Subgroups — C₂×#22574539 #31763421

Order 17152.

8814 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574539	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864137	C₂	1	4	yes	maximal, complemented
3	C₂×#16864131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16864068	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16864067	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864042	C₂	1	2	yes	maximal, complemented
7	C₂×#16864037	C₂	1	2	yes	maximal, complemented
8	C₂×D₄×D₂₆₈	C₂	1	2	yes	maximal, complemented
9	C₂×D₄×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16864030	C₂	1	2	yes	maximal, complemented
11	C₂×#16864002	C₂	1	2	yes	maximal, complemented
12	C₂×#16864001	C₂	1	2	yes	maximal, complemented
13	C₂×#16863965	C₂	1	2	yes	maximal, complemented
14	C₂×#16863964	C₂	1	2	yes	maximal, complemented
15	C₂×#16863957	C₂	1	4	yes	maximal, complemented
16	C₂²×#14524040	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#16863930	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#11761629	C₂²	1	2	yes	complemented
20	C₂²×#11761628	C₂²	1	2	yes	complemented
21	C₂³×D₂₆₈	C₂²	1	2	yes	complemented
22	C₂³×D₂₆₈	C₂²	1	2	yes	complemented
23	C₂³×D₂₆₈	C₂²	1	2	yes	complemented
24	C₂³×D₂₆₈	C₂²	1	2	yes	complemented
25	C₂²×D₄×D₆₇	C₂²	1	4	yes	complemented
26	C₂²×D₄×D₆₇	C₂²	1	2	yes	complemented
27	#16864137	C₂²	1	64	yes	complemented
28	#16864131	C₂²	1	16	yes	complemented
29	#16864068	C₂²	1	16	yes	complemented
30	#16864067	C₂²	1	16	yes	complemented
31	#16864042	C₂²	1	32	yes	complemented
32	#16864037	C₂²	1	32	yes	complemented
33	D₄×D₂₆₈	C₂²	1	32	yes	complemented
34	D₄×D₂₆₈	C₂²	1	16	yes	complemented
35	#16864030	C₂²	1	32	yes	complemented
36	#16864002	C₂²	1	32	yes	complemented
37	#16864001	C₂²	1	32	yes	complemented
38	#16863965	C₂²	1	32	yes	complemented
39	#16863964	C₂²	1	32	yes	complemented
40	#16863957	C₂²	1	64	yes	complemented
41	C₂×#14524040	C₂²	1	1	yes	characteristic
42	C₂×#14524040	C₂²	1	2	yes	complemented
43	C₂×#14524040	C₂²	1	2	yes	complemented
44	C₂×#14524040	C₂²	1	2	yes	complemented
45	C₂×#14524040	C₂²	1	1	yes	characteristic, complemented
46	C₂×#14524040	C₂²	1	2	yes	complemented
47	C₂×#14524040	C₂²	1	16	yes	complemented
48	C₂×#14524039	C₂²	1	2	yes	complemented
49	#16863930	C₂²	1	16	yes	complemented
50	C₂×#14524037	C₂²	1	2	yes	complemented
51	C₂×#14524035	C₂²	1	1	yes	characteristic, complemented
52	C₂×#14524032	C₂²	1	2	yes	complemented
53	C₂×#14524031	C₂²	1	2	yes	complemented
54	C₂×#14524031	C₂²	1	1	yes	characteristic, complemented
55	C₂×#14524028	C₂²	1	4	yes	complemented
56	C₂×#14524028	C₂²	1	4	yes	complemented
57	C₂×#14524028	C₂²	1	4	yes	complemented
58	C₂×#14524028	C₂²	1	4	yes	complemented
59	C₂×#14524026	C₂²	1	2	yes	complemented
60	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
61	C₂×#14524018	C₂²	1	2	yes	complemented
62	C₂×#14524018	C₂²	1	2	yes	complemented
63	C₂×#14524018	C₂²	1	4	yes	complemented
64	C₂×#14524018	C₂²	1	4	yes	complemented
65	C₂×#14524018	C₂²	1	4	yes	complemented
66	C₂×#14524018	C₂²	1	4	yes	complemented
67	C₂×#14524017	C₂²	1	1	yes	characteristic
68	C₂×#14524017	C₂²	1	2	yes	complemented
69	C₂×#14524017	C₂²	1	2	yes	complemented
70	C₂×#14524016	C₂²	1	4	yes	complemented
71	C₂×#14524016	C₂²	1	4	yes	complemented
72	C₂×#14524016	C₂²	1	4	yes	complemented
73	C₂×#14524016	C₂²	1	4	yes	complemented
74	C₂×#14524013	C₂²	1	4	yes	complemented
75	C₂×#14524013	C₂²	1	4	yes	complemented
76	C₂×#14524013	C₂²	1	4	yes	complemented
77	C₂×#14524013	C₂²	1	4	yes	complemented
78	C₂×#14524013	C₂²	1	4	yes	complemented
79	C₂×#14524011	C₂²	1	4	yes	complemented
80	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
82	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
83	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
84	C₂×#14524005	C₂²	1	2	yes	complemented
85	C₂×#14524005	C₂²	1	2	yes	complemented
86	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
87	C₂×#14524000	C₂²	1	2	yes	complemented
88	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
89	#529×C₆₇	C₂²	1	16	yes	complemented
90	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
91	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
96	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
98	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
100	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₂⁴×D₆₇	C₂³	1	4	yes	—
102	C₂⁴×D₆₇	C₂³	1	4	yes	—
103	C₂×#11761629	—	4	8	no	—
104	C₂×#11761629	C₂³	1	16	yes	complemented
105	C₂×#11761628	—	4	8	no	—
106	C₂×#11761628	C₂³	1	16	yes	complemented
107	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
108	C₂²×D₂₆₈	—	4	8	no	—
109	C₂²×D₂₆₈	—	4	8	no	—
110	C₂²×D₂₆₈	—	4	8	no	—
111	C₂²×D₂₆₈	—	4	8	no	—
112	C₂²×D₂₆₈	C₂³	1	2	yes	—
113	C₂²×D₂₆₈	C₂³	1	2	yes	—
114	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
115	C₂²×D₂₆₈	C₂³	1	2	yes	—
116	C₂²×D₂₆₈	C₂³	1	2	yes	—
117	C₂²×D₂₆₈	C₂³	1	4	yes	—
118	C₂²×D₂₆₈	C₂³	1	4	yes	—
119	C₂²×D₂₆₈	C₂³	1	2	yes	—
120	C₂²×D₂₆₈	C₂³	1	4	yes	—
121	C₂²×D₂₆₈	C₂³	1	4	yes	—
122	C₂²×D₂₆₈	C₂³	1	4	yes	—
123	C₂²×D₂₆₈	C₂³	1	4	yes	—
124	C₂²×D₂₆₈	C₂³	1	2	yes	—
125	C₂²×D₂₆₈	C₂³	1	16	yes	complemented
126	C₂²×D₂₆₈	C₂³	1	16	yes	complemented
127	C₂²×D₂₆₈	C₂³	1	16	yes	complemented
128	C₂²×D₂₆₈	C₂³	1	16	yes	complemented
129	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
130	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
131	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
132	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
133	C₂×D₄×D₆₇	—	4	8	no	—
134	C₂×D₄×D₆₇	—	4	16	no	—
135	C₂×D₄×D₆₇	C₂³	1	32	yes	complemented
136	C₂×D₄×D₆₇	C₂³	1	16	yes	complemented
137	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
138	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
139	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
140	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
141	#14524040	C₂³	1	8	yes	—
142	#14524040	C₂³	1	16	yes	complemented
143	#14524040	C₂³	1	16	yes	complemented
144	#14524040	C₂³	1	16	yes	complemented
145	#14524040	C₂³	1	8	yes	complemented
146	#14524040	C₂³	1	16	yes	complemented
147	#14524039	C₂³	1	16	yes	complemented
148	#14524037	C₂³	1	16	yes	complemented
149	#14524035	C₂³	1	8	yes	complemented
150	#14524032	C₂³	1	16	yes	complemented
151	#14524031	C₂³	1	16	yes	complemented
152	#14524031	C₂³	1	8	yes	complemented
153	#14524028	C₂³	1	32	yes	complemented
154	#14524028	C₂³	1	32	yes	complemented
155	#14524028	C₂³	1	32	yes	complemented
156	#14524028	C₂³	1	32	yes	complemented
157	#14524026	C₂³	1	16	yes	complemented
158	#14524022	C₂³	1	8	yes	complemented
159	#14524018	C₂³	1	16	yes	complemented
160	#14524018	C₂³	1	16	yes	complemented
161	#14524018	C₂³	1	32	yes	complemented
162	#14524018	C₂³	1	32	yes	complemented
163	#14524018	C₂³	1	32	yes	complemented
164	#14524018	C₂³	1	32	yes	complemented
165	#14524017	C₂³	1	8	yes	—
166	#14524017	C₂³	1	16	yes	complemented
167	#14524017	C₂³	1	16	yes	complemented
168	#14524016	C₂³	1	32	yes	complemented
169	#14524016	C₂³	1	32	yes	complemented
170	#14524016	C₂³	1	32	yes	complemented
171	#14524016	C₂³	1	32	yes	complemented
172	#14524013	C₂³	1	32	yes	complemented
173	#14524013	C₂³	1	32	yes	complemented
174	#14524013	C₂³	1	32	yes	complemented
175	#14524013	C₂³	1	32	yes	complemented
176	#14524013	C₂³	1	32	yes	complemented
177	#14524011	C₂³	1	32	yes	complemented
178	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
179	C₄×D₂₆₈	C₂³	1	16	yes	complemented
180	C₄×D₂₆₈	C₂³	1	16	yes	complemented
181	C₄×D₂₆₈	C₂³	1	8	yes	complemented
182	#14524005	C₂³	1	16	yes	complemented
183	#14524005	C₂³	1	16	yes	complemented
184	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
185	#14524000	C₂³	1	16	yes	complemented
186	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
188	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
189	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
190	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
191	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
192	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
193	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
194	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
195	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
196	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
197	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
198	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
199	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
200	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
201	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
202	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
203	C₂²⋊C₄×D₆₇	C₂³	1	32	yes	complemented
204	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
205	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
206	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
207	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
212	#126×C₆₇	C₂³	1	16	yes	complemented
213	#125×C₆₇	C₂³	1	8	yes	complemented
214	#124×C₆₇	C₂³	1	8	yes	complemented
215	#123×C₆₇	C₂³	1	16	yes	complemented
216	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
217	#121×C₆₇	C₂³	1	8	yes	—
218	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
219	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
220	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
221	#117×C₆₇	C₂³	1	16	yes	complemented
222	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
233	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
238	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
239	C₂³×D₆₇	—	2	16	no	—
240	C₂³×D₆₇	—	4	8	no	—
241	C₂³×D₆₇	—	4	8	no	—
242	C₂³×D₆₇	—	4	8	no	—
243	C₂³×D₆₇	—	4	8	no	—
244	C₂³×D₆₇	—	4	8	no	—
245	C₂³×D₆₇	C₂⁴	1	2	yes	—
246	C₂³×D₆₇	C₂⁴	1	4	yes	—
247	C₂³×D₆₇	C₂⁴	1	4	yes	—
248	C₂³×D₆₇	C₂⁴	1	16	yes	—
249	C₂³×D₆₇	C₂⁴	1	16	yes	—
250	#11761629	—	4	32	no	—
251	#11761628	—	4	32	no	—
252	C₂×Dic₁₃₄	—	2	4	no	—
253	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
254	C₂×D₂₆₈	—	2	8	no	—
255	C₂×D₂₆₈	—	2	4	no	—
256	C₂×D₂₆₈	—	2	8	no	—
257	C₂×D₂₆₈	—	2	8	no	—
258	C₂×D₂₆₈	—	2	8	no	—
259	C₂×D₂₆₈	—	4	32	no	—
260	C₂×D₂₆₈	—	4	32	no	—
261	C₂×D₂₆₈	—	4	32	no	—
262	C₂×D₂₆₈	—	4	8	no	—
263	C₂×D₂₆₈	—	4	8	no	—
264	C₂×D₂₆₈	—	4	8	no	—
265	C₂×D₂₆₈	—	4	8	no	—
266	C₂×D₂₆₈	—	4	4	no	—
267	C₂×D₂₆₈	—	4	8	no	—
268	C₂×D₂₆₈	—	4	4	no	—
269	C₂×D₂₆₈	—	4	32	no	—
270	C₂×D₂₆₈	—	4	8	no	—
271	C₂×D₂₆₈	C₂⁴	1	8	yes	—
272	C₂×D₂₆₈	C₂⁴	1	8	yes	—
273	C₂×D₂₆₈	C₂⁴	1	4	yes	—
274	C₂×D₂₆₈	C₂⁴	1	8	yes	—
275	C₂×D₂₆₈	C₂⁴	1	8	yes	—
276	C₂×D₂₆₈	C₂⁴	1	16	yes	—
277	C₂×D₂₆₈	C₂⁴	1	16	yes	—
278	C₂×D₂₆₈	C₂⁴	1	8	yes	—
279	C₂×D₂₆₈	C₂⁴	1	16	yes	—
280	C₂×D₂₆₈	C₂⁴	1	16	yes	—
281	C₂×D₂₆₈	C₂⁴	1	16	yes	—
282	C₂×D₂₆₈	C₂⁴	1	16	yes	—
283	C₂×D₂₆₈	C₂⁴	1	8	yes	—
284	C₂×C₂²⋊D₆₇	—	2	8	no	—
285	C₂×C₂²⋊D₆₇	—	4	8	no	—
286	C₂×C₂²⋊D₆₇	—	4	8	no	—
287	C₂×C₂²⋊D₆₇	—	4	8	no	—
288	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
289	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
290	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
291	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
292	D₄×D₆₇	—	4	32	no	—
293	D₄×D₆₇	—	4	64	no	—
294	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
295	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
296	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
297	C₂×C₄×D₆₇	—	2	8	no	—
298	C₂×C₄×D₆₇	—	4	8	no	—
299	C₂×C₄×D₆₇	—	4	8	no	—
300	C₂×C₄×D₆₇	—	4	8	no	—
301	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
302	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
303	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
304	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
305	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
306	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
307	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
308	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
309	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
310	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
311	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
312	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
313	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
314	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
315	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
316	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
317	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
318	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
319	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
320	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
321	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
322	C₄×Dic₆₇	C₂⁴	1	8	yes	—
323	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
324	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₆₇	—	2	4	no	—
326	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
327	C₂×D₄×C₆₇	—	2	8	no	—
328	C₂×D₄×C₆₇	—	2	4	no	—
329	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
330	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
331	C₂²×C₄×C₆₇	—	2	4	no	—
332	C₂²×C₄×C₆₇	—	2	4	no	—
333	C₂²×C₄×C₆₇	—	2	4	no	—
334	C₂²×C₄×C₆₇	—	2	8	no	—
335	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
342	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
343	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
344	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
346	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
349	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
350	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
351	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
352	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
353	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
354	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
355	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
356	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
357	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
358	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
359	C₄²×C₆₇	C₂⁴	1	4	yes	—
360	C₄²×C₆₇	C₂⁴	1	4	yes	—
361	C₄²×C₆₇	C₂⁴	1	4	yes	—
362	C₄²×C₆₇	C₂⁴	1	4	yes	—
363	C₄²×C₆₇	C₂⁴	1	8	yes	—
364	C₂³×C₆₇	—	2	2	no	—
365	C₂³×C₆₇	—	2	2	no	—
366	C₂³×C₆₇	—	2	4	no	—
367	C₂³×C₆₇	—	2	4	no	—
368	C₂³×C₆₇	—	2	4	no	—
369	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
370	C₂³×C₆₇	C₂⁵	1	4	yes	—
371	C₂³×C₆₇	C₂⁵	1	2	yes	—
372	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
373	C₂²×D₆₇	—	2	4	no	—
374	C₂²×D₆₇	—	2	8	no	—
375	C₂²×D₆₇	—	2	8	no	—
376	C₂²×D₆₇	—	2	8	no	—
377	C₂²×D₆₇	—	2	4	no	—
378	C₂²×D₆₇	—	2	8	no	—
379	C₂²×D₆₇	—	2	8	no	—
380	C₂²×D₆₇	—	2	4	no	—
381	C₂²×D₆₇	—	2	8	no	—
382	C₂²×D₆₇	—	2	32	no	—
383	C₂²×D₆₇	—	4	16	no	—
384	C₂²×D₆₇	—	4	16	no	—
385	C₂²×D₆₇	—	4	16	no	—
386	C₂²×D₆₇	—	4	16	no	—
387	C₂²×D₆₇	—	4	16	no	—
388	C₂²×D₆₇	—	8	32	no	—
389	C₂²×D₆₇	—	8	32	no	—
390	C₂²×D₆₇	C₂⁵	1	4	yes	—
391	C₂²×D₆₇	C₂⁵	1	8	yes	—
392	C₂²×D₆₇	C₂⁵	1	8	yes	—
393	Q₈×C₆₇	—	2	8	no	—
394	D₄×C₆₇	—	2	16	no	—
395	D₄×C₆₇	—	2	8	no	—
396	C₂×C₄×C₆₇	—	2	4	no	—
397	C₂×C₄×C₆₇	—	2	8	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	4	no	—
403	C₂×C₄×C₆₇	—	2	4	no	—
404	C₂×C₄×C₆₇	—	2	8	no	—
405	C₂×C₄×C₆₇	—	2	8	no	—
406	C₂×C₄×C₆₇	—	2	16	no	—
407	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
408	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
409	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
410	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
411	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
412	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
413	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
414	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
415	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
416	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
417	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
418	C₂²⋊D₆₇	—	2	16	no	—
419	C₂²⋊D₆₇	—	4	16	no	—
420	C₂²⋊D₆₇	—	4	16	no	—
421	C₂²⋊D₆₇	—	4	16	no	—
422	C₂×Dic₆₇	—	2	4	no	—
423	C₂×Dic₆₇	—	2	4	no	—
424	C₂×Dic₆₇	—	2	4	no	—
425	C₂×Dic₆₇	C₂⁵	1	4	yes	—
426	C₂×Dic₆₇	C₂⁵	1	4	yes	—
427	C₂×Dic₆₇	C₂⁵	1	4	yes	—
428	D₂₆₈	—	2	16	no	—
429	D₂₆₈	—	2	8	no	—
430	D₂₆₈	—	2	16	no	—
431	D₂₆₈	—	2	16	no	—
432	D₂₆₈	—	2	16	no	—
433	D₂₆₈	—	4	16	no	—
434	D₂₆₈	—	4	16	no	—
435	D₂₆₈	—	4	16	no	—
436	D₂₆₈	—	4	16	no	—
437	D₂₆₈	—	4	8	no	—
438	D₂₆₈	—	4	16	no	—
439	D₂₆₈	—	4	8	no	—
440	D₂₆₈	—	4	16	no	—
441	C₄×D₆₇	—	2	16	no	—
442	C₄×D₆₇	—	4	16	no	—
443	C₄×D₆₇	—	4	16	no	—
444	C₄×D₆₇	—	4	16	no	—
445	Dic₁₃₄	—	2	8	no	—
446	C₂²×C₆₇	—	2	2	no	—
447	C₂²×C₆₇	—	2	2	no	—
448	C₂²×C₆₇	—	2	8	no	—
449	C₂²×C₆₇	—	2	4	no	—
450	C₂²×C₆₇	—	2	4	no	—
451	C₂²×C₆₇	—	2	4	no	—
452	C₂²×C₆₇	—	4	8	no	—
453	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
454	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
455	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
456	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
457	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
458	C₂×D₆₇	—	2	4	no	—
459	C₂×D₆₇	—	2	8	no	—
460	C₂×D₆₇	—	2	8	no	—
461	C₂×D₆₇	—	2	8	no	—
462	C₂×D₆₇	—	2	4	no	—
463	C₂×D₆₇	—	2	8	no	—
464	C₂×D₆₇	—	2	8	no	—
465	C₂×D₆₇	—	2	8	no	—
466	C₂×D₆₇	—	2	4	no	—
467	C₂×D₆₇	—	4	16	no	—
468	C₂×D₆₇	—	4	8	no	—
469	C₂×D₆₇	—	4	16	no	—
470	C₂×D₆₇	—	8	32	no	—
471	C₂×D₆₇	—	8	32	no	—
472	C₄×C₆₇	—	2	4	no	—
473	C₄×C₆₇	—	2	4	no	—
474	C₄×C₆₇	—	2	4	no	—
475	C₄×C₆₇	—	2	2	no	—
476	C₄×C₆₇	—	2	2	no	—
477	C₄×C₆₇	—	2	2	no	—
478	C₄×C₆₇	—	2	2	no	—
479	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
480	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
481	Dic₆₇	—	2	4	no	—
482	Dic₆₇	—	2	4	no	—
483	Dic₆₇	—	2	4	no	—
484	C₂×#3543	—	67	1	no	maximal, Sylow
485	C₂×C₆₇	—	2	4	no	—
486	C₂×C₆₇	—	4	4	no	—
487	C₂×C₆₇	#3543	1	4	yes	complemented
488	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
490	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
491	D₆₇	—	4	8	no	—
492	D₆₇	—	4	4	no	—
493	D₆₇	—	4	8	no	—
494	#3543	—	67	32	no	—
495	C₂×#560	—	67	4	no	—
496	C₂×#559	—	67	1	no	—
497	C₂×#550	—	67	1	no	—
498	C₂×#550	—	67	1	no	—
499	C₂×#546	—	67	2	no	—
500	C₂×#546	—	67	2	no	—
501	C₂×D₄²	—	67	2	no	—
502	C₂×D₄²	—	67	1	no	—
503	C₂×D₄²	—	67	2	no	—
504	C₂×#540	—	67	2	no	—
505	C₂×#540	—	67	2	no	—
506	C₂×#535	—	67	2	no	—
507	C₂×#535	—	67	2	no	—
508	C₂×#534	—	67	4	no	—
509	C₂²×#127	—	67	1	no	—
510	C₂×#529	—	67	1	no	—
511	C₂×#529	D₆₇	1	1	yes	characteristic, complemented
512	C₆₇	C₂×#3543	1	1	yes	characteristic, complemented, Sylow
513	C₂²×#41	—	67	2	no	—
514	C₂²×#41	—	67	2	no	—
515	C₂³×D₄	—	67	4	no	—
516	C₂³×D₄	—	67	2	no	—
517	C₂³×D₄	—	67	2	no	—
518	C₂³×D₄	—	67	2	no	—
519	C₂³×D₄	—	67	2	no	—
520	C₂³×D₄	—	67	2	no	—
521	#560	—	67	64	no	—
522	#559	—	67	16	no	—
523	#550	—	67	16	no	—
524	#550	—	67	16	no	—
525	#546	—	67	32	no	—
526	#546	—	67	32	no	—
527	D₄²	—	67	32	no	—
528	D₄²	—	67	16	no	—
529	D₄²	—	67	32	no	—
530	#540	—	67	32	no	—
531	#540	—	67	32	no	—
532	#535	—	67	32	no	—
533	#535	—	67	32	no	—
534	#534	—	67	64	no	—
535	C₂×#127	—	67	2	no	—
536	C₂×#127	—	67	2	no	—
537	C₂×#127	—	67	2	no	—
538	C₂×#127	—	67	1	no	—
539	C₂×#127	—	67	1	no	—
540	C₂×#127	—	67	2	no	—
541	C₂×#127	—	67	2	no	—
542	C₂×#127	—	67	16	no	—
543	#529	—	67	16	no	—
544	#529	C₂×D₆₇	1	16	yes	complemented
545	C₂×#126	—	67	2	no	—
546	C₂×#126	C₂×D₆₇	1	2	yes	complemented
547	C₂×#125	—	67	1	no	—
548	C₂×#125	C₂×D₆₇	1	1	yes	characteristic, complemented
549	C₂×#124	—	67	2	no	—
550	C₂×#124	—	67	1	no	—
551	C₂×#124	—	67	2	no	—
552	C₂×#124	C₂×D₆₇	1	1	yes	characteristic, complemented
553	C₂×#123	—	67	2	no	—
554	C₂×#123	—	67	4	no	—
555	C₂×#123	—	67	4	no	—
556	C₂×#123	—	67	4	no	—
557	C₂×#123	—	67	4	no	—
558	C₂×#123	C₂×D₆₇	1	2	yes	complemented
559	C₂×C₂²⋊Q₈	—	67	1	no	—
560	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
561	C₂×#121	—	67	1	no	—
562	C₂×#121	—	67	2	no	—
563	C₂×#121	—	67	2	no	—
564	C₂×#121	—	67	4	no	—
565	C₂×#121	—	67	4	no	—
566	C₂×#121	—	67	4	no	—
567	C₂×#121	—	67	2	no	—
568	C₂×#121	—	67	2	no	—
569	C₂×#121	—	67	4	no	—
570	C₂×#121	—	67	4	no	—
571	C₂×#121	—	67	4	no	—
572	C₂×#121	—	67	4	no	—
573	C₂×#121	—	67	4	no	—
574	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
575	C₂×#120	—	67	4	no	—
576	C₂×#120	—	67	4	no	—
577	C₂×#120	—	67	4	no	—
578	C₂×#120	—	67	4	no	—
579	C₂×#120	—	67	4	no	—
580	C₂×#120	—	67	4	no	—
581	C₂×C₄×Q₈	—	67	1	no	—
582	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
583	C₂×C₄×D₄	—	67	2	no	—
584	C₂×C₄×D₄	—	67	2	no	—
585	C₂×C₄×D₄	—	67	2	no	—
586	C₂×C₄×D₄	—	67	1	no	—
587	C₂×C₄×D₄	—	67	2	no	—
588	C₂×C₄×D₄	—	67	2	no	—
589	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
590	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
591	C₂×#117	—	67	2	no	—
592	C₂×#117	C₂×D₆₇	1	2	yes	complemented
593	C₂²×C₂²⋊C₄	—	67	4	no	—
594	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
595	C₂⁵	—	67	4	no	—
596	C₂⁵	—	67	4	no	—
597	C₂×#41	—	268	8	no	—
598	C₂×#41	—	268	8	no	—
599	C₂×#41	—	67	16	no	—
600	C₂×#41	—	67	16	no	—
601	C₂²×Q₈	—	67	1	no	—
602	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
603	C₂²×D₄	—	268	8	no	—
604	C₂²×D₄	—	268	8	no	—
605	C₂²×D₄	—	268	8	no	—
606	C₂²×D₄	—	268	8	no	—
607	C₂²×D₄	—	268	16	no	—
608	C₂²×D₄	—	268	8	no	—
609	C₂²×D₄	—	67	4	no	—
610	C₂²×D₄	—	67	4	no	—
611	C₂²×D₄	—	67	4	no	—
612	C₂²×D₄	—	67	32	no	—
613	C₂²×D₄	—	67	16	no	—
614	C₂²×D₄	—	67	2	no	—
615	C₂²×D₄	—	67	4	no	—
616	C₂²×D₄	—	67	4	no	—
617	C₂²×D₄	—	67	2	no	—
618	C₂²×D₄	—	67	4	no	—
619	C₂²×D₄	—	67	4	no	—
620	C₂²×D₄	—	67	4	no	—
621	C₂²×D₄	—	67	4	no	—
622	C₂²×D₄	—	67	2	no	—
623	C₂²×D₄	—	67	16	no	—
624	C₂²×D₄	—	67	16	no	—
625	C₂²×D₄	—	67	16	no	—
626	C₂²×D₄	—	67	16	no	—
627	C₂²×D₄	—	67	2	no	—
628	C₂²×D₄	—	67	1	no	—
629	C₂²×D₄	—	67	2	no	—
630	C₂²×D₄	—	67	2	no	—
631	C₂²×D₄	—	67	2	no	—
632	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
633	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
634	C₂³×C₄	—	67	4	no	—
635	C₂³×C₄	—	67	4	no	—
636	C₂³×C₄	—	67	4	no	—
637	C₂³×C₄	—	67	2	no	—
638	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
639	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
640	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
641	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
642	#127	—	67	16	no	—
643	#127	—	67	16	no	—
644	#127	—	67	16	no	—
645	#127	—	67	8	no	—
646	#127	—	67	8	no	—
647	#127	—	67	16	no	—
648	#127	—	67	16	no	—
649	#126	—	67	16	no	—
650	#126	C₂²×D₆₇	1	16	yes	complemented
651	#125	—	67	8	no	—
652	#125	C₂²×D₆₇	1	8	yes	complemented
653	#124	—	67	16	no	—
654	#124	—	67	8	no	—
655	#124	—	67	16	no	—
656	#124	C₂²×D₆₇	1	8	yes	complemented
657	#123	—	67	16	no	—
658	#123	—	67	32	no	—
659	#123	—	67	32	no	—
660	#123	—	67	32	no	—
661	#123	—	67	32	no	—
662	#123	C₂²×D₆₇	1	16	yes	complemented
663	C₂²⋊Q₈	—	67	8	no	—
664	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
665	#121	—	67	8	no	—
666	#121	—	67	16	no	—
667	#121	—	67	16	no	—
668	#121	—	67	32	no	—
669	#121	—	67	32	no	—
670	#121	—	67	32	no	—
671	#121	—	67	16	no	—
672	#121	—	67	16	no	—
673	#121	—	67	32	no	—
674	#121	—	67	32	no	—
675	#121	—	67	32	no	—
676	#121	—	67	32	no	—
677	#121	—	67	32	no	—
678	#121	C₂²×D₆₇	1	8	yes	—
679	#120	—	67	32	no	—
680	#120	—	67	32	no	—
681	#120	—	67	32	no	—
682	#120	—	67	32	no	—
683	#120	—	67	32	no	—
684	#120	—	67	32	no	—
685	C₄×Q₈	—	67	8	no	—
686	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
687	C₄×D₄	—	67	16	no	—
688	C₄×D₄	—	67	16	no	—
689	C₄×D₄	—	67	16	no	—
690	C₄×D₄	—	67	8	no	—
691	C₄×D₄	—	67	16	no	—
692	C₄×D₄	—	67	16	no	—
693	C₄×D₄	C₂²×D₆₇	1	16	yes	complemented
694	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
695	#117	—	67	16	no	—
696	#117	C₂²×D₆₇	1	16	yes	complemented
697	C₂×C₄⋊C₄	—	67	2	no	—
698	C₂×C₄⋊C₄	—	67	2	no	—
699	C₂×C₄⋊C₄	—	67	1	no	—
700	C₂×C₄⋊C₄	—	67	1	no	—
701	C₂×C₄⋊C₄	—	67	2	no	—
702	C₂×C₄⋊C₄	—	67	2	no	—
703	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
704	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
705	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
708	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
709	C₂×C₂²⋊C₄	—	67	2	no	—
710	C₂×C₂²⋊C₄	—	67	4	no	—
711	C₂×C₂²⋊C₄	—	67	4	no	—
712	C₂×C₂²⋊C₄	—	67	2	no	—
713	C₂×C₂²⋊C₄	—	67	2	no	—
714	C₂×C₂²⋊C₄	—	67	2	no	—
715	C₂×C₂²⋊C₄	—	67	2	no	—
716	C₂×C₂²⋊C₄	—	67	4	no	—
717	C₂×C₂²⋊C₄	—	67	4	no	—
718	C₂×C₂²⋊C₄	—	67	4	no	—
719	C₂×C₂²⋊C₄	—	67	4	no	—
720	C₂×C₂²⋊C₄	—	67	32	no	—
721	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
726	C₂×C₄²	—	67	2	no	—
727	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
728	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
729	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
730	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
731	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
732	C₂×C₄²	C₂²×D₆₇	1	8	yes	complemented
733	C₂⁴	—	268	8	no	—
734	C₂⁴	—	268	8	no	—
735	C₂⁴	—	268	8	no	—
736	C₂⁴	—	268	8	no	—
737	C₂⁴	—	268	8	no	—
738	C₂⁴	—	67	16	no	—
739	C₂⁴	—	67	16	no	—
740	C₂⁴	—	67	4	no	—
741	C₂⁴	—	67	2	no	—
742	C₂⁴	—	67	4	no	—
743	C₂⁴	—	134	16	no	—
744	C₂⁴	C₂³×D₆₇	1	2	yes	—
745	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
746	#41	—	268	32	no	—
747	#41	—	268	32	no	—
748	C₂×Q₈	—	2	4	no	—
749	C₂×Q₈	—	67	4	no	—
750	C₂×Q₈	—	134	4	no	—
751	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
752	C₂×D₄	—	2	8	no	—
753	C₂×D₄	—	2	4	no	—
754	C₂×D₄	—	268	8	no	—
755	C₂×D₄	—	268	8	no	—
756	C₂×D₄	—	268	8	no	—
757	C₂×D₄	—	268	4	no	—
758	C₂×D₄	—	268	8	no	—
759	C₂×D₄	—	268	4	no	—
760	C₂×D₄	—	268	32	no	—
761	C₂×D₄	—	268	8	no	—
762	C₂×D₄	—	268	8	no	—
763	C₂×D₄	—	268	32	no	—
764	C₂×D₄	—	268	32	no	—
765	C₂×D₄	—	268	32	no	—
766	C₂×D₄	—	268	64	no	—
767	C₂×D₄	—	268	32	no	—
768	C₂×D₄	—	268	8	no	—
769	C₂×D₄	—	268	8	no	—
770	C₂×D₄	—	268	8	no	—
771	C₂×D₄	—	67	16	no	—
772	C₂×D₄	—	67	16	no	—
773	C₂×D₄	—	67	16	no	—
774	C₂×D₄	—	67	8	no	—
775	C₂×D₄	—	67	16	no	—
776	C₂×D₄	—	67	16	no	—
777	C₂×D₄	—	67	8	no	—
778	C₂×D₄	—	67	16	no	—
779	C₂×D₄	—	67	16	no	—
780	C₂×D₄	—	67	16	no	—
781	C₂×D₄	—	67	16	no	—
782	C₂×D₄	—	67	8	no	—
783	C₂×D₄	—	67	8	no	—
784	C₂×D₄	—	67	4	no	—
785	C₂×D₄	—	67	8	no	—
786	C₂×D₄	—	67	8	no	—
787	C₂×D₄	—	67	8	no	—
788	C₂×D₄	—	134	8	no	—
789	C₂×D₄	—	134	8	no	—
790	C₂×D₄	—	134	4	no	—
791	C₂×D₄	—	134	8	no	—
792	C₂×D₄	—	134	8	no	—
793	C₂×D₄	—	134	8	no	—
794	C₂×D₄	C₂³×D₆₇	1	8	yes	—
795	C₂×D₄	C₂³×D₆₇	1	4	yes	—
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	2	4	no	—
798	C₂²×C₄	—	2	4	no	—
799	C₂²×C₄	—	2	8	no	—
800	C₂²×C₄	—	268	8	no	—
801	C₂²×C₄	—	268	8	no	—
802	C₂²×C₄	—	268	8	no	—
803	C₂²×C₄	—	67	16	no	—
804	C₂²×C₄	—	67	16	no	—
805	C₂²×C₄	—	67	16	no	—
806	C₂²×C₄	—	67	2	no	—
807	C₂²×C₄	—	67	2	no	—
808	C₂²×C₄	—	67	2	no	—
809	C₂²×C₄	—	67	8	no	—
810	C₂²×C₄	—	134	8	no	—
811	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
812	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
813	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
814	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
815	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
816	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
817	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
818	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
819	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
820	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
821	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
822	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
823	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
824	C₄⋊C₄	—	67	8	no	—
825	C₄⋊C₄	—	67	8	no	—
826	C₄⋊C₄	—	67	4	no	—
827	C₄⋊C₄	—	67	4	no	—
828	C₄⋊C₄	—	67	8	no	—
829	C₄⋊C₄	—	67	8	no	—
830	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
831	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
832	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
833	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
834	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
835	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
836	C₂²⋊C₄	—	67	8	no	—
837	C₂²⋊C₄	—	67	16	no	—
838	C₂²⋊C₄	—	67	16	no	—
839	C₂²⋊C₄	—	67	8	no	—
840	C₂²⋊C₄	—	67	8	no	—
841	C₂²⋊C₄	—	67	8	no	—
842	C₂²⋊C₄	—	67	8	no	—
843	C₂²⋊C₄	—	67	16	no	—
844	C₂²⋊C₄	—	67	16	no	—
845	C₂²⋊C₄	—	67	16	no	—
846	C₂²⋊C₄	—	67	16	no	—
847	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
848	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
849	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
850	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
851	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
852	C₄²	—	67	8	no	—
853	C₄²	C₂³×D₆₇	1	4	yes	—
854	C₄²	C₂³×D₆₇	1	4	yes	—
855	C₄²	C₂³×D₆₇	1	4	yes	—
856	C₄²	C₂³×D₆₇	1	4	yes	—
857	C₄²	C₂³×D₆₇	1	8	yes	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	4	no	—
861	C₂³	—	2	4	no	—
862	C₂³	—	2	4	no	—
863	C₂³	—	268	16	no	—
864	C₂³	—	268	16	no	—
865	C₂³	—	268	16	no	—
866	C₂³	—	268	16	no	—
867	C₂³	—	268	16	no	—
868	C₂³	—	536	32	no	—
869	C₂³	—	536	32	no	—
870	C₂³	—	67	8	no	—
871	C₂³	—	67	4	no	—
872	C₂³	—	67	8	no	—
873	C₂³	—	134	8	no	—
874	C₂³	—	134	8	no	—
875	C₂³	—	134	8	no	—
876	C₂³	—	134	4	no	—
877	C₂³	—	134	8	no	—
878	C₂³	—	134	4	no	—
879	C₂³	—	134	8	no	—
880	C₂³	—	134	4	no	—
881	C₂³	—	134	8	no	—
882	C₂³	—	134	32	no	—
883	C₂³	#14524089	1	4	yes	—
884	C₂³	C₂⁴×D₆₇	1	4	yes	—
885	C₂³	C₂⁴×D₆₇	1	2	yes	—
886	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
887	Q₈	—	2	8	no	—
888	Q₈	—	134	8	no	—
889	D₄	—	2	16	no	—
890	D₄	—	2	8	no	—
891	D₄	—	268	16	no	—
892	D₄	—	268	16	no	—
893	D₄	—	268	16	no	—
894	D₄	—	268	8	no	—
895	D₄	—	268	16	no	—
896	D₄	—	268	8	no	—
897	D₄	—	268	16	no	—
898	D₄	—	268	16	no	—
899	D₄	—	268	16	no	—
900	D₄	—	268	16	no	—
901	D₄	—	268	16	no	—
902	D₄	—	134	16	no	—
903	D₄	—	134	16	no	—
904	D₄	—	134	8	no	—
905	D₄	—	134	16	no	—
906	D₄	—	134	16	no	—
907	D₄	—	134	16	no	—
908	C₂×C₄	—	2	4	no	—
909	C₂×C₄	—	2	8	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	4	no	—
915	C₂×C₄	—	2	4	no	—
916	C₂×C₄	—	2	8	no	—
917	C₂×C₄	—	2	8	no	—
918	C₂×C₄	—	2	16	no	—
919	C₂×C₄	—	268	16	no	—
920	C₂×C₄	—	268	16	no	—
921	C₂×C₄	—	268	16	no	—
922	C₂×C₄	—	67	4	no	—
923	C₂×C₄	—	67	4	no	—
924	C₂×C₄	—	67	4	no	—
925	C₂×C₄	—	134	4	no	—
926	C₂×C₄	—	134	4	no	—
927	C₂×C₄	—	134	4	no	—
928	C₂×C₄	—	134	16	no	—
929	C₂×C₄	#14524089	1	4	yes	—
930	C₂×C₄	#14524089	1	4	yes	—
931	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
932	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
933	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
934	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
935	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
936	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
937	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
938	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
939	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	8	no	—
943	C₂²	—	2	4	no	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	4	8	no	—
947	C₂²	—	268	16	no	—
948	C₂²	—	268	8	no	—
949	C₂²	—	268	16	no	—
950	C₂²	—	536	32	no	—
951	C₂²	—	536	32	no	—
952	C₂²	—	134	8	no	—
953	C₂²	—	134	8	no	—
954	C₂²	—	134	8	no	—
955	C₂²	—	134	4	no	—
956	C₂²	—	134	8	no	—
957	C₂²	—	134	4	no	—
958	C₂²	—	134	8	no	—
959	C₂²	—	134	4	no	—
960	C₂²	—	134	8	no	—
961	C₂²	C₂×#14524089	1	4	yes	—
962	C₂²	C₂×#14524089	1	2	yes	—
963	C₂²	C₂×#14524089	1	2	yes	—
964	C₂²	C₂×#14524089	1	2	yes	—
965	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
966	C₄	—	2	4	no	—
967	C₄	—	2	2	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	4	no	—
972	C₄	—	2	4	no	—
973	C₄	—	134	4	no	—
974	C₄	—	134	4	no	—
975	C₄	—	134	4	no	—
976	C₄	C₂×#14524089	1	4	yes	—
977	C₄	C₂×#14524089	1	4	yes	—
978	C₂	—	2	4	no	—
979	C₂	—	4	4	no	—
980	C₂	—	268	8	no	—
981	C₂	—	268	4	no	—
982	C₂	—	268	8	no	—
983	C₂	#22574539	1	4	yes	direct product factor
984	C₂	C₂²×#14524089	1	1	yes	characteristic
985	C₂	C₂²×#14524089	1	1	yes	characteristic
986	C₂	C₂²×#14524089	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#529×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#529	D₆₇
hypocenter	C₆₇	C₂×#3543
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #22574539	C₂	direct (N × H)
2. C₂×#16864137	C₂	semidirect
3. C₂×#16864131	C₂	semidirect
4. C₂×#16864068	C₂	semidirect
5. C₂×#16864067	C₂	semidirect
6. C₂×#16864042	C₂	semidirect
7. C₂×#16864037	C₂	semidirect
8. C₂×D₄×D₂₆₈	C₂	semidirect
9. C₂×D₄×D₂₆₈	C₂	semidirect
10. C₂×#16864030	C₂	semidirect
11. C₂×#16864002	C₂	semidirect
12. C₂×#16864001	C₂	semidirect
13. C₂×#16863965	C₂	semidirect
14. C₂×#16863964	C₂	semidirect
15. C₂×#16863957	C₂	semidirect
16. C₂²×#14524040	C₂	semidirect
17. C₂×#16863930	C₂	semidirect
18. C₂×#529×C₆₇	C₂	semidirect
19. C₂²×#11761629	C₂²	semidirect
20. C₂²×#11761628	C₂²	semidirect
21. C₂³×D₂₆₈	C₂²	semidirect
22. C₂³×D₂₆₈	C₂²	semidirect
23. C₂³×D₂₆₈	C₂²	semidirect
24. C₂³×D₂₆₈	C₂²	semidirect
25. C₂²×D₄×D₆₇	C₂²	semidirect
26. C₂²×D₄×D₆₇	C₂²	semidirect
27. #16864137	C₂²	semidirect
28. #16864131	C₂²	semidirect
29. #16864068	C₂²	semidirect
30. #16864067	C₂²	semidirect
31. #16864042	C₂²	semidirect
32. #16864037	C₂²	semidirect
33. D₄×D₂₆₈	C₂²	semidirect
34. D₄×D₂₆₈	C₂²	semidirect
35. #16864030	C₂²	semidirect
36. #16864002	C₂²	semidirect
37. #16864001	C₂²	semidirect
38. #16863965	C₂²	semidirect
39. #16863964	C₂²	semidirect
40. #16863957	C₂²	semidirect
42. C₂×#14524040	C₂²	semidirect
43. C₂×#14524040	C₂²	semidirect
44. C₂×#14524040	C₂²	semidirect
45. C₂×#14524040	C₂²	semidirect
46. C₂×#14524040	C₂²	semidirect
47. C₂×#14524040	C₂²	semidirect
48. C₂×#14524039	C₂²	semidirect
49. #16863930	C₂²	semidirect
50. C₂×#14524037	C₂²	semidirect
51. C₂×#14524035	C₂²	semidirect
52. C₂×#14524032	C₂²	semidirect
53. C₂×#14524031	C₂²	semidirect
54. C₂×#14524031	C₂²	semidirect
55. C₂×#14524028	C₂²	semidirect
56. C₂×#14524028	C₂²	semidirect
57. C₂×#14524028	C₂²	semidirect
58. C₂×#14524028	C₂²	semidirect
59. C₂×#14524026	C₂²	semidirect
60. C₂×#14524022	C₂²	semidirect
61. C₂×#14524018	C₂²	semidirect
62. C₂×#14524018	C₂²	semidirect
63. C₂×#14524018	C₂²	semidirect
64. C₂×#14524018	C₂²	semidirect
65. C₂×#14524018	C₂²	semidirect
66. C₂×#14524018	C₂²	semidirect
68. C₂×#14524017	C₂²	semidirect
69. C₂×#14524017	C₂²	semidirect
70. C₂×#14524016	C₂²	semidirect
71. C₂×#14524016	C₂²	semidirect
72. C₂×#14524016	C₂²	semidirect
73. C₂×#14524016	C₂²	semidirect
74. C₂×#14524013	C₂²	semidirect
75. C₂×#14524013	C₂²	semidirect
76. C₂×#14524013	C₂²	semidirect
77. C₂×#14524013	C₂²	semidirect
78. C₂×#14524013	C₂²	semidirect
79. C₂×#14524011	C₂²	semidirect
80. C₂×C₄×Dic₁₃₄	C₂²	semidirect
81. C₂×C₄×D₂₆₈	C₂²	semidirect
82. C₂×C₄×D₂₆₈	C₂²	semidirect
83. C₂×C₄×D₂₆₈	C₂²	semidirect
84. C₂×#14524005	C₂²	semidirect
85. C₂×#14524005	C₂²	semidirect
86. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
87. C₂×#14524000	C₂²	semidirect
88. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
89. #529×C₆₇	C₂²	semidirect
90. C₂×#126×C₆₇	C₂²	semidirect
91. C₂×#125×C₆₇	C₂²	semidirect
92. C₂×#124×C₆₇	C₂²	semidirect
93. C₂×#123×C₆₇	C₂²	semidirect
94. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
96. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
97. C₂×C₄×D₄×C₆₇	C₂²	semidirect
98. C₂×C₄×D₄×C₆₇	C₂²	semidirect
99. C₂×#117×C₆₇	C₂²	semidirect
100. C₂²×C₄²×C₆₇	C₂²	semidirect
104. C₂×#11761629	C₂³	semidirect
106. C₂×#11761628	C₂³	semidirect
125. C₂²×D₂₆₈	C₂³	semidirect
126. C₂²×D₂₆₈	C₂³	semidirect
127. C₂²×D₂₆₈	C₂³	semidirect
128. C₂²×D₂₆₈	C₂³	semidirect
135. C₂×D₄×D₆₇	C₂³	semidirect
136. C₂×D₄×D₆₇	C₂³	semidirect
142. #14524040	C₂³	semidirect
143. #14524040	C₂³	semidirect
144. #14524040	C₂³	semidirect
145. #14524040	C₂³	semidirect
146. #14524040	C₂³	semidirect
147. #14524039	C₂³	semidirect
148. #14524037	C₂³	semidirect
149. #14524035	C₂³	semidirect
150. #14524032	C₂³	semidirect
151. #14524031	C₂³	semidirect
152. #14524031	C₂³	semidirect
153. #14524028	C₂³	semidirect
154. #14524028	C₂³	semidirect
155. #14524028	C₂³	semidirect
156. #14524028	C₂³	semidirect
157. #14524026	C₂³	semidirect
158. #14524022	C₂³	semidirect
159. #14524018	C₂³	semidirect
160. #14524018	C₂³	semidirect
161. #14524018	C₂³	semidirect
162. #14524018	C₂³	semidirect
163. #14524018	C₂³	semidirect
164. #14524018	C₂³	semidirect
166. #14524017	C₂³	semidirect
167. #14524017	C₂³	semidirect
168. #14524016	C₂³	semidirect
169. #14524016	C₂³	semidirect
170. #14524016	C₂³	semidirect
171. #14524016	C₂³	semidirect
172. #14524013	C₂³	semidirect
173. #14524013	C₂³	semidirect
174. #14524013	C₂³	semidirect
175. #14524013	C₂³	semidirect
176. #14524013	C₂³	semidirect
177. #14524011	C₂³	semidirect
178. C₄×Dic₁₃₄	C₂³	semidirect
179. C₄×D₂₆₈	C₂³	semidirect
180. C₄×D₂₆₈	C₂³	semidirect
181. C₄×D₂₆₈	C₂³	semidirect
182. #14524005	C₂³	semidirect
183. #14524005	C₂³	semidirect
184. C₄×C₂²⋊D₆₇	C₂³	semidirect
185. #14524000	C₂³	semidirect
203. C₂²⋊C₄×D₆₇	C₂³	semidirect
212. #126×C₆₇	C₂³	semidirect
213. #125×C₆₇	C₂³	semidirect
214. #124×C₆₇	C₂³	semidirect
215. #123×C₆₇	C₂³	semidirect
216. C₂²⋊Q₈×C₆₇	C₂³	semidirect
218. C₄×Q₈×C₆₇	C₂³	semidirect
219. C₄×D₄×C₆₇	C₂³	semidirect
220. C₄×D₄×C₆₇	C₂³	semidirect
221. #117×C₆₇	C₂³	semidirect
238. C₂×C₄²×C₆₇	C₂³	semidirect
487. C₂×C₆₇	#3543	semidirect
511. C₂×#529	D₆₇	semidirect
512. C₆₇	C₂×#3543	semidirect
544. #529	C₂×D₆₇	semidirect
546. C₂×#126	C₂×D₆₇	semidirect
548. C₂×#125	C₂×D₆₇	semidirect
552. C₂×#124	C₂×D₆₇	semidirect
558. C₂×#123	C₂×D₆₇	semidirect
560. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
582. C₂×C₄×Q₈	C₂×D₆₇	semidirect
589. C₂×C₄×D₄	C₂×D₆₇	semidirect
590. C₂×C₄×D₄	C₂×D₆₇	semidirect
592. C₂×#117	C₂×D₆₇	semidirect
594. C₂²×C₄²	C₂×D₆₇	semidirect
650. #126	C₂²×D₆₇	semidirect
652. #125	C₂²×D₆₇	semidirect
656. #124	C₂²×D₆₇	semidirect
662. #123	C₂²×D₆₇	semidirect
664. C₂²⋊Q₈	C₂²×D₆₇	semidirect
686. C₄×Q₈	C₂²×D₆₇	semidirect
693. C₄×D₄	C₂²×D₆₇	semidirect
694. C₄×D₄	C₂²×D₆₇	semidirect
696. #117	C₂²×D₆₇	semidirect
732. C₂×C₄²	C₂²×D₆₇	semidirect
983. C₂	#22574539	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574539	2
C₂×#16864137	2
C₂×#16864131	2
C₂×#16864068	2
C₂×#16864067	2
C₂×#16864042	2
C₂×#16864037	2
C₂×D₄×D₂₆₈	2
C₂×#16864030	2
C₂×#16864002	2
C₂×#16864001	2
C₂×#16863965	2
C₂×#16863964	2
C₂×#16863957	2
C₂²×#14524040	2
C₂×#16863930	2
C₂×#529×C₆₇	2
C₂×#3543	67

Subgroups — C2×#22574539 #31763421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574539 #31763421