Subgroups — #15692287

Order 3232.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13108075	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#13108064	C₂	1	1	yes	maximal, characteristic, complemented
4	#13108063	C₂	1	1	yes	maximal, characteristic, complemented
5	#13108061	C₂	1	1	yes	maximal, characteristic, complemented
6	#13108057	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
9	Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
10	D₄₀₄	—	2	1	no	—
11	D₄₀₄	C₂²	1	1	yes	characteristic
12	C₄×D₁₀₁	—	2	1	no	—
13	C₄×D₁₀₁	—	2	1	no	—
14	C₄×D₁₀₁	C₂²	1	1	yes	characteristic
15	Dic₂₀₂	—	2	1	no	—
16	Dic₂₀₂	C₂²	1	1	yes	characteristic
17	C₈×C₁₀₁	C₂²	1	1	yes	characteristic
18	#11717579	C₂²	1	1	yes	characteristic
19	C₂×D₁₀₁	—	2	1	no	—
20	C₂×D₁₀₁	D₄	1	1	yes	characteristic
21	C₄×C₁₀₁	—	2	1	no	—
22	C₄×C₁₀₁	—	2	1	no	—
23	C₄×C₁₀₁	C₂³	1	1	yes	characteristic
24	Dic₁₀₁	—	2	1	no	—
25	Dic₁₀₁	D₄	1	1	yes	characteristic
26	C₂×C₁₀₁	C₂×D₄	1	1	yes	characteristic
27	D₁₀₁	—	2	1	no	—
28	D₁₀₁	—	4	1	no	—
29	C₁₀₁	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	101	1	no	maximal, Sylow
31	#41	—	101	1	no	—
32	C₂×Q₈	—	101	1	no	—
33	Q₁₆	—	101	1	no	—
34	Q₁₆	D₁₀₁	1	1	yes	characteristic, complemented
35	SD₁₆	—	101	1	no	—
36	SD₁₆	—	101	1	no	—
37	M₁₆	—	101	1	no	—
38	Q₈	—	101	1	no	—
39	Q₈	—	202	1	no	—
40	Q₈	C₂×D₁₀₁	1	1	yes	characteristic
41	Q₈	C₂×D₁₀₁	1	1	yes	characteristic
42	D₄	—	101	1	no	—
43	D₄	—	202	1	no	—
44	C₂×C₄	—	101	1	no	—
45	C₂×C₄	—	202	1	no	—
46	C₂×C₄	—	202	1	no	—
47	C₈	—	101	1	no	—
48	C₈	C₂×D₁₀₁	1	1	yes	characteristic
49	C₂²	—	101	1	no	—
50	C₂²	—	202	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	101	1	no	—
54	C₄	—	202	1	no	—
55	C₄	C₂²×D₁₀₁	1	1	yes	characteristic
56	C₂	—	404	1	no	—
57	C₂	—	202	1	no	—
58	C₂	D₄×D₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₁₀₁
commutator, cosocle	C₄×C₁₀₁	C₂³
Frattini	C₄	C₂²×D₁₀₁
Fitting	Q₁₆×C₁₀₁	C₂
socle	C₂×C₁₀₁	C₂×D₄
prime radical	#13108075	C₂
hypercenter	Q₁₆	D₁₀₁
hypocenter	C₁₀₁	#137
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×D₁₀₁	C₂	semidirect
3. #13108064	C₂	semidirect
4. #13108063	C₂	semidirect
5. #13108061	C₂	semidirect
6. #13108057	C₂	semidirect
7. Q₁₆×C₁₀₁	C₂	semidirect
29. C₁₀₁	#137	semidirect
34. Q₁₆	D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#13108075	2
Q₈×D₁₀₁	2
#13108064	2
#13108063	2
#13108061	2
#13108057	2
Q₁₆×C₁₀₁	2
#137	101