Subgroups — #563×D₁₅₁ #34083238

Order 19328.

1024 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23752966	C₂	1	2	yes	maximal, complemented
2	#23752965	C₂	1	2	yes	maximal, complemented
3	#23752964	C₂	1	4	yes	maximal, complemented
4	#23752963	C₂	1	4	yes	maximal, complemented
5	#23752962	C₂	1	1	yes	maximal, characteristic, complemented
6	#23752961	C₂	1	2	yes	maximal, complemented
7	C₄⋊Q₈×D₁₅₁	C₂	1	2	yes	maximal, complemented
8	#126×D₁₅₁	C₂	1	4	yes	maximal, complemented
9	#125×D₁₅₁	C₂	1	2	yes	maximal, complemented
10	#124×D₁₅₁	C₂	1	1	yes	maximal, characteristic
11	#123×D₁₅₁	C₂	1	2	yes	maximal
12	C₂²⋊Q₈×D₁₅₁	C₂	1	4	yes	maximal, complemented
13	#563×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×Q₈×D₁₅₁	C₂²	1	2	yes	—
15	C₂×Q₈×D₁₅₁	C₂²	1	1	yes	characteristic
16	C₂×D₄×D₁₅₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₁₅₁	C₂²	1	2	yes	—
18	#18012739	C₂²	1	2	yes	complemented
19	#18012738	C₂²	1	4	yes	complemented
20	#18012738	C₂²	1	4	yes	complemented
21	#18012737	C₂²	1	2	yes	complemented
22	#18012737	C₂²	1	2	yes	complemented
23	#18012734	C₂²	1	4	yes	complemented
24	#18012734	C₂²	1	4	yes	complemented
25	#18012734	C₂²	1	4	yes	complemented
26	#18012733	C₂²	1	4	yes	complemented
27	#18012732	C₂²	1	4	yes	complemented
28	#18012732	C₂²	1	4	yes	complemented
29	#18012732	C₂²	1	4	yes	complemented
30	#18012731	C₂²	1	2	yes	complemented
31	#18012730	C₂²	1	2	yes	complemented
32	#18012730	C₂²	1	2	yes	complemented
33	#18012729	C₂²	1	4	yes	complemented
34	#18012729	C₂²	1	4	yes	complemented
35	#18012728	C₂²	1	1	yes	characteristic
36	#18012727	C₂²	1	1	yes	characteristic
37	#18012726	C₂²	1	1	yes	characteristic
38	#18012725	C₂²	1	4	yes	—
39	#18012724	C₂²	1	4	yes	—
40	#18012723	C₂²	1	2	yes	—
41	#18012722	C₂²	1	2	yes	—
42	#18012721	C₂²	1	4	yes	—
43	#18012720	C₂²	1	2	yes	—
44	#18012719	C₂²	1	4	yes	complemented
45	#18012718	C₂²	1	4	yes	complemented
46	#18012717	C₂²	1	4	yes	complemented
47	#18012717	C₂²	1	4	yes	complemented
48	#18012716	C₂²	1	4	yes	complemented
49	#18012716	C₂²	1	4	yes	complemented
50	#18012715	C₂²	1	4	yes	complemented
51	C₄⋊C₄×D₁₅₁	C₂²	1	2	yes	—
52	C₄⋊C₄×D₁₅₁	C₂²	1	4	yes	—
53	C₄⋊C₄×D₁₅₁	C₂²	1	4	yes	—
54	C₄⋊C₄×D₁₅₁	C₂²	1	4	yes	—
55	C₄⋊C₄×D₁₅₁	C₂²	1	2	yes	—
56	C₂²⋊C₄×D₁₅₁	C₂²	1	4	yes	—
57	C₂²⋊C₄×D₁₅₁	C₂²	1	4	yes	—
58	C₂²⋊C₄×D₁₅₁	C₂²	1	2	yes	—
59	C₄²×D₁₅₁	C₂²	1	1	yes	characteristic
60	C₄²×D₁₅₁	C₂²	1	2	yes	—
61	C₄⋊Q₈×C₁₅₁	C₂²	1	2	yes	complemented
62	#126×C₁₅₁	C₂²	1	4	yes	complemented
63	#125×C₁₅₁	C₂²	1	2	yes	complemented
64	#124×C₁₅₁	C₂²	1	1	yes	characteristic
65	#123×C₁₅₁	C₂²	1	2	yes	—
66	C₂²⋊Q₈×C₁₅₁	C₂²	1	4	yes	complemented
67	C₂³×D₁₅₁	C₂³	1	2	yes	—
68	C₂×Dic₃₀₂	C₂³	1	2	yes	—
69	C₂×Dic₃₀₂	C₂³	1	4	yes	—
70	C₂×Dic₃₀₂	C₂³	1	2	yes	—
71	C₂×Dic₃₀₂	C₂³	1	1	yes	characteristic
72	Q₈×D₁₅₁	—	4	4	no	—
73	Q₈×D₁₅₁	—	4	2	no	—
74	C₂×D₆₀₄	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
76	D₄×D₁₅₁	—	4	2	no	—
77	C₂²×Dic₁₅₁	C₂³	1	2	yes	—
78	C₂×C₄×D₁₅₁	—	4	4	no	—
79	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
80	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
81	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
82	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
83	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
84	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
85	C₄⋊Dic₁₅₁	C₂³	1	4	yes	—
86	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
87	C₄⋊Dic₁₅₁	C₂³	1	4	yes	—
88	C₄⋊Dic₁₅₁	C₂³	1	4	yes	—
89	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
90	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
91	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
92	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
93	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
94	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
95	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
96	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
97	Dic₁₅₁⋊C₄	C₂³	1	4	yes	—
98	C₂²⋊Dic₁₅₁	C₂³	1	4	yes	—
99	C₂²⋊Dic₁₅₁	C₂³	1	4	yes	—
100	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
101	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
102	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
103	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
104	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
105	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
106	C₄×Dic₁₅₁	C₂³	1	2	yes	—
107	C₄×Dic₁₅₁	C₂³	1	1	yes	characteristic
108	C₄×Dic₁₅₁	C₂³	1	2	yes	—
109	C₄×Dic₁₅₁	C₂³	1	4	yes	—
110	C₂×Q₈×C₁₅₁	C₂³	1	2	yes	—
111	C₂×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
114	C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
115	C₄⋊C₄×C₁₅₁	C₂³	1	4	yes	—
116	C₄⋊C₄×C₁₅₁	C₂³	1	4	yes	—
117	C₄⋊C₄×C₁₅₁	C₂³	1	4	yes	—
118	C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
119	C₂²⋊C₄×C₁₅₁	C₂³	1	4	yes	—
120	C₂²⋊C₄×C₁₅₁	C₂³	1	4	yes	—
121	C₂²⋊C₄×C₁₅₁	C₂³	1	2	yes	—
122	C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
123	C₄²×C₁₅₁	C₂³	1	2	yes	—
124	C₂²×D₁₅₁	—	2	4	no	—
125	C₂²×D₁₅₁	—	2	8	no	—
126	C₂²×D₁₅₁	C₂⁴	1	2	yes	—
127	C₂²×D₁₅₁	C₂⁴	1	1	yes	characteristic
128	Dic₃₀₂	—	4	2	no	—
129	Dic₃₀₂	—	4	4	no	—
130	Dic₃₀₂	—	4	2	no	—
131	Dic₃₀₂	—	4	1	no	—
132	D₆₀₄	—	4	1	no	—
133	C₂²⋊D₁₅₁	—	4	2	no	—
134	C₂×Dic₁₅₁	—	4	2	no	—
135	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
136	C₂×Dic₁₅₁	C₂⁴	1	4	yes	—
137	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
138	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
139	C₂×Dic₁₅₁	C₂⁴	1	4	yes	—
140	C₄×D₁₅₁	—	2	8	no	—
141	C₄×D₁₅₁	—	2	2	no	—
142	C₄×D₁₅₁	—	2	4	no	—
143	C₄×D₁₅₁	—	2	4	no	—
144	C₄×D₁₅₁	—	2	8	no	—
145	C₄×D₁₅₁	—	4	4	no	—
146	C₂³×C₁₅₁	C₂⁴	1	2	yes	—
147	Q₈×C₁₅₁	—	4	2	no	—
148	Q₈×C₁₅₁	—	4	1	no	—
149	D₄×C₁₅₁	—	4	1	no	—
150	C₂×C₄×C₁₅₁	—	4	2	no	—
151	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
152	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
153	C₂×C₄×C₁₅₁	C₂⁴	1	4	yes	—
154	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
155	C₂×C₄×C₁₅₁	C₂⁴	1	4	yes	—
156	C₂²×C₁₅₁	—	2	2	no	—
157	C₂²×C₁₅₁	—	2	4	no	—
158	C₂²×C₁₅₁	C₂⁵	1	1	yes	characteristic
159	C₂×D₁₅₁	—	2	2	no	—
160	C₂×D₁₅₁	—	2	4	no	—
161	C₂×D₁₅₁	—	4	8	no	—
162	C₂×D₁₅₁	H(5,𝔽₂)	1	2	yes	—
163	C₂×D₁₅₁	2₋¹⁺⁴	1	4	yes	—
164	C₄×C₁₅₁	—	2	4	no	—
165	C₄×C₁₅₁	—	2	1	no	—
166	C₄×C₁₅₁	—	2	2	no	—
167	C₄×C₁₅₁	—	2	2	no	—
168	C₄×C₁₅₁	—	2	4	no	—
169	Dic₁₅₁	—	2	4	no	—
170	Dic₁₅₁	—	2	1	no	—
171	Dic₁₅₁	—	2	2	no	—
172	Dic₁₅₁	—	2	2	no	—
173	Dic₁₅₁	—	2	4	no	—
174	C₂×C₁₅₁	—	4	2	no	—
175	C₂×C₁₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₁₅₁	C₂×2₋¹⁺⁴	1	2	yes	—
177	D₁₅₁	—	4	2	no	—
178	D₁₅₁	#563	1	4	yes	direct product factor
179	C₁₅₁	C₂×#563	1	1	yes	characteristic, complemented, Sylow
180	C₂×#563	—	151	1	no	maximal, Sylow
181	#563	—	151	2	no	—
182	#563	—	151	4	no	—
183	#563	—	151	2	no	—
184	#563	—	151	1	no	—
185	#563	—	151	2	no	—
186	#563	—	151	4	no	—
187	#563	D₁₅₁	1	1	yes	characteristic, direct product factor
188	C₂×C₄⋊Q₈	—	151	2	no	—
189	C₂×#126	—	151	4	no	—
190	C₂×#125	—	151	2	no	—
191	C₂×#124	—	151	1	no	—
192	C₂×#123	—	151	2	no	—
193	C₂×C₂²⋊Q₈	—	151	4	no	—
194	C₂²×Q₈	—	151	2	no	—
195	C₂²×Q₈	—	151	1	no	—
196	C₂²×D₄	—	151	1	no	—
197	C₂³×C₄	—	151	2	no	—
198	C₄⋊Q₈	—	151	2	no	—
199	C₄⋊Q₈	—	151	2	no	—
200	C₄⋊Q₈	—	151	4	no	—
201	C₄⋊Q₈	—	151	4	no	—
202	C₄⋊Q₈	—	151	2	no	—
203	C₄⋊Q₈	C₂×D₁₅₁	1	2	yes	complemented
204	#126	—	151	4	no	—
205	#126	—	151	4	no	—
206	#126	—	151	4	no	—
207	#126	—	151	4	no	—
208	#126	—	151	4	no	—
209	#126	—	151	4	no	—
210	#126	—	151	4	no	—
211	#126	C₂×D₁₅₁	1	4	yes	complemented
212	#125	—	151	4	no	—
213	#125	—	151	4	no	—
214	#125	—	151	2	no	—
215	#125	—	151	2	no	—
216	#125	—	151	2	no	—
217	#125	C₂×D₁₅₁	1	2	yes	complemented
218	#124	—	151	1	no	—
219	#124	—	151	1	no	—
220	#124	—	151	4	no	—
221	#124	—	151	1	no	—
222	#124	C₂×D₁₅₁	1	1	yes	characteristic
223	#123	—	151	2	no	—
224	#123	—	151	2	no	—
225	#123	—	151	4	no	—
226	#123	—	151	4	no	—
227	#123	—	151	2	no	—
228	#123	C₂×D₁₅₁	1	2	yes	—
229	C₂²⋊Q₈	—	151	4	no	—
230	C₂²⋊Q₈	—	151	4	no	—
231	C₂²⋊Q₈	—	151	4	no	—
232	C₂²⋊Q₈	—	151	4	no	—
233	C₂²⋊Q₈	—	151	4	no	—
234	C₂²⋊Q₈	—	151	4	no	—
235	C₂²⋊Q₈	—	151	4	no	—
236	C₂²⋊Q₈	C₂×D₁₅₁	1	4	yes	complemented
237	C₂×C₄⋊C₄	—	151	2	no	—
238	C₂×C₄⋊C₄	—	151	4	no	—
239	C₂×C₄⋊C₄	—	151	4	no	—
240	C₂×C₄⋊C₄	—	151	4	no	—
241	C₂×C₄⋊C₄	—	151	2	no	—
242	C₂×C₂²⋊C₄	—	151	4	no	—
243	C₂×C₂²⋊C₄	—	151	4	no	—
244	C₂×C₂²⋊C₄	—	151	2	no	—
245	C₂×C₄²	—	151	1	no	—
246	C₂×C₄²	—	151	2	no	—
247	C₂⁴	—	151	2	no	—
248	C₂×Q₈	—	604	4	no	—
249	C₂×Q₈	—	604	2	no	—
250	C₂×Q₈	—	151	4	no	—
251	C₂×Q₈	—	151	2	no	—
252	C₂×Q₈	—	151	1	no	—
253	C₂×Q₈	—	151	2	no	—
254	C₂×Q₈	C₂²×D₁₅₁	1	2	yes	—
255	C₂×Q₈	C₂²×D₁₅₁	1	1	yes	characteristic
256	C₂×D₄	—	604	2	no	—
257	C₂×D₄	—	151	2	no	—
258	C₂×D₄	—	151	1	no	—
259	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
260	C₂²×C₄	—	604	4	no	—
261	C₂²×C₄	—	151	2	no	—
262	C₂²×C₄	—	151	4	no	—
263	C₂²×C₄	—	151	2	no	—
264	C₂²×C₄	—	151	1	no	—
265	C₂²×C₄	—	151	4	no	—
266	C₂²×C₄	—	151	2	no	—
267	C₂²×C₄	—	151	4	no	—
268	C₂²×C₄	C₂²×D₁₅₁	1	2	yes	—
269	C₄⋊C₄	—	151	4	no	—
270	C₄⋊C₄	—	151	4	no	—
271	C₄⋊C₄	—	151	4	no	—
272	C₄⋊C₄	—	151	4	no	—
273	C₄⋊C₄	—	151	4	no	—
274	C₄⋊C₄	—	151	4	no	—
275	C₄⋊C₄	—	151	4	no	—
276	C₄⋊C₄	—	151	4	no	—
277	C₄⋊C₄	—	151	2	no	—
278	C₄⋊C₄	—	151	4	no	—
279	C₄⋊C₄	—	151	4	no	—
280	C₄⋊C₄	—	151	4	no	—
281	C₄⋊C₄	—	151	2	no	—
282	C₄⋊C₄	C₂²×D₁₅₁	1	2	yes	—
283	C₄⋊C₄	C₂²×D₁₅₁	1	4	yes	—
284	C₄⋊C₄	C₂²×D₁₅₁	1	4	yes	—
285	C₄⋊C₄	C₂²×D₁₅₁	1	4	yes	—
286	C₄⋊C₄	C₂²×D₁₅₁	1	2	yes	—
287	C₂²⋊C₄	—	151	4	no	—
288	C₂²⋊C₄	—	151	4	no	—
289	C₂²⋊C₄	—	151	2	no	—
290	C₂²⋊C₄	—	151	4	no	—
291	C₂²⋊C₄	—	151	4	no	—
292	C₂²⋊C₄	—	151	4	no	—
293	C₂²⋊C₄	—	151	4	no	—
294	C₂²⋊C₄	—	151	4	no	—
295	C₂²⋊C₄	C₂²×D₁₅₁	1	4	yes	—
296	C₂²⋊C₄	C₂²×D₁₅₁	1	4	yes	—
297	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
298	C₄²	—	151	1	no	—
299	C₄²	—	151	2	no	—
300	C₄²	—	151	2	no	—
301	C₄²	—	151	4	no	—
302	C₄²	C₂²×D₁₅₁	1	1	yes	characteristic
303	C₄²	C₂²×D₁₅₁	1	2	yes	—
304	C₂³	—	302	4	no	—
305	C₂³	—	302	8	no	—
306	C₂³	—	151	2	no	—
307	C₂³	—	151	1	no	—
308	C₂³	C₂³×D₁₅₁	1	2	yes	—
309	Q₈	—	4	2	no	—
310	Q₈	—	4	1	no	—
311	Q₈	—	604	4	no	—
312	Q₈	—	604	1	no	—
313	Q₈	—	604	2	no	—
314	Q₈	—	604	2	no	—
315	D₄	—	4	1	no	—
316	D₄	—	604	1	no	—
317	D₄	—	604	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	302	8	no	—
320	C₂×C₄	—	302	2	no	—
321	C₂×C₄	—	302	4	no	—
322	C₂×C₄	—	302	4	no	—
323	C₂×C₄	—	302	8	no	—
324	C₂×C₄	—	604	4	no	—
325	C₂×C₄	—	604	2	no	—
326	C₂×C₄	—	151	2	no	—
327	C₂×C₄	—	151	4	no	—
328	C₂×C₄	—	151	2	no	—
329	C₂×C₄	—	151	1	no	—
330	C₂×C₄	—	151	4	no	—
331	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
332	C₂×C₄	C₂³×D₁₅₁	1	4	yes	—
333	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
334	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
335	C₂×C₄	C₂³×D₁₅₁	1	4	yes	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	4	no	—
338	C₂²	—	302	2	no	—
339	C₂²	—	302	4	no	—
340	C₂²	—	604	8	no	—
341	C₂²	—	151	2	no	—
342	C₂²	—	151	4	no	—
343	C₂²	C₂⁴×D₁₅₁	1	1	yes	characteristic
344	C₄	—	2	4	no	—
345	C₄	—	2	1	no	—
346	C₄	—	2	2	no	—
347	C₄	—	2	2	no	—
348	C₄	—	2	4	no	—
349	C₄	—	302	4	no	—
350	C₄	—	302	1	no	—
351	C₄	—	302	2	no	—
352	C₄	—	302	2	no	—
353	C₄	—	302	4	no	—
354	C₂	—	4	2	no	—
355	C₂	—	604	2	no	—
356	C₂	—	151	4	no	—
357	C₂	H(5,𝔽₂)×D₁₅₁	1	1	yes	characteristic
358	C₂	2₋¹⁺⁴×D₁₅₁	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₅₁
commutator, socle, cosocle	C₂²×C₁₅₁	C₂⁵
Fitting	#563×C₁₅₁	C₂
prime radical	C₂×D₄×D₁₅₁	C₂²
hypercenter	#563	D₁₅₁
hypocenter	C₁₅₁	C₂×#563
LCS	G ▷ C₂²×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ #563

Complements

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

N	H ≅ G/N	type
1. #23752966	C₂	semidirect
2. #23752965	C₂	semidirect
3. #23752964	C₂	semidirect
4. #23752963	C₂	semidirect
5. #23752962	C₂	semidirect
6. #23752961	C₂	semidirect
7. C₄⋊Q₈×D₁₅₁	C₂	semidirect
8. #126×D₁₅₁	C₂	semidirect
9. #125×D₁₅₁	C₂	semidirect
12. C₂²⋊Q₈×D₁₅₁	C₂	semidirect
13. #563×C₁₅₁	C₂	semidirect
18. #18012739	C₂²	semidirect
19. #18012738	C₂²	semidirect
20. #18012738	C₂²	semidirect
21. #18012737	C₂²	semidirect
22. #18012737	C₂²	semidirect
23. #18012734	C₂²	semidirect
24. #18012734	C₂²	semidirect
25. #18012734	C₂²	semidirect
26. #18012733	C₂²	semidirect
27. #18012732	C₂²	semidirect
28. #18012732	C₂²	semidirect
29. #18012732	C₂²	semidirect
30. #18012731	C₂²	semidirect
31. #18012730	C₂²	semidirect
32. #18012730	C₂²	semidirect
33. #18012729	C₂²	semidirect
34. #18012729	C₂²	semidirect
44. #18012719	C₂²	semidirect
45. #18012718	C₂²	semidirect
46. #18012717	C₂²	semidirect
47. #18012717	C₂²	semidirect
48. #18012716	C₂²	semidirect
49. #18012716	C₂²	semidirect
50. #18012715	C₂²	semidirect
61. C₄⋊Q₈×C₁₅₁	C₂²	semidirect
62. #126×C₁₅₁	C₂²	semidirect
63. #125×C₁₅₁	C₂²	semidirect
66. C₂²⋊Q₈×C₁₅₁	C₂²	semidirect
178. D₁₅₁	#563	direct (N × H)
179. C₁₅₁	C₂×#563	semidirect
187. #563	D₁₅₁	direct (N × H)
203. C₄⋊Q₈	C₂×D₁₅₁	semidirect
211. #126	C₂×D₁₅₁	semidirect
217. #125	C₂×D₁₅₁	semidirect
236. C₂²⋊Q₈	C₂×D₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#23752966	2
#23752965	2
#23752964	2
#23752963	2
#23752962	2
#23752961	2
C₄⋊Q₈×D₁₅₁	2
#126×D₁₅₁	2
#125×D₁₅₁	2
#124×D₁₅₁	2
#123×D₁₅₁	2
C₂²⋊Q₈×D₁₅₁	2
#563×C₁₅₁	2
C₂×#563	151

Subgroups — #563×D151 #34083238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #563×D₁₅₁ #34083238