C₂³	1	2	yes	—
276	#14523974	C₂³	1	1	yes	characteristic
277	#14523974	C₂³	1	2	yes	—
278	#14523974	C₂³	1	1	yes	characteristic
279	#14523954	C₂³	1	2	yes	—
280	#14523953	C₂³	1	2	yes	—
281	#14523953	C₂³	1	2	yes	—
282	C₄×C₆₇⋊C₈	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	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
287	C₄⋊Q₈×C₆₇	—	2	1	no	—
288	C₄⋊Q₈×C₆₇	—	2	1	no	—
289	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
290	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
291	#125×C₆₇	—	2	1	no	—
292	#125×C₆₇	—	2	1	no	—
293	#125×C₆₇	C₂³	1	2	yes	—
294	#125×C₆₇	C₂³	1	2	yes	—
295	C₂²⋊Q₈×C₆₇	—	2	2	no	—
296	C₂²⋊Q₈×C₆₇	—	2	2	no	—
297	#117×C₆₇	C₂³	1	1	yes	characteristic
298	#117×C₆₇	C₂³	1	1	yes	characteristic
299	#117×C₆₇	C₂³	1	1	yes	characteristic
300	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
302	#107×C₆₇	C₂³	1	1	yes	characteristic
303	#107×C₆₇	C₂³	1	2	yes	—
304	#107×C₆₇	C₂³	1	1	yes	characteristic
305	#107×C₆₇	C₂³	1	2	yes	—
306	#107×C₆₇	C₂³	1	2	yes	—
307	#107×C₆₇	C₂³	1	2	yes	—
308	#106×C₆₇	C₂³	1	1	yes	characteristic
309	#106×C₆₇	C₂³	1	2	yes	—
310	#106×C₆₇	C₂³	1	2	yes	—
311	#106×C₆₇	C₂³	1	1	yes	characteristic
312	#97×C₆₇	C₂³	1	2	yes	—
313	C₄×C₈×C₆₇	C₂³	1	2	yes	—
314	C₂³×D₆₇	C₂×D₄	1	1	yes	characteristic
315	C₂×Dic₁₃₄	—	2	2	no	—
316	C₂×Dic₁₃₄	—	2	2	no	—
317	C₂×Dic₁₃₄	—	2	2	no	—
318	C₂×Dic₁₃₄	—	2	2	no	—
319	C₂×Dic₁₃₄	—	2	2	no	—
320	C₂×Dic₁₃₄	—	2	2	no	—
321	Q₈×D₆₇	—	8	4	no	—
322	C₂²×Dic₆₇	—	2	1	no	—
323	C₂²×Dic₆₇	—	2	1	no	—
324	C₂²×Dic₆₇	C₂×D₄	1	1	yes	characteristic
325	C₂×C₄×D₆₇	—	2	1	no	—
326	C₂×C₄×D₆₇	—	2	1	no	—
327	C₂×C₄×D₆₇	—	2	2	no	—
328	C₂×C₄×D₆₇	—	2	1	no	—
329	C₂×C₄×D₆₇	—	2	1	no	—
330	C₂×C₄×D₆₇	—	2	2	no	—
331	C₂×C₄×D₆₇	—	8	2	no	—
332	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
333	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
334	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
335	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
336	C₂×C₄×D₆₇	C₂×Q₈	1	4	yes	—
337	C₂×C₄×D₆₇	C₂×Q₈	1	4	yes	—
338	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
339	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
340	#11761612	C₂×Q₈	1	4	yes	complemented
341	#11761611	C₂×Q₈	1	8	yes	—
342	#11761611	C₂×Q₈	1	4	yes	—
343	#11761611	C₂×Q₈	1	4	yes	—
344	#11761611	C₂×Q₈	1	4	yes	complemented
345	#11761611	C₂×Q₈	1	4	yes	complemented
346	C₂×C₆₇⋊C₈	C₂×Q₈	1	4	yes	complemented
347	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
348	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
349	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
350	C₈×D₆₇	C₂×Q₈	1	8	yes	complemented
351	C₄⋊Dic₆₇	—	2	1	no	—
352	C₄⋊Dic₆₇	—	2	2	no	—
353	C₄⋊Dic₆₇	—	2	1	no	—
354	C₄⋊Dic₆₇	—	2	2	no	—
355	C₄⋊Dic₆₇	—	2	2	no	—
356	C₄⋊Dic₆₇	—	2	2	no	—
357	C₄⋊Dic₆₇	—	2	2	no	—
358	C₄⋊Dic₆₇	—	2	2	no	—
359	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
360	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
361	C₄⋊Dic₆₇	C₂⁴	1	1	yes	characteristic
362	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
363	C₄⋊Dic₆₇	C₂⁴	1	1	yes	characteristic
364	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
365	C₄⋊Dic₆₇	C₂⁴	1	1	yes	characteristic
366	C₄⋊Dic₆₇	C₂⁴	1	1	yes	characteristic
367	Dic₆₇⋊C₄	—	2	2	no	—
368	Dic₆₇⋊C₄	—	2	2	no	—
369	Dic₆₇⋊C₄	—	2	2	no	—
370	Dic₆₇⋊C₄	—	2	2	no	—
371	Dic₆₇⋊C₄	—	2	2	no	—
372	Dic₆₇⋊C₄	—	2	2	no	—
373	Dic₆₇⋊C₄	—	2	2	no	—
374	Dic₆₇⋊C₄	—	2	2	no	—
375	Dic₆₇⋊C₄	—	2	2	no	—
376	Dic₆₇⋊C₄	—	2	2	no	—
377	Dic₆₇⋊C₄	—	2	1	no	—
378	Dic₆₇⋊C₄	—	2	1	no	—
379	Dic₆₇⋊C₄	—	2	1	no	—
380	Dic₆₇⋊C₄	—	2	1	no	—
381	Dic₆₇⋊C₄	—	2	2	no	—
382	Dic₆₇⋊C₄	—	2	2	no	—
383	Dic₆₇⋊C₄	—	2	2	no	—
384	Dic₆₇⋊C₄	—	2	2	no	—
385	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
386	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
387	C₂²⋊Dic₆₇	—	2	1	no	—
388	C₂²⋊Dic₆₇	—	2	1	no	—
389	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
390	(C₂×D₆₇)⋊C₄	—	2	1	no	—
391	(C₂×D₆₇)⋊C₄	—	2	1	no	—
392	(C₂×D₆₇)⋊C₄	—	2	1	no	—
393	(C₂×D₆₇)⋊C₄	—	2	1	no	—
394	(C₂×D₆₇)⋊C₄	—	2	2	no	—
395	(C₂×D₆₇)⋊C₄	—	2	2	no	—
396	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
397	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
398	C₄×Dic₆₇	—	2	1	no	—
399	C₄×Dic₆₇	—	2	1	no	—
400	C₄×Dic₆₇	—	2	1	no	—
401	C₄×Dic₆₇	—	2	1	no	—
402	C₄×Dic₆₇	—	2	1	no	—
403	C₄×Dic₆₇	—	2	1	no	—
404	C₄×Dic₆₇	—	2	2	no	—
405	C₄×Dic₆₇	—	2	2	no	—
406	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
407	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
408	C₄×Dic₆₇	C₂⁴	1	2	yes	—
409	C₂×Q₈×C₆₇	—	2	2	no	—
410	C₂×Q₈×C₆₇	—	2	2	no	—
411	C₂²×C₄×C₆₇	—	2	1	no	—
412	C₂²×C₄×C₆₇	—	2	1	no	—
413	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
414	M₁₆×C₆₇	C₂×Q₈	1	4	yes	complemented
415	C₂×C₈×C₆₇	C₂×Q₈	1	4	yes	complemented
416	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
418	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₆₇	—	2	1	no	—
420	C₄⋊C₄×C₆₇	—	2	1	no	—
421	C₄⋊C₄×C₆₇	—	2	2	no	—
422	C₄⋊C₄×C₆₇	—	2	2	no	—
423	C₄⋊C₄×C₆₇	—	2	2	no	—
424	C₄⋊C₄×C₆₇	—	2	2	no	—
425	C₄⋊C₄×C₆₇	—	2	2	no	—
426	C₄⋊C₄×C₆₇	—	2	2	no	—
427	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
428	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
429	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
430	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
432	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
433	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
434	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
435	C₂²⋊C₄×C₆₇	—	2	1	no	—
436	C₂²⋊C₄×C₆₇	—	2	1	no	—
437	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
438	C₄²×C₆₇	—	2	1	no	—
439	C₄²×C₆₇	—	2	1	no	—
440	C₄²×C₆₇	C₂⁴	1	2	yes	—
441	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
442	C₂²×D₆₇	—	4	1	no	—
443	C₂²×D₆₇	—	4	1	no	—
444	C₂²×D₆₇	C₄⋊Q₈	1	4	yes	—
445	C₂²×D₆₇	C₂²×D₄	1	1	yes	characteristic
446	C₂²×D₆₇	C₂²×D₄	1	1	yes	characteristic
447	Q₈×C₆₇	—	8	2	no	—
448	Q₈×C₆₇	—	8	2	no	—
449	C₂×C₄×C₆₇	—	2	1	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	2	1	no	—
453	C₂×C₄×C₆₇	—	2	2	no	—
454	C₂×C₄×C₆₇	—	2	2	no	—
455	C₂×C₄×C₆₇	—	8	1	no	—
456	C₂×C₄×C₆₇	—	8	1	no	—
457	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
461	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
462	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
463	C₂×Dic₆₇	—	2	2	no	—
464	C₂×Dic₆₇	—	2	1	no	—
465	C₂×Dic₆₇	—	2	1	no	—
466	C₂×Dic₆₇	—	2	1	no	—
467	C₂×Dic₆₇	—	2	1	no	—
468	C₂×Dic₆₇	—	2	2	no	—
469	C₂×Dic₆₇	—	8	1	no	—
470	C₂×Dic₆₇	—	8	1	no	—
471	C₂×Dic₆₇	C₄⋊Q₈	1	4	yes	—
472	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
473	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
474	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×Dic₆₇	C₂²×D₄	1	1	yes	characteristic
476	C₄×D₆₇	—	4	2	no	—
477	C₄×D₆₇	—	4	2	no	—
478	C₄×D₆₇	—	4	2	no	—
479	C₄×D₆₇	—	4	4	no	—
480	C₄×D₆₇	—	4	2	no	—
481	C₄×D₆₇	—	8	1	no	—
482	C₄×D₆₇	—	8	1	no	—
483	C₄×D₆₇	—	8	2	no	—
484	C₄×D₆₇	C₄⋊Q₈	1	4	yes	—
485	C₄×D₆₇	C₄⋊Q₈	1	4	yes	—
486	C₄×D₆₇	C₂²×Q₈	1	2	yes	—
487	C₄×D₆₇	C₂²×Q₈	1	2	yes	—
488	C₄×D₆₇	C₂²×Q₈	1	2	yes	—
489	C₄×D₆₇	C₂²×Q₈	1	2	yes	—
490	Dic₁₃₄	—	8	2	no	—
491	Dic₁₃₄	—	8	2	no	—
492	Dic₁₃₄	—	8	2	no	—
493	Dic₁₃₄	—	8	2	no	—
494	Dic₁₃₄	—	8	2	no	—
495	Dic₁₃₄	—	8	2	no	—
496	C₈×C₆₇	C₂²×Q₈	1	2	yes	—
497	C₈×C₆₇	C₂²×Q₈	1	2	yes	—
498	C₈×C₆₇	C₂²×Q₈	1	4	yes	—
499	C₆₇⋊C₈	C₂²×Q₈	1	4	yes	—
500	C₆₇⋊C₈	C₂²×Q₈	1	2	yes	—
501	C₆₇⋊C₈	C₂²×Q₈	1	2	yes	—
502	C₂²×C₆₇	—	2	1	no	—
503	C₂²×C₆₇	—	2	1	no	—
504	C₂²×C₆₇	C₂×C₄⋊Q₈	1	2	yes	—
505	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
506	C₂×D₆₇	—	2	1	no	—
507	C₂×D₆₇	—	2	1	no	—
508	C₂×D₆₇	—	2	1	no	—
509	C₂×D₆₇	—	2	1	no	—
510	C₂×D₆₇	—	4	4	no	—
511	C₂×D₆₇	C₂×C₄⋊Q₈	1	2	yes	—
512	C₂×D₆₇	C₂×C₄⋊Q₈	1	2	yes	—
513	C₄×C₆₇	—	2	2	no	—
514	C₄×C₆₇	—	2	2	no	—
515	C₄×C₆₇	—	4	1	no	—
516	C₄×C₆₇	—	4	2	no	—
517	C₄×C₆₇	—	4	2	no	—
518	C₄×C₆₇	—	4	1	no	—
519	C₄×C₆₇	—	4	1	no	—
520	C₄×C₆₇	—	4	1	no	—
521	C₄×C₆₇	C₂×C₄⋊Q₈	1	2	yes	—
522	C₄×C₆₇	C₂³×Q₈	1	1	yes	characteristic
523	C₄×C₆₇	C₂³×Q₈	1	1	yes	characteristic
524	Dic₆₇	—	2	2	no	—
525	Dic₆₇	—	2	2	no	—
526	Dic₆₇	—	4	1	no	—
527	Dic₆₇	—	4	2	no	—
528	Dic₆₇	—	4	1	no	—
529	Dic₆₇	—	4	1	no	—
530	Dic₆₇	—	4	2	no	—
531	Dic₆₇	—	4	1	no	—
532	Dic₆₇	C₂×C₄⋊Q₈	1	2	yes	—
533	Dic₆₇	C₂×C₄⋊Q₈	1	2	yes	—
534	#60664	—	67	1	no	maximal, Sylow
535	C₂×C₆₇	—	2	2	no	—
536	C₂×C₆₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
537	C₂×C₆₇	#3585	1	1	yes	characteristic
538	C₂×C₆₇	#3586	1	1	yes	characteristic
539	D₆₇	—	2	2	no	—
540	D₆₇	—	2	2	no	—
541	#3458	—	67	1	no	—
542	C₂×#544	—	67	1	no	—
543	#3166	—	67	2	no	—
544	#3166	—	67	2	no	—
545	#3165	—	67	2	no	—
546	#3165	—	67	2	no	—
547	#3164	—	67	2	no	—
548	#3164	—	67	2	no	—
549	#3164	—	67	1	no	—
550	#3164	—	67	1	no	—
551	#3164	—	67	1	no	—
552	#3164	D₆₇	1	1	yes	characteristic, complemented
553	#3163	—	67	2	no	—
554	#3163	—	67	2	no	—
555	#3163	—	67	1	no	—
556	#3163	—	67	1	no	—
557	#3163	—	67	1	no	—
558	#3163	—	67	1	no	—
559	#2911	—	67	1	no	—
560	#2911	—	67	1	no	—
561	C₂×#428	—	67	1	no	—
562	C₂×#428	—	67	1	no	—
563	#2873	—	67	1	no	—
564	C₆₇	#60664	1	1	yes	characteristic, complemented, Sylow
565	C₂²×M₁₆	—	67	1	no	—
566	C₂²×M₁₆	—	67	1	no	—
567	#544	—	67	2	no	—
568	#544	—	67	2	no	—
569	#544	—	67	2	no	—
570	#544	—	67	2	no	—
571	#544	—	67	1	no	—
572	#544	—	67	1	no	—
573	#544	—	67	1	no	—
574	#544	—	67	1	no	—
575	#544	—	67	1	no	—
576	#544	—	67	1	no	—
577	#544	—	134	1	no	—
578	#544	—	134	1	no	—
579	#544	—	134	2	no	—
580	#544	—	134	1	no	—
581	#544	—	134	1	no	—
582	#544	C₂×D₆₇	1	1	yes	characteristic
583	#544	C₂×D₆₇	1	1	yes	characteristic
584	#543	—	134	2	no	—
585	#533	—	67	2	no	—
586	#533	—	67	2	no	—
587	#533	—	134	2	no	—
588	#533	—	134	1	no	—
589	#533	—	134	1	no	—
590	C₂×C₄⋊Q₈	—	67	2	no	—
591	C₂×C₄⋊Q₈	—	134	1	no	—
592	C₂×#125	—	67	2	no	—
593	C₂×#125	—	134	1	no	—
594	C₂×C₂²⋊Q₈	—	134	2	no	—
595	C₂×#117	—	67	1	no	—
596	C₂×#117	—	67	1	no	—
597	C₂×#117	—	67	1	no	—
598	C₂×#117	—	67	1	no	—
599	C₂²×C₄⋊C₄	—	67	1	no	—
600	#501	—	67	2	no	—
601	#501	—	67	2	no	—
602	#501	—	67	2	no	—
603	#501	—	67	2	no	—
604	#501	—	67	2	no	—
605	#501	—	67	2	no	—
606	#501	—	67	2	no	—
607	#501	—	67	2	no	—
608	#501	—	67	2	no	—
609	#501	—	67	2	no	—
610	#501	—	67	2	no	—
611	#501	—	67	2	no	—
612	#501	—	67	2	no	—
613	#501	—	67	2	no	—
614	#501	C₂×D₆₇	1	2	yes	complemented
615	#501	C₂×D₆₇	1	2	yes	complemented
616	#500	—	67	2	no	—
617	#500	—	67	2	no	—
618	#500	—	67	2	no	—
619	#500	C₂×D₆₇	1	2	yes	complemented
620	#499	—	67	2	no	—
621	#499	—	67	2	no	—
622	#499	—	67	2	no	—
623	#499	—	67	2	no	—
624	#499	—	67	2	no	—
625	#499	—	67	2	no	—
626	#499	—	67	2	no	—
627	#499	C₂×D₆₇	1	2	yes	complemented
628	#498	—	67	2	no	—
629	#498	—	67	2	no	—
630	#498	—	67	2	no	—
631	#498	—	67	2	no	—
632	#428	—	67	1	no	—
633	#428	—	67	1	no	—
634	#428	—	67	1	no	—
635	#428	—	67	1	no	—
636	#428	—	67	1	no	—
637	#428	—	67	1	no	—
638	#428	—	67	1	no	—
639	#428	—	67	2	no	—
640	#428	—	67	2	no	—
641	#428	—	67	1	no	—
642	#428	—	67	2	no	—
643	#428	—	67	1	no	—
644	#428	—	67	2	no	—
645	#428	—	67	2	no	—
646	#428	—	67	2	no	—
647	#428	—	67	1	no	—
648	#428	—	67	1	no	—
649	#428	—	67	1	no	—
650	#428	—	67	1	no	—
651	#428	—	67	2	no	—
652	#428	—	67	2	no	—
653	#428	—	67	1	no	—
654	#428	C₂×D₆₇	1	1	yes	characteristic
655	#428	C₂×D₆₇	1	1	yes	characteristic
656	#427	—	67	1	no	—
657	#427	—	67	1	no	—
658	#427	—	67	1	no	—
659	#427	—	67	2	no	—
660	#427	—	67	2	no	—
661	#427	C₂×D₆₇	1	1	yes	characteristic
662	C₂×#107	—	67	1	no	—
663	C₂×#107	—	67	2	no	—
664	C₂×#107	C₂×D₆₇	1	1	yes	characteristic
665	C₂×#106	—	67	1	no	—
666	C₂×#106	—	67	1	no	—
667	C₂×#106	—	67	2	no	—
668	#405	—	67	1	no	—
669	#405	—	67	1	no	—
670	#405	—	67	1	no	—
671	#405	—	67	2	no	—
672	#405	—	67	2	no	—
673	#405	C₂×D₆₇	1	1	yes	characteristic
674	C₄×M₁₆	—	67	2	no	—
675	C₄×M₁₆	—	67	2	no	—
676	C₂²×Q₈	—	134	2	no	—
677	C₂³×C₄	—	67	1	no	—
678	C₂³×C₄	—	134	1	no	—
679	C₂×M₁₆	—	67	1	no	—
680	C₂×M₁₆	—	67	8	no	—
681	C₂×M₁₆	—	67	8	no	—
682	C₂×M₁₆	—	67	1	no	—
683	C₂×M₁₆	—	67	2	no	—
684	C₂×M₁₆	—	67	1	no	—
685	C₂×M₁₆	—	67	1	no	—
686	C₂×M₁₆	—	67	1	no	—
687	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
688	C₂²×C₈	—	67	1	no	—
689	C₂²×C₈	—	67	2	no	—
690	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
691	C₄⋊Q₈	—	2	1	no	—
692	C₄⋊Q₈	—	2	1	no	—
693	C₄⋊Q₈	—	67	2	no	—
694	C₄⋊Q₈	—	67	2	no	—
695	C₄⋊Q₈	—	67	2	no	—
696	C₄⋊Q₈	—	67	2	no	—
697	C₄⋊Q₈	—	67	2	no	—
698	C₄⋊Q₈	—	67	2	no	—
699	C₄⋊Q₈	—	134	1	no	—
700	C₄⋊Q₈	—	134	1	no	—
701	C₄⋊Q₈	—	134	2	no	—
702	C₄⋊Q₈	—	134	2	no	—
703	C₄⋊Q₈	—	134	2	no	—
704	C₄⋊Q₈	—	134	1	no	—
705	C₄⋊Q₈	—	134	2	no	—
706	C₄⋊Q₈	—	134	1	no	—
707	C₄⋊Q₈	—	134	2	no	—
708	C₄⋊Q₈	—	134	2	no	—
709	C₄⋊Q₈	—	134	1	no	—
710	C₄⋊Q₈	—	134	1	no	—
711	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
712	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
713	#125	—	2	1	no	—
714	#125	—	2	1	no	—
715	#125	—	67	2	no	—
716	#125	—	67	2	no	—
717	#125	—	67	2	no	—
718	#125	—	67	2	no	—
719	#125	—	67	2	no	—
720	#125	—	67	2	no	—
721	#125	—	134	1	no	—
722	#125	—	134	1	no	—
723	#125	—	134	2	no	—
724	#125	—	134	2	no	—
725	#125	—	134	2	no	—
726	#125	—	134	2	no	—
727	#125	—	134	1	no	—
728	#125	—	134	2	no	—
729	#125	—	134	2	no	—
730	#125	—	134	1	no	—
731	#125	—	134	1	no	—
732	#125	—	134	1	no	—
733	#125	C₂²×D₆₇	1	2	yes	—
734	#125	C₂²×D₆₇	1	2	yes	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	134	2	no	—
738	C₂²⋊Q₈	—	134	2	no	—
739	C₂²⋊Q₈	—	134	2	no	—
740	C₂²⋊Q₈	—	134	2	no	—
741	C₂²⋊Q₈	—	134	2	no	—
742	C₂²⋊Q₈	—	134	2	no	—
743	C₂²⋊Q₈	—	134	2	no	—
744	C₂²⋊Q₈	—	134	2	no	—
745	C₂²⋊Q₈	—	134	2	no	—
746	C₂²⋊Q₈	—	134	2	no	—
747	C₂²⋊Q₈	—	134	2	no	—
748	C₂²⋊Q₈	—	134	2	no	—
749	C₂²⋊Q₈	—	134	2	no	—
750	C₂²⋊Q₈	—	134	2	no	—
751	C₂²⋊Q₈	—	134	2	no	—
752	C₂²⋊Q₈	—	134	2	no	—
753	C₂²⋊Q₈	—	134	2	no	—
754	C₂²⋊Q₈	—	134	2	no	—
755	C₄×Q₈	—	134	2	no	—
756	C₄×Q₈	—	134	2	no	—
757	C₄×Q₈	—	134	2	no	—
758	C₄×Q₈	—	134	2	no	—
759	#117	—	67	1	no	—
760	#117	—	67	1	no	—
761	#117	—	67	1	no	—
762	#117	—	67	2	no	—
763	#117	—	67	2	no	—
764	#117	—	67	1	no	—
765	#117	—	67	1	no	—
766	#117	—	67	1	no	—
767	#117	—	67	2	no	—
768	#117	—	67	1	no	—
769	#117	—	67	2	no	—
770	#117	—	67	1	no	—
771	#117	—	67	1	no	—
772	#117	—	134	1	no	—
773	#117	—	134	1	no	—
774	#117	—	134	1	no	—
775	#117	—	134	1	no	—
776	#117	—	134	1	no	—
777	#117	—	134	1	no	—
778	#117	C₂²×D₆₇	1	1	yes	characteristic
779	#117	C₂²×D₆₇	1	1	yes	characteristic
780	#117	C₂²×D₆₇	1	1	yes	characteristic
781	C₂×C₄⋊C₄	—	67	1	no	—
782	C₂×C₄⋊C₄	—	67	1	no	—
783	C₂×C₄⋊C₄	—	67	1	no	—
784	C₂×C₄⋊C₄	—	67	1	no	—
785	C₂×C₄⋊C₄	—	67	2	no	—
786	C₂×C₄⋊C₄	—	67	2	no	—
787	C₂×C₄⋊C₄	—	67	1	no	—
788	C₂×C₄⋊C₄	—	67	1	no	—
789	C₂×C₄⋊C₄	—	67	1	no	—
790	C₂×C₄⋊C₄	—	67	1	no	—
791	C₂×C₄⋊C₄	—	134	1	no	—
792	C₂×C₄⋊C₄	—	134	1	no	—
793	C₂×C₄⋊C₄	—	134	2	no	—
794	C₂×C₄⋊C₄	—	134	2	no	—
795	C₂×C₄⋊C₄	—	134	2	no	—
796	C₂×C₄⋊C₄	—	134	1	no	—
797	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
798	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
799	C₂×C₂²⋊C₄	—	67	2	no	—
800	C₂×C₂²⋊C₄	—	134	1	no	—
801	C₂×C₂²⋊C₄	—	134	1	no	—
802	C₂×C₂²⋊C₄	—	134	1	no	—
803	C₂×C₄²	—	67	2	no	—
804	C₂×C₄²	—	134	1	no	—
805	C₂×C₄²	—	134	1	no	—
806	C₂×C₄²	—	134	1	no	—
807	#107	—	67	2	no	—
808	#107	—	67	1	no	—
809	#107	—	67	2	no	—
810	#107	—	67	1	no	—
811	#107	—	67	2	no	—
812	#107	—	67	2	no	—
813	#107	—	67	2	no	—
814	#107	—	67	2	no	—
815	#107	—	67	2	no	—
816	#107	—	67	1	no	—
817	#107	—	67	1	no	—
818	#107	—	67	1	no	—
819	#107	—	67	2	no	—
820	#107	—	67	1	no	—
821	#107	C₂²×D₆₇	1	2	yes	—
822	#107	C₂²×D₆₇	1	2	yes	—
823	#107	C₂²×D₆₇	1	2	yes	—
824	#107	C₂²×D₆₇	1	2	yes	—
825	#107	C₂²×D₆₇	1	1	yes	characteristic
826	#107	C₂²×D₆₇	1	1	yes	characteristic
827	#106	—	67	2	no	—
828	#106	—	67	2	no	—
829	#106	—	67	2	no	—
830	#106	—	67	2	no	—
831	#106	—	67	1	no	—
832	#106	—	67	1	no	—
833	#106	—	67	2	no	—
834	#106	—	67	2	no	—
835	#106	—	67	2	no	—
836	#106	—	67	2	no	—
837	#106	—	67	1	no	—
838	#106	—	67	2	no	—
839	#106	—	67	1	no	—
840	#106	—	67	1	no	—
841	#106	—	67	2	no	—
842	#106	—	67	1	no	—
843	#106	C₂²×D₆₇	1	2	yes	—
844	#106	C₂²×D₆₇	1	2	yes	—
845	#106	C₂²×D₆₇	1	1	yes	characteristic
846	#106	C₂²×D₆₇	1	1	yes	characteristic
847	#97	—	67	2	no	—
848	#97	—	67	2	no	—
849	#97	—	67	2	no	—
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	C₂²×D₆₇	1	2	yes	—
855	C₂⁴	—	67	1	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	2	no	—
858	C₂×Q₈	—	536	4	no	—
859	C₂×Q₈	—	134	2	no	—
860	C₂×Q₈	—	134	2	no	—
861	C₂×Q₈	—	134	2	no	—
862	C₂×Q₈	—	134	2	no	—
863	C₂×Q₈	—	134	2	no	—
864	C₂×Q₈	—	134	2	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	536	2	no	—
868	C₂²×C₄	—	67	2	no	—
869	C₂²×C₄	—	67	2	no	—
870	C₂²×C₄	—	67	1	no	—
871	C₂²×C₄	—	67	1	no	—
872	C₂²×C₄	—	67	1	no	—
873	C₂²×C₄	—	67	4	no	—
874	C₂²×C₄	—	67	4	no	—
875	C₂²×C₄	—	67	1	no	—
876	C₂²×C₄	—	67	1	no	—
877	C₂²×C₄	—	134	1	no	—
878	C₂²×C₄	—	134	1	no	—
879	C₂²×C₄	—	134	2	no	—
880	C₂²×C₄	—	134	1	no	—
881	C₂²×C₄	—	134	1	no	—
882	C₂²×C₄	—	134	2	no	—
883	C₂²×C₄	—	134	1	no	—
884	C₂²×C₄	—	134	1	no	—
885	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
886	M₁₆	—	67	4	no	—
887	M₁₆	—	67	8	no	—
888	M₁₆	—	67	4	no	—
889	M₁₆	—	67	4	no	—
890	M₁₆	—	67	4	no	—
891	M₁₆	—	67	4	no	—
892	M₁₆	Q₈×D₆₇	1	4	yes	complemented
893	C₂×C₈	—	67	4	no	—
894	C₂×C₈	—	67	1	no	—
895	C₂×C₈	—	67	2	no	—
896	C₂×C₈	—	67	1	no	—
897	C₂×C₈	—	67	8	no	—
898	C₂×C₈	Q₈×D₆₇	1	4	yes	complemented
899	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
900	C₂×C₈	C₂³×D₆₇	1	2	yes	—
901	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	67	2	no	—
911	C₄⋊C₄	—	67	1	no	—
912	C₄⋊C₄	—	67	2	no	—
913	C₄⋊C₄	—	67	1	no	—
914	C₄⋊C₄	—	67	2	no	—
915	C₄⋊C₄	—	67	1	no	—
916	C₄⋊C₄	—	67	2	no	—
917	C₄⋊C₄	—	67	1	no	—
918	C₄⋊C₄	—	67	1	no	—
919	C₄⋊C₄	—	67	1	no	—
920	C₄⋊C₄	—	134	2	no	—
921	C₄⋊C₄	—	134	2	no	—
922	C₄⋊C₄	—	134	1	no	—
923	C₄⋊C₄	—	134	1	no	—
924	C₄⋊C₄	—	134	1	no	—
925	C₄⋊C₄	—	134	1	no	—
926	C₄⋊C₄	—	134	2	no	—
927	C₄⋊C₄	—	134	2	no	—
928	C₄⋊C₄	—	134	2	no	—
929	C₄⋊C₄	—	134	2	no	—
930	C₄⋊C₄	—	134	2	no	—
931	C₄⋊C₄	—	134	2	no	—
932	C₄⋊C₄	—	134	2	no	—
933	C₄⋊C₄	—	134	2	no	—
934	C₄⋊C₄	—	134	2	no	—
935	C₄⋊C₄	—	134	2	no	—
936	C₄⋊C₄	—	134	2	no	—
937	C₄⋊C₄	—	134	2	no	—
938	C₄⋊C₄	—	134	1	no	—
939	C₄⋊C₄	—	134	1	no	—
940	C₄⋊C₄	—	134	2	no	—
941	C₄⋊C₄	—	134	2	no	—
942	C₄⋊C₄	—	134	2	no	—
943	C₄⋊C₄	—	134	2	no	—
944	C₄⋊C₄	—	134	2	no	—
945	C₄⋊C₄	—	134	2	no	—
946	C₄⋊C₄	D₄×D₆₇	1	1	yes	characteristic
947	C₄⋊C₄	D₄×D₆₇	1	1	yes	characteristic
948	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
949	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
950	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
951	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
952	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
953	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	67	2	no	—
957	C₂²⋊C₄	—	67	2	no	—
958	C₂²⋊C₄	—	67	2	no	—
959	C₂²⋊C₄	—	134	1	no	—
960	C₂²⋊C₄	—	134	1	no	—
961	C₂²⋊C₄	—	134	1	no	—
962	C₂²⋊C₄	—	134	1	no	—
963	C₂²⋊C₄	—	134	2	no	—
964	C₂²⋊C₄	—	134	2	no	—
965	C₂²⋊C₄	—	134	1	no	—
966	C₂²⋊C₄	—	134	1	no	—
967	C₂²⋊C₄	D₄×D₆₇	1	2	yes	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	67	2	no	—
971	C₄²	—	67	2	no	—
972	C₄²	—	67	2	no	—
973	C₄²	—	134	1	no	—
974	C₄²	—	134	1	no	—
975	C₄²	—	134	2	no	—
976	C₄²	—	134	1	no	—
977	C₄²	—	134	1	no	—
978	C₄²	—	134	2	no	—
979	C₄²	—	134	1	no	—
980	C₄²	—	134	1	no	—
981	C₄²	C₂³×D₆₇	1	2	yes	—
982	C₂³	—	268	1	no	—
983	C₂³	—	268	1	no	—
984	C₂³	—	67	4	no	—
985	C₂³	—	67	1	no	—
986	C₂³	—	67	1	no	—
987	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
988	Q₈	—	8	2	no	—
989	Q₈	—	8	2	no	—
990	Q₈	—	536	2	no	—
991	Q₈	—	536	2	no	—
992	Q₈	—	536	2	no	—
993	Q₈	—	536	2	no	—
994	Q₈	—	536	2	no	—
995	Q₈	—	536	2	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	8	1	no	—
1003	C₂×C₄	—	8	1	no	—
1004	C₂×C₄	—	268	2	no	—
1005	C₂×C₄	—	268	2	no	—
1006	C₂×C₄	—	268	4	no	—
1007	C₂×C₄	—	268	2	no	—
1008	C₂×C₄	—	268	2	no	—
1009	C₂×C₄	—	536	2	no	—
1010	C₂×C₄	—	536	1	no	—
1011	C₂×C₄	—	536	1	no	—
1012	C₂×C₄	—	536	1	no	—
1013	C₂×C₄	—	536	1	no	—
1014	C₂×C₄	—	67	4	no	—
1015	C₂×C₄	—	67	1	no	—
1016	C₂×C₄	—	67	1	no	—
1017	C₂×C₄	—	67	4	no	—
1018	C₂×C₄	—	67	4	no	—
1019	C₂×C₄	—	67	2	no	—
1020	C₂×C₄	—	67	2	no	—
1021	C₂×C₄	—	67	2	no	—
1022	C₂×C₄	—	67	2	no	—
1023	C₂×C₄	—	67	2	no	—
1024	C₂×C₄	—	67	2	no	—
1025	C₂×C₄	—	134	1	no	—
1026	C₂×C₄	—	134	1	no	—
1027	C₂×C₄	—	134	2	no	—
1028	C₂×C₄	—	134	1	no	—
1029	C₂×C₄	—	134	1	no	—
1030	C₂×C₄	—	134	2	no	—
1031	C₂×C₄	C₂×D₄×D₆₇	1	2	yes	—
1032	C₂×C₄	C₂×D₄×D₆₇	1	2	yes	—
1033	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1034	C₂×C₄	C₂×Q₈×D₆₇	1	2	yes	—
1035	C₂×C₄	C₂×Q₈×D₆₇	1	2	yes	—
1036	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1037	C₈	—	67	2	no	—
1038	C₈	—	67	2	no	—
1039	C₈	—	67	4	no	—
1040	C₈	C₂×Q₈×D₆₇	1	4	yes	—
1041	C₈	C₂×Q₈×D₆₇	1	2	yes	—
1042	C₈	C₂×Q₈×D₆₇	1	2	yes	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	268	4	no	—
1046	C₂²	—	67	2	no	—
1047	C₂²	—	67	2	no	—
1048	C₂²	—	134	1	no	—
1049	C₂²	—	134	1	no	—
1050	C₂²	—	134	1	no	—
1051	C₂²	—	134	1	no	—
1052	C₂²	C₄⋊Q₈×D₆₇	1	2	yes	—
1053	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	4	2	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	1	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	268	2	no	—
1063	C₄	—	268	1	no	—
1064	C₄	—	268	1	no	—
1065	C₄	—	268	1	no	—
1066	C₄	—	268	1	no	—
1067	C₄	—	268	2	no	—
1068	C₄	—	67	2	no	—
1069	C₄	—	67	2	no	—
1070	C₄	—	134	2	no	—
1071	C₄	—	134	2	no	—
1072	C₄	C₄⋊Q₈×D₆₇	1	2	yes	—
1073	C₄	C₂²×Q₈×D₆₇	1	1	yes	characteristic
1074	C₄	C₂²×Q₈×D₆₇	1	1	yes	characteristic
1075	C₂	—	2	2	no	—
1076	C₂	—	134	2	no	—
1077	C₂	—	134	2	no	—
1078	C₂	C₂×C₄⋊Q₈×D₆₇	1	1	yes	characteristic
1079	C₂	#22574984	1	1	yes	characteristic
1080	C₂	#22574994	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₆₇
commutator, cosocle	C₂×C₄×C₆₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₆₇×#3164	C₂
socle	C₂²×C₆₇	C₂³×D₄
prime radical	C₂³×D₆₇	C₂×D₄
hypercenter	#3164	D₆₇
hypocenter	C₆₇	#60664
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3164

Complements

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

N	H ≅ G/N	type
3. #22570760	C₂	semidirect
4. #22570757	C₂	semidirect
5. #22570754	C₂	semidirect
6. #22570752	C₂	semidirect
7. #22570747	C₂	semidirect
8. #22570745	C₂	semidirect
9. #22570744	C₂	semidirect
10. #22570743	C₂	semidirect
11. #22570742	C₂	semidirect
12. #22570741	C₂	semidirect
13. #22570740	C₂	semidirect
14. #22570739	C₂	semidirect
15. #22570738	C₂	semidirect
16. #22570736	C₂	semidirect
17. #22570735	C₂	semidirect
23. C₆₇×#3164	C₂	semidirect
57. #16863806	C₂²	semidirect
58. #16863806	C₂²	semidirect
59. #16863805	C₂²	semidirect
60. #16863805	C₂²	semidirect
61. #16863804	C₂²	semidirect
62. #16863804	C₂²	semidirect
63. #16863804	C₂²	semidirect
64. #16863804	C₂²	semidirect
65. #16863804	C₂²	semidirect
66. #16863804	C₂²	semidirect
67. #16863803	C₂²	semidirect
68. #16863803	C₂²	semidirect
69. #16863802	C₂²	semidirect
70. #16863802	C₂²	semidirect
71. #16863800	C₂²	semidirect
72. #16863800	C₂²	semidirect
73. #16863799	C₂²	semidirect
74. #16863798	C₂²	semidirect
75. #16863797	C₂²	semidirect
76. #16863797	C₂²	semidirect
77. #16863796	C₂²	semidirect
78. #16863796	C₂²	semidirect
79. #16863795	C₂²	semidirect
80. #16863795	C₂²	semidirect
81. #16863794	C₂²	semidirect
82. #16863793	C₂²	semidirect
83. #16863793	C₂²	semidirect
84. #16863792	C₂²	semidirect
126. #501×C₆₇	C₂²	semidirect
127. #501×C₆₇	C₂²	semidirect
128. #500×C₆₇	C₂²	semidirect
129. #499×C₆₇	C₂²	semidirect
139. C₂×#11761611	Q₈	semidirect
145. M₁₆×D₆₇	Q₈	semidirect
340. #11761612	C₂×Q₈	semidirect
344. #11761611	C₂×Q₈	semidirect
345. #11761611	C₂×Q₈	semidirect
346. C₂×C₆₇⋊C₈	C₂×Q₈	semidirect
350. C₈×D₆₇	C₂×Q₈	semidirect
414. M₁₆×C₆₇	C₂×Q₈	semidirect
415. C₂×C₈×C₆₇	C₂×Q₈	semidirect
552. #3164	D₆₇	semidirect
564. C₆₇	#60664	semidirect
614. #501	C₂×D₆₇	semidirect
615. #501	C₂×D₆₇	semidirect
619. #500	C₂×D₆₇	semidirect
627. #499	C₂×D₆₇	semidirect
892. M₁₆	Q₈×D₆₇	semidirect
898. C₂×C₈	Q₈×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22573613	2
#544×D₆₇	2
#22570760	2
#22570757	2
#22570754	2
#22570752	2
#22570747	2
#22570745	2
#22570744	2
#22570743	2
#22570742	2
#22570741	2
#22570740	2
#22570739	2
#22570738	2
#22570736	2
#22570735	2
#22568797	2
#22568796	2
C₂×#16863437	2
#428×D₆₇	2
#22568625	2
C₆₇×#3164	2
#60664	67