Subgroups — #23752619

Order 9664.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18012738	C₂	1	1	yes	maximal, characteristic
2	#18012730	C₂	1	1	yes	maximal, characteristic
3	#18012673	C₂	1	1	yes	maximal, characteristic
4	#18012672	C₂	1	1	yes	maximal, characteristic
5	#18012670	C₂	1	1	yes	maximal, characteristic
6	#18012649	C₂	1	1	yes	maximal, characteristic
7	#106×C₁₅₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₀₂	—	2	1	no	—
9	C₂×C₁₅₁⋊C₈	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₅₁	—	2	1	no	—
11	C₄⋊Dic₁₅₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₅₁	C₂²	1	1	yes	characteristic
13	Dic₁₅₁⋊C₄	—	2	1	no	—
14	Dic₁₅₁⋊C₄	—	2	1	no	—
15	C₄×Dic₁₅₁	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
19	Dic₃₀₂	—	4	2	no	—
20	C₂×Dic₁₅₁	—	2	1	no	—
21	C₂×Dic₁₅₁	—	2	1	no	—
22	C₂×Dic₁₅₁	D₄	1	1	yes	characteristic
23	C₂×Dic₁₅₁	D₄	1	1	yes	characteristic
24	C₁₅₁⋊C₈	Q₈	1	2	yes	complemented
25	C₂×C₄×C₁₅₁	—	2	1	no	—
26	C₂×C₄×C₁₅₁	—	2	1	no	—
27	C₂×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
28	C₈×C₁₅₁	Q₈	1	2	yes	complemented
29	C₂²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
30	C₄×C₁₅₁	—	4	1	no	—
31	C₄×C₁₅₁	—	4	1	no	—
32	C₄×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
34	Dic₁₅₁	—	2	1	no	—
35	Dic₁₅₁	—	2	1	no	—
36	Dic₁₅₁	—	4	1	no	—
37	Dic₁₅₁	—	4	1	no	—
38	C₂×C₁₅₁	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₁₅₁	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₁₅₁	#137	1	1	yes	characteristic
41	C₁₅₁	#501	1	1	yes	characteristic, complemented, Sylow
42	#501	—	151	1	no	maximal, Sylow
43	C₄⋊Q₈	—	151	1	no	—
44	#125	—	151	1	no	—
45	#107	—	151	1	no	—
46	#107	—	151	1	no	—
47	#106	—	151	1	no	—
48	#106	D₁₅₁	1	1	yes	characteristic
49	#97	—	151	1	no	—
50	C₂×Q₈	—	302	1	no	—
51	C₂×C₈	—	151	1	no	—
52	C₂×C₈	C₂×D₁₅₁	1	1	yes	characteristic
53	C₄⋊C₄	—	302	1	no	—
54	C₄⋊C₄	—	302	1	no	—
55	C₄⋊C₄	—	302	1	no	—
56	C₄⋊C₄	—	151	1	no	—
57	C₄⋊C₄	—	151	1	no	—
58	C₄⋊C₄	C₂×D₁₅₁	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₁₅₁	1	1	yes	characteristic
60	C₄²	—	151	1	no	—
61	Q₈	—	604	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	302	1	no	—
65	C₂×C₄	—	302	1	no	—
66	C₂×C₄	—	151	1	no	—
67	C₂×C₄	—	151	1	no	—
68	C₂×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
69	C₈	—	151	2	no	—
70	C₈	Dic₃₀₂	1	2	yes	complemented
71	C₂²	D₄×D₁₅₁	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	302	1	no	—
75	C₄	—	302	1	no	—
76	C₄	—	604	1	no	—
77	C₄	—	604	1	no	—
78	C₄	Q₈×D₁₅₁	1	1	yes	characteristic
79	C₄	C₂×Dic₃₀₂	1	1	yes	characteristic
80	C₂	#18012738	1	1	yes	characteristic
81	C₂	#18012766	1	1	yes	characteristic
82	C₂	#18012768	1	1	yes	characteristic

	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	#501
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
24. C₁₅₁⋊C₈	Q₈	semidirect
28. C₈×C₁₅₁	Q₈	semidirect
41. C₁₅₁	#501	semidirect
70. C₈	Dic₃₀₂	semidirect