Subgroups — #15693053

Order 3296.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13110106	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#13110095	C₂	1	1	yes	maximal, characteristic, complemented
4	#13110094	C₂	1	1	yes	maximal, characteristic, complemented
5	#13110092	C₂	1	1	yes	maximal, characteristic, complemented
6	#13110088	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
9	Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
10	D₄₁₂	—	2	1	no	—
11	D₄₁₂	C₂²	1	1	yes	characteristic
12	C₄×D₁₀₃	—	2	1	no	—
13	C₄×D₁₀₃	—	2	1	no	—
14	C₄×D₁₀₃	C₂²	1	1	yes	characteristic
15	Dic₂₀₆	—	2	1	no	—
16	Dic₂₀₆	C₂²	1	1	yes	characteristic
17	C₈×C₁₀₃	C₂²	1	1	yes	characteristic
18	C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×D₁₀₃	—	2	1	no	—
20	C₂×D₁₀₃	D₄	1	1	yes	characteristic
21	C₄×C₁₀₃	—	2	1	no	—
22	C₄×C₁₀₃	—	2	1	no	—
23	C₄×C₁₀₃	C₂³	1	1	yes	characteristic
24	Dic₁₀₃	—	2	1	no	—
25	Dic₁₀₃	D₄	1	1	yes	characteristic
26	C₂×C₁₀₃	C₂×D₄	1	1	yes	characteristic
27	D₁₀₃	—	2	1	no	—
28	D₁₀₃	—	4	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	D₁₀₃	1	1	yes	characteristic, complemented
35	SD₁₆	—	103	1	no	—
36	SD₁₆	—	103	1	no	—
37	M₁₆	—	103	1	no	—
38	Q₈	—	103	1	no	—
39	Q₈	—	206	1	no	—
40	Q₈	C₂×D₁₀₃	1	1	yes	characteristic
41	Q₈	C₂×D₁₀₃	1	1	yes	characteristic
42	D₄	—	103	1	no	—
43	D₄	—	206	1	no	—
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	—	103	1	no	—
50	C₂²	—	206	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	103	1	no	—
54	C₄	—	206	1	no	—
55	C₄	C₂²×D₁₀₃	1	1	yes	characteristic
56	C₂	—	412	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	Q₁₆×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂×D₄
prime radical	#13110106	C₂
hypercenter	Q₁₆	D₁₀₃
hypocenter	C₁₀₃	#137
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×D₁₀₃	C₂	semidirect
3. #13110095	C₂	semidirect
4. #13110094	C₂	semidirect
5. #13110092	C₂	semidirect
6. #13110088	C₂	semidirect
7. Q₁₆×C₁₀₃	C₂	semidirect
29. C₁₀₃	#137	semidirect
34. Q₁₆	D₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
#13110106	2
Q₈×D₁₀₃	2
#13110095	2
#13110094	2
#13110092	2
#13110088	2
Q₁₆×C₁₀₃	2
#137	103