Subgroups — #23757089

Order 10048.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097711	C₂	1	1	yes	maximal, characteristic
2	#19097707	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₁₆×C₁₅₇	C₂	1	1	yes	maximal, characteristic
4	#14578938	—	2	1	no	—
5	#14578929	—	2	1	no	—
6	C₂×Q₈×C₁₅₇	—	2	1	no	—
7	Q₁₆×C₁₅₇	—	2	1	no	—
8	Q₁₆×C₁₅₇	C₄	1	2	yes	—
9	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
10	#11929434	—	4	1	no	—
11	Q₈×C₁₅₇	—	2	2	no	—
12	Q₈×C₁₅₇	—	4	1	no	—
13	C₂×C₄×C₁₅₇	—	4	1	no	—
14	C₂×C₄×C₁₅₇	D₄	1	1	yes	characteristic
15	C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
16	C₈×C₁₅₇	D₄	1	1	yes	characteristic
17	C₂²×C₁₅₇	SD₁₆	1	1	yes	characteristic
18	C₄×C₁₅₇	—	4	2	no	—
19	C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₁₅₇	D₈	1	1	yes	characteristic
21	C₂×C₁₅₇	—	2	1	no	—
22	C₂×C₁₅₇	#102	1	1	yes	characteristic
23	C₁₅₇	#362	1	1	yes	characteristic, complemented, Sylow
24	#362	—	157	1	no	maximal, Sylow
25	C₂×Q₁₆	D₁₅₇	1	1	yes	characteristic
26	M₃₂	—	157	1	no	—
27	#108	—	157	1	no	—
28	C₂×Q₈	—	2	1	no	—
29	Q₁₆	—	2	1	no	—
30	Q₁₆	Dic₁₅₇	1	2	yes	—
31	M₁₆	—	314	1	no	—
32	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
33	C₁₆	—	314	1	no	—
34	Q₈	—	2	2	no	—
35	Q₈	—	4	1	no	—
36	C₂×C₄	—	4	1	no	—
37	C₂×C₄	C₂²⋊D₁₅₇	1	1	yes	characteristic
38	C₈	—	628	1	no	—
39	C₈	C₂×Dic₁₅₇	1	1	yes	characteristic
40	C₈	C₂²⋊D₁₅₇	1	1	yes	characteristic
41	C₂²	#14578942	1	1	yes	characteristic
42	C₄	—	4	2	no	—
43	C₄	C₂²⋊Dic₁₅₇	1	1	yes	characteristic
44	C₄	#14578939	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#19097692	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19097692
commutator	C₈×C₁₅₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₅₇
Fitting	C₂×Q₁₆×C₁₅₇	C₂
socle	C₂×C₁₅₇	#102
prime radical	C₂²×C₁₅₇	SD₁₆
cosocle	C₂×C₈×C₁₅₇	C₂²
hypercenter	C₂×Q₁₆	D₁₅₇
hypocenter	C₁₅₇	#362
LCS	G ▷ C₈×C₁₅₇ ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
23. C₁₅₇	#362	semidirect