Subgroups — #13066814

Order 1408.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
2	#10622137	C₂	1	2	yes	maximal
3	C₂×C₁₁×C₁₆	C₄	1	1	yes	characteristic
4	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
6	C₁₁⋊C₃₂	—	2	2	no	—
7	C₂×C₈×C₁₁	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₁₁	C₈	1	1	yes	characteristic
10	C₁₁×C₁₆	—	2	1	no	—
11	C₁₁×C₁₆	D₄	1	1	yes	characteristic
12	C₁₁×C₁₆	Q₈	1	1	yes	characteristic
13	#1422	—	11	1	no	maximal, Sylow
14	C₂×C₄×C₁₁	—	2	1	no	—
15	C₂×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
16	C₈×C₁₁	C₁₆	1	2	yes	—
17	C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₁	M₁₆	1	1	yes	characteristic
19	M₆₄	—	11	2	no	—
20	C₄×C₁₆	D₁₁	1	1	yes	characteristic
21	C₂²×C₁₁	M₃₂	1	1	yes	characteristic
22	C₄×C₁₁	—	2	2	no	—
23	C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
24	C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₁₆	Dic₁₁	1	1	yes	characteristic
26	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
27	C₄×C₈	Dic₁₁	1	1	yes	characteristic
28	C₃₂	—	22	2	no	—
29	C₂×C₁₁	—	2	1	no	—
30	C₂×C₁₁	C₄⋊C₁₆	1	1	yes	characteristic
31	C₂×C₈	C₁₁⋊C₈	1	1	yes	characteristic
32	C₂×C₈	C₂×Dic₁₁	1	1	yes	characteristic
33	C₄²	C₁₁⋊C₈	1	1	yes	characteristic
34	C₁₆	—	2	1	no	—
35	C₁₆	Dic₂₂	1	1	yes	characteristic
36	C₁₆	D₄₄	1	1	yes	characteristic
37	C₁₁	#1422	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
40	C₈	C₁₁⋊C₁₆	1	2	yes	—
41	C₈	#4318	1	1	yes	characteristic
42	C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
43	C₂²	#66876	1	1	yes	characteristic
44	C₄	—	2	2	no	—
45	C₄	C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
46	C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₄⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₄₄
commutator	C₄×C₁₁	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₁₁
Fitting	C₄×C₁₁×C₁₆	C₂
socle	C₂×C₁₁	C₄⋊C₁₆
prime radical	C₂²×C₁₁	M₃₂
cosocle	C₂×C₁₁×C₁₆	C₂²
hypercenter	C₄×C₁₆	D₁₁
hypocenter	C₁₁	#1422
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
37. C₁₁	#1422	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₁×C₁₆	2
#10622137	2
#1422	11