Subgroups — #15693052

Order 3296.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13110105	C₂	1	1	yes	maximal, characteristic
2	#13110095	C₂	1	2	yes	maximal, complemented
3	#13110092	C₂	1	2	yes	maximal, complemented
4	#13110089	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₁₀₃	—	2	1	no	—
7	Q₈×C₁₀₃	C₂²	1	2	yes	—
8	C₂×C₄×C₁₀₃	—	2	1	no	—
9	C₂×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
10	C₂²⋊D₁₀₃	—	2	1	no	—
11	D₄₁₂	C₂²	1	1	yes	characteristic
12	C₄×D₁₀₃	—	2	1	no	—
13	Dic₂₀₆	C₂²	1	1	yes	characteristic
14	C₁₀₃⋊C₈	C₂²	1	2	yes	—
15	C₂²×C₁₀₃	D₄	1	1	yes	characteristic
16	C₂×D₁₀₃	—	2	1	no	—
17	C₄×C₁₀₃	—	2	2	no	—
18	C₄×C₁₀₃	D₄	1	1	yes	characteristic
19	C₄×C₁₀₃	C₂³	1	1	yes	characteristic
20	Dic₁₀₃	—	2	1	no	—
21	C₂×C₁₀₃	—	2	1	no	—
22	C₂×C₁₀₃	C₂×D₄	1	1	yes	characteristic
23	D₁₀₃	—	4	1	no	—
24	C₁₀₃	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	103	1	no	maximal, Sylow
26	#41	—	103	1	no	—
27	C₂×Q₈	D₁₀₃	1	1	yes	characteristic, complemented
28	Q₁₆	—	103	2	no	—
29	SD₁₆	—	103	2	no	—
30	M₁₆	—	103	1	no	—
31	Q₈	—	2	1	no	—
32	Q₈	—	103	1	no	—
33	Q₈	C₂×D₁₀₃	1	2	yes	—
34	D₄	—	103	1	no	—
35	D₄	—	206	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	206	1	no	—
38	C₂×C₄	C₂×D₁₀₃	1	1	yes	characteristic
39	C₈	—	103	2	no	—
40	C₂²	—	206	1	no	—
41	C₂²	C₂²⋊D₁₀₃	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	206	1	no	—
44	C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
45	C₄	C₂²×D₁₀₃	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	412	1	no	—
48	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×Q₈×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂×D₄
prime radical	#13110105	C₂
hypercenter	C₂×Q₈	D₁₀₃
hypocenter	C₁₀₃	#137
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #13110095	C₂	semidirect
3. #13110092	C₂	semidirect
4. #13110089	C₂	semidirect
5. C₂×Q₈×C₁₀₃	C₂	semidirect
24. C₁₀₃	#137	semidirect
27. C₂×Q₈	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
#13110095	2
#13110092	2
#13110089	2
C₂×Q₈×C₁₀₃	2
#137	103