Subgroups — #22574057

Order 8576.

1140 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864131	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864129	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864128	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864118	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864115	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864108	C₂	1	2	yes	maximal, complemented
7	#16864095	C₂	1	2	yes	maximal, complemented
8	#16864091	C₂	1	2	yes	maximal, complemented
9	#16864067	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864066	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864044	C₂	1	2	yes	maximal, complemented
12	#16863982	C₂	1	2	yes	maximal, complemented
13	#16863980	C₂	1	2	yes	maximal, complemented
14	#16863964	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863959	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863950	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863945	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863905	C₂	1	2	yes	maximal, complemented
19	#16863904	C₂	1	2	yes	maximal, complemented
20	#16863878	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863875	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#559×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761629	C₂²	1	1	yes	characteristic
25	C₂×#11761628	C₂²	1	2	yes	complemented
26	C₂×#11761627	C₂²	1	1	yes	characteristic
27	C₂×#11761627	C₂²	1	2	yes	complemented
28	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₆₇	C₂²	1	2	yes	—
30	#14524042	C₂²	1	1	yes	characteristic, complemented
31	#14524041	C₂²	1	1	yes	characteristic, complemented
32	#14524041	C₂²	1	1	yes	characteristic, complemented
33	#14524040	C₂²	1	1	yes	characteristic
34	#14524039	C₂²	1	1	yes	characteristic
35	#14524039	C₂²	1	1	yes	characteristic
36	#14524039	C₂²	1	1	yes	characteristic, complemented
37	#14524038	C₂²	1	2	yes	complemented
38	#14524037	C₂²	1	2	yes	complemented
39	#14524036	C₂²	1	2	yes	complemented
40	#14524036	C₂²	1	2	yes	complemented
41	#14524033	C₂²	1	1	yes	characteristic, complemented
42	#14524033	C₂²	1	1	yes	characteristic, complemented
43	#14524032	C₂²	1	1	yes	characteristic
44	#14524032	C₂²	1	2	yes	complemented
45	#14524031	C₂²	1	1	yes	characteristic
46	#14524031	C₂²	1	1	yes	characteristic, complemented
47	#14524030	C₂²	1	1	yes	characteristic
48	#14524029	C₂²	1	2	yes	complemented
49	#14524029	C₂²	1	2	yes	complemented
50	#14524028	C₂²	1	2	yes	complemented
51	#14524028	C₂²	1	2	yes	complemented
52	#14524027	C₂²	1	2	yes	complemented
53	#14524026	C₂²	1	2	yes	complemented
54	#14524025	C₂²	1	2	yes	complemented
55	#14524025	C₂²	1	2	yes	complemented
56	#14524023	C₂²	1	1	yes	characteristic
57	#14524021	C₂²	1	1	yes	characteristic
58	#14524021	C₂²	1	1	yes	characteristic
59	#14524021	C₂²	1	2	yes	complemented
60	#14524020	C₂²	1	2	yes	complemented
61	#14524019	C₂²	1	1	yes	characteristic
62	#14524017	C₂²	1	2	yes	complemented
63	#14524016	C₂²	1	2	yes	—
64	#14524016	C₂²	1	2	yes	—
65	#14524016	C₂²	1	2	yes	—
66	#14524016	C₂²	1	2	yes	—
67	#14524016	C₂²	1	2	yes	complemented
68	#14524016	C₂²	1	2	yes	complemented
69	#14524015	C₂²	1	2	yes	—
70	#14524015	C₂²	1	2	yes	—
71	#14524015	C₂²	1	2	yes	complemented
72	#14524015	C₂²	1	2	yes	complemented
73	#14524014	C₂²	1	2	yes	complemented
74	#14524013	C₂²	1	2	yes	—
75	#14524013	C₂²	1	2	yes	—
76	#14524011	C₂²	1	2	yes	—
77	#14524011	C₂²	1	2	yes	—
78	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
83	#14524008	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
85	C₄×D₂₆₈	C₂²	1	2	yes	—
86	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
87	D₄×Dic₆₇	C₂²	1	1	yes	characteristic
88	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
89	#14524005	C₂²	1	1	yes	characteristic
90	#14524005	C₂²	1	2	yes	—
91	#14524005	C₂²	1	1	yes	characteristic, complemented
92	#14524005	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
95	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
96	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
97	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
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	#14524000	C₂²	1	1	yes	characteristic
102	#14524000	C₂²	1	1	yes	characteristic
103	#14524000	C₂²	1	2	yes	complemented
104	#14524000	C₂²	1	2	yes	complemented
105	#14523999	C₂²	1	2	yes	complemented
106	#14523999	C₂²	1	2	yes	complemented
107	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	complemented
108	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
111	C₄²×D₆₇	C₂²	1	1	yes	characteristic
112	#127×C₆₇	C₂²	1	1	yes	characteristic
113	#124×C₆₇	C₂²	1	1	yes	characteristic
114	#124×C₆₇	C₂²	1	2	yes	complemented
115	#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	#123×C₆₇	C₂²	1	2	yes	complemented
117	#123×C₆₇	C₂²	1	2	yes	complemented
118	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
123	C₂³×D₆₇	C₂³	1	2	yes	—
124	#11761629	—	2	4	no	—
125	#11761628	—	4	4	no	—
126	#11761627	—	2	4	no	—
127	#11761627	—	4	4	no	—
128	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
132	C₂×D₂₆₈	C₂³	1	2	yes	—
133	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
134	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
135	C₂×D₂₆₈	C₂³	1	2	yes	—
136	C₂×D₂₆₈	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
145	D₄×D₆₇	—	2	4	no	—
146	C₂²×Dic₆₇	C₂³	1	2	yes	—
147	C₂²×Dic₆₇	C₂³	1	2	yes	—
148	C₂²×Dic₆₇	C₂³	1	2	yes	—
149	C₂×C₄×D₆₇	—	4	4	no	—
150	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₆₇	C₂³	1	2	yes	—
152	C₂×C₄×D₆₇	C₂³	1	2	yes	—
153	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₆₇	C₂³	1	2	yes	—
155	C₂×C₄×D₆₇	C₂³	1	2	yes	—
156	C₂×C₄×D₆₇	C₂³	1	2	yes	—
157	C₂×C₄×D₆₇	C₂³	1	2	yes	—
158	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₆₇	C₂³	1	2	yes	—
161	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
164	Dic₆₇⋊C₄	C₂³	1	2	yes	—
165	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₆₇⋊C₄	C₂³	1	2	yes	—
168	Dic₆₇⋊C₄	C₂³	1	2	yes	—
169	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
170	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₆₇⋊C₄	C₂³	1	2	yes	—
172	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
175	Dic₆₇⋊C₄	C₂³	1	2	yes	—
176	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
177	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
178	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
183	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
201	C₄×Dic₆₇	C₂³	1	2	yes	—
202	C₄×Dic₆₇	C₂³	1	2	yes	—
203	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
204	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
205	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₆₇	C₂³	1	2	yes	—
210	C₂×D₄×C₆₇	C₂³	1	2	yes	—
211	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
212	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
213	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₄²×C₆₇	C₂³	1	1	yes	characteristic
225	C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₄²×C₆₇	C₂³	1	2	yes	—
227	C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	C₂³×C₆₇	C₂⁴	1	2	yes	—
229	C₂³×C₆₇	C₂⁴	1	2	yes	—
230	C₂²×D₆₇	—	2	4	no	—
231	C₂²×D₆₇	—	4	2	no	—
232	C₂²×D₆₇	—	4	2	no	—
233	C₂²×D₆₇	C₂⁴	1	2	yes	—
234	C₂²×D₆₇	C₂⁴	1	2	yes	—
235	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
236	Q₈×C₆₇	—	2	2	no	—
237	Q₈×C₆₇	—	4	1	no	—
238	D₄×C₆₇	—	2	2	no	—
239	D₄×C₆₇	—	2	2	no	—
240	D₄×C₆₇	—	4	2	no	—
241	D₄×C₆₇	—	4	2	no	—
242	C₂×C₄×C₆₇	—	4	2	no	—
243	C₂×C₄×C₆₇	—	4	2	no	—
244	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
248	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂²⋊D₆₇	—	2	4	no	—
254	C₂²⋊D₆₇	—	2	4	no	—
255	C₂²⋊D₆₇	—	2	4	no	—
256	C₂²⋊D₆₇	—	4	2	no	—
257	C₂²⋊D₆₇	—	4	2	no	—
258	C₂²⋊D₆₇	—	4	2	no	—
259	C₂²⋊D₆₇	—	4	2	no	—
260	C₂²⋊D₆₇	—	4	2	no	—
261	C₂×Dic₆₇	—	2	4	no	—
262	C₂×Dic₆₇	—	2	4	no	—
263	C₂×Dic₆₇	—	4	2	no	—
264	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₆₇	C₂⁴	1	2	yes	—
267	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₆₇	C₂⁴	1	2	yes	—
269	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
273	D₂₆₈	—	2	4	no	—
274	D₂₆₈	—	2	2	no	—
275	D₂₆₈	—	2	2	no	—
276	D₂₆₈	—	4	2	no	—
277	D₂₆₈	—	4	2	no	—
278	C₄×D₆₇	—	2	4	no	—
279	C₄×D₆₇	—	2	2	no	—
280	C₄×D₆₇	—	2	4	no	—
281	C₄×D₆₇	—	4	2	no	—
282	C₄×D₆₇	—	4	2	no	—
283	C₄×D₆₇	—	4	1	no	—
284	C₄×D₆₇	—	4	2	no	—
285	C₄×D₆₇	—	4	2	no	—
286	C₄×D₆₇	#41	1	4	yes	complemented
287	Dic₁₃₄	—	2	2	no	—
288	Dic₁₃₄	—	2	2	no	—
289	Dic₁₃₄	—	2	2	no	—
290	Dic₁₃₄	—	4	1	no	—
291	C₂²×C₆₇	—	2	2	no	—
292	C₂²×C₆₇	—	2	2	no	—
293	C₂²×C₆₇	—	2	2	no	—
294	C₂²×C₆₇	—	2	2	no	—
295	C₂²×C₆₇	—	2	2	no	—
296	C₂²×C₆₇	—	2	2	no	—
297	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
298	C₂×D₆₇	—	2	1	no	—
299	C₂×D₆₇	—	2	1	no	—
300	C₂×D₆₇	—	2	2	no	—
301	C₂×D₆₇	—	2	2	no	—
302	C₂×D₆₇	—	2	2	no	—
303	C₂×D₆₇	—	2	2	no	—
304	C₂×D₆₇	—	2	2	no	—
305	C₂×D₆₇	—	2	2	no	—
306	C₂×D₆₇	—	4	8	no	—
307	C₂×D₆₇	C₂×#41	1	2	yes	—
308	C₄×C₆₇	—	2	2	no	—
309	C₄×C₆₇	—	2	1	no	—
310	C₄×C₆₇	—	2	1	no	—
311	C₄×C₆₇	—	2	1	no	—
312	C₄×C₆₇	—	2	2	no	—
313	C₄×C₆₇	—	2	1	no	—
314	C₄×C₆₇	—	2	1	no	—
315	C₄×C₆₇	—	2	1	no	—
316	C₄×C₆₇	C₂×#41	1	2	yes	—
317	Dic₆₇	—	2	2	no	—
318	Dic₆₇	—	2	1	no	—
319	Dic₆₇	—	2	1	no	—
320	Dic₆₇	—	2	2	no	—
321	Dic₆₇	—	2	1	no	—
322	Dic₆₇	—	2	1	no	—
323	Dic₆₇	—	2	1	no	—
324	Dic₆₇	C₂×#41	1	2	yes	—
325	Dic₆₇	H(5,𝔽₂)	1	2	yes	—
326	C₂×C₆₇	—	4	2	no	—
327	C₂×C₆₇	—	4	2	no	—
328	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
329	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₆₇	#585	1	1	yes	characteristic
331	D₆₇	—	2	2	no	—
332	D₆₇	—	4	2	no	—
333	D₆₇	—	4	2	no	—
334	#3506	—	67	1	no	maximal, Sylow
335	C₆₇	#3506	1	1	yes	characteristic, complemented, Sylow
336	#559	—	67	1	no	—
337	#559	—	67	1	no	—
338	#559	—	67	1	no	—
339	#559	D₆₇	1	1	yes	characteristic, complemented
340	#556	—	67	1	no	—
341	#556	—	67	1	no	—
342	#555	—	67	2	no	—
343	#553	—	67	2	no	—
344	#553	—	67	2	no	—
345	#550	—	67	1	no	—
346	#550	—	67	1	no	—
347	#547	—	67	2	no	—
348	#538	—	67	2	no	—
349	#538	—	67	2	no	—
350	#535	—	67	1	no	—
351	#535	—	67	1	no	—
352	#533	—	67	1	no	—
353	#532	—	67	1	no	—
354	#525	—	67	2	no	—
355	#525	—	67	2	no	—
356	#520	—	67	1	no	—
357	#520	—	67	1	no	—
358	C₂×C₄×D₄	—	67	1	no	—
359	C₂×#41	—	67	1	no	—
360	C₂×#41	—	67	2	no	—
361	C₂×#41	—	67	1	no	—
362	C₂×#41	—	67	2	no	—
363	C₂²×D₄	—	67	1	no	—
364	C₂³×C₄	—	67	2	no	—
365	C₄⋊Q₈	—	67	1	no	—
366	C₄⋊Q₈	—	67	1	no	—
367	C₄⋊Q₈	—	67	1	no	—
368	#127	—	67	1	no	—
369	#127	—	67	1	no	—
370	#127	—	67	1	no	—
371	#127	—	67	1	no	—
372	#127	C₂×D₆₇	1	1	yes	characteristic
373	#126	—	67	2	no	—
374	#126	—	67	2	no	—
375	#126	—	67	2	no	—
376	#126	—	67	2	no	—
377	#125	—	67	1	no	—
378	#125	—	67	1	no	—
379	#124	—	67	1	no	—
380	#124	—	67	2	no	—
381	#124	—	67	1	no	—
382	#124	—	67	2	no	—
383	#124	—	67	2	no	—
384	#124	—	67	1	no	—
385	#124	—	67	1	no	—
386	#124	C₂×D₆₇	1	1	yes	characteristic
387	#124	C₂×D₆₇	1	1	yes	characteristic, complemented
388	#124	C₂×D₆₇	1	2	yes	complemented
389	#123	—	67	2	no	—
390	#123	—	67	2	no	—
391	#123	—	67	2	no	—
392	#123	—	67	2	no	—
393	#123	—	67	2	no	—
394	#123	—	67	2	no	—
395	#123	C₂×D₆₇	1	2	yes	complemented
396	#123	C₂×D₆₇	1	2	yes	complemented
397	C₂²⋊Q₈	—	67	1	no	—
398	C₂²⋊Q₈	—	67	1	no	—
399	C₂²⋊Q₈	—	67	1	no	—
400	C₂²⋊Q₈	—	67	2	no	—
401	C₂²⋊Q₈	—	67	1	no	—
402	C₂²⋊Q₈	—	67	2	no	—
403	#121	—	67	2	no	—
404	#121	—	67	2	no	—
405	#121	—	67	2	no	—
406	#121	—	67	2	no	—
407	#121	—	67	2	no	—
408	#121	—	67	2	no	—
409	#121	—	67	2	no	—
410	#121	—	67	2	no	—
411	#121	—	67	2	no	—
412	#121	—	67	2	no	—
413	#121	—	67	2	no	—
414	#121	—	67	2	no	—
415	#120	—	67	2	no	—
416	#120	—	67	2	no	—
417	#120	—	67	2	no	—
418	#120	—	67	2	no	—
419	C₄×Q₈	—	67	1	no	—
420	C₄×Q₈	—	67	1	no	—
421	C₄×Q₈	—	67	1	no	—
422	C₄×Q₈	—	67	1	no	—
423	C₄×Q₈	—	67	1	no	—
424	C₄×Q₈	—	67	1	no	—
425	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
426	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
427	C₄×D₄	—	67	1	no	—
428	C₄×D₄	—	67	1	no	—
429	C₄×D₄	—	67	2	no	—
430	C₄×D₄	—	67	2	no	—
431	C₄×D₄	—	67	2	no	—
432	C₄×D₄	—	67	1	no	—
433	C₄×D₄	—	67	2	no	—
434	C₄×D₄	—	67	1	no	—
435	C₄×D₄	—	67	2	no	—
436	C₄×D₄	—	67	2	no	—
437	C₄×D₄	—	67	2	no	—
438	C₄×D₄	—	67	2	no	—
439	C₄×D₄	—	67	2	no	—
440	C₄×D₄	—	67	2	no	—
441	C₄×D₄	—	67	1	no	—
442	C₄×D₄	—	67	2	no	—
443	C₄×D₄	—	67	1	no	—
444	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
445	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
446	C₄×D₄	C₂×D₆₇	1	2	yes	complemented
447	#117	—	67	2	no	—
448	#117	—	67	2	no	—
449	#117	—	67	1	no	—
450	#117	—	67	1	no	—
451	#117	—	67	2	no	—
452	#117	—	67	2	no	—
453	C₂×C₄⋊C₄	—	67	2	no	—
454	C₂×C₄⋊C₄	—	67	1	no	—
455	C₂×C₄⋊C₄	—	67	2	no	—
456	C₂×C₂²⋊C₄	—	67	2	no	—
457	C₂×C₄²	—	67	1	no	—
458	C₂⁴	—	67	2	no	—
459	#41	—	268	4	no	—
460	#41	—	268	4	no	—
461	#41	—	134	4	no	—
462	#41	—	134	4	no	—
463	C₂×Q₈	—	67	1	no	—
464	C₂×Q₈	—	67	1	no	—
465	C₂×Q₈	—	67	1	no	—
466	C₂×Q₈	—	67	1	no	—
467	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
468	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
469	C₂×D₄	—	67	2	no	—
470	C₂×D₄	—	67	2	no	—
471	C₂×D₄	—	67	2	no	—
472	C₂×D₄	—	67	2	no	—
473	C₂×D₄	—	67	2	no	—
474	C₂×D₄	—	67	2	no	—
475	C₂×D₄	—	67	2	no	—
476	C₂×D₄	—	67	2	no	—
477	C₂×D₄	—	67	2	no	—
478	C₂×D₄	—	67	2	no	—
479	C₂×D₄	—	67	2	no	—
480	C₂×D₄	—	67	1	no	—
481	C₂×D₄	—	67	1	no	—
482	C₂×D₄	—	134	4	no	—
483	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
485	C₂×D₄	C₂²×D₆₇	1	2	yes	—
486	C₂×D₄	C₂²×D₆₇	1	2	yes	—
487	C₂²×C₄	—	268	4	no	—
488	C₂²×C₄	—	67	2	no	—
489	C₂²×C₄	—	67	1	no	—
490	C₂²×C₄	—	67	2	no	—
491	C₂²×C₄	—	67	2	no	—
492	C₂²×C₄	—	67	2	no	—
493	C₂²×C₄	—	67	2	no	—
494	C₂²×C₄	—	67	1	no	—
495	C₂²×C₄	—	67	2	no	—
496	C₂²×C₄	—	67	2	no	—
497	C₂²×C₄	—	67	1	no	—
498	C₂²×C₄	—	67	2	no	—
499	C₂²×C₄	—	67	2	no	—
500	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
501	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
502	C₄⋊C₄	—	67	2	no	—
503	C₄⋊C₄	—	67	1	no	—
504	C₄⋊C₄	—	67	1	no	—
505	C₄⋊C₄	—	67	1	no	—
506	C₄⋊C₄	—	67	2	no	—
507	C₄⋊C₄	—	67	2	no	—
508	C₄⋊C₄	—	67	2	no	—
509	C₄⋊C₄	—	67	1	no	—
510	C₄⋊C₄	—	67	1	no	—
511	C₄⋊C₄	—	67	2	no	—
512	C₄⋊C₄	—	67	1	no	—
513	C₄⋊C₄	—	67	1	no	—
514	C₄⋊C₄	—	67	1	no	—
515	C₄⋊C₄	—	67	1	no	—
516	C₄⋊C₄	—	67	2	no	—
517	C₄⋊C₄	—	67	1	no	—
518	C₄⋊C₄	—	67	1	no	—
519	C₄⋊C₄	—	67	1	no	—
520	C₄⋊C₄	—	67	1	no	—
521	C₄⋊C₄	—	67	1	no	—
522	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
524	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
527	C₂²⋊C₄	—	67	2	no	—
528	C₂²⋊C₄	—	67	2	no	—
529	C₂²⋊C₄	—	67	2	no	—
530	C₂²⋊C₄	—	67	2	no	—
531	C₂²⋊C₄	—	67	2	no	—
532	C₂²⋊C₄	—	67	2	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	—	67	2	no	—
538	C₂²⋊C₄	—	67	2	no	—
539	C₂²⋊C₄	—	67	2	no	—
540	C₂²⋊C₄	—	67	2	no	—
541	C₂²⋊C₄	—	67	2	no	—
542	C₂²⋊C₄	—	67	2	no	—
543	C₂²⋊C₄	—	67	2	no	—
544	C₂²⋊C₄	—	67	2	no	—
545	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
551	C₄²	—	67	1	no	—
552	C₄²	—	67	1	no	—
553	C₄²	—	67	1	no	—
554	C₄²	—	67	2	no	—
555	C₄²	—	67	2	no	—
556	C₄²	—	67	2	no	—
557	C₄²	—	67	1	no	—
558	C₄²	—	67	1	no	—
559	C₄²	C₂²×D₆₇	1	1	yes	characteristic
560	C₄²	C₂²×D₆₇	1	2	yes	—
561	C₄²	C₂²×D₆₇	1	1	yes	characteristic
562	C₄²	C₂²×D₆₇	1	1	yes	characteristic
563	C₂³	—	268	2	no	—
564	C₂³	—	268	2	no	—
565	C₂³	—	67	1	no	—
566	C₂³	—	67	2	no	—
567	C₂³	—	67	2	no	—
568	C₂³	—	134	4	no	—
569	C₂³	C₂³×D₆₇	1	2	yes	—
570	C₂³	C₂³×D₆₇	1	2	yes	—
571	Q₈	—	2	2	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	268	1	no	—
574	Q₈	—	134	2	no	—
575	Q₈	—	134	2	no	—
576	Q₈	—	134	2	no	—
577	D₄	—	2	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	268	2	no	—
582	D₄	—	268	2	no	—
583	D₄	—	268	2	no	—
584	D₄	—	268	2	no	—
585	D₄	—	268	2	no	—
586	D₄	—	268	2	no	—
587	D₄	—	268	2	no	—
588	D₄	—	134	4	no	—
589	D₄	—	134	4	no	—
590	D₄	—	134	4	no	—
591	D₄	—	134	4	no	—
592	D₄	—	134	2	no	—
593	D₄	—	134	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	268	2	no	—
597	C₂×C₄	—	268	2	no	—
598	C₂×C₄	—	268	2	no	—
599	C₂×C₄	—	268	2	no	—
600	C₂×C₄	—	268	1	no	—
601	C₂×C₄	—	268	2	no	—
602	C₂×C₄	—	67	1	no	—
603	C₂×C₄	—	67	1	no	—
604	C₂×C₄	—	67	4	no	—
605	C₂×C₄	—	67	1	no	—
606	C₂×C₄	—	67	1	no	—
607	C₂×C₄	—	67	2	no	—
608	C₂×C₄	—	67	1	no	—
609	C₂×C₄	—	67	2	no	—
610	C₂×C₄	—	67	1	no	—
611	C₂×C₄	—	67	1	no	—
612	C₂×C₄	—	134	2	no	—
613	C₂×C₄	—	134	4	no	—
614	C₂×C₄	—	134	4	no	—
615	C₂×C₄	—	134	4	no	—
616	C₂×C₄	—	134	4	no	—
617	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₆₇	1	2	yes	—
620	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₆₇	1	2	yes	—
622	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	268	8	no	—
633	C₂²	—	67	2	no	—
634	C₂²	—	134	2	no	—
635	C₂²	—	134	2	no	—
636	C₂²	—	134	2	no	—
637	C₂²	—	134	2	no	—
638	C₂²	—	134	2	no	—
639	C₂²	—	134	2	no	—
640	C₂²	—	134	1	no	—
641	C₂²	—	134	1	no	—
642	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
643	C₄	—	2	2	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	2	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	67	2	no	—
652	C₄	—	67	2	no	—
653	C₄	—	134	2	no	—
654	C₄	—	134	2	no	—
655	C₄	—	134	1	no	—
656	C₄	—	134	1	no	—
657	C₄	—	134	1	no	—
658	C₄	—	134	1	no	—
659	C₄	—	134	1	no	—
660	C₄	#41×D₆₇	1	2	yes	—
661	C₂	—	4	2	no	—
662	C₂	—	4	2	no	—
663	C₂	—	268	2	no	—
664	C₂	—	268	2	no	—
665	C₂	—	134	2	no	—
666	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
667	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
668	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#559×C₆₇	C₂
hypercenter	#559	D₆₇
hypocenter	C₆₇	#3506
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #559

Complements

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

N	H ≅ G/N	type
1. #16864131	C₂	semidirect
2. #16864129	C₂	semidirect
3. #16864128	C₂	semidirect
4. #16864118	C₂	semidirect
5. #16864115	C₂	semidirect
6. #16864108	C₂	semidirect
7. #16864095	C₂	semidirect
8. #16864091	C₂	semidirect
9. #16864067	C₂	semidirect
10. #16864066	C₂	semidirect
11. #16864044	C₂	semidirect
12. #16863982	C₂	semidirect
13. #16863980	C₂	semidirect
14. #16863964	C₂	semidirect
15. #16863959	C₂	semidirect
16. #16863950	C₂	semidirect
17. #16863945	C₂	semidirect
18. #16863905	C₂	semidirect
19. #16863904	C₂	semidirect
20. #16863878	C₂	semidirect
21. #16863875	C₂	semidirect
22. C₄×D₄×D₆₇	C₂	semidirect
23. #559×C₆₇	C₂	semidirect
25. C₂×#11761628	C₂²	semidirect
27. C₂×#11761627	C₂²	semidirect
30. #14524042	C₂²	semidirect
31. #14524041	C₂²	semidirect
32. #14524041	C₂²	semidirect
36. #14524039	C₂²	semidirect
37. #14524038	C₂²	semidirect
38. #14524037	C₂²	semidirect
39. #14524036	C₂²	semidirect
40. #14524036	C₂²	semidirect
41. #14524033	C₂²	semidirect
42. #14524033	C₂²	semidirect
44. #14524032	C₂²	semidirect
46. #14524031	C₂²	semidirect
48. #14524029	C₂²	semidirect
49. #14524029	C₂²	semidirect
50. #14524028	C₂²	semidirect
51. #14524028	C₂²	semidirect
52. #14524027	C₂²	semidirect
53. #14524026	C₂²	semidirect
54. #14524025	C₂²	semidirect
55. #14524025	C₂²	semidirect
59. #14524021	C₂²	semidirect
60. #14524020	C₂²	semidirect
62. #14524017	C₂²	semidirect
67. #14524016	C₂²	semidirect
68. #14524016	C₂²	semidirect
71. #14524015	C₂²	semidirect
72. #14524015	C₂²	semidirect
73. #14524014	C₂²	semidirect
78. Q₈×Dic₆₇	C₂²	semidirect
79. C₄×Dic₁₃₄	C₂²	semidirect
80. C₄×Dic₁₃₄	C₂²	semidirect
81. C₄×Dic₁₃₄	C₂²	semidirect
82. C₄×Dic₁₃₄	C₂²	semidirect
83. #14524008	C₂²	semidirect
86. C₄×D₂₆₈	C₂²	semidirect
88. D₄×Dic₆₇	C₂²	semidirect
91. #14524005	C₂²	semidirect
92. #14524005	C₂²	semidirect
95. C₄×C₂²⋊D₆₇	C₂²	semidirect
98. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
100. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
103. #14524000	C₂²	semidirect
104. #14524000	C₂²	semidirect
105. #14523999	C₂²	semidirect
106. #14523999	C₂²	semidirect
107. C₂×Dic₆₇⋊C₄	C₂²	semidirect
109. C₄⋊C₄×D₆₇	C₂²	semidirect
114. #124×C₆₇	C₂²	semidirect
115. #124×C₆₇	C₂²	semidirect
116. #123×C₆₇	C₂²	semidirect
117. #123×C₆₇	C₂²	semidirect
118. C₄×Q₈×C₆₇	C₂²	semidirect
119. C₄×Q₈×C₆₇	C₂²	semidirect
121. C₄×D₄×C₆₇	C₂²	semidirect
122. C₄×D₄×C₆₇	C₂²	semidirect
286. C₄×D₆₇	#41	semidirect
335. C₆₇	#3506	semidirect
339. #559	D₆₇	semidirect
387. #124	C₂×D₆₇	semidirect
388. #124	C₂×D₆₇	semidirect
395. #123	C₂×D₆₇	semidirect
396. #123	C₂×D₆₇	semidirect
425. C₄×Q₈	C₂×D₆₇	semidirect
426. C₄×Q₈	C₂×D₆₇	semidirect
445. C₄×D₄	C₂×D₆₇	semidirect
446. C₄×D₄	C₂×D₆₇	semidirect