Subgroups — #34115252

Order 20096.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23758205	C₂	1	2	yes	maximal, complemented
2	C₂×#19097710	C₂	1	1	yes	maximal, characteristic
3	#19097821	—	2	2	no	—
4	C₂×C₈×D₁₅₇	C₄	1	1	yes	characteristic
5	#19097710	—	2	2	no	—
6	C₂×#14578929	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₅₇	C₄	1	1	yes	characteristic
8	C₂×C₄×D₁₅₇	C₈	1	1	yes	characteristic
9	C₂×#11929434	C₈	1	1	yes	characteristic
10	C₈×D₁₅₇	—	2	1	no	—
11	C₈×D₁₅₇	—	2	1	no	—
12	#14578929	D₄	1	2	yes	—
13	C₂×C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
14	C₁₆×C₁₅₇	—	2	1	no	—
15	C₂²×D₁₅₇	C₁₆	1	1	yes	characteristic
16	C₂×Dic₁₅₇	C₁₆	1	1	yes	characteristic
17	C₄×D₁₅₇	—	2	1	no	—
18	C₄×D₁₅₇	—	2	1	no	—
19	#11929434	—	2	1	no	—
20	C₂×C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
21	C₈×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₁₅₇	M₁₆	1	1	yes	characteristic
23	C₂²×C₁₅₇	C₂×C₁₆	1	1	yes	characteristic
24	C₂×D₁₅₇	—	2	1	no	—
25	C₂×D₁₅₇	—	4	1	no	—
26	C₄×C₁₅₇	C₂²⋊C₈	1	1	yes	characteristic
27	C₄×C₁₅₇	M₃₂	1	1	yes	characteristic
28	Dic₁₅₇	—	2	1	no	—
29	C₂×C₁₅₇	—	2	1	no	—
30	C₂×C₁₅₇	C₂²⋊C₁₆	1	1	yes	characteristic
31	D₁₅₇	—	4	1	no	—
32	C₁₅₇	#1400	1	1	yes	characteristic, complemented, Sylow
33	#1400	—	157	1	no	maximal, Sylow
34	C₂×M₃₂	—	157	1	no	—
35	M₆₄	—	157	2	no	—
36	C₂²×C₈	—	157	1	no	—
37	M₃₂	—	314	2	no	—
38	C₂×C₁₆	—	157	1	no	—
39	C₂×C₁₆	#10597845	1	1	yes	characteristic
40	C₃₂	—	314	2	no	—
41	C₂²×C₄	—	157	1	no	—
42	C₂×C₈	—	314	1	no	—
43	C₂×C₈	—	314	1	no	—
44	C₂×C₈	—	157	1	no	—
45	C₂×C₈	C₂×#10597845	1	1	yes	characteristic
46	C₁₆	—	2	1	no	—
47	C₁₆	—	157	2	no	—
48	C₂³	—	157	1	no	—
49	C₂×C₄	—	314	1	no	—
50	C₂×C₄	—	314	1	no	—
51	C₂×C₄	—	157	1	no	—
52	C₂×C₄	D₁₅₇⋊C₈	1	1	yes	characteristic
53	C₈	—	314	1	no	—
54	C₈	C₂²⋊#10597845	1	1	yes	characteristic
55	C₈	#14578964	1	1	yes	characteristic
56	C₂²	—	314	1	no	—
57	C₂²	—	628	1	no	—
58	C₂²	D₁₅₇⋊C₁₆	1	1	yes	characteristic
59	C₄	—	314	1	no	—
60	C₄	#19097828	1	1	yes	characteristic
61	C₄	#19097846	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	628	1	no	—
64	C₂	#23758168	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#10597845
commutator	C₂²×C₁₅₇	C₂×C₁₆
Frattini	C₂×C₈	C₂×#10597845
Fitting	C₂×C₁₆×C₁₅₇	C₄
socle	C₂×C₁₅₇	C₂²⋊C₁₆
prime radical	C₂²×D₁₅₇	C₁₆
cosocle	C₂×#14578929	C₂²
hypercenter	C₂×C₁₆	#10597845
hypocenter	C₁₅₇	#1400
LCS	G ▷ C₂²×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #23758205	C₂	semidirect
32. C₁₅₇	#1400	semidirect

Maximal subgroups

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

subgroup	index
#23758205	2
C₂×#19097710	2
#1400	157