Subgroups — #34115053

Order 20096.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23758162	C₂	1	1	yes	maximal, characteristic
2	#23758114	C₂	1	1	yes	maximal, characteristic
3	#23757048	C₂	1	1	yes	maximal, characteristic
4	C₂×#14578957	C₄	1	2	yes	—
5	C₄×#11929441	C₄	1	2	yes	—
6	C₂×#14578929	C₄	1	1	yes	characteristic
7	C₈×Dic₁₅₇	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₁₅₇	C₄	1	1	yes	characteristic
9	C₂×#11929441	—	2	2	no	—
10	#14578957	—	2	2	no	—
11	C₂×#11929434	C₂×C₄	1	1	yes	characteristic
12	C₄×Dic₁₅₇	C₂×C₄	1	1	yes	characteristic
13	#14578929	C₈	1	2	yes	complemented
14	C₂×C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
15	C₁₆×C₁₅₇	C₈	1	2	yes	complemented
16	#11929441	—	4	2	no	—
17	C₂×Dic₁₅₇	M₁₆	1	2	yes	—
18	#11929434	M₁₆	1	2	yes	—
19	C₂×C₄×C₁₅₇	C₄²	1	1	yes	characteristic
20	C₈×C₁₅₇	C₂×C₈	1	1	yes	characteristic
21	C₈×C₁₅₇	C₂×C₈	1	1	yes	characteristic
22	C₂²×C₁₅₇	#97	1	1	yes	characteristic
23	C₄×C₁₅₇	C₄×C₈	1	1	yes	characteristic
24	C₄×C₁₅₇	#97	1	1	yes	characteristic
25	Dic₁₅₇	—	2	2	no	—
26	C₂×C₁₅₇	#322	1	1	yes	characteristic
27	C₂×C₁₅₇	#347	1	2	yes	—
28	C₁₅₇	#1313	1	1	yes	characteristic, complemented, Sylow
29	#1313	—	157	1	no	maximal, Sylow
30	#346	—	157	1	no	—
31	#346	—	157	1	no	—
32	#322	—	157	1	no	—
33	C₂×C₁₆	—	157	2	no	—
34	C₂×C₁₆	—	157	1	no	—
35	C₂×C₁₆	#10597845	1	1	yes	characteristic
36	C₄×C₈	—	157	2	no	—
37	C₄×C₈	—	157	1	no	—
38	C₂×C₈	—	314	2	no	—
39	C₂×C₈	—	157	1	no	—
40	C₂×C₈	C₂×#10597845	1	1	yes	characteristic
41	C₄²	—	157	1	no	—
42	C₁₆	—	314	2	no	—
43	C₁₆	—	157	2	no	—
44	C₁₆	#11929441	1	2	yes	complemented
45	C₂×C₄	—	157	2	no	—
46	C₂×C₄	C₄×#10597845	1	1	yes	characteristic
47	C₈	—	628	2	no	—
48	C₈	—	157	2	no	—
49	C₈	C₂×#11929441	1	1	yes	characteristic
50	C₈	D₁₅₇⋊C₈	1	1	yes	characteristic
51	C₂²	#19097825	1	1	yes	characteristic
52	C₄	—	314	2	no	—
53	C₄	C₄×#11929441	1	1	yes	characteristic
54	C₄	#19097825	1	1	yes	characteristic
55	C₂	#23758114	1	1	yes	characteristic
56	C₂	#23758164	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄×#10597845
commutator	C₄×C₁₅₇	C₄×C₈
Frattini	C₂×C₈	C₂×#10597845
Fitting	C₂×C₁₆×C₁₅₇	C₄
socle, prime radical	C₂²×C₁₅₇	#97
cosocle	C₈×Dic₁₅₇	C₂²
hypercenter	C₂×C₁₆	#10597845
hypocenter	C₁₅₇	#1313
LCS	G ▷ C₄×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
13. #14578929	C₈	semidirect
15. C₁₆×C₁₅₇	C₈	semidirect
28. C₁₅₇	#1313	semidirect
44. C₁₆	#11929441	semidirect

Maximal subgroups

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

subgroup	index
#23758162	2
#23758114	2
#23757048	2
#1313	157