Subgroups — #23757021

Order 10048.

64 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	C₄⋊#11929434	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₁₅₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₁₄	C₄	1	2	yes	—
5	C₂×#11929434	—	2	1	no	—
6	C₄⋊Dic₁₅₇	—	2	1	no	—
7	C₄⋊Dic₁₅₇	—	2	1	no	—
8	C₂×C₈×C₁₅₇	—	2	1	no	—
9	C₄²×C₁₅₇	C₂²	1	1	yes	characteristic
10	Dic₃₁₄	—	4	2	no	—
11	C₂×Dic₁₅₇	—	2	2	no	—
12	#11929434	—	4	1	no	—
13	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₅₇	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₅₇	D₄	1	1	yes	characteristic
16	C₈×C₁₅₇	—	4	1	no	—
17	C₂²×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₄×C₁₅₇	—	2	1	no	—
19	C₄×C₁₅₇	SD₁₆	1	1	yes	characteristic
20	C₄×C₁₅₇	SD₁₆	1	1	yes	characteristic
21	C₄×C₁₅₇	Q₁₆	1	1	yes	characteristic
22	C₄×C₁₅₇	Q₁₆	1	1	yes	characteristic
23	Dic₁₅₇	—	4	2	no	—
24	C₂×C₁₅₇	#100	1	1	yes	characteristic
25	C₂×C₁₅₇	#103	1	1	yes	characteristic
26	C₂×C₁₅₇	#103	1	1	yes	characteristic
27	C₁₅₇	#333	1	1	yes	characteristic, complemented, Sylow
28	#333	—	157	1	no	maximal, Sylow
29	C₄⋊Q₈	—	157	1	no	—
30	C₄⋊C₈	—	157	1	no	—
31	C₄⋊C₈	D₁₅₇	1	1	yes	characteristic
32	C₂×Q₈	—	157	2	no	—
33	C₂×C₈	—	2	1	no	—
34	C₂×C₈	—	314	1	no	—
35	C₄⋊C₄	—	314	1	no	—
36	C₄⋊C₄	—	314	1	no	—
37	C₄²	C₂×D₁₅₇	1	1	yes	characteristic
38	Q₈	—	628	2	no	—
39	C₂×C₄	—	314	2	no	—
40	C₂×C₄	C₄×D₁₅₇	1	1	yes	characteristic
41	C₂×C₄	C₂²⋊D₁₅₇	1	1	yes	characteristic
42	C₂×C₄	D₆₂₈	1	1	yes	characteristic
43	C₈	—	4	1	no	—
44	C₈	—	628	1	no	—
45	C₂²	#14578931	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	628	2	no	—
48	C₄	#14578942	1	1	yes	characteristic
49	C₄	#14578943	1	1	yes	characteristic
50	C₄	#14578944	1	1	yes	characteristic
51	C₄	Dic₆₂₈	1	1	yes	characteristic
52	C₂	#19097687	1	1	yes	characteristic
53	C₂	#19097694	1	1	yes	characteristic
54	C₂	#19097696	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14578931
commutator	C₂×C₄×C₁₅₇	C₂×C₄
Frattini	C₄²	C₂×D₁₅₇
Fitting	C₄⋊C₈×C₁₅₇	C₂
socle, prime radical	C₂²×C₁₅₇	C₂²⋊C₄
cosocle	C₄²×C₁₅₇	C₂²
hypercenter	C₄⋊C₈	D₁₅₇
hypocenter	C₁₅₇	#333
LCS	G ▷ C₂×C₄×C₁₅₇ ▷ C₂²×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
27. C₁₅₇	#333	semidirect