Subgroups — #23752612

Order 9664.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18012730	C₂	1	2	yes	maximal
2	#18012672	C₂	1	2	yes	maximal
3	#18012671	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₁₅₁	C₂	1	1	yes	maximal, characteristic
5	#106×C₁₅₁	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₅₁⋊C₈	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₁₅₁	—	2	2	no	—
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	C₂×Dic₁₅₁	—	2	2	no	—
14	C₂×Dic₁₅₁	D₄	1	2	yes	—
15	C₁₅₁⋊C₈	Q₈	1	2	yes	—
16	C₂×C₄×C₁₅₁	—	2	2	no	—
17	C₂×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
18	C₈×C₁₅₁	Q₈	1	2	yes	—
19	C₂²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
20	C₄×C₁₅₁	—	4	2	no	—
21	C₄×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
22	C₄×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
23	Dic₁₅₁	—	2	2	no	—
24	Dic₁₅₁	—	4	2	no	—
25	C₂×C₁₅₁	C₄⋊Q₈	1	1	yes	characteristic
26	C₂×C₁₅₁	#135	1	2	yes	—
27	C₁₅₁	#499	1	1	yes	characteristic, complemented, Sylow
28	#499	—	151	1	no	maximal, Sylow
29	#125	—	151	2	no	—
30	#107	—	151	2	no	—
31	#106	—	151	1	no	—
32	#106	D₁₅₁	1	1	yes	characteristic
33	C₄×C₈	—	151	1	no	—
34	C₂×C₈	—	151	1	no	—
35	C₂×C₈	C₂×D₁₅₁	1	1	yes	characteristic
36	C₄⋊C₄	—	302	2	no	—
37	C₄⋊C₄	—	302	2	no	—
38	C₄⋊C₄	—	151	2	no	—
39	C₄⋊C₄	C₂×D₁₅₁	1	2	yes	—
40	C₄²	—	151	1	no	—
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	—	302	2	no	—
43	C₂×C₄	—	151	2	no	—
44	C₂×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
45	C₈	—	151	2	no	—
46	C₈	Dic₃₀₂	1	2	yes	—
47	C₂²	D₄×D₁₅₁	1	1	yes	characteristic
48	C₄	—	4	2	no	—
49	C₄	—	302	2	no	—
50	C₄	—	604	2	no	—
51	C₄	Q₈×D₁₅₁	1	1	yes	characteristic
52	C₄	C₂×Dic₃₀₂	1	1	yes	characteristic
53	C₂	#18012738	1	1	yes	characteristic
54	C₂	#18012760	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₅₁
commutator, cosocle	C₂×C₄×C₁₅₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₅₁
Fitting	#106×C₁₅₁	C₂
socle, prime radical	C₂²×C₁₅₁	C₂×D₄
hypercenter	#106	D₁₅₁
hypocenter	C₁₅₁	#499
LCS	G ▷ C₂×C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
27. C₁₅₁	#499	semidirect