Subgroups — #23752616

Order 9664.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18012738	C₂	1	2	yes	maximal
2	#18012673	C₂	1	1	yes	maximal, characteristic
3	#18012672	C₂	1	2	yes	maximal
4	C₈×Dic₁₅₁	C₂	1	1	yes	maximal, characteristic
5	#107×C₁₅₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₀₂	—	2	2	no	—
7	C₂×C₁₅₁⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₁₅₁	C₂²	1	2	yes	—
9	Dic₁₅₁⋊C₄	—	2	2	no	—
10	C₄×Dic₁₅₁	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₅₁	C₂²	1	2	yes	—
13	Dic₃₀₂	—	4	4	no	—
14	C₂×Dic₁₅₁	—	2	2	no	—
15	C₂×Dic₁₅₁	D₄	1	1	yes	characteristic
16	C₂×Dic₁₅₁	D₄	1	1	yes	characteristic
17	C₁₅₁⋊C₈	Q₈	1	2	yes	complemented
18	C₂×C₄×C₁₅₁	—	2	2	no	—
19	C₂×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
20	C₈×C₁₅₁	Q₈	1	2	yes	complemented
21	C₂²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
22	C₄×C₁₅₁	—	4	2	no	—
23	C₄×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
25	Dic₁₅₁	—	4	2	no	—
26	Dic₁₅₁	D₈	1	2	yes	—
27	Dic₁₅₁	Q₁₆	1	2	yes	—
28	C₂×C₁₅₁	C₄⋊Q₈	1	1	yes	characteristic
29	C₂×C₁₅₁	C₂×D₈	1	1	yes	characteristic
30	C₂×C₁₅₁	C₂×Q₁₆	1	1	yes	characteristic
31	C₁₅₁	#500	1	1	yes	characteristic, complemented, Sylow
32	#500	—	151	1	no	maximal, Sylow
33	C₄⋊Q₈	—	151	2	no	—
34	#107	—	151	1	no	—
35	#107	—	151	2	no	—
36	#107	D₁₅₁	1	1	yes	characteristic
37	C₄×C₈	—	151	1	no	—
38	C₂×Q₈	—	302	2	no	—
39	C₂×C₈	—	151	1	no	—
40	C₂×C₈	C₂×D₁₅₁	1	1	yes	characteristic
41	C₄⋊C₄	—	302	2	no	—
42	C₄⋊C₄	—	151	2	no	—
43	C₄⋊C₄	C₂×D₁₅₁	1	2	yes	—
44	C₄²	—	151	1	no	—
45	Q₈	—	604	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	302	2	no	—
48	C₂×C₄	—	151	1	no	—
49	C₂×C₄	—	151	1	no	—
50	C₂×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
51	C₈	—	151	2	no	—
52	C₈	Dic₃₀₂	1	2	yes	complemented
53	C₂²	D₄×D₁₅₁	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	604	2	no	—
56	C₄	—	151	2	no	—
57	C₄	—	151	2	no	—
58	C₄	Q₈×D₁₅₁	1	1	yes	characteristic
59	C₄	C₂×Dic₃₀₂	1	1	yes	characteristic
60	C₂	#18012738	1	1	yes	characteristic
61	C₂	D₈×D₁₅₁	1	1	yes	characteristic
62	C₂	Q₁₆×D₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₅₁
commutator, cosocle	C₂×C₄×C₁₅₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₅₁
Fitting	#107×C₁₅₁	C₂
socle, prime radical	C₂²×C₁₅₁	C₂×D₄
hypercenter	#107	D₁₅₁
hypocenter	C₁₅₁	#500
LCS	G ▷ C₂×C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
17. C₁₅₁⋊C₈	Q₈	semidirect
20. C₈×C₁₅₁	Q₈	semidirect
31. C₁₅₁	#500	semidirect
52. C₈	Dic₃₀₂	semidirect