Subgroups — #13070910

Order 1408.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#504	C₂	1	1	yes	maximal, characteristic
2	#10622137	C₂	1	3	yes	maximal, complemented
3	C₂×C₁₁⋊C₃₂	C₂	1	3	yes	maximal, complemented
4	C₁₁×#131	C₄	1	1	yes	characteristic
5	C₁₁×M₃₂	C₄	1	3	yes	—
6	C₂×C₁₁×C₁₆	C₂²	1	3	yes	—
7	C₁₁⋊C₃₂	C₂²	1	1	yes	characteristic
8	C₁₁⋊C₃₂	C₂²	1	3	yes	—
9	C₁₁×#41	C₈	1	1	yes	characteristic
10	C₁₁×M₁₆	C₈	1	3	yes	—
11	C₂×C₈×C₁₁	C₂×C₄	1	3	yes	—
12	C₁₁×C₁₆	C₂×C₄	1	3	yes	—
13	C₁₁×C₁₆	C₂³	1	1	yes	characteristic
14	#2258	—	11	1	no	maximal, Sylow
15	Q₈×C₁₁	C₁₆	1	1	yes	characteristic
16	D₄×C₁₁	C₁₆	1	3	yes	—
17	C₂×C₄×C₁₁	C₂×C₈	1	3	yes	—
18	C₈×C₁₁	C₂×C₈	1	3	yes	—
19	C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
20	#504	D₁₁	1	1	yes	characteristic
21	M₆₄	—	11	3	no	—
22	C₂×C₃₂	—	11	3	no	—
23	C₂²×C₁₁	C₂×C₁₆	1	3	yes	—
24	C₄×C₁₁	C₂×C₁₆	1	3	yes	—
25	C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
26	#131	Dic₁₁	1	1	yes	characteristic
27	M₃₂	Dic₁₁	1	3	yes	—
28	C₂×C₁₆	C₂×D₁₁	1	3	yes	—
29	C₃₂	—	11	1	no	—
30	C₃₂	—	11	3	no	—
31	C₂×C₁₁	—	2	3	no	—
32	C₂×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
33	#41	C₁₁⋊C₈	1	1	yes	characteristic
34	M₁₆	C₁₁⋊C₈	1	3	yes	—
35	C₂×C₈	C₂×Dic₁₁	1	3	yes	—
36	C₁₆	C₂×Dic₁₁	1	3	yes	—
37	C₁₆	C₂²×D₁₁	1	1	yes	characteristic
38	C₁₁	#2258	1	1	yes	characteristic, complemented, Sylow
39	Q₈	C₁₁⋊C₁₆	1	1	yes	characteristic
40	D₄	C₁₁⋊C₁₆	1	3	yes	—
41	C₂×C₄	C₂×C₁₁⋊C₈	1	3	yes	—
42	C₈	C₂×C₁₁⋊C₈	1	3	yes	—
43	C₈	C₂²×Dic₁₁	1	1	yes	characteristic
44	C₂²	C₂×C₁₁⋊C₁₆	1	3	yes	—
45	C₄	C₂×C₁₁⋊C₁₆	1	3	yes	—
46	C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×C₁₁⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×D₁₁
commutator, socle	C₂×C₁₁	C₂²×C₁₆
Fitting	C₁₁×#504	C₂
prime radical	C₁₁×#41	C₈
cosocle	C₁₁×C₁₆	C₂³
hypercenter	#504	D₁₁
hypocenter	C₁₁	#2258
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₁₆ ◁ #504

Complements

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

N	H ≅ G/N	type
2. #10622137	C₂	semidirect
3. C₂×C₁₁⋊C₃₂	C₂	semidirect
38. C₁₁	#2258	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#504	2
#10622137	2
C₂×C₁₁⋊C₃₂	2
#2258	11