Subgroups — #23752289

Order 9664.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14558987	C₂	1	2	yes	maximal, complemented
2	C₄×D₆₀₄	C₂	1	1	yes	maximal, characteristic
3	(C₂×D₁₅₁)⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₄×C₁₅₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊C₈×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₆₀₄	C₄	1	1	yes	characteristic
7	C₂×C₄×D₁₅₁	C₂²	1	2	yes	—
8	#14558987	—	2	4	no	—
9	C₂×C₁₅₁⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₅₁⋊C₈	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₅₁	C₄	1	1	yes	characteristic
12	(C₂×D₁₅₁)⋊C₄	C₄	1	2	yes	—
13	C₂×C₈×C₁₅₁	C₂²	1	2	yes	—
14	C₄²×C₁₅₁	C₂²	1	1	yes	characteristic
15	C₂²×D₁₅₁	C₂×C₄	1	2	yes	—
16	D₆₀₄	—	2	2	no	—
17	C₂×Dic₁₅₁	C₂×C₄	1	2	yes	—
18	C₄×D₁₅₁	—	2	2	no	—
19	C₄×D₁₅₁	—	2	2	no	—
20	C₁₅₁⋊C₈	—	2	1	no	—
21	C₁₅₁⋊C₈	D₄	1	2	yes	complemented
22	C₂×C₄×C₁₅₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₅₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
25	C₈×C₁₅₁	—	2	2	no	—
26	C₂²×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₁₅₁	—	2	2	no	—
28	C₂×D₁₅₁	—	2	2	no	—
29	C₂×D₁₅₁	—	2	2	no	—
30	C₄×C₁₅₁	—	2	1	no	—
31	C₄×C₁₅₁	M₁₆	1	2	yes	complemented
32	C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₅₁	#41	1	1	yes	characteristic
34	Dic₁₅₁	—	2	2	no	—
35	C₂×C₁₅₁	C₄×D₄	1	1	yes	characteristic
36	C₂×C₁₅₁	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₁₅₁	#131	1	1	yes	characteristic
38	D₁₅₁	—	4	2	no	—
39	C₁₅₁	#436	1	1	yes	characteristic, complemented, Sylow
40	#436	—	151	1	no	maximal, Sylow
41	C₂×M₁₆	—	151	2	no	—
42	C₄×D₄	—	151	1	no	—
43	C₄⋊C₈	D₁₅₁	1	1	yes	characteristic, complemented
44	C₂²⋊C₈	—	151	2	no	—
45	C₄×C₈	—	151	1	no	—
46	C₂×D₄	—	151	1	no	—
47	C₂²×C₄	—	151	2	no	—
48	M₁₆	—	302	4	no	—
49	C₂×C₈	—	151	1	no	—
50	C₂×C₈	—	151	1	no	—
51	C₂×C₈	C₂×D₁₅₁	1	2	yes	—
52	C₄⋊C₄	—	151	1	no	—
53	C₂²⋊C₄	—	151	2	no	—
54	C₄²	C₂×D₁₅₁	1	1	yes	characteristic
55	C₂³	—	151	2	no	—
56	D₄	—	302	2	no	—
57	C₂×C₄	—	302	2	no	—
58	C₂×C₄	—	302	2	no	—
59	C₂×C₄	—	151	2	no	—
60	C₂×C₄	C₄×D₁₅₁	1	1	yes	characteristic
61	C₂×C₄	C₄×D₁₅₁	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
63	C₈	—	2	2	no	—
64	C₈	—	302	1	no	—
65	C₈	—	151	2	no	—
66	C₂²	—	302	2	no	—
67	C₂²	—	302	2	no	—
68	C₂²	—	302	2	no	—
69	C₂²	C₂×C₄×D₁₅₁	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	302	2	no	—
72	C₄	#14558987	1	2	yes	complemented
73	C₄	D₄×D₁₅₁	1	1	yes	characteristic
74	C₄	#14559005	1	1	yes	characteristic
75	C₂	—	604	2	no	—
76	C₂	#18012701	1	1	yes	characteristic
77	C₂	C₂×#14558987	1	1	yes	characteristic
78	C₂	#18012747	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₅₁
commutator, socle	C₂²×C₁₅₁	C₂²×C₄
Fitting	C₄⋊C₈×C₁₅₁	C₂
prime radical	C₂×D₆₀₄	C₄
cosocle	C₂×C₄×C₁₅₁	C₂³
hypercenter	C₄⋊C₈	D₁₅₁
hypocenter	C₁₅₁	#436
LCS	G ▷ C₂²×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#14558987	C₂	semidirect
3. (C₂×D₁₅₁)⋊C₈	C₂	semidirect
4. C₄×C₁₅₁⋊C₈	C₂	semidirect
5. C₄⋊C₈×C₁₅₁	C₂	semidirect
21. C₁₅₁⋊C₈	D₄	semidirect
31. C₄×C₁₅₁	M₁₆	semidirect
39. C₁₅₁	#436	semidirect
43. C₄⋊C₈	D₁₅₁	semidirect
72. C₄	#14558987	semidirect