Subgroups — #27186159

Order 12928.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266099	C₂	1	2	yes	maximal
2	#20264952	C₂	1	1	yes	maximal, characteristic
3	#15692329	—	2	2	no	—
4	C₂×#13108049	C₄	1	1	yes	characteristic
5	C₈×Dic₁₀₁	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₁₀₁	C₄	1	1	yes	characteristic
7	#13108077	—	4	2	no	—
8	C₂×#11717579	D₄	1	1	yes	characteristic
9	C₄×Dic₁₀₁	Q₈	1	1	yes	characteristic
10	#13108049	—	2	1	no	—
11	C₂×C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₀₁	C₈	1	2	yes	—
13	C₂×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
14	C₂×Dic₁₀₁	—	2	1	no	—
15	C₈×C₁₀₁	C₂×C₈	1	1	yes	characteristic
16	C₈×C₁₀₁	M₁₆	1	1	yes	characteristic
17	#11717579	SD₁₆	1	2	yes	—
18	C₂²×C₁₀₁	#108	1	1	yes	characteristic
19	C₄×C₁₀₁	C₄⋊C₈	1	1	yes	characteristic
20	C₄×C₁₀₁	#106	1	1	yes	characteristic
21	Dic₁₀₁	—	4	1	no	—
22	C₂×C₁₀₁	—	2	1	no	—
23	C₂×C₁₀₁	#334	1	1	yes	characteristic
24	#1369	—	101	1	no	maximal, Sylow
25	C₁₀₁	#1369	1	1	yes	characteristic, complemented, Sylow
26	#364	—	101	2	no	—
27	#346	—	101	1	no	—
28	M₃₂	—	202	2	no	—
29	C₂×C₁₆	—	101	1	no	—
30	C₂×C₁₆	#87938	1	1	yes	characteristic
31	C₄×C₈	—	101	1	no	—
32	C₂×C₈	—	101	1	no	—
33	C₂×C₈	C₂×#87938	1	1	yes	characteristic
34	C₄²	—	101	1	no	—
35	C₁₆	—	404	2	no	—
36	C₁₆	—	202	1	no	—
37	C₁₆	#11717581	1	2	yes	—
38	C₂×C₄	—	202	1	no	—
39	C₂×C₄	C₄⋊#87938	1	1	yes	characteristic
40	C₈	—	101	2	no	—
41	C₈	C₂×#11717581	1	1	yes	characteristic
42	C₈	#13108084	1	1	yes	characteristic
43	C₂²	#15692325	1	1	yes	characteristic
44	C₄	—	404	1	no	—
45	C₄	C₄⋊#11717581	1	1	yes	characteristic
46	C₄	#15692323	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#20266038	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15692323
commutator	C₈×C₁₀₁	C₂×C₈
Frattini	C₂×C₈	C₂×#87938
Fitting	C₂×C₁₆×C₁₀₁	C₄
socle	C₂×C₁₀₁	#334
prime radical	C₂²×C₁₀₁	#108
cosocle	C₈×Dic₁₀₁	C₂²
hypercenter	C₂×C₁₆	#87938
hypocenter	C₁₀₁	#1369
LCS	G ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
25. C₁₀₁	#1369	semidirect

Maximal subgroups

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

subgroup	index
#20266099	2
#20264952	2
#1369	101