Subgroups — #22573954

Order 8576.

1022 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864114	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864107	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864104	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864087	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864087	C₂	1	2	yes	maximal, complemented
6	#16864086	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864085	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864082	C₂	1	2	yes	maximal, complemented
9	#16864080	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864076	C₂	1	2	yes	maximal, complemented
11	#16864071	C₂	1	2	yes	maximal, complemented
12	#16864023	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864010	C₂	1	2	yes	maximal, complemented
14	#16864003	C₂	1	2	yes	maximal, complemented
15	#16863969	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863950	C₂	1	2	yes	maximal, complemented
17	#16863929	C₂	1	2	yes	maximal, complemented
18	#16863905	C₂	1	1	yes	maximal, characteristic
19	C₂²⋊Q₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863876	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863872	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#556×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761628	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
27	#14524042	C₂²	1	2	yes	complemented
28	#14524042	C₂²	1	1	yes	characteristic, complemented
29	#14524041	C₂²	1	2	yes	complemented
30	#14524037	C₂²	1	2	yes	complemented
31	#14524037	C₂²	1	2	yes	complemented
32	#14524036	C₂²	1	2	yes	—
33	#14524036	C₂²	1	2	yes	—
34	#14524036	C₂²	1	2	yes	—
35	#14524036	C₂²	1	2	yes	complemented
36	#14524035	C₂²	1	2	yes	complemented
37	#14524035	C₂²	1	1	yes	characteristic, complemented
38	#14524034	C₂²	1	2	yes	complemented
39	#14524034	C₂²	1	1	yes	characteristic, complemented
40	#14524033	C₂²	1	2	yes	complemented
41	#14524033	C₂²	1	2	yes	complemented
42	#14524033	C₂²	1	2	yes	complemented
43	#14524033	C₂²	1	2	yes	complemented
44	#14524033	C₂²	1	2	yes	complemented
45	#14524029	C₂²	1	2	yes	—
46	#14524029	C₂²	1	2	yes	complemented
47	#14524028	C₂²	1	2	yes	—
48	#14524028	C₂²	1	2	yes	—
49	#14524028	C₂²	1	1	yes	characteristic
50	#14524025	C₂²	1	2	yes	—
51	#14524025	C₂²	1	2	yes	—
52	#14524025	C₂²	1	2	yes	—
53	#14524025	C₂²	1	1	yes	characteristic
54	#14524024	C₂²	1	2	yes	—
55	#14524023	C₂²	1	2	yes	—
56	#14524023	C₂²	1	1	yes	characteristic
57	#14524023	C₂²	1	1	yes	characteristic, complemented
58	#14524022	C₂²	1	1	yes	characteristic
59	#14524022	C₂²	1	1	yes	characteristic, complemented
60	#14524021	C₂²	1	2	yes	—
61	#14524021	C₂²	1	2	yes	—
62	#14524021	C₂²	1	1	yes	characteristic
63	#14524020	C₂²	1	1	yes	characteristic
64	#14524020	C₂²	1	2	yes	—
65	#14524020	C₂²	1	2	yes	complemented
66	#14524019	C₂²	1	2	yes	—
67	#14524019	C₂²	1	2	yes	—
68	#14524019	C₂²	1	1	yes	characteristic
69	#14524019	C₂²	1	2	yes	complemented
70	#14524019	C₂²	1	1	yes	characteristic, complemented
71	#14524016	C₂²	1	1	yes	characteristic
72	#14524015	C₂²	1	1	yes	characteristic
73	#14524013	C₂²	1	1	yes	characteristic
74	#14524011	C₂²	1	1	yes	characteristic
75	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
77	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
78	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
79	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
80	#14524008	C₂²	1	2	yes	complemented
81	#14524008	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₂₆₈	C₂²	1	2	yes	—
83	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
84	#14524005	C₂²	1	2	yes	—
85	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
87	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
88	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
89	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
90	#14524002	C₂²	1	1	yes	characteristic
91	#14524001	C₂²	1	1	yes	characteristic
92	#14524001	C₂²	1	2	yes	—
93	#14524001	C₂²	1	1	yes	characteristic
94	#14524001	C₂²	1	2	yes	complemented
95	#14524001	C₂²	1	1	yes	characteristic, complemented
96	#14524000	C₂²	1	1	yes	characteristic
97	#14524000	C₂²	1	2	yes	—
98	#14524000	C₂²	1	2	yes	—
99	#14524000	C₂²	1	2	yes	—
100	#14524000	C₂²	1	2	yes	—
101	#14523999	C₂²	1	2	yes	—
102	#14523999	C₂²	1	2	yes	complemented
103	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
104	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
105	C₄⋊C₄×D₆₇	C₂²	1	2	yes	—
106	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
109	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
111	C₄²×D₆₇	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#126×C₆₇	C₂²	1	2	yes	—
114	#126×C₆₇	C₂²	1	2	yes	complemented
115	#124×C₆₇	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
120	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
121	#117×C₆₇	C₂²	1	1	yes	characteristic
122	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₇	C₂³	1	1	yes	characteristic
124	#11761628	—	2	4	no	—
125	C₂×Dic₁₃₄	C₂³	1	2	yes	—
126	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₃₄	C₂³	1	2	yes	—
129	Q₈×D₆₇	—	2	4	no	—
130	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
131	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
136	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
137	C₂²×Dic₆₇	C₂³	1	2	yes	—
138	C₂×C₄×D₆₇	—	2	4	no	—
139	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₆₇	C₂³	1	2	yes	—
141	C₂×C₄×D₆₇	C₂³	1	2	yes	—
142	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₆₇	C₂³	1	2	yes	—
146	C₂×C₄×D₆₇	C₂³	1	2	yes	—
147	C₂×C₄×D₆₇	C₂³	1	2	yes	—
148	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₆₇	C₂³	1	2	yes	—
153	C₄⋊Dic₆₇	C₂³	1	2	yes	—
154	C₄⋊Dic₆₇	C₂³	1	2	yes	—
155	C₄⋊Dic₆₇	C₂³	1	2	yes	—
156	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₆₇	C₂³	1	2	yes	—
158	Dic₆₇⋊C₄	C₂³	1	2	yes	—
159	Dic₆₇⋊C₄	C₂³	1	2	yes	—
160	Dic₆₇⋊C₄	C₂³	1	2	yes	—
161	Dic₆₇⋊C₄	C₂³	1	2	yes	—
162	Dic₆₇⋊C₄	C₂³	1	2	yes	—
163	Dic₆₇⋊C₄	C₂³	1	2	yes	—
164	Dic₆₇⋊C₄	C₂³	1	2	yes	—
165	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₆₇⋊C₄	C₂³	1	2	yes	—
167	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₆₇⋊C₄	C₂³	1	2	yes	—
169	Dic₆₇⋊C₄	C₂³	1	2	yes	—
170	Dic₆₇⋊C₄	C₂³	1	2	yes	—
171	Dic₆₇⋊C₄	C₂³	1	2	yes	—
172	Dic₆₇⋊C₄	C₂³	1	2	yes	—
173	Dic₆₇⋊C₄	C₂³	1	2	yes	—
174	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
175	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
177	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
181	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₆₇)⋊C₄	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	1	yes	characteristic
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	1	yes	characteristic
194	C₄×Dic₆₇	C₂³	1	2	yes	—
195	C₄×Dic₆₇	C₂³	1	2	yes	—
196	C₄×Dic₆₇	C₂³	1	2	yes	—
197	C₄×Dic₆₇	C₂³	1	2	yes	—
198	C₄×Dic₆₇	C₂³	1	2	yes	—
199	C₄×Dic₆₇	C₂³	1	2	yes	—
200	C₄×Dic₆₇	C₂³	1	2	yes	—
201	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
202	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
204	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₄²×C₆₇	C₂³	1	2	yes	—
222	C₄²×C₆₇	C₂³	1	2	yes	—
223	C₄²×C₆₇	C₂³	1	1	yes	characteristic
224	C₄²×C₆₇	C₂³	1	2	yes	—
225	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
226	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
227	C₂²×D₆₇	—	2	2	no	—
228	C₂²×D₆₇	—	2	2	no	—
229	C₂²×D₆₇	—	4	1	no	—
230	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
232	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
233	Q₈×C₆₇	—	2	2	no	—
234	Q₈×C₆₇	—	4	2	no	—
235	D₄×C₆₇	—	4	1	no	—
236	C₂×C₄×C₆₇	—	2	2	no	—
237	C₂×C₄×C₆₇	—	2	2	no	—
238	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂²⋊D₆₇	—	2	2	no	—
248	C₂²⋊D₆₇	—	2	2	no	—
249	C₂²⋊D₆₇	—	2	2	no	—
250	C₂²⋊D₆₇	—	4	1	no	—
251	C₂×Dic₆₇	—	2	2	no	—
252	C₂×Dic₆₇	—	4	2	no	—
253	C₂×Dic₆₇	C₂⁴	1	2	yes	—
254	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₆₇	C₂⁴	1	2	yes	—
257	C₂×Dic₆₇	C₂⁴	1	2	yes	—
258	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₆₇	C₂⁴	1	2	yes	—
260	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
262	D₂₆₈	—	2	2	no	—
263	D₂₆₈	—	2	2	no	—
264	C₄×D₆₇	—	2	2	no	—
265	C₄×D₆₇	—	2	4	no	—
266	C₄×D₆₇	—	2	4	no	—
267	C₄×D₆₇	—	2	2	no	—
268	C₄×D₆₇	—	2	2	no	—
269	C₄×D₆₇	—	2	2	no	—
270	C₄×D₆₇	—	4	2	no	—
271	C₄×D₆₇	—	4	2	no	—
272	C₄×D₆₇	—	4	2	no	—
273	C₄×D₆₇	#41	1	4	yes	—
274	Dic₁₃₄	—	2	2	no	—
275	Dic₁₃₄	—	2	4	no	—
276	Dic₁₃₄	—	2	2	no	—
277	Dic₁₃₄	—	4	2	no	—
278	C₂²×C₆₇	—	2	1	no	—
279	C₂²×C₆₇	—	2	1	no	—
280	C₂²×C₆₇	—	2	1	no	—
281	C₂²×C₆₇	—	2	1	no	—
282	C₂²×C₆₇	—	2	1	no	—
283	C₂²×C₆₇	—	2	1	no	—
284	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
285	C₂×D₆₇	—	2	1	no	—
286	C₂×D₆₇	—	2	1	no	—
287	C₂×D₆₇	—	2	1	no	—
288	C₂×D₆₇	—	2	1	no	—
289	C₂×D₆₇	—	2	1	no	—
290	C₂×D₆₇	—	2	1	no	—
291	C₂×D₆₇	—	2	1	no	—
292	C₂×D₆₇	—	4	4	no	—
293	C₂×D₆₇	C₂×#41	1	2	yes	—
294	C₂×D₆₇	2₋¹⁺⁴	1	2	yes	—
295	C₄×C₆₇	—	2	2	no	—
296	C₄×C₆₇	—	2	1	no	—
297	C₄×C₆₇	—	2	1	no	—
298	C₄×C₆₇	—	2	2	no	—
299	C₄×C₆₇	—	2	1	no	—
300	C₄×C₆₇	—	2	2	no	—
301	C₄×C₆₇	—	2	2	no	—
302	C₄×C₆₇	—	2	1	no	—
303	C₄×C₆₇	C₂×#41	1	2	yes	—
304	Dic₆₇	—	2	2	no	—
305	Dic₆₇	—	2	1	no	—
306	Dic₆₇	—	2	1	no	—
307	Dic₆₇	—	2	2	no	—
308	Dic₆₇	—	2	1	no	—
309	Dic₆₇	—	2	1	no	—
310	Dic₆₇	—	2	2	no	—
311	Dic₆₇	—	2	2	no	—
312	Dic₆₇	C₂×#41	1	2	yes	—
313	C₂×C₆₇	—	4	1	no	—
314	C₂×C₆₇	—	4	1	no	—
315	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
316	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
317	C₂×C₆₇	#585	1	1	yes	characteristic
318	D₆₇	—	2	2	no	—
319	D₆₇	—	2	2	no	—
320	D₆₇	—	4	1	no	—
321	#3495	—	67	1	no	maximal, Sylow
322	C₆₇	#3495	1	1	yes	characteristic, complemented, Sylow
323	#556	—	67	1	no	—
324	#556	D₆₇	1	1	yes	characteristic, complemented
325	#554	—	67	1	no	—
326	#554	—	67	1	no	—
327	#552	—	67	2	no	—
328	#552	—	67	1	no	—
329	#552	—	67	1	no	—
330	#552	—	67	2	no	—
331	#552	—	67	1	no	—
332	#552	—	67	1	no	—
333	#551	—	67	2	no	—
334	#551	—	67	2	no	—
335	#544	—	67	1	no	—
336	#542	—	67	2	no	—
337	#541	—	67	2	no	—
338	#536	—	67	1	no	—
339	#533	—	67	2	no	—
340	#529	—	67	2	no	—
341	#525	—	67	1	no	—
342	C₂×C₂²⋊Q₈	—	67	1	no	—
343	#520	—	67	1	no	—
344	#519	—	67	1	no	—
345	C₂×#117	—	67	1	no	—
346	C₂×#41	—	67	1	no	—
347	C₂²×Q₈	—	67	1	no	—
348	C₂³×C₄	—	67	1	no	—
349	C₄⋊Q₈	—	67	2	no	—
350	C₄⋊Q₈	—	67	2	no	—
351	C₄⋊Q₈	—	67	1	no	—
352	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
353	#126	—	67	2	no	—
354	#126	—	67	2	no	—
355	#126	—	67	2	no	—
356	#126	—	67	2	no	—
357	#126	—	67	2	no	—
358	#126	—	67	2	no	—
359	#126	C₂×D₆₇	1	2	yes	—
360	#126	C₂×D₆₇	1	2	yes	complemented
361	#125	—	67	2	no	—
362	#125	—	67	2	no	—
363	#125	—	67	2	no	—
364	#125	—	67	2	no	—
365	#125	—	67	2	no	—
366	#125	—	67	2	no	—
367	#125	—	67	1	no	—
368	#125	—	67	2	no	—
369	#125	—	67	1	no	—
370	#124	—	67	2	no	—
371	#124	—	67	2	no	—
372	#124	C₂×D₆₇	1	2	yes	—
373	#123	—	67	2	no	—
374	#123	—	67	1	no	—
375	#123	—	67	2	no	—
376	#123	—	67	2	no	—
377	#123	—	67	1	no	—
378	#123	—	67	2	no	—
379	#123	—	67	2	no	—
380	#123	—	67	2	no	—
381	C₂²⋊Q₈	—	67	1	no	—
382	C₂²⋊Q₈	—	67	2	no	—
383	C₂²⋊Q₈	—	67	1	no	—
384	C₂²⋊Q₈	—	67	2	no	—
385	C₂²⋊Q₈	—	67	2	no	—
386	C₂²⋊Q₈	—	67	1	no	—
387	C₂²⋊Q₈	—	67	1	no	—
388	C₂²⋊Q₈	—	67	2	no	—
389	C₂²⋊Q₈	—	67	1	no	—
390	C₂²⋊Q₈	—	67	1	no	—
391	C₂²⋊Q₈	—	67	2	no	—
392	C₂²⋊Q₈	—	67	1	no	—
393	C₂²⋊Q₈	—	67	2	no	—
394	C₂²⋊Q₈	—	67	2	no	—
395	C₂²⋊Q₈	—	67	1	no	—
396	C₂²⋊Q₈	—	67	2	no	—
397	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
398	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
399	#121	—	67	1	no	—
400	#121	—	67	1	no	—
401	#120	—	67	1	no	—
402	#120	—	67	1	no	—
403	C₄×Q₈	—	67	1	no	—
404	C₄×Q₈	—	67	2	no	—
405	C₄×Q₈	—	67	1	no	—
406	C₄×Q₈	—	67	2	no	—
407	C₄×Q₈	—	67	1	no	—
408	C₄×Q₈	—	67	2	no	—
409	C₄×Q₈	—	67	2	no	—
410	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
411	C₄×Q₈	C₂×D₆₇	1	2	yes	complemented
412	C₄×D₄	—	67	1	no	—
413	C₄×D₄	—	67	1	no	—
414	C₄×D₄	—	67	2	no	—
415	C₄×D₄	—	67	2	no	—
416	C₄×D₄	—	67	2	no	—
417	C₄×D₄	—	67	2	no	—
418	C₄×D₄	—	67	2	no	—
419	C₄×D₄	—	67	1	no	—
420	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
421	#117	—	67	1	no	—
422	#117	—	67	1	no	—
423	#117	—	67	1	no	—
424	#117	—	67	2	no	—
425	#117	—	67	1	no	—
426	#117	—	67	2	no	—
427	#117	—	67	2	no	—
428	#117	—	67	2	no	—
429	#117	—	67	2	no	—
430	#117	—	67	1	no	—
431	#117	—	67	2	no	—
432	#117	—	67	2	no	—
433	#117	—	67	2	no	—
434	#117	C₂×D₆₇	1	1	yes	characteristic
435	#117	C₂×D₆₇	1	1	yes	characteristic, complemented
436	C₂×C₄⋊C₄	—	67	1	no	—
437	C₂×C₄⋊C₄	—	67	1	no	—
438	C₂×C₄⋊C₄	—	67	1	no	—
439	C₂×C₄⋊C₄	—	67	1	no	—
440	C₂×C₄⋊C₄	—	67	1	no	—
441	C₂×C₄⋊C₄	—	67	2	no	—
442	C₂×C₂²⋊C₄	—	67	2	no	—
443	C₂×C₂²⋊C₄	—	67	2	no	—
444	C₂×C₄²	—	67	2	no	—
445	C₂⁴	—	67	1	no	—
446	#41	—	134	4	no	—
447	C₂×Q₈	—	67	2	no	—
448	C₂×Q₈	—	67	1	no	—
449	C₂×Q₈	—	67	2	no	—
450	C₂×Q₈	—	67	1	no	—
451	C₂×Q₈	—	134	4	no	—
452	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
453	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
454	C₂×D₄	—	67	1	no	—
455	C₂×D₄	—	67	1	no	—
456	C₂×D₄	—	67	1	no	—
457	C₂×D₄	—	67	1	no	—
458	C₂×D₄	—	67	1	no	—
459	C₂×D₄	—	67	1	no	—
460	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
461	C₂²×C₄	—	67	2	no	—
462	C₂²×C₄	—	67	2	no	—
463	C₂²×C₄	—	67	2	no	—
464	C₂²×C₄	—	67	2	no	—
465	C₂²×C₄	—	67	1	no	—
466	C₂²×C₄	—	67	1	no	—
467	C₂²×C₄	—	67	1	no	—
468	C₂²×C₄	—	67	2	no	—
469	C₂²×C₄	—	67	2	no	—
470	C₂²×C₄	—	67	1	no	—
471	C₂²×C₄	—	67	1	no	—
472	C₂²×C₄	—	67	1	no	—
473	C₂²×C₄	—	134	4	no	—
474	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
476	C₄⋊C₄	—	67	1	no	—
477	C₄⋊C₄	—	67	1	no	—
478	C₄⋊C₄	—	67	2	no	—
479	C₄⋊C₄	—	67	1	no	—
480	C₄⋊C₄	—	67	2	no	—
481	C₄⋊C₄	—	67	2	no	—
482	C₄⋊C₄	—	67	2	no	—
483	C₄⋊C₄	—	67	2	no	—
484	C₄⋊C₄	—	67	2	no	—
485	C₄⋊C₄	—	67	2	no	—
486	C₄⋊C₄	—	67	2	no	—
487	C₄⋊C₄	—	67	1	no	—
488	C₄⋊C₄	—	67	1	no	—
489	C₄⋊C₄	—	67	2	no	—
490	C₄⋊C₄	—	67	2	no	—
491	C₄⋊C₄	—	67	2	no	—
492	C₄⋊C₄	—	67	2	no	—
493	C₄⋊C₄	—	67	2	no	—
494	C₄⋊C₄	—	67	2	no	—
495	C₄⋊C₄	—	67	2	no	—
496	C₄⋊C₄	—	67	2	no	—
497	C₄⋊C₄	—	67	2	no	—
498	C₄⋊C₄	—	67	1	no	—
499	C₄⋊C₄	—	67	1	no	—
500	C₄⋊C₄	—	67	1	no	—
501	C₄⋊C₄	—	67	2	no	—
502	C₄⋊C₄	—	67	2	no	—
503	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
507	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
508	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
509	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
511	C₂²⋊C₄	—	67	2	no	—
512	C₂²⋊C₄	—	67	2	no	—
513	C₂²⋊C₄	—	67	2	no	—
514	C₂²⋊C₄	—	67	1	no	—
515	C₂²⋊C₄	—	67	1	no	—
516	C₂²⋊C₄	—	67	2	no	—
517	C₂²⋊C₄	—	67	2	no	—
518	C₂²⋊C₄	—	67	2	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	—	67	1	no	—
524	C₂²⋊C₄	—	67	1	no	—
525	C₂²⋊C₄	—	67	2	no	—
526	C₂²⋊C₄	—	67	2	no	—
527	C₂²⋊C₄	—	67	1	no	—
528	C₂²⋊C₄	—	67	2	no	—
529	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
530	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
532	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
535	C₄²	—	67	2	no	—
536	C₄²	—	67	2	no	—
537	C₄²	—	67	2	no	—
538	C₄²	—	67	2	no	—
539	C₄²	—	67	2	no	—
540	C₄²	—	67	2	no	—
541	C₄²	—	67	2	no	—
542	C₄²	—	67	1	no	—
543	C₄²	C₂²×D₆₇	1	2	yes	—
544	C₄²	C₂²×D₆₇	1	2	yes	—
545	C₄²	C₂²×D₆₇	1	2	yes	—
546	C₄²	C₂²×D₆₇	1	1	yes	characteristic
547	C₂³	—	268	1	no	—
548	C₂³	—	67	1	no	—
549	C₂³	—	67	1	no	—
550	C₂³	—	67	1	no	—
551	C₂³	—	134	2	no	—
552	C₂³	—	134	2	no	—
553	C₂³	C₂³×D₆₇	1	1	yes	characteristic
554	C₂³	C₂³×D₆₇	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	268	2	no	—
558	Q₈	—	134	4	no	—
559	Q₈	—	134	2	no	—
560	Q₈	—	134	2	no	—
561	D₄	—	4	1	no	—
562	D₄	—	268	1	no	—
563	D₄	—	134	2	no	—
564	D₄	—	134	2	no	—
565	D₄	—	134	2	no	—
566	D₄	—	134	2	no	—
567	D₄	—	134	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	268	2	no	—
571	C₂×C₄	—	268	2	no	—
572	C₂×C₄	—	268	2	no	—
573	C₂×C₄	—	268	2	no	—
574	C₂×C₄	—	67	1	no	—
575	C₂×C₄	—	67	4	no	—
576	C₂×C₄	—	67	2	no	—
577	C₂×C₄	—	67	1	no	—
578	C₂×C₄	—	67	1	no	—
579	C₂×C₄	—	67	2	no	—
580	C₂×C₄	—	67	2	no	—
581	C₂×C₄	—	67	1	no	—
582	C₂×C₄	—	67	2	no	—
583	C₂×C₄	—	67	1	no	—
584	C₂×C₄	—	134	2	no	—
585	C₂×C₄	—	134	2	no	—
586	C₂×C₄	—	134	4	no	—
587	C₂×C₄	—	134	4	no	—
588	C₂×C₄	—	134	2	no	—
589	C₂×C₄	—	134	2	no	—
590	C₂×C₄	—	134	2	no	—
591	C₂×C₄	C₂³×D₆₇	1	2	yes	—
592	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₆₇	1	2	yes	—
595	C₂×C₄	C₂³×D₆₇	1	2	yes	—
596	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₆₇	1	2	yes	—
599	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	268	4	no	—
607	C₂²	—	67	2	no	—
608	C₂²	—	67	2	no	—
609	C₂²	—	134	1	no	—
610	C₂²	—	134	1	no	—
611	C₂²	—	134	1	no	—
612	C₂²	—	134	1	no	—
613	C₂²	—	134	1	no	—
614	C₂²	—	134	1	no	—
615	C₂²	—	134	1	no	—
616	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	67	2	no	—
626	C₄	—	134	1	no	—
627	C₄	—	134	1	no	—
628	C₄	—	134	2	no	—
629	C₄	—	134	2	no	—
630	C₄	—	134	1	no	—
631	C₄	—	134	2	no	—
632	C₄	—	134	2	no	—
633	C₄	—	134	1	no	—
634	C₄	#41×D₆₇	1	2	yes	—
635	C₂	—	4	1	no	—
636	C₂	—	4	1	no	—
637	C₂	—	268	1	no	—
638	C₂	—	134	2	no	—
639	C₂	—	134	2	no	—
640	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
641	C₂	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
642	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#556×C₆₇	C₂
hypercenter	#556	D₆₇
hypocenter	C₆₇	#3495
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #16864114	C₂	semidirect
2. #16864107	C₂	semidirect
3. #16864104	C₂	semidirect
4. #16864087	C₂	semidirect
5. #16864087	C₂	semidirect
6. #16864086	C₂	semidirect
7. #16864085	C₂	semidirect
8. #16864082	C₂	semidirect
9. #16864080	C₂	semidirect
10. #16864076	C₂	semidirect
11. #16864071	C₂	semidirect
12. #16864023	C₂	semidirect
13. #16864010	C₂	semidirect
14. #16864003	C₂	semidirect
15. #16863969	C₂	semidirect
16. #16863950	C₂	semidirect
17. #16863929	C₂	semidirect
19. C₂²⋊Q₈×D₆₇	C₂	semidirect
20. #16863876	C₂	semidirect
21. #16863872	C₂	semidirect
22. #117×D₆₇	C₂	semidirect
23. #556×C₆₇	C₂	semidirect
27. #14524042	C₂²	semidirect
28. #14524042	C₂²	semidirect
29. #14524041	C₂²	semidirect
30. #14524037	C₂²	semidirect
31. #14524037	C₂²	semidirect
35. #14524036	C₂²	semidirect
36. #14524035	C₂²	semidirect
37. #14524035	C₂²	semidirect
38. #14524034	C₂²	semidirect
39. #14524034	C₂²	semidirect
40. #14524033	C₂²	semidirect
41. #14524033	C₂²	semidirect
42. #14524033	C₂²	semidirect
43. #14524033	C₂²	semidirect
44. #14524033	C₂²	semidirect
46. #14524029	C₂²	semidirect
57. #14524023	C₂²	semidirect
59. #14524022	C₂²	semidirect
65. #14524020	C₂²	semidirect
69. #14524019	C₂²	semidirect
70. #14524019	C₂²	semidirect
75. Q₈×Dic₆₇	C₂²	semidirect
76. C₄×Dic₁₃₄	C₂²	semidirect
77. C₄×Dic₁₃₄	C₂²	semidirect
78. C₄×Dic₁₃₄	C₂²	semidirect
79. C₄×Dic₁₃₄	C₂²	semidirect
80. #14524008	C₂²	semidirect
81. #14524008	C₂²	semidirect
89. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
94. #14524001	C₂²	semidirect
95. #14524001	C₂²	semidirect
102. #14523999	C₂²	semidirect
103. C₂×C₄⋊Dic₆₇	C₂²	semidirect
108. C₄⋊C₄×D₆₇	C₂²	semidirect
112. C₄⋊Q₈×C₆₇	C₂²	semidirect
114. #126×C₆₇	C₂²	semidirect
117. C₂²⋊Q₈×C₆₇	C₂²	semidirect
118. C₄×Q₈×C₆₇	C₂²	semidirect
119. C₄×Q₈×C₆₇	C₂²	semidirect
122. #117×C₆₇	C₂²	semidirect
322. C₆₇	#3495	semidirect
324. #556	D₆₇	semidirect
352. C₄⋊Q₈	C₂×D₆₇	semidirect
360. #126	C₂×D₆₇	semidirect
398. C₂²⋊Q₈	C₂×D₆₇	semidirect
410. C₄×Q₈	C₂×D₆₇	semidirect
411. C₄×Q₈	C₂×D₆₇	semidirect
435. #117	C₂×D₆₇	semidirect