Subgroups — #23752255

Order 9664.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14558988	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₁₅₁	C₂	1	1	yes	maximal, characteristic
3	#18012672	C₂	1	2	yes	maximal, complemented
4	#18012670	C₂	1	2	yes	maximal, complemented
5	#117×C₁₅₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₅₁	—	2	1	no	—
7	#14558988	C₄	1	4	yes	complemented
8	C₂×C₁₅₁⋊C₈	C₂²	1	2	yes	—
9	C₄⋊Dic₁₅₁	—	2	1	no	—
10	C₄⋊Dic₁₅₁	C₂²	1	2	yes	—
11	C₂²×C₄×C₁₅₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
14	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
15	C₄²×C₁₅₁	—	2	1	no	—
16	C₂×Dic₁₅₁	—	2	2	no	—
17	C₂×Dic₁₅₁	—	4	2	no	—
18	C₁₅₁⋊C₈	C₂×C₄	1	4	yes	complemented
19	C₂³×C₁₅₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₅₁	—	2	1	no	—
21	C₂×C₄×C₁₅₁	—	2	1	no	—
22	C₂×C₄×C₁₅₁	C₂×C₄	1	2	yes	—
23	C₂×C₄×C₁₅₁	D₄	1	1	yes	characteristic
24	C₂×C₄×C₁₅₁	Q₈	1	2	yes	—
25	C₂×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
26	C₂²×C₁₅₁	—	2	1	no	—
27	C₂²×C₁₅₁	—	2	1	no	—
28	C₂²×C₁₅₁	C₄⋊C₄	1	2	yes	—
29	C₂²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
30	C₄×C₁₅₁	—	4	1	no	—
31	C₄×C₁₅₁	—	4	1	no	—
32	C₄×C₁₅₁	C₄⋊C₄	1	2	yes	—
33	C₄×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
34	C₄×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
35	Dic₁₅₁	—	4	2	no	—
36	C₂×C₁₅₁	—	2	2	no	—
37	C₂×C₁₅₁	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₁₅₁	AGL(1,ℤ/8)	1	1	yes	characteristic
39	C₂×C₁₅₁	#137	1	1	yes	characteristic
40	C₁₅₁	#428	1	1	yes	characteristic, complemented, Sylow
41	#428	—	151	1	no	maximal, Sylow
42	C₂×M₁₆	—	151	1	no	—
43	#117	D₁₅₁	1	1	yes	characteristic
44	C₂×C₄⋊C₄	—	151	1	no	—
45	#107	—	151	2	no	—
46	#106	—	151	2	no	—
47	C₂²×C₄	—	302	1	no	—
48	C₂²×C₄	C₂×D₁₅₁	1	1	yes	characteristic
49	M₁₆	—	151	4	no	—
50	C₂×C₈	—	151	2	no	—
51	C₄⋊C₄	—	302	1	no	—
52	C₄⋊C₄	—	151	2	no	—
53	C₄⋊C₄	C₂×D₁₅₁	1	1	yes	characteristic
54	C₄⋊C₄	C₂×D₁₅₁	1	1	yes	characteristic
55	C₂²⋊C₄	—	2	1	no	—
56	C₄²	—	2	1	no	—
57	C₂³	C₂²⋊D₁₅₁	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	302	2	no	—
61	C₂×C₄	—	604	2	no	—
62	C₂×C₄	C₄×D₁₅₁	1	2	yes	—
63	C₂×C₄	C₂²⋊D₁₅₁	1	1	yes	characteristic
64	C₂×C₄	Dic₃₀₂	1	2	yes	—
65	C₂×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
66	C₈	—	151	4	no	—
67	C₂²	—	2	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	Dic₁₅₁⋊C₄	1	2	yes	—
70	C₂²	C₂×C₂²⋊D₁₅₁	1	1	yes	characteristic
71	C₄	—	4	1	no	—
72	C₄	—	4	1	no	—
73	C₄	—	604	2	no	—
74	C₄	Dic₁₅₁⋊C₄	1	2	yes	—
75	C₄	C₂×C₄×D₁₅₁	1	1	yes	characteristic
76	C₄	C₂×Dic₃₀₂	1	1	yes	characteristic
77	C₂	—	2	2	no	—
78	C₂	C₂×Dic₁₅₁⋊C₄	1	1	yes	characteristic
79	C₂	#18012764	1	1	yes	characteristic
80	C₂	#18012769	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₅₁
commutator	C₄×C₁₅₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₅₁
Fitting	#117×C₁₅₁	C₂
socle	C₂²×C₁₅₁	C₂×D₄
prime radical	C₂³×C₁₅₁	D₄
cosocle	C₂×C₄×C₁₅₁	C₂³
hypercenter	#117	D₁₅₁
hypocenter	C₁₅₁	#428
LCS	G ▷ C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. #18012672	C₂	semidirect
4. #18012670	C₂	semidirect
7. #14558988	C₄	semidirect
18. C₁₅₁⋊C₈	C₂×C₄	semidirect
40. C₁₅₁	#428	semidirect