Subgroups — C₂²×#14578964 #23758347

Order 10048.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14578964	C₂	1	12	yes	maximal, direct product factor
2	C₂²×#11929441	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₁₅₇	C₂	1	1	yes	maximal, characteristic
4	#14578964	C₂²	1	16	yes	direct product factor
5	C₂×#11929441	C₂²	1	12	yes	complemented
6	C₂³×D₁₅₇	C₄	1	1	yes	characteristic
7	C₂²×Dic₁₅₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₁₅₇	C₄	1	6	yes	—
9	C₂×C₄×D₁₅₇	C₂²	1	6	yes	—
10	C₂²×C₄×C₁₅₇	C₄	1	1	yes	characteristic
11	#11929441	C₂³	1	8	yes	complemented
12	C₂²×D₁₅₇	—	2	4	no	—
13	C₂²×D₁₅₇	C₂×C₄	1	6	yes	—
14	C₂×Dic₁₅₇	C₂×C₄	1	3	yes	—
15	C₂×Dic₁₅₇	C₂³	1	3	yes	—
16	C₄×D₁₅₇	C₂×C₄	1	12	yes	—
17	C₄×D₁₅₇	C₂³	1	4	yes	—
18	C₂³×C₁₅₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₅₇	C₂×C₄	1	6	yes	—
20	C₂²×C₁₅₇	M₁₆	1	4	yes	complemented
21	C₂²×C₁₅₇	C₂²×C₄	1	3	yes	—
22	C₂×D₁₅₇	—	2	12	no	—
23	C₂×D₁₅₇	C₂²×C₄	1	4	yes	—
24	C₄×C₁₅₇	C₂²×C₄	1	4	yes	—
25	Dic₁₅₇	C₂²×C₄	1	3	yes	—
26	Dic₁₅₇	C₂⁴	1	1	yes	characteristic
27	C₂×C₁₅₇	C₂×M₁₆	1	6	yes	complemented
28	C₂×C₁₅₇	C₂³×C₄	1	1	yes	characteristic
29	D₁₅₇	—	2	4	no	—
30	C₁₅₇	C₂²×M₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂²×M₁₆	—	157	1	no	maximal, Sylow
32	C₂³×C₄	—	157	1	no	—
33	C₂×M₁₆	—	157	12	no	—
34	C₂²×C₈	—	157	2	no	—
35	C₂⁴	—	157	1	no	—
36	C₂²×C₄	—	157	1	no	—
37	C₂²×C₄	—	157	6	no	—
38	C₂²×C₄	—	157	6	no	—
39	C₂²×C₄	#10597845	1	1	yes	characteristic
40	M₁₆	—	157	16	no	—
41	C₂×C₈	—	157	12	no	—
42	C₂³	—	314	4	no	—
43	C₂³	—	157	6	no	—
44	C₂³	C₂×#10597845	1	1	yes	characteristic
45	C₂×C₄	—	157	3	no	—
46	C₂×C₄	—	157	3	no	—
47	C₂×C₄	—	157	4	no	—
48	C₂×C₄	—	157	12	no	—
49	C₂×C₄	C₂×#10597845	1	6	yes	—
50	C₈	—	157	8	no	—
51	C₂²	—	314	12	no	—
52	C₂²	—	157	4	no	—
53	C₂²	#14578964	1	4	yes	direct product factor
54	C₂²	C₂²×#10597845	1	3	yes	—
55	C₄	—	157	1	no	—
56	C₄	—	157	3	no	—
57	C₄	C₂²×#10597845	1	4	yes	—
58	C₂	—	314	4	no	—
59	C₂	C₂×#14578964	1	6	yes	direct product factor
60	C₂	C₂³×#10597845	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#10597845
commutator	C₂×C₁₅₇	C₂³×C₄
Frattini	C₂	C₂³×#10597845
Fitting	C₂²×C₄×C₁₅₇	C₄
socle	C₂³×C₁₅₇	C₂×C₄
prime radical	C₂³×D₁₅₇	C₄
cosocle	Dic₁₅₇	C₂⁴
hypercenter	C₂²×C₄	#10597845
hypocenter	C₁₅₇	C₂²×M₁₆
LCS	G ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#14578964	C₂	direct (N × H)
2. C₂²×#11929441	C₂	semidirect
4. #14578964	C₂²	direct (N × H)
5. C₂×#11929441	C₂²	semidirect
11. #11929441	C₂³	semidirect
20. C₂²×C₁₅₇	M₁₆	semidirect
27. C₂×C₁₅₇	C₂×M₁₆	semidirect
30. C₁₅₇	C₂²×M₁₆	semidirect
53. C₂²	#14578964	direct (N × H)
59. C₂	C₂×#14578964	direct (N × H)

Subgroups — C22×#14578964 #23758347

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#14578964 #23758347