Subgroups — #31730681

Order 17152.

1728 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574120	C₂	1	1	yes	maximal, characteristic, complemented
2	#22571674	C₂	1	2	yes	maximal, complemented
3	#22571665	C₂	1	2	yes	maximal, complemented
4	#22571436	C₂	1	1	yes	maximal, characteristic, complemented
5	#22571427	C₂	1	1	yes	maximal, characteristic, complemented
6	#22571423	C₂	1	1	yes	maximal, characteristic, complemented
7	#22571407	C₂	1	1	yes	maximal, characteristic, complemented
8	#22571242	C₂	1	1	yes	maximal, characteristic, complemented
9	#22571242	C₂	1	1	yes	maximal, characteristic, complemented
10	#22571212	C₂	1	1	yes	maximal, characteristic, complemented
11	#22571196	C₂	1	1	yes	maximal, characteristic, complemented
12	#22571091	C₂	1	2	yes	maximal, complemented
13	#22571061	C₂	1	2	yes	maximal, complemented
14	#22570919	C₂	1	1	yes	maximal, characteristic, complemented
15	#22570908	C₂	1	1	yes	maximal, characteristic, complemented
16	#22570816	C₂	1	1	yes	maximal, characteristic, complemented
17	#22570805	C₂	1	1	yes	maximal, characteristic, complemented
18	#22570480	C₂	1	2	yes	maximal, complemented
19	#22570465	C₂	1	2	yes	maximal, complemented
20	#22570438	C₂	1	2	yes	maximal, complemented
21	#22570393	C₂	1	2	yes	maximal, complemented
22	#22568860	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#3510	C₂	1	1	yes	maximal, characteristic, complemented
24	#16864119	—	2	1	no	—
25	#16864111	—	2	1	no	—
26	#16864106	—	2	1	no	—
27	#16864092	—	2	1	no	—
28	#16864092	—	2	1	no	—
29	#16864055	—	2	1	no	—
30	#16864055	—	2	1	no	—
31	#16864051	—	2	1	no	—
32	#16864017	C₂²	1	2	yes	—
33	#16864017	C₂²	1	2	yes	complemented
34	#16863974	C₂²	1	2	yes	—
35	#16863953	C₂²	1	1	yes	characteristic
36	#16863953	C₂²	1	1	yes	characteristic, complemented
37	#16863946	C₂²	1	1	yes	characteristic
38	#16863946	C₂²	1	1	yes	characteristic, complemented
39	#16863946	C₂²	1	1	yes	characteristic, complemented
40	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
41	#16863876	C₂²	1	2	yes	complemented
42	#16863806	C₂²	1	1	yes	characteristic, complemented
43	#16863806	C₂²	1	1	yes	characteristic, complemented
44	#16863806	C₂²	1	1	yes	characteristic, complemented
45	#16863806	C₂²	1	1	yes	characteristic, complemented
46	#16863791	C₂²	1	1	yes	characteristic
47	#16863791	C₂²	1	1	yes	characteristic
48	#16863786	C₂²	1	1	yes	characteristic
49	#16863786	C₂²	1	1	yes	characteristic
50	#16863766	C₂²	1	1	yes	characteristic, complemented
51	#16863766	C₂²	1	1	yes	characteristic, complemented
52	#16863762	C₂²	1	1	yes	characteristic, complemented
53	#16863762	C₂²	1	1	yes	characteristic, complemented
54	#16863755	C₂²	1	1	yes	characteristic
55	#16863755	C₂²	1	1	yes	characteristic
56	#16863755	C₂²	1	1	yes	characteristic
57	#16863755	C₂²	1	1	yes	characteristic
58	#16863737	C₂²	1	2	yes	—
59	#16863737	C₂²	1	2	yes	—
60	#16863729	C₂²	1	2	yes	complemented
61	#16863724	C₂²	1	2	yes	complemented
62	#16863720	C₂²	1	2	yes	—
63	#16863720	C₂²	1	2	yes	—
64	#16863712	C₂²	1	2	yes	—
65	#16863707	C₂²	1	2	yes	—
66	#16863691	C₂²	1	2	yes	complemented
67	#16863688	C₂²	1	2	yes	complemented
68	#16863686	C₂²	1	2	yes	—
69	#16863683	C₂²	1	2	yes	complemented
70	#16863681	C₂²	1	2	yes	complemented
71	#16863678	C₂²	1	2	yes	complemented
72	#16863676	C₂²	1	2	yes	—
73	#16863673	C₂²	1	2	yes	complemented
74	#16863652	C₂²	1	2	yes	complemented
75	#16863647	C₂²	1	2	yes	—
76	#16863644	C₂²	1	2	yes	complemented
77	#16863640	C₂²	1	2	yes	—
78	#16863635	C₂²	1	2	yes	complemented
79	#16863630	C₂²	1	2	yes	—
80	#16863627	C₂²	1	2	yes	complemented
81	#16863623	C₂²	1	2	yes	—
82	#16863618	C₂²	1	2	yes	complemented
83	#16863618	C₂²	1	2	yes	complemented
84	#16863615	C₂²	1	2	yes	—
85	#16863615	C₂²	1	2	yes	—
86	#16863611	C₂²	1	2	yes	—
87	#16863611	C₂²	1	2	yes	—
88	#16863608	C₂²	1	2	yes	—
89	#16863608	C₂²	1	2	yes	—
90	#16863556	C₂²	1	2	yes	complemented
91	#16863556	C₂²	1	2	yes	complemented
92	#16863552	C₂²	1	2	yes	—
93	#16863547	C₂²	1	2	yes	—
94	#16863539	C₂²	1	2	yes	—
95	#16863539	C₂²	1	2	yes	—
96	#16863535	C₂²	1	2	yes	—
97	#16863530	C₂²	1	2	yes	—
98	#16863506	C₂²	1	2	yes	—
99	#16863501	C₂²	1	2	yes	complemented
100	#16863496	C₂²	1	2	yes	—
101	#16863494	C₂²	1	2	yes	complemented
102	C₄×#11761618	C₂²	1	2	yes	complemented
103	C₄×#11761615	C₂²	1	2	yes	complemented
104	C₄×#11761616	C₂²	1	2	yes	—
105	C₄×#11761613	C₂²	1	2	yes	—
106	#16863457	C₂²	1	2	yes	—
107	#16863457	C₂²	1	2	yes	complemented
108	#16863453	C₂²	1	1	yes	characteristic
109	#16863453	C₂²	1	1	yes	characteristic
110	#16863453	C₂²	1	1	yes	characteristic, complemented
111	#16863453	C₂²	1	1	yes	characteristic, complemented
112	#16863423	C₂²	1	2	yes	complemented
113	#16863363	C₂²	1	2	yes	—
114	C₄×#11761612	C₂²	1	1	yes	characteristic, complemented
115	C₂×#14523954	C₂²	1	1	yes	characteristic, complemented
116	#559×C₆₇	—	2	1	no	—
117	#559×C₆₇	—	2	1	no	—
118	#556×C₆₇	—	2	1	no	—
119	#556×C₆₇	—	2	1	no	—
120	#551×C₆₇	—	2	1	no	—
121	#551×C₆₇	—	2	1	no	—
122	#551×C₆₇	—	2	1	no	—
123	#551×C₆₇	—	2	1	no	—
124	#542×C₆₇	C₂²	1	1	yes	characteristic
125	#542×C₆₇	C₂²	1	1	yes	characteristic
126	#542×C₆₇	C₂²	1	1	yes	characteristic
127	#542×C₆₇	C₂²	1	1	yes	characteristic
128	#536×C₆₇	C₂²	1	1	yes	characteristic
129	#535×C₆₇	C₂²	1	1	yes	characteristic
130	#533×C₆₇	C₂²	1	1	yes	characteristic
131	#529×C₆₇	C₂²	1	1	yes	characteristic
132	#529×C₆₇	C₂²	1	1	yes	characteristic
133	#529×C₆₇	C₂²	1	1	yes	characteristic
134	#529×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
136	#519×C₆₇	C₂²	1	1	yes	characteristic
137	#518×C₆₇	C₂²	1	1	yes	characteristic
138	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
139	C₂×#11761628	—	2	1	no	—
140	C₂×#11761628	—	2	1	no	—
141	C₂×#11761628	C₂³	1	2	yes	—
142	C₂²×Dic₁₃₄	—	2	1	no	—
143	C₂×#11761618	C₂³	1	2	yes	—
144	C₂×#11761618	C₂³	1	2	yes	—
145	C₂×#11761616	C₂³	1	2	yes	—
146	C₂×#11761616	C₂³	1	2	yes	—
147	C₂×#11761615	C₂³	1	2	yes	—
148	C₂×#11761615	C₂³	1	2	yes	—
149	C₂×#11761613	C₂³	1	2	yes	—
150	C₂×#11761613	C₂³	1	2	yes	—
151	C₂×#11761612	C₂³	1	2	yes	—
152	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
153	#14524043	—	2	1	no	—
154	#14524043	—	2	1	no	—
155	#14524043	C₂³	1	1	yes	characteristic
156	#14524043	C₂³	1	1	yes	characteristic
157	#14524043	C₂³	1	1	yes	characteristic
158	#14524043	C₂³	1	2	yes	—
159	#14524040	C₂³	1	1	yes	characteristic
160	#14524038	—	2	2	no	—
161	#14524038	—	2	2	no	—
162	#14524035	—	2	1	no	—
163	#14524035	—	2	1	no	—
164	#14524031	—	2	1	no	—
165	#14524031	—	2	1	no	—
166	#14524031	C₂³	1	2	yes	—
167	#14524029	—	2	2	no	—
168	#14524029	—	2	2	no	—
169	#14524025	—	2	2	no	—
170	#14524025	—	2	2	no	—
171	#14524022	—	2	1	no	—
172	#14524022	—	2	1	no	—
173	#14524022	C₂³	1	2	yes	—
174	#14524022	C₂³	1	2	yes	—
175	#14524021	—	2	2	no	—
176	#14524021	—	2	2	no	—
177	#14524019	—	2	2	no	—
178	#14524017	—	2	1	no	—
179	#14524017	—	2	1	no	—
180	#14524017	—	2	1	no	—
181	#14524017	—	2	1	no	—
182	#14524017	C₂³	1	2	yes	—
183	#14524017	C₂³	1	2	yes	—
184	#14524015	—	2	2	no	—
185	#14524015	—	2	2	no	—
186	#14524014	—	2	2	no	—
187	C₄×Dic₁₃₄	—	2	1	no	—
188	C₄×Dic₁₃₄	—	2	1	no	—
189	C₄×Dic₁₃₄	C₂³	1	2	yes	—
190	C₄×Dic₁₃₄	C₂³	1	2	yes	—
191	C₄×D₂₆₈	—	2	1	no	—
192	C₄×D₂₆₈	—	2	1	no	—
193	C₄×D₂₆₈	—	2	1	no	—
194	C₄×D₂₆₈	—	2	1	no	—
195	C₄×D₂₆₈	C₂³	1	2	yes	—
196	C₄×D₂₆₈	C₂³	1	2	yes	—
197	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
198	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
199	#14524002	—	2	1	no	—
200	#14524002	—	2	1	no	—
201	#14524001	—	2	2	no	—
202	C₂×C₄⋊Dic₆₇	—	2	1	no	—
203	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
204	C₄⋊C₄×D₆₇	—	2	2	no	—
205	#14523976	C₂³	1	2	yes	—
206	#14523976	C₂³	1	2	yes	—
207	#14523976	C₂³	1	2	yes	—
208	#14523976	C₂³	1	2	yes	—
209	#14523974	C₂³	1	2	yes	—
210	#14523974	C₂³	1	2	yes	—
211	#14523974	C₂³	1	2	yes	—
212	#14523974	C₂³	1	2	yes	—
213	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
214	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
215	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
216	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
217	#14523967	C₂³	1	2	yes	—
218	#14523967	C₂³	1	2	yes	—
219	#14523967	C₂³	1	2	yes	—
220	#14523967	C₂³	1	2	yes	—
221	#14523966	C₂³	1	2	yes	—
222	#14523966	C₂³	1	2	yes	—
223	#14523966	C₂³	1	2	yes	—
224	#14523966	C₂³	1	2	yes	—
225	#14523964	C₂³	1	2	yes	—
226	#14523964	C₂³	1	2	yes	—
227	#14523964	C₂³	1	2	yes	—
228	#14523964	C₂³	1	2	yes	—
229	#14523963	C₂³	1	2	yes	—
230	#14523963	C₂³	1	2	yes	—
231	#14523963	C₂³	1	2	yes	—
232	#14523963	C₂³	1	2	yes	—
233	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
234	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
235	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
236	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
237	#14523954	C₂³	1	2	yes	—
238	#14523954	C₂³	1	1	yes	characteristic
239	#14523954	C₂³	1	1	yes	characteristic
240	#14523954	C₂³	1	1	yes	characteristic
241	#14523954	C₂³	1	1	yes	characteristic
242	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
243	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
244	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
245	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
246	C₄⋊Q₈×C₆₇	—	2	1	no	—
247	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
248	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
249	#127×C₆₇	—	2	1	no	—
250	#126×C₆₇	—	2	1	no	—
251	#126×C₆₇	—	2	1	no	—
252	#126×C₆₇	—	2	1	no	—
253	#126×C₆₇	—	2	1	no	—
254	#126×C₆₇	—	2	1	no	—
255	#126×C₆₇	—	2	1	no	—
256	#126×C₆₇	—	2	1	no	—
257	#126×C₆₇	—	2	1	no	—
258	#125×C₆₇	C₂³	1	1	yes	characteristic
259	#125×C₆₇	C₂³	1	1	yes	characteristic
260	#124×C₆₇	—	2	1	no	—
261	#124×C₆₇	—	2	1	no	—
262	#124×C₆₇	—	2	1	no	—
263	#124×C₆₇	—	2	1	no	—
264	#124×C₆₇	—	2	1	no	—
265	#124×C₆₇	—	2	1	no	—
266	#124×C₆₇	—	2	1	no	—
267	#124×C₆₇	—	2	1	no	—
268	#124×C₆₇	C₂³	1	1	yes	characteristic
269	#124×C₆₇	C₂³	1	1	yes	characteristic
270	#124×C₆₇	C₂³	1	1	yes	characteristic
271	#124×C₆₇	C₂³	1	1	yes	characteristic
272	#123×C₆₇	—	2	1	no	—
273	#123×C₆₇	—	2	1	no	—
274	#123×C₆₇	—	2	1	no	—
275	#123×C₆₇	—	2	1	no	—
276	#123×C₆₇	—	2	1	no	—
277	#123×C₆₇	—	2	1	no	—
278	#123×C₆₇	—	2	1	no	—
279	#123×C₆₇	—	2	1	no	—
280	#123×C₆₇	—	2	1	no	—
281	#123×C₆₇	—	2	1	no	—
282	C₂²⋊Q₈×C₆₇	—	2	1	no	—
283	C₂²⋊Q₈×C₆₇	—	2	1	no	—
284	C₂²⋊Q₈×C₆₇	—	2	1	no	—
285	C₂²⋊Q₈×C₆₇	—	2	1	no	—
286	C₂²⋊Q₈×C₆₇	—	2	1	no	—
287	C₂²⋊Q₈×C₆₇	—	2	1	no	—
288	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
289	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
290	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
291	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
292	#121×C₆₇	C₂³	1	1	yes	characteristic
293	#121×C₆₇	C₂³	1	1	yes	characteristic
294	#121×C₆₇	C₂³	1	1	yes	characteristic
295	#121×C₆₇	C₂³	1	1	yes	characteristic
296	#120×C₆₇	—	2	1	no	—
297	#120×C₆₇	—	2	1	no	—
298	C₄×Q₈×C₆₇	—	2	1	no	—
299	C₄×Q₈×C₆₇	—	2	1	no	—
300	C₄×Q₈×C₆₇	—	2	1	no	—
301	C₄×Q₈×C₆₇	—	2	1	no	—
302	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
303	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
304	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
305	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
306	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
307	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
308	C₄×D₄×C₆₇	—	2	1	no	—
309	C₄×D₄×C₆₇	—	2	1	no	—
310	C₄×D₄×C₆₇	—	2	1	no	—
311	C₄×D₄×C₆₇	—	2	1	no	—
312	C₄×D₄×C₆₇	—	2	1	no	—
313	C₄×D₄×C₆₇	—	2	1	no	—
314	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
315	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
316	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
317	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
318	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
319	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
320	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
321	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
322	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
323	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
324	#117×C₆₇	—	2	1	no	—
325	#117×C₆₇	—	2	1	no	—
326	#117×C₆₇	—	2	1	no	—
327	#117×C₆₇	—	2	1	no	—
328	#117×C₆₇	—	2	1	no	—
329	#117×C₆₇	—	2	1	no	—
330	#117×C₆₇	C₂³	1	1	yes	characteristic
331	#117×C₆₇	C₂³	1	1	yes	characteristic
332	#117×C₆₇	C₂³	1	1	yes	characteristic
333	#117×C₆₇	C₂³	1	1	yes	characteristic
334	#117×C₆₇	C₂³	1	1	yes	characteristic
335	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
336	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
337	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
338	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
339	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
340	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
341	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
342	#11761628	—	4	2	no	—
343	#11761628	—	4	2	no	—
344	#11761628	—	8	2	no	—
345	#11761628	—	8	2	no	—
346	C₂×Dic₁₃₄	—	2	1	no	—
347	C₂×Dic₁₃₄	—	2	1	no	—
348	C₂×Dic₁₃₄	—	2	2	no	—
349	C₂×Dic₁₃₄	—	8	2	no	—
350	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
351	C₂×D₂₆₈	—	2	1	no	—
352	C₂×D₂₆₈	—	2	1	no	—
353	C₂×D₂₆₈	C₂⁴	1	2	yes	—
354	C₂×C₂²⋊D₆₇	—	2	2	no	—
355	C₂×C₂²⋊D₆₇	—	2	2	no	—
356	C₂×C₂²⋊D₆₇	—	2	2	no	—
357	C₂²×Dic₆₇	—	2	2	no	—
358	C₂×C₄×D₆₇	—	2	2	no	—
359	C₂×C₄×D₆₇	—	2	2	no	—
360	C₂×C₄×D₆₇	—	2	2	no	—
361	#11761618	—	4	2	no	—
362	#11761618	—	4	2	no	—
363	#11761616	—	4	2	no	—
364	#11761616	—	4	2	no	—
365	#11761615	—	4	2	no	—
366	#11761615	—	4	2	no	—
367	#11761613	—	4	2	no	—
368	#11761613	—	4	2	no	—
369	#11761612	—	4	2	no	—
370	C₂×C₆₇⋊C₈	—	4	2	no	—
371	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
372	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
373	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
374	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
375	C₄⋊Dic₆₇	—	2	2	no	—
376	C₄⋊Dic₆₇	—	2	1	no	—
377	C₄⋊Dic₆₇	—	2	1	no	—
378	C₄⋊Dic₆₇	—	2	2	no	—
379	C₄⋊Dic₆₇	—	2	1	no	—
380	C₄⋊Dic₆₇	—	2	1	no	—
381	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
382	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
383	Dic₆₇⋊C₄	—	2	2	no	—
384	Dic₆₇⋊C₄	—	2	2	no	—
385	Dic₆₇⋊C₄	—	2	2	no	—
386	Dic₆₇⋊C₄	—	2	2	no	—
387	C₂²⋊Dic₆₇	—	2	2	no	—
388	C₂²⋊Dic₆₇	—	2	2	no	—
389	(C₂×D₆₇)⋊C₄	—	2	2	no	—
390	(C₂×D₆₇)⋊C₄	—	2	2	no	—
391	(C₂×D₆₇)⋊C₄	—	2	2	no	—
392	(C₂×D₆₇)⋊C₄	—	2	2	no	—
393	(C₂×D₆₇)⋊C₄	—	2	2	no	—
394	(C₂×D₆₇)⋊C₄	—	2	2	no	—
395	C₄×Dic₆₇	—	2	2	no	—
396	C₄×Dic₆₇	—	2	2	no	—
397	C₂⁴×C₆₇	—	2	1	no	—
398	#41×C₆₇	—	4	2	no	—
399	C₂×Q₈×C₆₇	—	2	1	no	—
400	C₂×Q₈×C₆₇	—	2	1	no	—
401	C₂×Q₈×C₆₇	—	2	1	no	—
402	C₂×Q₈×C₆₇	—	4	2	no	—
403	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
404	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
406	C₂×D₄×C₆₇	—	2	1	no	—
407	C₂×D₄×C₆₇	—	2	1	no	—
408	C₂×D₄×C₆₇	—	2	1	no	—
409	C₂×D₄×C₆₇	—	2	1	no	—
410	C₂×D₄×C₆₇	—	2	1	no	—
411	C₂×D₄×C₆₇	—	4	2	no	—
412	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
413	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
414	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
415	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
416	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₆₇	—	2	1	no	—
418	C₂²×C₄×C₆₇	—	2	1	no	—
419	C₂²×C₄×C₆₇	—	2	1	no	—
420	C₂²×C₄×C₆₇	—	2	1	no	—
421	C₂²×C₄×C₆₇	—	2	1	no	—
422	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
423	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
424	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
425	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
426	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
427	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
428	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	—	2	1	no	—
433	C₄⋊C₄×C₆₇	—	2	1	no	—
434	C₄⋊C₄×C₆₇	—	2	1	no	—
435	C₄⋊C₄×C₆₇	—	2	1	no	—
436	C₄⋊C₄×C₆₇	—	2	1	no	—
437	C₄⋊C₄×C₆₇	—	2	1	no	—
438	C₄⋊C₄×C₆₇	—	2	1	no	—
439	C₄⋊C₄×C₆₇	—	2	1	no	—
440	C₄⋊C₄×C₆₇	—	2	1	no	—
441	C₄⋊C₄×C₆₇	—	2	1	no	—
442	C₄⋊C₄×C₆₇	—	2	1	no	—
443	C₄⋊C₄×C₆₇	—	2	1	no	—
444	C₄⋊C₄×C₆₇	—	2	1	no	—
445	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₂²⋊C₄×C₆₇	—	2	1	no	—
456	C₂²⋊C₄×C₆₇	—	2	1	no	—
457	C₂²⋊C₄×C₆₇	—	2	1	no	—
458	C₂²⋊C₄×C₆₇	—	2	1	no	—
459	C₂²⋊C₄×C₆₇	—	2	1	no	—
460	C₂²⋊C₄×C₆₇	—	2	1	no	—
461	C₂²⋊C₄×C₆₇	—	2	1	no	—
462	C₂²⋊C₄×C₆₇	—	2	1	no	—
463	C₂²⋊C₄×C₆₇	—	2	1	no	—
464	C₂²⋊C₄×C₆₇	—	2	1	no	—
465	C₂²⋊C₄×C₆₇	—	2	1	no	—
466	C₂²⋊C₄×C₆₇	—	2	1	no	—
467	C₂²⋊C₄×C₆₇	—	2	1	no	—
468	C₂²⋊C₄×C₆₇	—	2	1	no	—
469	C₂²⋊C₄×C₆₇	—	2	1	no	—
470	C₂²⋊C₄×C₆₇	—	2	1	no	—
471	C₂²⋊C₄×C₆₇	—	2	1	no	—
472	C₂²⋊C₄×C₆₇	—	2	1	no	—
473	C₂²⋊C₄×C₆₇	—	2	1	no	—
474	C₂²⋊C₄×C₆₇	—	2	1	no	—
475	C₂²⋊C₄×C₆₇	—	2	1	no	—
476	C₂²⋊C₄×C₆₇	—	2	1	no	—
477	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
483	C₄²×C₆₇	—	2	1	no	—
484	C₄²×C₆₇	—	2	1	no	—
485	C₄²×C₆₇	—	2	1	no	—
486	C₄²×C₆₇	—	2	1	no	—
487	C₄²×C₆₇	—	2	1	no	—
488	C₄²×C₆₇	—	2	1	no	—
489	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
490	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
497	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
498	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
499	C₂³×C₆₇	—	2	1	no	—
500	C₂³×C₆₇	—	2	1	no	—
501	C₂³×C₆₇	—	4	2	no	—
502	C₂³×C₆₇	—	8	1	no	—
503	C₂³×C₆₇	—	8	1	no	—
504	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
505	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
506	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
507	C₂²×D₆₇	—	2	2	no	—
508	Q₈×C₆₇	—	2	2	no	—
509	Q₈×C₆₇	—	2	2	no	—
510	Q₈×C₆₇	—	4	1	no	—
511	Q₈×C₆₇	—	4	2	no	—
512	Q₈×C₆₇	—	8	1	no	—
513	Q₈×C₆₇	—	8	1	no	—
514	D₄×C₆₇	—	2	2	no	—
515	D₄×C₆₇	—	2	2	no	—
516	D₄×C₆₇	—	4	1	no	—
517	D₄×C₆₇	—	4	1	no	—
518	D₄×C₆₇	—	4	1	no	—
519	D₄×C₆₇	—	4	2	no	—
520	D₄×C₆₇	—	8	1	no	—
521	D₄×C₆₇	—	8	1	no	—
522	D₄×C₆₇	—	8	1	no	—
523	D₄×C₆₇	—	8	1	no	—
524	C₂×C₄×C₆₇	—	2	2	no	—
525	C₂×C₄×C₆₇	—	2	2	no	—
526	C₂×C₄×C₆₇	—	2	2	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	1	no	—
529	C₂×C₄×C₆₇	—	2	1	no	—
530	C₂×C₄×C₆₇	—	2	1	no	—
531	C₂×C₄×C₆₇	—	2	1	no	—
532	C₂×C₄×C₆₇	—	2	1	no	—
533	C₂×C₄×C₆₇	—	4	1	no	—
534	C₂×C₄×C₆₇	—	4	1	no	—
535	C₂×C₄×C₆₇	—	4	1	no	—
536	C₂×C₄×C₆₇	—	4	1	no	—
537	C₂×C₄×C₆₇	—	4	1	no	—
538	C₂×C₄×C₆₇	—	4	1	no	—
539	C₂×C₄×C₆₇	—	4	2	no	—
540	C₂×C₄×C₆₇	—	8	1	no	—
541	C₂×C₄×C₆₇	—	8	1	no	—
542	C₂×C₄×C₆₇	—	8	1	no	—
543	C₂×C₄×C₆₇	—	8	1	no	—
544	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
556	C₂²⋊D₆₇	—	4	4	no	—
557	C₂²⋊D₆₇	—	8	2	no	—
558	C₂²⋊D₆₇	—	8	2	no	—
559	C₂×Dic₆₇	—	2	2	no	—
560	C₂×Dic₆₇	—	2	2	no	—
561	C₂×Dic₆₇	—	2	2	no	—
562	C₂×Dic₆₇	—	8	2	no	—
563	D₂₆₈	—	2	2	no	—
564	D₂₆₈	—	2	2	no	—
565	D₂₆₈	—	4	2	no	—
566	D₂₆₈	—	4	2	no	—
567	C₄×D₆₇	—	4	4	no	—
568	C₄×D₆₇	—	8	2	no	—
569	C₄×D₆₇	—	8	2	no	—
570	Dic₁₃₄	—	2	2	no	—
571	Dic₁₃₄	—	2	2	no	—
572	Dic₁₃₄	—	4	2	no	—
573	Dic₁₃₄	—	4	2	no	—
574	Dic₁₃₄	—	8	2	no	—
575	C₆₇⋊C₈	—	2	2	no	—
576	C₆₇⋊C₈	—	2	2	no	—
577	C₆₇⋊C₈	—	2	2	no	—
578	C₆₇⋊C₈	—	2	2	no	—
579	C₂²×C₆₇	—	2	1	no	—
580	C₂²×C₆₇	—	2	1	no	—
581	C₂²×C₆₇	—	2	1	no	—
582	C₂²×C₆₇	—	2	1	no	—
583	C₂²×C₆₇	—	2	1	no	—
584	C₂²×C₆₇	—	2	1	no	—
585	C₂²×C₆₇	—	2	1	no	—
586	C₂²×C₆₇	—	2	1	no	—
587	C₂²×C₆₇	—	2	1	no	—
588	C₂²×C₆₇	—	4	1	no	—
589	C₂²×C₆₇	—	4	1	no	—
590	C₂²×C₆₇	—	4	1	no	—
591	C₂²×C₆₇	—	4	1	no	—
592	C₂²×C₆₇	—	4	1	no	—
593	C₂²×C₆₇	—	4	1	no	—
594	C₂²×C₆₇	—	16	2	no	—
595	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
596	C₂×D₆₇	—	4	2	no	—
597	C₂×D₆₇	—	4	2	no	—
598	C₂×D₆₇	—	4	2	no	—
599	C₄×C₆₇	—	2	1	no	—
600	C₄×C₆₇	—	2	1	no	—
601	C₄×C₆₇	—	2	1	no	—
602	C₄×C₆₇	—	2	1	no	—
603	C₄×C₆₇	—	2	1	no	—
604	C₄×C₆₇	—	2	1	no	—
605	C₄×C₆₇	—	2	1	no	—
606	C₄×C₆₇	—	2	1	no	—
607	C₄×C₆₇	—	2	1	no	—
608	C₄×C₆₇	—	2	1	no	—
609	C₄×C₆₇	—	2	1	no	—
610	C₄×C₆₇	—	4	1	no	—
611	C₄×C₆₇	—	4	1	no	—
612	C₄×C₆₇	—	4	1	no	—
613	C₄×C₆₇	—	4	1	no	—
614	C₄×C₆₇	—	4	1	no	—
615	C₄×C₆₇	—	4	1	no	—
616	C₄×C₆₇	#585	1	2	yes	—
617	Dic₆₇	—	4	2	no	—
618	Dic₆₇	—	4	2	no	—
619	Dic₆₇	—	4	2	no	—
620	#61016	—	67	1	no	maximal, Sylow
621	C₂×C₆₇	—	4	1	no	—
622	C₂×C₆₇	—	4	1	no	—
623	C₂×C₆₇	—	4	1	no	—
624	C₂×C₆₇	—	8	1	no	—
625	C₂×C₆₇	—	8	1	no	—
626	C₂×C₆₇	#3449	1	1	yes	characteristic
627	C₂×C₆₇	#3585	1	1	yes	characteristic
628	C₂×C₆₇	#3586	1	1	yes	characteristic
629	D₆₇	—	8	2	no	—
630	#3511	—	67	1	no	—
631	#3510	D₆₇	1	1	yes	characteristic, complemented
632	#3263	—	67	2	no	—
633	#3262	—	67	2	no	—
634	#3239	—	67	1	no	—
635	#3238	—	67	1	no	—
636	#3237	—	67	1	no	—
637	#3235	—	67	1	no	—
638	#3219	—	67	1	no	—
639	#3219	—	67	1	no	—
640	#3215	—	67	1	no	—
641	#3213	—	67	1	no	—
642	#3201	—	67	2	no	—
643	#3198	—	67	2	no	—
644	#3181	—	67	1	no	—
645	#3180	—	67	1	no	—
646	#3172	—	67	1	no	—
647	#3171	—	67	1	no	—
648	#3125	—	67	2	no	—
649	#3124	—	67	2	no	—
650	#3121	—	67	2	no	—
651	#3118	—	67	2	no	—
652	#2923	—	67	1	no	—
653	C₆₇	#61016	1	1	yes	characteristic, complemented, Sylow
654	#559	—	2	1	no	—
655	#559	—	2	1	no	—
656	#556	—	2	1	no	—
657	#556	—	2	1	no	—
658	#556	—	134	1	no	—
659	#555	—	134	1	no	—
660	#554	—	134	1	no	—
661	#553	—	134	1	no	—
662	#553	—	134	1	no	—
663	#551	—	2	1	no	—
664	#551	—	2	1	no	—
665	#551	—	2	1	no	—
666	#551	—	2	1	no	—
667	#548	—	134	1	no	—
668	#548	—	134	1	no	—
669	#547	—	134	1	no	—
670	#542	—	67	2	no	—
671	#542	—	67	2	no	—
672	#542	C₂×D₆₇	1	1	yes	characteristic
673	#542	C₂×D₆₇	1	1	yes	characteristic
674	#542	C₂×D₆₇	1	1	yes	characteristic
675	#542	C₂×D₆₇	1	1	yes	characteristic
676	#537	—	67	2	no	—
677	#536	C₂×D₆₇	1	1	yes	characteristic
678	#535	C₂×D₆₇	1	1	yes	characteristic
679	#533	—	67	1	no	—
680	#533	—	67	1	no	—
681	#533	C₂×D₆₇	1	1	yes	characteristic
682	#532	—	67	1	no	—
683	#532	—	67	1	no	—
684	#532	—	67	1	no	—
685	C₂×C₄⋊Q₈	—	67	1	no	—
686	#529	C₂×D₆₇	1	1	yes	characteristic
687	#529	C₂×D₆₇	1	1	yes	characteristic
688	#529	C₂×D₆₇	1	1	yes	characteristic
689	#529	C₂×D₆₇	1	1	yes	characteristic
690	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
691	#520	—	67	2	no	—
692	#519	C₂×D₆₇	1	1	yes	characteristic
693	#518	C₂×D₆₇	1	1	yes	characteristic
694	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
695	#501	—	67	1	no	—
696	#501	—	67	1	no	—
697	#501	—	67	1	no	—
698	#501	—	67	1	no	—
699	#497	—	67	1	no	—
700	#497	—	67	1	no	—
701	#496	—	67	1	no	—
702	#496	—	67	1	no	—
703	#491	—	67	1	no	—
704	#491	—	67	1	no	—
705	#490	—	67	1	no	—
706	#490	—	67	1	no	—
707	#489	—	67	1	no	—
708	#489	—	67	1	no	—
709	#489	—	67	1	no	—
710	#489	—	67	1	no	—
711	#485	—	67	2	no	—
712	#485	—	67	2	no	—
713	#484	—	67	2	no	—
714	#483	—	67	2	no	—
715	#482	—	67	2	no	—
716	#482	—	67	2	no	—
717	#481	—	67	2	no	—
718	#480	—	67	2	no	—
719	#477	—	67	2	no	—
720	#477	—	67	2	no	—
721	#476	—	67	2	no	—
722	#476	—	67	2	no	—
723	#475	—	67	2	no	—
724	#475	—	67	2	no	—
725	#474	—	67	2	no	—
726	#474	—	67	2	no	—
727	#470	—	67	2	no	—
728	#469	—	67	2	no	—
729	#468	—	67	2	no	—
730	#468	—	67	2	no	—
731	#467	—	67	2	no	—
732	#466	—	67	2	no	—
733	#465	—	67	2	no	—
734	#465	—	67	2	no	—
735	#464	—	67	2	no	—
736	#464	—	67	2	no	—
737	#464	—	67	2	no	—
738	#464	—	67	2	no	—
739	#463	—	67	2	no	—
740	#463	—	67	2	no	—
741	#463	—	67	2	no	—
742	#463	—	67	2	no	—
743	#452	—	67	2	no	—
744	#452	—	67	2	no	—
745	#451	—	67	2	no	—
746	#450	—	67	2	no	—
747	#449	—	67	2	no	—
748	#449	—	67	2	no	—
749	#448	—	67	2	no	—
750	#447	—	67	2	no	—
751	#442	—	67	2	no	—
752	#441	—	67	2	no	—
753	#440	—	67	2	no	—
754	#440	—	67	2	no	—
755	C₄×Q₁₆	—	67	2	no	—
756	C₄×SD₁₆	—	67	2	no	—
757	C₄×SD₁₆	—	67	2	no	—
758	C₄×D₈	—	67	2	no	—
759	#433	—	67	2	no	—
760	#433	—	67	2	no	—
761	#432	—	67	1	no	—
762	#432	—	67	1	no	—
763	#432	—	67	1	no	—
764	#432	—	67	1	no	—
765	#424	—	67	2	no	—
766	#408	—	67	2	no	—
767	C₄×M₁₆	—	67	1	no	—
768	C₂×#97	—	67	1	no	—
769	C₂×#41	—	67	2	no	—
770	C₂×#41	—	134	1	no	—
771	C₂×#41	—	134	1	no	—
772	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
773	C₂²×Q₈	—	134	1	no	—
774	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
775	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
776	C₂×Q₁₆	—	67	2	no	—
777	C₂×Q₁₆	—	67	2	no	—
778	C₂×SD₁₆	—	67	2	no	—
779	C₂×SD₁₆	—	67	2	no	—
780	C₂×SD₁₆	—	67	2	no	—
781	C₂×SD₁₆	—	67	2	no	—
782	C₂×D₈	—	67	2	no	—
783	C₂×D₈	—	67	2	no	—
784	C₂×M₁₆	—	67	2	no	—
785	C₂²×C₈	—	67	2	no	—
786	C₄⋊Q₈	—	2	1	no	—
787	C₄⋊Q₈	—	67	1	no	—
788	C₄⋊Q₈	—	67	1	no	—
789	C₄⋊Q₈	—	67	2	no	—
790	C₄⋊Q₈	—	67	1	no	—
791	C₄⋊Q₈	—	134	1	no	—
792	C₄⋊Q₈	—	134	1	no	—
793	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
794	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
795	#127	—	2	1	no	—
796	#127	—	67	1	no	—
797	#126	—	2	1	no	—
798	#126	—	2	1	no	—
799	#126	—	2	1	no	—
800	#126	—	2	1	no	—
801	#126	—	2	1	no	—
802	#126	—	2	1	no	—
803	#126	—	2	1	no	—
804	#126	—	2	1	no	—
805	#126	—	134	2	no	—
806	#126	—	134	2	no	—
807	#125	—	134	1	no	—
808	#125	—	134	1	no	—
809	#125	C₂²×D₆₇	1	1	yes	characteristic
810	#125	C₂²×D₆₇	1	1	yes	characteristic
811	#124	—	2	1	no	—
812	#124	—	2	1	no	—
813	#124	—	2	1	no	—
814	#124	—	2	1	no	—
815	#124	—	2	1	no	—
816	#124	—	2	1	no	—
817	#124	—	2	1	no	—
818	#124	—	2	1	no	—
819	#124	—	67	2	no	—
820	#124	—	134	2	no	—
821	#124	—	134	2	no	—
822	#124	—	134	1	no	—
823	#124	—	134	1	no	—
824	#124	C₂²×D₆₇	1	1	yes	characteristic
825	#124	C₂²×D₆₇	1	1	yes	characteristic
826	#124	C₂²×D₆₇	1	1	yes	characteristic
827	#124	C₂²×D₆₇	1	1	yes	characteristic
828	#123	—	2	1	no	—
829	#123	—	2	1	no	—
830	#123	—	2	1	no	—
831	#123	—	2	1	no	—
832	#123	—	2	1	no	—
833	#123	—	2	1	no	—
834	#123	—	2	1	no	—
835	#123	—	2	1	no	—
836	#123	—	2	1	no	—
837	#123	—	2	1	no	—
838	#123	—	134	2	no	—
839	#123	—	134	2	no	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	—	67	2	no	—
847	C₂²⋊Q₈	—	67	2	no	—
848	C₂²⋊Q₈	—	134	2	no	—
849	C₂²⋊Q₈	—	134	1	no	—
850	C₂²⋊Q₈	—	134	1	no	—
851	C₂²⋊Q₈	—	134	2	no	—
852	C₂²⋊Q₈	—	134	2	no	—
853	C₂²⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
854	C₂²⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
855	C₂²⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
856	C₂²⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
857	#121	—	67	2	no	—
858	#121	—	67	2	no	—
859	#121	—	134	2	no	—
860	#121	—	134	2	no	—
861	#121	—	134	2	no	—
862	#121	—	134	1	no	—
863	#121	—	134	1	no	—
864	#121	—	134	1	no	—
865	#121	—	134	1	no	—
866	#121	C₂²×D₆₇	1	1	yes	characteristic
867	#121	C₂²×D₆₇	1	1	yes	characteristic
868	#121	C₂²×D₆₇	1	1	yes	characteristic
869	#121	C₂²×D₆₇	1	1	yes	characteristic
870	#120	—	2	1	no	—
871	#120	—	2	1	no	—
872	C₄×Q₈	—	2	1	no	—
873	C₄×Q₈	—	2	1	no	—
874	C₄×Q₈	—	2	1	no	—
875	C₄×Q₈	—	2	1	no	—
876	C₄×Q₈	—	67	2	no	—
877	C₄×Q₈	—	67	2	no	—
878	C₄×Q₈	—	134	1	no	—
879	C₄×Q₈	—	134	1	no	—
880	C₄×Q₈	C₂²⋊D₆₇	1	1	yes	characteristic
881	C₄×Q₈	C₂²⋊D₆₇	1	1	yes	characteristic
882	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
883	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
884	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
885	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	1	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	67	2	no	—
893	C₄×D₄	—	67	2	no	—
894	C₄×D₄	—	134	2	no	—
895	C₄×D₄	—	134	2	no	—
896	C₄×D₄	—	134	1	no	—
897	C₄×D₄	—	134	1	no	—
898	C₄×D₄	—	134	1	no	—
899	C₄×D₄	—	134	1	no	—
900	C₄×D₄	C₂²⋊D₆₇	1	1	yes	characteristic
901	C₄×D₄	C₂²⋊D₆₇	1	1	yes	characteristic
902	C₄×D₄	C₂²⋊D₆₇	1	1	yes	characteristic
903	C₄×D₄	C₂²⋊D₆₇	1	1	yes	characteristic
904	C₄×D₄	C₂²⋊D₆₇	1	1	yes	characteristic
905	C₄×D₄	C₂²⋊D₆₇	1	1	yes	characteristic
906	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
907	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
908	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
909	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
910	#117	—	2	1	no	—
911	#117	—	2	1	no	—
912	#117	—	2	1	no	—
913	#117	—	2	1	no	—
914	#117	—	2	1	no	—
915	#117	—	2	1	no	—
916	#117	—	134	1	no	—
917	#117	—	134	1	no	—
918	#117	—	134	2	no	—
919	#117	C₂²×D₆₇	1	1	yes	characteristic
920	#117	C₂²×D₆₇	1	1	yes	characteristic
921	#117	C₂²×D₆₇	1	1	yes	characteristic
922	#117	C₂²×D₆₇	1	1	yes	characteristic
923	#117	C₂²×D₆₇	1	1	yes	characteristic
924	C₂×C₄⋊C₄	—	67	2	no	—
925	C₂×C₄⋊C₄	—	134	1	no	—
926	C₂×C₄⋊C₄	—	134	2	no	—
927	C₂×C₂²⋊C₄	—	2	1	no	—
928	C₂×C₂²⋊C₄	—	2	1	no	—
929	C₂×C₂²⋊C₄	—	2	1	no	—
930	C₂×C₂²⋊C₄	—	2	1	no	—
931	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
932	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
933	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
934	#107	—	67	2	no	—
935	#107	—	67	2	no	—
936	#107	—	67	2	no	—
937	#107	—	67	2	no	—
938	#106	—	67	2	no	—
939	#106	—	67	2	no	—
940	#106	—	67	2	no	—
941	#106	—	67	2	no	—
942	C₄⋊C₈	—	67	2	no	—
943	C₄⋊C₈	—	67	2	no	—
944	C₄⋊C₈	—	67	2	no	—
945	C₄⋊C₈	—	67	2	no	—
946	#103	—	67	2	no	—
947	#103	—	67	2	no	—
948	#103	—	67	2	no	—
949	#103	—	67	2	no	—
950	#103	—	67	2	no	—
951	#103	—	67	2	no	—
952	#103	—	67	2	no	—
953	#103	—	67	2	no	—
954	#102	—	67	2	no	—
955	#102	—	67	2	no	—
956	#102	—	67	2	no	—
957	#102	—	67	2	no	—
958	#102	—	67	2	no	—
959	#102	—	67	2	no	—
960	#102	—	67	2	no	—
961	#102	—	67	2	no	—
962	C₂²⋊C₈	—	67	2	no	—
963	C₂²⋊C₈	—	67	2	no	—
964	C₂²⋊C₈	—	67	2	no	—
965	C₂²⋊C₈	—	67	2	no	—
966	#97	—	67	1	no	—
967	#97	—	67	1	no	—
968	#97	—	67	2	no	—
969	#97	—	67	1	no	—
970	#97	—	67	1	no	—
971	C₄×C₈	—	67	2	no	—
972	C₂⁴	—	2	1	no	—
973	#41	—	4	2	no	—
974	#41	—	268	2	no	—
975	#41	—	268	2	no	—
976	#41	—	536	2	no	—
977	#41	—	536	2	no	—
978	C₂×Q₈	—	2	1	no	—
979	C₂×Q₈	—	2	1	no	—
980	C₂×Q₈	—	2	1	no	—
981	C₂×Q₈	—	4	2	no	—
982	C₂×Q₈	—	536	2	no	—
983	C₂×Q₈	—	67	2	no	—
984	C₂×Q₈	—	134	1	no	—
985	C₂×Q₈	—	134	1	no	—
986	C₂×Q₈	—	134	2	no	—
987	C₂×Q₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
988	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
989	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	4	2	no	—
996	C₂×D₄	—	67	2	no	—
997	C₂×D₄	—	134	2	no	—
998	C₂×D₄	—	134	2	no	—
999	C₂×D₄	—	134	2	no	—
1000	C₂×D₄	—	134	1	no	—
1001	C₂×D₄	—	134	1	no	—
1002	C₂×D₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1003	C₂×D₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1004	C₂×D₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1005	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
1006	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	134	2	no	—
1013	C₂²×C₄	—	134	2	no	—
1014	C₂²×C₄	—	134	2	no	—
1015	C₂²×C₄	—	134	2	no	—
1016	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1017	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1018	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1019	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1020	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1021	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1022	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1023	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1024	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1025	Q₁₆	—	268	2	no	—
1026	Q₁₆	—	268	2	no	—
1027	SD₁₆	—	268	2	no	—
1028	SD₁₆	—	268	2	no	—
1029	SD₁₆	—	268	2	no	—
1030	SD₁₆	—	268	2	no	—
1031	D₈	—	268	2	no	—
1032	D₈	—	268	2	no	—
1033	M₁₆	—	268	2	no	—
1034	C₂×C₈	—	268	2	no	—
1035	C₂×C₈	—	67	2	no	—
1036	C₂×C₈	—	67	2	no	—
1037	C₂×C₈	—	67	2	no	—
1038	C₂×C₈	—	67	2	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	67	2	no	—
1054	C₄⋊C₄	—	67	2	no	—
1055	C₄⋊C₄	—	134	2	no	—
1056	C₄⋊C₄	—	134	1	no	—
1057	C₄⋊C₄	—	134	1	no	—
1058	C₄⋊C₄	—	134	2	no	—
1059	C₄⋊C₄	—	134	2	no	—
1060	C₄⋊C₄	—	134	2	no	—
1061	C₄⋊C₄	—	134	1	no	—
1062	C₄⋊C₄	—	134	1	no	—
1063	C₄⋊C₄	—	134	2	no	—
1064	C₄⋊C₄	—	134	2	no	—
1065	C₄⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1066	C₄⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1067	C₄⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1068	C₄⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1069	C₄⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1070	C₄⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1071	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1072	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1073	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1074	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	134	2	no	—
1098	C₂²⋊C₄	—	134	2	no	—
1099	C₂²⋊C₄	—	134	2	no	—
1100	C₂²⋊C₄	—	134	2	no	—
1101	C₂²⋊C₄	—	134	2	no	—
1102	C₂²⋊C₄	—	134	2	no	—
1103	C₂²⋊C₄	—	134	2	no	—
1104	C₂²⋊C₄	—	134	2	no	—
1105	C₂²⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1106	C₂²⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1107	C₂²⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1108	C₂²⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1109	C₂²⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1110	C₂²⋊C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1111	C₄²	—	2	1	no	—
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	—	2	1	no	—
1116	C₄²	—	2	1	no	—
1117	C₄²	—	134	2	no	—
1118	C₄²	—	134	2	no	—
1119	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1120	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1121	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1122	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1123	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1124	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
1125	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1126	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1127	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1128	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1129	C₂³	—	2	1	no	—
1130	C₂³	—	2	1	no	—
1131	C₂³	—	4	2	no	—
1132	C₂³	—	8	1	no	—
1133	C₂³	—	8	1	no	—
1134	C₂³	—	134	2	no	—
1135	C₂³	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1136	C₂³	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1137	C₂³	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1138	Q₈	—	2	2	no	—
1139	Q₈	—	2	2	no	—
1140	Q₈	—	4	1	no	—
1141	Q₈	—	4	2	no	—
1142	Q₈	—	8	1	no	—
1143	Q₈	—	8	1	no	—
1144	Q₈	—	268	2	no	—
1145	Q₈	—	268	2	no	—
1146	Q₈	—	536	2	no	—
1147	Q₈	—	134	2	no	—
1148	Q₈	—	134	2	no	—
1149	D₄	—	2	2	no	—
1150	D₄	—	2	2	no	—
1151	D₄	—	4	1	no	—
1152	D₄	—	4	1	no	—
1153	D₄	—	4	1	no	—
1154	D₄	—	4	2	no	—
1155	D₄	—	8	1	no	—
1156	D₄	—	8	1	no	—
1157	D₄	—	8	1	no	—
1158	D₄	—	8	1	no	—
1159	D₄	—	268	2	no	—
1160	D₄	—	268	2	no	—
1161	D₄	—	268	4	no	—
1162	D₄	—	536	2	no	—
1163	D₄	—	536	2	no	—
1164	D₄	—	134	2	no	—
1165	D₄	—	134	2	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	1	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	4	2	no	—
1182	C₂×C₄	—	8	1	no	—
1183	C₂×C₄	—	8	1	no	—
1184	C₂×C₄	—	8	1	no	—
1185	C₂×C₄	—	8	1	no	—
1186	C₂×C₄	—	268	4	no	—
1187	C₂×C₄	—	536	2	no	—
1188	C₂×C₄	—	536	2	no	—
1189	C₂×C₄	—	536	2	no	—
1190	C₂×C₄	—	134	2	no	—
1191	C₂×C₄	—	134	2	no	—
1192	C₂×C₄	—	134	2	no	—
1193	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1194	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1195	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1196	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1197	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1198	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1199	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1200	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1201	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1202	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1203	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
1204	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1205	C₈	—	134	2	no	—
1206	C₈	—	134	2	no	—
1207	C₈	—	134	2	no	—
1208	C₈	—	134	2	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	1	no	—
1212	C₂²	—	2	1	no	—
1213	C₂²	—	2	1	no	—
1214	C₂²	—	2	1	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	1	no	—
1224	C₂²	—	268	2	no	—
1225	C₂²	—	268	2	no	—
1226	C₂²	—	268	2	no	—
1227	C₂²	—	16	2	no	—
1228	C₂²	C₂³×C₂²⋊D₆₇	1	1	yes	characteristic
1229	C₄	—	2	1	no	—
1230	C₄	—	2	1	no	—
1231	C₄	—	2	1	no	—
1232	C₄	—	2	1	no	—
1233	C₄	—	2	1	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	1	no	—
1236	C₄	—	2	1	no	—
1237	C₄	—	2	1	no	—
1238	C₄	—	2	1	no	—
1239	C₄	—	2	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	268	2	no	—
1247	C₄	—	268	2	no	—
1248	C₄	—	268	2	no	—
1249	C₄	#16864232	1	2	yes	—
1250	C₂	—	4	1	no	—
1251	C₂	—	4	1	no	—
1252	C₂	—	4	1	no	—
1253	C₂	—	8	1	no	—
1254	C₂	—	8	1	no	—
1255	C₂	—	536	2	no	—
1256	C₂	#22573538	1	1	yes	characteristic
1257	C₂	#22574988	1	1	yes	characteristic
1258	C₂	#22574995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₆₇
commutator, cosocle	C₂×C₄×C₆₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₆₇×#3510	C₂
socle	C₂²×C₆₇	C₂³×D₄
hypercenter	#3510	D₆₇
hypocenter	C₆₇	#61016
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3510

Complements

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

N	H ≅ G/N	type
1. #22574120	C₂	semidirect
2. #22571674	C₂	semidirect
3. #22571665	C₂	semidirect
4. #22571436	C₂	semidirect
5. #22571427	C₂	semidirect
6. #22571423	C₂	semidirect
7. #22571407	C₂	semidirect
8. #22571242	C₂	semidirect
9. #22571242	C₂	semidirect
10. #22571212	C₂	semidirect
11. #22571196	C₂	semidirect
12. #22571091	C₂	semidirect
13. #22571061	C₂	semidirect
14. #22570919	C₂	semidirect
15. #22570908	C₂	semidirect
16. #22570816	C₂	semidirect
17. #22570805	C₂	semidirect
18. #22570480	C₂	semidirect
19. #22570465	C₂	semidirect
20. #22570438	C₂	semidirect
21. #22570393	C₂	semidirect
22. #22568860	C₂	semidirect
23. C₆₇×#3510	C₂	semidirect
33. #16864017	C₂²	semidirect
36. #16863953	C₂²	semidirect
38. #16863946	C₂²	semidirect
39. #16863946	C₂²	semidirect
40. C₂×#14524043	C₂²	semidirect
41. #16863876	C₂²	semidirect
42. #16863806	C₂²	semidirect
43. #16863806	C₂²	semidirect
44. #16863806	C₂²	semidirect
45. #16863806	C₂²	semidirect
50. #16863766	C₂²	semidirect
51. #16863766	C₂²	semidirect
52. #16863762	C₂²	semidirect
53. #16863762	C₂²	semidirect
60. #16863729	C₂²	semidirect
61. #16863724	C₂²	semidirect
66. #16863691	C₂²	semidirect
67. #16863688	C₂²	semidirect
69. #16863683	C₂²	semidirect
70. #16863681	C₂²	semidirect
71. #16863678	C₂²	semidirect
73. #16863673	C₂²	semidirect
74. #16863652	C₂²	semidirect
76. #16863644	C₂²	semidirect
78. #16863635	C₂²	semidirect
80. #16863627	C₂²	semidirect
82. #16863618	C₂²	semidirect
83. #16863618	C₂²	semidirect
90. #16863556	C₂²	semidirect
91. #16863556	C₂²	semidirect
99. #16863501	C₂²	semidirect
101. #16863494	C₂²	semidirect
102. C₄×#11761618	C₂²	semidirect
103. C₄×#11761615	C₂²	semidirect
107. #16863457	C₂²	semidirect
110. #16863453	C₂²	semidirect
111. #16863453	C₂²	semidirect
112. #16863423	C₂²	semidirect
114. C₄×#11761612	C₂²	semidirect
115. C₂×#14523954	C₂²	semidirect
631. #3510	D₆₇	semidirect
653. C₆₇	#61016	semidirect

Maximal subgroups

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

subgroup	index
#22574120	2
#22571674	2
#22571665	2
#22571436	2
#22571427	2
#22571423	2
#22571407	2
#22571242	2
#22571212	2
#22571196	2
#22571091	2
#22571061	2
#22570919	2
#22570908	2
#22570816	2
#22570805	2
#22570480	2
#22570465	2
#22570438	2
#22570393	2
#22568860	2
C₆₇×#3510	2
#61016	67