Subgroups — #20268195

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	#15692955	C₂	1	1	yes	maximal, characteristic
3	#15692954	C₂	1	2	yes	maximal
4	C₈×Dic₁₀₃	C₂	1	1	yes	maximal, characteristic
5	#107×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	1	yes	characteristic
17	C₂×Dic₁₀₃	D₄	1	1	yes	characteristic
18	Dic₂₀₆	—	4	4	no	—
19	C₈×C₁₀₃	Q₈	1	2	yes	complemented
20	C₁₀₃⋊C₈	Q₈	1	2	yes	complemented
21	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
22	C₄×C₁₀₃	—	4	2	no	—
23	C₄×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
25	Dic₁₀₃	—	4	2	no	—
26	Dic₁₀₃	D₈	1	2	yes	—
27	Dic₁₀₃	Q₁₆	1	2	yes	—
28	C₂×C₁₀₃	C₄⋊Q₈	1	1	yes	characteristic
29	C₂×C₁₀₃	C₂×D₈	1	1	yes	characteristic
30	C₂×C₁₀₃	C₂×Q₁₆	1	1	yes	characteristic
31	C₁₀₃	#500	1	1	yes	characteristic, complemented, Sylow
32	#500	—	103	1	no	maximal, Sylow
33	C₄⋊Q₈	—	103	2	no	—
34	#107	—	103	1	no	—
35	#107	—	103	2	no	—
36	#107	D₁₀₃	1	1	yes	characteristic
37	C₄×C₈	—	103	1	no	—
38	C₂×Q₈	—	206	2	no	—
39	C₂×C₈	—	103	1	no	—
40	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
41	C₄⋊C₄	—	103	2	no	—
42	C₄⋊C₄	—	206	2	no	—
43	C₄⋊C₄	C₂×D₁₀₃	1	2	yes	—
44	C₄²	—	103	1	no	—
45	Q₈	—	412	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	103	1	no	—
48	C₂×C₄	—	103	1	no	—
49	C₂×C₄	—	206	2	no	—
50	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
51	C₈	—	103	2	no	—
52	C₈	Dic₂₀₆	1	2	yes	complemented
53	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	103	2	no	—
56	C₄	—	103	2	no	—
57	C₄	—	412	2	no	—
58	C₄	Q₈×D₁₀₃	1	1	yes	characteristic
59	C₄	C₂×Dic₂₀₆	1	1	yes	characteristic
60	C₂	#15693020	1	1	yes	characteristic
61	C₂	D₈×D₁₀₃	1	1	yes	characteristic
62	C₂	Q₁₆×D₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₃
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#107×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	#107	D₁₀₃
hypocenter	C₁₀₃	#500
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
19. C₈×C₁₀₃	Q₈	semidirect
20. C₁₀₃⋊C₈	Q₈	semidirect
31. C₁₀₃	#500	semidirect
52. C₈	Dic₂₀₆	semidirect