Subgroups — #23756529

Order 10016.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097562	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₃₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#19097551	C₂	1	1	yes	maximal, characteristic, complemented
4	#19097550	C₂	1	1	yes	maximal, characteristic, complemented
5	#19097548	C₂	1	1	yes	maximal, characteristic, complemented
6	#19097544	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₁₆×C₃₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₆₂₆	—	2	1	no	—
9	Dic₆₂₆	C₂²	1	1	yes	characteristic
10	D₁₂₅₂	—	2	1	no	—
11	D₁₂₅₂	C₂²	1	1	yes	characteristic
12	C₄×D₃₁₃	—	2	1	no	—
13	C₄×D₃₁₃	—	2	1	no	—
14	C₄×D₃₁₃	C₂²	1	1	yes	characteristic
15	#14578809	C₂²	1	1	yes	characteristic
16	Q₈×C₃₁₃	C₂²	1	1	yes	characteristic
17	Q₈×C₃₁₃	C₂²	1	1	yes	characteristic
18	C₈×C₃₁₃	C₂²	1	1	yes	characteristic
19	C₂×D₃₁₃	—	2	1	no	—
20	C₂×D₃₁₃	D₄	1	1	yes	characteristic
21	C₄×C₃₁₃	—	2	1	no	—
22	C₄×C₃₁₃	—	2	1	no	—
23	C₄×C₃₁₃	C₂³	1	1	yes	characteristic
24	Dic₃₁₃	—	2	1	no	—
25	Dic₃₁₃	D₄	1	1	yes	characteristic
26	C₂×C₃₁₃	C₂×D₄	1	1	yes	characteristic
27	D₃₁₃	—	2	1	no	—
28	D₃₁₃	—	4	1	no	—
29	C₃₁₃	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	313	1	no	maximal, Sylow
31	#41	—	313	1	no	—
32	C₂×Q₈	—	313	1	no	—
33	Q₁₆	—	313	1	no	—
34	Q₁₆	D₃₁₃	1	1	yes	characteristic, complemented
35	SD₁₆	—	313	1	no	—
36	SD₁₆	—	313	1	no	—
37	M₁₆	—	313	1	no	—
38	Q₈	—	313	1	no	—
39	Q₈	—	626	1	no	—
40	Q₈	C₂×D₃₁₃	1	1	yes	characteristic
41	Q₈	C₂×D₃₁₃	1	1	yes	characteristic
42	D₄	—	313	1	no	—
43	D₄	—	626	1	no	—
44	C₂×C₄	—	313	1	no	—
45	C₂×C₄	—	626	1	no	—
46	C₂×C₄	—	626	1	no	—
47	C₈	—	313	1	no	—
48	C₈	C₂×D₃₁₃	1	1	yes	characteristic
49	C₂²	—	313	1	no	—
50	C₂²	—	626	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	313	1	no	—
54	C₄	—	626	1	no	—
55	C₄	C₂²×D₃₁₃	1	1	yes	characteristic
56	C₂	—	626	1	no	—
57	C₂	—	1252	1	no	—
58	C₂	D₄×D₃₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₃₁₃
commutator, cosocle	C₄×C₃₁₃	C₂³
Frattini	C₄	C₂²×D₃₁₃
Fitting	Q₁₆×C₃₁₃	C₂
socle	C₂×C₃₁₃	C₂×D₄
prime radical	#19097562	C₂
hypercenter	Q₁₆	D₃₁₃
hypocenter	C₃₁₃	#137
LCS	G ▷ C₄×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×D₃₁₃	C₂	semidirect
3. #19097551	C₂	semidirect
4. #19097550	C₂	semidirect
5. #19097548	C₂	semidirect
6. #19097544	C₂	semidirect
7. Q₁₆×C₃₁₃	C₂	semidirect
29. C₃₁₃	#137	semidirect
34. Q₁₆	D₃₁₃	semidirect