Subgroups — #34115108

Order 20096.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23758170	C₂	1	1	yes	maximal, characteristic
2	#23758141	C₂	1	1	yes	maximal, characteristic
3	#23757528	C₂	1	1	yes	maximal, characteristic
4	#19097850	—	2	1	no	—
5	#19097845	—	2	1	no	—
6	C₂×#14578937	C₂²	1	1	yes	characteristic
7	#19097747	—	2	1	no	—
8	#19097703	C₄	1	1	yes	characteristic, complemented
9	#19097695	—	2	1	no	—
10	C₂×Q₁₆×C₁₅₇	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#10597845	—	4	1	no	—
12	C₂²⋊#10597845	—	4	1	no	—
13	C₄×#10597845	—	2	2	no	—
14	#14578957	—	4	1	no	—
15	C₂×C₄×D₁₅₇	D₄	1	1	yes	characteristic
16	#14578937	—	4	1	no	—
17	C₂×#11929434	D₄	1	1	yes	characteristic
18	C₄⋊Dic₁₅₇	—	2	1	no	—
19	#14578933	—	4	1	no	—
20	#14578931	—	4	1	no	—
21	C₂×Q₈×C₁₅₇	—	2	1	no	—
22	Q₁₆×C₁₅₇	—	4	1	no	—
23	C₂×C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
24	C₂×#10597845	—	4	2	no	—
25	C₂²×D₁₅₇	D₈	1	1	yes	characteristic
26	C₂×Dic₁₅₇	—	4	1	no	—
27	C₂×Dic₁₅₇	SD₁₆	1	1	yes	characteristic
28	C₄×D₁₅₇	—	2	1	no	—
29	C₄×D₁₅₇	—	2	1	no	—
30	#11929434	—	2	1	no	—
31	Q₈×C₁₅₇	—	4	1	no	—
32	Q₈×C₁₅₇	—	4	1	no	—
33	C₂×C₄×C₁₅₇	—	4	1	no	—
34	C₂×C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
35	C₈×C₁₅₇	—	2	1	no	—
36	C₂²×C₁₅₇	#102	1	1	yes	characteristic
37	C₂×D₁₅₇	—	2	1	no	—
38	C₂×D₁₅₇	—	4	1	no	—
39	#10597845	—	8	2	no	—
40	C₄×C₁₅₇	—	8	1	no	—
41	C₄×C₁₅₇	#99	1	1	yes	characteristic
42	C₄×C₁₅₇	#104	1	1	yes	characteristic
43	Dic₁₅₇	—	2	1	no	—
44	Dic₁₅₇	—	8	1	no	—
45	C₂×C₁₅₇	—	2	1	no	—
46	C₂×C₁₅₇	#327	1	1	yes	characteristic
47	D₁₅₇	—	4	1	no	—
48	C₁₅₇	#1340	1	1	yes	characteristic, complemented, Sylow
49	#1340	—	157	1	no	maximal, Sylow
50	#470	—	157	1	no	—
51	#349	—	157	1	no	—
52	H(3,ℤ/4)	—	157	1	no	—
53	C₂×Q₁₆	#10597845	1	1	yes	characteristic, complemented
54	C₂×M₁₆	—	157	1	no	—
55	C₂²⋊Q₈	—	314	1	no	—
56	#117	—	314	1	no	—
57	M₃₂	—	314	1	no	—
58	#106	—	157	1	no	—
59	#103	—	314	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂²×C₄	—	157	1	no	—
62	Q₁₆	—	4	1	no	—
63	M₁₆	—	628	1	no	—
64	C₂×C₈	—	157	1	no	—
65	C₂×C₈	C₂×#10597845	1	1	yes	characteristic
66	C₄⋊C₄	—	314	1	no	—
67	C₄⋊C₄	—	628	1	no	—
68	C₄⋊C₄	—	628	1	no	—
69	C₂²⋊C₄	—	628	1	no	—
70	C₂²⋊C₄	—	628	1	no	—
71	C₄²	—	314	2	no	—
72	C₁₆	—	628	1	no	—
73	C₂³	—	157	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	4	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	314	1	no	—
78	C₂×C₄	—	314	1	no	—
79	C₂×C₄	—	628	2	no	—
80	C₂×C₄	—	628	1	no	—
81	C₂×C₄	—	157	1	no	—
82	C₂×C₄	C₂²⋊#10597845	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	314	1	no	—
85	C₂²	—	314	1	no	—
86	C₂²	—	628	1	no	—
87	C₂²	#19097833	1	1	yes	characteristic
88	C₄	—	8	1	no	—
89	C₄	—	314	1	no	—
90	C₄	—	1256	1	no	—
91	C₄	—	1256	2	no	—
92	C₄	#19097829	1	1	yes	characteristic
93	C₄	#19097835	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	628	1	no	—
96	C₂	#23758124	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23758124
commutator	C₂×C₈×C₁₅₇	C₂×C₄
Frattini	C₂×C₈	C₂×#10597845
Fitting	C₂×Q₁₆×C₁₅₇	C₄
socle	C₂×C₁₅₇	#327
prime radical	C₂²×D₁₅₇	D₈
cosocle	C₂×#14578937	C₂²
hypercenter	C₂×Q₁₆	#10597845
hypocenter	C₁₅₇	#1340
LCS	G ▷ C₂×C₈×C₁₅₇ ▷ C₂×C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
8. #19097703	C₄	semidirect
10. C₂×Q₁₆×C₁₅₇	C₄	semidirect
48. C₁₅₇	#1340	semidirect
53. C₂×Q₁₆	#10597845	semidirect

Maximal subgroups

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

subgroup	index
#23758170	2
#23758141	2
#23757528	2
#1340	157