Subgroups — #20268062

Order 6592.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693049	C₂	1	2	yes	maximal, complemented
2	C₂×D₈₂₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#15693027	C₂	1	1	yes	maximal, characteristic, complemented
4	#15692937	C₂	1	2	yes	maximal, complemented
5	#108×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#13110105	C₂²	1	1	yes	characteristic
7	C₂×D₄₁₂	C₂²	1	2	yes	—
8	#13110094	—	2	2	no	—
9	D₈₂₄	—	2	2	no	—
10	D₈₂₄	—	2	1	no	—
11	D₈₂₄	—	2	1	no	—
12	#13110089	C₂²	1	1	yes	characteristic
13	#13110088	—	2	1	no	—
14	C₈×D₁₀₃	—	2	1	no	—
15	M₁₆×C₁₀₃	C₂²	1	2	yes	—
16	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
17	C₂²×D₁₀₃	—	2	2	no	—
18	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
19	C₂²⋊D₁₀₃	—	2	1	no	—
20	D₄₁₂	—	2	2	no	—
21	D₄₁₂	—	2	2	no	—
22	D₄₁₂	D₄	1	1	yes	characteristic
23	C₄×D₁₀₃	—	2	1	no	—
24	Dic₂₀₆	D₄	1	1	yes	characteristic
25	C₈×C₁₀₃	—	2	2	no	—
26	C₈×C₁₀₃	D₄	1	1	yes	characteristic
27	C₈×C₁₀₃	D₄	1	1	yes	characteristic
28	C₁₀₃⋊C₈	—	2	1	no	—
29	C₂²×C₁₀₃	#41	1	1	yes	characteristic
30	C₂×D₁₀₃	—	2	1	no	—
31	C₂×D₁₀₃	—	4	2	no	—
32	C₂×D₁₀₃	—	8	2	no	—
33	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
34	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
35	Dic₁₀₃	—	2	1	no	—
36	C₂×C₁₀₃	—	2	1	no	—
37	C₂×C₁₀₃	#121	1	1	yes	characteristic
38	D₁₀₃	—	4	1	no	—
39	D₁₀₃	—	8	2	no	—
40	C₁₀₃	#472	1	1	yes	characteristic, complemented, Sylow
41	#472	—	103	1	no	maximal, Sylow
42	AGL(1,ℤ/8)	—	103	2	no	—
43	C₂×D₈	—	103	1	no	—
44	#131	—	103	1	no	—
45	#108	D₁₀₃	1	1	yes	characteristic, complemented
46	#100	—	103	2	no	—
47	#41	—	103	1	no	—
48	C₂×D₄	—	103	2	no	—
49	SD₁₆	—	206	2	no	—
50	D₈	—	206	2	no	—
51	D₈	—	206	1	no	—
52	D₈	—	206	1	no	—
53	M₁₆	—	103	1	no	—
54	M₁₆	—	206	1	no	—
55	M₁₆	C₂×D₁₀₃	1	2	yes	—
56	C₂×C₈	—	206	1	no	—
57	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
58	C₂³	—	206	2	no	—
59	Q₈	—	103	1	no	—
60	D₄	—	103	1	no	—
61	D₄	—	206	1	no	—
62	D₄	—	206	2	no	—
63	D₄	—	206	2	no	—
64	C₂×C₄	—	206	1	no	—
65	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₈	—	206	1	no	—
68	C₈	D₄₁₂	1	1	yes	characteristic
69	C₈	D₄₁₂	1	1	yes	characteristic
70	C₂²	—	824	2	no	—
71	C₂²	—	412	2	no	—
72	C₂²	—	206	1	no	—
73	C₂²	#13110106	1	1	yes	characteristic
74	C₄	—	206	1	no	—
75	C₄	D₄×D₁₀₃	1	1	yes	characteristic
76	C₄	C₂×D₄₁₂	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	824	2	no	—
79	C₂	—	412	1	no	—
80	C₂	#15692996	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15692996
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#108×C₁₀₃	C₂
socle	C₂×C₁₀₃	#121
hypercenter	#108	D₁₀₃
hypocenter	C₁₀₃	#472
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
1. #15693049	C₂	semidirect
2. C₂×D₈₂₄	C₂	semidirect
3. #15693027	C₂	semidirect
4. #15692937	C₂	semidirect
5. #108×C₁₀₃	C₂	semidirect
40. C₁₀₃	#472	semidirect
45. #108	D₁₀₃	semidirect