Subgroups — #20267605

Order 6592.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₂₄	C₂	1	1	yes	maximal, characteristic
2	#15692957	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₁₂	—	2	1	no	—
5	D₈₂₄	—	2	1	no	—
6	D₈₂₄	C₄	1	2	yes	—
7	#13110089	—	2	1	no	—
8	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
9	C₁₆×C₁₀₃	—	2	1	no	—
10	C₂²×D₁₀₃	—	4	1	no	—
11	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
12	D₄₁₂	—	2	2	no	—
13	D₄₁₂	—	4	1	no	—
14	C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
15	C₈×C₁₀₃	D₄	1	1	yes	characteristic
16	C₁₀₃⋊C₈	—	4	1	no	—
17	C₂²×C₁₀₃	SD₁₆	1	1	yes	characteristic
18	C₂×D₁₀₃	—	4	2	no	—
19	C₂×D₁₀₃	—	8	2	no	—
20	C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₀₃	D₈	1	1	yes	characteristic
22	C₂×C₁₀₃	—	2	1	no	—
23	C₂×C₁₀₃	#102	1	1	yes	characteristic
24	D₁₀₃	—	8	2	no	—
25	C₁₀₃	#361	1	1	yes	characteristic, complemented, Sylow
26	#361	—	103	1	no	maximal, Sylow
27	C₂×D₈	—	103	1	no	—
28	M₃₂	D₁₀₃	1	1	yes	characteristic, complemented
29	#108	—	103	1	no	—
30	C₂×D₄	—	206	1	no	—
31	D₈	—	103	2	no	—
32	D₈	—	206	1	no	—
33	M₁₆	—	206	1	no	—
34	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₂³	—	412	1	no	—
37	D₄	—	412	1	no	—
38	D₄	—	206	2	no	—
39	C₂×C₄	D₄₁₂	1	1	yes	characteristic
40	C₈	—	412	1	no	—
41	C₈	C₄×D₁₀₃	1	1	yes	characteristic
42	C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
43	C₂²	—	824	2	no	—
44	C₂²	—	412	2	no	—
45	C₂²	#13110094	1	1	yes	characteristic
46	C₄	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
47	C₄	D₈₂₄	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	824	2	no	—
50	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	#361
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. #15692957	C₂	semidirect
3. M₃₂×C₁₀₃	C₂	semidirect
25. C₁₀₃	#361	semidirect
28. M₃₂	D₁₀₃	semidirect