Subgroups — #20268074

Order 6592.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693020	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₁₀₃	C₂	1	1	yes	maximal, characteristic
3	#15692953	C₂	1	1	yes	maximal, characteristic
4	#15692952	C₂	1	1	yes	maximal, characteristic
5	Dic₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#15692945	C₂	1	1	yes	maximal, characteristic
7	#103×C₁₀₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₀₆	—	2	1	no	—
9	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₀₃	—	2	1	no	—
11	C₄⋊Dic₁₀₃	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₀₃	C₂²	1	1	yes	characteristic
13	Dic₁₀₃⋊C₄	—	2	1	no	—
14	C₄×Dic₁₀₃	—	2	1	no	—
15	C₄×Dic₁₀₃	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
19	Q₈×C₁₀₃	—	2	1	no	—
20	Q₈×C₁₀₃	Q₈	1	2	yes	complemented
21	C₂×C₄×C₁₀₃	—	2	1	no	—
22	C₂×C₄×C₁₀₃	—	2	1	no	—
23	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
24	C₂×Dic₁₀₃	—	2	1	no	—
25	C₂×Dic₁₀₃	—	2	1	no	—
26	C₂×Dic₁₀₃	D₄	1	1	yes	characteristic
27	C₂×Dic₁₀₃	D₄	1	1	yes	characteristic
28	Dic₂₀₆	—	4	2	no	—
29	C₈×C₁₀₃	—	2	1	no	—
30	C₁₀₃⋊C₈	—	2	1	no	—
31	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
32	C₄×C₁₀₃	—	2	2	no	—
33	C₄×C₁₀₃	—	4	1	no	—
34	C₄×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₁₀₃	#41	1	1	yes	characteristic
36	Dic₁₀₃	—	2	1	no	—
37	Dic₁₀₃	—	4	1	no	—
38	Dic₁₀₃	—	4	1	no	—
39	Dic₁₀₃	SD₁₆	1	2	yes	—
40	C₂×C₁₀₃	C₂²⋊Q₈	1	1	yes	characteristic
41	C₂×C₁₀₃	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₁₀₃	#137	1	1	yes	characteristic
43	C₁₀₃	#475	1	1	yes	characteristic, complemented, Sylow
44	#475	—	103	1	no	maximal, Sylow
45	C₄⋊Q₈	—	103	1	no	—
46	C₄×Q₈	—	103	1	no	—
47	#106	—	103	1	no	—
48	#106	—	103	1	no	—
49	C₄⋊C₈	—	103	1	no	—
50	#103	—	103	1	no	—
51	#103	D₁₀₃	1	1	yes	characteristic
52	C₂×Q₈	—	206	1	no	—
53	C₂×Q₈	C₂×D₁₀₃	1	1	yes	characteristic
54	C₂×C₈	—	103	1	no	—
55	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
56	C₄⋊C₄	—	103	1	no	—
57	C₄⋊C₄	—	103	1	no	—
58	C₄⋊C₄	—	206	1	no	—
59	C₄⋊C₄	—	206	1	no	—
60	C₄⋊C₄	C₂×D₁₀₃	1	1	yes	characteristic
61	C₄²	—	103	1	no	—
62	C₄²	—	206	1	no	—
63	Q₈	—	2	1	no	—
64	Q₈	—	412	2	no	—
65	Q₈	Dic₂₀₆	1	2	yes	complemented
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	103	1	no	—
69	C₂×C₄	—	103	1	no	—
70	C₂×C₄	—	206	1	no	—
71	C₂×C₄	—	206	1	no	—
72	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	206	1	no	—
75	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	4	1	no	—
78	C₄	—	103	2	no	—
79	C₄	—	412	1	no	—
80	C₄	—	412	1	no	—
81	C₄	—	206	1	no	—
82	C₄	C₂×Dic₂₀₆	1	1	yes	characteristic
83	C₄	#13110104	1	1	yes	characteristic
84	C₂	#15692998	1	1	yes	characteristic
85	C₂	SD₁₆×D₁₀₃	1	1	yes	characteristic
86	C₂	#15693053	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₃
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#103×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	#103	D₁₀₃
hypocenter	C₁₀₃	#475
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
20. Q₈×C₁₀₃	Q₈	semidirect
43. C₁₀₃	#475	semidirect
65. Q₈	Dic₂₀₆	semidirect