Subgroups — #13066819

Order 1408.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#368	C₂	1	1	yes	maximal, characteristic
2	#10622144	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×#108	—	2	1	no	—
6	#66883	—	2	1	no	—
7	C₁₁⋊C₃₂	C₄	1	2	yes	—
8	C₁₁×M₁₆	—	4	1	no	—
9	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
10	#4318	—	4	1	no	—
11	C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₁₁×C₁₆	Q₈	1	1	yes	characteristic
13	#1425	—	11	1	no	maximal, Sylow
14	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
15	C₈×C₁₁	—	8	1	no	—
16	C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₁	Q₁₆	1	1	yes	characteristic
18	C₁₁⋊C₈	—	8	1	no	—
19	C₂×C₃₂	—	11	1	no	—
20	#368	—	11	1	no	—
21	#368	D₁₁	1	1	yes	characteristic
22	C₂²×C₁₁	Q₃₂	1	1	yes	characteristic
23	C₄×C₁₁	#107	1	1	yes	characteristic
24	C₄×C₁₁	D₁₆	1	1	yes	characteristic
25	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
26	#108	—	2	1	no	—
27	#108	—	22	1	no	—
28	C₃₂	—	11	2	no	—
29	C₂×C₁₁	—	2	1	no	—
30	C₂×C₁₁	#366	1	1	yes	characteristic
31	M₁₆	—	4	1	no	—
32	M₁₆	—	44	1	no	—
33	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
34	C₁₆	Dic₂₂	1	1	yes	characteristic
35	C₁₆	C₄×D₁₁	1	1	yes	characteristic
36	C₁₁	#1425	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₄	#4323	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	88	1	no	—
40	C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
41	C₈	#4326	1	1	yes	characteristic
42	C₂²	#66893	1	1	yes	characteristic
43	C₄	#66871	1	1	yes	characteristic
44	C₄	#66890	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#10622127	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#66890
commutator	C₁₁×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₁
Fitting	C₁₁×#368	C₂
socle	C₂×C₁₁	#366
prime radical	C₂²×C₁₁	Q₃₂
cosocle	C₂×C₁₁×C₁₆	C₂²
hypercenter	#368	D₁₁
hypocenter	C₁₁	#1425
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
36. C₁₁	#1425	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#368	2
#10622144	2
C₂×C₁₁⋊C₃₂	2
#1425	11