Subgroups — #34099737

Order 20096.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23757671	C₂	1	1	yes	maximal, characteristic, complemented
2	#23757646	C₂	1	1	yes	maximal, characteristic
3	#23757624	C₂	1	2	yes	maximal, complemented
4	#23757620	C₂	1	2	yes	maximal
5	C₈²×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14578943	—	2	2	no	—
7	#19097771	C₂²	1	2	yes	—
8	#19097771	C₂²	1	1	yes	characteristic
9	#19097768	C₂²	1	1	yes	characteristic
10	#19097703	—	2	2	no	—
11	#19097696	—	2	4	no	—
12	#19097693	—	2	4	no	—
13	C₄×C₈×C₁₅₇	C₂²	1	2	yes	—
14	C₄×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
15	C₂×Dic₃₁₄	—	2	2	no	—
16	C₂×Dic₃₁₄	—	2	1	no	—
17	C₂×D₆₂₈	—	2	2	no	—
18	C₂×D₆₂₈	—	2	1	no	—
19	#14578943	—	4	4	no	—
20	C₄⋊Dic₁₅₇	—	2	2	no	—
21	C₄⋊Dic₁₅₇	—	2	2	no	—
22	C₄⋊Dic₁₅₇	—	2	2	no	—
23	C₂×C₈×C₁₅₇	D₄	1	4	yes	—
24	C₂×C₈×C₁₅₇	D₄	1	2	yes	—
25	C₄²×C₁₅₇	C₂³	1	1	yes	characteristic
26	C₂²×D₁₅₇	—	4	1	no	—
27	Dic₃₁₄	—	4	2	no	—
28	Dic₃₁₄	—	4	4	no	—
29	D₆₂₈	—	4	2	no	—
30	D₆₂₈	—	4	4	no	—
31	C₂×Dic₁₅₇	—	4	1	no	—
32	C₂×Dic₁₅₇	—	4	2	no	—
33	C₂×C₄×C₁₅₇	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₅₇	C₂×D₄	1	2	yes	—
35	C₈×C₁₅₇	—	2	4	no	—
36	C₈×C₁₅₇	SD₁₆	1	4	yes	—
37	C₂²×C₁₅₇	#127	1	1	yes	characteristic
38	C₂×D₁₅₇	—	8	1	no	—
39	C₂×D₁₅₇	—	8	2	no	—
40	C₄×C₁₅₇	C₂×SD₁₆	1	2	yes	—
41	C₄×C₁₅₇	#135	1	4	yes	—
42	Dic₁₅₇	—	8	1	no	—
43	Dic₁₅₇	—	8	2	no	—
44	C₂×C₁₅₇	#492	1	1	yes	characteristic
45	C₂×C₁₅₇	#495	1	2	yes	—
46	D₁₅₇	—	16	1	no	—
47	C₁₅₇	#1708	1	1	yes	characteristic, complemented, Sylow
48	#1708	—	157	1	no	maximal, Sylow
49	#498	—	157	1	no	—
50	#492	—	157	1	no	—
51	#487	—	157	2	no	—
52	#486	—	157	2	no	—
53	C₈²	D₁₅₇	1	1	yes	characteristic, complemented
54	C₂×SD₁₆	—	314	2	no	—
55	C₄⋊Q₈	—	157	2	no	—
56	C₄⋊Q₈	—	157	1	no	—
57	#127	—	157	1	no	—
58	#106	—	314	2	no	—
59	#103	—	314	4	no	—
60	#102	—	314	4	no	—
61	C₄×C₈	C₂×D₁₅₇	1	2	yes	—
62	C₄×C₈	C₂×D₁₅₇	1	1	yes	characteristic
63	C₂×Q₈	—	314	2	no	—
64	C₂×Q₈	—	314	1	no	—
65	C₂×D₄	—	314	2	no	—
66	C₂×D₄	—	314	1	no	—
67	SD₁₆	—	628	4	no	—
68	C₂×C₈	D₆₂₈	1	4	yes	—
69	C₂×C₈	D₆₂₈	1	2	yes	—
70	C₄⋊C₄	—	314	2	no	—
71	C₄⋊C₄	—	314	2	no	—
72	C₄⋊C₄	—	314	2	no	—
73	C₄²	C₂²×D₁₅₇	1	1	yes	characteristic
74	C₂³	—	628	1	no	—
75	Q₈	—	628	2	no	—
76	Q₈	—	628	4	no	—
77	D₄	—	628	2	no	—
78	D₄	—	628	4	no	—
79	C₂×C₄	—	628	1	no	—
80	C₂×C₄	—	628	2	no	—
81	C₂×C₄	C₂×D₆₂₈	1	1	yes	characteristic
82	C₂×C₄	C₂×D₆₂₈	1	2	yes	—
83	C₈	—	2	4	no	—
84	C₈	#14578943	1	4	yes	—
85	C₂²	—	1256	1	no	—
86	C₂²	—	1256	2	no	—
87	C₂²	#19097768	1	1	yes	characteristic
88	C₄	—	1256	1	no	—
89	C₄	—	1256	2	no	—
90	C₄	C₂×#14578943	1	2	yes	—
91	C₄	#19097793	1	4	yes	—
92	C₂	—	2512	1	no	—
93	C₂	#23757646	1	1	yes	characteristic
94	C₂	#23757657	1	2	yes	—

	subgroup	G/H
center	C₂²	#19097768
commutator, cosocle	C₄²×C₁₅₇	C₂³
Frattini	C₄²	C₂²×D₁₅₇
Fitting	C₈²×C₁₅₇	C₂
socle	C₂²×C₁₅₇	#127
prime radical	#19097768	C₂²
hypercenter	C₈²	D₁₅₇
hypocenter	C₁₅₇	#1708
LCS	G ▷ C₄²×C₁₅₇ ▷ C₂²×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #23757671	C₂	semidirect
3. #23757624	C₂	semidirect
5. C₈²×C₁₅₇	C₂	semidirect
47. C₁₅₇	#1708	semidirect
53. C₈²	D₁₅₇	semidirect

Maximal subgroups

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

subgroup	index
#23757671	2
#23757646	2
#23757624	2
#23757620	2
C₈²×C₁₅₇	2
#1708	157