Subgroups — #23756462

Order 10016.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆₂₆	C₂	1	1	yes	maximal, characteristic
2	#19097540	C₂	1	2	yes	maximal
3	C₄×Dic₃₁₃	C₂	1	2	yes	maximal
4	C₄×Dic₃₁₃	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₄×C₃₁₃	C₂	1	1	yes	maximal, characteristic
6	Dic₆₂₆	C₄	1	4	yes	complemented
7	C₂×Dic₃₁₃	C₂²	1	1	yes	characteristic
8	C₂×Dic₃₁₃	C₂²	1	2	yes	—
9	C₂×Dic₃₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₃₁₃	C₂²	1	2	yes	—
11	C₂×C₄×C₃₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₃₁₃	C₂³	1	1	yes	characteristic
13	C₄×C₃₁₃	—	2	2	no	—
14	C₄×C₃₁₃	C₂×C₄	1	2	yes	—
15	Dic₃₁₃	—	2	1	no	—
16	Dic₃₁₃	C₂×C₄	1	4	yes	—
17	Dic₃₁₃	Q₈	1	2	yes	complemented
18	C₂×C₃₁₃	C₂²×C₄	1	1	yes	characteristic
19	C₂×C₃₁₃	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₃₁₃	#41	1	1	yes	characteristic
21	C₃₁₃	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
22	C₄×Q₈	—	313	1	no	maximal, Sylow
23	C₂×Q₈	—	313	1	no	—
24	C₄⋊C₄	—	313	2	no	—
25	C₄⋊C₄	D₃₁₃	1	1	yes	characteristic
26	C₄²	—	313	2	no	—
27	C₄²	—	313	1	no	—
28	Q₈	—	313	4	no	—
29	C₂×C₄	—	313	1	no	—
30	C₂×C₄	—	313	2	no	—
31	C₂×C₄	—	313	1	no	—
32	C₂×C₄	C₂×D₃₁₃	1	2	yes	—
33	C₂×C₄	C₂×D₃₁₃	1	1	yes	characteristic
34	C₂²	C₂²×D₃₁₃	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	313	4	no	—
37	C₄	—	313	2	no	—
38	C₄	—	626	1	no	—
39	C₄	C₄×D₃₁₃	1	2	yes	—
40	C₂	C₂×C₄×D₃₁₃	1	1	yes	characteristic
41	C₂	Q₈×D₃₁₃	1	1	yes	characteristic
42	C₂	#19097560	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃₁₃
commutator	C₂×C₃₁₃	C₂²×C₄
Fitting	C₄⋊C₄×C₃₁₃	C₂
socle, prime radical, cosocle	C₂²×C₃₁₃	C₂³
hypercenter	C₄⋊C₄	D₃₁₃
hypocenter	C₃₁₃	C₄×Q₈
LCS	G ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. Dic₆₂₆	C₄	semidirect
17. Dic₃₁₃	Q₈	semidirect
21. C₃₁₃	C₄×Q₈	semidirect