Subgroups — #23757003

Order 10048.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₃₁₄	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	1	yes	characteristic
5	C₂×#11929434	—	2	1	no	—
6	C₄⋊Dic₁₅₇	C₄	1	1	yes	characteristic
7	#14578933	—	2	1	no	—
8	C₄×Dic₁₅₇	—	2	1	no	—
9	C₂×C₈×C₁₅₇	—	2	1	no	—
10	C₄²×C₁₅₇	C₂²	1	1	yes	characteristic
11	Dic₃₁₄	—	2	1	no	—
12	Dic₃₁₄	C₈	1	2	yes	complemented
13	C₂×Dic₁₅₇	—	2	1	no	—
14	C₂×Dic₁₅₇	—	2	1	no	—
15	#11929434	—	2	2	no	—
16	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₅₇	D₄	1	1	yes	characteristic
18	C₂×C₄×C₁₅₇	D₄	1	1	yes	characteristic
19	C₈×C₁₅₇	—	4	1	no	—
20	C₂²×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₅₇	—	2	1	no	—
22	C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
23	C₄×C₁₅₇	M₁₆	1	1	yes	characteristic
24	C₄×C₁₅₇	SD₁₆	1	1	yes	characteristic
25	C₄×C₁₅₇	Q₁₆	1	1	yes	characteristic
26	Dic₁₅₇	—	2	2	no	—
27	Dic₁₅₇	—	4	1	no	—
28	C₂×C₁₅₇	C₂²⋊C₈	1	1	yes	characteristic
29	C₂×C₁₅₇	#103	1	1	yes	characteristic
30	C₂×C₁₅₇	#104	1	1	yes	characteristic
31	C₁₅₇	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
32	Q₈⋊C₈	—	157	1	no	maximal, Sylow
33	C₄×Q₈	—	157	1	no	—
34	C₄⋊C₈	D₁₅₇	1	1	yes	characteristic
35	C₄×C₈	—	157	1	no	—
36	C₂×Q₈	—	157	1	no	—
37	C₂×C₈	—	2	1	no	—
38	C₂×C₈	—	314	1	no	—
39	C₄⋊C₄	—	314	1	no	—
40	C₄⋊C₄	—	157	1	no	—
41	C₄²	—	314	1	no	—
42	C₄²	C₂×D₁₅₇	1	1	yes	characteristic
43	Q₈	—	314	1	no	—
44	Q₈	—	157	2	no	—
45	C₂×C₄	—	314	1	no	—
46	C₂×C₄	—	314	1	no	—
47	C₂×C₄	C₄×D₁₅₇	1	1	yes	characteristic
48	C₂×C₄	C₂²⋊D₁₅₇	1	1	yes	characteristic
49	C₂×C₄	D₆₂₈	1	1	yes	characteristic
50	C₈	—	4	1	no	—
51	C₈	—	314	2	no	—
52	C₂²	#14578931	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	314	2	no	—
55	C₄	—	628	1	no	—
56	C₄	C₈×D₁₅₇	1	1	yes	characteristic
57	C₄	#14578937	1	1	yes	characteristic
58	C₄	#14578942	1	1	yes	characteristic
59	C₄	#14578944	1	1	yes	characteristic
60	C₂	#19097683	1	1	yes	characteristic
61	C₂	#19097694	1	1	yes	characteristic
62	C₂	#19097697	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₁₅₇
commutator	C₄×C₁₅₇	C₂×C₈
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	Q₈⋊C₈
LCS	G ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
12. Dic₃₁₄	C₈	semidirect
31. C₁₅₇	Q₈⋊C₈	semidirect