Subgroups — #34115302

Order 20096.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23758202	C₂	1	1	yes	maximal, characteristic
2	#23758200	C₂	1	1	yes	maximal, characteristic
3	#23757106	C₂	1	1	yes	maximal, characteristic
4	#19097842	—	2	1	no	—
5	#19097840	—	2	1	no	—
6	C₁₆×D₁₅₇	C₂²	1	1	yes	characteristic
7	#19097677	C₄	1	1	yes	characteristic, complemented
8	C₃₂×C₁₅₇	C₄	1	1	yes	characteristic, complemented
9	#14578964	—	4	1	no	—
10	C₄⋊#10597845	—	4	1	no	—
11	C₈×D₁₅₇	D₄	1	1	yes	characteristic
12	#14578929	Q₈	1	1	yes	characteristic
13	C₁₆×C₁₅₇	C₂×C₄	1	1	yes	characteristic
14	C₂×#10597845	—	8	1	no	—
15	#11929441	—	8	1	no	—
16	C₄×D₁₅₇	D₈	1	1	yes	characteristic
17	#11929434	Q₁₆	1	1	yes	characteristic
18	C₈×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₁₅₇	SD₃₂	1	1	yes	characteristic
20	#10597845	—	16	1	no	—
21	C₄×C₁₅₇	#107	1	1	yes	characteristic
22	Dic₁₅₇	SD₃₂	1	1	yes	characteristic
23	C₂×C₁₅₇	#367	1	1	yes	characteristic
24	D₁₅₇	—	2	1	no	—
25	C₁₅₇	#1426	1	1	yes	characteristic, complemented, Sylow
26	#1426	—	157	1	no	maximal, Sylow
27	M₆₄	—	157	1	no	—
28	#368	—	157	1	no	—
29	#367	—	157	1	no	—
30	C₂×C₁₆	—	157	1	no	—
31	#108	—	314	1	no	—
32	#107	—	314	1	no	—
33	C₃₂	—	157	1	no	—
34	C₃₂	#10597845	1	1	yes	characteristic, complemented
35	M₁₆	—	628	1	no	—
36	C₂×C₈	—	157	1	no	—
37	C₄⋊C₄	—	628	1	no	—
38	C₁₆	—	157	1	no	—
39	C₁₆	C₂×#10597845	1	1	yes	characteristic
40	C₂×C₄	—	157	1	no	—
41	C₂×C₄	—	1256	1	no	—
42	C₈	—	157	1	no	—
43	C₈	—	1256	1	no	—
44	C₈	C₄⋊#10597845	1	1	yes	characteristic
45	C₂²	—	157	1	no	—
46	C₄	—	157	1	no	—
47	C₄	—	2512	1	no	—
48	C₄	#19097840	1	1	yes	characteristic
49	C₂	—	314	1	no	—
50	C₂	#23758200	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23758200
commutator	C₁₆×C₁₅₇	C₂×C₄
Frattini	C₁₆	C₂×#10597845
Fitting	C₃₂×C₁₅₇	C₄
socle	C₂×C₁₅₇	#367
prime radical	C₂×D₁₅₇	SD₃₂
cosocle	C₁₆×D₁₅₇	C₂²
hypercenter	C₃₂	#10597845
hypocenter	C₁₅₇	#1426
LCS	G ▷ C₁₆×C₁₅₇ ▷ C₈×C₁₅₇ ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
7. #19097677	C₄	semidirect
8. C₃₂×C₁₅₇	C₄	semidirect
25. C₁₅₇	#1426	semidirect
34. C₃₂	#10597845	semidirect

Maximal subgroups

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

subgroup	index
#23758202	2
#23758200	2
#23757106	2
#1426	157