Subgroups — C₂×#19097842 #23758287

Order 10048.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14578964	C₂	1	2	yes	maximal
2	#19097842	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×D₁₅₇	C₂	1	1	yes	maximal, characteristic
4	#14578964	—	2	2	no	—
5	#14578964	C₂²	1	4	yes	—
6	C₂×#11929441	—	2	2	no	—
7	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
8	C₂×#11929434	C₄	1	1	yes	characteristic
9	C₈×D₁₅₇	C₄	1	2	yes	—
10	C₈×D₁₅₇	C₂²	1	2	yes	—
11	C₂×C₈×C₁₅₇	C₄	1	1	yes	characteristic
12	#11929441	—	2	4	no	—
13	C₂²×D₁₅₇	Q₈	1	1	yes	characteristic
14	C₂×Dic₁₅₇	D₄	1	1	yes	characteristic
15	C₄×D₁₅₇	C₂×C₄	1	1	yes	characteristic
16	C₄×D₁₅₇	D₄	1	1	yes	characteristic
17	C₄×D₁₅₇	Q₈	1	1	yes	characteristic
18	C₄×D₁₅₇	C₂³	1	1	yes	characteristic
19	#11929434	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
21	C₈×C₁₅₇	C₂×C₄	1	2	yes	—
22	C₂²×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
23	C₂×D₁₅₇	—	2	2	no	—
24	C₂×D₁₅₇	C₄⋊C₄	1	1	yes	characteristic
25	C₂×D₁₅₇	C₂×Q₈	1	1	yes	characteristic
26	C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
27	C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
28	Dic₁₅₇	C₄⋊C₄	1	1	yes	characteristic
29	Dic₁₅₇	C₂×D₄	1	1	yes	characteristic
30	C₂×C₁₅₇	#108	1	2	yes	complemented
31	C₂×C₁₅₇	C₂×C₄⋊C₄	1	1	yes	characteristic
32	D₁₅₇	—	2	1	no	—
33	D₁₅₇	—	2	1	no	—
34	C₁₅₇	C₂×#108	1	1	yes	characteristic, complemented, Sylow
35	C₂×#108	—	157	1	no	maximal, Sylow
36	C₂×M₁₆	—	157	2	no	—
37	C₂²×C₈	—	157	1	no	—
38	#108	—	157	4	no	—
39	C₂²×C₄	—	157	1	no	—
40	M₁₆	—	314	2	no	—
41	M₁₆	—	157	4	no	—
42	C₂×C₈	—	314	2	no	—
43	C₂×C₈	—	157	1	no	—
44	C₂×C₈	—	157	2	no	—
45	C₂×C₈	—	157	2	no	—
46	C₂×C₈	#10597845	1	1	yes	characteristic
47	C₂³	—	157	1	no	—
48	C₂×C₄	—	157	1	no	—
49	C₂×C₄	—	157	1	no	—
50	C₂×C₄	—	157	1	no	—
51	C₂×C₄	—	157	1	no	—
52	C₂×C₄	—	157	1	no	—
53	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
54	C₈	—	314	4	no	—
55	C₈	—	157	2	no	—
56	C₈	C₂×#10597845	1	2	yes	—
57	C₂²	—	314	2	no	—
58	C₂²	—	157	1	no	—
59	C₂²	—	157	1	no	—
60	C₂²	C₄⋊#10597845	1	1	yes	characteristic
61	C₄	—	157	1	no	—
62	C₄	—	157	1	no	—
63	C₄	C₄⋊#10597845	1	1	yes	characteristic
64	C₄	C₂²×#10597845	1	1	yes	characteristic
65	C₂	—	314	1	no	—
66	C₂	—	314	1	no	—
67	C₂	#19097842	1	2	yes	direct product factor
68	C₂	C₂×C₄⋊#10597845	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#10597845
commutator	C₄×C₁₅₇	C₂²×C₄
Frattini	C₄	C₂²×#10597845
Fitting	C₂×C₈×C₁₅₇	C₄
socle	C₂²×C₁₅₇	C₄⋊C₄
prime radical	C₂²×D₁₅₇	Q₈
cosocle	C₄×D₁₅₇	C₂³
hypercenter	C₂×C₈	#10597845
hypocenter	C₁₅₇	C₂×#108
LCS	G ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #19097842	C₂	direct (N × H)
30. C₂×C₁₅₇	#108	semidirect
34. C₁₅₇	C₂×#108	semidirect
67. C₂	#19097842	direct (N × H)

Subgroups — C2×#19097842 #23758287

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19097842 #23758287