Subgroups — #23757320

Order 10048.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14578937	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₁₅₇	C₂	1	2	yes	maximal
3	#19097707	C₂	1	1	yes	maximal, characteristic, complemented
4	#19097706	C₂	1	2	yes	maximal, complemented
5	#108×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
7	#14578938	C₂²	1	2	yes	—
8	#14578937	—	2	2	no	—
9	#14578937	C₄	1	4	yes	—
10	C₂×#11929434	C₂²	1	1	yes	characteristic
11	C₈×D₁₅₇	—	2	2	no	—
12	M₁₆×C₁₅₇	C₂²	1	2	yes	—
13	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
14	C₂²×D₁₅₇	Q₈	1	1	yes	characteristic
15	C₂×Dic₁₅₇	Q₈	1	1	yes	characteristic
16	C₄×D₁₅₇	C₂×C₄	1	2	yes	—
17	C₄×D₁₅₇	D₄	1	2	yes	—
18	#11929434	—	2	2	no	—
19	#11929434	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
21	C₈×C₁₅₇	—	2	2	no	—
22	C₈×C₁₅₇	C₂×C₄	1	2	yes	—
23	C₂²×C₁₅₇	C₂×Q₈	1	1	yes	characteristic
24	C₂×D₁₅₇	—	4	1	no	—
25	C₂×D₁₅₇	C₄⋊C₄	1	2	yes	—
26	C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₁₅₇	C₂×D₄	1	1	yes	characteristic
28	Dic₁₅₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₁₅₇	—	2	1	no	—
30	C₂×C₁₅₇	C₂×C₄⋊C₄	1	1	yes	characteristic
31	D₁₅₇	—	2	2	no	—
32	C₁₅₇	#430	1	1	yes	characteristic, complemented, Sylow
33	#430	—	157	1	no	maximal, Sylow
34	C₂×M₁₆	—	157	2	no	—
35	C₂×M₁₆	—	157	1	no	—
36	#108	—	157	2	no	—
37	#108	—	157	1	no	—
38	#108	D₁₅₇	1	1	yes	characteristic, complemented
39	C₂²×C₄	—	157	1	no	—
40	M₁₆	—	314	2	no	—
41	M₁₆	—	157	2	no	—
42	M₁₆	—	157	4	no	—
43	M₁₆	C₂×D₁₅₇	1	2	yes	—
44	C₂×C₈	—	314	2	no	—
45	C₂×C₈	—	157	1	no	—
46	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
47	C₂³	—	157	1	no	—
48	C₂×C₄	—	157	1	no	—
49	C₂×C₄	—	157	2	no	—
50	C₂×C₄	—	157	2	no	—
51	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
52	C₈	—	2	2	no	—
53	C₈	—	314	2	no	—
54	C₈	—	157	2	no	—
55	C₈	C₄×D₁₅₇	1	2	yes	—
56	C₂²	—	628	1	no	—
57	C₂²	—	157	2	no	—
58	C₂²	Q₈×D₁₅₇	1	1	yes	characteristic
59	C₄	—	157	2	no	—
60	C₄	C₂×C₄×D₁₅₇	1	1	yes	characteristic
61	C₄	D₄×D₁₅₇	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	314	2	no	—
64	C₂	C₄⋊C₄×D₁₅₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₁₅₇
commutator	C₄×C₁₅₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₅₇
Fitting	#108×C₁₅₇	C₂
socle	C₂×C₁₅₇	C₂×C₄⋊C₄
prime radical	C₂²×D₁₅₇	Q₈
cosocle	C₂×C₄×C₁₅₇	C₂³
hypercenter	#108	D₁₅₇
hypocenter	C₁₅₇	#430
LCS	G ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. #19097707	C₂	semidirect
4. #19097706	C₂	semidirect
5. #108×C₁₅₇	C₂	semidirect
32. C₁₅₇	#430	semidirect
38. #108	D₁₅₇	semidirect