Subgroups — #23757630

Order 10048.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097759	C₂	1	1	yes	maximal, characteristic
2	#19097694	C₂	1	2	yes	maximal, complemented
3	#19097691	C₂	1	2	yes	maximal
4	C₄×#11929434	C₂	1	1	yes	maximal, characteristic, complemented
5	#125×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₃₁₄	C₂²	1	1	yes	characteristic
7	C₂×D₆₂₈	C₂²	1	1	yes	characteristic
8	C₂×#11929434	C₂²	1	2	yes	—
9	#14578931	—	2	2	no	—
10	C₄⋊C₄×C₁₅₇	—	2	2	no	—
11	C₄⋊C₄×C₁₅₇	C₂²	1	2	yes	—
12	C₄²×C₁₅₇	C₂²	1	1	yes	characteristic
13	C₂²×D₁₅₇	—	2	1	no	—
14	Dic₃₁₄	—	2	2	no	—
15	D₆₂₈	—	2	2	no	—
16	C₂×Dic₁₅₇	—	2	1	no	—
17	#11929434	—	2	2	no	—
18	C₂×C₄×C₁₅₇	—	2	2	no	—
19	C₂×C₄×C₁₅₇	D₄	1	2	yes	—
20	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
21	C₂²×C₁₅₇	C₂×D₄	1	1	yes	characteristic
22	C₂×D₁₅₇	—	4	1	no	—
23	C₂×D₁₅₇	—	4	2	no	—
24	C₄×C₁₅₇	—	2	2	no	—
25	C₄×C₁₅₇	—	4	2	no	—
26	C₄×C₁₅₇	#41	1	2	yes	—
27	Dic₁₅₇	—	4	1	no	—
28	C₂×C₁₅₇	#124	1	1	yes	characteristic
29	C₂×C₁₅₇	#135	1	2	yes	—
30	D₁₅₇	—	8	1	no	—
31	C₁₅₇	#488	1	1	yes	characteristic, complemented, Sylow
32	#488	—	157	1	no	maximal, Sylow
33	#125	D₁₅₇	1	1	yes	characteristic, complemented
34	#124	—	157	1	no	—
35	#103	—	157	2	no	—
36	#102	—	157	2	no	—
37	C₄×C₈	—	157	1	no	—
38	C₂×Q₈	—	157	1	no	—
39	C₂×D₄	—	157	1	no	—
40	C₂×C₈	—	157	2	no	—
41	C₄⋊C₄	—	2	2	no	—
42	C₄⋊C₄	C₂×D₁₅₇	1	2	yes	—
43	C₂²⋊C₄	—	314	2	no	—
44	C₄²	C₂×D₁₅₇	1	1	yes	characteristic
45	C₂³	—	314	1	no	—
46	Q₈	—	314	2	no	—
47	D₄	—	314	2	no	—
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	—	314	1	no	—
50	C₂×C₄	C₂²⋊D₁₅₇	1	2	yes	—
51	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
52	C₈	—	314	2	no	—
53	C₂²	—	628	1	no	—
54	C₂²	—	628	2	no	—
55	C₂²	C₂×C₂²⋊D₁₅₇	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	4	2	no	—
58	C₄	—	628	1	no	—
59	C₄	#14578955	1	2	yes	—
60	C₂	—	1256	1	no	—
61	C₂	#19097760	1	1	yes	characteristic
62	C₂	#19097791	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₅₇
commutator, cosocle	C₂×C₄×C₁₅₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₅₇
Fitting	#125×C₁₅₇	C₂
socle	C₂²×C₁₅₇	C₂×D₄
prime radical	C₂×D₆₂₈	C₂²
hypercenter	#125	D₁₅₇
hypocenter	C₁₅₇	#488
LCS	G ▷ C₂×C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
2. #19097694	C₂	semidirect
4. C₄×#11929434	C₂	semidirect
5. #125×C₁₅₇	C₂	semidirect
31. C₁₅₇	#488	semidirect
33. #125	D₁₅₇	semidirect