Subgroups — #20268067

Order 6592.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693054	C₂	1	2	yes	maximal
2	C₂×Dic₄₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#15693027	C₂	1	1	yes	maximal, characteristic
4	#15692939	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×Dic₂₀₆	C₂²	1	2	yes	—
8	Dic₄₁₂	—	2	2	no	—
9	Dic₄₁₂	—	2	1	no	—
10	Dic₄₁₂	—	2	1	no	—
11	#13110094	—	2	2	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	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
18	C₂²⋊D₁₀₃	—	2	1	no	—
19	C₂×Dic₁₀₃	—	2	2	no	—
20	D₄₁₂	D₄	1	1	yes	characteristic
21	C₄×D₁₀₃	—	2	1	no	—
22	Dic₂₀₆	—	2	2	no	—
23	Dic₂₀₆	—	2	2	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	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
32	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
33	Dic₁₀₃	—	2	1	no	—
34	Dic₁₀₃	—	4	2	no	—
35	C₂×C₁₀₃	—	2	1	no	—
36	C₂×C₁₀₃	#121	1	1	yes	characteristic
37	D₁₀₃	—	4	1	no	—
38	C₁₀₃	#473	1	1	yes	characteristic, complemented, Sylow
39	#473	—	103	1	no	maximal, Sylow
40	#137	—	103	2	no	—
41	C₂×Q₁₆	—	103	1	no	—
42	#131	—	103	1	no	—
43	#108	D₁₀₃	1	1	yes	characteristic, complemented
44	#101	—	103	2	no	—
45	#41	—	103	1	no	—
46	C₂×Q₈	—	103	2	no	—
47	Q₁₆	—	206	2	no	—
48	Q₁₆	—	206	1	no	—
49	Q₁₆	—	206	1	no	—
50	SD₁₆	—	206	2	no	—
51	M₁₆	—	103	1	no	—
52	M₁₆	—	206	1	no	—
53	M₁₆	C₂×D₁₀₃	1	2	yes	—
54	C₂×C₈	—	206	1	no	—
55	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
56	Q₈	—	103	1	no	—
57	Q₈	—	206	2	no	—
58	Q₈	—	206	2	no	—
59	D₄	—	103	1	no	—
60	D₄	—	206	1	no	—
61	C₂×C₄	—	206	2	no	—
62	C₂×C₄	—	206	1	no	—
63	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
64	C₈	—	2	2	no	—
65	C₈	—	206	1	no	—
66	C₈	D₄₁₂	1	1	yes	characteristic
67	C₈	D₄₁₂	1	1	yes	characteristic
68	C₂²	—	206	1	no	—
69	C₂²	#13110106	1	1	yes	characteristic
70	C₄	—	412	2	no	—
71	C₄	—	206	1	no	—
72	C₄	D₄×D₁₀₃	1	1	yes	characteristic
73	C₄	C₂×D₄₁₂	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	412	1	no	—
76	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	#473
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
2. C₂×Dic₄₁₂	C₂	semidirect
4. #15692939	C₂	semidirect
5. #108×C₁₀₃	C₂	semidirect
38. C₁₀₃	#473	semidirect
43. #108	D₁₀₃	semidirect