Subgroups — #22574437

Order 8576.

1134 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864144	C₂	1	2	yes	maximal, complemented
2	#16864142	C₂	1	2	yes	maximal, complemented
3	#16864101	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864058	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864056	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864049	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864047	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864042	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864042	C₂	1	2	yes	maximal, complemented
10	#16864037	C₂	1	2	yes	maximal, complemented
11	#16864037	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864021	C₂	1	2	yes	maximal, complemented
13	#16864020	C₂	1	1	yes	maximal, characteristic, complemented
14	#16864018	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863994	C₂	1	2	yes	maximal, complemented
16	#16863979	C₂	1	2	yes	maximal, complemented
17	#16863977	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863976	C₂	1	1	yes	maximal, characteristic, complemented
19	#16863976	C₂	1	2	yes	maximal, complemented
20	#16863905	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²⋊Q₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#14524018	C₂	1	1	yes	maximal, characteristic, complemented
23	#554×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761629	C₂²	1	2	yes	complemented
25	C₂×#11761629	C₂²	1	1	yes	characteristic, complemented
26	C₂×#11761628	C₂²	1	2	yes	complemented
27	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
28	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
29	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₂₆₈	C₂²	1	1	yes	characteristic
31	C₂²×D₂₆₈	C₂²	1	2	yes	—
32	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
33	#14524042	C₂²	1	1	yes	characteristic, complemented
34	#14524038	C₂²	1	2	yes	complemented
35	#14524037	C₂²	1	2	yes	complemented
36	#14524033	C₂²	1	2	yes	complemented
37	#14524032	C₂²	1	1	yes	characteristic, complemented
38	#14524032	C₂²	1	2	yes	complemented
39	#14524031	C₂²	1	2	yes	complemented
40	#14524031	C₂²	1	1	yes	characteristic, complemented
41	#14524031	C₂²	1	2	yes	complemented
42	#14524029	C₂²	1	2	yes	complemented
43	#14524028	C₂²	1	2	yes	complemented
44	#14524028	C₂²	1	2	yes	complemented
45	#14524028	C₂²	1	2	yes	complemented
46	#14524028	C₂²	1	2	yes	complemented
47	#14524028	C₂²	1	2	yes	complemented
48	#14524028	C₂²	1	2	yes	complemented
49	#14524028	C₂²	1	2	yes	complemented
50	#14524028	C₂²	1	1	yes	characteristic, complemented
51	#14524026	C₂²	1	2	yes	complemented
52	#14524025	C₂²	1	1	yes	characteristic, complemented
53	#14524023	C₂²	1	1	yes	characteristic, complemented
54	#14524023	C₂²	1	2	yes	complemented
55	#14524023	C₂²	1	2	yes	complemented
56	#14524023	C₂²	1	1	yes	characteristic, complemented
57	#14524022	C₂²	1	2	yes	—
58	#14524022	C₂²	1	1	yes	characteristic
59	#14524021	C₂²	1	2	yes	complemented
60	#14524021	C₂²	1	2	yes	complemented
61	#14524021	C₂²	1	2	yes	complemented
62	#14524021	C₂²	1	2	yes	complemented
63	#14524021	C₂²	1	2	yes	complemented
64	#14524021	C₂²	1	2	yes	complemented
65	#14524021	C₂²	1	1	yes	characteristic, complemented
66	#14524020	C₂²	1	1	yes	characteristic
67	#14524020	C₂²	1	2	yes	—
68	#14524019	C₂²	1	1	yes	characteristic, complemented
69	#14524019	C₂²	1	2	yes	complemented
70	#14524019	C₂²	1	2	yes	complemented
71	#14524018	C₂²	1	1	yes	characteristic
72	#14524018	C₂²	1	1	yes	characteristic
73	#14524018	C₂²	1	1	yes	characteristic
74	#14524018	C₂²	1	1	yes	characteristic
75	#14524018	C₂²	1	2	yes	—
76	#14524018	C₂²	1	2	yes	—
77	#14524018	C₂²	1	1	yes	characteristic, complemented
78	#14524018	C₂²	1	2	yes	complemented
79	#14524018	C₂²	1	2	yes	complemented
80	#14524018	C₂²	1	2	yes	complemented
81	#14524018	C₂²	1	2	yes	complemented
82	#14524017	C₂²	1	1	yes	characteristic, complemented
83	#14524017	C₂²	1	2	yes	complemented
84	#14524017	C₂²	1	2	yes	complemented
85	#14524016	C₂²	1	2	yes	complemented
86	#14524016	C₂²	1	2	yes	complemented
87	#14524016	C₂²	1	2	yes	complemented
88	#14524016	C₂²	1	1	yes	characteristic, complemented
89	#14524016	C₂²	1	2	yes	complemented
90	#14524015	C₂²	1	1	yes	characteristic
91	#14524013	C₂²	1	1	yes	characteristic
92	#14524013	C₂²	1	2	yes	—
93	#14524011	C₂²	1	1	yes	characteristic
94	#14524011	C₂²	1	2	yes	—
95	#14524008	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
97	C₄×D₂₆₈	C₂²	1	2	yes	complemented
98	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
99	#14524005	C₂²	1	1	yes	characteristic, complemented
100	#14524005	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
104	#14524000	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
106	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
108	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#125×C₆₇	C₂²	1	2	yes	complemented
114	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
115	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
118	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₆₇	C₂²	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₇	C₂³	1	1	yes	characteristic
124	C₂³×D₆₇	C₂³	1	2	yes	—
125	#11761629	—	4	4	no	—
126	#11761629	—	4	2	no	—
127	#11761628	—	4	2	no	—
128	#11761628	—	4	2	no	—
129	#11761628	—	4	4	no	—
130	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
132	C₂×Dic₁₃₄	C₂³	1	2	yes	—
133	C₂×Dic₁₃₄	C₂³	1	2	yes	—
134	Q₈×D₆₇	—	4	2	no	—
135	C₂×D₂₆₈	—	4	2	no	—
136	C₂×D₂₆₈	—	4	4	no	—
137	C₂×D₂₆₈	C₂³	1	2	yes	—
138	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
139	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
140	C₂×D₂₆₈	C₂³	1	2	yes	—
141	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
142	C₂×D₂₆₈	C₂³	1	2	yes	—
143	C₂×D₂₆₈	C₂³	1	2	yes	—
144	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
145	C₂×D₂₆₈	C₂³	1	2	yes	—
146	C₂×D₂₆₈	C₂³	1	2	yes	—
147	C₂×D₂₆₈	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
154	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₆₇	—	4	2	no	—
156	C₂×C₄×D₆₇	C₂³	1	2	yes	—
157	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₆₇	C₂³	1	2	yes	—
161	C₂×C₄×D₆₇	C₂³	1	2	yes	—
162	C₂×C₄×D₆₇	C₂³	1	2	yes	—
163	C₂×C₄×D₆₇	C₂³	1	2	yes	—
164	C₂×C₄×D₆₇	C₂³	1	2	yes	—
165	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₆₇	C₂³	1	2	yes	—
167	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
168	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
169	C₄⋊Dic₆₇	C₂³	1	2	yes	—
170	C₄⋊Dic₆₇	C₂³	1	2	yes	—
171	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
172	Dic₆₇⋊C₄	C₂³	1	2	yes	—
173	Dic₆₇⋊C₄	C₂³	1	2	yes	—
174	Dic₆₇⋊C₄	C₂³	1	2	yes	—
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	Dic₆₇⋊C₄	C₂³	1	2	yes	—
180	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
181	Dic₆₇⋊C₄	C₂³	1	2	yes	—
182	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
184	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
185	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₆₇)⋊C₄	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	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	1	yes	characteristic
196	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
200	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
206	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
207	C₄×Dic₆₇	C₂³	1	2	yes	—
208	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
210	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
214	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
215	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
227	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
228	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
229	C₄²×C₆₇	C₂³	1	2	yes	—
230	C₄²×C₆₇	C₂³	1	1	yes	characteristic
231	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
232	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₂²×D₆₇	—	2	2	no	—
234	C₂²×D₆₇	—	2	4	no	—
235	C₂²×D₆₇	—	2	2	no	—
236	C₂²×D₆₇	—	4	1	no	—
237	C₂²×D₆₇	—	4	2	no	—
238	C₂²×D₆₇	—	4	2	no	—
239	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
240	C₂²×D₆₇	C₂⁴	1	2	yes	—
241	C₂²×D₆₇	C₂⁴	1	2	yes	—
242	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
243	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
244	Q₈×C₆₇	—	2	2	no	—
245	Q₈×C₆₇	—	4	2	no	—
246	D₄×C₆₇	—	2	2	no	—
247	C₂×C₄×C₆₇	—	2	2	no	—
248	C₂×C₄×C₆₇	—	2	2	no	—
249	C₂×C₄×C₆₇	—	4	2	no	—
250	C₂×C₄×C₆₇	—	4	2	no	—
251	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
255	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
258	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
259	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
260	C₂²⋊D₆₇	—	2	2	no	—
261	C₂²⋊D₆₇	—	2	2	no	—
262	C₂²⋊D₆₇	—	4	2	no	—
263	C₂²⋊D₆₇	—	4	1	no	—
264	C₂²⋊D₆₇	—	4	2	no	—
265	C₂²⋊D₆₇	—	4	1	no	—
266	C₂×Dic₆₇	—	4	1	no	—
267	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₆₇	C₂⁴	1	2	yes	—
270	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₆₇	C₂⁴	1	2	yes	—
273	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
274	D₂₆₈	—	2	4	no	—
275	D₂₆₈	—	2	4	no	—
276	D₂₆₈	—	2	2	no	—
277	D₂₆₈	—	2	2	no	—
278	D₂₆₈	—	2	2	no	—
279	D₂₆₈	—	4	2	no	—
280	D₂₆₈	—	4	2	no	—
281	D₂₆₈	—	4	2	no	—
282	D₂₆₈	—	4	1	no	—
283	D₂₆₈	—	4	2	no	—
284	D₂₆₈	—	4	2	no	—
285	C₄×D₆₇	—	2	4	no	—
286	C₄×D₆₇	—	2	2	no	—
287	C₄×D₆₇	—	2	2	no	—
288	C₄×D₆₇	—	2	2	no	—
289	C₄×D₆₇	—	4	1	no	—
290	C₄×D₆₇	—	4	1	no	—
291	C₄×D₆₇	—	4	2	no	—
292	C₄×D₆₇	—	4	2	no	—
293	C₄×D₆₇	—	4	2	no	—
294	C₄×D₆₇	—	4	2	no	—
295	C₄×D₆₇	—	4	2	no	—
296	C₄×D₆₇	—	4	2	no	—
297	Dic₁₃₄	—	2	2	no	—
298	Dic₁₃₄	—	4	2	no	—
299	Dic₁₃₄	—	4	2	no	—
300	Dic₁₃₄	—	4	1	no	—
301	C₂²×C₆₇	—	2	1	no	—
302	C₂²×C₆₇	—	2	1	no	—
303	C₂²×C₆₇	—	2	1	no	—
304	C₂²×C₆₇	—	2	1	no	—
305	C₂²×C₆₇	—	2	1	no	—
306	C₂²×C₆₇	2₋¹⁺⁴	1	2	yes	—
307	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
308	C₂×D₆₇	—	2	1	no	—
309	C₂×D₆₇	—	2	1	no	—
310	C₂×D₆₇	—	2	1	no	—
311	C₂×D₆₇	—	2	1	no	—
312	C₂×D₆₇	—	2	1	no	—
313	C₂×D₆₇	—	2	2	no	—
314	C₂×D₆₇	—	2	2	no	—
315	C₂×D₆₇	—	2	2	no	—
316	C₂×D₆₇	—	2	2	no	—
317	C₂×D₆₇	—	2	1	no	—
318	C₂×D₆₇	—	2	1	no	—
319	C₂×D₆₇	—	2	1	no	—
320	C₂×D₆₇	—	2	2	no	—
321	C₂×D₆₇	—	2	2	no	—
322	C₂×D₆₇	—	4	4	no	—
323	C₂×D₆₇	—	8	4	no	—
324	C₂×D₆₇	H(5,𝔽₂)	1	2	yes	—
325	C₄×C₆₇	—	2	1	no	—
326	C₄×C₆₇	—	2	2	no	—
327	C₄×C₆₇	—	2	2	no	—
328	C₄×C₆₇	—	2	2	no	—
329	C₄×C₆₇	—	2	1	no	—
330	C₄×C₆₇	—	2	1	no	—
331	C₄×C₆₇	—	2	2	no	—
332	C₄×C₆₇	—	2	1	no	—
333	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
334	Dic₆₇	—	2	2	no	—
335	Dic₆₇	—	2	1	no	—
336	Dic₆₇	—	2	1	no	—
337	Dic₆₇	—	2	2	no	—
338	Dic₆₇	—	2	1	no	—
339	Dic₆₇	—	2	1	no	—
340	Dic₆₇	—	2	1	no	—
341	C₂×C₆₇	—	2	2	no	—
342	C₂×C₆₇	—	4	1	no	—
343	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
346	D₆₇	—	2	2	no	—
347	D₆₇	—	4	1	no	—
348	D₆₇	—	4	1	no	—
349	D₆₇	—	4	2	no	—
350	D₆₇	—	4	2	no	—
351	#3536	—	67	1	no	maximal, Sylow
352	C₆₇	#3536	1	1	yes	characteristic, complemented, Sylow
353	#562	—	67	2	no	—
354	#562	—	67	2	no	—
355	#554	—	67	1	no	—
356	#554	D₆₇	1	1	yes	characteristic, complemented
357	#548	—	67	1	no	—
358	#548	—	67	1	no	—
359	#547	—	67	1	no	—
360	#547	—	67	1	no	—
361	#546	—	67	2	no	—
362	#546	—	67	1	no	—
363	#546	—	67	2	no	—
364	#546	—	67	1	no	—
365	#543	—	67	2	no	—
366	#542	—	67	1	no	—
367	#542	—	67	1	no	—
368	#539	—	67	2	no	—
369	#538	—	67	2	no	—
370	#537	—	67	2	no	—
371	#537	—	67	1	no	—
372	#537	—	67	1	no	—
373	#525	—	67	1	no	—
374	C₂×C₂²⋊Q₈	—	67	1	no	—
375	C₂×#121	—	67	1	no	—
376	C₂×#41	—	67	2	no	—
377	C₂×#41	—	67	1	no	—
378	C₂×#41	—	67	1	no	—
379	C₂×#41	—	67	2	no	—
380	C₂×#41	—	67	1	no	—
381	C₂²×Q₈	—	67	1	no	—
382	C₂²×D₄	—	67	1	no	—
383	C₂²×D₄	—	67	2	no	—
384	C₂³×C₄	—	67	1	no	—
385	C₄⋊Q₈	—	67	1	no	—
386	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
387	#126	—	67	2	no	—
388	#126	—	67	2	no	—
389	#125	—	67	2	no	—
390	#125	C₂×D₆₇	1	2	yes	complemented
391	#124	—	67	1	no	—
392	#124	—	67	2	no	—
393	#124	—	67	2	no	—
394	#124	—	67	2	no	—
395	#124	—	67	1	no	—
396	#124	—	67	2	no	—
397	#123	—	67	2	no	—
398	#123	—	67	1	no	—
399	#123	—	67	2	no	—
400	#123	—	67	2	no	—
401	#123	—	67	2	no	—
402	#123	—	67	2	no	—
403	#123	—	67	2	no	—
404	#123	—	67	2	no	—
405	#123	—	67	2	no	—
406	#123	—	67	1	no	—
407	C₂²⋊Q₈	—	67	1	no	—
408	C₂²⋊Q₈	—	67	2	no	—
409	C₂²⋊Q₈	—	67	2	no	—
410	C₂²⋊Q₈	—	67	1	no	—
411	C₂²⋊Q₈	—	67	2	no	—
412	C₂²⋊Q₈	—	67	1	no	—
413	C₂²⋊Q₈	—	67	2	no	—
414	C₂²⋊Q₈	—	67	1	no	—
415	C₂²⋊Q₈	—	67	2	no	—
416	C₂²⋊Q₈	—	67	2	no	—
417	C₂²⋊Q₈	—	67	2	no	—
418	C₂²⋊Q₈	—	67	1	no	—
419	C₂²⋊Q₈	—	67	2	no	—
420	C₂²⋊Q₈	—	67	2	no	—
421	C₂²⋊Q₈	—	67	2	no	—
422	C₂²⋊Q₈	—	67	2	no	—
423	C₂²⋊Q₈	—	67	2	no	—
424	C₂²⋊Q₈	—	67	1	no	—
425	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
426	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	—
427	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
428	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
429	#121	—	67	1	no	—
430	#121	—	67	2	no	—
431	#121	—	67	1	no	—
432	#121	—	67	2	no	—
433	#121	—	67	2	no	—
434	#121	—	67	1	no	—
435	#121	—	67	1	no	—
436	#121	—	67	1	no	—
437	#121	—	67	1	no	—
438	#121	—	67	2	no	—
439	#121	—	67	1	no	—
440	#121	—	67	2	no	—
441	#121	—	67	2	no	—
442	#121	—	67	2	no	—
443	#121	—	67	2	no	—
444	#121	—	67	1	no	—
445	#121	—	67	2	no	—
446	#121	—	67	2	no	—
447	#121	—	67	2	no	—
448	#121	—	67	2	no	—
449	#120	—	67	1	no	—
450	#120	—	67	2	no	—
451	#120	—	67	1	no	—
452	#120	—	67	2	no	—
453	C₄×Q₈	—	67	1	no	—
454	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
455	C₄×D₄	—	67	1	no	—
456	C₄×D₄	—	67	1	no	—
457	C₄×D₄	—	67	2	no	—
458	C₄×D₄	—	67	2	no	—
459	C₄×D₄	—	67	1	no	—
460	C₄×D₄	—	67	1	no	—
461	C₄×D₄	—	67	2	no	—
462	C₄×D₄	—	67	1	no	—
463	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
464	C₄×D₄	C₂×D₆₇	1	2	yes	—
465	#117	—	67	1	no	—
466	C₂×C₄⋊C₄	—	67	2	no	—
467	C₂×C₄⋊C₄	—	67	1	no	—
468	C₂×C₄⋊C₄	—	67	1	no	—
469	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
471	C₂×C₂²⋊C₄	—	67	2	no	—
472	C₂×C₂²⋊C₄	—	67	2	no	—
473	C₂×C₂²⋊C₄	—	67	2	no	—
474	C₂×C₂²⋊C₄	—	67	2	no	—
475	C₂⁴	—	67	2	no	—
476	C₂⁴	—	67	1	no	—
477	#41	—	268	2	no	—
478	#41	—	268	2	no	—
479	#41	—	268	4	no	—
480	#41	—	268	2	no	—
481	#41	—	268	4	no	—
482	C₂×Q₈	—	268	2	no	—
483	C₂×Q₈	—	67	1	no	—
484	C₂×Q₈	—	67	2	no	—
485	C₂×Q₈	—	67	2	no	—
486	C₂×Q₈	—	67	1	no	—
487	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
488	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
489	C₂×D₄	—	268	2	no	—
490	C₂×D₄	—	268	4	no	—
491	C₂×D₄	—	67	1	no	—
492	C₂×D₄	—	67	2	no	—
493	C₂×D₄	—	67	2	no	—
494	C₂×D₄	—	67	1	no	—
495	C₂×D₄	—	67	1	no	—
496	C₂×D₄	—	67	1	no	—
497	C₂×D₄	—	67	2	no	—
498	C₂×D₄	—	67	1	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	1	no	—
504	C₂×D₄	—	67	2	no	—
505	C₂×D₄	—	67	2	no	—
506	C₂×D₄	—	67	1	no	—
507	C₂×D₄	—	67	1	no	—
508	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
509	C₂²×C₄	—	268	2	no	—
510	C₂²×C₄	—	67	1	no	—
511	C₂²×C₄	—	67	2	no	—
512	C₂²×C₄	—	67	2	no	—
513	C₂²×C₄	—	67	2	no	—
514	C₂²×C₄	—	67	2	no	—
515	C₂²×C₄	—	67	2	no	—
516	C₂²×C₄	—	67	1	no	—
517	C₂²×C₄	—	67	2	no	—
518	C₂²×C₄	—	67	1	no	—
519	C₂²×C₄	—	67	2	no	—
520	C₂²×C₄	—	67	1	no	—
521	C₂²×C₄	—	67	1	no	—
522	C₂²×C₄	—	67	1	no	—
523	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
525	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
526	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
527	C₄⋊C₄	—	67	1	no	—
528	C₄⋊C₄	—	67	2	no	—
529	C₄⋊C₄	—	67	2	no	—
530	C₄⋊C₄	—	67	2	no	—
531	C₄⋊C₄	—	67	2	no	—
532	C₄⋊C₄	—	67	2	no	—
533	C₄⋊C₄	—	67	1	no	—
534	C₄⋊C₄	—	67	1	no	—
535	C₄⋊C₄	—	67	2	no	—
536	C₄⋊C₄	—	67	1	no	—
537	C₄⋊C₄	—	67	1	no	—
538	C₄⋊C₄	—	67	1	no	—
539	C₄⋊C₄	—	67	2	no	—
540	C₄⋊C₄	—	67	2	no	—
541	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
544	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
546	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
547	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
548	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
549	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
550	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
551	C₂²⋊C₄	—	67	2	no	—
552	C₂²⋊C₄	—	67	1	no	—
553	C₂²⋊C₄	—	67	1	no	—
554	C₂²⋊C₄	—	67	2	no	—
555	C₂²⋊C₄	—	67	2	no	—
556	C₂²⋊C₄	—	67	2	no	—
557	C₂²⋊C₄	—	67	2	no	—
558	C₂²⋊C₄	—	67	2	no	—
559	C₂²⋊C₄	—	67	2	no	—
560	C₂²⋊C₄	—	67	2	no	—
561	C₂²⋊C₄	—	67	2	no	—
562	C₂²⋊C₄	—	67	2	no	—
563	C₂²⋊C₄	—	67	2	no	—
564	C₂²⋊C₄	—	67	1	no	—
565	C₂²⋊C₄	—	67	1	no	—
566	C₂²⋊C₄	—	67	1	no	—
567	C₂²⋊C₄	—	67	1	no	—
568	C₂²⋊C₄	—	67	2	no	—
569	C₂²⋊C₄	—	67	2	no	—
570	C₂²⋊C₄	—	67	2	no	—
571	C₂²⋊C₄	—	67	2	no	—
572	C₂²⋊C₄	—	67	1	no	—
573	C₂²⋊C₄	—	67	2	no	—
574	C₂²⋊C₄	—	67	1	no	—
575	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
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	C₄²	—	67	1	no	—
580	C₄²	—	67	2	no	—
581	C₄²	C₂²×D₆₇	1	1	yes	characteristic
582	C₄²	C₂²×D₆₇	1	2	yes	—
583	C₂³	—	268	1	no	—
584	C₂³	—	268	2	no	—
585	C₂³	—	268	2	no	—
586	C₂³	—	67	1	no	—
587	C₂³	—	67	2	no	—
588	C₂³	—	67	2	no	—
589	C₂³	—	67	1	no	—
590	C₂³	—	67	1	no	—
591	C₂³	—	134	2	no	—
592	C₂³	—	134	2	no	—
593	C₂³	—	134	4	no	—
594	C₂³	C₂³×D₆₇	1	1	yes	characteristic
595	C₂³	C₂³×D₆₇	1	1	yes	characteristic
596	Q₈	—	2	2	no	—
597	Q₈	—	4	2	no	—
598	Q₈	—	268	2	no	—
599	Q₈	—	268	2	no	—
600	Q₈	—	268	1	no	—
601	Q₈	—	134	2	no	—
602	D₄	—	2	2	no	—
603	D₄	—	268	2	no	—
604	D₄	—	268	2	no	—
605	D₄	—	268	2	no	—
606	D₄	—	268	2	no	—
607	D₄	—	268	1	no	—
608	D₄	—	268	2	no	—
609	D₄	—	268	2	no	—
610	D₄	—	268	1	no	—
611	D₄	—	268	1	no	—
612	D₄	—	268	2	no	—
613	D₄	—	134	4	no	—
614	D₄	—	134	4	no	—
615	D₄	—	134	2	no	—
616	D₄	—	134	2	no	—
617	D₄	—	134	2	no	—
618	D₄	—	134	2	no	—
619	D₄	—	134	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	268	1	no	—
625	C₂×C₄	—	268	1	no	—
626	C₂×C₄	—	268	2	no	—
627	C₂×C₄	—	268	2	no	—
628	C₂×C₄	—	268	2	no	—
629	C₂×C₄	—	268	2	no	—
630	C₂×C₄	—	268	2	no	—
631	C₂×C₄	—	268	2	no	—
632	C₂×C₄	—	268	1	no	—
633	C₂×C₄	—	67	1	no	—
634	C₂×C₄	—	67	1	no	—
635	C₂×C₄	—	67	2	no	—
636	C₂×C₄	—	67	1	no	—
637	C₂×C₄	—	67	2	no	—
638	C₂×C₄	—	67	1	no	—
639	C₂×C₄	—	67	1	no	—
640	C₂×C₄	—	134	4	no	—
641	C₂×C₄	—	134	2	no	—
642	C₂×C₄	—	134	2	no	—
643	C₂×C₄	—	134	2	no	—
644	C₂×C₄	C₂³×D₆₇	1	2	yes	—
645	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₆₇	1	2	yes	—
648	C₂×C₄	C₂³×D₆₇	1	2	yes	—
649	C₂×C₄	C₂³×D₆₇	1	2	yes	—
650	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	268	4	no	—
659	C₂²	—	536	4	no	—
660	C₂²	—	67	2	no	—
661	C₂²	—	134	1	no	—
662	C₂²	—	134	2	no	—
663	C₂²	—	134	2	no	—
664	C₂²	—	134	1	no	—
665	C₂²	—	134	1	no	—
666	C₂²	—	134	2	no	—
667	C₂²	—	134	2	no	—
668	C₂²	—	134	1	no	—
669	C₂²	—	134	1	no	—
670	C₂²	—	134	1	no	—
671	C₂²	—	134	2	no	—
672	C₂²	—	134	2	no	—
673	C₂²	—	134	1	no	—
674	C₂²	—	134	1	no	—
675	C₂²	#14524091	1	2	yes	—
676	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	1	no	—
685	C₄	—	134	2	no	—
686	C₄	—	134	1	no	—
687	C₄	—	134	1	no	—
688	C₄	—	134	1	no	—
689	C₄	—	134	1	no	—
690	C₄	—	134	2	no	—
691	C₄	—	134	1	no	—
692	C₄	#14524089	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	268	1	no	—
696	C₂	—	268	2	no	—
697	C₂	—	268	2	no	—
698	C₂	—	268	1	no	—
699	C₂	—	134	2	no	—
700	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
701	C₂	C₂×#14524089	1	1	yes	characteristic
702	C₂	C₂×#14524091	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#554×C₆₇	C₂
hypercenter	#554	D₆₇
hypocenter	C₆₇	#3536
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #16864144	C₂	semidirect
2. #16864142	C₂	semidirect
3. #16864101	C₂	semidirect
4. #16864058	C₂	semidirect
5. #16864056	C₂	semidirect
6. #16864049	C₂	semidirect
7. #16864047	C₂	semidirect
8. #16864042	C₂	semidirect
9. #16864042	C₂	semidirect
10. #16864037	C₂	semidirect
11. #16864037	C₂	semidirect
12. #16864021	C₂	semidirect
13. #16864020	C₂	semidirect
14. #16864018	C₂	semidirect
15. #16863994	C₂	semidirect
16. #16863979	C₂	semidirect
17. #16863977	C₂	semidirect
18. #16863976	C₂	semidirect
19. #16863976	C₂	semidirect
20. #16863905	C₂	semidirect
21. C₂²⋊Q₈×D₆₇	C₂	semidirect
22. C₂×#14524018	C₂	semidirect
23. #554×C₆₇	C₂	semidirect
24. C₂×#11761629	C₂²	semidirect
25. C₂×#11761629	C₂²	semidirect
26. C₂×#11761628	C₂²	semidirect
27. C₂×#11761628	C₂²	semidirect
28. C₂×#11761628	C₂²	semidirect
29. C₂×Q₈×D₆₇	C₂²	semidirect
33. #14524042	C₂²	semidirect
34. #14524038	C₂²	semidirect
35. #14524037	C₂²	semidirect
36. #14524033	C₂²	semidirect
37. #14524032	C₂²	semidirect
38. #14524032	C₂²	semidirect
39. #14524031	C₂²	semidirect
40. #14524031	C₂²	semidirect
41. #14524031	C₂²	semidirect
42. #14524029	C₂²	semidirect
43. #14524028	C₂²	semidirect
44. #14524028	C₂²	semidirect
45. #14524028	C₂²	semidirect
46. #14524028	C₂²	semidirect
47. #14524028	C₂²	semidirect
48. #14524028	C₂²	semidirect
49. #14524028	C₂²	semidirect
50. #14524028	C₂²	semidirect
51. #14524026	C₂²	semidirect
52. #14524025	C₂²	semidirect
53. #14524023	C₂²	semidirect
54. #14524023	C₂²	semidirect
55. #14524023	C₂²	semidirect
56. #14524023	C₂²	semidirect
59. #14524021	C₂²	semidirect
60. #14524021	C₂²	semidirect
61. #14524021	C₂²	semidirect
62. #14524021	C₂²	semidirect
63. #14524021	C₂²	semidirect
64. #14524021	C₂²	semidirect
65. #14524021	C₂²	semidirect
68. #14524019	C₂²	semidirect
69. #14524019	C₂²	semidirect
70. #14524019	C₂²	semidirect
77. #14524018	C₂²	semidirect
78. #14524018	C₂²	semidirect
79. #14524018	C₂²	semidirect
80. #14524018	C₂²	semidirect
81. #14524018	C₂²	semidirect
82. #14524017	C₂²	semidirect
83. #14524017	C₂²	semidirect
84. #14524017	C₂²	semidirect
85. #14524016	C₂²	semidirect
86. #14524016	C₂²	semidirect
87. #14524016	C₂²	semidirect
88. #14524016	C₂²	semidirect
89. #14524016	C₂²	semidirect
95. #14524008	C₂²	semidirect
96. C₄×D₂₆₈	C₂²	semidirect
97. C₄×D₂₆₈	C₂²	semidirect
98. C₄×D₂₆₈	C₂²	semidirect
99. #14524005	C₂²	semidirect
100. #14524005	C₂²	semidirect
103. C₄×C₂²⋊D₆₇	C₂²	semidirect
104. #14524000	C₂²	semidirect
105. C₄⋊C₄×D₆₇	C₂²	semidirect
106. C₄⋊C₄×D₆₇	C₂²	semidirect
107. C₄⋊C₄×D₆₇	C₂²	semidirect
112. C₄⋊Q₈×C₆₇	C₂²	semidirect
113. #125×C₆₇	C₂²	semidirect
116. C₂²⋊Q₈×C₆₇	C₂²	semidirect
117. C₂²⋊Q₈×C₆₇	C₂²	semidirect
118. C₄×Q₈×C₆₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₆₇	C₂²	semidirect
352. C₆₇	#3536	semidirect
356. #554	D₆₇	semidirect
386. C₄⋊Q₈	C₂×D₆₇	semidirect
390. #125	C₂×D₆₇	semidirect
427. C₂²⋊Q₈	C₂×D₆₇	semidirect
428. C₂²⋊Q₈	C₂×D₆₇	semidirect
454. C₄×Q₈	C₂×D₆₇	semidirect
470. C₂×C₄⋊C₄	C₂×D₆₇	semidirect