Subgroups — #23756559

Order 10016.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097569	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊#11929411	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×D₃₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11929411	—	2	1	no	—
5	#14578816	—	2	1	no	—
6	C₂²×D₃₁₃	—	2	1	no	—
7	D₁₂₅₂	C₄	1	1	yes	characteristic, complemented
8	C₂²⋊D₃₁₃	—	2	1	no	—
9	C₄×D₃₁₃	C₂²	1	1	yes	characteristic
10	D₄×C₃₁₃	C₄	1	1	yes	characteristic, complemented
11	C₂²×C₃₁₃	—	2	1	no	—
12	C₂×D₃₁₃	—	2	1	no	—
13	C₂×D₃₁₃	—	4	1	no	—
14	C₂×D₃₁₃	—	4	1	no	—
15	C₂×D₃₁₃	D₄	1	1	yes	characteristic
16	#11929411	—	4	1	no	—
17	C₄×C₃₁₃	C₂×C₄	1	1	yes	characteristic
18	Dic₃₁₃	D₄	1	1	yes	characteristic
19	C₂×C₃₁₃	—	4	1	no	—
20	C₂×C₃₁₃	C₂²⋊C₄	1	1	yes	characteristic
21	D₃₁₃	—	4	1	no	—
22	D₃₁₃	D₈	1	1	yes	characteristic
23	D₃₁₃	SD₁₆	1	1	yes	characteristic
24	C₃₁₃	#102	1	1	yes	characteristic, complemented, Sylow
25	#102	—	313	1	no	maximal, Sylow
26	C₂×D₄	—	313	1	no	—
27	C₂×C₈	—	313	1	no	—
28	C₄⋊C₄	—	313	1	no	—
29	C₂³	—	626	1	no	—
30	D₄	—	313	1	no	—
31	D₄	—	626	1	no	—
32	D₄	#11929411	1	1	yes	characteristic, complemented
33	C₂×C₄	—	313	1	no	—
34	C₂×C₄	—	626	1	no	—
35	C₈	—	626	1	no	—
36	C₂²	—	2	1	no	—
37	C₂²	—	313	1	no	—
38	C₂²	—	626	1	no	—
39	C₂²	—	1252	1	no	—
40	C₂²	—	1252	1	no	—
41	C₄	—	313	1	no	—
42	C₄	—	1252	1	no	—
43	C₄	C₂×#11929411	1	1	yes	characteristic
44	C₂	—	4	1	no	—
45	C₂	—	313	1	no	—
46	C₂	—	313	1	no	—
47	C₂	—	1252	1	no	—
48	C₂	C₂²⋊#11929411	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#11929411
commutator	C₄×C₃₁₃	C₂×C₄
Frattini	C₄	C₂×#11929411
Fitting	D₄×C₃₁₃	C₄
socle	C₂×C₃₁₃	C₂²⋊C₄
prime radical	D₄×D₃₁₃	C₂
cosocle	C₄×D₃₁₃	C₂²
hypercenter	D₄	#11929411
hypocenter	C₃₁₃	#102
LCS	G ▷ C₄×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. #19097569	C₂	semidirect
2. C₄⋊#11929411	C₂	semidirect
7. D₁₂₅₂	C₄	semidirect
10. D₄×C₃₁₃	C₄	semidirect
24. C₃₁₃	#102	semidirect
32. D₄	#11929411	semidirect