Subgroups — C₂×#19097763 #23757795

Order 10048.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097763	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₄⋊Dic₁₅₇	C₂	1	2	yes	maximal
3	C₂×#14578933	C₂	1	4	yes	maximal
4	C₂×C₄²×C₁₅₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₅₇	C₂²	1	4	yes	—
6	C₄⋊Dic₁₅₇	C₂²	1	8	yes	—
7	#14578933	C₂²	1	16	yes	—
8	C₂²×C₄×C₁₅₇	C₂²	1	2	yes	—
9	C₂²×C₄×C₁₅₇	C₂²	1	1	yes	characteristic
10	C₄²×C₁₅₇	C₂²	1	4	yes	—
11	C₂×Dic₁₅₇	—	2	8	no	—
12	C₂×Dic₁₅₇	C₂³	1	8	yes	—
13	C₂³×C₁₅₇	C₂³	1	1	yes	characteristic
14	C₂×C₄×C₁₅₇	—	2	4	no	—
15	C₂×C₄×C₁₅₇	Q₈	1	4	yes	—
16	C₂×C₄×C₁₅₇	C₂³	1	4	yes	—
17	C₂×C₄×C₁₅₇	C₂³	1	2	yes	—
18	C₂²×C₁₅₇	C₂×Q₈	1	2	yes	—
19	C₂²×C₁₅₇	#41	1	4	yes	—
20	C₂²×C₁₅₇	C₂⁴	1	1	yes	characteristic
21	C₄×C₁₅₇	—	2	4	no	—
22	C₄×C₁₅₇	C₂×Q₈	1	4	yes	—
23	Dic₁₅₇	—	2	8	no	—
24	C₂×C₁₅₇	#125	1	4	yes	complemented
25	C₂×C₁₅₇	C₂²×Q₈	1	1	yes	characteristic
26	C₂×C₁₅₇	C₂×#41	1	2	yes	—
27	C₁₅₇	C₂×#125	1	1	yes	characteristic, complemented, Sylow
28	C₂×#125	—	157	1	no	maximal, Sylow
29	#125	—	157	8	no	—
30	C₂×C₄⋊C₄	—	157	4	no	—
31	C₂×C₄⋊C₄	—	157	2	no	—
32	C₂×C₄²	D₁₅₇	1	1	yes	characteristic
33	C₂²×C₄	—	157	4	no	—
34	C₂²×C₄	C₂×D₁₅₇	1	2	yes	—
35	C₂²×C₄	C₂×D₁₅₇	1	1	yes	characteristic
36	C₄⋊C₄	—	157	16	no	—
37	C₄⋊C₄	—	157	8	no	—
38	C₄²	C₂×D₁₅₇	1	4	yes	—
39	C₂³	C₂²×D₁₅₇	1	1	yes	characteristic
40	C₂×C₄	—	2	4	no	—
41	C₂×C₄	—	314	8	no	—
42	C₂×C₄	—	157	8	no	—
43	C₂×C₄	Dic₃₁₄	1	4	yes	—
44	C₂×C₄	C₂²×D₁₅₇	1	4	yes	—
45	C₂×C₄	C₂²×D₁₅₇	1	2	yes	—
46	C₂²	C₂×Dic₃₁₄	1	2	yes	—
47	C₂²	#14578954	1	4	yes	—
48	C₂²	C₂³×D₁₅₇	1	1	yes	characteristic
49	C₄	—	2	4	no	—
50	C₄	—	314	8	no	—
51	C₄	C₂×Dic₃₁₄	1	4	yes	—
52	C₂	#19097763	1	4	yes	direct product factor
53	C₂	C₂²×Dic₃₁₄	1	1	yes	characteristic
54	C₂	C₂×#14578954	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₁₅₇
commutator, cosocle	C₂²×C₁₅₇	C₂⁴
Frattini	C₂²	C₂³×D₁₅₇
Fitting	C₂×C₄²×C₁₅₇	C₂
socle, prime radical	C₂³×C₁₅₇	C₂³
hypercenter	C₂×C₄²	D₁₅₇
hypocenter	C₁₅₇	C₂×#125
LCS	G ▷ C₂²×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #19097763	C₂	direct (N × H)
24. C₂×C₁₅₇	#125	semidirect
27. C₁₅₇	C₂×#125	semidirect
52. C₂	#19097763	direct (N × H)

Subgroups — C2×#19097763 #23757795

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19097763 #23757795