Subgroups — #23757367

Order 10048.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆₂₈	C₂	1	1	yes	maximal, characteristic
2	#19097736	C₂	1	2	yes	maximal
3	#19097694	C₂	1	2	yes	maximal
4	C₈×Dic₁₅₇	C₂	1	1	yes	maximal, characteristic
5	#107×C₁₅₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₁₄	C₂²	1	2	yes	—
7	Dic₆₂₈	C₄	1	4	yes	complemented
8	C₂×#11929434	C₂²	1	1	yes	characteristic
9	#14578933	—	2	2	no	—
10	C₄×Dic₁₅₇	—	2	2	no	—
11	C₄×Dic₁₅₇	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₅₇	C₂²	1	2	yes	—
14	Dic₃₁₄	—	2	2	no	—
15	Dic₃₁₄	C₂×C₄	1	4	yes	—
16	C₂×Dic₁₅₇	—	2	2	no	—
17	C₂×Dic₁₅₇	D₄	1	1	yes	characteristic
18	C₂×Dic₁₅₇	D₄	1	1	yes	characteristic
19	#11929434	—	2	1	no	—
20	C₂×C₄×C₁₅₇	—	2	2	no	—
21	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
22	C₈×C₁₅₇	C₂×C₄	1	2	yes	—
23	C₂²×C₁₅₇	C₂×D₄	1	1	yes	characteristic
24	C₄×C₁₅₇	—	4	2	no	—
25	C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₁₅₇	#41	1	1	yes	characteristic
27	Dic₁₅₇	—	2	4	no	—
28	Dic₁₅₇	—	2	1	no	—
29	Dic₁₅₇	Q₁₆	1	2	yes	complemented
30	C₂×C₁₅₇	C₄×D₄	1	1	yes	characteristic
31	C₂×C₁₅₇	C₂×Q₁₆	1	1	yes	characteristic
32	C₂×C₁₅₇	#135	1	1	yes	characteristic
33	C₁₅₇	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₄×Q₁₆	—	157	1	no	maximal, Sylow
35	C₂×Q₁₆	—	157	1	no	—
36	C₄×Q₈	—	157	2	no	—
37	#107	D₁₅₇	1	1	yes	characteristic
38	#103	—	157	2	no	—
39	C₄×C₈	—	157	1	no	—
40	C₂×Q₈	—	157	2	no	—
41	Q₁₆	—	157	4	no	—
42	C₂×C₈	—	157	1	no	—
43	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
44	C₄⋊C₄	—	314	2	no	—
45	C₄⋊C₄	C₂×D₁₅₇	1	2	yes	—
46	C₄²	—	314	2	no	—
47	C₄²	—	157	1	no	—
48	Q₈	—	314	2	no	—
49	Q₈	—	157	4	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	314	2	no	—
52	C₂×C₄	—	157	1	no	—
53	C₂×C₄	—	157	1	no	—
54	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
55	C₈	—	314	1	no	—
56	C₈	C₄×D₁₅₇	1	2	yes	—
57	C₂²	D₄×D₁₅₇	1	1	yes	characteristic
58	C₄	—	4	2	no	—
59	C₄	—	314	4	no	—
60	C₄	—	314	1	no	—
61	C₄	—	157	2	no	—
62	C₄	C₂×C₄×D₁₅₇	1	1	yes	characteristic
63	C₄	#14578955	1	1	yes	characteristic
64	C₂	#19097733	1	1	yes	characteristic
65	C₂	Q₁₆×D₁₅₇	1	1	yes	characteristic
66	C₂	#19097790	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₅₇
commutator	C₄×C₁₅₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₅₇
Fitting	#107×C₁₅₇	C₂
socle, prime radical	C₂²×C₁₅₇	C₂×D₄
cosocle	C₂×C₄×C₁₅₇	C₂³
hypercenter	#107	D₁₅₇
hypocenter	C₁₅₇	C₄×Q₁₆
LCS	G ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
7. Dic₆₂₈	C₄	semidirect
29. Dic₁₅₇	Q₁₆	semidirect
33. C₁₅₇	C₄×Q₁₆	semidirect