Subgroups — #34115295

Order 20096.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23758205	C₂	1	2	yes	maximal
2	C₄×#14578929	C₂	1	1	yes	maximal, characteristic
3	#19097821	—	2	2	no	—
4	C₂×#14578929	C₄	1	1	yes	characteristic
5	C₂×#14578929	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₁₅₇	C₄	1	1	yes	characteristic
7	#14578929	—	2	1	no	—
8	#14578929	D₄	1	1	yes	characteristic
9	#14578929	Q₈	1	1	yes	characteristic
10	C₂×C₈×C₁₅₇	C₈	1	1	yes	characteristic
11	C₂×C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
12	C₄²×C₁₅₇	C₈	1	1	yes	characteristic
13	C₂×C₄×C₁₅₇	—	2	1	no	—
14	C₂×C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₅₇	C₁₆	1	2	yes	—
16	C₈×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₅₇	M₁₆	1	1	yes	characteristic
18	C₂²×C₁₅₇	M₃₂	1	1	yes	characteristic
19	C₄×C₁₅₇	—	2	2	no	—
20	C₄×C₁₅₇	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₁₅₇	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₁₅₇	—	2	1	no	—
23	C₂×C₁₅₇	C₄⋊C₁₆	1	1	yes	characteristic
24	C₁₅₇	#1422	1	1	yes	characteristic, complemented, Sylow
25	#1422	—	157	1	no	maximal, Sylow
26	M₆₄	—	157	2	no	—
27	C₄×C₁₆	—	157	1	no	—
28	C₂×C₁₆	—	157	1	no	—
29	C₂×C₁₆	—	157	1	no	—
30	C₄×C₈	#10597845	1	1	yes	characteristic
31	C₃₂	—	314	2	no	—
32	C₂×C₈	#11929441	1	1	yes	characteristic
33	C₂×C₈	C₂×#10597845	1	1	yes	characteristic
34	C₄²	#11929441	1	1	yes	characteristic
35	C₁₆	—	314	1	no	—
36	C₁₆	—	157	1	no	—
37	C₁₆	—	157	1	no	—
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₂×#11929441	1	1	yes	characteristic
40	C₈	#14578957	1	2	yes	—
41	C₈	C₄⋊#10597845	1	1	yes	characteristic
42	C₈	#14578964	1	1	yes	characteristic
43	C₂²	#19097845	1	1	yes	characteristic
44	C₄	—	2	2	no	—
45	C₄	C₄⋊#11929441	1	1	yes	characteristic
46	C₄	C₂×#14578957	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₄⋊#14578957	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄⋊#10597845
commutator	C₄×C₁₅₇	C₂×C₁₆
Frattini	C₂×C₈	C₂×#10597845
Fitting	C₄×C₈×C₁₅₇	C₄
socle	C₂×C₁₅₇	C₄⋊C₁₆
prime radical	C₂²×C₁₅₇	M₃₂
cosocle	C₂×#14578929	C₂²
hypercenter	C₄×C₈	#10597845
hypocenter	C₁₅₇	#1422
LCS	G ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
24. C₁₅₇	#1422	semidirect

Maximal subgroups

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

subgroup	index
#23758205	2
C₄×#14578929	2
#1422	157