Subgroups — #13066813

Order 1408.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×M₆₄	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	#10622137	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
5	C₈×Dic₁₁	C₄	1	1	yes	characteristic
6	C₂×C₁₁⋊C₁₆	C₄	1	1	yes	characteristic
7	C₁₁×C₃₂	—	2	1	no	—
8	C₁₁⋊C₃₂	—	2	1	no	—
9	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
10	C₄×Dic₁₁	C₈	1	1	yes	characteristic
11	C₂×C₁₁⋊C₈	C₈	1	1	yes	characteristic
12	C₁₁×C₁₆	D₄	1	1	yes	characteristic
13	C₁₁×C₁₆	Q₈	1	1	yes	characteristic
14	C₁₁⋊C₁₆	—	2	1	no	—
15	#1422	—	11	1	no	maximal, Sylow
16	C₂×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
17	C₂×Dic₁₁	—	2	1	no	—
18	C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
19	C₈×C₁₁	M₁₆	1	1	yes	characteristic
20	C₁₁⋊C₈	C₁₆	1	2	yes	—
21	M₆₄	—	11	1	no	—
22	M₆₄	D₁₁	1	1	yes	characteristic
23	C₄×C₁₆	—	11	1	no	—
24	C₂²×C₁₁	M₃₂	1	1	yes	characteristic
25	C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
26	C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
27	Dic₁₁	—	2	2	no	—
28	C₂×C₁₆	—	11	1	no	—
29	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
30	C₄×C₈	—	11	1	no	—
31	C₃₂	—	2	1	no	—
32	C₃₂	—	22	1	no	—
33	C₂×C₁₁	—	2	1	no	—
34	C₂×C₁₁	C₄⋊C₁₆	1	1	yes	characteristic
35	C₂×C₈	—	11	1	no	—
36	C₂×C₈	C₄×D₁₁	1	1	yes	characteristic
37	C₄²	—	11	1	no	—
38	C₁₆	—	22	1	no	—
39	C₁₆	Dic₂₂	1	1	yes	characteristic
40	C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
41	C₁₁	#1422	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₄	—	22	1	no	—
43	C₂×C₄	C₈×D₁₁	1	1	yes	characteristic
44	C₈	—	11	2	no	—
45	C₈	#4313	1	1	yes	characteristic
46	C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
47	C₂²	#66862	1	1	yes	characteristic
48	C₄	—	22	2	no	—
49	C₄	C₁₆×D₁₁	1	1	yes	characteristic
50	C₄	Dic₁₁⋊C₈	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	Dic₁₁⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₁₁
Fitting	C₁₁×M₆₄	C₂
socle	C₂×C₁₁	C₄⋊C₁₆
prime radical	C₂²×C₁₁	M₃₂
cosocle	C₂×C₁₁×C₁₆	C₂²
hypercenter	M₆₄	D₁₁
hypocenter	C₁₁	#1422
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

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

Maximal subgroups

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

subgroup	index
C₁₁×M₆₄	2
C₁₆×Dic₁₁	2
#10622137	2
#1422	11