Subgroups — #15693047

Order 3296.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13110105	C₂	1	1	yes	maximal, characteristic, complemented
2	#13110093	C₂	1	2	yes	maximal, complemented
3	#13110090	C₂	1	2	yes	maximal, complemented
4	#13110089	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₁₀₃	—	2	1	no	—
7	D₄×C₁₀₃	—	2	1	no	—
8	D₄×C₁₀₃	C₂²	1	2	yes	—
9	C₂×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
10	C₂²⋊D₁₀₃	—	2	1	no	—
11	D₄₁₂	C₂²	1	1	yes	characteristic, complemented
12	C₄×D₁₀₃	—	2	1	no	—
13	Dic₂₀₆	C₂²	1	1	yes	characteristic, complemented
14	C₁₀₃⋊C₈	C₂²	1	2	yes	complemented
15	C₂²×C₁₀₃	—	2	2	no	—
16	C₂²×C₁₀₃	—	4	2	no	—
17	C₂²×C₁₀₃	D₄	1	1	yes	characteristic
18	C₂×D₁₀₃	—	2	1	no	—
19	C₄×C₁₀₃	D₄	1	1	yes	characteristic
20	C₄×C₁₀₃	C₂³	1	1	yes	characteristic
21	Dic₁₀₃	—	2	1	no	—
22	C₂×C₁₀₃	—	2	1	no	—
23	C₂×C₁₀₃	—	4	2	no	—
24	C₂×C₁₀₃	C₂×D₄	1	1	yes	characteristic
25	D₁₀₃	—	4	1	no	—
26	C₁₀₃	AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
27	AGL(1,ℤ/8)	—	103	1	no	maximal, Sylow
28	#41	—	103	1	no	—
29	C₂×D₄	D₁₀₃	1	1	yes	characteristic, complemented
30	SD₁₆	—	103	2	no	—
31	D₈	—	103	2	no	—
32	M₁₆	—	103	1	no	—
33	C₂³	—	2	1	no	—
34	Q₈	—	103	1	no	—
35	D₄	—	2	1	no	—
36	D₄	—	103	1	no	—
37	D₄	—	206	1	no	—
38	D₄	C₂×D₁₀₃	1	2	yes	—
39	C₂×C₄	—	206	1	no	—
40	C₂×C₄	C₂×D₁₀₃	1	1	yes	characteristic
41	C₈	—	103	2	no	—
42	C₂²	—	2	2	no	—
43	C₂²	—	4	2	no	—
44	C₂²	—	206	1	no	—
45	C₂²	C₂²⋊D₁₀₃	1	1	yes	characteristic
46	C₄	—	206	1	no	—
47	C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
48	C₄	C₂²×D₁₀₃	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	—	4	2	no	—
51	C₂	—	412	1	no	—
52	C₂	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊D₁₀₃
commutator, cosocle	C₄×C₁₀₃	C₂³
Frattini	C₄	C₂²×D₁₀₃
Fitting	C₂×D₄×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂×D₄
hypercenter	C₂×D₄	D₁₀₃
hypocenter	C₁₀₃	AGL(1,ℤ/8)
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. #13110105	C₂	semidirect
2. #13110093	C₂	semidirect
3. #13110090	C₂	semidirect
4. #13110089	C₂	semidirect
5. C₂×D₄×C₁₀₃	C₂	semidirect
11. D₄₁₂	C₂²	semidirect
13. Dic₂₀₆	C₂²	semidirect
14. C₁₀₃⋊C₈	C₂²	semidirect
26. C₁₀₃	AGL(1,ℤ/8)	semidirect
29. C₂×D₄	D₁₀₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13110105	2
#13110093	2
#13110090	2
#13110089	2
C₂×D₄×C₁₀₃	2
AGL(1,ℤ/8)	103