Subgroups — #15693029

Order 3296.

62 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	#13110088	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₁₀₃	C₂	1	2	yes	maximal, complemented
5	M₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
7	C₂²⋊D₁₀₃	C₄	1	2	yes	—
8	D₄₁₂	C₄	1	1	yes	characteristic
9	C₄×D₁₀₃	C₂²	1	2	yes	—
10	Dic₂₀₆	C₄	1	1	yes	characteristic
11	C₈×C₁₀₃	C₂²	1	2	yes	—
12	C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₁₀₃	C₂×C₄	1	1	yes	characteristic
15	C₂×D₁₀₃	C₂×C₄	1	2	yes	—
16	C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
17	C₄×C₁₀₃	C₂³	1	1	yes	characteristic
18	Dic₁₀₃	C₂×C₄	1	2	yes	—
19	C₂×C₁₀₃	—	2	1	no	—
20	C₂×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
21	D₁₀₃	—	2	2	no	—
22	C₁₀₃	#131	1	1	yes	characteristic, complemented, Sylow
23	#131	—	103	1	no	maximal, Sylow
24	#41	—	103	1	no	—
25	M₁₆	—	103	2	no	—
26	M₁₆	D₁₀₃	1	1	yes	characteristic, complemented
27	C₂×C₈	—	103	1	no	—
28	C₂×C₈	—	103	2	no	—
29	Q₈	—	103	1	no	—
30	D₄	—	103	2	no	—
31	D₄	—	103	1	no	—
32	C₂×C₄	—	103	2	no	—
33	C₂×C₄	C₂×D₁₀₃	1	1	yes	characteristic
34	C₈	—	103	1	no	—
35	C₈	—	103	1	no	—
36	C₈	C₂×D₁₀₃	1	2	yes	—
37	C₂²	—	103	2	no	—
38	C₂²	C₄×D₁₀₃	1	1	yes	characteristic
39	C₄	—	103	2	no	—
40	C₄	C₄×D₁₀₃	1	1	yes	characteristic
41	C₄	C₂²×D₁₀₃	1	1	yes	characteristic
42	C₂	—	2	1	no	—
43	C₂	—	206	2	no	—
44	C₂	C₂×C₄×D₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×D₁₀₃
commutator, socle	C₂×C₁₀₃	C₂²×C₄
Fitting	M₁₆×C₁₀₃	C₂
prime radical	#13110105	C₂
cosocle	C₄×C₁₀₃	C₂³
hypercenter	M₁₆	D₁₀₃
hypocenter	C₁₀₃	#131
LCS	G ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. #13110088	C₂	semidirect
3. C₂×C₁₀₃⋊C₈	C₂	semidirect
4. C₈×D₁₀₃	C₂	semidirect
5. M₁₆×C₁₀₃	C₂	semidirect
22. C₁₀₃	#131	semidirect
26. M₁₆	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
#13110088	2
C₂×C₁₀₃⋊C₈	2
C₈×D₁₀₃	2
M₁₆×C₁₀₃	2
#131	103