Subgroups — #20267618

Order 6592.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₀₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#15692955	C₂	1	1	yes	maximal, characteristic
3	#107×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₀₃	—	2	1	no	—
5	C₁₀₃⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₀₃	—	2	1	no	—
8	C₂×C₄×C₁₀₃	—	4	1	no	—
9	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
10	C₂×Dic₁₀₃	—	4	1	no	—
11	C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₀₃	Q₈	1	1	yes	characteristic
13	C₂²×C₁₀₃	D₈	1	1	yes	characteristic
14	C₄×C₁₀₃	—	8	1	no	—
15	C₄×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₀₃	Q₁₆	1	1	yes	characteristic
17	Dic₁₀₃	—	8	1	no	—
18	C₂×C₁₀₃	#107	1	1	yes	characteristic
19	C₂×C₁₀₃	SD₃₂	1	1	yes	characteristic
20	C₂×C₁₀₃	SD₃₂	1	1	yes	characteristic
21	C₁₀₃	#367	1	1	yes	characteristic, complemented, Sylow
22	#367	—	103	1	no	maximal, Sylow
23	C₂×C₁₆	—	103	1	no	—
24	#107	—	103	1	no	—
25	#107	D₁₀₃	1	1	yes	characteristic
26	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	206	1	no	—
29	C₁₆	—	103	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	412	1	no	—
32	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
33	C₈	Dic₂₀₆	1	1	yes	characteristic
34	C₈	C₄×D₁₀₃	1	1	yes	characteristic
35	C₂²	#13110090	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	824	1	no	—
38	C₄	Dic₁₀₃⋊C₄	1	1	yes	characteristic
39	C₄	#13110095	1	1	yes	characteristic
40	C₂	#15692954	1	1	yes	characteristic
41	C₂	#15692964	1	1	yes	characteristic
42	C₂	#15692965	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13110090
commutator	C₈×C₁₀₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₃
Fitting	#107×C₁₀₃	C₂
socle	C₂²×C₁₀₃	D₈
hypercenter	#107	D₁₀₃
hypocenter	C₁₀₃	#367
LCS	G ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. C₁₀₃⋊C₁₆	C₄	semidirect
21. C₁₀₃	#367	semidirect