Subgroups — #20268164

Order 6592.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13110094	C₂	1	4	yes	maximal, complemented
2	#15693021	C₂	1	1	yes	maximal, characteristic, complemented
3	#15693018	C₂	1	1	yes	maximal, characteristic
4	C₄×C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₂₀₆	C₂²	1	2	yes	—
6	C₂×D₄₁₂	—	2	2	no	—
7	C₂×D₄₁₂	C₂²	1	2	yes	—
8	#13110094	—	2	8	no	—
9	C₄⋊Dic₁₀₃	—	2	2	no	—
10	C₂×C₈×C₁₀₃	C₂²	1	2	yes	—
11	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
12	C₂²×D₁₀₃	—	2	2	no	—
13	C₂×C₄×C₁₀₃	D₄	1	2	yes	—
14	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
15	C₂×Dic₁₀₃	—	2	2	no	—
16	D₄₁₂	—	2	4	no	—
17	D₄₁₂	—	4	4	no	—
18	Dic₂₀₆	—	2	4	no	—
19	C₈×C₁₀₃	D₄	1	4	yes	complemented
20	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
21	C₂×D₁₀₃	—	4	2	no	—
22	C₂×D₁₀₃	—	4	4	no	—
23	C₄×C₁₀₃	SD₁₆	1	4	yes	complemented
24	C₄×C₁₀₃	C₂×D₄	1	2	yes	—
25	Dic₁₀₃	—	4	2	no	—
26	C₂×C₁₀₃	#127	1	1	yes	characteristic
27	C₂×C₁₀₃	C₂×SD₁₆	1	2	yes	—
28	D₁₀₃	—	8	2	no	—
29	C₁₀₃	#492	1	1	yes	characteristic, complemented, Sylow
30	#492	—	103	1	no	maximal, Sylow
31	C₂×SD₁₆	—	103	4	no	—
32	C₄⋊Q₈	—	103	1	no	—
33	#127	—	103	1	no	—
34	C₄×C₈	D₁₀₃	1	1	yes	characteristic, complemented
35	C₂×Q₈	—	103	2	no	—
36	C₂×D₄	—	103	2	no	—
37	C₂×D₄	—	206	2	no	—
38	SD₁₆	—	206	8	no	—
39	C₂×C₈	C₂×D₁₀₃	1	2	yes	—
40	C₄⋊C₄	—	206	2	no	—
41	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
42	C₂³	—	206	2	no	—
43	Q₈	—	206	4	no	—
44	D₄	—	412	4	no	—
45	D₄	—	206	4	no	—
46	C₂×C₄	—	206	2	no	—
47	C₂×C₄	D₄₁₂	1	2	yes	—
48	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
49	C₈	D₄₁₂	1	4	yes	complemented
50	C₂²	—	412	2	no	—
51	C₂²	—	412	4	no	—
52	C₂²	C₂×D₄₁₂	1	1	yes	characteristic
53	C₄	—	412	2	no	—
54	C₄	#13110094	1	4	yes	complemented
55	C₄	C₂×D₄₁₂	1	2	yes	—
56	C₂	—	824	2	no	—
57	C₂	#15693018	1	1	yes	characteristic
58	C₂	C₂×#13110094	1	2	yes	—

	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	#492
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
1. C₂×#13110094	C₂	semidirect
2. #15693021	C₂	semidirect
4. C₄×C₈×C₁₀₃	C₂	semidirect
19. C₈×C₁₀₃	D₄	semidirect
23. C₄×C₁₀₃	SD₁₆	semidirect
29. C₁₀₃	#492	semidirect
34. C₄×C₈	D₁₀₃	semidirect
49. C₈	D₄₁₂	semidirect
54. C₄	#13110094	semidirect