Subgroups — C₄×C₂²⋊Q₈×C₁₅₁ #34065634

Order 19328.

656 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊Q₈×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄²×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#391×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#389×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#387×C₁₅₁	C₂	1	2	yes	maximal, complemented
7	#385×C₁₅₁	C₂	1	2	yes	maximal
8	#380×C₁₅₁	C₂	1	1	yes	maximal, characteristic
9	C₄×C₄⋊C₄×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	C₄×C₄⋊C₄×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂²⋊C₄×C₁₅₁	C₂	1	2	yes	maximal
12	C₂²×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
13	C₂³×C₄×C₁₅₁	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₁₅₁	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₁₅₁	C₂²	1	1	yes	characteristic
16	C₂²⋊Q₈×C₁₅₁	C₄	1	8	yes	direct product factor
17	C₄×Q₈×C₁₅₁	—	2	4	no	—
18	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	2	yes	—
20	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	2	yes	—
22	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	2	yes	—
23	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	2	yes	—
26	C₂×C₄²×C₁₅₁	—	2	4	no	—
27	C₂×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic
28	C₂×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic
29	C₂×C₄²×C₁₅₁	C₂²	1	2	yes	—
30	C₂×C₄²×C₁₅₁	C₂²	1	2	yes	—
31	C₂×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic
32	C₂×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic
33	#95×C₁₅₁	C₂²	1	2	yes	—
34	#95×C₁₅₁	C₂²	1	2	yes	—
35	#95×C₁₅₁	C₂²	1	2	yes	—
36	#95×C₁₅₁	C₂²	1	2	yes	—
37	#95×C₁₅₁	C₂²	1	2	yes	—
38	C₂⁴×C₁₅₁	C₂³	1	1	yes	characteristic
39	C₂×Q₈×C₁₅₁	—	2	2	no	—
40	C₂×Q₈×C₁₅₁	—	2	2	no	—
41	C₂×Q₈×C₁₅₁	C₂×C₄	1	4	yes	complemented
42	C₂²×C₄×C₁₅₁	—	2	2	no	—
43	C₂²×C₄×C₁₅₁	—	2	2	no	—
44	C₂²×C₄×C₁₅₁	—	2	2	no	—
45	C₂²×C₄×C₁₅₁	—	2	2	no	—
46	C₂²×C₄×C₁₅₁	—	2	2	no	—
47	C₂²×C₄×C₁₅₁	—	2	2	no	—
48	C₂²×C₄×C₁₅₁	—	2	2	no	—
49	C₂²×C₄×C₁₅₁	C₂×C₄	1	4	yes	—
50	C₂²×C₄×C₁₅₁	Q₈	1	4	yes	complemented
51	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
52	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
53	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
55	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
56	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
61	C₄⋊C₄×C₁₅₁	—	2	4	no	—
62	C₄⋊C₄×C₁₅₁	—	2	2	no	—
63	C₄⋊C₄×C₁₅₁	—	2	4	no	—
64	C₄⋊C₄×C₁₅₁	—	2	2	no	—
65	C₄⋊C₄×C₁₅₁	C₂×C₄	1	8	yes	complemented
66	C₄⋊C₄×C₁₅₁	C₂×C₄	1	4	yes	complemented
67	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
68	C₂²⋊C₄×C₁₅₁	C₂×C₄	1	8	yes	—
69	C₄²×C₁₅₁	—	2	2	no	—
70	C₄²×C₁₅₁	—	2	2	no	—
71	C₄²×C₁₅₁	—	2	2	no	—
72	C₄²×C₁₅₁	—	2	4	no	—
73	C₄²×C₁₅₁	—	2	4	no	—
74	C₄²×C₁₅₁	D₄	1	4	yes	—
75	C₂³×C₁₅₁	—	2	1	no	—
76	C₂³×C₁₅₁	—	2	1	no	—
77	C₂³×C₁₅₁	—	2	1	no	—
78	C₂³×C₁₅₁	—	2	1	no	—
79	C₂³×C₁₅₁	C₂²×C₄	1	2	yes	—
80	C₂³×C₁₅₁	C₂×Q₈	1	2	yes	—
81	C₂³×C₁₅₁	#41	1	2	yes	—
82	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
83	Q₈×C₁₅₁	—	2	8	no	—
84	C₂×C₄×C₁₅₁	—	2	8	no	—
85	C₂×C₄×C₁₅₁	—	2	2	no	—
86	C₂×C₄×C₁₅₁	—	2	1	no	—
87	C₂×C₄×C₁₅₁	—	2	1	no	—
88	C₂×C₄×C₁₅₁	—	2	1	no	—
89	C₂×C₄×C₁₅₁	—	2	2	no	—
90	C₂×C₄×C₁₅₁	—	2	2	no	—
91	C₂×C₄×C₁₅₁	—	2	2	no	—
92	C₂×C₄×C₁₅₁	—	2	1	no	—
93	C₂×C₄×C₁₅₁	—	2	1	no	—
94	C₂×C₄×C₁₅₁	—	2	1	no	—
95	C₂×C₄×C₁₅₁	—	2	1	no	—
96	C₂×C₄×C₁₅₁	—	2	1	no	—
97	C₂×C₄×C₁₅₁	—	2	8	no	—
98	C₂×C₄×C₁₅₁	—	2	8	no	—
99	C₂×C₄×C₁₅₁	—	2	2	no	—
100	C₂×C₄×C₁₅₁	—	2	2	no	—
101	C₂×C₄×C₁₅₁	—	2	2	no	—
102	C₂×C₄×C₁₅₁	—	2	2	no	—
103	C₂×C₄×C₁₅₁	—	2	2	no	—
104	C₂×C₄×C₁₅₁	—	2	2	no	—
105	C₂×C₄×C₁₅₁	C₂²×C₄	1	4	yes	—
106	C₂×C₄×C₁₅₁	C₂²×C₄	1	4	yes	—
107	C₂×C₄×C₁₅₁	C₂²×C₄	1	2	yes	—
108	C₂×C₄×C₁₅₁	C₂²×C₄	1	2	yes	—
109	C₂×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
110	C₂×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
111	C₂×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
112	C₂×C₄×C₁₅₁	C₂×Q₈	1	2	yes	—
113	C₂×C₄×C₁₅₁	C₂×Q₈	1	2	yes	—
114	C₂×C₄×C₁₅₁	#41	1	2	yes	—
115	C₂×C₄×C₁₅₁	#41	1	2	yes	—
116	C₂×C₄×C₁₅₁	#41	1	2	yes	—
117	C₂²×C₁₅₁	—	2	2	no	—
118	C₂²×C₁₅₁	—	2	2	no	—
119	C₂²×C₁₅₁	—	2	2	no	—
120	C₂²×C₁₅₁	—	2	2	no	—
121	C₂²×C₁₅₁	—	2	2	no	—
122	C₂²×C₁₅₁	—	2	2	no	—
123	C₂²×C₁₅₁	C₄×Q₈	1	4	yes	complemented
124	C₂²×C₁₅₁	C₂³×C₄	1	1	yes	characteristic
125	C₂²×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
126	C₂²×C₁₅₁	C₂²×Q₈	1	1	yes	characteristic
127	C₂²×C₁₅₁	C₂×#41	1	1	yes	characteristic
128	C₂²×C₁₅₁	C₂×#41	1	1	yes	characteristic
129	C₂²×C₁₅₁	C₂×#41	1	1	yes	characteristic
130	C₂²×C₁₅₁	C₂×#41	1	1	yes	characteristic
131	C₄×C₁₅₁	—	2	2	no	—
132	C₄×C₁₅₁	—	2	4	no	—
133	C₄×C₁₅₁	—	2	4	no	—
134	C₄×C₁₅₁	—	2	2	no	—
135	C₄×C₁₅₁	—	2	2	no	—
136	C₄×C₁₅₁	—	2	2	no	—
137	C₄×C₁₅₁	—	4	2	no	—
138	C₄×C₁₅₁	—	4	2	no	—
139	C₄×C₁₅₁	C₄×D₄	1	4	yes	—
140	C₄×C₁₅₁	C₂²⋊Q₈	1	4	yes	direct product factor
141	C₂×C₁₅₁	—	2	4	no	—
142	C₂×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
143	C₂×C₁₅₁	C₂×C₄×Q₈	1	1	yes	characteristic
144	C₂×C₁₅₁	C₄×#41	1	1	yes	characteristic
145	C₂×C₁₅₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
146	C₂×C₁₅₁	#525	1	1	yes	characteristic
147	C₂×C₁₅₁	#529	1	1	yes	characteristic
148	C₂×C₁₅₁	#533	1	1	yes	characteristic
149	C₁₅₁	C₄×C₂²⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
150	C₄×C₂²⋊Q₈	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂×C₂²⋊Q₈	C₂×C₁₅₁	1	1	yes	characteristic
152	C₂×C₄×Q₈	C₂×C₁₅₁	1	1	yes	characteristic, complemented
153	C₂²×C₄²	C₂×C₁₅₁	1	1	yes	characteristic
154	#391	C₂×C₁₅₁	1	1	yes	characteristic, complemented
155	#389	C₂×C₁₅₁	1	1	yes	characteristic, complemented
156	#387	C₂×C₁₅₁	1	2	yes	complemented
157	#385	C₂×C₁₅₁	1	2	yes	—
158	#380	C₂×C₁₅₁	1	1	yes	characteristic
159	C₄×C₄⋊C₄	C₂×C₁₅₁	1	2	yes	complemented
160	C₄×C₄⋊C₄	C₂×C₁₅₁	1	1	yes	characteristic, complemented
161	C₄×C₂²⋊C₄	C₂×C₁₅₁	1	2	yes	—
162	C₂²×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
163	C₂³×C₄	C₂²×C₁₅₁	1	1	yes	characteristic
164	C₂³×C₄	C₂²×C₁₅₁	1	1	yes	characteristic
165	C₂³×C₄	C₂²×C₁₅₁	1	1	yes	characteristic
166	C₂²⋊Q₈	C₄×C₁₅₁	1	8	yes	direct product factor
167	C₄×Q₈	—	2	4	no	—
168	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
169	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	2	yes	—
170	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
171	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	2	yes	—
172	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	2	yes	—
173	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
174	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	2	yes	—
175	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	2	yes	—
176	C₂×C₄²	—	2	4	no	—
177	C₂×C₄²	C₂²×C₁₅₁	1	2	yes	—
178	C₂×C₄²	C₂²×C₁₅₁	1	2	yes	—
179	C₂×C₄²	C₂²×C₁₅₁	1	1	yes	characteristic
180	C₂×C₄²	C₂²×C₁₅₁	1	1	yes	characteristic
181	C₂×C₄²	C₂²×C₁₅₁	1	1	yes	characteristic
182	C₂×C₄²	C₂²×C₁₅₁	1	1	yes	characteristic
183	#95	C₂²×C₁₅₁	1	2	yes	—
184	#95	C₂²×C₁₅₁	1	2	yes	—
185	#95	C₂²×C₁₅₁	1	2	yes	—
186	#95	C₂²×C₁₅₁	1	2	yes	—
187	#95	C₂²×C₁₅₁	1	2	yes	—
188	C₂⁴	C₂³×C₁₅₁	1	1	yes	characteristic
189	C₂×Q₈	—	2	2	no	—
190	C₂×Q₈	—	2	2	no	—
191	C₂×Q₈	C₂×C₄×C₁₅₁	1	4	yes	complemented
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	—	2	2	no	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	2	2	no	—
198	C₂²×C₄	—	2	2	no	—
199	C₂²×C₄	C₂×C₄×C₁₅₁	1	4	yes	—
200	C₂²×C₄	Q₈×C₁₅₁	1	4	yes	complemented
201	C₂²×C₄	C₂³×C₁₅₁	1	2	yes	—
202	C₂²×C₄	C₂³×C₁₅₁	1	2	yes	—
203	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
204	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
205	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
206	C₂²×C₄	C₂³×C₁₅₁	1	2	yes	—
207	C₂²×C₄	C₂³×C₁₅₁	1	2	yes	—
208	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
209	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
210	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
211	C₄⋊C₄	—	2	4	no	—
212	C₄⋊C₄	—	2	2	no	—
213	C₄⋊C₄	—	2	4	no	—
214	C₄⋊C₄	—	2	2	no	—
215	C₄⋊C₄	C₂×C₄×C₁₅₁	1	4	yes	complemented
216	C₄⋊C₄	C₂×C₄×C₁₅₁	1	8	yes	complemented
217	C₂²⋊C₄	—	2	4	no	—
218	C₂²⋊C₄	C₂×C₄×C₁₅₁	1	8	yes	—
219	C₄²	—	2	4	no	—
220	C₄²	—	2	2	no	—
221	C₄²	—	2	2	no	—
222	C₄²	—	2	2	no	—
223	C₄²	—	2	4	no	—
224	C₄²	D₄×C₁₅₁	1	4	yes	—
225	C₂³	—	2	1	no	—
226	C₂³	—	2	1	no	—
227	C₂³	—	2	1	no	—
228	C₂³	—	2	1	no	—
229	C₂³	C₂²×C₄×C₁₅₁	1	2	yes	—
230	C₂³	C₂×Q₈×C₁₅₁	1	2	yes	—
231	C₂³	#41×C₁₅₁	1	2	yes	—
232	C₂³	C₂⁴×C₁₅₁	1	1	yes	characteristic
233	Q₈	—	2	8	no	—
234	C₂×C₄	—	2	8	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	1	no	—
245	C₂×C₄	—	2	1	no	—
246	C₂×C₄	—	2	2	no	—
247	C₂×C₄	—	2	8	no	—
248	C₂×C₄	—	2	8	no	—
249	C₂×C₄	—	2	2	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	C₂²×C₄×C₁₅₁	1	4	yes	—
256	C₂×C₄	C₂²×C₄×C₁₅₁	1	4	yes	—
257	C₂×C₄	C₂²×C₄×C₁₅₁	1	2	yes	—
258	C₂×C₄	C₂²×C₄×C₁₅₁	1	2	yes	—
259	C₂×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
260	C₂×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
261	C₂×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
262	C₂×C₄	C₂×Q₈×C₁₅₁	1	2	yes	—
263	C₂×C₄	C₂×Q₈×C₁₅₁	1	2	yes	—
264	C₂×C₄	#41×C₁₅₁	1	2	yes	—
265	C₂×C₄	#41×C₁₅₁	1	2	yes	—
266	C₂×C₄	#41×C₁₅₁	1	2	yes	—
267	C₂²	—	2	2	no	—
268	C₂²	—	2	2	no	—
269	C₂²	—	2	2	no	—
270	C₂²	—	2	2	no	—
271	C₂²	—	2	2	no	—
272	C₂²	—	2	2	no	—
273	C₂²	C₄×Q₈×C₁₅₁	1	4	yes	complemented
274	C₂²	C₂³×C₄×C₁₅₁	1	1	yes	characteristic
275	C₂²	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
276	C₂²	C₂²×Q₈×C₁₅₁	1	1	yes	characteristic
277	C₂²	C₂×#41×C₁₅₁	1	1	yes	characteristic
278	C₂²	C₂×#41×C₁₅₁	1	1	yes	characteristic
279	C₂²	C₂×#41×C₁₅₁	1	1	yes	characteristic
280	C₂²	C₂×#41×C₁₅₁	1	1	yes	characteristic
281	C₄	—	2	2	no	—
282	C₄	—	2	4	no	—
283	C₄	—	2	4	no	—
284	C₄	—	2	2	no	—
285	C₄	—	2	2	no	—
286	C₄	—	2	2	no	—
287	C₄	—	4	2	no	—
288	C₄	—	4	2	no	—
289	C₄	C₄×D₄×C₁₅₁	1	4	yes	—
290	C₄	C₂²⋊Q₈×C₁₅₁	1	4	yes	direct product factor
291	C₂	—	2	4	no	—
292	C₂	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
293	C₂	C₂×C₄×Q₈×C₁₅₁	1	1	yes	characteristic
294	C₂	C₄×#41×C₁₅₁	1	1	yes	characteristic
295	C₂	C₂×C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
296	C₂	#525×C₁₅₁	1	1	yes	characteristic
297	C₂	#529×C₁₅₁	1	1	yes	characteristic
298	C₂	#533×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₅₁	C₂³
commutator	C₂²	C₂³×C₄×C₁₅₁
Frattini, cosocle	C₂³	C₂⁴×C₁₅₁
socle	C₂³×C₁₅₁	C₂⁴
prime radical	C₂⁴×C₁₅₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₈×C₁₅₁	C₂	semidirect
4. #391×C₁₅₁	C₂	semidirect
5. #389×C₁₅₁	C₂	semidirect
6. #387×C₁₅₁	C₂	semidirect
9. C₄×C₄⋊C₄×C₁₅₁	C₂	semidirect
10. C₄×C₄⋊C₄×C₁₅₁	C₂	semidirect
16. C₂²⋊Q₈×C₁₅₁	C₄	direct (N × H)
41. C₂×Q₈×C₁₅₁	C₂×C₄	semidirect
50. C₂²×C₄×C₁₅₁	Q₈	semidirect
65. C₄⋊C₄×C₁₅₁	C₂×C₄	semidirect
66. C₄⋊C₄×C₁₅₁	C₂×C₄	semidirect
123. C₂²×C₁₅₁	C₄×Q₈	semidirect
140. C₄×C₁₅₁	C₂²⋊Q₈	direct (N × H)
149. C₁₅₁	C₄×C₂²⋊Q₈	direct (N × H)
150. C₄×C₂²⋊Q₈	C₁₅₁	direct (N × H)
152. C₂×C₄×Q₈	C₂×C₁₅₁	semidirect
154. #391	C₂×C₁₅₁	semidirect
155. #389	C₂×C₁₅₁	semidirect
156. #387	C₂×C₁₅₁	semidirect
159. C₄×C₄⋊C₄	C₂×C₁₅₁	semidirect
160. C₄×C₄⋊C₄	C₂×C₁₅₁	semidirect
166. C₂²⋊Q₈	C₄×C₁₅₁	direct (N × H)
191. C₂×Q₈	C₂×C₄×C₁₅₁	semidirect
200. C₂²×C₄	Q₈×C₁₅₁	semidirect
215. C₄⋊C₄	C₂×C₄×C₁₅₁	semidirect
216. C₄⋊C₄	C₂×C₄×C₁₅₁	semidirect
273. C₂²	C₄×Q₈×C₁₅₁	semidirect
290. C₄	C₂²⋊Q₈×C₁₅₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂²⋊Q₈×C₁₅₁	2
C₂×C₄×Q₈×C₁₅₁	2
C₂²×C₄²×C₁₅₁	2
#391×C₁₅₁	2
#389×C₁₅₁	2
#387×C₁₅₁	2
#385×C₁₅₁	2
#380×C₁₅₁	2
C₄×C₄⋊C₄×C₁₅₁	2
C₄×C₂²⋊C₄×C₁₅₁	2
C₄×C₂²⋊Q₈	151

Subgroups — C4×C22⋊Q8×C151 #34065634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂²⋊Q₈×C₁₅₁ #34065634