Subgroups — #27186045

Order 12928.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13108077	C₂	1	2	yes	maximal
2	C₈×#11717579	C₂	1	1	yes	maximal, characteristic
3	C₂×#13108077	C₄	1	4	yes	—
4	C₄×#11717579	C₄	1	1	yes	characteristic
5	C₄×#11717579	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₁₀₁	C₄	1	1	yes	characteristic
7	#13108077	—	2	4	no	—
8	C₂×#11717579	C₈	1	2	yes	—
9	C₂×#11717579	C₂×C₄	1	2	yes	—
10	C₂×C₈×C₁₀₁	C₈	1	2	yes	—
11	C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₀₁	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₀₁	C₁₆	1	4	yes	complemented
16	#11717579	—	2	2	no	—
17	#11717579	M₁₆	1	4	yes	—
18	C₂²×C₁₀₁	C₄×C₈	1	1	yes	characteristic
19	C₄×C₁₀₁	#97	1	2	yes	—
20	C₄×C₁₀₁	C₂×C₁₆	1	2	yes	—
21	C₄×C₁₀₁	M₃₂	1	2	yes	—
22	C₂×C₁₀₁	#322	1	1	yes	characteristic
23	C₂×C₁₀₁	C₄×C₁₆	1	1	yes	characteristic
24	C₂×C₁₀₁	#346	1	1	yes	characteristic
25	#1312	—	101	1	no	maximal, Sylow
26	C₁₀₁	#1312	1	1	yes	characteristic, complemented, Sylow
27	C₄×C₁₆	—	101	2	no	—
28	C₈²	—	101	1	no	—
29	C₂×C₁₆	—	101	4	no	—
30	C₄×C₈	—	101	1	no	—
31	C₄×C₈	—	101	1	no	—
32	C₄×C₈	#87938	1	1	yes	characteristic
33	C₂×C₈	—	101	2	no	—
34	C₂×C₈	—	101	2	no	—
35	C₂×C₈	#11717581	1	2	yes	—
36	C₄²	C₂×#87938	1	1	yes	characteristic
37	C₁₆	—	202	4	no	—
38	C₂×C₄	C₄×#87938	1	1	yes	characteristic
39	C₂×C₄	C₂×#11717581	1	1	yes	characteristic
40	C₂×C₄	D₁₀₁⋊C₈	1	1	yes	characteristic
41	C₈	—	101	4	no	—
42	C₈	—	202	2	no	—
43	C₈	#13108077	1	4	yes	complemented
44	C₂²	C₄×#11717581	1	1	yes	characteristic
45	C₄	#15692309	1	2	yes	—
46	C₄	C₂×#13108077	1	2	yes	—
47	C₄	#15692330	1	2	yes	—
48	C₂	#20266018	1	1	yes	characteristic
49	C₂	C₄×#13108077	1	1	yes	characteristic
50	C₂	#20266066	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×#87938
commutator	C₂×C₁₀₁	C₄×C₁₆
Fitting	C₄×C₈×C₁₀₁	C₄
socle, prime radical	C₂²×C₁₀₁	C₄×C₈
cosocle	C₄×#11717579	C₂²
hypercenter	C₄×C₈	#87938
hypocenter	C₁₀₁	#1312
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
15. C₈×C₁₀₁	C₁₆	semidirect
26. C₁₀₁	#1312	semidirect
43. C₈	#13108077	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13108077	2
C₈×#11717579	2
#1312	101