Subgroups — #31733408

Order 17152.

2286 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573944	C₂	1	1	yes	maximal, characteristic, complemented
2	#22573842	C₂	1	1	yes	maximal, characteristic, complemented
3	#22572449	C₂	1	2	yes	maximal, complemented
4	#22572408	C₂	1	2	yes	maximal, complemented
5	#22572368	C₂	1	2	yes	maximal, complemented
6	#22572353	C₂	1	2	yes	maximal, complemented
7	#22572348	C₂	1	2	yes	maximal, complemented
8	#22572168	C₂	1	2	yes	maximal, complemented
9	#22572057	C₂	1	2	yes	maximal, complemented
10	#22572020	C₂	1	2	yes	maximal, complemented
11	#22570567	C₂	1	1	yes	maximal, characteristic, complemented
12	#22570170	C₂	1	1	yes	maximal, characteristic, complemented
13	#22570043	C₂	1	1	yes	maximal, characteristic, complemented
14	#22569858	C₂	1	1	yes	maximal, characteristic, complemented
15	#22569830	C₂	1	1	yes	maximal, characteristic, complemented
16	#22569715	C₂	1	1	yes	maximal, characteristic, complemented
17	#22569480	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16863532	C₂	1	1	yes	maximal, characteristic, complemented
19	#22569060	C₂	1	1	yes	maximal, characteristic, complemented
20	#22568930	C₂	1	1	yes	maximal, characteristic, complemented
21	#22568731	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16863400	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14524089	C₂²	1	1	yes	characteristic
25	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
26	C₂×#14524068	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₅₃₆	C₂²	1	1	yes	characteristic
28	C₂²×D₅₃₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×#14524049	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#11761612	C₂²	1	1	yes	characteristic, complemented
31	#16864109	C₂²	1	2	yes	complemented
32	#16864094	C₂²	1	2	yes	complemented
33	#16864090	C₂²	1	2	yes	complemented
34	#16864070	—	2	2	no	—
35	#16864047	C₂²	1	2	yes	complemented
36	#16864042	—	2	1	no	—
37	#16864042	—	2	1	no	—
38	#16864037	C₂²	1	2	yes	complemented
39	#16864037	C₂²	1	2	yes	complemented
40	#16864036	—	2	2	no	—
41	D₄×D₂₆₈	—	2	1	no	—
42	D₄×D₂₆₈	—	2	1	no	—
43	#16864030	C₂²	1	2	yes	complemented
44	#16864030	C₂²	1	2	yes	complemented
45	#16864024	C₂²	1	1	yes	characteristic, complemented
46	#16864017	—	2	1	no	—
47	#16864001	—	2	1	no	—
48	#16863965	C₂²	1	1	yes	characteristic
49	#16863965	C₂²	1	1	yes	characteristic, complemented
50	#16863960	C₂²	1	1	yes	characteristic
51	#16863957	—	2	2	no	—
52	#16863946	—	2	1	no	—
53	#16863930	—	2	1	no	—
54	#16863907	C₂²	1	1	yes	characteristic
55	C₂×#14524017	C₂²	1	1	yes	characteristic, complemented
56	#120×D₆₇	—	2	2	no	—
57	#16863876	C₂²	1	1	yes	characteristic, complemented
58	#16863870	C₂²	1	1	yes	characteristic
59	#16863870	C₂²	1	1	yes	characteristic, complemented
60	#16863759	C₂²	1	2	yes	complemented
61	#16863757	C₂²	1	2	yes	complemented
62	#16863752	C₂²	1	2	yes	complemented
63	#16863741	C₂²	1	2	yes	complemented
64	#16863723	C₂²	1	2	yes	complemented
65	#16863722	C₂²	1	2	yes	complemented
66	#16863716	C₂²	1	2	yes	complemented
67	#16863711	C₂²	1	2	yes	complemented
68	#16863699	C₂²	1	2	yes	complemented
69	#16863695	C₂²	1	2	yes	complemented
70	#16863685	C₂²	1	2	yes	complemented
71	#16863675	C₂²	1	2	yes	complemented
72	#16863650	C₂²	1	2	yes	complemented
73	#16863650	C₂²	1	2	yes	complemented
74	#16863647	C₂²	1	2	yes	complemented
75	#16863644	C₂²	1	2	yes	complemented
76	#16863633	C₂²	1	2	yes	complemented
77	#16863633	C₂²	1	2	yes	complemented
78	#16863630	C₂²	1	2	yes	complemented
79	#16863627	C₂²	1	2	yes	complemented
80	#16863614	C₂²	1	2	yes	complemented
81	#16863614	C₂²	1	2	yes	complemented
82	#16863590	C₂²	1	2	yes	complemented
83	#16863590	C₂²	1	2	yes	complemented
84	#16863544	C₂²	1	2	yes	complemented
85	#16863544	C₂²	1	2	yes	complemented
86	#16863532	C₂²	1	2	yes	complemented
87	#16863532	C₂²	1	2	yes	complemented
88	#16863532	C₂²	1	2	yes	complemented
89	#16863532	C₂²	1	2	yes	complemented
90	#16863531	C₂²	1	2	yes	complemented
91	#16863531	C₂²	1	2	yes	complemented
92	#16863507	C₂²	1	2	yes	complemented
93	#16863507	C₂²	1	2	yes	complemented
94	#16863478	C₂²	1	2	yes	complemented
95	#16863478	C₂²	1	2	yes	complemented
96	#16863471	C₂²	1	2	yes	complemented
97	#16863470	C₂²	1	2	yes	complemented
98	#16863464	C₂²	1	2	yes	complemented
99	(C₂²⋊D₆₇)⋊C₈	C₂²	1	2	yes	complemented
100	#16863439	C₂²	1	1	yes	characteristic, complemented
101	#16863422	C₂²	1	1	yes	characteristic, complemented
102	#16863400	C₂²	1	1	yes	characteristic
103	#16863400	C₂²	1	1	yes	characteristic
104	#16863400	C₂²	1	2	yes	complemented
105	#16863400	C₂²	1	1	yes	characteristic, complemented
106	#16863400	C₂²	1	2	yes	complemented
107	#16863400	C₂²	1	1	yes	characteristic, complemented
108	#16863400	C₂²	1	1	yes	characteristic, complemented
109	#16863399	C₂²	1	2	yes	complemented
110	#16863397	C₂²	1	1	yes	characteristic, complemented
111	#16863396	C₂²	1	2	yes	complemented
112	#16863391	C₂²	1	2	yes	complemented
113	C₂×#14523965	C₂²	1	1	yes	characteristic
114	C₂×#14523965	C₂²	1	1	yes	characteristic, complemented
115	C₂×#14523963	C₂²	1	2	yes	complemented
116	C₂×#14523963	C₂²	1	2	yes	complemented
117	#102×D₆₇	C₂²	1	2	yes	complemented
118	#16863362	C₂²	1	1	yes	characteristic, complemented
119	#16863351	C₂²	1	1	yes	characteristic, complemented
120	#525×C₆₇	C₂²	1	1	yes	characteristic
121	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
126	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂⁴×D₆₇	—	2	1	no	—
136	#14524089	—	2	4	no	—
137	#14524089	—	4	2	no	—
138	C₂×#11761629	C₂³	1	2	yes	—
139	C₂×#11761628	—	2	1	no	—
140	C₂×#11761628	—	2	2	no	—
141	C₂×#11761628	C₂³	1	1	yes	characteristic
142	C₂²×D₂₆₈	—	2	4	no	—
143	C₂²×D₂₆₈	—	2	1	no	—
144	C₂²×D₂₆₈	—	2	1	no	—
145	C₂²×D₂₆₈	—	2	1	no	—
146	C₂²×D₂₆₈	—	2	1	no	—
147	C₂²×D₂₆₈	—	4	2	no	—
148	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
149	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
150	C₂²×D₂₆₈	C₂³	1	2	yes	—
151	C₂²×D₂₆₈	C₂³	1	2	yes	—
152	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
153	C₂²×C₂²⋊D₆₇	—	2	1	no	—
154	C₂×D₄×D₆₇	—	2	2	no	—
155	C₂×D₄×D₆₇	—	2	2	no	—
156	C₂×D₄×D₆₇	—	2	2	no	—
157	C₂×D₄×D₆₇	C₂³	1	2	yes	—
158	#14524068	—	4	2	no	—
159	C₂×#11761615	C₂³	1	2	yes	complemented
160	C₂×D₅₃₆	—	2	4	no	—
161	C₂×D₅₃₆	—	4	2	no	—
162	C₂×D₅₃₆	C₂³	1	2	yes	—
163	C₂×D₅₃₆	C₂³	1	2	yes	—
164	C₂×D₅₃₆	C₂³	1	2	yes	—
165	C₂×D₅₃₆	C₂³	1	2	yes	—
166	C₂×#11761613	C₂³	1	2	yes	complemented
167	#14524049	—	4	2	no	—
168	C₂×#11761612	—	4	2	no	—
169	C₂×#11761612	C₂³	1	1	yes	characteristic
170	C₂×#11761612	C₂³	1	1	yes	characteristic
171	C₂×#11761612	C₂³	1	2	yes	—
172	C₂×#11761611	C₂³	1	2	yes	complemented
173	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
174	C₂×C₈×D₆₇	C₂³	1	2	yes	complemented
175	#14524043	—	2	1	no	—
176	#14524042	C₂³	1	2	yes	complemented
177	#14524040	—	2	1	no	—
178	#14524040	—	2	1	no	—
179	#14524039	C₂³	1	2	yes	—
180	#14524038	—	2	2	no	—
181	#14524037	—	2	2	no	—
182	#14524035	—	2	1	no	—
183	#14524034	C₂³	1	2	yes	complemented
184	#14524032	C₂³	1	2	yes	—
185	#14524031	—	2	1	no	—
186	#14524031	—	2	1	no	—
187	#14524031	—	2	2	no	—
188	#14524029	—	2	2	no	—
189	#14524028	—	2	2	no	—
190	#14524028	—	2	2	no	—
191	#14524028	—	2	2	no	—
192	#14524028	—	2	2	no	—
193	#14524026	—	2	2	no	—
194	#14524026	D₄	1	2	yes	—
195	#14524025	—	2	2	no	—
196	#14524022	D₄	1	1	yes	characteristic
197	#14524022	D₄	1	1	yes	characteristic
198	#14524021	—	2	2	no	—
199	#14524020	—	2	2	no	—
200	#14524018	—	2	2	no	—
201	#14524018	—	2	2	no	—
202	#14524018	C₂³	1	2	yes	—
203	#14524018	C₂³	1	2	yes	—
204	#14524018	C₂³	1	2	yes	complemented
205	#14524018	C₂³	1	2	yes	complemented
206	#14524017	—	2	2	no	—
207	#14524017	—	2	1	no	—
208	#14524017	—	2	1	no	—
209	#14524017	—	2	1	no	—
210	#14524017	—	2	1	no	—
211	#14524017	D₄	1	1	yes	characteristic
212	#14524017	D₄	1	1	yes	characteristic
213	#14524017	C₂³	1	2	yes	—
214	#14524017	C₂³	1	2	yes	—
215	#14524016	—	2	2	no	—
216	#14524016	—	2	2	no	—
217	#14524016	—	2	2	no	—
218	#14524016	—	2	2	no	—
219	#14524013	—	2	2	no	—
220	#14524013	—	2	2	no	—
221	#14524013	—	2	2	no	—
222	#14524013	—	2	2	no	—
223	#14524013	—	2	2	no	—
224	#14524013	—	2	2	no	—
225	#14524012	D₄	1	2	yes	—
226	#14524011	—	2	2	no	—
227	#14524011	—	2	2	no	—
228	#14524011	—	2	2	no	—
229	C₄×Dic₁₃₄	—	2	1	no	—
230	C₄×D₂₆₈	—	2	1	no	—
231	C₄×D₂₆₈	—	2	1	no	—
232	C₄×D₂₆₈	—	2	1	no	—
233	C₄×D₂₆₈	—	2	1	no	—
234	C₄×D₂₆₈	—	2	1	no	—
235	C₄×D₂₆₈	—	2	2	no	—
236	#14524005	C₂³	1	2	yes	—
237	#14524005	C₂³	1	2	yes	—
238	#14524005	C₂³	1	2	yes	complemented
239	#14524005	C₂³	1	2	yes	complemented
240	C₄×C₂²⋊D₆₇	—	2	2	no	—
241	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
242	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
243	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
244	#14524002	C₂³	1	1	yes	characteristic
245	#14524001	C₂³	1	2	yes	complemented
246	#14524000	—	2	2	no	—
247	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
248	C₄⋊C₄×D₆₇	C₂³	1	2	yes	complemented
249	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
250	C₂²⋊C₄×D₆₇	—	2	2	no	—
251	C₂²⋊C₄×D₆₇	—	2	2	no	—
252	C₂²⋊C₄×D₆₇	—	2	2	no	—
253	C₂²⋊C₄×D₆₇	—	2	2	no	—
254	#14523976	C₂³	1	2	yes	complemented
255	#14523974	C₂³	1	2	yes	complemented
256	Dic₆₇⋊C₈	C₂³	1	2	yes	complemented
257	Dic₆₇⋊C₈	C₂³	1	2	yes	complemented
258	#14523967	C₂³	1	2	yes	complemented
259	#14523965	C₂³	1	2	yes	—
260	#14523965	C₂³	1	2	yes	—
261	#14523965	C₂³	1	2	yes	—
262	#14523965	C₂³	1	2	yes	—
263	#14523964	C₂³	1	2	yes	complemented
264	#14523963	C₂³	1	2	yes	—
265	#14523963	C₂³	1	2	yes	—
266	#14523963	C₂³	1	2	yes	—
267	#14523963	C₂³	1	2	yes	—
268	#14523963	C₂³	1	2	yes	—
269	#14523963	C₂³	1	2	yes	—
270	#14523963	C₂³	1	2	yes	—
271	#14523963	C₂³	1	2	yes	—
272	#14523963	C₂³	1	2	yes	complemented
273	#14523963	C₂³	1	2	yes	complemented
274	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	complemented
275	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	complemented
276	#14523953	C₂³	1	2	yes	complemented
277	C₈×Dic₆₇	C₂³	1	2	yes	complemented
278	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
279	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
280	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
282	#123×C₆₇	—	2	1	no	—
283	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
284	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
285	#121×C₆₇	C₂³	1	1	yes	characteristic
286	#121×C₆₇	C₂³	1	1	yes	characteristic
287	#120×C₆₇	—	2	1	no	—
288	C₄×D₄×C₆₇	—	2	1	no	—
289	C₄×D₄×C₆₇	—	2	1	no	—
290	#117×C₆₇	—	2	1	no	—
291	#117×C₆₇	—	2	1	no	—
292	#117×C₆₇	C₂³	1	1	yes	characteristic
293	#117×C₆₇	C₂³	1	1	yes	characteristic
294	#117×C₆₇	C₂³	1	1	yes	characteristic
295	#117×C₆₇	C₂³	1	1	yes	characteristic
296	#117×C₆₇	C₂³	1	1	yes	characteristic
297	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
300	C₂×C₄²×C₆₇	—	2	1	no	—
301	#107×C₆₇	C₂³	1	1	yes	characteristic, complemented
302	#107×C₆₇	C₂³	1	1	yes	characteristic, complemented
303	#107×C₆₇	C₂³	1	1	yes	characteristic, complemented
304	#107×C₆₇	C₂³	1	1	yes	characteristic, complemented
305	#106×C₆₇	C₂³	1	1	yes	characteristic, complemented
306	#106×C₆₇	C₂³	1	1	yes	characteristic, complemented
307	#106×C₆₇	C₂³	1	1	yes	characteristic, complemented
308	#106×C₆₇	C₂³	1	1	yes	characteristic, complemented
309	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
310	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
311	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
312	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
313	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
314	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
315	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
316	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
317	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
318	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
319	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
320	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
321	C₂³×D₆₇	—	2	1	no	—
322	C₂³×D₆₇	—	2	2	no	—
323	C₂³×D₆₇	—	2	2	no	—
324	C₂³×D₆₇	—	2	1	no	—
325	C₂³×D₆₇	—	2	1	no	—
326	C₂³×D₆₇	—	2	2	no	—
327	C₂³×D₆₇	—	4	4	no	—
328	C₂³×D₆₇	—	8	2	no	—
329	C₂³×D₆₇	—	8	2	no	—
330	#11761629	—	2	4	no	—
331	#11761629	—	4	2	no	—
332	#11761628	—	2	2	no	—
333	#11761628	—	2	2	no	—
334	#11761628	—	4	4	no	—
335	#11761628	—	8	4	no	—
336	C₂×Dic₁₃₄	—	2	2	no	—
337	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
338	C₂×D₂₆₈	—	2	1	no	—
339	C₂×D₂₆₈	—	2	2	no	—
340	C₂×D₂₆₈	—	2	2	no	—
341	C₂×D₂₆₈	—	2	2	no	—
342	C₂×D₂₆₈	—	2	2	no	—
343	C₂×D₂₆₈	—	2	2	no	—
344	C₂×D₂₆₈	—	2	4	no	—
345	C₂×D₂₆₈	—	2	4	no	—
346	C₂×D₂₆₈	—	2	2	no	—
347	C₂×D₂₆₈	—	2	1	no	—
348	C₂×D₂₆₈	—	2	2	no	—
349	C₂×D₂₆₈	—	2	2	no	—
350	C₂×D₂₆₈	—	2	1	no	—
351	C₂×D₂₆₈	—	2	2	no	—
352	C₂×D₂₆₈	—	2	2	no	—
353	C₂×D₂₆₈	—	2	2	no	—
354	C₂×D₂₆₈	—	2	2	no	—
355	C₂×D₂₆₈	—	4	2	no	—
356	C₂×D₂₆₈	—	4	2	no	—
357	C₂×D₂₆₈	—	4	4	no	—
358	C₂×D₂₆₈	—	4	4	no	—
359	C₂×D₂₆₈	—	4	4	no	—
360	C₂×D₂₆₈	—	4	4	no	—
361	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
362	C₂×D₂₆₈	#41	1	4	yes	complemented
363	C₂×D₂₆₈	C₂⁴	1	2	yes	—
364	C₂×D₂₆₈	C₂⁴	1	2	yes	—
365	C₂×D₂₆₈	C₂⁴	1	2	yes	—
366	C₂×C₂²⋊D₆₇	—	2	2	no	—
367	C₂×C₂²⋊D₆₇	—	2	2	no	—
368	C₂×C₂²⋊D₆₇	—	2	2	no	—
369	C₂×C₂²⋊D₆₇	—	2	2	no	—
370	C₂×C₂²⋊D₆₇	—	2	2	no	—
371	C₂×C₂²⋊D₆₇	—	8	2	no	—
372	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
373	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
374	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
375	D₄×D₆₇	—	2	4	no	—
376	D₄×D₆₇	—	4	2	no	—
377	D₄×D₆₇	—	4	8	no	—
378	D₄×D₆₇	—	8	4	no	—
379	D₄×D₆₇	—	8	4	no	—
380	C₂²×Dic₆₇	—	2	1	no	—
381	C₂×C₄×D₆₇	—	2	2	no	—
382	C₂×C₄×D₆₇	—	2	2	no	—
383	C₂×C₄×D₆₇	—	2	2	no	—
384	C₂×C₄×D₆₇	—	2	2	no	—
385	C₂×C₄×D₆₇	—	2	2	no	—
386	C₂×C₄×D₆₇	—	2	2	no	—
387	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
388	#11761615	—	4	2	no	—
389	D₅₃₆	—	2	4	no	—
390	D₅₃₆	—	2	4	no	—
391	D₅₃₆	—	4	2	no	—
392	D₅₃₆	—	4	2	no	—
393	#11761613	—	4	2	no	—
394	#11761612	—	2	2	no	—
395	#11761612	—	2	2	no	—
396	#11761612	—	4	2	no	—
397	#11761611	—	4	2	no	—
398	C₂×C₆₇⋊C₈	—	4	2	no	—
399	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
400	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
401	C₈×D₆₇	—	4	2	no	—
402	C₄⋊Dic₆₇	—	2	1	no	—
403	C₄⋊Dic₆₇	—	2	2	no	—
404	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
405	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
406	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
407	Dic₆₇⋊C₄	—	2	2	no	—
408	Dic₆₇⋊C₄	—	2	2	no	—
409	Dic₆₇⋊C₄	—	2	2	no	—
410	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
411	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
412	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
413	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
414	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
415	(C₂×D₆₇)⋊C₄	—	2	2	no	—
416	(C₂×D₆₇)⋊C₄	—	2	2	no	—
417	(C₂×D₆₇)⋊C₄	—	2	2	no	—
418	(C₂×D₆₇)⋊C₄	—	2	2	no	—
419	(C₂×D₆₇)⋊C₄	—	2	2	no	—
420	(C₂×D₆₇)⋊C₄	—	2	2	no	—
421	(C₂×D₆₇)⋊C₄	—	2	2	no	—
422	(C₂×D₆₇)⋊C₄	—	2	2	no	—
423	(C₂×D₆₇)⋊C₄	—	2	2	no	—
424	(C₂×D₆₇)⋊C₄	—	2	2	no	—
425	(C₂×D₆₇)⋊C₄	—	2	2	no	—
426	(C₂×D₆₇)⋊C₄	—	2	2	no	—
427	(C₂×D₆₇)⋊C₄	—	2	2	no	—
428	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
429	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
430	C₄×Dic₆₇	—	2	2	no	—
431	C₄×Dic₆₇	C₂⁴	1	2	yes	—
432	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
433	#41×C₆₇	—	2	2	no	—
434	#41×C₆₇	—	2	2	no	—
435	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₂×D₄×C₆₇	—	2	1	no	—
437	C₂×D₄×C₆₇	—	2	1	no	—
438	C₂×D₄×C₆₇	—	2	1	no	—
439	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
440	C₂²×C₄×C₆₇	—	2	2	no	—
441	C₂²×C₄×C₆₇	—	2	2	no	—
442	C₂²×C₄×C₆₇	—	2	1	no	—
443	C₂²×C₄×C₆₇	—	2	1	no	—
444	C₂²×C₄×C₆₇	—	2	1	no	—
445	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
447	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
448	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
451	C₂×C₈×C₆₇	—	2	2	no	—
452	C₂×C₈×C₆₇	—	2	2	no	—
453	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
456	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₆₇	—	2	1	no	—
458	C₄⋊C₄×C₆₇	—	2	1	no	—
459	C₄⋊C₄×C₆₇	—	2	1	no	—
460	C₄⋊C₄×C₆₇	—	2	1	no	—
461	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
462	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
463	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
464	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
465	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
466	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	C₄²×C₆₇	—	2	1	no	—
477	C₄²×C₆₇	—	2	1	no	—
478	C₄²×C₆₇	—	2	1	no	—
479	C₄²×C₆₇	—	2	1	no	—
480	C₄²×C₆₇	—	2	1	no	—
481	C₂³×C₆₇	—	2	2	no	—
482	C₂³×C₆₇	—	2	2	no	—
483	C₂³×C₆₇	—	2	1	no	—
484	C₂³×C₆₇	—	4	1	no	—
485	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
486	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
487	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
488	C₂²×D₆₇	—	2	2	no	—
489	C₂²×D₆₇	—	2	4	no	—
490	C₂²×D₆₇	—	2	2	no	—
491	C₂²×D₆₇	—	2	2	no	—
492	C₂²×D₆₇	—	4	4	no	—
493	C₂²×D₆₇	—	4	4	no	—
494	C₂²×D₆₇	—	4	4	no	—
495	C₂²×D₆₇	—	4	4	no	—
496	C₂²×D₆₇	—	4	2	no	—
497	C₂²×D₆₇	—	4	4	no	—
498	C₂²×D₆₇	—	4	2	no	—
499	C₂²×D₆₇	—	8	2	no	—
500	C₂²×D₆₇	—	8	2	no	—
501	C₂²×D₆₇	—	8	1	no	—
502	C₂²×D₆₇	—	8	2	no	—
503	C₂²×D₆₇	—	8	1	no	—
504	C₂²×D₆₇	—	8	2	no	—
505	C₂²×D₆₇	—	8	1	no	—
506	C₂²×D₆₇	—	8	1	no	—
507	C₂²×D₆₇	—	8	1	no	—
508	C₂²×D₆₇	—	8	1	no	—
509	C₂²×D₆₇	—	8	16	no	—
510	C₂²×D₆₇	C₂²×D₄	1	2	yes	—
511	Q₈×C₆₇	—	2	1	no	—
512	Q₈×C₆₇	—	2	1	no	—
513	D₄×C₆₇	—	2	1	no	—
514	D₄×C₆₇	—	2	1	no	—
515	D₄×C₆₇	—	4	2	no	—
516	D₄×C₆₇	—	4	2	no	—
517	D₄×C₆₇	—	4	2	no	—
518	C₂×C₄×C₆₇	—	2	2	no	—
519	C₂×C₄×C₆₇	—	2	2	no	—
520	C₂×C₄×C₆₇	—	2	2	no	—
521	C₂×C₄×C₆₇	—	2	1	no	—
522	C₂×C₄×C₆₇	—	2	1	no	—
523	C₂×C₄×C₆₇	—	2	1	no	—
524	C₂×C₄×C₆₇	—	2	1	no	—
525	C₂×C₄×C₆₇	—	2	1	no	—
526	C₂×C₄×C₆₇	—	2	1	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	—	4	2	no	—
533	C₂×C₄×C₆₇	—	4	2	no	—
534	C₂×C₄×C₆₇	—	8	1	no	—
535	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
539	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
540	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
541	C₂²⋊D₆₇	—	2	4	no	—
542	C₂²⋊D₆₇	—	2	4	no	—
543	C₂²⋊D₆₇	—	4	2	no	—
544	C₂²⋊D₆₇	—	4	4	no	—
545	C₂²⋊D₆₇	—	4	4	no	—
546	C₂²⋊D₆₇	—	8	2	no	—
547	C₂²⋊D₆₇	—	8	2	no	—
548	C₂²⋊D₆₇	—	8	2	no	—
549	C₂×Dic₆₇	—	2	2	no	—
550	C₂×Dic₆₇	—	8	1	no	—
551	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
552	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
553	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
554	D₂₆₈	—	2	4	no	—
555	D₂₆₈	—	2	2	no	—
556	D₂₆₈	—	2	2	no	—
557	D₂₆₈	—	2	2	no	—
558	D₂₆₈	—	2	2	no	—
559	D₂₆₈	—	2	2	no	—
560	D₂₆₈	—	2	2	no	—
561	D₂₆₈	—	4	4	no	—
562	D₂₆₈	—	4	4	no	—
563	D₂₆₈	—	4	4	no	—
564	D₂₆₈	—	4	2	no	—
565	D₂₆₈	—	4	2	no	—
566	D₂₆₈	—	8	2	no	—
567	D₂₆₈	—	8	2	no	—
568	D₂₆₈	—	8	2	no	—
569	D₂₆₈	—	8	2	no	—
570	D₂₆₈	C₂×#41	1	4	yes	—
571	C₄×D₆₇	—	2	2	no	—
572	C₄×D₆₇	—	2	2	no	—
573	C₄×D₆₇	—	4	4	no	—
574	C₄×D₆₇	—	8	2	no	—
575	C₄×D₆₇	—	8	2	no	—
576	C₄×D₆₇	—	8	2	no	—
577	C₄×D₆₇	—	8	2	no	—
578	C₄×D₆₇	—	8	2	no	—
579	Dic₁₃₄	—	2	2	no	—
580	Dic₁₃₄	—	8	2	no	—
581	C₈×C₆₇	—	2	1	no	—
582	C₈×C₆₇	—	2	1	no	—
583	C₈×C₆₇	—	2	1	no	—
584	C₈×C₆₇	—	2	1	no	—
585	C₆₇⋊C₈	—	2	2	no	—
586	C₆₇⋊C₈	—	2	2	no	—
587	C₂²×C₆₇	—	2	1	no	—
588	C₂²×C₆₇	—	2	1	no	—
589	C₂²×C₆₇	—	2	1	no	—
590	C₂²×C₆₇	—	2	1	no	—
591	C₂²×C₆₇	—	2	1	no	—
592	C₂²×C₆₇	—	2	1	no	—
593	C₂²×C₆₇	—	2	1	no	—
594	C₂²×C₆₇	—	4	4	no	—
595	C₂²×C₆₇	—	4	1	no	—
596	C₂²×C₆₇	—	4	1	no	—
597	C₂²×C₆₇	—	4	1	no	—
598	C₂²×C₆₇	#546	1	2	yes	—
599	C₂²×C₆₇	#576	1	2	yes	—
600	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
601	C₂×D₆₇	—	2	2	no	—
602	C₂×D₆₇	—	2	2	no	—
603	C₂×D₆₇	—	2	4	no	—
604	C₂×D₆₇	—	2	2	no	—
605	C₂×D₆₇	—	4	2	no	—
606	C₂×D₆₇	—	4	2	no	—
607	C₂×D₆₇	—	4	2	no	—
608	C₂×D₆₇	—	4	2	no	—
609	C₂×D₆₇	—	4	2	no	—
610	C₂×D₆₇	—	4	2	no	—
611	C₂×D₆₇	—	4	2	no	—
612	C₂×D₆₇	—	4	2	no	—
613	C₂×D₆₇	—	8	4	no	—
614	C₂×D₆₇	—	8	8	no	—
615	C₂×D₆₇	—	8	8	no	—
616	C₂×D₆₇	—	8	4	no	—
617	C₂×D₆₇	—	16	4	no	—
618	C₂×D₆₇	—	16	2	no	—
619	C₄×C₆₇	—	2	1	no	—
620	C₄×C₆₇	—	2	1	no	—
621	C₄×C₆₇	—	4	1	no	—
622	C₄×C₆₇	—	4	1	no	—
623	C₄×C₆₇	—	4	1	no	—
624	C₄×C₆₇	—	4	1	no	—
625	C₄×C₆₇	—	4	1	no	—
626	C₄×C₆₇	—	4	1	no	—
627	C₄×C₆₇	—	4	1	no	—
628	C₄×C₆₇	#546	1	2	yes	—
629	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
630	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
631	Dic₆₇	—	2	2	no	—
632	Dic₆₇	—	2	2	no	—
633	Dic₆₇	—	2	2	no	—
634	Dic₆₇	—	4	2	no	—
635	#61183	—	67	1	no	maximal, Sylow
636	C₂×C₆₇	—	2	2	no	—
637	C₂×C₆₇	—	2	2	no	—
638	C₂×C₆₇	—	4	1	no	—
639	C₂×C₆₇	—	8	1	no	—
640	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
641	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
642	C₂×C₆₇	#3585	1	1	yes	characteristic
643	D₆₇	—	4	2	no	—
644	D₆₇	—	4	4	no	—
645	D₆₇	—	8	2	no	—
646	D₆₇	—	8	2	no	—
647	#3494	—	67	1	no	—
648	#3484	—	67	1	no	—
649	#3325	—	67	2	no	—
650	#3322	—	67	2	no	—
651	#3319	—	67	2	no	—
652	#3318	—	67	2	no	—
653	#3318	—	67	2	no	—
654	#3306	—	67	2	no	—
655	#3297	—	67	2	no	—
656	#3294	—	67	2	no	—
657	#3136	—	67	1	no	—
658	#3096	—	67	1	no	—
659	#3091	D₆₇	1	1	yes	characteristic, complemented
660	#3081	—	67	1	no	—
661	#3058	—	67	1	no	—
662	#3055	—	67	1	no	—
663	#3041	—	67	1	no	—
664	#3008	—	67	1	no	—
665	C₂×#447	—	67	1	no	—
666	#2948	—	67	1	no	—
667	#2933	—	67	1	no	—
668	#2897	—	67	1	no	—
669	C₂×#418	—	67	1	no	—
670	C₆₇	#61183	1	1	yes	characteristic, complemented, Sylow
671	C₂×H(5,𝔽₂)	—	67	1	no	—
672	C₂³×D₄	—	67	1	no	—
673	C₂×AGL(1,ℤ/8)	—	67	1	no	—
674	C₂²×D₈	—	67	1	no	—
675	C₂²×D₈	—	67	1	no	—
676	C₂×#131	—	67	1	no	—
677	C₂²×M₁₆	—	67	1	no	—
678	#555	—	67	2	no	—
679	#553	—	67	2	no	—
680	#553	—	67	2	no	—
681	#551	—	134	2	no	—
682	#547	—	67	2	no	—
683	#546	—	67	2	no	—
684	#546	—	67	2	no	—
685	#546	—	134	2	no	—
686	#546	—	134	1	no	—
687	#546	—	134	1	no	—
688	D₄²	—	67	2	no	—
689	D₄²	—	67	2	no	—
690	D₄²	—	134	1	no	—
691	D₄²	—	134	1	no	—
692	#544	—	67	1	no	—
693	#542	—	134	1	no	—
694	#540	—	134	1	no	—
695	#535	—	67	1	no	—
696	#535	—	67	1	no	—
697	#535	—	67	1	no	—
698	#534	—	134	2	no	—
699	#532	—	134	1	no	—
700	#529	—	134	1	no	—
701	#525	—	67	1	no	—
702	#525	C₂×D₆₇	1	1	yes	characteristic
703	C₂×#121	—	67	1	no	—
704	C₂×#120	—	134	2	no	—
705	#520	—	67	1	no	—
706	#518	—	67	1	no	—
707	#518	—	67	1	no	—
708	C₂×#117	C₂×D₆₇	1	1	yes	characteristic, complemented
709	#490	—	67	2	no	—
710	#489	—	67	2	no	—
711	#488	—	67	2	no	—
712	#486	—	67	2	no	—
713	#485	C₂×D₆₇	1	1	yes	characteristic, complemented
714	#485	C₂×D₆₇	1	1	yes	characteristic, complemented
715	#484	C₂×D₆₇	1	1	yes	characteristic, complemented
716	#483	C₂×D₆₇	1	1	yes	characteristic, complemented
717	#482	—	67	2	no	—
718	#482	—	67	2	no	—
719	#482	C₂×D₆₇	1	1	yes	characteristic, complemented
720	#482	C₂×D₆₇	1	1	yes	characteristic, complemented
721	#481	—	67	2	no	—
722	#481	C₂×D₆₇	1	1	yes	characteristic, complemented
723	#480	—	67	2	no	—
724	#480	C₂×D₆₇	1	1	yes	characteristic, complemented
725	#478	—	67	2	no	—
726	#478	—	67	2	no	—
727	#476	—	67	2	no	—
728	#474	—	67	2	no	—
729	#469	—	67	2	no	—
730	#469	—	67	2	no	—
731	#469	—	67	2	no	—
732	#468	—	67	2	no	—
733	#466	—	67	2	no	—
734	#466	—	67	2	no	—
735	#466	—	67	2	no	—
736	#465	—	67	2	no	—
737	#463	—	67	2	no	—
738	#463	—	67	2	no	—
739	#459	—	67	2	no	—
740	#459	—	67	2	no	—
741	#449	—	67	2	no	—
742	#449	—	67	2	no	—
743	#447	—	67	2	no	—
744	#447	—	67	2	no	—
745	#447	—	67	2	no	—
746	#447	—	67	2	no	—
747	#447	—	67	2	no	—
748	#447	—	67	2	no	—
749	#442	—	67	2	no	—
750	#442	—	67	2	no	—
751	C₄×D₈	—	67	2	no	—
752	C₄×D₈	—	67	2	no	—
753	#436	—	67	2	no	—
754	#435	—	67	2	no	—
755	#435	—	67	2	no	—
756	C₈×D₄	—	67	2	no	—
757	#428	—	67	1	no	—
758	#427	C₂×D₆₇	1	1	yes	characteristic, complemented
759	#427	C₂×D₆₇	1	1	yes	characteristic, complemented
760	#424	—	67	1	no	—
761	#418	—	67	1	no	—
762	#418	—	67	1	no	—
763	#418	—	67	1	no	—
764	#418	—	67	1	no	—
765	#418	—	67	2	no	—
766	#418	—	67	2	no	—
767	#418	—	67	1	no	—
768	#418	—	67	2	no	—
769	#417	—	67	1	no	—
770	#417	—	67	2	no	—
771	#416	—	67	2	no	—
772	#416	C₂×D₆₇	1	1	yes	characteristic, complemented
773	#416	C₂×D₆₇	1	1	yes	characteristic, complemented
774	C₂×#102	—	67	1	no	—
775	C₂×#102	—	67	1	no	—
776	C₂×#102	—	67	2	no	—
777	C₂×#102	—	67	2	no	—
778	C₂×#102	—	67	2	no	—
779	#408	—	67	1	no	—
780	C₂×C₂²⋊C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
781	#405	—	67	1	no	—
782	C₂⁵	—	134	1	no	—
783	H(5,𝔽₂)	—	268	2	no	—
784	H(5,𝔽₂)	—	134	4	no	—
785	C₂×#41	—	67	1	no	—
786	C₂×#41	—	67	2	no	—
787	C₂×#41	—	134	2	no	—
788	C₂×#41	—	134	1	no	—
789	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
790	C₂²×D₄	—	268	2	no	—
791	C₂²×D₄	—	67	2	no	—
792	C₂²×D₄	—	67	2	no	—
793	C₂²×D₄	—	67	2	no	—
794	C₂²×D₄	—	67	1	no	—
795	C₂²×D₄	—	67	1	no	—
796	C₂²×D₄	—	67	1	no	—
797	C₂²×D₄	—	134	1	no	—
798	C₂²×D₄	—	134	4	no	—
799	C₂²×D₄	—	134	2	no	—
800	C₂²×D₄	—	134	2	no	—
801	C₂²×D₄	—	134	2	no	—
802	C₂²×D₄	—	134	1	no	—
803	C₂²×D₄	—	134	1	no	—
804	C₂²×D₄	—	134	1	no	—
805	C₂²×D₄	—	134	1	no	—
806	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
807	AGL(1,ℤ/8)	—	268	2	no	—
808	C₂×SD₁₆	—	67	2	no	—
809	C₂×D₈	—	268	2	no	—
810	C₂×D₈	—	67	2	no	—
811	C₂×D₈	—	67	2	no	—
812	C₂×D₈	—	67	2	no	—
813	C₂×D₈	—	67	2	no	—
814	C₂×D₈	—	67	2	no	—
815	C₂×D₈	—	134	4	no	—
816	#131	—	268	2	no	—
817	C₂×M₁₆	—	268	2	no	—
818	C₂×M₁₆	—	67	2	no	—
819	C₂×M₁₆	—	67	1	no	—
820	C₂×M₁₆	—	67	1	no	—
821	C₂×M₁₆	—	67	2	no	—
822	C₂²×C₈	—	67	2	no	—
823	C₂²×C₈	—	67	2	no	—
824	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
825	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
826	C₄⋊Q₈	—	67	2	no	—
827	C₄⋊Q₈	—	134	1	no	—
828	#127	—	67	2	no	—
829	#127	—	134	1	no	—
830	#127	—	134	1	no	—
831	#126	—	134	2	no	—
832	#126	—	134	2	no	—
833	#125	—	67	2	no	—
834	#125	—	134	1	no	—
835	#124	—	67	2	no	—
836	#124	—	134	2	no	—
837	#124	—	134	1	no	—
838	#124	—	134	1	no	—
839	#124	—	134	2	no	—
840	#123	—	2	1	no	—
841	#123	—	67	2	no	—
842	#123	—	134	2	no	—
843	#123	—	134	2	no	—
844	#123	—	134	2	no	—
845	#123	—	134	2	no	—
846	#123	—	134	2	no	—
847	#123	—	134	2	no	—
848	C₂²⋊Q₈	—	67	1	no	—
849	C₂²⋊Q₈	—	67	1	no	—
850	C₂²⋊Q₈	—	134	2	no	—
851	C₂²⋊Q₈	—	134	2	no	—
852	C₂²⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
853	C₂²⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
854	#121	—	67	1	no	—
855	#121	—	67	1	no	—
856	#121	—	67	2	no	—
857	#121	—	67	2	no	—
858	#121	—	67	2	no	—
859	#121	—	67	2	no	—
860	#121	—	67	2	no	—
861	#121	—	67	2	no	—
862	#121	—	134	2	no	—
863	#121	—	134	2	no	—
864	#121	—	134	2	no	—
865	#121	—	134	2	no	—
866	#121	—	134	2	no	—
867	#121	—	134	2	no	—
868	#121	—	134	1	no	—
869	#121	—	134	1	no	—
870	#121	—	134	2	no	—
871	#121	—	134	1	no	—
872	#121	—	134	1	no	—
873	#121	C₂²×D₆₇	1	1	yes	characteristic
874	#121	C₂²×D₆₇	1	1	yes	characteristic
875	#120	—	2	1	no	—
876	#120	—	67	2	no	—
877	#120	—	134	2	no	—
878	#120	—	134	2	no	—
879	#120	—	134	2	no	—
880	#120	—	134	2	no	—
881	#120	—	134	2	no	—
882	#120	—	134	2	no	—
883	#120	—	134	2	no	—
884	#120	—	134	2	no	—
885	#120	—	134	2	no	—
886	C₄×Q₈	—	134	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	1	no	—
889	C₄×D₄	—	67	2	no	—
890	C₄×D₄	—	67	2	no	—
891	C₄×D₄	—	67	2	no	—
892	C₄×D₄	—	67	2	no	—
893	C₄×D₄	—	67	2	no	—
894	C₄×D₄	—	67	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	—	134	1	no	—
901	C₄×D₄	—	134	2	no	—
902	C₄×D₄	—	134	2	no	—
903	#117	—	2	1	no	—
904	#117	—	2	1	no	—
905	#117	—	67	1	no	—
906	#117	—	67	2	no	—
907	#117	—	134	2	no	—
908	#117	C₂²×D₆₇	1	1	yes	characteristic
909	#117	C₂²×D₆₇	1	1	yes	characteristic
910	#117	C₂²×D₆₇	1	1	yes	characteristic
911	#117	C₂²×D₆₇	1	1	yes	characteristic
912	#117	C₂²×D₆₇	1	1	yes	characteristic
913	C₂×C₄⋊C₄	—	67	1	no	—
914	C₂×C₄⋊C₄	—	67	2	no	—
915	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
916	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
917	C₂×C₂²⋊C₄	—	2	1	no	—
918	C₂×C₂²⋊C₄	—	134	2	no	—
919	C₂×C₂²⋊C₄	—	134	2	no	—
920	C₂×C₂²⋊C₄	—	134	2	no	—
921	C₂×C₂²⋊C₄	—	134	2	no	—
922	C₂×C₂²⋊C₄	—	134	1	no	—
923	C₂×C₄²	—	2	1	no	—
924	#107	—	67	2	no	—
925	#107	C₂²×D₆₇	1	1	yes	characteristic, complemented
926	#107	C₂²×D₆₇	1	1	yes	characteristic, complemented
927	#107	C₂²×D₆₇	1	1	yes	characteristic, complemented
928	#107	C₂²×D₆₇	1	1	yes	characteristic, complemented
929	#106	—	67	2	no	—
930	#106	C₂²×D₆₇	1	1	yes	characteristic, complemented
931	#106	C₂²×D₆₇	1	1	yes	characteristic, complemented
932	#106	C₂²×D₆₇	1	1	yes	characteristic, complemented
933	#106	C₂²×D₆₇	1	1	yes	characteristic, complemented
934	C₄⋊C₈	—	67	2	no	—
935	C₄⋊C₈	—	67	2	no	—
936	#103	—	67	2	no	—
937	#103	C₂²×D₆₇	1	1	yes	characteristic, complemented
938	#103	C₂²×D₆₇	1	1	yes	characteristic, complemented
939	#103	C₂²×D₆₇	1	1	yes	characteristic, complemented
940	#103	C₂²×D₆₇	1	1	yes	characteristic, complemented
941	#102	—	67	2	no	—
942	#102	—	67	2	no	—
943	#102	—	67	2	no	—
944	#102	—	67	2	no	—
945	#102	—	67	2	no	—
946	#102	—	67	2	no	—
947	#102	—	67	2	no	—
948	#102	—	67	2	no	—
949	#102	—	67	2	no	—
950	#102	—	67	2	no	—
951	#102	—	67	2	no	—
952	#102	—	67	2	no	—
953	#102	—	67	2	no	—
954	#102	—	67	2	no	—
955	#102	—	67	2	no	—
956	#102	C₂²×D₆₇	1	1	yes	characteristic, complemented
957	#102	C₂²×D₆₇	1	1	yes	characteristic, complemented
958	#102	C₂²×D₆₇	1	1	yes	characteristic, complemented
959	#102	C₂²×D₆₇	1	1	yes	characteristic, complemented
960	C₂²⋊C₈	—	67	2	no	—
961	C₂²⋊C₈	—	67	2	no	—
962	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
963	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
964	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
965	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
966	#97	—	67	2	no	—
967	C₄×C₈	—	67	2	no	—
968	C₂⁴	—	268	4	no	—
969	C₂⁴	—	536	2	no	—
970	C₂⁴	—	536	2	no	—
971	C₂⁴	—	134	2	no	—
972	C₂⁴	—	134	2	no	—
973	C₂⁴	—	134	2	no	—
974	C₂⁴	—	134	1	no	—
975	C₂⁴	—	134	1	no	—
976	C₂⁴	—	134	1	no	—
977	C₂⁴	D₄×D₆₇	1	1	yes	characteristic
978	#41	—	2	2	no	—
979	#41	—	2	2	no	—
980	#41	—	268	4	no	—
981	#41	—	268	2	no	—
982	#41	—	536	4	no	—
983	#41	—	134	4	no	—
984	#41	—	134	2	no	—
985	#41	—	134	2	no	—
986	C₂×Q₈	—	67	1	no	—
987	C₂×Q₈	—	134	2	no	—
988	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	268	4	no	—
993	C₂×D₄	—	268	4	no	—
994	C₂×D₄	—	268	4	no	—
995	C₂×D₄	—	268	2	no	—
996	C₂×D₄	—	268	2	no	—
997	C₂×D₄	—	268	4	no	—
998	C₂×D₄	—	268	8	no	—
999	C₂×D₄	—	268	2	no	—
1000	C₂×D₄	—	536	4	no	—
1001	C₂×D₄	—	536	4	no	—
1002	C₂×D₄	—	536	2	no	—
1003	C₂×D₄	—	67	2	no	—
1004	C₂×D₄	—	67	2	no	—
1005	C₂×D₄	—	67	2	no	—
1006	C₂×D₄	—	67	1	no	—
1007	C₂×D₄	—	67	4	no	—
1008	C₂×D₄	—	67	2	no	—
1009	C₂×D₄	—	67	2	no	—
1010	C₂×D₄	—	67	2	no	—
1011	C₂×D₄	—	134	2	no	—
1012	C₂×D₄	—	134	4	no	—
1013	C₂×D₄	—	134	4	no	—
1014	C₂×D₄	—	134	2	no	—
1015	C₂×D₄	—	134	2	no	—
1016	C₂×D₄	—	134	2	no	—
1017	C₂×D₄	—	134	2	no	—
1018	C₂×D₄	—	134	2	no	—
1019	C₂×D₄	—	134	2	no	—
1020	C₂×D₄	—	134	2	no	—
1021	C₂×D₄	—	134	4	no	—
1022	C₂×D₄	—	134	2	no	—
1023	C₂×D₄	—	134	2	no	—
1024	C₂×D₄	—	134	1	no	—
1025	C₂×D₄	—	134	2	no	—
1026	C₂×D₄	—	134	2	no	—
1027	C₂×D₄	—	134	1	no	—
1028	C₂×D₄	—	134	1	no	—
1029	C₂×D₄	—	134	2	no	—
1030	C₂×D₄	—	134	2	no	—
1031	C₂×D₄	—	134	2	no	—
1032	C₂×D₄	—	134	2	no	—
1033	C₂×D₄	—	134	2	no	—
1034	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	1	no	—
1040	C₂²×C₄	—	67	2	no	—
1041	C₂²×C₄	—	134	2	no	—
1042	C₂²×C₄	—	134	2	no	—
1043	C₂²×C₄	—	134	2	no	—
1044	C₂²×C₄	—	134	2	no	—
1045	C₂²×C₄	—	134	2	no	—
1046	C₂²×C₄	—	134	2	no	—
1047	C₂²×C₄	—	134	1	no	—
1048	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
1049	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
1050	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
1051	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1052	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1053	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1054	SD₁₆	—	268	2	no	—
1055	D₈	—	268	2	no	—
1056	D₈	—	268	2	no	—
1057	D₈	—	268	2	no	—
1058	D₈	—	134	4	no	—
1059	D₈	—	134	4	no	—
1060	M₁₆	—	268	2	no	—
1061	M₁₆	—	268	2	no	—
1062	M₁₆	—	134	2	no	—
1063	M₁₆	—	134	2	no	—
1064	C₂×C₈	—	2	2	no	—
1065	C₂×C₈	—	2	2	no	—
1066	C₂×C₈	—	268	2	no	—
1067	C₂×C₈	—	268	2	no	—
1068	C₂×C₈	—	67	2	no	—
1069	C₂×C₈	—	67	2	no	—
1070	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
1071	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
1072	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
1073	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	1	no	—
1078	C₄⋊C₄	—	67	1	no	—
1079	C₄⋊C₄	—	67	1	no	—
1080	C₄⋊C₄	—	67	2	no	—
1081	C₄⋊C₄	—	67	2	no	—
1082	C₄⋊C₄	—	67	2	no	—
1083	C₄⋊C₄	—	134	2	no	—
1084	C₄⋊C₄	—	134	2	no	—
1085	C₄⋊C₄	—	134	2	no	—
1086	C₄⋊C₄	—	134	2	no	—
1087	C₄⋊C₄	—	134	1	no	—
1088	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1089	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1090	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1091	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1092	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1093	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	67	2	no	—
1104	C₂²⋊C₄	—	67	2	no	—
1105	C₂²⋊C₄	—	67	2	no	—
1106	C₂²⋊C₄	—	67	2	no	—
1107	C₂²⋊C₄	—	67	2	no	—
1108	C₂²⋊C₄	—	134	2	no	—
1109	C₂²⋊C₄	—	134	2	no	—
1110	C₂²⋊C₄	—	134	2	no	—
1111	C₂²⋊C₄	—	134	2	no	—
1112	C₂²⋊C₄	—	134	2	no	—
1113	C₂²⋊C₄	—	134	2	no	—
1114	C₂²⋊C₄	—	134	2	no	—
1115	C₂²⋊C₄	—	134	2	no	—
1116	C₂²⋊C₄	—	134	2	no	—
1117	C₂²⋊C₄	—	134	2	no	—
1118	C₂²⋊C₄	—	134	2	no	—
1119	C₂²⋊C₄	—	134	2	no	—
1120	C₂²⋊C₄	—	134	2	no	—
1121	C₄²	—	2	1	no	—
1122	C₄²	—	2	1	no	—
1123	C₄²	—	2	1	no	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	—	67	2	no	—
1127	C₄²	—	134	2	no	—
1128	C₂³	—	2	2	no	—
1129	C₂³	—	2	2	no	—
1130	C₂³	—	2	1	no	—
1131	C₂³	—	4	1	no	—
1132	C₂³	—	268	4	no	—
1133	C₂³	—	268	4	no	—
1134	C₂³	—	268	4	no	—
1135	C₂³	—	268	4	no	—
1136	C₂³	—	268	2	no	—
1137	C₂³	—	268	4	no	—
1138	C₂³	—	268	2	no	—
1139	C₂³	—	536	1	no	—
1140	C₂³	—	536	1	no	—
1141	C₂³	—	536	2	no	—
1142	C₂³	—	536	1	no	—
1143	C₂³	—	536	1	no	—
1144	C₂³	—	536	2	no	—
1145	C₂³	—	536	1	no	—
1146	C₂³	—	536	1	no	—
1147	C₂³	—	536	2	no	—
1148	C₂³	—	536	2	no	—
1149	C₂³	—	536	16	no	—
1150	C₂³	—	67	2	no	—
1151	C₂³	—	134	2	no	—
1152	C₂³	—	134	2	no	—
1153	C₂³	—	134	2	no	—
1154	C₂³	—	134	4	no	—
1155	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1156	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1157	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1158	Q₈	—	2	1	no	—
1159	Q₈	—	2	1	no	—
1160	Q₈	—	536	2	no	—
1161	Q₈	—	134	2	no	—
1162	D₄	—	2	1	no	—
1163	D₄	—	2	1	no	—
1164	D₄	—	4	2	no	—
1165	D₄	—	4	2	no	—
1166	D₄	—	4	2	no	—
1167	D₄	—	268	4	no	—
1168	D₄	—	268	4	no	—
1169	D₄	—	268	4	no	—
1170	D₄	—	268	4	no	—
1171	D₄	—	268	2	no	—
1172	D₄	—	268	4	no	—
1173	D₄	—	268	2	no	—
1174	D₄	—	268	2	no	—
1175	D₄	—	536	2	no	—
1176	D₄	—	536	2	no	—
1177	D₄	—	536	2	no	—
1178	D₄	—	536	2	no	—
1179	D₄	—	536	2	no	—
1180	D₄	—	536	2	no	—
1181	D₄	—	536	2	no	—
1182	D₄	—	67	4	no	—
1183	D₄	—	134	4	no	—
1184	D₄	—	134	4	no	—
1185	D₄	—	134	4	no	—
1186	D₄	—	134	2	no	—
1187	D₄	—	134	2	no	—
1188	D₄	—	134	2	no	—
1189	D₄	—	134	2	no	—
1190	D₄	—	134	2	no	—
1191	D₄	—	134	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	4	2	no	—
1207	C₂×C₄	—	4	2	no	—
1208	C₂×C₄	—	8	1	no	—
1209	C₂×C₄	—	268	4	no	—
1210	C₂×C₄	—	536	2	no	—
1211	C₂×C₄	—	536	2	no	—
1212	C₂×C₄	—	536	2	no	—
1213	C₂×C₄	—	536	2	no	—
1214	C₂×C₄	—	536	2	no	—
1215	C₂×C₄	—	536	1	no	—
1216	C₂×C₄	—	67	2	no	—
1217	C₂×C₄	—	67	2	no	—
1218	C₂×C₄	—	67	2	no	—
1219	C₂×C₄	—	134	2	no	—
1220	C₂×C₄	—	134	2	no	—
1221	C₂×C₄	—	134	2	no	—
1222	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1223	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1224	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1225	C₂×C₄	#41×D₆₇	1	2	yes	—
1226	C₂×C₄	#14524089	1	2	yes	—
1227	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1228	C₈	—	2	1	no	—
1229	C₈	—	2	1	no	—
1230	C₈	—	2	1	no	—
1231	C₈	—	2	1	no	—
1232	C₈	—	134	2	no	—
1233	C₈	—	134	2	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	1	no	—
1236	C₂²	—	2	1	no	—
1237	C₂²	—	2	1	no	—
1238	C₂²	—	2	1	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	4	4	no	—
1242	C₂²	—	4	1	no	—
1243	C₂²	—	4	1	no	—
1244	C₂²	—	4	1	no	—
1245	C₂²	—	268	2	no	—
1246	C₂²	—	268	2	no	—
1247	C₂²	—	268	2	no	—
1248	C₂²	—	268	2	no	—
1249	C₂²	—	268	2	no	—
1250	C₂²	—	268	2	no	—
1251	C₂²	—	268	2	no	—
1252	C₂²	—	268	2	no	—
1253	C₂²	—	536	4	no	—
1254	C₂²	—	536	8	no	—
1255	C₂²	—	536	4	no	—
1256	C₂²	—	536	8	no	—
1257	C₂²	—	1072	2	no	—
1258	C₂²	—	1072	4	no	—
1259	C₂²	—	134	4	no	—
1260	C₂²	—	134	2	no	—
1261	C₂²	—	134	2	no	—
1262	C₂²	—	134	2	no	—
1263	C₂²	#16864038	1	2	yes	—
1264	C₂²	#16864198	1	2	yes	—
1265	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1266	C₄	—	2	1	no	—
1267	C₄	—	2	1	no	—
1268	C₄	—	4	1	no	—
1269	C₄	—	4	1	no	—
1270	C₄	—	4	1	no	—
1271	C₄	—	4	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	1	no	—
1275	C₄	—	268	2	no	—
1276	C₄	—	134	2	no	—
1277	C₄	—	134	2	no	—
1278	C₄	—	134	2	no	—
1279	C₄	#16864038	1	2	yes	—
1280	C₄	C₂×#41×D₆₇	1	1	yes	characteristic
1281	C₄	C₂×#14524089	1	1	yes	characteristic
1282	C₂	—	2	2	no	—
1283	C₂	—	2	2	no	—
1284	C₂	—	4	1	no	—
1285	C₂	—	8	1	no	—
1286	C₂	—	268	4	no	—
1287	C₂	—	268	2	no	—
1288	C₂	—	536	2	no	—
1289	C₂	—	536	2	no	—
1290	C₂	C₂×#16864038	1	1	yes	characteristic
1291	C₂	C₂×#16864198	1	1	yes	characteristic
1292	C₂	#22574986	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×#3091	C₂
socle	C₂²×C₆₇	C₂³×D₄
hypercenter	#3091	D₆₇
hypocenter	C₆₇	#61183
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #3091

Complements

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

N	H ≅ G/N	type
1. #22573944	C₂	semidirect
2. #22573842	C₂	semidirect
3. #22572449	C₂	semidirect
4. #22572408	C₂	semidirect
5. #22572368	C₂	semidirect
6. #22572353	C₂	semidirect
7. #22572348	C₂	semidirect
8. #22572168	C₂	semidirect
9. #22572057	C₂	semidirect
10. #22572020	C₂	semidirect
11. #22570567	C₂	semidirect
12. #22570170	C₂	semidirect
13. #22570043	C₂	semidirect
14. #22569858	C₂	semidirect
15. #22569830	C₂	semidirect
16. #22569715	C₂	semidirect
17. #22569480	C₂	semidirect
18. C₂×#16863532	C₂	semidirect
19. #22569060	C₂	semidirect
20. #22568930	C₂	semidirect
21. #22568731	C₂	semidirect
22. C₂×#16863400	C₂	semidirect
23. C₆₇×#3091	C₂	semidirect
26. C₂×#14524068	C₂²	semidirect
28. C₂²×D₅₃₆	C₂²	semidirect
29. C₂×#14524049	C₂²	semidirect
30. C₂²×#11761612	C₂²	semidirect
31. #16864109	C₂²	semidirect
32. #16864094	C₂²	semidirect
33. #16864090	C₂²	semidirect
35. #16864047	C₂²	semidirect
38. #16864037	C₂²	semidirect
39. #16864037	C₂²	semidirect
43. #16864030	C₂²	semidirect
44. #16864030	C₂²	semidirect
45. #16864024	C₂²	semidirect
49. #16863965	C₂²	semidirect
55. C₂×#14524017	C₂²	semidirect
57. #16863876	C₂²	semidirect
59. #16863870	C₂²	semidirect
60. #16863759	C₂²	semidirect
61. #16863757	C₂²	semidirect
62. #16863752	C₂²	semidirect
63. #16863741	C₂²	semidirect
64. #16863723	C₂²	semidirect
65. #16863722	C₂²	semidirect
66. #16863716	C₂²	semidirect
67. #16863711	C₂²	semidirect
68. #16863699	C₂²	semidirect
69. #16863695	C₂²	semidirect
70. #16863685	C₂²	semidirect
71. #16863675	C₂²	semidirect
72. #16863650	C₂²	semidirect
73. #16863650	C₂²	semidirect
74. #16863647	C₂²	semidirect
75. #16863644	C₂²	semidirect
76. #16863633	C₂²	semidirect
77. #16863633	C₂²	semidirect
78. #16863630	C₂²	semidirect
79. #16863627	C₂²	semidirect
80. #16863614	C₂²	semidirect
81. #16863614	C₂²	semidirect
82. #16863590	C₂²	semidirect
83. #16863590	C₂²	semidirect
84. #16863544	C₂²	semidirect
85. #16863544	C₂²	semidirect
86. #16863532	C₂²	semidirect
87. #16863532	C₂²	semidirect
88. #16863532	C₂²	semidirect
89. #16863532	C₂²	semidirect
90. #16863531	C₂²	semidirect
91. #16863531	C₂²	semidirect
92. #16863507	C₂²	semidirect
93. #16863507	C₂²	semidirect
94. #16863478	C₂²	semidirect
95. #16863478	C₂²	semidirect
96. #16863471	C₂²	semidirect
97. #16863470	C₂²	semidirect
98. #16863464	C₂²	semidirect
99. (C₂²⋊D₆₇)⋊C₈	C₂²	semidirect
100. #16863439	C₂²	semidirect
101. #16863422	C₂²	semidirect
104. #16863400	C₂²	semidirect
105. #16863400	C₂²	semidirect
106. #16863400	C₂²	semidirect
107. #16863400	C₂²	semidirect
108. #16863400	C₂²	semidirect
109. #16863399	C₂²	semidirect
110. #16863397	C₂²	semidirect
111. #16863396	C₂²	semidirect
112. #16863391	C₂²	semidirect
114. C₂×#14523965	C₂²	semidirect
115. C₂×#14523963	C₂²	semidirect
116. C₂×#14523963	C₂²	semidirect
117. #102×D₆₇	C₂²	semidirect
118. #16863362	C₂²	semidirect
119. #16863351	C₂²	semidirect
121. C₂×#117×C₆₇	C₂²	semidirect
122. #485×C₆₇	C₂²	semidirect
123. #485×C₆₇	C₂²	semidirect
124. #484×C₆₇	C₂²	semidirect
125. #483×C₆₇	C₂²	semidirect
126. #482×C₆₇	C₂²	semidirect
127. #482×C₆₇	C₂²	semidirect
128. #481×C₆₇	C₂²	semidirect
129. #480×C₆₇	C₂²	semidirect
130. #427×C₆₇	C₂²	semidirect
131. #427×C₆₇	C₂²	semidirect
132. #416×C₆₇	C₂²	semidirect
133. #416×C₆₇	C₂²	semidirect
134. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
159. C₂×#11761615	C₂³	semidirect
166. C₂×#11761613	C₂³	semidirect
172. C₂×#11761611	C₂³	semidirect
174. C₂×C₈×D₆₇	C₂³	semidirect
176. #14524042	C₂³	semidirect
183. #14524034	C₂³	semidirect
204. #14524018	C₂³	semidirect
205. #14524018	C₂³	semidirect
238. #14524005	C₂³	semidirect
239. #14524005	C₂³	semidirect
245. #14524001	C₂³	semidirect
248. C₄⋊C₄×D₆₇	C₂³	semidirect
254. #14523976	C₂³	semidirect
255. #14523974	C₂³	semidirect
256. Dic₆₇⋊C₈	C₂³	semidirect
257. Dic₆₇⋊C₈	C₂³	semidirect
258. #14523967	C₂³	semidirect
263. #14523964	C₂³	semidirect
272. #14523963	C₂³	semidirect
273. #14523963	C₂³	semidirect
274. (C₂×D₆₇)⋊C₈	C₂³	semidirect
275. (C₂×D₆₇)⋊C₈	C₂³	semidirect
276. #14523953	C₂³	semidirect
277. C₈×Dic₆₇	C₂³	semidirect
301. #107×C₆₇	C₂³	semidirect
302. #107×C₆₇	C₂³	semidirect
303. #107×C₆₇	C₂³	semidirect
304. #107×C₆₇	C₂³	semidirect
305. #106×C₆₇	C₂³	semidirect
306. #106×C₆₇	C₂³	semidirect
307. #106×C₆₇	C₂³	semidirect
308. #106×C₆₇	C₂³	semidirect
309. #103×C₆₇	C₂³	semidirect
310. #103×C₆₇	C₂³	semidirect
311. #103×C₆₇	C₂³	semidirect
312. #103×C₆₇	C₂³	semidirect
313. #102×C₆₇	C₂³	semidirect
314. #102×C₆₇	C₂³	semidirect
315. #102×C₆₇	C₂³	semidirect
316. #102×C₆₇	C₂³	semidirect
362. C₂×D₂₆₈	#41	semidirect
659. #3091	D₆₇	semidirect
670. C₆₇	#61183	semidirect
708. C₂×#117	C₂×D₆₇	semidirect
713. #485	C₂×D₆₇	semidirect
714. #485	C₂×D₆₇	semidirect
715. #484	C₂×D₆₇	semidirect
716. #483	C₂×D₆₇	semidirect
719. #482	C₂×D₆₇	semidirect
720. #482	C₂×D₆₇	semidirect
722. #481	C₂×D₆₇	semidirect
724. #480	C₂×D₆₇	semidirect
758. #427	C₂×D₆₇	semidirect
759. #427	C₂×D₆₇	semidirect
772. #416	C₂×D₆₇	semidirect
773. #416	C₂×D₆₇	semidirect
780. C₂×C₂²⋊C₈	C₂×D₆₇	semidirect
925. #107	C₂²×D₆₇	semidirect
926. #107	C₂²×D₆₇	semidirect
927. #107	C₂²×D₆₇	semidirect
928. #107	C₂²×D₆₇	semidirect
930. #106	C₂²×D₆₇	semidirect
931. #106	C₂²×D₆₇	semidirect
932. #106	C₂²×D₆₇	semidirect
933. #106	C₂²×D₆₇	semidirect
937. #103	C₂²×D₆₇	semidirect
938. #103	C₂²×D₆₇	semidirect
939. #103	C₂²×D₆₇	semidirect
940. #103	C₂²×D₆₇	semidirect
956. #102	C₂²×D₆₇	semidirect
957. #102	C₂²×D₆₇	semidirect
958. #102	C₂²×D₆₇	semidirect
959. #102	C₂²×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22573944	2
#22573842	2
#22572449	2
#22572408	2
#22572368	2
#22572353	2
#22572348	2
#22572168	2
#22572057	2
#22572020	2
#22570567	2
#22570170	2
#22570043	2
#22569858	2
#22569830	2
#22569715	2
#22569480	2
C₂×#16863532	2
#22569060	2
#22568930	2
#22568731	2
C₂×#16863400	2
C₆₇×#3091	2
#61183	67