Subgroups — #34095067

Order 20032.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23756570	C₂	1	1	yes	maximal, characteristic, complemented
2	#23756568	C₂	1	1	yes	maximal, characteristic, complemented
3	#23756520	C₂	1	1	yes	maximal, characteristic
4	#19097571	—	2	1	no	—
5	#19097564	—	2	1	no	—
6	#19097562	—	2	1	no	—
7	#19097548	—	2	1	no	—
8	D₂₅₀₄	C₄	1	1	yes	characteristic
9	C₈×D₃₁₃	C₂²	1	1	yes	characteristic
10	Q₁₆×C₃₁₃	C₄	1	1	yes	characteristic
11	#14578816	—	4	1	no	—
12	D₁₂₅₂	—	2	1	no	—
13	D₁₂₅₂	—	4	1	no	—
14	C₄×D₃₁₃	—	4	1	no	—
15	C₄×D₃₁₃	D₄	1	1	yes	characteristic
16	#14578809	D₄	1	1	yes	characteristic
17	Q₈×C₃₁₃	—	2	1	no	—
18	C₈×C₃₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×D₃₁₃	—	4	1	no	—
20	C₂×D₃₁₃	SD₁₆	1	1	yes	characteristic
21	C₄×C₃₁₃	—	4	1	no	—
22	C₄×C₃₁₃	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₃₁₃	D₈	1	1	yes	characteristic
24	C₂×C₃₁₃	#102	1	1	yes	characteristic
25	D₃₁₃	—	2	1	no	—
26	D₃₁₃	—	8	1	no	—
27	C₃₁₃	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	313	1	no	maximal, Sylow
29	#135	—	313	1	no	—
30	C₂×C₁₆	—	313	1	no	—
31	#108	—	313	1	no	—
32	#41	—	626	1	no	—
33	Q₁₆	#11929411	1	1	yes	characteristic
34	SD₁₆	—	626	1	no	—
35	D₈	—	313	1	no	—
36	M₁₆	—	626	1	no	—
37	C₂×C₈	—	313	1	no	—
38	C₁₆	—	626	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	626	1	no	—
41	D₄	—	1252	1	no	—
42	C₂×C₄	—	313	1	no	—
43	C₂×C₄	—	1252	1	no	—
44	C₈	—	313	1	no	—
45	C₈	—	1252	1	no	—
46	C₈	C₂×#11929411	1	1	yes	characteristic
47	C₂²	—	313	1	no	—
48	C₂²	—	1252	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	313	1	no	—
51	C₄	C₂²⋊#11929411	1	1	yes	characteristic
52	C₂	—	626	1	no	—
53	C₂	—	2504	1	no	—
54	C₂	#23756559	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23756559
commutator	C₈×C₃₁₃	C₂×C₄
Frattini	C₈	C₂×#11929411
Fitting	Q₁₆×C₃₁₃	C₄
socle	C₂×C₃₁₃	#102
prime radical	#23756520	C₂
cosocle	C₈×D₃₁₃	C₂²
hypercenter	Q₁₆	#11929411
hypocenter	C₃₁₃	#359
LCS	G ▷ C₈×C₃₁₃ ▷ C₄×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #23756570	C₂	semidirect
2. #23756568	C₂	semidirect
27. C₃₁₃	#359	semidirect

Maximal subgroups

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

subgroup	index
#23756570	2
#23756568	2
#23756520	2
#359	313