Subgroups — #34098196

Order 20096.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23757675	C₂	1	1	yes	maximal, characteristic
2	#23757094	C₂	1	1	yes	maximal, characteristic
3	#364×C₁₅₇	C₂	1	1	yes	maximal, characteristic
4	#19097763	C₄	1	2	yes	—
5	#19097711	—	2	1	no	—
6	#19097705	—	2	1	no	—
7	#19097703	—	2	1	no	—
8	M₃₂×C₁₅₇	—	2	1	no	—
9	C₄×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₅₇	—	2	2	no	—
11	#14578933	—	4	2	no	—
12	#14578929	—	4	1	no	—
13	C₂×C₈×C₁₅₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₅₇	D₄	1	1	yes	characteristic
15	C₄²×C₁₅₇	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₁₅₇	—	4	1	no	—
17	C₂×Dic₁₅₇	—	4	2	no	—
18	C₂×C₄×C₁₅₇	—	2	1	no	—
19	C₂×C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₁₅₇	SD₁₆	1	1	yes	characteristic
21	C₈×C₁₅₇	SD₁₆	1	1	yes	characteristic
22	C₈×C₁₅₇	Q₁₆	1	1	yes	characteristic
23	C₈×C₁₅₇	Q₁₆	1	1	yes	characteristic
24	C₂²×C₁₅₇	#100	1	1	yes	characteristic
25	C₄×C₁₅₇	—	4	1	no	—
26	C₄×C₁₅₇	#103	1	1	yes	characteristic
27	C₄×C₁₅₇	#103	1	1	yes	characteristic
28	Dic₁₅₇	—	8	2	no	—
29	C₂×C₁₅₇	—	2	1	no	—
30	C₂×C₁₅₇	#333	1	1	yes	characteristic
31	C₁₅₇	#1366	1	1	yes	characteristic, complemented, Sylow
32	#1366	—	157	1	no	maximal, Sylow
33	#499	—	157	1	no	—
34	#364	—	157	1	no	—
35	#364	D₁₅₇	1	1	yes	characteristic
36	#125	—	157	2	no	—
37	M₃₂	—	2	1	no	—
38	M₃₂	—	314	1	no	—
39	#107	—	314	1	no	—
40	#106	—	314	1	no	—
41	C₄×C₈	C₂×D₁₅₇	1	1	yes	characteristic
42	C₂×C₈	C₂²⋊D₁₅₇	1	1	yes	characteristic
43	C₂×C₈	D₆₂₈	1	1	yes	characteristic
44	C₄⋊C₄	—	314	2	no	—
45	C₄⋊C₄	—	628	2	no	—
46	C₄²	C₄×D₁₅₇	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	628	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	628	2	no	—
51	C₂×C₄	#14578931	1	1	yes	characteristic
52	C₈	#14578942	1	1	yes	characteristic
53	C₈	#14578943	1	1	yes	characteristic
54	C₈	#14578944	1	1	yes	characteristic
55	C₈	Dic₆₂₈	1	1	yes	characteristic
56	C₂²	#19097687	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	1256	2	no	—
59	C₄	#19097694	1	1	yes	characteristic
60	C₄	#19097696	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#23757021	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23757021
commutator	C₄²×C₁₅₇	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₅₇
Fitting	#364×C₁₅₇	C₂
socle	C₂×C₁₅₇	#333
prime radical	C₂²×C₁₅₇	#100
cosocle	C₄×C₈×C₁₅₇	C₂²
hypercenter	#364	D₁₅₇
hypocenter	C₁₅₇	#1366
LCS	G ▷ C₄²×C₁₅₇ ▷ C₂×C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
31. C₁₅₇	#1366	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23757675	2
#23757094	2
#364×C₁₅₇	2
#1366	157