Subgroups — #20267902

Order 6592.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₂₄	C₂	1	1	yes	maximal, characteristic
2	#15692983	C₂	1	2	yes	maximal, complemented
3	#15692941	C₂	1	2	yes	maximal, complemented
4	#15692931	C₂	1	1	yes	maximal, characteristic, complemented
5	#106×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₁₂	C₂²	1	2	yes	—
7	C₂×C₄×D₁₀₃	—	2	2	no	—
8	D₈₂₄	C₄	1	4	yes	complemented
9	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
10	(C₂×D₁₀₃)⋊C₄	—	2	2	no	—
11	C₄×Dic₁₀₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
14	C₂²×D₁₀₃	—	2	2	no	—
15	C₂×C₄×C₁₀₃	—	2	2	no	—
16	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₁₀₃	D₄	1	2	yes	—
18	D₄₁₂	—	2	2	no	—
19	D₄₁₂	C₂×C₄	1	4	yes	complemented
20	C₄×D₁₀₃	—	4	4	no	—
21	C₈×C₁₀₃	C₂×C₄	1	2	yes	complemented
22	C₁₀₃⋊C₈	—	2	1	no	—
23	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
24	C₂×D₁₀₃	—	2	4	no	—
25	C₂×D₁₀₃	—	4	2	no	—
26	C₂×D₁₀₃	—	4	2	no	—
27	C₄×C₁₀₃	—	4	2	no	—
28	C₄×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₁₀₃	#41	1	1	yes	characteristic
30	Dic₁₀₃	—	2	2	no	—
31	C₂×C₁₀₃	C₄×D₄	1	1	yes	characteristic
32	C₂×C₁₀₃	AGL(1,ℤ/8)	1	2	yes	—
33	D₁₀₃	—	4	4	no	—
34	C₁₀₃	#442	1	1	yes	characteristic, complemented, Sylow
35	#442	—	103	1	no	maximal, Sylow
36	C₂×D₈	—	103	1	no	—
37	C₄×D₄	—	103	2	no	—
38	#106	D₁₀₃	1	1	yes	characteristic, complemented
39	#102	—	103	2	no	—
40	#97	—	103	1	no	—
41	C₂×D₄	—	103	2	no	—
42	C₂²×C₄	—	206	2	no	—
43	D₈	—	103	4	no	—
44	C₂×C₈	—	103	1	no	—
45	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
46	C₄⋊C₄	C₂×D₁₀₃	1	2	yes	—
47	C₂²⋊C₄	—	206	2	no	—
48	C₄²	—	103	1	no	—
49	C₂³	—	206	2	no	—
50	D₄	—	103	4	no	—
51	D₄	—	206	2	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	103	2	no	—
54	C₂×C₄	—	412	4	no	—
55	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
56	C₈	—	206	1	no	—
57	C₈	C₄×D₁₀₃	1	2	yes	complemented
58	C₂²	—	412	2	no	—
59	C₂²	—	412	2	no	—
60	C₂²	—	206	4	no	—
61	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
62	C₄	—	4	2	no	—
63	C₄	—	206	2	no	—
64	C₄	C₂×C₄×D₁₀₃	1	1	yes	characteristic
65	C₄	#13110106	1	1	yes	characteristic
66	C₂	—	412	4	no	—
67	C₂	#15692983	1	1	yes	characteristic
68	C₂	#15693048	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₀₃
commutator	C₄×C₁₀₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#106×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	#106	D₁₀₃
hypocenter	C₁₀₃	#442
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
2. #15692983	C₂	semidirect
3. #15692941	C₂	semidirect
4. #15692931	C₂	semidirect
5. #106×C₁₀₃	C₂	semidirect
8. D₈₂₄	C₄	semidirect
19. D₄₁₂	C₂×C₄	semidirect
21. C₈×C₁₀₃	C₂×C₄	semidirect
34. C₁₀₃	#442	semidirect
38. #106	D₁₀₃	semidirect
57. C₈	C₄×D₁₀₃	semidirect