Subgroups — #15693050

Order 3296.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13110104	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₄₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#13110095	C₂	1	1	yes	maximal, characteristic, complemented
5	#13110093	C₂	1	1	yes	maximal, characteristic, complemented
6	#13110088	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
9	D₄×C₁₀₃	C₂²	1	1	yes	characteristic
10	C₂²⋊D₁₀₃	—	2	1	no	—
11	C₂×Dic₁₀₃	—	2	1	no	—
12	C₄×D₁₀₃	—	2	1	no	—
13	C₄×D₁₀₃	C₂²	1	1	yes	characteristic
14	Dic₂₀₆	—	2	1	no	—
15	Dic₂₀₆	C₂²	1	1	yes	characteristic
16	Dic₂₀₆	C₂²	1	1	yes	characteristic
17	C₈×C₁₀₃	C₂²	1	1	yes	characteristic
18	C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₁₀₃	—	2	1	no	—
20	C₂×D₁₀₃	D₄	1	1	yes	characteristic
21	C₄×C₁₀₃	—	2	1	no	—
22	C₄×C₁₀₃	C₂³	1	1	yes	characteristic
23	Dic₁₀₃	—	2	1	no	—
24	Dic₁₀₃	—	2	1	no	—
25	Dic₁₀₃	D₄	1	1	yes	characteristic
26	C₂×C₁₀₃	—	4	1	no	—
27	C₂×C₁₀₃	C₂×D₄	1	1	yes	characteristic
28	D₁₀₃	—	2	1	no	—
29	C₁₀₃	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	103	1	no	maximal, Sylow
31	#41	—	103	1	no	—
32	C₂×Q₈	—	103	1	no	—
33	Q₁₆	—	103	1	no	—
34	Q₁₆	—	103	1	no	—
35	SD₁₆	—	103	1	no	—
36	SD₁₆	D₁₀₃	1	1	yes	characteristic, complemented
37	M₁₆	—	103	1	no	—
38	Q₈	—	103	1	no	—
39	Q₈	—	103	1	no	—
40	Q₈	—	206	1	no	—
41	Q₈	C₂×D₁₀₃	1	1	yes	characteristic
42	D₄	—	206	1	no	—
43	D₄	C₂×D₁₀₃	1	1	yes	characteristic
44	C₂×C₄	—	103	1	no	—
45	C₂×C₄	—	206	1	no	—
46	C₂×C₄	—	206	1	no	—
47	C₈	—	103	1	no	—
48	C₈	C₂×D₁₀₃	1	1	yes	characteristic
49	C₂²	—	2	1	no	—
50	C₂²	—	103	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	103	1	no	—
53	C₄	—	206	1	no	—
54	C₄	—	206	1	no	—
55	C₄	C₂²×D₁₀₃	1	1	yes	characteristic
56	C₂	—	4	1	no	—
57	C₂	—	206	1	no	—
58	C₂	D₄×D₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₁₀₃
commutator, cosocle	C₄×C₁₀₃	C₂³
Frattini	C₄	C₂²×D₁₀₃
Fitting	SD₁₆×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂×D₄
prime radical	#13110104	C₂
hypercenter	SD₁₆	D₁₀₃
hypocenter	C₁₀₃	#137
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×D₁₀₃	C₂	semidirect
3. Dic₄₁₂	C₂	semidirect
4. #13110095	C₂	semidirect
5. #13110093	C₂	semidirect
6. #13110088	C₂	semidirect
7. SD₁₆×C₁₀₃	C₂	semidirect
29. C₁₀₃	#137	semidirect
36. SD₁₆	D₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
#13110104	2
Q₈×D₁₀₃	2
Dic₄₁₂	2
#13110095	2
#13110093	2
#13110088	2
SD₁₆×C₁₀₃	2
#137	103