Subgroups — #23752018

Order 9664.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18012761	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₅₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#108×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#14559004	—	2	1	no	—
5	Dic₆₀₄	C₄	1	1	yes	characteristic
6	#14558993	—	2	1	no	—
7	D₁₂₀₈	C₄	1	1	yes	characteristic
8	C₁₅₁⋊C₁₆	—	2	1	no	—
9	M₁₆×C₁₅₁	—	2	1	no	—
10	C₂×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
11	Dic₃₀₂	—	2	1	no	—
12	D₆₀₄	—	2	1	no	—
13	C₂²⋊D₁₅₁	—	4	1	no	—
14	C₄×D₁₅₁	—	4	1	no	—
15	C₂×C₄×C₁₅₁	D₄	1	1	yes	characteristic
16	C₈×C₁₅₁	—	4	1	no	—
17	C₈×C₁₅₁	C₂×C₄	1	1	yes	characteristic
18	C₈×C₁₅₁	D₄	1	1	yes	characteristic
19	C₂²×C₁₅₁	SD₁₆	1	1	yes	characteristic
20	C₂×D₁₅₁	—	4	1	no	—
21	C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₁₅₁	D₈	1	1	yes	characteristic
23	Dic₁₅₁	—	4	1	no	—
24	C₂×C₁₅₁	—	2	1	no	—
25	C₂×C₁₅₁	#102	1	1	yes	characteristic
26	D₁₅₁	—	8	1	no	—
27	C₁₅₁	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	151	1	no	maximal, Sylow
29	#135	—	151	1	no	—
30	C₂×C₁₆	—	151	1	no	—
31	#108	D₁₅₁	1	1	yes	characteristic, complemented
32	#41	—	302	1	no	—
33	Q₁₆	—	151	1	no	—
34	SD₁₆	—	302	1	no	—
35	D₈	—	151	1	no	—
36	M₁₆	—	2	1	no	—
37	C₂×C₈	C₂×D₁₅₁	1	1	yes	characteristic
38	C₁₆	—	302	1	no	—
39	Q₈	—	302	1	no	—
40	D₄	—	302	1	no	—
41	D₄	—	604	1	no	—
42	C₂×C₄	—	604	1	no	—
43	C₂×C₄	C₂²⋊D₁₅₁	1	1	yes	characteristic
44	C₈	—	4	1	no	—
45	C₈	C₄×D₁₅₁	1	1	yes	characteristic
46	C₈	D₆₀₄	1	1	yes	characteristic
47	C₂²	—	604	1	no	—
48	C₂²	#14558991	1	1	yes	characteristic
49	C₄	—	604	1	no	—
50	C₄	(C₂×D₁₅₁)⋊C₄	1	1	yes	characteristic
51	C₄	#14558989	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	1208	1	no	—
54	C₂	#18012659	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14558989
commutator	C₈×C₁₅₁	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₅₁
Fitting	#108×C₁₅₁	C₂
socle	C₂×C₁₅₁	#102
prime radical	#18012761	C₂
cosocle	C₂×C₈×C₁₅₁	C₂²
hypercenter	#108	D₁₅₁
hypocenter	C₁₅₁	#359
LCS	G ▷ C₈×C₁₅₁ ▷ C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₅₁⋊C₁₆	C₂	semidirect
3. #108×C₁₅₁	C₂	semidirect
27. C₁₅₁	#359	semidirect
31. #108	D₁₅₁	semidirect