Subgroups — C₂×#22573903 #31763883

Order 17152.

7390 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573903	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864084	C₂	1	2	yes	maximal, complemented
3	C₂×#16864082	C₂	1	2	yes	maximal, complemented
4	C₂×#16864080	C₂	1	2	yes	maximal, complemented
5	C₂×#16864078	C₂	1	2	yes	maximal, complemented
6	C₂×#16864074	C₂	1	2	yes	maximal, complemented
7	C₂×#16864073	C₂	1	2	yes	maximal, complemented
8	C₂×#16864071	C₂	1	2	yes	maximal, complemented
9	C₂×#16864069	C₂	1	2	yes	maximal, complemented
10	C₂×#16864021	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16863993	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16863990	C₂	1	2	yes	maximal, complemented
13	C₂×#16863954	C₂	1	1	yes	maximal, characteristic
14	C₂×#16863932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16863927	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16863926	C₂	1	2	yes	maximal, complemented
17	C₂×#123×D₆₇	C₂	1	2	yes	maximal, complemented
18	C₂×#16863868	C₂	1	2	yes	maximal, complemented
19	C₂²×#14524001	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#539×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×D₄×D₆₇	C₂²	1	2	yes	—
22	C₂³×C₄×D₆₇	C₂²	1	1	yes	characteristic
23	#16864084	C₂²	1	32	yes	complemented
24	#16864082	C₂²	1	32	yes	complemented
25	#16864080	C₂²	1	32	yes	complemented
26	#16864078	C₂²	1	32	yes	complemented
27	#16864074	C₂²	1	32	yes	complemented
28	#16864073	C₂²	1	32	yes	complemented
29	#16864071	C₂²	1	32	yes	complemented
30	#16864069	C₂²	1	32	yes	complemented
31	#16864021	C₂²	1	16	yes	complemented
32	#16863993	C₂²	1	16	yes	complemented
33	#16863990	C₂²	1	32	yes	complemented
34	#16863954	C₂²	1	16	yes	—
35	#16863932	C₂²	1	16	yes	complemented
36	#16863927	C₂²	1	16	yes	complemented
37	#16863926	C₂²	1	32	yes	complemented
38	C₂×#14524038	C₂²	1	2	yes	complemented
39	C₂×#14524038	C₂²	1	2	yes	complemented
40	C₂×#14524038	C₂²	1	2	yes	complemented
41	C₂×#14524038	C₂²	1	2	yes	complemented
42	C₂×#14524036	C₂²	1	2	yes	complemented
43	C₂×#14524036	C₂²	1	2	yes	complemented
44	C₂×#14524036	C₂²	1	2	yes	complemented
45	C₂×#14524034	C₂²	1	2	yes	complemented
46	C₂×#14524034	C₂²	1	1	yes	characteristic, complemented
47	C₂×#14524034	C₂²	1	1	yes	characteristic, complemented
48	C₂×#14524033	C₂²	1	2	yes	complemented
49	C₂×#14524033	C₂²	1	2	yes	complemented
50	C₂×#14524033	C₂²	1	2	yes	complemented
51	C₂×#14524032	C₂²	1	1	yes	characteristic, complemented
52	C₂×#14524030	C₂²	1	1	yes	characteristic, complemented
53	C₂×#14524029	C₂²	1	2	yes	complemented
54	C₂×#14524028	C₂²	1	2	yes	—
55	C₂×#14524028	C₂²	1	2	yes	—
56	C₂×#14524028	C₂²	1	2	yes	—
57	C₂×#14524028	C₂²	1	2	yes	complemented
58	C₂×#14524027	C₂²	1	2	yes	complemented
59	C₂×#14524027	C₂²	1	2	yes	complemented
60	C₂×#14524026	C₂²	1	2	yes	complemented
61	C₂×#14524025	C₂²	1	2	yes	—
62	C₂×#14524025	C₂²	1	2	yes	—
63	C₂×#14524025	C₂²	1	2	yes	—
64	C₂×#14524025	C₂²	1	2	yes	complemented
65	C₂×#14524024	C₂²	1	2	yes	complemented
66	#123×D₆₇	C₂²	1	32	yes	complemented
67	C₂×#14524023	C₂²	1	2	yes	complemented
68	C₂×#14524023	C₂²	1	2	yes	complemented
69	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
70	C₂×#14524021	C₂²	1	2	yes	complemented
71	C₂×#14524021	C₂²	1	2	yes	complemented
72	C₂×#14524021	C₂²	1	2	yes	complemented
73	C₂×#14524020	C₂²	1	2	yes	complemented
74	C₂×#14524020	C₂²	1	2	yes	complemented
75	C₂×#14524019	C₂²	1	2	yes	complemented
76	C₂×#14524017	C₂²	1	1	yes	characteristic
77	C₂×#14524015	C₂²	1	2	yes	—
78	C₂×#14524013	C₂²	1	2	yes	—
79	C₂×#14524011	C₂²	1	2	yes	—
80	#16863868	C₂²	1	32	yes	complemented
81	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
83	C₂×#14524008	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₄×D₂₆₈	C₂²	1	2	yes	—
85	C₂×D₄×Dic₆₇	C₂²	1	2	yes	complemented
86	C₂×D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
87	C₂×#14524005	C₂²	1	2	yes	—
88	C₂×#14524005	C₂²	1	1	yes	characteristic, complemented
89	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
90	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
91	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
92	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
93	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
94	C₂×#14524002	C₂²	1	2	yes	complemented
95	C₂×#14524001	C₂²	1	2	yes	complemented
96	C₂×#14524001	C₂²	1	2	yes	complemented
97	C₂×#14524001	C₂²	1	2	yes	complemented
98	C₂×#14524001	C₂²	1	2	yes	complemented
99	C₂×#14524001	C₂²	1	2	yes	complemented
100	C₂×#14524001	C₂²	1	2	yes	complemented
101	C₂×#14524001	C₂²	1	16	yes	complemented
102	C₂×#14524000	C₂²	1	2	yes	complemented
103	C₂×#14524000	C₂²	1	2	yes	complemented
104	C₂×#14523999	C₂²	1	2	yes	complemented
105	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
107	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
108	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
109	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
110	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
111	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
112	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
113	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
114	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
115	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
117	#539×C₆₇	C₂²	1	16	yes	complemented
118	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
119	C₂×#125×C₆₇	C₂²	1	2	yes	complemented
120	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
121	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
122	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
124	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
125	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
126	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	C₂⁴×D₆₇	C₂³	1	2	yes	—
128	C₂⁴×D₆₇	C₂³	1	1	yes	characteristic
129	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
130	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
131	C₂²×D₂₆₈	C₂³	1	2	yes	—
132	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
133	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
134	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
135	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
136	C₂×D₄×D₆₇	—	2	16	no	—
137	C₂×D₄×D₆₇	C₂³	1	16	yes	—
138	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
139	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
140	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
141	C₂³×Dic₆₇	C₂³	1	2	yes	—
142	C₂²×C₄×D₆₇	—	2	8	no	—
143	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
144	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
145	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
146	C₂²×C₄×D₆₇	C₂³	1	8	yes	—
147	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
148	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
149	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
150	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
151	#14524038	C₂³	1	16	yes	complemented
152	#14524038	C₂³	1	16	yes	complemented
153	#14524038	C₂³	1	16	yes	complemented
154	#14524038	C₂³	1	16	yes	complemented
155	#14524036	C₂³	1	16	yes	complemented
156	#14524036	C₂³	1	16	yes	complemented
157	#14524036	C₂³	1	16	yes	complemented
158	#14524034	C₂³	1	16	yes	complemented
159	#14524034	C₂³	1	8	yes	complemented
160	#14524034	C₂³	1	8	yes	complemented
161	#14524033	C₂³	1	16	yes	complemented
162	#14524033	C₂³	1	16	yes	complemented
163	#14524033	C₂³	1	16	yes	complemented
164	#14524032	C₂³	1	8	yes	complemented
165	#14524030	C₂³	1	8	yes	complemented
166	#14524029	C₂³	1	16	yes	complemented
167	#14524028	C₂³	1	16	yes	—
168	#14524028	C₂³	1	16	yes	—
169	#14524028	C₂³	1	16	yes	—
170	#14524028	C₂³	1	16	yes	complemented
171	#14524027	C₂³	1	16	yes	complemented
172	#14524027	C₂³	1	16	yes	complemented
173	#14524026	C₂³	1	16	yes	complemented
174	#14524025	C₂³	1	16	yes	—
175	#14524025	C₂³	1	16	yes	—
176	#14524025	C₂³	1	16	yes	—
177	#14524025	C₂³	1	16	yes	complemented
178	#14524024	C₂³	1	16	yes	complemented
179	#14524023	C₂³	1	16	yes	complemented
180	#14524023	C₂³	1	16	yes	complemented
181	#14524022	C₂³	1	8	yes	complemented
182	#14524021	C₂³	1	16	yes	complemented
183	#14524021	C₂³	1	16	yes	complemented
184	#14524021	C₂³	1	16	yes	complemented
185	#14524020	C₂³	1	16	yes	complemented
186	#14524020	C₂³	1	16	yes	complemented
187	#14524019	C₂³	1	16	yes	complemented
188	#14524017	C₂³	1	8	yes	—
189	#14524015	C₂³	1	16	yes	—
190	#14524013	C₂³	1	16	yes	—
191	#14524011	C₂³	1	16	yes	—
192	Q₈×Dic₆₇	C₂³	1	8	yes	complemented
193	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
194	#14524008	C₂³	1	8	yes	complemented
195	C₄×D₂₆₈	C₂³	1	16	yes	—
196	D₄×Dic₆₇	C₂³	1	8	yes	complemented
197	D₄×Dic₆₇	C₂³	1	16	yes	complemented
198	#14524005	C₂³	1	16	yes	—
199	#14524005	C₂³	1	8	yes	complemented
200	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	—
201	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
202	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
203	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	—
204	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
205	#14524002	C₂³	1	16	yes	complemented
206	#14524001	C₂³	1	16	yes	complemented
207	#14524001	C₂³	1	16	yes	complemented
208	#14524001	C₂³	1	16	yes	complemented
209	#14524001	C₂³	1	16	yes	complemented
210	#14524001	C₂³	1	16	yes	complemented
211	#14524001	C₂³	1	16	yes	complemented
212	#14524000	C₂³	1	16	yes	complemented
213	#14524000	C₂³	1	16	yes	complemented
214	#14523999	C₂³	1	16	yes	complemented
215	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
216	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
217	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
218	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
219	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
220	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
221	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₆₇	C₂³	1	8	yes	complemented
224	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
225	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
226	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
227	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
228	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
229	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
230	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
231	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
232	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
233	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
234	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
235	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
236	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
237	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
238	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
239	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
240	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
241	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	—
242	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
243	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
244	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
245	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
246	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
247	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
248	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
249	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
250	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	—
251	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
252	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
253	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
254	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
255	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
256	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
257	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	complemented
258	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
259	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
260	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
261	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
262	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
264	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
266	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
267	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
268	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
269	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
270	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
271	C₂×C₄×Dic₆₇	C₂³	1	8	yes	complemented
272	C₂×C₄×Dic₆₇	C₂³	1	8	yes	complemented
273	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
274	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
275	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
276	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
277	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
278	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
279	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
280	#126×C₆₇	C₂³	1	16	yes	complemented
281	#125×C₆₇	C₂³	1	16	yes	complemented
282	#123×C₆₇	C₂³	1	16	yes	complemented
283	#123×C₆₇	C₂³	1	16	yes	complemented
284	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
285	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
286	#121×C₆₇	C₂³	1	8	yes	—
287	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
288	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
289	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
290	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
291	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
293	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
294	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
296	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
297	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
298	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
299	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
300	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
301	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
302	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
303	C₂³×D₆₇	—	2	8	no	—
304	C₂³×D₆₇	—	4	2	no	—
305	C₂³×D₆₇	—	4	2	no	—
306	C₂³×D₆₇	—	4	4	no	—
307	C₂³×D₆₇	—	4	4	no	—
308	C₂³×D₆₇	#41	1	8	yes	—
309	C₂³×D₆₇	C₂⁴	1	2	yes	—
310	C₂³×D₆₇	C₂⁴	1	2	yes	—
311	C₂³×D₆₇	C₂⁴	1	8	yes	—
312	C₂³×D₆₇	C₂⁴	1	4	yes	—
313	C₂×Dic₁₃₄	—	4	2	no	—
314	C₂×Dic₁₃₄	—	4	4	no	—
315	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
316	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
317	C₂×D₂₆₈	—	2	8	no	—
318	C₂×D₂₆₈	—	4	2	no	—
319	C₂×D₂₆₈	C₂⁴	1	8	yes	—
320	C₂×D₂₆₈	C₂⁴	1	4	yes	—
321	C₂×C₂²⋊D₆₇	—	2	8	no	—
322	C₂×C₂²⋊D₆₇	—	2	8	no	—
323	C₂×C₂²⋊D₆₇	—	4	4	no	—
324	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
325	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
326	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
327	D₄×D₆₇	—	2	64	no	—
328	C₂²×Dic₆₇	—	2	4	no	—
329	C₂²×Dic₆₇	—	4	2	no	—
330	C₂²×Dic₆₇	—	4	4	no	—
331	C₂²×Dic₆₇	—	4	2	no	—
332	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
333	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
334	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
335	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
336	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
337	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
338	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
339	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
340	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
341	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
342	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
343	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
344	C₂×C₄×D₆₇	—	2	8	no	—
345	C₂×C₄×D₆₇	—	2	8	no	—
346	C₂×C₄×D₆₇	—	2	32	no	—
347	C₂×C₄×D₆₇	—	2	8	no	—
348	C₂×C₄×D₆₇	—	4	4	no	—
349	C₂×C₄×D₆₇	—	4	4	no	—
350	C₂×C₄×D₆₇	—	4	4	no	—
351	C₂×C₄×D₆₇	—	4	4	no	—
352	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
353	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
354	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
355	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
356	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
357	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
358	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
359	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
360	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
361	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
362	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
363	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
364	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
365	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
366	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
367	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
368	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
369	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
370	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
371	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
372	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
373	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
374	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
375	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
376	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
377	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
378	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
379	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
380	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
381	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
382	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
383	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
384	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
385	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
386	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
387	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
388	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
389	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
390	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
391	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
392	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
393	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
394	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
395	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
396	C₄×Dic₆₇	C₂⁴	1	4	yes	—
397	C₄×Dic₆₇	C₂⁴	1	8	yes	—
398	C₄×Dic₆₇	C₂⁴	1	4	yes	—
399	C₄×Dic₆₇	C₂⁴	1	8	yes	—
400	C₄×Dic₆₇	C₂⁴	1	4	yes	—
401	C₄×Dic₆₇	C₂⁴	1	4	yes	—
402	C₄×Dic₆₇	C₂⁴	1	8	yes	—
403	C₄×Dic₆₇	C₂⁴	1	8	yes	—
404	C₄×Dic₆₇	C₂⁴	1	8	yes	—
405	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
406	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
407	C₂×Q₈×C₆₇	—	4	2	no	—
408	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
409	C₂×D₄×C₆₇	—	2	8	no	—
410	C₂×D₄×C₆₇	—	4	2	no	—
411	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
412	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
413	C₂²×C₄×C₆₇	—	2	4	no	—
414	C₂²×C₄×C₆₇	—	4	2	no	—
415	C₂²×C₄×C₆₇	—	4	4	no	—
416	C₂²×C₄×C₆₇	—	4	2	no	—
417	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
418	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
419	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
420	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
421	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
423	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
425	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
426	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
427	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
428	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
429	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
430	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
431	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
432	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
433	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
434	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
435	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
436	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
437	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
438	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
439	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
440	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
441	C₄²×C₆₇	C₂⁴	1	8	yes	—
442	C₂³×C₆₇	—	2	2	no	—
443	C₂³×C₆₇	—	2	2	no	—
444	C₂³×C₆₇	—	2	4	no	—
445	C₂³×C₆₇	—	2	4	no	—
446	C₂³×C₆₇	—	2	4	no	—
447	C₂³×C₆₇	C₂×#41	1	4	yes	—
448	C₂³×C₆₇	C₂⁵	1	4	yes	—
449	C₂³×C₆₇	C₂⁵	1	2	yes	—
450	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
451	C₂²×D₆₇	—	2	4	no	—
452	C₂²×D₆₇	—	2	4	no	—
453	C₂²×D₆₇	—	2	4	no	—
454	C₂²×D₆₇	—	2	4	no	—
455	C₂²×D₆₇	—	2	4	no	—
456	C₂²×D₆₇	—	2	16	no	—
457	C₂²×D₆₇	—	4	16	no	—
458	C₂²×D₆₇	—	4	4	no	—
459	C₂²×D₆₇	—	4	4	no	—
460	C₂²×D₆₇	—	4	8	no	—
461	C₂²×D₆₇	—	4	8	no	—
462	C₂²×D₆₇	—	8	16	no	—
463	C₂²×D₆₇	C₂×#41	1	8	yes	—
464	C₂²×D₆₇	C₂×#41	1	16	yes	—
465	C₂²×D₆₇	C₂⁵	1	4	yes	—
466	C₂²×D₆₇	C₂⁵	1	4	yes	—
467	Q₈×C₆₇	—	4	4	no	—
468	D₄×C₆₇	—	2	16	no	—
469	D₄×C₆₇	—	4	4	no	—
470	C₂×C₄×C₆₇	—	2	8	no	—
471	C₂×C₄×C₆₇	—	2	4	no	—
472	C₂×C₄×C₆₇	—	2	4	no	—
473	C₂×C₄×C₆₇	—	2	4	no	—
474	C₂×C₄×C₆₇	—	2	2	no	—
475	C₂×C₄×C₆₇	—	2	4	no	—
476	C₂×C₄×C₆₇	—	2	2	no	—
477	C₂×C₄×C₆₇	—	2	4	no	—
478	C₂×C₄×C₆₇	—	4	4	no	—
479	C₂×C₄×C₆₇	—	4	4	no	—
480	C₂×C₄×C₆₇	—	4	8	no	—
481	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
482	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
483	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
484	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
485	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
486	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
487	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
488	C₂²⋊D₆₇	—	2	16	no	—
489	C₂²⋊D₆₇	—	2	16	no	—
490	C₂²⋊D₆₇	—	4	8	no	—
491	C₂×Dic₆₇	—	2	8	no	—
492	C₂×Dic₆₇	—	2	2	no	—
493	C₂×Dic₆₇	—	2	2	no	—
494	C₂×Dic₆₇	—	2	4	no	—
495	C₂×Dic₆₇	—	2	2	no	—
496	C₂×Dic₆₇	—	2	4	no	—
497	C₂×Dic₆₇	—	2	4	no	—
498	C₂×Dic₆₇	—	2	2	no	—
499	C₂×Dic₆₇	—	2	4	no	—
500	C₂×Dic₆₇	—	4	8	no	—
501	C₂×Dic₆₇	—	4	4	no	—
502	C₂×Dic₆₇	—	4	4	no	—
503	C₂×Dic₆₇	C₂⁵	1	2	yes	—
504	C₂×Dic₆₇	C₂⁵	1	2	yes	—
505	C₂×Dic₆₇	C₂⁵	1	2	yes	—
506	C₂×Dic₆₇	C₂⁵	1	2	yes	—
507	C₂×Dic₆₇	C₂⁵	1	4	yes	—
508	C₂×Dic₆₇	C₂⁵	1	4	yes	—
509	C₂×Dic₆₇	C₂⁵	1	4	yes	—
510	C₂×Dic₆₇	C₂⁵	1	4	yes	—
511	D₂₆₈	—	2	16	no	—
512	D₂₆₈	—	4	4	no	—
513	C₄×D₆₇	—	2	16	no	—
514	C₄×D₆₇	—	2	16	no	—
515	C₄×D₆₇	—	2	16	no	—
516	C₄×D₆₇	—	4	8	no	—
517	C₄×D₆₇	—	4	8	no	—
518	C₄×D₆₇	—	4	8	no	—
519	C₄×D₆₇	—	4	8	no	—
520	Dic₁₃₄	—	4	4	no	—
521	Dic₁₃₄	—	4	8	no	—
522	C₂²×C₆₇	—	2	2	no	—
523	C₂²×C₆₇	—	2	2	no	—
524	C₂²×C₆₇	—	2	8	no	—
525	C₂²×C₆₇	—	2	4	no	—
526	C₂²×C₆₇	—	2	4	no	—
527	C₂²×C₆₇	—	2	4	no	—
528	C₂²×C₆₇	—	4	8	no	—
529	C₂²×C₆₇	C₂²×#41	1	4	yes	—
530	C₂²×C₆₇	C₂²×#41	1	2	yes	—
531	C₂²×C₆₇	#585	1	2	yes	—
532	C₂²×C₆₇	#585	1	2	yes	—
533	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
534	C₂×D₆₇	—	2	4	no	—
535	C₂×D₆₇	—	2	4	no	—
536	C₂×D₆₇	—	2	16	no	—
537	C₂×D₆₇	—	2	4	no	—
538	C₂×D₆₇	—	2	4	no	—
539	C₂×D₆₇	—	2	4	no	—
540	C₂×D₆₇	—	4	16	no	—
541	C₂×D₆₇	—	4	8	no	—
542	C₂×D₆₇	—	8	16	no	—
543	C₂×D₆₇	C₂²×#41	1	8	yes	—
544	C₄×C₆₇	—	2	4	no	—
545	C₄×C₆₇	—	2	4	no	—
546	C₄×C₆₇	—	2	4	no	—
547	C₄×C₆₇	—	2	2	no	—
548	C₄×C₆₇	—	2	4	no	—
549	C₄×C₆₇	—	2	4	no	—
550	C₄×C₆₇	—	2	2	no	—
551	Dic₆₇	—	2	2	no	—
552	Dic₆₇	—	2	2	no	—
553	Dic₆₇	—	2	4	no	—
554	Dic₆₇	—	2	4	no	—
555	Dic₆₇	—	2	4	no	—
556	Dic₆₇	—	2	4	no	—
557	Dic₆₇	—	2	2	no	—
558	Dic₆₇	—	2	2	no	—
559	C₂×#3491	—	67	1	no	maximal, Sylow
560	C₂×C₆₇	—	2	4	no	—
561	C₂×C₆₇	—	4	4	no	—
562	C₂×C₆₇	#3491	1	4	yes	complemented
563	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
564	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
565	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
566	D₆₇	—	2	8	no	—
567	D₆₇	—	4	4	no	—
568	#3491	—	67	32	no	—
569	C₂×#552	—	67	2	no	—
570	C₂×#552	—	67	2	no	—
571	C₂×#552	—	67	2	no	—
572	C₂×#552	—	67	2	no	—
573	C₂×#551	—	67	2	no	—
574	C₂×#551	—	67	2	no	—
575	C₂×#551	—	67	2	no	—
576	C₂×#551	—	67	2	no	—
577	C₂×#543	—	67	1	no	—
578	C₂×#539	—	67	2	no	—
579	C₂×#539	—	67	1	no	—
580	C₂×#539	D₆₇	1	1	yes	characteristic, complemented
581	C₂×#534	—	67	1	no	—
582	C₂×#529	—	67	1	no	—
583	C₂×#529	—	67	1	no	—
584	C₂×#529	—	67	2	no	—
585	C₂²×#123	—	67	2	no	—
586	C₂×#518	—	67	2	no	—
587	C₂²×#117	—	67	1	no	—
588	C₆₇	C₂×#3491	1	1	yes	characteristic, complemented, Sylow
589	C₂³×D₄	—	67	2	no	—
590	C₂⁴×C₄	—	67	1	no	—
591	#552	—	67	32	no	—
592	#552	—	67	32	no	—
593	#552	—	67	32	no	—
594	#552	—	67	32	no	—
595	#551	—	67	32	no	—
596	#551	—	67	32	no	—
597	#551	—	67	32	no	—
598	#551	—	67	32	no	—
599	#543	—	67	16	no	—
600	#539	—	67	32	no	—
601	#539	—	67	16	no	—
602	#539	C₂×D₆₇	1	16	yes	complemented
603	#534	—	67	16	no	—
604	#529	—	67	16	no	—
605	#529	—	67	16	no	—
606	#529	—	67	32	no	—
607	C₂×#126	—	67	2	no	—
608	C₂×#126	—	67	2	no	—
609	C₂×#126	—	67	2	no	—
610	C₂×#126	—	67	2	no	—
611	C₂×#126	—	67	2	no	—
612	C₂×#126	—	67	2	no	—
613	C₂×#126	—	67	2	no	—
614	C₂×#126	C₂×D₆₇	1	2	yes	complemented
615	C₂×#125	—	67	2	no	—
616	C₂×#125	—	67	1	no	—
617	C₂×#125	—	67	1	no	—
618	C₂×#125	—	67	2	no	—
619	C₂×#125	—	67	2	no	—
620	C₂×#125	—	67	2	no	—
621	C₂×#125	C₂×D₆₇	1	2	yes	complemented
622	C₂×#124	—	67	1	no	—
623	C₂×#124	—	67	1	no	—
624	C₂×#124	—	67	2	no	—
625	C₂×#123	—	67	2	no	—
626	C₂×#123	—	67	2	no	—
627	C₂×#123	—	67	32	no	—
628	C₂×#123	—	67	2	no	—
629	C₂×#123	—	67	2	no	—
630	C₂×#123	—	67	2	no	—
631	C₂×#123	—	67	2	no	—
632	C₂×#123	—	67	2	no	—
633	C₂×#123	—	67	2	no	—
634	C₂×#123	—	67	2	no	—
635	C₂×#123	—	67	2	no	—
636	C₂×#123	—	67	2	no	—
637	C₂×#123	—	67	2	no	—
638	C₂×#123	C₂×D₆₇	1	2	yes	complemented
639	C₂×#123	C₂×D₆₇	1	2	yes	complemented
640	C₂×C₂²⋊Q₈	—	67	2	no	—
641	C₂×C₂²⋊Q₈	—	67	1	no	—
642	C₂×C₂²⋊Q₈	—	67	2	no	—
643	C₂×C₂²⋊Q₈	—	67	2	no	—
644	C₂×C₂²⋊Q₈	—	67	2	no	—
645	C₂×C₂²⋊Q₈	—	67	2	no	—
646	C₂×C₂²⋊Q₈	—	67	2	no	—
647	C₂×C₂²⋊Q₈	—	67	2	no	—
648	C₂×C₂²⋊Q₈	—	67	2	no	—
649	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
650	C₂×C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
651	C₂×#121	—	67	2	no	—
652	C₂×#121	—	67	1	no	—
653	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
654	C₂×#120	—	67	2	no	—
655	C₂×#120	—	67	2	no	—
656	#518	—	67	32	no	—
657	C₂×C₄×Q₈	—	67	1	no	—
658	C₂×C₄×Q₈	—	67	1	no	—
659	C₂×C₄×Q₈	—	67	2	no	—
660	C₂×C₄×D₄	—	67	2	no	—
661	C₂×C₄×D₄	—	67	1	no	—
662	C₂×C₄×D₄	—	67	2	no	—
663	C₂×C₄×D₄	—	67	2	no	—
664	C₂×C₄×D₄	—	67	2	no	—
665	C₂×C₄×D₄	—	67	2	no	—
666	C₂×C₄×D₄	—	67	1	no	—
667	C₂×C₄×D₄	—	67	2	no	—
668	C₂×C₄×D₄	—	67	2	no	—
669	C₂×C₄×D₄	—	67	2	no	—
670	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
671	C₂×#117	—	67	2	no	—
672	C₂×#117	—	67	2	no	—
673	C₂×#117	—	67	2	no	—
674	C₂×#117	—	67	2	no	—
675	C₂×#117	—	67	2	no	—
676	C₂×#117	—	67	2	no	—
677	C₂×#117	—	67	2	no	—
678	C₂×#117	—	67	16	no	—
679	C₂×#117	—	67	2	no	—
680	C₂×#117	—	67	2	no	—
681	C₂×#117	—	67	2	no	—
682	C₂²×C₄⋊C₄	—	67	1	no	—
683	C₂²×C₄⋊C₄	—	67	2	no	—
684	C₂²×C₄⋊C₄	—	67	2	no	—
685	C₂²×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
686	C₂²×C₂²⋊C₄	—	67	1	no	—
687	C₂²×C₂²⋊C₄	—	67	1	no	—
688	C₂²×C₂²⋊C₄	—	67	2	no	—
689	C₂²×C₂²⋊C₄	—	67	2	no	—
690	C₂²×C₂²⋊C₄	—	67	2	no	—
691	C₂²×C₂²⋊C₄	—	67	2	no	—
692	C₂²×C₂²⋊C₄	—	67	2	no	—
693	C₂²×C₄²	—	67	1	no	—
694	C₂²×C₄²	—	67	1	no	—
695	C₂⁵	—	67	1	no	—
696	C₂⁵	—	67	2	no	—
697	C₂²×Q₈	—	67	2	no	—
698	C₂²×Q₈	—	67	1	no	—
699	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
700	C₂²×D₄	—	67	2	no	—
701	C₂²×D₄	—	67	2	no	—
702	C₂²×D₄	—	67	2	no	—
703	C₂²×D₄	—	67	16	no	—
704	C₂²×D₄	—	67	1	no	—
705	C₂²×D₄	—	67	2	no	—
706	C₂²×D₄	—	134	16	no	—
707	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
708	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
709	C₂³×C₄	—	67	1	no	—
710	C₂³×C₄	—	67	1	no	—
711	C₂³×C₄	—	67	2	no	—
712	C₂³×C₄	—	67	2	no	—
713	C₂³×C₄	—	67	2	no	—
714	C₂³×C₄	—	67	2	no	—
715	C₂³×C₄	—	67	2	no	—
716	C₂³×C₄	—	67	1	no	—
717	C₂³×C₄	—	67	2	no	—
718	C₂³×C₄	—	67	2	no	—
719	C₂³×C₄	—	67	2	no	—
720	C₂³×C₄	—	67	8	no	—
721	C₂³×C₄	—	134	8	no	—
722	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
723	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
724	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
725	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
726	#126	—	67	16	no	—
727	#126	—	67	16	no	—
728	#126	—	67	16	no	—
729	#126	—	67	16	no	—
730	#126	—	67	16	no	—
731	#126	—	67	16	no	—
732	#126	—	67	16	no	—
733	#126	C₂²×D₆₇	1	16	yes	complemented
734	#125	—	67	16	no	—
735	#125	—	67	8	no	—
736	#125	—	67	8	no	—
737	#125	—	67	16	no	—
738	#125	—	67	16	no	—
739	#125	—	67	16	no	—
740	#125	C₂²×D₆₇	1	16	yes	complemented
741	#124	—	67	8	no	—
742	#124	—	67	8	no	—
743	#124	—	67	16	no	—
744	#123	—	67	16	no	—
745	#123	—	67	16	no	—
746	#123	—	67	16	no	—
747	#123	—	67	16	no	—
748	#123	—	67	16	no	—
749	#123	—	67	16	no	—
750	#123	—	67	16	no	—
751	#123	—	67	16	no	—
752	#123	—	67	16	no	—
753	#123	—	67	16	no	—
754	#123	—	67	16	no	—
755	#123	—	67	16	no	—
756	#123	C₂²×D₆₇	1	16	yes	complemented
757	#123	C₂²×D₆₇	1	16	yes	complemented
758	C₂²⋊Q₈	—	67	16	no	—
759	C₂²⋊Q₈	—	67	8	no	—
760	C₂²⋊Q₈	—	67	16	no	—
761	C₂²⋊Q₈	—	67	16	no	—
762	C₂²⋊Q₈	—	67	16	no	—
763	C₂²⋊Q₈	—	67	16	no	—
764	C₂²⋊Q₈	—	67	16	no	—
765	C₂²⋊Q₈	—	67	16	no	—
766	C₂²⋊Q₈	—	67	16	no	—
767	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
768	C₂²⋊Q₈	C₂²×D₆₇	1	16	yes	complemented
769	#121	—	67	16	no	—
770	#121	—	67	8	no	—
771	#121	C₂²×D₆₇	1	8	yes	—
772	#120	—	67	16	no	—
773	#120	—	67	16	no	—
774	C₄×Q₈	—	67	8	no	—
775	C₄×Q₈	—	67	8	no	—
776	C₄×Q₈	—	67	16	no	—
777	C₄×D₄	—	67	16	no	—
778	C₄×D₄	—	67	8	no	—
779	C₄×D₄	—	67	16	no	—
780	C₄×D₄	—	67	16	no	—
781	C₄×D₄	—	67	16	no	—
782	C₄×D₄	—	67	16	no	—
783	C₄×D₄	—	67	8	no	—
784	C₄×D₄	—	67	16	no	—
785	C₄×D₄	—	67	16	no	—
786	C₄×D₄	—	67	16	no	—
787	C₄×D₄	C₂²×D₆₇	1	16	yes	complemented
788	#117	—	67	16	no	—
789	#117	—	67	16	no	—
790	#117	—	67	16	no	—
791	#117	—	67	16	no	—
792	#117	—	67	16	no	—
793	#117	—	67	16	no	—
794	#117	—	67	16	no	—
795	#117	—	67	16	no	—
796	#117	—	67	16	no	—
797	#117	—	67	16	no	—
798	C₂×C₄⋊C₄	—	67	2	no	—
799	C₂×C₄⋊C₄	—	67	2	no	—
800	C₂×C₄⋊C₄	—	67	8	no	—
801	C₂×C₄⋊C₄	—	67	2	no	—
802	C₂×C₄⋊C₄	—	67	2	no	—
803	C₂×C₄⋊C₄	—	67	2	no	—
804	C₂×C₄⋊C₄	—	67	2	no	—
805	C₂×C₄⋊C₄	—	67	2	no	—
806	C₂×C₄⋊C₄	—	67	2	no	—
807	C₂×C₄⋊C₄	—	67	2	no	—
808	C₂×C₄⋊C₄	—	67	2	no	—
809	C₂×C₄⋊C₄	—	67	2	no	—
810	C₂×C₄⋊C₄	—	67	2	no	—
811	C₂×C₄⋊C₄	—	67	2	no	—
812	C₂×C₄⋊C₄	—	67	2	no	—
813	C₂×C₄⋊C₄	—	67	2	no	—
814	C₂×C₄⋊C₄	—	67	1	no	—
815	C₂×C₄⋊C₄	—	67	2	no	—
816	C₂×C₄⋊C₄	—	67	1	no	—
817	C₂×C₄⋊C₄	—	67	16	no	—
818	C₂×C₄⋊C₄	—	67	16	no	—
819	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
820	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
821	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
822	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
823	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
824	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
825	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
826	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
827	C₂×C₄⋊C₄	C₂²×D₆₇	1	8	yes	complemented
828	C₂×C₂²⋊C₄	—	67	2	no	—
829	C₂×C₂²⋊C₄	—	67	2	no	—
830	C₂×C₂²⋊C₄	—	67	2	no	—
831	C₂×C₂²⋊C₄	—	67	2	no	—
832	C₂×C₂²⋊C₄	—	67	2	no	—
833	C₂×C₂²⋊C₄	—	67	2	no	—
834	C₂×C₂²⋊C₄	—	67	2	no	—
835	C₂×C₂²⋊C₄	—	67	2	no	—
836	C₂×C₂²⋊C₄	—	67	2	no	—
837	C₂×C₂²⋊C₄	—	67	8	no	—
838	C₂×C₂²⋊C₄	—	67	2	no	—
839	C₂×C₂²⋊C₄	—	67	2	no	—
840	C₂×C₂²⋊C₄	—	67	8	no	—
841	C₂×C₂²⋊C₄	—	67	2	no	—
842	C₂×C₂²⋊C₄	—	67	2	no	—
843	C₂×C₂²⋊C₄	—	67	2	no	—
844	C₂×C₂²⋊C₄	—	67	2	no	—
845	C₂×C₂²⋊C₄	—	67	16	no	—
846	C₂×C₂²⋊C₄	—	67	2	no	—
847	C₂×C₂²⋊C₄	—	67	2	no	—
848	C₂×C₂²⋊C₄	—	67	2	no	—
849	C₂×C₂²⋊C₄	—	67	2	no	—
850	C₂×C₂²⋊C₄	—	67	16	no	—
851	C₂×C₂²⋊C₄	—	67	16	no	—
852	C₂×C₂²⋊C₄	—	67	16	no	—
853	C₂×C₂²⋊C₄	—	67	16	no	—
854	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
855	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
856	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
857	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
858	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
859	C₂×C₄²	—	67	1	no	—
860	C₂×C₄²	—	67	1	no	—
861	C₂×C₄²	—	67	2	no	—
862	C₂×C₄²	—	67	2	no	—
863	C₂×C₄²	—	67	2	no	—
864	C₂×C₄²	—	67	2	no	—
865	C₂×C₄²	—	67	1	no	—
866	C₂×C₄²	—	67	1	no	—
867	C₂×C₄²	—	67	2	no	—
868	C₂×C₄²	—	67	8	no	—
869	C₂×C₄²	—	67	8	no	—
870	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
871	C₂⁴	—	268	2	no	—
872	C₂⁴	—	268	2	no	—
873	C₂⁴	—	268	4	no	—
874	C₂⁴	—	268	4	no	—
875	C₂⁴	—	67	8	no	—
876	C₂⁴	—	67	4	no	—
877	C₂⁴	—	67	8	no	—
878	C₂⁴	—	67	2	no	—
879	C₂⁴	—	67	2	no	—
880	C₂⁴	—	134	8	no	—
881	C₂⁴	C₂³×D₆₇	1	2	yes	—
882	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
883	C₂×Q₈	—	4	2	no	—
884	C₂×Q₈	—	268	2	no	—
885	C₂×Q₈	—	268	4	no	—
886	C₂×Q₈	—	67	8	no	—
887	C₂×Q₈	—	67	4	no	—
888	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
889	C₂×D₄	—	2	8	no	—
890	C₂×D₄	—	4	2	no	—
891	C₂×D₄	—	268	2	no	—
892	C₂×D₄	—	268	4	no	—
893	C₂×D₄	—	67	8	no	—
894	C₂×D₄	—	67	8	no	—
895	C₂×D₄	—	67	8	no	—
896	C₂×D₄	—	67	4	no	—
897	C₂×D₄	—	67	8	no	—
898	C₂×D₄	—	134	8	no	—
899	C₂×D₄	—	134	64	no	—
900	C₂×D₄	—	134	8	no	—
901	C₂×D₄	—	134	8	no	—
902	C₂×D₄	C₂³×D₆₇	1	8	yes	—
903	C₂×D₄	C₂³×D₆₇	1	4	yes	—
904	C₂²×C₄	—	2	4	no	—
905	C₂²×C₄	—	4	2	no	—
906	C₂²×C₄	—	4	4	no	—
907	C₂²×C₄	—	4	2	no	—
908	C₂²×C₄	—	268	4	no	—
909	C₂²×C₄	—	268	4	no	—
910	C₂²×C₄	—	268	4	no	—
911	C₂²×C₄	—	268	4	no	—
912	C₂²×C₄	—	268	2	no	—
913	C₂²×C₄	—	268	4	no	—
914	C₂²×C₄	—	268	2	no	—
915	C₂²×C₄	—	67	4	no	—
916	C₂²×C₄	—	67	4	no	—
917	C₂²×C₄	—	67	8	no	—
918	C₂²×C₄	—	67	8	no	—
919	C₂²×C₄	—	67	8	no	—
920	C₂²×C₄	—	67	8	no	—
921	C₂²×C₄	—	67	8	no	—
922	C₂²×C₄	—	67	4	no	—
923	C₂²×C₄	—	67	1	no	—
924	C₂²×C₄	—	67	1	no	—
925	C₂²×C₄	—	67	1	no	—
926	C₂²×C₄	—	67	1	no	—
927	C₂²×C₄	—	67	2	no	—
928	C₂²×C₄	—	67	2	no	—
929	C₂²×C₄	—	67	2	no	—
930	C₂²×C₄	—	67	2	no	—
931	C₂²×C₄	—	67	8	no	—
932	C₂²×C₄	—	67	8	no	—
933	C₂²×C₄	—	67	8	no	—
934	C₂²×C₄	—	134	32	no	—
935	C₂²×C₄	—	134	8	no	—
936	C₂²×C₄	—	134	8	no	—
937	C₂²×C₄	—	134	8	no	—
938	C₂²×C₄	—	134	4	no	—
939	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
940	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
941	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
942	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
943	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
944	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
945	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
946	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
947	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
948	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
949	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
950	C₄⋊C₄	—	67	8	no	—
951	C₄⋊C₄	—	67	8	no	—
952	C₄⋊C₄	—	67	8	no	—
953	C₄⋊C₄	—	67	8	no	—
954	C₄⋊C₄	—	67	8	no	—
955	C₄⋊C₄	—	67	8	no	—
956	C₄⋊C₄	—	67	8	no	—
957	C₄⋊C₄	—	67	8	no	—
958	C₄⋊C₄	—	67	8	no	—
959	C₄⋊C₄	—	67	8	no	—
960	C₄⋊C₄	—	67	8	no	—
961	C₄⋊C₄	—	67	8	no	—
962	C₄⋊C₄	—	67	8	no	—
963	C₄⋊C₄	—	67	8	no	—
964	C₄⋊C₄	—	67	8	no	—
965	C₄⋊C₄	—	67	4	no	—
966	C₄⋊C₄	—	67	8	no	—
967	C₄⋊C₄	—	67	4	no	—
968	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
969	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
970	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
971	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
972	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
973	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
974	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
975	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
976	C₂²⋊C₄	—	67	8	no	—
977	C₂²⋊C₄	—	67	8	no	—
978	C₂²⋊C₄	—	67	8	no	—
979	C₂²⋊C₄	—	67	8	no	—
980	C₂²⋊C₄	—	67	8	no	—
981	C₂²⋊C₄	—	67	8	no	—
982	C₂²⋊C₄	—	67	8	no	—
983	C₂²⋊C₄	—	67	8	no	—
984	C₂²⋊C₄	—	67	8	no	—
985	C₂²⋊C₄	—	67	8	no	—
986	C₂²⋊C₄	—	67	8	no	—
987	C₂²⋊C₄	—	67	8	no	—
988	C₂²⋊C₄	—	67	8	no	—
989	C₂²⋊C₄	—	67	8	no	—
990	C₂²⋊C₄	—	67	8	no	—
991	C₂²⋊C₄	—	67	8	no	—
992	C₂²⋊C₄	—	67	8	no	—
993	C₂²⋊C₄	—	67	8	no	—
994	C₂²⋊C₄	—	67	8	no	—
995	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
996	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
997	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
998	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
999	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1000	C₄²	—	67	4	no	—
1001	C₄²	—	67	4	no	—
1002	C₄²	—	67	8	no	—
1003	C₄²	—	67	4	no	—
1004	C₄²	—	67	4	no	—
1005	C₄²	—	67	8	no	—
1006	C₄²	—	67	8	no	—
1007	C₄²	—	67	8	no	—
1008	C₄²	—	67	8	no	—
1009	C₄²	C₂³×D₆₇	1	8	yes	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	2	no	—
1012	C₂³	—	2	4	no	—
1013	C₂³	—	2	4	no	—
1014	C₂³	—	2	4	no	—
1015	C₂³	—	268	16	no	—
1016	C₂³	—	268	4	no	—
1017	C₂³	—	268	4	no	—
1018	C₂³	—	268	8	no	—
1019	C₂³	—	268	8	no	—
1020	C₂³	—	536	16	no	—
1021	C₂³	—	67	16	no	—
1022	C₂³	—	67	8	no	—
1023	C₂³	—	67	4	no	—
1024	C₂³	—	67	4	no	—
1025	C₂³	—	134	16	no	—
1026	C₂³	—	134	4	no	—
1027	C₂³	—	134	4	no	—
1028	C₂³	—	134	4	no	—
1029	C₂³	—	134	4	no	—
1030	C₂³	—	134	4	no	—
1031	C₂³	#41×D₆₇	1	4	yes	—
1032	C₂³	C₂⁴×D₆₇	1	4	yes	—
1033	C₂³	C₂⁴×D₆₇	1	2	yes	—
1034	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1035	Q₈	—	4	4	no	—
1036	Q₈	—	268	4	no	—
1037	Q₈	—	268	8	no	—
1038	D₄	—	2	16	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	268	4	no	—
1041	D₄	—	268	8	no	—
1042	D₄	—	134	16	no	—
1043	D₄	—	134	16	no	—
1044	D₄	—	134	16	no	—
1045	C₂×C₄	—	2	8	no	—
1046	C₂×C₄	—	2	4	no	—
1047	C₂×C₄	—	2	4	no	—
1048	C₂×C₄	—	2	4	no	—
1049	C₂×C₄	—	2	4	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	4	no	—
1053	C₂×C₄	—	4	4	no	—
1054	C₂×C₄	—	4	8	no	—
1055	C₂×C₄	—	4	4	no	—
1056	C₂×C₄	—	268	8	no	—
1057	C₂×C₄	—	268	8	no	—
1058	C₂×C₄	—	268	8	no	—
1059	C₂×C₄	—	268	8	no	—
1060	C₂×C₄	—	268	4	no	—
1061	C₂×C₄	—	268	8	no	—
1062	C₂×C₄	—	268	4	no	—
1063	C₂×C₄	—	67	2	no	—
1064	C₂×C₄	—	67	2	no	—
1065	C₂×C₄	—	67	2	no	—
1066	C₂×C₄	—	67	2	no	—
1067	C₂×C₄	—	67	4	no	—
1068	C₂×C₄	—	67	4	no	—
1069	C₂×C₄	—	67	4	no	—
1070	C₂×C₄	—	67	4	no	—
1071	C₂×C₄	—	134	16	no	—
1072	C₂×C₄	—	134	16	no	—
1073	C₂×C₄	—	134	16	no	—
1074	C₂×C₄	—	134	8	no	—
1075	C₂×C₄	—	134	2	no	—
1076	C₂×C₄	—	134	2	no	—
1077	C₂×C₄	—	134	4	no	—
1078	C₂×C₄	—	134	4	no	—
1079	C₂×C₄	—	134	2	no	—
1080	C₂×C₄	—	134	2	no	—
1081	C₂×C₄	—	134	4	no	—
1082	C₂×C₄	—	134	4	no	—
1083	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1084	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1085	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1086	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1087	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1088	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1089	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1090	C₂²	—	2	8	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	4	no	—
1094	C₂²	—	2	4	no	—
1095	C₂²	—	2	4	no	—
1096	C₂²	—	4	8	no	—
1097	C₂²	—	268	16	no	—
1098	C₂²	—	268	8	no	—
1099	C₂²	—	536	16	no	—
1100	C₂²	—	67	8	no	—
1101	C₂²	—	134	4	no	—
1102	C₂²	—	134	4	no	—
1103	C₂²	—	134	4	no	—
1104	C₂²	—	134	16	no	—
1105	C₂²	—	134	4	no	—
1106	C₂²	—	134	4	no	—
1107	C₂²	C₂×#41×D₆₇	1	4	yes	—
1108	C₂²	C₂×#41×D₆₇	1	2	yes	—
1109	C₂²	#16864231	1	2	yes	—
1110	C₂²	#16864233	1	2	yes	—
1111	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1112	C₄	—	2	4	no	—
1113	C₄	—	2	4	no	—
1114	C₄	—	2	4	no	—
1115	C₄	—	2	4	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	4	no	—
1119	C₄	—	134	2	no	—
1120	C₄	—	134	2	no	—
1121	C₄	—	134	4	no	—
1122	C₄	—	134	4	no	—
1123	C₄	—	134	2	no	—
1124	C₄	—	134	2	no	—
1125	C₄	—	134	4	no	—
1126	C₄	—	134	4	no	—
1127	C₂	—	2	4	no	—
1128	C₂	—	4	4	no	—
1129	C₂	—	268	4	no	—
1130	C₂	—	134	8	no	—
1131	C₂	#22573903	1	4	yes	direct product factor
1132	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
1133	C₂	C₂×#16864231	1	1	yes	characteristic
1134	C₂	C₂×#16864233	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#539×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
prime radical	C₂×#16863954	C₂
hypercenter	C₂×#539	D₆₇
hypocenter	C₆₇	C₂×#3491
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#539

Complements

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

N	H ≅ G/N	type
1. #22573903	C₂	direct (N × H)
2. C₂×#16864084	C₂	semidirect
3. C₂×#16864082	C₂	semidirect
4. C₂×#16864080	C₂	semidirect
5. C₂×#16864078	C₂	semidirect
6. C₂×#16864074	C₂	semidirect
7. C₂×#16864073	C₂	semidirect
8. C₂×#16864071	C₂	semidirect
9. C₂×#16864069	C₂	semidirect
10. C₂×#16864021	C₂	semidirect
11. C₂×#16863993	C₂	semidirect
12. C₂×#16863990	C₂	semidirect
14. C₂×#16863932	C₂	semidirect
15. C₂×#16863927	C₂	semidirect
16. C₂×#16863926	C₂	semidirect
17. C₂×#123×D₆₇	C₂	semidirect
18. C₂×#16863868	C₂	semidirect
19. C₂²×#14524001	C₂	semidirect
20. C₂×#539×C₆₇	C₂	semidirect
23. #16864084	C₂²	semidirect
24. #16864082	C₂²	semidirect
25. #16864080	C₂²	semidirect
26. #16864078	C₂²	semidirect
27. #16864074	C₂²	semidirect
28. #16864073	C₂²	semidirect
29. #16864071	C₂²	semidirect
30. #16864069	C₂²	semidirect
31. #16864021	C₂²	semidirect
32. #16863993	C₂²	semidirect
33. #16863990	C₂²	semidirect
35. #16863932	C₂²	semidirect
36. #16863927	C₂²	semidirect
37. #16863926	C₂²	semidirect
38. C₂×#14524038	C₂²	semidirect
39. C₂×#14524038	C₂²	semidirect
40. C₂×#14524038	C₂²	semidirect
41. C₂×#14524038	C₂²	semidirect
42. C₂×#14524036	C₂²	semidirect
43. C₂×#14524036	C₂²	semidirect
44. C₂×#14524036	C₂²	semidirect
45. C₂×#14524034	C₂²	semidirect
46. C₂×#14524034	C₂²	semidirect
47. C₂×#14524034	C₂²	semidirect
48. C₂×#14524033	C₂²	semidirect
49. C₂×#14524033	C₂²	semidirect
50. C₂×#14524033	C₂²	semidirect
51. C₂×#14524032	C₂²	semidirect
52. C₂×#14524030	C₂²	semidirect
53. C₂×#14524029	C₂²	semidirect
57. C₂×#14524028	C₂²	semidirect
58. C₂×#14524027	C₂²	semidirect
59. C₂×#14524027	C₂²	semidirect
60. C₂×#14524026	C₂²	semidirect
64. C₂×#14524025	C₂²	semidirect
65. C₂×#14524024	C₂²	semidirect
66. #123×D₆₇	C₂²	semidirect
67. C₂×#14524023	C₂²	semidirect
68. C₂×#14524023	C₂²	semidirect
69. C₂×#14524022	C₂²	semidirect
70. C₂×#14524021	C₂²	semidirect
71. C₂×#14524021	C₂²	semidirect
72. C₂×#14524021	C₂²	semidirect
73. C₂×#14524020	C₂²	semidirect
74. C₂×#14524020	C₂²	semidirect
75. C₂×#14524019	C₂²	semidirect
80. #16863868	C₂²	semidirect
81. C₂×Q₈×Dic₆₇	C₂²	semidirect
82. C₂×C₄×Dic₁₃₄	C₂²	semidirect
83. C₂×#14524008	C₂²	semidirect
85. C₂×D₄×Dic₆₇	C₂²	semidirect
86. C₂×D₄×Dic₆₇	C₂²	semidirect
88. C₂×#14524005	C₂²	semidirect
90. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
91. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
93. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
94. C₂×#14524002	C₂²	semidirect
95. C₂×#14524001	C₂²	semidirect
96. C₂×#14524001	C₂²	semidirect
97. C₂×#14524001	C₂²	semidirect
98. C₂×#14524001	C₂²	semidirect
99. C₂×#14524001	C₂²	semidirect
100. C₂×#14524001	C₂²	semidirect
101. C₂×#14524001	C₂²	semidirect
102. C₂×#14524000	C₂²	semidirect
103. C₂×#14524000	C₂²	semidirect
104. C₂×#14523999	C₂²	semidirect
105. C₂²×C₄⋊Dic₆₇	C₂²	semidirect
106. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
107. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
110. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
112. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
113. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
114. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
115. C₂²×C₄×Dic₆₇	C₂²	semidirect
116. C₂²×C₄×Dic₆₇	C₂²	semidirect
117. #539×C₆₇	C₂²	semidirect
118. C₂×#126×C₆₇	C₂²	semidirect
119. C₂×#125×C₆₇	C₂²	semidirect
120. C₂×#123×C₆₇	C₂²	semidirect
121. C₂×#123×C₆₇	C₂²	semidirect
122. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
123. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
125. C₂×C₄×D₄×C₆₇	C₂²	semidirect
126. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
151. #14524038	C₂³	semidirect
152. #14524038	C₂³	semidirect
153. #14524038	C₂³	semidirect
154. #14524038	C₂³	semidirect
155. #14524036	C₂³	semidirect
156. #14524036	C₂³	semidirect
157. #14524036	C₂³	semidirect
158. #14524034	C₂³	semidirect
159. #14524034	C₂³	semidirect
160. #14524034	C₂³	semidirect
161. #14524033	C₂³	semidirect
162. #14524033	C₂³	semidirect
163. #14524033	C₂³	semidirect
164. #14524032	C₂³	semidirect
165. #14524030	C₂³	semidirect
166. #14524029	C₂³	semidirect
170. #14524028	C₂³	semidirect
171. #14524027	C₂³	semidirect
172. #14524027	C₂³	semidirect
173. #14524026	C₂³	semidirect
177. #14524025	C₂³	semidirect
178. #14524024	C₂³	semidirect
179. #14524023	C₂³	semidirect
180. #14524023	C₂³	semidirect
181. #14524022	C₂³	semidirect
182. #14524021	C₂³	semidirect
183. #14524021	C₂³	semidirect
184. #14524021	C₂³	semidirect
185. #14524020	C₂³	semidirect
186. #14524020	C₂³	semidirect
187. #14524019	C₂³	semidirect
192. Q₈×Dic₆₇	C₂³	semidirect
193. C₄×Dic₁₃₄	C₂³	semidirect
194. #14524008	C₂³	semidirect
196. D₄×Dic₆₇	C₂³	semidirect
197. D₄×Dic₆₇	C₂³	semidirect
199. #14524005	C₂³	semidirect
201. C₄×C₂²⋊D₆₇	C₂³	semidirect
202. C₄×C₂²⋊D₆₇	C₂³	semidirect
204. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
205. #14524002	C₂³	semidirect
206. #14524001	C₂³	semidirect
207. #14524001	C₂³	semidirect
208. #14524001	C₂³	semidirect
209. #14524001	C₂³	semidirect
210. #14524001	C₂³	semidirect
211. #14524001	C₂³	semidirect
212. #14524000	C₂³	semidirect
213. #14524000	C₂³	semidirect
214. #14523999	C₂³	semidirect
223. C₂×C₄⋊Dic₆₇	C₂³	semidirect
234. C₄⋊C₄×D₆₇	C₂³	semidirect
235. C₄⋊C₄×D₆₇	C₂³	semidirect
257. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
259. C₂²⋊C₄×D₆₇	C₂³	semidirect
260. C₂²⋊C₄×D₆₇	C₂³	semidirect
261. C₂²⋊C₄×D₆₇	C₂³	semidirect
271. C₂×C₄×Dic₆₇	C₂³	semidirect
272. C₂×C₄×Dic₆₇	C₂³	semidirect
280. #126×C₆₇	C₂³	semidirect
281. #125×C₆₇	C₂³	semidirect
282. #123×C₆₇	C₂³	semidirect
283. #123×C₆₇	C₂³	semidirect
284. C₂²⋊Q₈×C₆₇	C₂³	semidirect
285. C₂²⋊Q₈×C₆₇	C₂³	semidirect
287. C₄×D₄×C₆₇	C₂³	semidirect
296. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
562. C₂×C₆₇	#3491	semidirect
580. C₂×#539	D₆₇	semidirect
588. C₆₇	C₂×#3491	semidirect
602. #539	C₂×D₆₇	semidirect
614. C₂×#126	C₂×D₆₇	semidirect
621. C₂×#125	C₂×D₆₇	semidirect
638. C₂×#123	C₂×D₆₇	semidirect
639. C₂×#123	C₂×D₆₇	semidirect
649. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
650. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
670. C₂×C₄×D₄	C₂×D₆₇	semidirect
685. C₂²×C₄⋊C₄	C₂×D₆₇	semidirect
733. #126	C₂²×D₆₇	semidirect
740. #125	C₂²×D₆₇	semidirect
756. #123	C₂²×D₆₇	semidirect
757. #123	C₂²×D₆₇	semidirect
767. C₂²⋊Q₈	C₂²×D₆₇	semidirect
768. C₂²⋊Q₈	C₂²×D₆₇	semidirect
787. C₄×D₄	C₂²×D₆₇	semidirect
827. C₂×C₄⋊C₄	C₂²×D₆₇	semidirect
1131. C₂	#22573903	direct (N × H)

Maximal subgroups

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

subgroup	index
#22573903	2
C₂×#16864084	2
C₂×#16864082	2
C₂×#16864080	2
C₂×#16864078	2
C₂×#16864074	2
C₂×#16864073	2
C₂×#16864071	2
C₂×#16864069	2
C₂×#16864021	2
C₂×#16863993	2
C₂×#16863990	2
C₂×#16863954	2
C₂×#16863932	2
C₂×#16863927	2
C₂×#16863926	2
C₂×#123×D₆₇	2
C₂×#16863868	2
C₂²×#14524001	2
C₂×#539×C₆₇	2
C₂×#3491	67

Subgroups — C2×#22573903 #31763883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22573903 #31763883