Subgroups — #20267576

Order 6592.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693027	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₀₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#13110105	C₄	1	1	yes	characteristic
5	#13110089	C₄	1	1	yes	characteristic
6	#13110088	—	2	1	no	—
7	C₈×D₁₀₃	—	2	1	no	—
8	C₁₀₃⋊C₁₆	—	2	1	no	—
9	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
10	C₁₆×C₁₀₃	—	2	1	no	—
11	C₂×C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
12	C₂²⋊D₁₀₃	—	2	1	no	—
13	D₄₁₂	C₈	1	1	yes	characteristic
14	C₄×D₁₀₃	—	2	1	no	—
15	Dic₂₀₆	C₈	1	1	yes	characteristic
16	C₈×C₁₀₃	D₄	1	1	yes	characteristic
17	C₈×C₁₀₃	D₄	1	1	yes	characteristic
18	C₁₀₃⋊C₈	—	2	1	no	—
19	C₂²×C₁₀₃	M₁₆	1	1	yes	characteristic
20	C₂×D₁₀₃	—	2	1	no	—
21	C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₁₀₃	C₂×C₈	1	1	yes	characteristic
23	Dic₁₀₃	—	2	1	no	—
24	C₂×C₁₀₃	—	2	1	no	—
25	C₂×C₁₀₃	C₂²⋊C₈	1	1	yes	characteristic
26	D₁₀₃	—	4	1	no	—
27	C₁₀₃	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	103	1	no	maximal, Sylow
29	#131	—	103	1	no	—
30	M₃₂	D₁₀₃	1	1	yes	characteristic, complemented
31	C₂×C₁₆	—	103	1	no	—
32	#41	—	103	1	no	—
33	M₁₆	—	103	1	no	—
34	M₁₆	—	206	1	no	—
35	C₂×C₈	—	206	1	no	—
36	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	—	206	1	no	—
39	Q₈	—	103	1	no	—
40	D₄	—	103	1	no	—
41	D₄	—	206	1	no	—
42	C₂×C₄	—	206	1	no	—
43	C₂×C₄	C₄×D₁₀₃	1	1	yes	characteristic
44	C₈	—	206	1	no	—
45	C₈	D₄₁₂	1	1	yes	characteristic
46	C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
47	C₂²	—	206	1	no	—
48	C₂²	#13110088	1	1	yes	characteristic
49	C₄	—	206	1	no	—
50	C₄	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
51	C₄	C₈×D₁₀₃	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	412	1	no	—
54	C₂	(C₂×D₁₀₃)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊D₁₀₃
commutator	C₄×C₁₀₃	C₂×C₈
Frattini	C₂×C₈	C₂×D₁₀₃
Fitting	M₃₂×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂²⋊C₈
hypercenter	M₃₂	D₁₀₃
hypocenter	C₁₀₃	#350
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₀₃⋊C₁₆	C₂	semidirect
3. M₃₂×C₁₀₃	C₂	semidirect
27. C₁₀₃	#350	semidirect
30. M₃₂	D₁₀₃	semidirect