Subgroups — #20267597

Order 6592.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693043	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₀₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#108×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#13110105	—	2	1	no	—
5	Dic₄₁₂	C₄	1	1	yes	characteristic
6	#13110094	—	2	1	no	—
7	D₈₂₄	C₄	1	1	yes	characteristic
8	C₁₀₃⋊C₁₆	—	2	1	no	—
9	M₁₆×C₁₀₃	—	2	1	no	—
10	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
12	C₂²⋊D₁₀₃	—	4	1	no	—
13	D₄₁₂	—	2	1	no	—
14	C₄×D₁₀₃	—	4	1	no	—
15	Dic₂₀₆	—	2	1	no	—
16	C₈×C₁₀₃	—	4	1	no	—
17	C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
18	C₈×C₁₀₃	D₄	1	1	yes	characteristic
19	C₂²×C₁₀₃	SD₁₆	1	1	yes	characteristic
20	C₂×D₁₀₃	—	4	1	no	—
21	C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₁₀₃	D₈	1	1	yes	characteristic
23	Dic₁₀₃	—	4	1	no	—
24	C₂×C₁₀₃	—	2	1	no	—
25	C₂×C₁₀₃	#102	1	1	yes	characteristic
26	D₁₀₃	—	8	1	no	—
27	C₁₀₃	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	103	1	no	maximal, Sylow
29	#135	—	103	1	no	—
30	C₂×C₁₆	—	103	1	no	—
31	#108	D₁₀₃	1	1	yes	characteristic, complemented
32	#41	—	206	1	no	—
33	Q₁₆	—	103	1	no	—
34	SD₁₆	—	206	1	no	—
35	D₈	—	103	1	no	—
36	M₁₆	—	2	1	no	—
37	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
38	C₁₆	—	206	1	no	—
39	Q₈	—	206	1	no	—
40	D₄	—	412	1	no	—
41	D₄	—	206	1	no	—
42	C₂×C₄	—	412	1	no	—
43	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
44	C₈	—	4	1	no	—
45	C₈	C₄×D₁₀₃	1	1	yes	characteristic
46	C₈	D₄₁₂	1	1	yes	characteristic
47	C₂²	—	412	1	no	—
48	C₂²	#13110092	1	1	yes	characteristic
49	C₄	—	412	1	no	—
50	C₄	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
51	C₄	#13110090	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	824	1	no	—
54	C₂	#15692941	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13110090
commutator	C₈×C₁₀₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₃
Fitting	#108×C₁₀₃	C₂
socle	C₂×C₁₀₃	#102
hypercenter	#108	D₁₀₃
hypocenter	C₁₀₃	#359
LCS	G ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₀₃⋊C₁₆	C₂	semidirect
3. #108×C₁₀₃	C₂	semidirect
27. C₁₀₃	#359	semidirect
31. #108	D₁₀₃	semidirect