Subgroups — #34115151

Order 20096.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23758194	C₂	1	1	yes	maximal, characteristic
2	#23758137	C₂	1	1	yes	maximal, characteristic
3	#23757651	C₂	1	1	yes	maximal, characteristic
4	C₂×#14578957	—	2	1	no	—
5	C₄⋊#11929441	—	2	1	no	—
6	C₂×Dic₆₂₈	C₄	1	1	yes	characteristic
7	C₂×#14578944	—	2	1	no	—
8	#19097769	—	2	1	no	—
9	C₈×Dic₁₅₇	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₁₅₇	C₄	1	1	yes	characteristic
11	C₂×#11929441	—	4	1	no	—
12	#14578957	—	4	1	no	—
13	C₂×Dic₃₁₄	—	2	1	no	—
14	Dic₆₂₈	—	4	1	no	—
15	#14578944	—	4	1	no	—
16	#14578944	—	4	1	no	—
17	C₂×#11929434	D₄	1	1	yes	characteristic
18	#14578933	—	4	1	no	—
19	#14578933	—	4	1	no	—
20	C₄×Dic₁₅₇	D₄	1	1	yes	characteristic
21	C₂×Q₈×C₁₅₇	—	2	1	no	—
22	Q₁₆×C₁₅₇	—	4	1	no	—
23	C₂×C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
24	#11929441	—	8	1	no	—
25	Dic₃₁₄	—	4	1	no	—
26	Dic₃₁₄	—	4	1	no	—
27	C₂×Dic₁₅₇	—	4	1	no	—
28	C₂×Dic₁₅₇	D₈	1	1	yes	characteristic
29	C₂×Dic₁₅₇	SD₁₆	1	1	yes	characteristic
30	#11929434	D₈	1	1	yes	characteristic
31	#11929434	SD₁₆	1	1	yes	characteristic
32	Q₈×C₁₅₇	—	4	1	no	—
33	Q₈×C₁₅₇	—	4	1	no	—
34	C₂×C₄×C₁₅₇	—	4	1	no	—
35	C₂×C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
36	C₈×C₁₅₇	—	2	1	no	—
37	C₂²×C₁₅₇	#102	1	1	yes	characteristic
38	C₄×C₁₅₇	—	8	1	no	—
39	C₄×C₁₅₇	#100	1	1	yes	characteristic
40	C₄×C₁₅₇	#102	1	1	yes	characteristic
41	Dic₁₅₇	—	2	1	no	—
42	Dic₁₅₇	—	8	1	no	—
43	Dic₁₅₇	SD₃₂	1	1	yes	characteristic
44	Dic₁₅₇	Q₃₂	1	1	yes	characteristic
45	C₂×C₁₅₇	#331	1	1	yes	characteristic
46	C₂×C₁₅₇	#358	1	1	yes	characteristic
47	C₂×C₁₅₇	#362	1	1	yes	characteristic
48	C₁₅₇	#1362	1	1	yes	characteristic, complemented, Sylow
49	#1362	—	157	1	no	maximal, Sylow
50	#494	—	157	1	no	—
51	C₄⋊C₁₆	—	157	1	no	—
52	#335	—	157	1	no	—
53	C₂×Q₁₆	—	314	1	no	—
54	C₂×Q₁₆	—	157	1	no	—
55	C₂×Q₁₆	#10597845	1	1	yes	characteristic
56	C₄⋊Q₈	—	314	1	no	—
57	C₂×C₁₆	—	314	1	no	—
58	C₄⋊C₈	—	314	1	no	—
59	C₄×C₈	—	157	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂×Q₈	—	314	1	no	—
62	Q₁₆	—	4	1	no	—
63	Q₁₆	—	628	1	no	—
64	Q₁₆	—	628	1	no	—
65	Q₁₆	—	628	1	no	—
66	C₂×C₈	—	628	1	no	—
67	C₂×C₈	—	157	1	no	—
68	C₂×C₈	C₂×#10597845	1	1	yes	characteristic
69	C₄⋊C₄	—	628	1	no	—
70	C₄⋊C₄	—	628	1	no	—
71	C₄²	—	157	1	no	—
72	C₁₆	—	628	1	no	—
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	628	1	no	—
76	Q₈	—	628	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	628	1	no	—
79	C₂×C₄	—	157	1	no	—
80	C₂×C₄	—	157	1	no	—
81	C₂×C₄	C₂²⋊#10597845	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	157	1	no	—
84	C₈	—	157	1	no	—
85	C₈	—	1256	1	no	—
86	C₂²	#19097833	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	314	1	no	—
89	C₄	—	157	1	no	—
90	C₄	—	157	1	no	—
91	C₄	—	1256	1	no	—
92	C₄	#19097831	1	1	yes	characteristic
93	C₄	#19097833	1	1	yes	characteristic
94	C₂	#23758131	1	1	yes	characteristic
95	C₂	#23758186	1	1	yes	characteristic
96	C₂	#23758192	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19097833
commutator	C₂×C₈×C₁₅₇	C₂×C₄
Frattini	C₂×C₈	C₂×#10597845
Fitting	C₂×Q₁₆×C₁₅₇	C₄
socle, prime radical	C₂²×C₁₅₇	#102
cosocle	C₈×Dic₁₅₇	C₂²
hypercenter	C₂×Q₁₆	#10597845
hypocenter	C₁₅₇	#1362
LCS	G ▷ C₂×C₈×C₁₅₇ ▷ C₂×C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
48. C₁₅₇	#1362	semidirect

Maximal subgroups

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

subgroup	index
#23758194	2
#23758137	2
#23757651	2
#1362	157