Subgroups — #27186298

Order 12928.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266106	C₂	1	1	yes	maximal, characteristic
2	#20266104	C₂	1	1	yes	maximal, characteristic
3	#20265010	C₂	1	1	yes	maximal, characteristic
4	#15692326	—	2	1	no	—
5	#15692324	—	2	1	no	—
6	C₁₆×D₁₀₁	C₂²	1	1	yes	characteristic
7	#15692161	C₄	1	1	yes	characteristic, complemented
8	C₃₂×C₁₀₁	C₄	1	1	yes	characteristic, complemented
9	#13108084	—	4	1	no	—
10	C₄⋊#87938	—	4	1	no	—
11	C₈×D₁₀₁	D₄	1	1	yes	characteristic
12	#13108049	Q₈	1	1	yes	characteristic
13	C₁₆×C₁₀₁	C₂×C₄	1	1	yes	characteristic
14	C₂×#87938	—	8	1	no	—
15	C₄×D₁₀₁	D₈	1	1	yes	characteristic
16	#11717581	—	8	1	no	—
17	C₈×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
18	#11717579	Q₁₆	1	1	yes	characteristic
19	C₂×D₁₀₁	SD₃₂	1	1	yes	characteristic
20	#87938	—	16	1	no	—
21	C₄×C₁₀₁	#107	1	1	yes	characteristic
22	Dic₁₀₁	SD₃₂	1	1	yes	characteristic
23	C₂×C₁₀₁	#367	1	1	yes	characteristic
24	D₁₀₁	—	2	1	no	—
25	#1426	—	101	1	no	maximal, Sylow
26	C₁₀₁	#1426	1	1	yes	characteristic, complemented, Sylow
27	M₆₄	—	101	1	no	—
28	#368	—	101	1	no	—
29	#367	—	101	1	no	—
30	C₂×C₁₆	—	101	1	no	—
31	#108	—	202	1	no	—
32	#107	—	202	1	no	—
33	C₃₂	—	101	1	no	—
34	C₃₂	#87938	1	1	yes	characteristic, complemented
35	M₁₆	—	404	1	no	—
36	C₂×C₈	—	101	1	no	—
37	C₄⋊C₄	—	404	1	no	—
38	C₁₆	—	101	1	no	—
39	C₁₆	C₂×#87938	1	1	yes	characteristic
40	C₂×C₄	—	808	1	no	—
41	C₂×C₄	—	101	1	no	—
42	C₈	—	808	1	no	—
43	C₈	—	101	1	no	—
44	C₈	C₄⋊#87938	1	1	yes	characteristic
45	C₂²	—	101	1	no	—
46	C₄	—	1616	1	no	—
47	C₄	—	101	1	no	—
48	C₄	#15692324	1	1	yes	characteristic
49	C₂	—	202	1	no	—
50	C₂	#20266104	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20266104
commutator	C₁₆×C₁₀₁	C₂×C₄
Frattini	C₁₆	C₂×#87938
Fitting	C₃₂×C₁₀₁	C₄
socle	C₂×C₁₀₁	#367
prime radical	C₂×D₁₀₁	SD₃₂
cosocle	C₁₆×D₁₀₁	C₂²
hypercenter	C₃₂	#87938
hypocenter	C₁₀₁	#1426
LCS	G ▷ C₁₆×C₁₀₁ ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
7. #15692161	C₄	semidirect
8. C₃₂×C₁₀₁	C₄	semidirect
26. C₁₀₁	#1426	semidirect
34. C₃₂	#87938	semidirect

Maximal subgroups

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

subgroup	index
#20266106	2
#20266104	2
#20265010	2
#1426	101