Subgroups — #20267602

Order 6592.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693043	C₂	1	1	yes	maximal, characteristic
2	#15692953	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#13110105	—	2	1	no	—
5	Dic₄₁₂	C₄	1	1	yes	characteristic, complemented
6	#13110094	—	2	1	no	—
7	D₈₂₄	C₄	1	1	yes	characteristic, complemented
8	C₄⋊Dic₁₀₃	—	2	1	no	—
9	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
10	C₁₆×C₁₀₃	—	2	1	no	—
11	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
12	C₂²⋊D₁₀₃	—	4	1	no	—
13	C₂×Dic₁₀₃	—	4	1	no	—
14	D₄₁₂	—	2	1	no	—
15	C₄×D₁₀₃	—	4	1	no	—
16	Dic₂₀₆	—	2	1	no	—
17	C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
18	C₈×C₁₀₃	D₄	1	1	yes	characteristic
19	C₂²×C₁₀₃	D₈	1	1	yes	characteristic
20	C₂×D₁₀₃	—	4	1	no	—
21	C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₁₀₃	SD₁₆	1	1	yes	characteristic
23	Dic₁₀₃	—	4	1	no	—
24	Dic₁₀₃	—	8	1	no	—
25	C₂×C₁₀₃	—	2	1	no	—
26	C₂×C₁₀₃	#102	1	1	yes	characteristic
27	D₁₀₃	—	8	1	no	—
28	C₁₀₃	#360	1	1	yes	characteristic, complemented, Sylow
29	#360	—	103	1	no	maximal, Sylow
30	#135	—	103	1	no	—
31	M₃₂	D₁₀₃	1	1	yes	characteristic, complemented
32	#106	—	103	1	no	—
33	#41	—	206	1	no	—
34	Q₁₆	—	103	1	no	—
35	SD₁₆	—	206	1	no	—
36	D₈	—	103	1	no	—
37	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
38	C₄⋊C₄	—	206	1	no	—
39	C₁₆	—	2	1	no	—
40	Q₈	—	206	1	no	—
41	D₄	—	412	1	no	—
42	D₄	—	206	1	no	—
43	C₂×C₄	—	412	1	no	—
44	C₂×C₄	—	412	1	no	—
45	C₂×C₄	D₄₁₂	1	1	yes	characteristic
46	C₈	C₄×D₁₀₃	1	1	yes	characteristic
47	C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
48	C₂²	—	412	1	no	—
49	C₂²	D₈₂₄	1	1	yes	characteristic
50	C₄	—	824	1	no	—
51	C₄	—	412	1	no	—
52	C₄	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
53	C₄	#13110094	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	824	1	no	—
56	C₂	#15692943	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15692943
commutator	C₈×C₁₀₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₃
Fitting	M₃₂×C₁₀₃	C₂
socle	C₂×C₁₀₃	#102
hypercenter	M₃₂	D₁₀₃
hypocenter	C₁₀₃	#360
LCS	G ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #15692953	C₂	semidirect
3. M₃₂×C₁₀₃	C₂	semidirect
5. Dic₄₁₂	C₄	semidirect
7. D₈₂₄	C₄	semidirect
28. C₁₀₃	#360	semidirect
31. M₃₂	D₁₀₃	semidirect