Subgroups — #27186050

Order 12928.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266065	C₂	1	1	yes	maximal, characteristic
2	#20266065	C₂	1	1	yes	maximal, characteristic
3	#20264899	C₂	1	1	yes	maximal, characteristic
4	C₂×#13108077	C₄	1	2	yes	—
5	C₂×#13108077	C₄	1	2	yes	—
6	C₄×#11717579	C₄	1	1	yes	characteristic
7	C₄×#11717579	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₁₀₁	C₄	1	1	yes	characteristic
9	#13108077	—	2	2	no	—
10	#13108077	C₈	1	4	yes	complemented
11	C₂×#11717579	—	2	1	no	—
12	C₂×#11717579	C₂×C₄	1	1	yes	characteristic
13	C₂×#11717579	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₀₁	—	2	1	no	—
15	C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₁	C₄²	1	1	yes	characteristic
17	C₂×C₄×C₁₀₁	M₁₆	1	1	yes	characteristic
18	C₂×C₄×C₁₀₁	M₁₆	1	1	yes	characteristic
19	C₈×C₁₀₁	—	4	1	no	—
20	#11717579	—	4	1	no	—
21	#11717579	C₂×C₈	1	2	yes	—
22	#11717579	M₁₆	1	2	yes	—
23	C₂²×C₁₀₁	#97	1	1	yes	characteristic
24	C₄×C₁₀₁	—	2	1	no	—
25	C₄×C₁₀₁	—	2	1	no	—
26	C₄×C₁₀₁	C₄×C₈	1	1	yes	characteristic
27	C₄×C₁₀₁	#97	1	1	yes	characteristic
28	C₂×C₁₀₁	#322	1	1	yes	characteristic
29	C₂×C₁₀₁	#347	1	1	yes	characteristic
30	C₂×C₁₀₁	#347	1	1	yes	characteristic
31	#1313	—	101	1	no	maximal, Sylow
32	C₁₀₁	#1313	1	1	yes	characteristic, complemented, Sylow
33	#346	—	101	1	no	—
34	#346	—	101	1	no	—
35	#322	—	101	1	no	—
36	C₂×C₁₆	—	101	2	no	—
37	C₂×C₁₆	—	101	2	no	—
38	C₄×C₈	—	101	1	no	—
39	C₄×C₈	—	101	1	no	—
40	C₄×C₈	#87938	1	1	yes	characteristic
41	C₂×C₈	—	2	1	no	—
42	C₂×C₈	—	101	1	no	—
43	C₂×C₈	—	101	1	no	—
44	C₂×C₈	—	202	1	no	—
45	C₄²	C₂×#87938	1	1	yes	characteristic
46	C₁₆	—	101	4	no	—
47	C₁₆	—	202	2	no	—
48	C₂×C₄	C₄×#87938	1	1	yes	characteristic
49	C₂×C₄	#13108083	1	1	yes	characteristic
50	C₂×C₄	#13108084	1	1	yes	characteristic
51	C₈	—	4	1	no	—
52	C₈	—	101	2	no	—
53	C₈	—	101	2	no	—
54	C₈	—	404	1	no	—
55	C₂²	#15692310	1	1	yes	characteristic
56	C₄	—	2	1	no	—
57	C₄	—	2	1	no	—
58	C₄	C₈×#87938	1	1	yes	characteristic
59	C₄	#15692309	1	1	yes	characteristic
60	C₂	#11717581⋊C₈	1	1	yes	characteristic
61	C₂	#20266069	1	1	yes	characteristic
62	C₂	#20266070	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#87938
commutator	C₄×C₁₀₁	C₄×C₈
Frattini	C₄²	C₂×#87938
Fitting	C₄×C₈×C₁₀₁	C₄
socle, prime radical	C₂²×C₁₀₁	#97
cosocle	C₄×#11717579	C₂²
hypercenter	C₄×C₈	#87938
hypocenter	C₁₀₁	#1313
LCS	G ▷ C₄×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
10. #13108077	C₈	semidirect
32. C₁₀₁	#1313	semidirect

Maximal subgroups

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

subgroup	index
#20266065	2
#20264899	2
#1313	101