Subgroups — #23757642

Order 10048.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097771	C₂	1	1	yes	maximal, characteristic
2	#19097763	C₂	1	1	yes	maximal, characteristic
3	#19097696	C₂	1	4	yes	maximal
4	#97×C₁₅₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₃₁₄	C₂²	1	2	yes	—
6	C₄⋊Dic₁₅₇	—	2	2	no	—
7	C₄⋊Dic₁₅₇	C₂²	1	2	yes	—
8	#14578933	—	2	2	no	—
9	C₂×C₈×C₁₅₇	C₂²	1	2	yes	—
10	C₄²×C₁₅₇	C₂²	1	1	yes	characteristic
11	Dic₃₁₄	—	2	4	no	—
12	C₂×Dic₁₅₇	—	2	2	no	—
13	C₂×Dic₁₅₇	—	2	2	no	—
14	C₂×C₄×C₁₅₇	D₄	1	2	yes	—
15	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
16	C₈×C₁₅₇	—	2	2	no	—
17	C₂²×C₁₅₇	C₂×D₄	1	1	yes	characteristic
18	C₄×C₁₅₇	—	2	2	no	—
19	C₄×C₁₅₇	#41	1	2	yes	—
20	Dic₁₅₇	—	4	2	no	—
21	Dic₁₅₇	—	4	2	no	—
22	C₂×C₁₅₇	#124	1	1	yes	characteristic
23	C₂×C₁₅₇	#137	1	2	yes	—
24	C₁₅₇	#491	1	1	yes	characteristic, complemented, Sylow
25	#491	—	157	1	no	maximal, Sylow
26	C₄⋊Q₈	—	157	1	no	—
27	#125	—	157	1	no	—
28	#103	—	157	4	no	—
29	#97	D₁₅₇	1	1	yes	characteristic
30	C₂×Q₈	—	157	2	no	—
31	C₂×C₈	C₂×D₁₅₇	1	2	yes	—
32	C₄⋊C₄	—	314	2	no	—
33	C₄⋊C₄	—	314	2	no	—
34	C₄⋊C₄	—	157	2	no	—
35	C₄²	C₂×D₁₅₇	1	1	yes	characteristic
36	Q₈	—	314	4	no	—
37	C₂×C₄	—	314	2	no	—
38	C₂×C₄	—	314	2	no	—
39	C₂×C₄	D₆₂₈	1	2	yes	—
40	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₂²	C₂×D₆₂₈	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	628	2	no	—
45	C₄	—	628	2	no	—
46	C₄	#14578954	1	2	yes	—
47	C₂	#19097759	1	1	yes	characteristic
48	C₂	#19097804	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₆₂₈
commutator, cosocle	C₂×C₄×C₁₅₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₅₇
Fitting	#97×C₁₅₇	C₂
socle, prime radical	C₂²×C₁₅₇	C₂×D₄
hypercenter	#97	D₁₅₇
hypocenter	C₁₅₇	#491
LCS	G ▷ C₂×C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
24. C₁₅₇	#491	semidirect