Subgroups — #34115055

Order 20096.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23758162	C₂	1	1	yes	maximal, characteristic
2	#23758114	C₂	1	1	yes	maximal, characteristic
3	#23757048	C₂	1	1	yes	maximal, characteristic
4	C₂×#14578957	C₄	1	2	yes	—
5	C₄×#11929441	C₄	1	1	yes	characteristic
6	C₄×#11929441	C₄	1	1	yes	characteristic
7	C₂×#14578929	C₄	1	1	yes	characteristic
8	C₈×Dic₁₅₇	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₅₇	C₄	1	1	yes	characteristic
10	C₂×#11929441	—	2	1	no	—
11	C₂×#11929441	—	2	1	no	—
12	#14578957	C₈	1	4	yes	complemented
13	C₂×#11929434	C₂×C₄	1	1	yes	characteristic
14	C₄×Dic₁₅₇	C₂×C₄	1	1	yes	characteristic
15	#14578929	—	2	1	no	—
16	C₂×C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₁₅₇	—	2	1	no	—
18	#11929441	—	4	1	no	—
19	#11929441	—	4	1	no	—
20	C₂×Dic₁₅₇	M₁₆	1	1	yes	characteristic
21	C₂×Dic₁₅₇	M₁₆	1	1	yes	characteristic
22	#11929434	C₂×C₈	1	2	yes	—
23	C₂×C₄×C₁₅₇	C₄²	1	1	yes	characteristic
24	C₈×C₁₅₇	M₁₆	1	1	yes	characteristic
25	C₈×C₁₅₇	M₁₆	1	1	yes	characteristic
26	C₂²×C₁₅₇	#97	1	1	yes	characteristic
27	C₄×C₁₅₇	C₄×C₈	1	1	yes	characteristic
28	C₄×C₁₅₇	#97	1	1	yes	characteristic
29	Dic₁₅₇	—	2	1	no	—
30	Dic₁₅₇	—	2	1	no	—
31	C₂×C₁₅₇	#322	1	1	yes	characteristic
32	C₂×C₁₅₇	#347	1	1	yes	characteristic
33	C₂×C₁₅₇	#347	1	1	yes	characteristic
34	C₁₅₇	#1313	1	1	yes	characteristic, complemented, Sylow
35	#1313	—	157	1	no	maximal, Sylow
36	#346	—	157	1	no	—
37	#346	—	157	1	no	—
38	#322	—	157	1	no	—
39	C₂×C₁₆	—	157	1	no	—
40	C₂×C₁₆	—	157	2	no	—
41	C₂×C₁₆	#10597845	1	1	yes	characteristic
42	C₄×C₈	—	157	1	no	—
43	C₄×C₈	—	157	1	no	—
44	C₄×C₈	—	157	1	no	—
45	C₂×C₈	—	314	1	no	—
46	C₂×C₈	—	314	1	no	—
47	C₂×C₈	—	157	1	no	—
48	C₂×C₈	C₂×#10597845	1	1	yes	characteristic
49	C₄²	—	157	1	no	—
50	C₁₆	—	2	1	no	—
51	C₁₆	—	314	1	no	—
52	C₁₆	—	157	4	no	—
53	C₂×C₄	—	157	1	no	—
54	C₂×C₄	—	157	1	no	—
55	C₂×C₄	C₄×#10597845	1	1	yes	characteristic
56	C₈	—	628	1	no	—
57	C₈	—	628	1	no	—
58	C₈	—	157	2	no	—
59	C₈	#14578963	1	1	yes	characteristic
60	C₈	#14578964	1	1	yes	characteristic
61	C₂²	#19097825	1	1	yes	characteristic
62	C₄	—	314	1	no	—
63	C₄	—	314	1	no	—
64	C₄	C₈×#10597845	1	1	yes	characteristic
65	C₄	#19097826	1	1	yes	characteristic
66	C₂	#11929441⋊C₈	1	1	yes	characteristic
67	C₂	#23758163	1	1	yes	characteristic
68	C₂	#23758164	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#10597845
commutator	C₄×C₁₅₇	C₄×C₈
Frattini	C₂×C₈	C₂×#10597845
Fitting	C₂×C₁₆×C₁₅₇	C₄
socle, prime radical	C₂²×C₁₅₇	#97
cosocle	C₈×Dic₁₅₇	C₂²
hypercenter	C₂×C₁₆	#10597845
hypocenter	C₁₅₇	#1313
LCS	G ▷ C₄×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
12. #14578957	C₈	semidirect
34. C₁₅₇	#1313	semidirect

Maximal subgroups

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

subgroup	index
#23758162	2
#23758114	2
#23757048	2
#1313	157