Subgroups — #22574450

Order 8576.

1014 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864147	C₂	1	2	yes	maximal, complemented
2	#16864145	C₂	1	2	yes	maximal, complemented
3	#16864088	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864087	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864086	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864080	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864075	C₂	1	2	yes	maximal, complemented
8	#16864073	C₂	1	2	yes	maximal, complemented
9	#16864061	C₂	1	1	yes	maximal, characteristic, complemented
10	Q₈×C₂²⋊D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₂²⋊D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864025	C₂	1	2	yes	maximal, complemented
13	#16864023	C₂	1	2	yes	maximal, complemented
14	#16864007	C₂	1	1	yes	maximal, characteristic, complemented
15	#16864004	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863992	C₂	1	2	yes	maximal, complemented
17	#16863988	C₂	1	2	yes	maximal, complemented
18	#16863970	C₂	1	1	yes	maximal, characteristic, complemented
19	#16863969	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863905	C₂	1	1	yes	maximal, characteristic
21	C₂×#14524019	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂²⋊Q₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×Q₈×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	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
28	#14524042	C₂²	1	2	yes	complemented
29	#14524042	C₂²	1	2	yes	complemented
30	#14524041	C₂²	1	1	yes	characteristic, complemented
31	#14524041	C₂²	1	2	yes	complemented
32	#14524041	C₂²	1	2	yes	complemented
33	#14524041	C₂²	1	2	yes	complemented
34	#14524038	C₂²	1	2	yes	—
35	#14524038	C₂²	1	2	yes	—
36	#14524038	C₂²	1	2	yes	—
37	#14524038	C₂²	1	2	yes	complemented
38	#14524037	C₂²	1	2	yes	—
39	#14524037	C₂²	1	2	yes	complemented
40	#14524036	C₂²	1	2	yes	complemented
41	#14524036	C₂²	1	2	yes	complemented
42	#14524035	C₂²	1	2	yes	complemented
43	#14524035	C₂²	1	1	yes	characteristic, complemented
44	#14524034	C₂²	1	1	yes	characteristic, complemented
45	#14524034	C₂²	1	2	yes	complemented
46	#14524033	C₂²	1	2	yes	complemented
47	#14524033	C₂²	1	2	yes	complemented
48	#14524033	C₂²	1	2	yes	complemented
49	#14524033	C₂²	1	2	yes	complemented
50	#14524033	C₂²	1	2	yes	complemented
51	#14524033	C₂²	1	2	yes	complemented
52	#14524032	C₂²	1	2	yes	—
53	#14524029	C₂²	1	2	yes	—
54	#14524028	C₂²	1	2	yes	—
55	#14524028	C₂²	1	2	yes	—
56	#14524028	C₂²	1	1	yes	characteristic
57	#14524027	C₂²	1	2	yes	—
58	#14524026	C₂²	1	2	yes	—
59	#14524026	C₂²	1	2	yes	complemented
60	#14524025	C₂²	1	2	yes	—
61	#14524025	C₂²	1	1	yes	characteristic
62	#14524025	C₂²	1	2	yes	complemented
63	#14524024	C₂²	1	2	yes	—
64	#14524023	C₂²	1	1	yes	characteristic
65	#14524022	C₂²	1	2	yes	—
66	#14524022	C₂²	1	1	yes	characteristic
67	#14524022	C₂²	1	1	yes	characteristic, complemented
68	#14524022	C₂²	1	2	yes	complemented
69	#14524021	C₂²	1	1	yes	characteristic
70	#14524021	C₂²	1	2	yes	—
71	#14524021	C₂²	1	2	yes	—
72	#14524021	C₂²	1	2	yes	complemented
73	#14524020	C₂²	1	1	yes	characteristic
74	#14524020	C₂²	1	2	yes	—
75	#14524019	C₂²	1	1	yes	characteristic
76	#14524019	C₂²	1	1	yes	characteristic
77	#14524019	C₂²	1	1	yes	characteristic
78	#14524019	C₂²	1	2	yes	—
79	#14524019	C₂²	1	2	yes	—
80	#14524019	C₂²	1	1	yes	characteristic
81	#14524019	C₂²	1	1	yes	characteristic
82	#14524019	C₂²	1	2	yes	—
83	#14524019	C₂²	1	1	yes	characteristic, complemented
84	#14524019	C₂²	1	2	yes	complemented
85	#14524019	C₂²	1	1	yes	characteristic, complemented
86	#14524016	C₂²	1	1	yes	characteristic
87	#14524015	C₂²	1	1	yes	characteristic
88	#14524013	C₂²	1	1	yes	characteristic
89	#14524011	C₂²	1	1	yes	characteristic
90	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
91	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
92	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
93	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
94	#14524005	C₂²	1	2	yes	—
95	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
96	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
97	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
99	#14524002	C₂²	1	1	yes	characteristic, complemented
100	#14524001	C₂²	1	2	yes	—
101	#14524001	C₂²	1	1	yes	characteristic, complemented
102	#14524000	C₂²	1	1	yes	characteristic
103	#14524000	C₂²	1	2	yes	—
104	#14523999	C₂²	1	2	yes	—
105	#14523999	C₂²	1	2	yes	—
106	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
107	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	—
108	C₄⋊C₄×D₆₇	C₂²	1	2	yes	—
109	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
110	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
112	C₂²×Q₈×C₆₇	C₂²	1	1	yes	characteristic
113	C₂²×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
117	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
118	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
120	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₆₇	C₂²	1	2	yes	—
122	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
123	C₂³×D₆₇	C₂³	1	1	yes	characteristic
124	#11761628	—	4	2	no	—
125	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
126	C₂×Dic₁₃₄	C₂³	1	2	yes	—
127	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₃₄	C₂³	1	2	yes	—
129	Q₈×D₆₇	—	4	2	no	—
130	Q₈×D₆₇	—	4	2	no	—
131	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
132	C₂×D₂₆₈	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	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
137	C₂²×Dic₆₇	C₂³	1	2	yes	—
138	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₆₇	—	4	2	no	—
140	C₂×C₄×D₆₇	C₂³	1	2	yes	—
141	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₆₇	C₂³	1	2	yes	—
145	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₆₇	C₂³	1	2	yes	—
147	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
155	C₄⋊Dic₆₇	C₂³	1	2	yes	—
156	C₄⋊Dic₆₇	C₂³	1	2	yes	—
157	Dic₆₇⋊C₄	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	2	yes	—
166	Dic₆₇⋊C₄	C₂³	1	2	yes	—
167	Dic₆₇⋊C₄	C₂³	1	2	yes	—
168	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
169	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
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	Dic₆₇⋊C₄	C₂³	1	2	yes	—
177	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₆₇	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	2	yes	—
186	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
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	C₄×Dic₆₇	C₂³	1	2	yes	—
203	C₂×Q₈×C₆₇	—	4	2	no	—
204	C₂×Q₈×C₆₇	—	4	2	no	—
205	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
216	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₄²×C₆₇	C₂³	1	2	yes	—
228	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
230	C₂²×D₆₇	—	2	2	no	—
231	C₂²×D₆₇	—	2	2	no	—
232	C₂²×D₆₇	—	4	1	no	—
233	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
234	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
235	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
236	Q₈×C₆₇	—	2	2	no	—
237	Q₈×C₆₇	—	2	2	no	—
238	Q₈×C₆₇	—	2	2	no	—
239	Q₈×C₆₇	—	4	2	no	—
240	Q₈×C₆₇	—	4	2	no	—
241	D₄×C₆₇	—	2	2	no	—
242	C₂×C₄×C₆₇	—	2	2	no	—
243	C₂×C₄×C₆₇	—	2	2	no	—
244	C₂×C₄×C₆₇	—	4	2	no	—
245	C₂×C₄×C₆₇	—	4	2	no	—
246	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
249	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
252	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₆₇	—	2	2	no	—
256	C₂²⋊D₆₇	—	2	2	no	—
257	C₂²⋊D₆₇	—	4	1	no	—
258	C₂²⋊D₆₇	—	4	1	no	—
259	C₂×Dic₆₇	—	2	4	no	—
260	C₂×Dic₆₇	—	4	1	no	—
261	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₆₇	C₂⁴	1	2	yes	—
264	C₂×Dic₆₇	C₂⁴	1	2	yes	—
265	C₂×Dic₆₇	C₂⁴	1	2	yes	—
266	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₆₇	C₂⁴	1	2	yes	—
268	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
270	D₂₆₈	—	2	2	no	—
271	D₂₆₈	—	4	1	no	—
272	C₄×D₆₇	—	2	4	no	—
273	C₄×D₆₇	—	2	2	no	—
274	C₄×D₆₇	—	2	2	no	—
275	C₄×D₆₇	—	2	2	no	—
276	C₄×D₆₇	—	4	1	no	—
277	C₄×D₆₇	—	4	1	no	—
278	C₄×D₆₇	—	4	2	no	—
279	C₄×D₆₇	—	4	2	no	—
280	Dic₁₃₄	—	2	2	no	—
281	Dic₁₃₄	—	4	2	no	—
282	Dic₁₃₄	—	4	2	no	—
283	Dic₁₃₄	—	4	1	no	—
284	C₂²×C₆₇	—	2	1	no	—
285	C₂²×C₆₇	—	2	1	no	—
286	C₂²×C₆₇	—	2	1	no	—
287	C₂²×C₆₇	—	2	1	no	—
288	C₂²×C₆₇	—	2	1	no	—
289	C₂²×C₆₇	2₋¹⁺⁴	1	2	yes	—
290	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
291	C₂×D₆₇	—	2	1	no	—
292	C₂×D₆₇	—	2	1	no	—
293	C₂×D₆₇	—	2	1	no	—
294	C₂×D₆₇	—	2	1	no	—
295	C₂×D₆₇	—	2	1	no	—
296	C₂×D₆₇	—	2	1	no	—
297	C₂×D₆₇	—	2	1	no	—
298	C₂×D₆₇	—	2	1	no	—
299	C₂×D₆₇	—	4	4	no	—
300	C₂×D₆₇	2₋¹⁺⁴	1	2	yes	—
301	C₄×C₆₇	—	2	2	no	—
302	C₄×C₆₇	—	2	2	no	—
303	C₄×C₆₇	—	2	1	no	—
304	C₄×C₆₇	—	2	1	no	—
305	C₄×C₆₇	—	2	2	no	—
306	C₄×C₆₇	—	2	2	no	—
307	C₄×C₆₇	—	2	1	no	—
308	C₄×C₆₇	—	2	1	no	—
309	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
310	Dic₆₇	—	2	2	no	—
311	Dic₆₇	—	2	1	no	—
312	Dic₆₇	—	2	1	no	—
313	Dic₆₇	—	2	1	no	—
314	Dic₆₇	—	2	2	no	—
315	Dic₆₇	—	2	2	no	—
316	Dic₆₇	—	2	2	no	—
317	Dic₆₇	—	2	1	no	—
318	Dic₆₇	—	2	1	no	—
319	C₂×C₆₇	—	2	2	no	—
320	C₂×C₆₇	—	4	1	no	—
321	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
323	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
324	D₆₇	—	2	2	no	—
325	D₆₇	—	4	1	no	—
326	D₆₇	—	4	1	no	—
327	#3538	—	67	1	no	maximal, Sylow
328	C₆₇	#3538	1	1	yes	characteristic, complemented, Sylow
329	#563	—	67	2	no	—
330	#563	—	67	2	no	—
331	#552	—	67	1	no	—
332	#552	—	67	1	no	—
333	#552	—	67	1	no	—
334	#552	—	67	1	no	—
335	#551	—	67	2	no	—
336	#551	—	67	2	no	—
337	D₄×Q₈	—	67	1	no	—
338	D₄×Q₈	—	67	1	no	—
339	D₄×Q₈	—	67	1	no	—
340	D₄×Q₈	D₆₇	1	1	yes	characteristic, complemented
341	#544	—	67	2	no	—
342	#544	—	67	2	no	—
343	#541	—	67	1	no	—
344	#541	—	67	1	no	—
345	#539	—	67	2	no	—
346	#539	—	67	2	no	—
347	#536	—	67	1	no	—
348	#536	—	67	1	no	—
349	#525	—	67	1	no	—
350	C₂×C₂²⋊Q₈	—	67	1	no	—
351	C₂×C₂²⋊Q₈	—	67	1	no	—
352	C₂×#41	—	67	1	no	—
353	C₂²×Q₈	—	67	1	no	—
354	C₂²×Q₈	—	67	1	no	—
355	C₂²×Q₈	C₂×D₆₇	1	1	yes	characteristic
356	C₂²×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
357	C₂³×C₄	—	67	1	no	—
358	C₄⋊Q₈	—	67	2	no	—
359	C₄⋊Q₈	—	67	1	no	—
360	C₄⋊Q₈	—	67	2	no	—
361	C₄⋊Q₈	—	67	2	no	—
362	C₄⋊Q₈	—	67	2	no	—
363	C₄⋊Q₈	—	67	2	no	—
364	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
365	C₄⋊Q₈	C₂×D₆₇	1	2	yes	complemented
366	#126	—	67	2	no	—
367	#126	—	67	2	no	—
368	#126	—	67	2	no	—
369	#126	—	67	2	no	—
370	#126	—	67	2	no	—
371	#126	—	67	2	no	—
372	#126	—	67	2	no	—
373	#126	—	67	2	no	—
374	#125	—	67	2	no	—
375	#125	—	67	2	no	—
376	#125	—	67	2	no	—
377	#125	—	67	1	no	—
378	#125	—	67	2	no	—
379	#125	—	67	2	no	—
380	#125	—	67	2	no	—
381	#125	—	67	2	no	—
382	#125	—	67	2	no	—
383	#125	—	67	1	no	—
384	#124	—	67	2	no	—
385	#124	—	67	2	no	—
386	#123	—	67	2	no	—
387	#123	—	67	2	no	—
388	#123	—	67	2	no	—
389	#123	—	67	1	no	—
390	#123	—	67	2	no	—
391	#123	—	67	2	no	—
392	#123	—	67	1	no	—
393	#123	—	67	2	no	—
394	#123	—	67	2	no	—
395	#123	—	67	2	no	—
396	C₂²⋊Q₈	—	67	1	no	—
397	C₂²⋊Q₈	—	67	1	no	—
398	C₂²⋊Q₈	—	67	1	no	—
399	C₂²⋊Q₈	—	67	2	no	—
400	C₂²⋊Q₈	—	67	1	no	—
401	C₂²⋊Q₈	—	67	1	no	—
402	C₂²⋊Q₈	—	67	2	no	—
403	C₂²⋊Q₈	—	67	1	no	—
404	C₂²⋊Q₈	—	67	1	no	—
405	C₂²⋊Q₈	—	67	2	no	—
406	C₂²⋊Q₈	—	67	2	no	—
407	C₂²⋊Q₈	—	67	1	no	—
408	C₂²⋊Q₈	—	67	1	no	—
409	C₂²⋊Q₈	—	67	2	no	—
410	C₂²⋊Q₈	—	67	2	no	—
411	C₂²⋊Q₈	—	67	1	no	—
412	C₂²⋊Q₈	—	67	2	no	—
413	C₂²⋊Q₈	—	67	1	no	—
414	C₂²⋊Q₈	—	67	2	no	—
415	C₂²⋊Q₈	—	67	2	no	—
416	C₂²⋊Q₈	—	67	2	no	—
417	C₂²⋊Q₈	—	67	1	no	—
418	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
419	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	—
420	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
421	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
422	#121	—	67	1	no	—
423	#121	—	67	1	no	—
424	#120	—	67	1	no	—
425	#120	—	67	1	no	—
426	C₄×Q₈	—	67	1	no	—
427	C₄×Q₈	—	67	1	no	—
428	C₄×Q₈	—	67	1	no	—
429	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
430	C₄×D₄	—	67	1	no	—
431	C₄×D₄	—	67	1	no	—
432	C₄×D₄	—	67	2	no	—
433	C₄×D₄	—	67	2	no	—
434	C₄×D₄	—	67	2	no	—
435	C₄×D₄	—	67	1	no	—
436	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
437	C₄×D₄	C₂×D₆₇	1	2	yes	—
438	#117	—	67	1	no	—
439	#117	—	67	1	no	—
440	#117	—	67	2	no	—
441	#117	—	67	2	no	—
442	#117	—	67	2	no	—
443	#117	—	67	1	no	—
444	#117	—	67	2	no	—
445	C₂×C₄⋊C₄	—	67	2	no	—
446	C₂×C₄⋊C₄	—	67	1	no	—
447	C₂×C₄⋊C₄	—	67	2	no	—
448	C₂×C₄⋊C₄	—	67	1	no	—
449	C₂×C₂²⋊C₄	—	67	2	no	—
450	C₂×C₂²⋊C₄	—	67	2	no	—
451	C₂⁴	—	67	1	no	—
452	#41	—	268	2	no	—
453	C₂×Q₈	—	4	2	no	—
454	C₂×Q₈	—	4	2	no	—
455	C₂×Q₈	—	268	2	no	—
456	C₂×Q₈	—	268	2	no	—
457	C₂×Q₈	—	67	2	no	—
458	C₂×Q₈	—	67	2	no	—
459	C₂×Q₈	—	67	1	no	—
460	C₂×Q₈	—	67	1	no	—
461	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
462	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
463	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
464	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
465	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
466	C₂×D₄	—	67	1	no	—
467	C₂×D₄	—	67	1	no	—
468	C₂×D₄	—	67	1	no	—
469	C₂×D₄	—	67	1	no	—
470	C₂×D₄	—	67	1	no	—
471	C₂×D₄	—	67	1	no	—
472	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
473	C₂²×C₄	—	268	2	no	—
474	C₂²×C₄	—	67	1	no	—
475	C₂²×C₄	—	67	2	no	—
476	C₂²×C₄	—	67	1	no	—
477	C₂²×C₄	—	67	2	no	—
478	C₂²×C₄	—	67	1	no	—
479	C₂²×C₄	—	67	2	no	—
480	C₂²×C₄	—	67	2	no	—
481	C₂²×C₄	—	67	1	no	—
482	C₂²×C₄	—	67	1	no	—
483	C₂²×C₄	—	67	1	no	—
484	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
485	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
487	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
488	C₄⋊C₄	—	67	1	no	—
489	C₄⋊C₄	—	67	1	no	—
490	C₄⋊C₄	—	67	1	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	2	no	—
499	C₄⋊C₄	—	67	2	no	—
500	C₄⋊C₄	—	67	1	no	—
501	C₄⋊C₄	—	67	1	no	—
502	C₄⋊C₄	—	67	2	no	—
503	C₄⋊C₄	—	67	2	no	—
504	C₄⋊C₄	—	67	2	no	—
505	C₄⋊C₄	—	67	2	no	—
506	C₄⋊C₄	—	67	2	no	—
507	C₄⋊C₄	—	67	2	no	—
508	C₄⋊C₄	—	67	2	no	—
509	C₄⋊C₄	—	67	2	no	—
510	C₄⋊C₄	—	67	2	no	—
511	C₄⋊C₄	—	67	1	no	—
512	C₄⋊C₄	—	67	1	no	—
513	C₄⋊C₄	—	67	1	no	—
514	C₄⋊C₄	—	67	2	no	—
515	C₄⋊C₄	—	67	2	no	—
516	C₄⋊C₄	—	67	2	no	—
517	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
519	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
520	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
521	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
522	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
524	C₂²⋊C₄	—	67	2	no	—
525	C₂²⋊C₄	—	67	1	no	—
526	C₂²⋊C₄	—	67	2	no	—
527	C₂²⋊C₄	—	67	1	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	2	no	—
534	C₂²⋊C₄	—	67	2	no	—
535	C₂²⋊C₄	—	67	1	no	—
536	C₂²⋊C₄	—	67	1	no	—
537	C₂²⋊C₄	—	67	1	no	—
538	C₂²⋊C₄	—	67	1	no	—
539	C₂²⋊C₄	—	67	2	no	—
540	C₂²⋊C₄	—	67	1	no	—
541	C₂²⋊C₄	—	67	1	no	—
542	C₂²⋊C₄	—	67	2	no	—
543	C₂²⋊C₄	—	67	2	no	—
544	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
547	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
548	C₄²	—	67	2	no	—
549	C₄²	—	67	2	no	—
550	C₄²	—	67	1	no	—
551	C₄²	—	67	2	no	—
552	C₄²	—	67	2	no	—
553	C₄²	—	67	2	no	—
554	C₄²	C₂²×D₆₇	1	1	yes	characteristic
555	C₄²	C₂²×D₆₇	1	2	yes	—
556	C₂³	—	268	1	no	—
557	C₂³	—	67	1	no	—
558	C₂³	—	67	1	no	—
559	C₂³	—	67	1	no	—
560	C₂³	—	134	2	no	—
561	C₂³	—	134	2	no	—
562	C₂³	C₂³×D₆₇	1	1	yes	characteristic
563	C₂³	C₂³×D₆₇	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	4	2	no	—
569	Q₈	—	268	2	no	—
570	Q₈	—	268	2	no	—
571	Q₈	—	268	1	no	—
572	Q₈	—	134	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	268	1	no	—
575	D₄	—	268	1	no	—
576	D₄	—	268	1	no	—
577	D₄	—	134	2	no	—
578	D₄	—	134	2	no	—
579	D₄	—	134	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	268	1	no	—
585	C₂×C₄	—	268	1	no	—
586	C₂×C₄	—	268	2	no	—
587	C₂×C₄	—	268	2	no	—
588	C₂×C₄	—	268	1	no	—
589	C₂×C₄	—	67	1	no	—
590	C₂×C₄	—	67	1	no	—
591	C₂×C₄	—	67	2	no	—
592	C₂×C₄	—	67	2	no	—
593	C₂×C₄	—	67	2	no	—
594	C₂×C₄	—	67	1	no	—
595	C₂×C₄	—	67	2	no	—
596	C₂×C₄	—	67	1	no	—
597	C₂×C₄	—	67	1	no	—
598	C₂×C₄	—	134	4	no	—
599	C₂×C₄	—	134	4	no	—
600	C₂×C₄	—	134	2	no	—
601	C₂×C₄	—	134	2	no	—
602	C₂×C₄	—	134	2	no	—
603	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₆₇	1	2	yes	—
606	C₂×C₄	C₂³×D₆₇	1	2	yes	—
607	C₂×C₄	C₂³×D₆₇	1	2	yes	—
608	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₆₇	1	2	yes	—
610	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	268	4	no	—
618	C₂²	—	67	2	no	—
619	C₂²	—	134	1	no	—
620	C₂²	—	134	1	no	—
621	C₂²	—	134	1	no	—
622	C₂²	—	134	1	no	—
623	C₂²	—	134	1	no	—
624	C₂²	—	134	1	no	—
625	C₂²	—	134	1	no	—
626	C₂²	—	134	1	no	—
627	C₂²	#14524091	1	2	yes	—
628	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	134	1	no	—
638	C₄	—	134	1	no	—
639	C₄	—	134	2	no	—
640	C₄	—	134	1	no	—
641	C₄	—	134	2	no	—
642	C₄	—	134	1	no	—
643	C₄	—	134	2	no	—
644	C₄	—	134	2	no	—
645	C₄	—	134	1	no	—
646	C₄	#14524088	1	2	yes	—
647	C₂	—	2	2	no	—
648	C₂	—	4	1	no	—
649	C₂	—	268	1	no	—
650	C₂	—	268	1	no	—
651	C₂	—	134	2	no	—
652	C₂	C₂×#14524088	1	1	yes	characteristic
653	C₂	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
654	C₂	C₂×#14524091	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	D₄×Q₈×C₆₇	C₂
hypercenter	D₄×Q₈	D₆₇
hypocenter	C₆₇	#3538
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #16864147	C₂	semidirect
2. #16864145	C₂	semidirect
3. #16864088	C₂	semidirect
4. #16864087	C₂	semidirect
5. #16864086	C₂	semidirect
6. #16864080	C₂	semidirect
7. #16864075	C₂	semidirect
8. #16864073	C₂	semidirect
9. #16864061	C₂	semidirect
10. Q₈×C₂²⋊D₆₇	C₂	semidirect
11. Q₈×C₂²⋊D₆₇	C₂	semidirect
12. #16864025	C₂	semidirect
13. #16864023	C₂	semidirect
14. #16864007	C₂	semidirect
15. #16864004	C₂	semidirect
16. #16863992	C₂	semidirect
17. #16863988	C₂	semidirect
18. #16863970	C₂	semidirect
19. #16863969	C₂	semidirect
21. C₂×#14524019	C₂	semidirect
22. C₂²⋊Q₈×D₆₇	C₂	semidirect
23. D₄×Q₈×C₆₇	C₂	semidirect
26. C₂×Q₈×D₆₇	C₂²	semidirect
28. #14524042	C₂²	semidirect
29. #14524042	C₂²	semidirect
30. #14524041	C₂²	semidirect
31. #14524041	C₂²	semidirect
32. #14524041	C₂²	semidirect
33. #14524041	C₂²	semidirect
37. #14524038	C₂²	semidirect
39. #14524037	C₂²	semidirect
40. #14524036	C₂²	semidirect
41. #14524036	C₂²	semidirect
42. #14524035	C₂²	semidirect
43. #14524035	C₂²	semidirect
44. #14524034	C₂²	semidirect
45. #14524034	C₂²	semidirect
46. #14524033	C₂²	semidirect
47. #14524033	C₂²	semidirect
48. #14524033	C₂²	semidirect
49. #14524033	C₂²	semidirect
50. #14524033	C₂²	semidirect
51. #14524033	C₂²	semidirect
59. #14524026	C₂²	semidirect
62. #14524025	C₂²	semidirect
67. #14524022	C₂²	semidirect
68. #14524022	C₂²	semidirect
72. #14524021	C₂²	semidirect
83. #14524019	C₂²	semidirect
84. #14524019	C₂²	semidirect
85. #14524019	C₂²	semidirect
90. Q₈×Dic₆₇	C₂²	semidirect
91. Q₈×Dic₆₇	C₂²	semidirect
92. C₄×Dic₁₃₄	C₂²	semidirect
99. #14524002	C₂²	semidirect
101. #14524001	C₂²	semidirect
113. C₂²×Q₈×C₆₇	C₂²	semidirect
114. C₄⋊Q₈×C₆₇	C₂²	semidirect
115. C₄⋊Q₈×C₆₇	C₂²	semidirect
118. C₂²⋊Q₈×C₆₇	C₂²	semidirect
119. C₂²⋊Q₈×C₆₇	C₂²	semidirect
120. C₄×Q₈×C₆₇	C₂²	semidirect
328. C₆₇	#3538	semidirect
340. D₄×Q₈	D₆₇	semidirect
356. C₂²×Q₈	C₂×D₆₇	semidirect
364. C₄⋊Q₈	C₂×D₆₇	semidirect
365. C₄⋊Q₈	C₂×D₆₇	semidirect
420. C₂²⋊Q₈	C₂×D₆₇	semidirect
421. C₂²⋊Q₈	C₂×D₆₇	semidirect
429. C₄×Q₈	C₂×D₆₇	semidirect