Subgroups — #20268188

Order 6592.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693020	C₂	1	2	yes	maximal
2	#15692953	C₂	1	1	yes	maximal, characteristic
3	#15692952	C₂	1	2	yes	maximal
4	C₈×Dic₁₀₃	C₂	1	1	yes	maximal, characteristic
5	#106×C₁₀₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₀₆	—	2	2	no	—
7	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₁₀₃	C₂²	1	2	yes	—
9	Dic₁₀₃⋊C₄	—	2	2	no	—
10	C₄×Dic₁₀₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
13	C₂×C₄×C₁₀₃	—	2	2	no	—
14	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
15	C₂×Dic₁₀₃	—	2	2	no	—
16	C₂×Dic₁₀₃	D₄	1	2	yes	—
17	Dic₂₀₆	—	4	4	no	—
18	C₈×C₁₀₃	Q₈	1	2	yes	complemented
19	C₁₀₃⋊C₈	Q₈	1	2	yes	complemented
20	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
21	C₄×C₁₀₃	—	4	2	no	—
22	C₄×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
24	Dic₁₀₃	—	4	2	no	—
25	Dic₁₀₃	SD₁₆	1	4	yes	—
26	C₂×C₁₀₃	C₄⋊Q₈	1	1	yes	characteristic
27	C₂×C₁₀₃	C₂×SD₁₆	1	2	yes	—
28	C₁₀₃	#498	1	1	yes	characteristic, complemented, Sylow
29	#498	—	103	1	no	maximal, Sylow
30	C₄⋊Q₈	—	103	2	no	—
31	#106	—	103	1	no	—
32	#106	—	103	2	no	—
33	#106	D₁₀₃	1	1	yes	characteristic
34	C₄×C₈	—	103	1	no	—
35	C₂×Q₈	—	206	2	no	—
36	C₂×C₈	—	103	1	no	—
37	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
38	C₄⋊C₄	—	103	2	no	—
39	C₄⋊C₄	—	206	2	no	—
40	C₄⋊C₄	C₂×D₁₀₃	1	2	yes	—
41	C₄²	—	103	1	no	—
42	Q₈	—	412	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	103	2	no	—
45	C₂×C₄	—	206	2	no	—
46	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
47	C₈	—	103	2	no	—
48	C₈	Dic₂₀₆	1	2	yes	complemented
49	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	103	4	no	—
52	C₄	—	412	2	no	—
53	C₄	Q₈×D₁₀₃	1	1	yes	characteristic
54	C₄	C₂×Dic₂₀₆	1	1	yes	characteristic
55	C₂	#15693020	1	1	yes	characteristic
56	C₂	SD₁₆×D₁₀₃	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₀₃
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#106×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	#106	D₁₀₃
hypocenter	C₁₀₃	#498
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
18. C₈×C₁₀₃	Q₈	semidirect
19. C₁₀₃⋊C₈	Q₈	semidirect
28. C₁₀₃	#498	semidirect
48. C₈	Dic₂₀₆	semidirect