Subgroups — #20268165

Order 6592.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13110092	C₂	1	4	yes	maximal, complemented
2	#15693018	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊Q₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄₁₂	—	2	2	no	—
6	C₂×D₄₁₂	C₂²	1	2	yes	—
7	#13110092	—	2	8	no	—
8	C₂×C₁₀₃⋊C₈	C₂²	1	2	yes	—
9	C₂×Q₈×C₁₀₃	C₂²	1	2	yes	—
10	C₄⋊C₄×C₁₀₃	—	2	2	no	—
11	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
12	C₂²×D₁₀₃	—	2	2	no	—
13	Q₈×C₁₀₃	—	2	4	no	—
14	C₂×C₄×C₁₀₃	—	2	2	no	—
15	C₂×C₄×C₁₀₃	D₄	1	2	yes	—
16	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
17	D₄₁₂	—	2	4	no	—
18	D₄₁₂	—	4	4	no	—
19	C₁₀₃⋊C₈	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	—	4	2	no	—
24	C₄×C₁₀₃	SD₁₆	1	4	yes	complemented
25	C₄×C₁₀₃	C₂×D₄	1	2	yes	—
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	D₁₀₃	1	1	yes	characteristic, complemented
33	#127	—	103	1	no	—
34	C₄×C₈	—	103	1	no	—
35	C₂×Q₈	C₂×D₁₀₃	1	2	yes	—
36	C₂×D₄	—	103	2	no	—
37	C₂×D₄	—	206	2	no	—
38	SD₁₆	—	206	8	no	—
39	C₂×C₈	—	103	2	no	—
40	C₄⋊C₄	—	2	2	no	—
41	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
42	C₂³	—	206	2	no	—
43	Q₈	—	2	4	no	—
44	D₄	—	412	4	no	—
45	D₄	—	206	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	C₂²⋊D₁₀₃	1	2	yes	—
48	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
49	C₈	—	103	4	no	—
50	C₂²	—	412	2	no	—
51	C₂²	—	412	4	no	—
52	C₂²	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	#13110092	1	4	yes	complemented
55	C₄	D₄×D₁₀₃	1	2	yes	—
56	C₂	—	824	2	no	—
57	C₂	#15693017	1	1	yes	characteristic
58	C₂	C₂×#13110092	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₀₃
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₄⋊Q₈×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	C₄⋊Q₈	D₁₀₃
hypocenter	C₁₀₃	#492
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#13110092	C₂	semidirect
3. C₄×C₁₀₃⋊C₈	C₂	semidirect
4. C₄⋊Q₈×C₁₀₃	C₂	semidirect
19. C₁₀₃⋊C₈	D₄	semidirect
24. C₄×C₁₀₃	SD₁₆	semidirect
29. C₁₀₃	#492	semidirect
32. C₄⋊Q₈	D₁₀₃	semidirect
54. C₄	#13110092	semidirect