Subgroups — #34115059

Order 20096.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#14578957	C₂	1	2	yes	maximal, complemented
2	#23757241	C₂	1	1	yes	maximal, characteristic
3	C₂×#14578957	—	2	2	no	—
4	C₂×#14578954	C₄	1	1	yes	characteristic
5	C₂²×#11929434	C₂²	1	1	yes	characteristic
6	#19097683	—	2	2	no	—
7	C₂×M₁₆×C₁₅₇	C₄	1	1	yes	characteristic
8	#14578957	—	4	2	no	—
9	#14578954	—	4	1	no	—
10	#14578954	—	4	1	no	—
11	C₂×Dic₃₁₄	C₈	1	1	yes	characteristic
12	C₂×D₆₂₈	C₈	1	1	yes	characteristic
13	C₂×C₂²⋊D₁₅₇	—	2	1	no	—
14	C₂×C₄×D₁₅₇	—	2	1	no	—
15	C₂×#11929434	—	4	1	no	—
16	C₂×#11929434	D₄	1	2	yes	—
17	C₂²×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
18	M₁₆×C₁₅₇	—	4	1	no	—
19	C₂×C₈×C₁₅₇	—	2	1	no	—
20	C₂²×D₁₅₇	—	2	1	no	—
21	Dic₃₁₄	—	4	1	no	—
22	D₆₂₈	—	4	1	no	—
23	C₂²⋊D₁₅₇	—	4	2	no	—
24	C₂×Dic₁₅₇	—	2	1	no	—
25	C₄×D₁₅₇	—	4	1	no	—
26	C₄×D₁₅₇	—	4	1	no	—
27	#11929434	—	2	2	no	—
28	C₂³×C₁₅₇	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₁₅₇	—	2	1	no	—
30	C₂×C₄×C₁₅₇	—	2	1	no	—
31	C₂×C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
33	C₈×C₁₅₇	—	4	1	no	—
34	C₂²×C₁₅₇	—	2	1	no	—
35	C₂²×C₁₅₇	—	2	2	no	—
36	C₂²×C₁₅₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×D₁₅₇	—	4	1	no	—
38	C₂×D₁₅₇	—	4	2	no	—
39	C₄×C₁₅₇	—	2	1	no	—
40	C₄×C₁₅₇	#99	1	1	yes	characteristic
41	C₄×C₁₅₇	#100	1	1	yes	characteristic
42	Dic₁₅₇	—	4	1	no	—
43	C₂×C₁₅₇	—	4	1	no	—
44	C₂×C₁₅₇	#323	1	1	yes	characteristic
45	C₂×C₁₅₇	#350	1	2	yes	—
46	D₁₅₇	—	8	1	no	—
47	C₁₅₇	#1315	1	1	yes	characteristic, complemented, Sylow
48	#1315	—	157	1	no	maximal, Sylow
49	#408	—	157	1	no	—
50	C₂²⋊C₁₆	—	157	2	no	—
51	C₂×#41	—	157	1	no	—
52	C₂×M₁₆	#10597845	1	1	yes	characteristic
53	C₂²×C₈	—	157	1	no	—
54	C₂×C₁₆	—	314	2	no	—
55	C₂²⋊C₈	—	314	2	no	—
56	#41	—	628	1	no	—
57	#41	—	628	1	no	—
58	C₂×Q₈	—	157	1	no	—
59	C₂×D₄	—	314	1	no	—
60	C₂×D₄	—	157	1	no	—
61	C₂²×C₄	—	314	1	no	—
62	C₂²×C₄	C₂×#10597845	1	1	yes	characteristic
63	M₁₆	—	4	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	628	1	no	—
66	C₂×C₈	—	157	2	no	—
67	C₁₆	—	628	2	no	—
68	C₂³	—	314	1	no	—
69	C₂³	#14578964	1	1	yes	characteristic
70	Q₈	—	628	1	no	—
71	D₄	—	628	1	no	—
72	D₄	—	628	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	314	1	no	—
76	C₂×C₄	—	628	1	no	—
77	C₂×C₄	—	628	1	no	—
78	C₂×C₄	C₂²⋊#10597845	1	1	yes	characteristic
79	C₂×C₄	D₁₅₇⋊C₈	1	1	yes	characteristic
80	C₈	—	4	1	no	—
81	C₈	—	314	2	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	2	2	no	—
84	C₂²	—	628	1	no	—
85	C₂²	—	628	2	no	—
86	C₂²	#19097828	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	628	1	no	—
89	C₄	#19097830	1	1	yes	characteristic
90	C₄	#19097831	1	1	yes	characteristic
91	C₂	—	4	1	no	—
92	C₂	—	1256	1	no	—
93	C₂	#23758117	1	1	yes	characteristic
94	C₂	#23758172	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊#10597845
commutator	C₂×C₄×C₁₅₇	C₂×C₈
Frattini	C₂²×C₄	C₂×#10597845
Fitting	C₂×M₁₆×C₁₅₇	C₄
socle	C₂²×C₁₅₇	C₂²⋊C₈
prime radical	C₂×#14578954	C₄
cosocle	C₂²×#11929434	C₂²
hypercenter	C₂×M₁₆	#10597845
hypocenter	C₁₅₇	#1315
LCS	G ▷ C₂×C₄×C₁₅₇ ▷ C₂²×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²⋊#14578957	C₂	semidirect
47. C₁₅₇	#1315	semidirect

Maximal subgroups

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

subgroup	index
C₂²⋊#14578957	2
#23757241	2
#1315	157