Subgroups — #23758332

Order 10048.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097846	C₂	1	2	yes	maximal, complemented
2	#19097845	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₅₇⋊C₁₆	C₂	1	2	yes	maximal, complemented
4	C₂×#14578957	C₂	1	1	yes	maximal, characteristic, complemented
5	#19097779	C₂	1	1	yes	maximal, characteristic
6	#14578957	C₂²	1	1	yes	characteristic
7	#14578957	C₂²	1	1	yes	characteristic
8	#14578957	C₂²	1	2	yes	—
9	#14578954	C₄	1	1	yes	characteristic
10	#14578937	C₄	1	2	yes	—
11	C₂×#11929434	C₂²	1	1	yes	characteristic
12	C₈×D₁₅₇	C₂²	1	2	yes	—
13	M₁₆×C₁₅₇	C₄	1	1	yes	characteristic
14	Dic₃₁₄	C₈	1	1	yes	characteristic
15	D₆₂₈	C₈	1	1	yes	characteristic
16	C₂²⋊D₁₅₇	C₈	1	2	yes	—
17	C₄×D₁₅₇	C₂×C₄	1	2	yes	—
18	#11929434	C₂×C₄	1	1	yes	characteristic
19	#11929434	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
21	C₈×C₁₅₇	C₂×C₄	1	2	yes	—
22	C₂²×C₁₅₇	C₂×C₈	1	1	yes	characteristic
23	C₂×D₁₅₇	C₂×C₈	1	2	yes	—
24	C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
25	C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
26	Dic₁₅₇	C₂×C₈	1	2	yes	—
27	C₂×C₁₅₇	—	2	1	no	—
28	C₂×C₁₅₇	C₂²×C₈	1	1	yes	characteristic
29	D₁₅₇	—	2	2	no	—
30	C₁₅₇	#504	1	1	yes	characteristic, complemented, Sylow
31	#504	—	157	1	no	maximal, Sylow
32	#131	—	157	1	no	—
33	M₃₂	—	157	1	no	—
34	M₃₂	—	157	2	no	—
35	C₂×C₁₆	—	157	1	no	—
36	C₂×C₁₆	—	157	2	no	—
37	#41	—	157	1	no	—
38	M₁₆	—	157	2	no	—
39	M₁₆	#10597845	1	1	yes	characteristic
40	C₂×C₈	—	157	1	no	—
41	C₂×C₈	—	157	2	no	—
42	C₁₆	—	157	1	no	—
43	C₁₆	—	157	1	no	—
44	C₁₆	—	157	2	no	—
45	Q₈	—	157	1	no	—
46	D₄	—	157	2	no	—
47	D₄	—	157	1	no	—
48	C₂×C₄	—	157	2	no	—
49	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
50	C₈	—	157	1	no	—
51	C₈	—	157	1	no	—
52	C₈	C₂×#10597845	1	2	yes	—
53	C₂²	—	157	2	no	—
54	C₂²	D₁₅₇⋊C₈	1	1	yes	characteristic
55	C₄	—	157	2	no	—
56	C₄	D₁₅₇⋊C₈	1	1	yes	characteristic
57	C₄	C₂²×#10597845	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	314	2	no	—
60	C₂	C₂×D₁₅₇⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#10597845
commutator, socle	C₂×C₁₅₇	C₂²×C₈
Fitting	M₁₆×C₁₅₇	C₄
prime radical	#14578954	C₄
cosocle	#11929434	C₂³
hypercenter	M₁₆	#10597845
hypocenter	C₁₅₇	#504
LCS	G ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #19097846	C₂	semidirect
2. #19097845	C₂	semidirect
3. D₁₅₇⋊C₁₆	C₂	semidirect
4. C₂×#14578957	C₂	semidirect
30. C₁₅₇	#504	semidirect