Subgroups — #23758118

Order 10048.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#11929441	C₂	1	2	yes	maximal
2	C₂×C₄⋊Dic₁₅₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#11929441	—	2	2	no	—
4	C₂²×Dic₁₅₇	C₄	1	1	yes	characteristic
5	C₂²×Dic₁₅₇	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₁₅₇	—	2	2	no	—
7	C₂²×C₄×C₁₅₇	C₄	1	1	yes	characteristic
8	#11929441	—	4	2	no	—
9	C₂×Dic₁₅₇	—	2	1	no	—
10	C₂×Dic₁₅₇	—	4	1	no	—
11	C₂×Dic₁₅₇	—	4	1	no	—
12	C₂×Dic₁₅₇	D₄	1	2	yes	—
13	C₂³×C₁₅₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₅₇	—	2	1	no	—
15	C₂×C₄×C₁₅₇	—	2	1	no	—
16	C₂×C₄×C₁₅₇	C₈	1	2	yes	complemented
17	C₂²×C₁₅₇	—	2	1	no	—
18	C₂²×C₁₅₇	—	2	1	no	—
19	C₂²×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₂²×C₁₅₇	C₂×C₈	1	1	yes	characteristic
21	C₂²×C₁₅₇	M₁₆	1	1	yes	characteristic
22	C₄×C₁₅₇	—	2	2	no	—
23	Dic₁₅₇	—	2	2	no	—
24	Dic₁₅₇	—	4	1	no	—
25	C₂×C₁₅₇	—	2	1	no	—
26	C₂×C₁₅₇	—	2	1	no	—
27	C₂×C₁₅₇	C₂²⋊C₈	1	1	yes	characteristic
28	C₂×C₁₅₇	#99	1	1	yes	characteristic
29	C₂×C₁₅₇	#101	1	1	yes	characteristic
30	C₁₅₇	#324	1	1	yes	characteristic, complemented, Sylow
31	#324	—	157	1	no	maximal, Sylow
32	C₂×C₄⋊C₄	—	157	1	no	—
33	C₂²⋊C₈	—	157	2	no	—
34	C₂²×C₄	—	157	1	no	—
35	C₂²×C₄	—	157	1	no	—
36	C₂²×C₄	#10597845	1	1	yes	characteristic
37	C₂×C₈	—	314	2	no	—
38	C₄⋊C₄	—	314	2	no	—
39	C₂³	C₂×#10597845	1	1	yes	characteristic
40	C₂×C₄	—	2	1	no	—
41	C₂×C₄	—	2	1	no	—
42	C₂×C₄	—	314	1	no	—
43	C₂×C₄	—	628	1	no	—
44	C₂×C₄	—	628	1	no	—
45	C₂×C₄	—	157	2	no	—
46	C₂×C₄	#11929441	1	2	yes	complemented
47	C₈	—	628	2	no	—
48	C₂²	—	2	1	no	—
49	C₂²	—	2	1	no	—
50	C₂²	C₂²⋊#10597845	1	1	yes	characteristic
51	C₂²	C₂×#11929441	1	1	yes	characteristic
52	C₂²	#14578963	1	1	yes	characteristic
53	C₄	—	2	2	no	—
54	C₄	—	314	2	no	—
55	C₄	—	628	1	no	—
56	C₂	—	2	1	no	—
57	C₂	—	2	1	no	—
58	C₂	C₂²⋊#11929441	1	1	yes	characteristic
59	C₂	#19097830	1	1	yes	characteristic
60	C₂	#19097832	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#10597845
commutator	C₂²×C₁₅₇	C₂×C₈
Frattini	C₂³	C₂×#10597845
Fitting	C₂²×C₄×C₁₅₇	C₄
socle	C₂²×C₁₅₇	C₂²⋊C₄
prime radical	C₂³×C₁₅₇	C₂×C₄
cosocle	C₂²×Dic₁₅₇	C₂²
hypercenter	C₂²×C₄	#10597845
hypocenter	C₁₅₇	#324
LCS	G ▷ C₂²×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
16. C₂×C₄×C₁₅₇	C₈	semidirect
30. C₁₅₇	#324	semidirect
46. C₂×C₄	#11929441	semidirect