Subgroups — #14641442

Order 2816.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066752	C₂	1	1	yes	maximal, characteristic
2	#13066684	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1368	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#346	C₂²	1	1	yes	characteristic
5	C₁₁×#334	—	2	1	no	—
6	#10622137	C₄	1	1	yes	characteristic
7	#10622137	C₄	1	1	yes	characteristic
8	#10622101	—	2	1	no	—
9	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
10	C₂×C₁₁×C₁₆	Q₈	1	1	yes	characteristic
11	C₁₁×C₄⋊C₈	—	4	1	no	—
12	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
13	#66876	—	4	1	no	—
14	C₁₁⋊C₃₂	—	2	1	no	—
15	C₁₁⋊C₃₂	C₈	1	2	yes	complemented
16	#7457	—	11	1	no	maximal, Sylow
17	C₂×C₈×C₁₁	—	8	1	no	—
18	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
20	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
21	C₁₁×C₁₆	—	2	1	no	—
22	C₁₁×C₁₆	C₂×C₈	1	1	yes	characteristic
23	C₁₁×C₁₆	M₁₆	1	1	yes	characteristic
24	C₁₁⋊C₁₆	—	8	1	no	—
25	#1398	—	11	1	no	—
26	#1369	—	11	1	no	—
27	#1368	D₁₁	1	1	yes	characteristic
28	C₂×C₄×C₁₁	—	2	1	no	—
29	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
30	C₈×C₁₁	—	2	1	no	—
31	C₈×C₁₁	—	16	1	no	—
32	C₈×C₁₁	C₄⋊C₈	1	1	yes	characteristic
33	C₈×C₁₁	#108	1	1	yes	characteristic
34	M₆₄	—	11	1	no	—
35	M₆₄	—	11	1	no	—
36	#364	—	22	1	no	—
37	#346	C₂×D₁₁	1	1	yes	characteristic
38	#334	—	2	1	no	—
39	C₂²×C₁₁	#365	1	1	yes	characteristic
40	C₄×C₁₁	—	4	1	no	—
41	C₄×C₁₁	#334	1	1	yes	characteristic
42	C₄×C₁₁	#365	1	1	yes	characteristic
43	M₃₂	—	44	1	no	—
44	C₂×C₁₆	Dic₂₂	1	1	yes	characteristic
45	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
46	C₄⋊C₈	—	4	1	no	—
47	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
48	C₃₂	—	11	2	no	—
49	C₃₂	—	22	1	no	—
50	C₂×C₁₁	—	2	1	no	—
51	C₂×C₁₁	#1368	1	1	yes	characteristic
52	C₂×C₈	—	8	1	no	—
53	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
54	C₂×C₈	#4325	1	1	yes	characteristic
55	C₄²	#4324	1	1	yes	characteristic
56	C₁₆	—	2	1	no	—
57	C₁₆	—	88	1	no	—
58	C₁₆	C₈×D₁₁	1	1	yes	characteristic
59	C₁₆	#4313	1	1	yes	characteristic
60	C₁₁	#7457	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	#66872	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	16	1	no	—
65	C₈	Dic₁₁⋊C₈	1	1	yes	characteristic
66	C₈	#66886	1	1	yes	characteristic
67	C₂²	#10622125	1	1	yes	characteristic
68	C₄	—	4	1	no	—
69	C₄	#10622118	1	1	yes	characteristic
70	C₄	#10622132	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#13066681	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13066681
commutator	C₁₁×C₁₆	C₂×C₈
Frattini	#346	C₂×D₁₁
Fitting	C₁₁×#1368	C₂
socle	C₂×C₁₁	#1368
prime radical	C₂²×C₁₁	#365
cosocle	C₁₁×#346	C₂²
hypercenter	#1368	D₁₁
hypocenter	C₁₁	#7457
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346 ◁ #1368

Complements

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

N	H ≅ G/N	type
15. C₁₁⋊C₃₂	C₈	semidirect
60. C₁₁	#7457	semidirect

Maximal subgroups

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

subgroup	index
#13066752	2
#13066684	2
C₁₁×#1368	2
#7457	11