Subgroups — #13066815

Order 1408.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#366	C₂	1	1	yes	maximal, characteristic
2	#10622142	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
5	C₁₁×#107	—	2	1	no	—
6	#66882	—	2	1	no	—
7	C₁₁⋊C₃₂	C₄	1	2	yes	complemented
8	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
9	C₁₁×C₄⋊C₄	—	4	1	no	—
10	C₄⋊Dic₁₁	—	4	1	no	—
11	C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₁₁×C₁₆	Q₈	1	1	yes	characteristic
13	#1423	—	11	1	no	maximal, Sylow
14	C₂×C₄×C₁₁	—	8	1	no	—
15	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
16	C₂×Dic₁₁	—	8	1	no	—
17	C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₁	Q₁₆	1	1	yes	characteristic
19	C₂×C₃₂	—	11	1	no	—
20	#366	—	11	1	no	—
21	#366	D₁₁	1	1	yes	characteristic
22	C₂²×C₁₁	D₁₆	1	1	yes	characteristic
23	C₄×C₁₁	—	16	1	no	—
24	C₄×C₁₁	#107	1	1	yes	characteristic
25	C₄×C₁₁	Q₃₂	1	1	yes	characteristic
26	Dic₁₁	—	16	1	no	—
27	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
28	#107	—	2	1	no	—
29	#107	—	22	1	no	—
30	C₃₂	—	11	2	no	—
31	C₂×C₁₁	#366	1	1	yes	characteristic
32	C₂×C₁₁	D₃₂	1	1	yes	characteristic
33	C₂×C₁₁	Q₆₄	1	1	yes	characteristic
34	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
35	C₄⋊C₄	—	4	1	no	—
36	C₄⋊C₄	—	44	1	no	—
37	C₁₆	Dic₂₂	1	1	yes	characteristic
38	C₁₆	C₄×D₁₁	1	1	yes	characteristic
39	C₁₁	#1423	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	88	1	no	—
42	C₂×C₄	#4323	1	1	yes	characteristic
43	C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
44	C₈	#4326	1	1	yes	characteristic
45	C₂²	#66890	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	176	1	no	—
48	C₄	#66871	1	1	yes	characteristic
49	C₄	#66893	1	1	yes	characteristic
50	C₂	#10622127	1	1	yes	characteristic
51	C₂	#10622157	1	1	yes	characteristic
52	C₂	#10622160	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#66890
commutator	C₁₁×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₁
Fitting	C₁₁×#366	C₂
socle, prime radical	C₂²×C₁₁	D₁₆
cosocle	C₂×C₁₁×C₁₆	C₂²
hypercenter	#366	D₁₁
hypocenter	C₁₁	#1423
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
7. C₁₁⋊C₃₂	C₄	semidirect
39. C₁₁	#1423	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#366	2
#10622142	2
C₂×C₁₁⋊C₃₂	2
#1423	11