Subgroups — #20268194

Order 6592.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693021	C₂	1	1	yes	maximal, characteristic
2	#15692954	C₂	1	4	yes	maximal
3	C₄×C₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₀₆	—	2	1	no	—
6	C₂×C₁₀₃⋊C₈	C₂²	1	2	yes	—
7	C₄⋊Dic₁₀₃	—	2	1	no	—
8	C₄⋊Dic₁₀₃	C₂²	1	2	yes	—
9	C₂×Q₈×C₁₀₃	—	2	1	no	—
10	C₄⋊C₄×C₁₀₃	—	2	1	no	—
11	C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
12	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
13	Q₈×C₁₀₃	—	4	2	no	—
14	C₂×C₄×C₁₀₃	—	2	2	no	—
15	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₁₀₃	—	2	2	no	—
19	Dic₂₀₆	—	4	2	no	—
20	C₁₀₃⋊C₈	Q₈	1	4	yes	complemented
21	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
22	C₄×C₁₀₃	—	4	2	no	—
23	C₄×C₁₀₃	D₈	1	2	yes	—
24	C₄×C₁₀₃	Q₁₆	1	2	yes	—
25	C₄×C₁₀₃	C₂×Q₈	1	2	yes	—
26	Dic₁₀₃	—	4	2	no	—
27	C₂×C₁₀₃	C₄⋊Q₈	1	1	yes	characteristic
28	C₂×C₁₀₃	C₂×D₈	1	1	yes	characteristic
29	C₂×C₁₀₃	C₂×Q₁₆	1	1	yes	characteristic
30	C₁₀₃	#500	1	1	yes	characteristic, complemented, Sylow
31	#500	—	103	1	no	maximal, Sylow
32	C₄⋊Q₈	—	103	1	no	—
33	C₄⋊Q₈	D₁₀₃	1	1	yes	characteristic
34	#107	—	103	4	no	—
35	C₄×C₈	—	103	1	no	—
36	C₂×Q₈	—	2	1	no	—
37	C₂×Q₈	—	206	1	no	—
38	C₂×C₈	—	103	2	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	103	2	no	—
41	C₄⋊C₄	—	206	1	no	—
42	C₄⋊C₄	C₂×D₁₀₃	1	2	yes	—
43	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
44	Q₈	—	4	2	no	—
45	Q₈	—	412	2	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	206	2	no	—
48	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
51	C₈	—	103	4	no	—
52	C₂²	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	412	2	no	—
55	C₄	#13110090	1	2	yes	—
56	C₄	#13110095	1	2	yes	—
57	C₄	Q₈×D₁₀₃	1	2	yes	—
58	C₂	#15693019	1	1	yes	characteristic
59	C₂	C₂×#13110090	1	1	yes	characteristic
60	C₂	C₂×#13110095	1	1	yes	characteristic

	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	#500
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
20. C₁₀₃⋊C₈	Q₈	semidirect
30. C₁₀₃	#500	semidirect