Subgroups — #34115294

Order 20096.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19097821	C₂	1	2	yes	maximal
2	C₁₆×Dic₁₅₇	C₂	1	1	yes	maximal, characteristic
3	#19097821	—	2	2	no	—
4	C₂×#14578929	C₂²	1	1	yes	characteristic
5	C₈×Dic₁₅₇	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₁₅₇	C₄	1	1	yes	characteristic
7	C₂×#11929434	C₈	1	1	yes	characteristic
8	C₄×Dic₁₅₇	C₈	1	1	yes	characteristic
9	#14578929	D₄	1	1	yes	characteristic
10	#14578929	Q₈	1	1	yes	characteristic
11	C₂×C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₅₇	—	2	1	no	—
13	C₂×Dic₁₅₇	C₁₆	1	1	yes	characteristic
14	C₂×Dic₁₅₇	C₁₆	1	1	yes	characteristic
15	#11929434	—	2	1	no	—
16	C₂×C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
17	C₈×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₅₇	M₁₆	1	1	yes	characteristic
19	C₂²×C₁₅₇	C₂×C₁₆	1	1	yes	characteristic
20	C₄×C₁₅₇	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₁₅₇	M₃₂	1	1	yes	characteristic
22	Dic₁₅₇	—	2	1	no	—
23	Dic₁₅₇	C₃₂	1	2	yes	complemented
24	C₂×C₁₅₇	C₄⋊C₁₆	1	1	yes	characteristic
25	C₂×C₁₅₇	C₂×C₃₂	1	1	yes	characteristic
26	C₂×C₁₅₇	M₆₄	1	1	yes	characteristic
27	C₁₅₇	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₄⋊C₃₂	—	157	1	no	maximal, Sylow
29	C₂×C₃₂	—	157	2	no	—
30	C₄×C₁₆	—	157	1	no	—
31	C₂×C₁₆	—	157	1	no	—
32	C₂×C₁₆	#10597845	1	1	yes	characteristic
33	C₄×C₈	—	157	1	no	—
34	C₃₂	—	314	2	no	—
35	C₂×C₈	—	157	1	no	—
36	C₂×C₈	C₂×#10597845	1	1	yes	characteristic
37	C₄²	—	157	1	no	—
38	C₁₆	—	2	1	no	—
39	C₁₆	—	157	1	no	—
40	C₁₆	—	157	1	no	—
41	C₂×C₄	—	157	1	no	—
42	C₂×C₄	—	157	1	no	—
43	C₂×C₄	D₁₅₇⋊C₈	1	1	yes	characteristic
44	C₈	—	314	1	no	—
45	C₈	C₄⋊#10597845	1	1	yes	characteristic
46	C₈	#14578963	1	1	yes	characteristic
47	C₂²	D₁₅₇⋊C₁₆	1	1	yes	characteristic
48	C₄	—	314	1	no	—
49	C₄	—	157	2	no	—
50	C₄	#19097838	1	1	yes	characteristic
51	C₄	#19097846	1	1	yes	characteristic
52	C₂	#23758194	1	1	yes	characteristic
53	C₂	D₁₅₇⋊C₃₂	1	1	yes	characteristic
54	C₂	#23758206	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#10597845
commutator	C₂×C₁₅₇	C₂×C₃₂
Fitting	C₂×C₁₆×C₁₅₇	C₄
socle, prime radical	C₂²×C₁₅₇	C₂×C₁₆
cosocle	C₂×#14578929	C₂²
hypercenter	C₂×C₁₆	#10597845
hypocenter	C₁₅₇	C₄⋊C₃₂
LCS	G ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
23. Dic₁₅₇	C₃₂	semidirect
27. C₁₅₇	C₄⋊C₃₂	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#19097821	2
C₁₆×Dic₁₅₇	2
C₄⋊C₃₂	157