Subgroups — #20268002

Order 6592.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₁₂	C₂	1	2	yes	maximal
2	#15693021	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₂₀₆	C₂	1	1	yes	maximal, characteristic
4	#15692946	C₂	1	2	yes	maximal
5	C₄⋊C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₀₆	C₂²	1	2	yes	—
7	C₂×Dic₂₀₆	C₂²	1	1	yes	characteristic
8	Dic₄₁₂	—	2	4	no	—
9	C₄⋊Dic₁₀₃	—	2	1	no	—
10	C₄⋊Dic₁₀₃	—	2	1	no	—
11	C₄⋊Dic₁₀₃	C₂²	1	1	yes	characteristic
12	Dic₁₀₃⋊C₄	—	2	1	no	—
13	C₄×Dic₁₀₃	—	2	1	no	—
14	C₂×C₈×C₁₀₃	C₂²	1	2	yes	—
15	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
18	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₀₃	—	2	1	no	—
20	C₂×Dic₁₀₃	—	2	1	no	—
21	C₂×Dic₁₀₃	—	2	2	no	—
22	Dic₂₀₆	—	2	1	no	—
23	Dic₂₀₆	—	2	2	no	—
24	Dic₂₀₆	—	2	2	no	—
25	Dic₂₀₆	D₄	1	2	yes	—
26	C₈×C₁₀₃	—	2	2	no	—
27	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
28	C₄×C₁₀₃	—	2	1	no	—
29	C₄×C₁₀₃	Q₁₆	1	2	yes	complemented
30	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₀₃	#41	1	1	yes	characteristic
32	Dic₁₀₃	—	2	2	no	—
33	Dic₁₀₃	—	4	2	no	—
34	Dic₁₀₃	—	4	1	no	—
35	C₂×C₁₀₃	#121	1	1	yes	characteristic
36	C₂×C₁₀₃	C₂×Q₁₆	1	1	yes	characteristic
37	C₂×C₁₀₃	#137	1	1	yes	characteristic
38	C₁₀₃	#462	1	1	yes	characteristic, complemented, Sylow
39	#462	—	103	1	no	maximal, Sylow
40	C₂×Q₁₆	—	103	2	no	—
41	C₄⋊Q₈	—	103	1	no	—
42	C₄×Q₈	—	103	1	no	—
43	C₄⋊C₈	D₁₀₃	1	1	yes	characteristic
44	#103	—	103	2	no	—
45	C₂×Q₈	—	103	1	no	—
46	C₂×Q₈	—	103	2	no	—
47	Q₁₆	—	206	4	no	—
48	C₂×C₈	C₂×D₁₀₃	1	2	yes	—
49	C₄⋊C₄	—	103	1	no	—
50	C₄⋊C₄	—	206	1	no	—
51	C₄⋊C₄	—	206	1	no	—
52	C₄⋊C₄	—	206	1	no	—
53	C₄²	—	206	1	no	—
54	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
55	Q₈	—	103	2	no	—
56	Q₈	—	206	2	no	—
57	Q₈	—	206	2	no	—
58	Q₈	—	206	1	no	—
59	C₂×C₄	—	206	1	no	—
60	C₂×C₄	—	206	2	no	—
61	C₂×C₄	—	206	1	no	—
62	C₂×C₄	D₄₁₂	1	1	yes	characteristic
63	C₂×C₄	D₄₁₂	1	1	yes	characteristic
64	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
65	C₈	—	2	2	no	—
66	C₂²	C₂×D₄₁₂	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	412	2	no	—
69	C₄	—	412	1	no	—
70	C₄	—	206	2	no	—
71	C₄	Dic₄₁₂	1	2	yes	complemented
72	C₄	D₄×D₁₀₃	1	1	yes	characteristic
73	C₄	#13110106	1	1	yes	characteristic
74	C₂	#15692996	1	1	yes	characteristic
75	C₂	C₂×Dic₄₁₂	1	1	yes	characteristic
76	C₂	#15693054	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄₁₂
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₄⋊C₈×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	C₄⋊C₈	D₁₀₃
hypocenter	C₁₀₃	#462
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
29. C₄×C₁₀₃	Q₁₆	semidirect
38. C₁₀₃	#462	semidirect
71. C₄	Dic₄₁₂	semidirect