Subgroups — #23758192

Order 10048.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097846	C₂	1	1	yes	maximal, characteristic
2	#19097841	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₁₅₇	C₂	1	1	yes	maximal, characteristic
4	#14578964	—	2	1	no	—
5	#14578957	—	2	1	no	—
6	Q₈×D₁₅₇	—	2	1	no	—
7	Dic₆₂₈	C₄	1	1	yes	characteristic
8	#14578944	—	2	1	no	—
9	C₈×D₁₅₇	C₂²	1	1	yes	characteristic
10	Q₁₆×C₁₅₇	C₄	1	1	yes	characteristic
11	#11929441	—	4	1	no	—
12	Dic₃₁₄	—	2	1	no	—
13	Dic₃₁₄	—	4	1	no	—
14	C₄×D₁₅₇	—	4	1	no	—
15	C₄×D₁₅₇	D₄	1	1	yes	characteristic
16	#11929434	D₄	1	1	yes	characteristic
17	Q₈×C₁₅₇	—	2	1	no	—
18	C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
19	C₂×D₁₅₇	SD₁₆	1	1	yes	characteristic
20	C₄×C₁₅₇	—	4	1	no	—
21	C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₁₅₇	—	4	1	no	—
23	Dic₁₅₇	D₈	1	1	yes	characteristic
24	C₂×C₁₅₇	#102	1	1	yes	characteristic
25	D₁₅₇	—	2	1	no	—
26	C₁₅₇	#362	1	1	yes	characteristic, complemented, Sylow
27	#362	—	157	1	no	maximal, Sylow
28	C₂×Q₁₆	—	157	1	no	—
29	M₃₂	—	157	1	no	—
30	#108	—	157	1	no	—
31	C₂×Q₈	—	314	1	no	—
32	Q₁₆	—	314	1	no	—
33	Q₁₆	—	157	1	no	—
34	Q₁₆	#10597845	1	1	yes	characteristic
35	M₁₆	—	314	1	no	—
36	C₂×C₈	—	157	1	no	—
37	C₁₆	—	314	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	314	1	no	—
40	Q₈	—	628	1	no	—
41	C₂×C₄	—	628	1	no	—
42	C₂×C₄	—	157	1	no	—
43	C₈	—	628	1	no	—
44	C₈	—	157	1	no	—
45	C₈	C₂×#10597845	1	1	yes	characteristic
46	C₂²	—	157	1	no	—
47	C₄	—	4	1	no	—
48	C₄	—	628	1	no	—
49	C₄	—	157	1	no	—
50	C₄	C₂²⋊#10597845	1	1	yes	characteristic
51	C₂	—	314	1	no	—
52	C₂	#19097833	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19097833
commutator	C₈×C₁₅₇	C₂×C₄
Frattini	C₈	C₂×#10597845
Fitting	Q₁₆×C₁₅₇	C₄
socle	C₂×C₁₅₇	#102
prime radical	C₂×D₁₅₇	SD₁₆
cosocle	C₈×D₁₅₇	C₂²
hypercenter	Q₁₆	#10597845
hypocenter	C₁₅₇	#362
LCS	G ▷ C₈×C₁₅₇ ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

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