Subgroups — #20267608

Order 6592.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₁₂	C₂	1	1	yes	maximal, characteristic
2	#15692957	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₀₆	—	2	1	no	—
5	Dic₄₁₂	—	2	1	no	—
6	Dic₄₁₂	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	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
11	C₂×Dic₁₀₃	—	4	1	no	—
12	Dic₂₀₆	—	2	2	no	—
13	Dic₂₀₆	—	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	C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₀₃	D₈	1	1	yes	characteristic
20	Dic₁₀₃	—	4	2	no	—
21	C₂×C₁₀₃	—	2	1	no	—
22	C₂×C₁₀₃	#102	1	1	yes	characteristic
23	C₁₀₃	#362	1	1	yes	characteristic, complemented, Sylow
24	#362	—	103	1	no	maximal, Sylow
25	C₂×Q₁₆	—	103	1	no	—
26	M₃₂	D₁₀₃	1	1	yes	characteristic
27	#108	—	103	1	no	—
28	C₂×Q₈	—	206	1	no	—
29	Q₁₆	—	103	2	no	—
30	Q₁₆	—	206	1	no	—
31	M₁₆	—	206	1	no	—
32	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
33	C₁₆	—	2	1	no	—
34	Q₈	—	412	1	no	—
35	Q₈	—	206	2	no	—
36	C₂×C₄	—	412	1	no	—
37	C₂×C₄	D₄₁₂	1	1	yes	characteristic
38	C₈	—	412	1	no	—
39	C₈	C₄×D₁₀₃	1	1	yes	characteristic
40	C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
41	C₂²	#13110094	1	1	yes	characteristic
42	C₄	—	412	2	no	—
43	C₄	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
44	C₄	D₈₂₄	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	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	#362
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
23. C₁₀₃	#362	semidirect