Subgroups — #22574077

Order 8576.

1232 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864130	C₂	1	2	yes	maximal, complemented
2	#16864129	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864128	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864065	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864064	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864064	C₂	1	2	yes	maximal, complemented
7	#16864042	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864040	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864037	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864036	C₂	1	2	yes	maximal, complemented
11	#16864033	C₂	1	2	yes	maximal, complemented
12	#16863998	C₂	1	2	yes	maximal, complemented
13	#16863996	C₂	1	2	yes	maximal, complemented
14	#16863961	C₂	1	2	yes	maximal, complemented
15	#16863948	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863945	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863943	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863942	C₂	1	1	yes	maximal, characteristic, complemented
19	#16863941	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14524039	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863869	C₂	1	2	yes	maximal, complemented
22	C₄×#11761627	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761629	C₂²	1	1	yes	characteristic, complemented
25	C₂×#11761628	C₂²	1	2	yes	complemented
26	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
27	C₂×#11761627	C₂²	1	1	yes	characteristic
28	C₂×#11761627	C₂²	1	2	yes	complemented
29	C₂×#11761627	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₂₆₈	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊D₆₇	C₂²	1	2	yes	—
32	C₂²×C₂²⋊D₆₇	C₂²	1	2	yes	—
33	#14524042	C₂²	1	1	yes	characteristic, complemented
34	#14524041	C₂²	1	1	yes	characteristic, complemented
35	#14524039	C₂²	1	1	yes	characteristic
36	#14524039	C₂²	1	2	yes	—
37	#14524039	C₂²	1	1	yes	characteristic
38	#14524039	C₂²	1	1	yes	characteristic
39	#14524039	C₂²	1	1	yes	characteristic
40	#14524039	C₂²	1	2	yes	—
41	#14524039	C₂²	1	2	yes	complemented
42	#14524039	C₂²	1	2	yes	complemented
43	#14524033	C₂²	1	2	yes	complemented
44	#14524032	C₂²	1	1	yes	characteristic, complemented
45	#14524031	C₂²	1	1	yes	characteristic, complemented
46	#14524030	C₂²	1	1	yes	characteristic, complemented
47	#14524029	C₂²	1	2	yes	complemented
48	#14524029	C₂²	1	2	yes	complemented
49	#14524029	C₂²	1	2	yes	complemented
50	#14524029	C₂²	1	2	yes	complemented
51	#14524028	C₂²	1	2	yes	complemented
52	#14524028	C₂²	1	2	yes	complemented
53	#14524027	C₂²	1	2	yes	complemented
54	#14524026	C₂²	1	2	yes	complemented
55	#14524025	C₂²	1	2	yes	complemented
56	#14524025	C₂²	1	2	yes	complemented
57	#14524024	C₂²	1	2	yes	complemented
58	#14524022	C₂²	1	1	yes	characteristic
59	#14524020	C₂²	1	2	yes	—
60	#14524018	C₂²	1	1	yes	characteristic, complemented
61	#14524018	C₂²	1	2	yes	complemented
62	#14524017	C₂²	1	2	yes	complemented
63	#14524017	C₂²	1	1	yes	characteristic, complemented
64	#14524016	C₂²	1	2	yes	complemented
65	#14524016	C₂²	1	2	yes	complemented
66	#14524016	C₂²	1	2	yes	complemented
67	#14524016	C₂²	1	2	yes	complemented
68	#14524016	C₂²	1	2	yes	complemented
69	#14524015	C₂²	1	2	yes	complemented
70	#14524015	C₂²	1	2	yes	complemented
71	#14524015	C₂²	1	2	yes	complemented
72	#14524015	C₂²	1	2	yes	complemented
73	#14524015	C₂²	1	2	yes	complemented
74	#14524014	C₂²	1	2	yes	complemented
75	#14524014	C₂²	1	1	yes	characteristic, complemented
76	#14524013	C₂²	1	2	yes	—
77	#14524012	C₂²	1	2	yes	—
78	#14524011	C₂²	1	2	yes	—
79	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
81	#14524008	C₂²	1	1	yes	characteristic, complemented
82	#14524008	C₂²	1	2	yes	complemented
83	#14524008	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
85	D₄×Dic₆₇	C₂²	1	1	yes	characteristic
86	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
87	#14524005	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
92	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
95	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
96	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
97	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
98	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
100	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
101	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
102	#14524001	C₂²	1	1	yes	characteristic, complemented
103	#14523999	C₂²	1	1	yes	characteristic
104	#14523999	C₂²	1	2	yes	—
105	#14523999	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊Dic₆₇	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
109	C₂×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
110	C₂×C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₂²×D₄×C₆₇	C₂²	1	1	yes	characteristic
114	#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	#123×C₆₇	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
117	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#121×C₆₇	C₂²	1	2	yes	complemented
119	#120×C₆₇	C₂²	1	2	yes	—
120	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
123	C₂³×D₆₇	C₂³	1	2	yes	—
124	#11761629	—	4	2	no	—
125	#11761628	—	4	4	no	—
126	#11761628	—	4	2	no	—
127	#11761627	—	2	4	no	—
128	#11761627	—	4	2	no	—
129	#11761627	—	4	4	no	—
130	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₃₄	C₂³	1	2	yes	—
132	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
133	C₂×D₂₆₈	—	4	2	no	—
134	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
135	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
136	C₂×D₂₆₈	C₂³	1	2	yes	—
137	C₂×D₂₆₈	C₂³	1	2	yes	—
138	C₂×D₂₆₈	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₆₇	—	2	8	no	—
140	C₂×C₂²⋊D₆₇	—	4	4	no	—
141	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
155	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
156	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
157	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
158	C₂²×Dic₆₇	C₂³	1	2	yes	—
159	C₂²×Dic₆₇	C₂³	1	2	yes	—
160	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₆₇	C₂³	1	2	yes	—
165	C₂×C₄×D₆₇	C₂³	1	2	yes	—
166	C₂×C₄×D₆₇	C₂³	1	2	yes	—
167	C₂×C₄×D₆₇	C₂³	1	2	yes	—
168	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
169	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
170	C₄⋊Dic₆₇	C₂³	1	2	yes	—
171	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₆₇⋊C₄	C₂³	1	2	yes	—
174	Dic₆₇⋊C₄	C₂³	1	2	yes	—
175	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
176	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
177	Dic₆₇⋊C₄	C₂³	1	2	yes	—
178	Dic₆₇⋊C₄	C₂³	1	2	yes	—
179	Dic₆₇⋊C₄	C₂³	1	2	yes	—
180	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
184	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
186	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
187	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
197	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
198	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
199	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
200	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
201	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
202	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
203	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
204	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
205	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
206	C₄×Dic₆₇	C₂³	1	2	yes	—
207	C₄×Dic₆₇	C₂³	1	2	yes	—
208	C₂⁴×C₆₇	C₂³	1	2	yes	—
209	#41×C₆₇	—	4	2	no	—
210	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₆₇	—	4	2	no	—
212	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×D₄×C₆₇	C₂³	1	2	yes	—
216	C₂×D₄×C₆₇	C₂³	1	2	yes	—
217	C₂×D₄×C₆₇	C₂³	1	2	yes	—
218	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
221	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
222	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
223	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
224	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
226	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
229	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
230	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
231	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
232	C₄²×C₆₇	C₂³	1	1	yes	characteristic
233	C₂³×C₆₇	—	2	4	no	—
234	C₂³×C₆₇	—	4	2	no	—
235	C₂³×C₆₇	—	4	2	no	—
236	C₂³×C₆₇	C₂⁴	1	2	yes	—
237	C₂³×C₆₇	C₂⁴	1	2	yes	—
238	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
239	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂²×D₆₇	—	2	4	no	—
241	C₂²×D₆₇	—	4	2	no	—
242	C₂²×D₆₇	—	4	2	no	—
243	C₂²×D₆₇	C₂⁴	1	2	yes	—
244	C₂²×D₆₇	C₂⁴	1	2	yes	—
245	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
246	Q₈×C₆₇	—	2	2	no	—
247	D₄×C₆₇	—	2	2	no	—
248	D₄×C₆₇	—	2	2	no	—
249	D₄×C₆₇	—	2	2	no	—
250	D₄×C₆₇	—	4	2	no	—
251	D₄×C₆₇	—	4	2	no	—
252	D₄×C₆₇	—	4	2	no	—
253	C₂×C₄×C₆₇	—	2	2	no	—
254	C₂×C₄×C₆₇	—	2	2	no	—
255	C₂×C₄×C₆₇	—	4	2	no	—
256	C₂×C₄×C₆₇	—	4	2	no	—
257	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	C₂²⋊D₆₇	—	2	2	no	—
265	C₂²⋊D₆₇	—	2	4	no	—
266	C₂²⋊D₆₇	—	2	4	no	—
267	C₂²⋊D₆₇	—	2	4	no	—
268	C₂²⋊D₆₇	—	2	4	no	—
269	C₂²⋊D₆₇	—	2	2	no	—
270	C₂²⋊D₆₇	—	2	4	no	—
271	C₂²⋊D₆₇	—	2	4	no	—
272	C₂²⋊D₆₇	—	4	2	no	—
273	C₂²⋊D₆₇	—	4	2	no	—
274	C₂²⋊D₆₇	—	4	2	no	—
275	C₂²⋊D₆₇	—	4	2	no	—
276	C₂²⋊D₆₇	—	4	2	no	—
277	C₂²⋊D₆₇	—	4	2	no	—
278	C₂×Dic₆₇	—	2	2	no	—
279	C₂×Dic₆₇	—	2	2	no	—
280	C₂×Dic₆₇	—	2	2	no	—
281	C₂×Dic₆₇	—	4	2	no	—
282	C₂×Dic₆₇	—	4	2	no	—
283	C₂×Dic₆₇	#41	1	4	yes	complemented
284	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₆₇	C₂⁴	1	2	yes	—
289	C₂×Dic₆₇	C₂⁴	1	2	yes	—
290	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
292	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
293	D₂₆₈	—	2	2	no	—
294	D₂₆₈	—	2	2	no	—
295	D₂₆₈	—	4	2	no	—
296	D₂₆₈	—	4	2	no	—
297	D₂₆₈	—	4	2	no	—
298	C₄×D₆₇	—	2	2	no	—
299	C₄×D₆₇	—	2	2	no	—
300	C₄×D₆₇	—	2	2	no	—
301	C₄×D₆₇	—	4	2	no	—
302	C₄×D₆₇	—	4	2	no	—
303	C₄×D₆₇	—	4	2	no	—
304	C₄×D₆₇	—	4	2	no	—
305	Dic₁₃₄	—	2	2	no	—
306	Dic₁₃₄	—	2	2	no	—
307	Dic₁₃₄	—	2	4	no	—
308	C₂²×C₆₇	—	2	1	no	—
309	C₂²×C₆₇	—	2	1	no	—
310	C₂²×C₆₇	—	2	1	no	—
311	C₂²×C₆₇	—	2	2	no	—
312	C₂²×C₆₇	—	2	2	no	—
313	C₂²×C₆₇	—	2	1	no	—
314	C₂²×C₆₇	—	2	2	no	—
315	C₂²×C₆₇	—	2	2	no	—
316	C₂²×C₆₇	—	2	2	no	—
317	C₂²×C₆₇	—	2	1	no	—
318	C₂²×C₆₇	—	2	2	no	—
319	C₂²×C₆₇	—	8	4	no	—
320	C₂²×C₆₇	C₂×#41	1	2	yes	—
321	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
322	C₂×D₆₇	—	2	1	no	—
323	C₂×D₆₇	—	2	2	no	—
324	C₂×D₆₇	—	2	2	no	—
325	C₂×D₆₇	—	2	1	no	—
326	C₂×D₆₇	—	2	1	no	—
327	C₂×D₆₇	—	2	2	no	—
328	C₂×D₆₇	—	2	2	no	—
329	C₂×D₆₇	—	2	2	no	—
330	C₂×D₆₇	—	2	2	no	—
331	C₂×D₆₇	—	8	4	no	—
332	C₄×C₆₇	—	2	1	no	—
333	C₄×C₆₇	—	2	2	no	—
334	C₄×C₆₇	—	2	1	no	—
335	C₄×C₆₇	—	2	1	no	—
336	C₄×C₆₇	—	2	2	no	—
337	C₄×C₆₇	—	2	1	no	—
338	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
339	Dic₆₇	—	2	1	no	—
340	Dic₆₇	—	2	2	no	—
341	Dic₆₇	—	2	2	no	—
342	Dic₆₇	—	2	1	no	—
343	Dic₆₇	—	2	1	no	—
344	Dic₆₇	—	2	1	no	—
345	Dic₆₇	C₂×#41	1	2	yes	—
346	Dic₆₇	C₂×#41	1	2	yes	—
347	Dic₆₇	H(5,𝔽₂)	1	2	yes	—
348	C₂×C₆₇	—	2	2	no	—
349	C₂×C₆₇	—	4	1	no	—
350	C₂×C₆₇	—	4	2	no	—
351	C₂×C₆₇	—	4	2	no	—
352	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
353	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	D₆₇	—	4	1	no	—
356	D₆₇	—	4	2	no	—
357	D₆₇	—	4	2	no	—
358	#3508	—	67	1	no	maximal, Sylow
359	C₆₇	#3508	1	1	yes	characteristic, complemented, Sylow
360	#559	—	67	1	no	—
361	#559	—	67	2	no	—
362	#559	—	67	1	no	—
363	#550	—	67	1	no	—
364	#550	—	67	1	no	—
365	#550	—	67	2	no	—
366	#546	—	67	1	no	—
367	#546	—	67	1	no	—
368	#546	—	67	2	no	—
369	#546	—	67	1	no	—
370	#546	—	67	2	no	—
371	#546	D₆₇	1	1	yes	characteristic, complemented
372	#540	—	67	2	no	—
373	#540	—	67	2	no	—
374	#535	—	67	2	no	—
375	#533	—	67	1	no	—
376	#532	—	67	1	no	—
377	#532	—	67	1	no	—
378	#532	—	67	1	no	—
379	#532	—	67	1	no	—
380	C₂×#127	—	67	1	no	—
381	#518	—	67	2	no	—
382	C₄×#41	—	67	1	no	—
383	C₂×#41	—	67	1	no	—
384	C₂×#41	—	67	1	no	—
385	C₂×#41	—	67	2	no	—
386	C₂×#41	—	67	1	no	—
387	C₂×#41	—	67	1	no	—
388	C₂×#41	—	67	2	no	—
389	C₂×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
390	C₂²×D₄	—	67	2	no	—
391	C₂²×D₄	—	67	2	no	—
392	C₂²×D₄	—	67	1	no	—
393	C₂²×D₄	C₂×D₆₇	1	1	yes	characteristic
394	C₄⋊Q₈	—	67	1	no	—
395	C₄⋊Q₈	—	67	1	no	—
396	#127	—	67	1	no	—
397	#127	—	67	1	no	—
398	#127	—	67	2	no	—
399	#127	—	67	1	no	—
400	#127	—	67	1	no	—
401	#127	—	67	2	no	—
402	#127	—	67	2	no	—
403	#127	—	67	2	no	—
404	#125	—	67	2	no	—
405	#124	—	67	1	no	—
406	#124	—	67	1	no	—
407	#124	—	67	2	no	—
408	#124	—	67	2	no	—
409	#124	—	67	2	no	—
410	#124	—	67	2	no	—
411	#124	—	67	1	no	—
412	#124	C₂×D₆₇	1	1	yes	characteristic, complemented
413	#123	—	67	2	no	—
414	#123	—	67	2	no	—
415	#123	—	67	2	no	—
416	#123	—	67	2	no	—
417	#123	—	67	2	no	—
418	#123	—	67	2	no	—
419	#123	—	67	2	no	—
420	#123	C₂×D₆₇	1	2	yes	complemented
421	C₂²⋊Q₈	—	67	1	no	—
422	C₂²⋊Q₈	—	67	2	no	—
423	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
424	#121	—	67	2	no	—
425	#121	—	67	2	no	—
426	#121	—	67	1	no	—
427	#121	—	67	2	no	—
428	#121	—	67	2	no	—
429	#121	—	67	2	no	—
430	#121	—	67	2	no	—
431	#121	—	67	1	no	—
432	#121	—	67	2	no	—
433	#121	—	67	1	no	—
434	#121	—	67	2	no	—
435	#121	—	67	2	no	—
436	#121	—	67	2	no	—
437	#121	—	67	2	no	—
438	#121	—	67	2	no	—
439	#121	—	67	2	no	—
440	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
441	#121	C₂×D₆₇	1	2	yes	complemented
442	#120	—	67	2	no	—
443	#120	—	67	2	no	—
444	#120	—	67	2	no	—
445	#120	C₂×D₆₇	1	2	yes	—
446	C₄×Q₈	—	67	1	no	—
447	C₄×Q₈	—	67	1	no	—
448	C₄×Q₈	—	67	2	no	—
449	C₄×Q₈	—	67	1	no	—
450	C₄×Q₈	—	67	1	no	—
451	C₄×D₄	—	67	1	no	—
452	C₄×D₄	—	67	1	no	—
453	C₄×D₄	—	67	1	no	—
454	C₄×D₄	—	67	1	no	—
455	C₄×D₄	—	67	2	no	—
456	C₄×D₄	—	67	2	no	—
457	C₄×D₄	—	67	2	no	—
458	C₄×D₄	—	67	2	no	—
459	C₄×D₄	—	67	2	no	—
460	C₄×D₄	—	67	1	no	—
461	C₄×D₄	—	67	1	no	—
462	C₄×D₄	—	67	1	no	—
463	C₄×D₄	—	67	2	no	—
464	C₄×D₄	—	67	2	no	—
465	C₄×D₄	—	67	2	no	—
466	C₄×D₄	—	67	2	no	—
467	C₄×D₄	—	67	2	no	—
468	C₄×D₄	—	67	1	no	—
469	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
470	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
471	#117	—	67	1	no	—
472	#117	—	67	1	no	—
473	#117	—	67	1	no	—
474	#117	—	67	2	no	—
475	C₂×C₂²⋊C₄	—	67	2	no	—
476	C₂×C₂²⋊C₄	—	67	2	no	—
477	C₂×C₂²⋊C₄	—	67	2	no	—
478	C₂×C₂²⋊C₄	C₂×D₆₇	1	2	yes	—
479	C₂×C₄²	—	67	1	no	—
480	C₂×C₄²	—	67	1	no	—
481	C₂×C₄²	—	67	1	no	—
482	C₂⁴	—	67	2	no	—
483	C₂⁴	C₂²×D₆₇	1	2	yes	—
484	#41	—	4	2	no	—
485	#41	—	268	2	no	—
486	#41	—	268	4	no	—
487	#41	—	268	2	no	—
488	#41	—	268	4	no	—
489	#41	—	268	2	no	—
490	#41	—	134	4	no	—
491	C₂×Q₈	—	67	1	no	—
492	C₂×Q₈	—	67	2	no	—
493	C₂×Q₈	—	67	1	no	—
494	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	268	2	no	—
497	C₂×D₄	—	268	4	no	—
498	C₂×D₄	—	67	2	no	—
499	C₂×D₄	—	67	2	no	—
500	C₂×D₄	—	67	2	no	—
501	C₂×D₄	—	67	2	no	—
502	C₂×D₄	—	67	2	no	—
503	C₂×D₄	—	67	2	no	—
504	C₂×D₄	—	67	1	no	—
505	C₂×D₄	—	67	2	no	—
506	C₂×D₄	—	67	2	no	—
507	C₂×D₄	—	67	2	no	—
508	C₂×D₄	—	67	2	no	—
509	C₂×D₄	—	67	1	no	—
510	C₂×D₄	—	67	2	no	—
511	C₂×D₄	—	67	2	no	—
512	C₂×D₄	—	67	2	no	—
513	C₂×D₄	—	67	2	no	—
514	C₂×D₄	—	67	2	no	—
515	C₂×D₄	—	67	1	no	—
516	C₂×D₄	—	67	1	no	—
517	C₂×D₄	—	134	8	no	—
518	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
519	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
520	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
521	C₂×D₄	C₂²×D₆₇	1	2	yes	—
522	C₂×D₄	C₂²×D₆₇	1	2	yes	—
523	C₂×D₄	C₂²×D₆₇	1	2	yes	—
524	C₂²×C₄	—	67	2	no	—
525	C₂²×C₄	—	67	2	no	—
526	C₂²×C₄	—	67	2	no	—
527	C₂²×C₄	—	67	2	no	—
528	C₂²×C₄	—	67	2	no	—
529	C₂²×C₄	—	67	2	no	—
530	C₂²×C₄	—	67	1	no	—
531	C₂²×C₄	—	67	1	no	—
532	C₂²×C₄	—	67	1	no	—
533	C₂²×C₄	—	67	1	no	—
534	C₂²×C₄	—	67	1	no	—
535	C₂²×C₄	—	67	1	no	—
536	C₂²×C₄	—	67	1	no	—
537	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
538	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
539	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
540	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
541	C₄⋊C₄	—	67	1	no	—
542	C₄⋊C₄	—	67	1	no	—
543	C₄⋊C₄	—	67	2	no	—
544	C₄⋊C₄	—	67	2	no	—
545	C₄⋊C₄	—	67	1	no	—
546	C₄⋊C₄	—	67	1	no	—
547	C₄⋊C₄	—	67	1	no	—
548	C₄⋊C₄	—	67	2	no	—
549	C₄⋊C₄	—	67	1	no	—
550	C₄⋊C₄	—	67	2	no	—
551	C₄⋊C₄	—	67	2	no	—
552	C₄⋊C₄	—	67	2	no	—
553	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
554	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
555	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
556	C₂²⋊C₄	—	67	1	no	—
557	C₂²⋊C₄	—	67	2	no	—
558	C₂²⋊C₄	—	67	2	no	—
559	C₂²⋊C₄	—	67	2	no	—
560	C₂²⋊C₄	—	67	1	no	—
561	C₂²⋊C₄	—	67	2	no	—
562	C₂²⋊C₄	—	67	2	no	—
563	C₂²⋊C₄	—	67	2	no	—
564	C₂²⋊C₄	—	67	2	no	—
565	C₂²⋊C₄	—	67	2	no	—
566	C₂²⋊C₄	—	67	2	no	—
567	C₂²⋊C₄	—	67	1	no	—
568	C₂²⋊C₄	—	67	1	no	—
569	C₂²⋊C₄	—	67	2	no	—
570	C₂²⋊C₄	—	67	2	no	—
571	C₂²⋊C₄	—	67	2	no	—
572	C₂²⋊C₄	—	67	2	no	—
573	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
574	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
576	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
577	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
578	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
579	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
580	C₄²	—	67	1	no	—
581	C₄²	—	67	1	no	—
582	C₄²	—	67	1	no	—
583	C₄²	—	67	1	no	—
584	C₄²	—	67	1	no	—
585	C₄²	—	67	1	no	—
586	C₄²	—	67	1	no	—
587	C₄²	—	67	1	no	—
588	C₄²	—	67	1	no	—
589	C₄²	—	67	2	no	—
590	C₄²	—	67	2	no	—
591	C₄²	C₂²×D₆₇	1	1	yes	characteristic
592	C₂³	—	2	4	no	—
593	C₂³	—	4	2	no	—
594	C₂³	—	4	2	no	—
595	C₂³	—	268	2	no	—
596	C₂³	—	268	2	no	—
597	C₂³	—	67	2	no	—
598	C₂³	—	67	2	no	—
599	C₂³	—	67	1	no	—
600	C₂³	—	134	4	no	—
601	C₂³	C₂³×D₆₇	1	2	yes	—
602	C₂³	C₂³×D₆₇	1	2	yes	—
603	C₂³	C₂³×D₆₇	1	1	yes	characteristic
604	C₂³	C₂³×D₆₇	1	1	yes	characteristic
605	Q₈	—	2	2	no	—
606	Q₈	—	134	4	no	—
607	Q₈	—	134	2	no	—
608	Q₈	—	134	2	no	—
609	D₄	—	2	2	no	—
610	D₄	—	2	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	4	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	268	2	no	—
616	D₄	—	268	2	no	—
617	D₄	—	268	2	no	—
618	D₄	—	268	2	no	—
619	D₄	—	268	2	no	—
620	D₄	—	268	2	no	—
621	D₄	—	268	2	no	—
622	D₄	—	268	2	no	—
623	D₄	—	268	2	no	—
624	D₄	—	134	4	no	—
625	D₄	—	134	4	no	—
626	D₄	—	134	4	no	—
627	D₄	—	134	4	no	—
628	D₄	—	134	4	no	—
629	D₄	—	134	4	no	—
630	D₄	—	134	2	no	—
631	D₄	—	134	2	no	—
632	D₄	—	134	2	no	—
633	D₄	—	134	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	2	no	—
638	C₂×C₄	—	268	2	no	—
639	C₂×C₄	—	268	2	no	—
640	C₂×C₄	—	268	2	no	—
641	C₂×C₄	—	268	2	no	—
642	C₂×C₄	—	268	2	no	—
643	C₂×C₄	—	268	2	no	—
644	C₂×C₄	—	67	4	no	—
645	C₂×C₄	—	67	1	no	—
646	C₂×C₄	—	67	1	no	—
647	C₂×C₄	—	67	1	no	—
648	C₂×C₄	—	67	1	no	—
649	C₂×C₄	—	67	1	no	—
650	C₂×C₄	—	67	1	no	—
651	C₂×C₄	—	67	1	no	—
652	C₂×C₄	—	67	2	no	—
653	C₂×C₄	—	67	2	no	—
654	C₂×C₄	—	134	2	no	—
655	C₂×C₄	—	134	2	no	—
656	C₂×C₄	—	134	2	no	—
657	C₂×C₄	—	134	2	no	—
658	C₂×C₄	—	134	2	no	—
659	C₂×C₄	—	134	2	no	—
660	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₆₇	1	2	yes	—
665	C₂×C₄	C₂³×D₆₇	1	2	yes	—
666	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	8	4	no	—
679	C₂²	—	536	4	no	—
680	C₂²	—	134	1	no	—
681	C₂²	—	134	2	no	—
682	C₂²	—	134	2	no	—
683	C₂²	—	134	2	no	—
684	C₂²	—	134	2	no	—
685	C₂²	—	134	1	no	—
686	C₂²	—	134	2	no	—
687	C₂²	—	134	2	no	—
688	C₂²	—	134	1	no	—
689	C₂²	#41×D₆₇	1	2	yes	—
690	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
691	C₄	—	2	1	no	—
692	C₄	—	2	1	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	2	no	—
697	C₄	—	67	2	no	—
698	C₄	—	67	2	no	—
699	C₄	—	67	2	no	—
700	C₄	—	134	1	no	—
701	C₄	—	134	1	no	—
702	C₄	—	134	2	no	—
703	C₄	—	134	1	no	—
704	C₄	—	134	1	no	—
705	C₄	—	134	2	no	—
706	C₄	#14524088	1	2	yes	—
707	C₂	—	2	2	no	—
708	C₂	—	4	2	no	—
709	C₂	—	4	2	no	—
710	C₂	—	4	1	no	—
711	C₂	—	268	2	no	—
712	C₂	—	268	2	no	—
713	C₂	—	268	1	no	—
714	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
715	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
716	C₂	C₂×#14524088	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#546×C₆₇	C₂
hypercenter	#546	D₆₇
hypocenter	C₆₇	#3508
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #16864130	C₂	semidirect
2. #16864129	C₂	semidirect
3. #16864128	C₂	semidirect
4. #16864065	C₂	semidirect
5. #16864064	C₂	semidirect
6. #16864064	C₂	semidirect
7. #16864042	C₂	semidirect
8. #16864040	C₂	semidirect
9. #16864037	C₂	semidirect
10. #16864036	C₂	semidirect
11. #16864033	C₂	semidirect
12. #16863998	C₂	semidirect
13. #16863996	C₂	semidirect
14. #16863961	C₂	semidirect
15. #16863948	C₂	semidirect
16. #16863945	C₂	semidirect
17. #16863943	C₂	semidirect
18. #16863942	C₂	semidirect
19. #16863941	C₂	semidirect
20. C₂×#14524039	C₂	semidirect
21. #16863869	C₂	semidirect
22. C₄×#11761627	C₂	semidirect
23. #546×C₆₇	C₂	semidirect
24. C₂×#11761629	C₂²	semidirect
25. C₂×#11761628	C₂²	semidirect
26. C₂×#11761628	C₂²	semidirect
28. C₂×#11761627	C₂²	semidirect
29. C₂×#11761627	C₂²	semidirect
33. #14524042	C₂²	semidirect
34. #14524041	C₂²	semidirect
41. #14524039	C₂²	semidirect
42. #14524039	C₂²	semidirect
43. #14524033	C₂²	semidirect
44. #14524032	C₂²	semidirect
45. #14524031	C₂²	semidirect
46. #14524030	C₂²	semidirect
47. #14524029	C₂²	semidirect
48. #14524029	C₂²	semidirect
49. #14524029	C₂²	semidirect
50. #14524029	C₂²	semidirect
51. #14524028	C₂²	semidirect
52. #14524028	C₂²	semidirect
53. #14524027	C₂²	semidirect
54. #14524026	C₂²	semidirect
55. #14524025	C₂²	semidirect
56. #14524025	C₂²	semidirect
57. #14524024	C₂²	semidirect
60. #14524018	C₂²	semidirect
61. #14524018	C₂²	semidirect
62. #14524017	C₂²	semidirect
63. #14524017	C₂²	semidirect
64. #14524016	C₂²	semidirect
65. #14524016	C₂²	semidirect
66. #14524016	C₂²	semidirect
67. #14524016	C₂²	semidirect
68. #14524016	C₂²	semidirect
69. #14524015	C₂²	semidirect
70. #14524015	C₂²	semidirect
71. #14524015	C₂²	semidirect
72. #14524015	C₂²	semidirect
73. #14524015	C₂²	semidirect
74. #14524014	C₂²	semidirect
75. #14524014	C₂²	semidirect
79. Q₈×Dic₆₇	C₂²	semidirect
80. C₄×Dic₁₃₄	C₂²	semidirect
81. #14524008	C₂²	semidirect
82. #14524008	C₂²	semidirect
83. #14524008	C₂²	semidirect
84. C₄×D₂₆₈	C₂²	semidirect
86. D₄×Dic₆₇	C₂²	semidirect
87. #14524005	C₂²	semidirect
89. C₄×C₂²⋊D₆₇	C₂²	semidirect
90. C₄×C₂²⋊D₆₇	C₂²	semidirect
91. C₄×C₂²⋊D₆₇	C₂²	semidirect
92. C₄×C₂²⋊D₆₇	C₂²	semidirect
93. C₄×C₂²⋊D₆₇	C₂²	semidirect
94. C₄×C₂²⋊D₆₇	C₂²	semidirect
96. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
97. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
98. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
100. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
101. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
102. #14524001	C₂²	semidirect
105. #14523999	C₂²	semidirect
110. C₂×C₄×Dic₆₇	C₂²	semidirect
111. C₄²×D₆₇	C₂²	semidirect
112. C₂×#41×C₆₇	C₂²	semidirect
114. #124×C₆₇	C₂²	semidirect
115. #123×C₆₇	C₂²	semidirect
117. #121×C₆₇	C₂²	semidirect
118. #121×C₆₇	C₂²	semidirect
121. C₄×D₄×C₆₇	C₂²	semidirect
283. C₂×Dic₆₇	#41	semidirect
359. C₆₇	#3508	semidirect
371. #546	D₆₇	semidirect
389. C₂×#41	C₂×D₆₇	semidirect
412. #124	C₂×D₆₇	semidirect
420. #123	C₂×D₆₇	semidirect
440. #121	C₂×D₆₇	semidirect
441. #121	C₂×D₆₇	semidirect
470. C₄×D₄	C₂×D₆₇	semidirect