Subgroups — #20267520

Order 6592.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄₁₂	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₁₀₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₁₂	C₄	1	1	yes	characteristic
5	C₂×C₄×D₁₀₃	—	2	1	no	—
6	C₂×C₁₀₃⋊C₈	—	2	1	no	—
7	C₄⋊Dic₁₀₃	C₄	1	1	yes	characteristic
8	(C₂×D₁₀₃)⋊C₄	—	2	1	no	—
9	C₂×C₈×C₁₀₃	—	2	1	no	—
10	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
11	C₂²×D₁₀₃	—	2	1	no	—
12	C₂×C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
14	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
15	C₂×Dic₁₀₃	—	2	1	no	—
16	D₄₁₂	—	2	1	no	—
17	D₄₁₂	C₈	1	2	yes	complemented
18	C₄×D₁₀₃	—	4	1	no	—
19	C₄×D₁₀₃	—	4	1	no	—
20	C₈×C₁₀₃	—	2	2	no	—
21	C₁₀₃⋊C₈	—	4	1	no	—
22	C₂²×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₁₀₃	—	2	2	no	—
24	C₂×D₁₀₃	—	4	1	no	—
25	C₂×D₁₀₃	—	4	1	no	—
26	C₄×C₁₀₃	—	2	1	no	—
27	C₄×C₁₀₃	C₂×C₈	1	1	yes	characteristic
28	C₄×C₁₀₃	M₁₆	1	1	yes	characteristic
29	C₄×C₁₀₃	D₈	1	1	yes	characteristic
30	C₄×C₁₀₃	SD₁₆	1	1	yes	characteristic
31	Dic₁₀₃	—	4	1	no	—
32	C₂×C₁₀₃	C₂²⋊C₈	1	1	yes	characteristic
33	C₂×C₁₀₃	#102	1	1	yes	characteristic
34	C₂×C₁₀₃	#104	1	1	yes	characteristic
35	D₁₀₃	—	4	2	no	—
36	C₁₀₃	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
37	D₄⋊C₈	—	103	1	no	maximal, Sylow
38	C₄×D₄	—	103	1	no	—
39	C₄⋊C₈	—	103	1	no	—
40	C₄×C₈	D₁₀₃	1	1	yes	characteristic, complemented
41	C₂×D₄	—	103	1	no	—
42	C₂²×C₄	—	206	1	no	—
43	C₂×C₈	—	2	1	no	—
44	C₂×C₈	—	206	1	no	—
45	C₄⋊C₄	—	103	1	no	—
46	C₂²⋊C₄	—	206	1	no	—
47	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
48	C₂³	—	206	1	no	—
49	D₄	—	103	2	no	—
50	D₄	—	206	1	no	—
51	C₂×C₄	—	412	1	no	—
52	C₂×C₄	—	412	1	no	—
53	C₂×C₄	—	206	1	no	—
54	C₂×C₄	C₄×D₁₀₃	1	1	yes	characteristic
55	C₂×C₄	D₄₁₂	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
57	C₈	—	2	2	no	—
58	C₈	—	412	1	no	—
59	C₂²	—	412	1	no	—
60	C₂²	—	412	1	no	—
61	C₂²	—	206	2	no	—
62	C₂²	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	—	412	1	no	—
65	C₄	C₈×D₁₀₃	1	1	yes	characteristic
66	C₄	#13110088	1	1	yes	characteristic
67	C₄	D₈₂₄	1	1	yes	characteristic
68	C₄	#13110094	1	1	yes	characteristic
69	C₂	—	412	2	no	—
70	C₂	(C₂×D₁₀₃)⋊C₈	1	1	yes	characteristic
71	C₂	#15692943	1	1	yes	characteristic
72	C₂	#15692949	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₄⋊(C₁₀₃⋊C₈)	C₂	semidirect
3. C₄×C₈×C₁₀₃	C₂	semidirect
17. D₄₁₂	C₈	semidirect
36. C₁₀₃	D₄⋊C₈	semidirect
40. C₄×C₈	D₁₀₃	semidirect