Subgroups — #20267903

Order 6592.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×Dic₁₀₃	C₂	1	2	yes	maximal, complemented
2	#15692953	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692942	C₂	1	2	yes	maximal, complemented
4	#15692931	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₀₃	—	2	2	no	—
7	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₁₀₃	C₂²	1	2	yes	—
9	C₂²⋊Dic₁₀₃	—	2	2	no	—
10	C₄×Dic₁₀₃	C₂²	1	1	yes	characteristic
11	C₂×D₄×C₁₀₃	C₂²	1	2	yes	—
12	D₈×C₁₀₃	C₄	1	4	yes	complemented
13	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂³×C₁₀₃	—	2	2	no	—
15	D₄×C₁₀₃	—	2	2	no	—
16	D₄×C₁₀₃	C₂×C₄	1	4	yes	complemented
17	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₁₀₃	—	2	2	no	—
19	C₂×Dic₁₀₃	—	4	4	no	—
20	C₂×Dic₁₀₃	D₄	1	2	yes	—
21	C₈×C₁₀₃	C₂×C₄	1	2	yes	complemented
22	C₁₀₃⋊C₈	—	2	1	no	—
23	C₂²×C₁₀₃	—	2	4	no	—
24	C₂²×C₁₀₃	—	4	2	no	—
25	C₂²×C₁₀₃	—	4	2	no	—
26	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
27	C₄×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₁₀₃	#41	1	1	yes	characteristic
29	Dic₁₀₃	—	2	2	no	—
30	Dic₁₀₃	—	4	2	no	—
31	C₂×C₁₀₃	—	4	4	no	—
32	C₂×C₁₀₃	C₄×D₄	1	1	yes	characteristic
33	C₂×C₁₀₃	AGL(1,ℤ/8)	1	2	yes	—
34	C₁₀₃	#442	1	1	yes	characteristic, complemented, Sylow
35	#442	—	103	1	no	maximal, Sylow
36	C₂×D₈	D₁₀₃	1	1	yes	characteristic
37	C₄×D₄	—	103	2	no	—
38	#106	—	103	1	no	—
39	#102	—	103	2	no	—
40	#97	—	103	1	no	—
41	C₂×D₄	C₂×D₁₀₃	1	2	yes	—
42	C₂²×C₄	—	206	2	no	—
43	D₈	Dic₁₀₃	1	4	yes	complemented
44	C₂×C₈	—	103	1	no	—
45	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
46	C₄⋊C₄	—	103	2	no	—
47	C₂²⋊C₄	—	206	2	no	—
48	C₄²	—	103	1	no	—
49	C₂³	—	2	2	no	—
50	D₄	—	2	2	no	—
51	D₄	C₂×Dic₁₀₃	1	4	yes	complemented
52	C₂×C₄	—	103	2	no	—
53	C₂×C₄	—	412	4	no	—
54	C₂×C₄	—	206	2	no	—
55	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
56	C₈	—	206	1	no	—
57	C₈	C₂×Dic₁₀₃	1	2	yes	complemented
58	C₂²	—	2	4	no	—
59	C₂²	—	4	2	no	—
60	C₂²	—	4	2	no	—
61	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
62	C₄	—	412	2	no	—
63	C₄	—	206	2	no	—
64	C₄	C₂²×Dic₁₀₃	1	1	yes	characteristic
65	C₄	#13110104	1	1	yes	characteristic
66	C₂	—	4	4	no	—
67	C₂	D₄×Dic₁₀₃	1	1	yes	characteristic
68	C₂	#15693045	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₀₃
commutator	C₄×C₁₀₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₂×D₈×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	C₂×D₈	D₁₀₃
hypocenter	C₁₀₃	#442
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. D₄×Dic₁₀₃	C₂	semidirect
2. #15692953	C₂	semidirect
3. #15692942	C₂	semidirect
4. #15692931	C₂	semidirect
12. D₈×C₁₀₃	C₄	semidirect
16. D₄×C₁₀₃	C₂×C₄	semidirect
21. C₈×C₁₀₃	C₂×C₄	semidirect
34. C₁₀₃	#442	semidirect
43. D₈	Dic₁₀₃	semidirect
51. D₄	C₂×Dic₁₀₃	semidirect
57. C₈	C₂×Dic₁₀₃	semidirect