Subgroups — #27169334

Order 12928.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265003	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	#15692189	—	2	2	no	—
4	C₂×C₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
5	C₃₂×C₁₀₁	C₄	1	2	yes	complemented
6	C₄⋊Dic₁₀₁	—	4	2	no	—
7	C₂×C₈×C₁₀₁	D₄	1	1	yes	characteristic
8	C₁₆×C₁₀₁	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₁₀₁	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₀₁	D₈	1	1	yes	characteristic
11	C₂×Dic₁₀₁	—	8	2	no	—
12	C₈×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₁₀₁	Q₁₆	1	1	yes	characteristic
14	C₂²×C₁₀₁	D₁₆	1	1	yes	characteristic
15	C₄×C₁₀₁	#107	1	1	yes	characteristic
16	C₄×C₁₀₁	Q₃₂	1	1	yes	characteristic
17	Dic₁₀₁	—	16	2	no	—
18	C₂×C₁₀₁	#366	1	1	yes	characteristic
19	C₂×C₁₀₁	SD₆₄	1	2	yes	—
20	#1424	—	101	1	no	maximal, Sylow
21	C₁₀₁	#1424	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃₂	D₁₀₁	1	1	yes	characteristic
23	#366	—	101	2	no	—
24	C₂×C₁₆	C₂×D₁₀₁	1	1	yes	characteristic
25	#107	—	202	2	no	—
26	C₃₂	Dic₁₀₁	1	2	yes	complemented
27	C₂×C₈	D₄₀₄	1	1	yes	characteristic
28	C₄⋊C₄	—	404	2	no	—
29	C₁₆	Dic₂₀₂	1	1	yes	characteristic
30	C₁₆	C₂×Dic₁₀₁	1	1	yes	characteristic
31	C₂×C₄	—	808	2	no	—
32	C₂×C₄	D₈₀₈	1	1	yes	characteristic
33	C₈	C₄⋊Dic₁₀₁	1	1	yes	characteristic
34	C₈	Dic₄₀₄	1	1	yes	characteristic
35	C₂²	D₁₆₁₆	1	1	yes	characteristic
36	C₄	—	1616	2	no	—
37	C₄	#15692189	1	1	yes	characteristic
38	C₄	Dic₈₀₈	1	1	yes	characteristic
39	C₂	#20265003	1	1	yes	characteristic
40	C₂	#20265016	1	2	yes	—

	subgroup	G/H
center	C₂²	D₁₆₁₆
commutator	C₁₆×C₁₀₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₀₁
Fitting	C₂×C₃₂×C₁₀₁	C₂
socle, prime radical	C₂²×C₁₀₁	D₁₆
cosocle	C₂×C₁₆×C₁₀₁	C₂²
hypercenter	C₂×C₃₂	D₁₀₁
hypocenter	C₁₀₁	#1424
LCS	G ▷ C₁₆×C₁₀₁ ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
5. C₃₂×C₁₀₁	C₄	semidirect
21. C₁₀₁	#1424	semidirect
26. C₃₂	Dic₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265003	2
C₂×C₃₂×C₁₀₁	2
#1424	101