Subgroups — #14641440

Order 2816.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066814	C₂	1	1	yes	maximal, characteristic
2	#13066532	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1422	C₂	1	1	yes	maximal, characteristic
4	C₁₁×M₆₄	—	2	1	no	—
5	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
6	#10622137	—	2	1	no	—
7	C₄×C₁₁⋊C₁₆	C₄	1	1	yes	characteristic
8	C₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
9	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
10	C₂×C₁₁×C₁₆	Q₈	1	1	yes	characteristic
11	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₁⋊C₁₆	C₈	1	1	yes	characteristic
13	C₂×C₁₁⋊C₁₆	C₈	1	1	yes	characteristic
14	C₄×C₁₁⋊C₈	—	2	1	no	—
15	C₁₁×C₃₂	—	4	1	no	—
16	C₁₁⋊C₃₂	—	4	1	no	—
17	#7456	—	11	1	no	maximal, Sylow
18	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
20	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
21	C₂×C₁₁⋊C₈	—	2	2	no	—
22	C₁₁×C₁₆	—	2	1	no	—
23	C₁₁×C₁₆	SD₁₆	1	1	yes	characteristic
24	C₁₁×C₁₆	SD₁₆	1	1	yes	characteristic
25	C₁₁⋊C₁₆	—	2	1	no	—
26	C₁₁⋊C₁₆	C₁₆	1	2	yes	—
27	#1422	—	11	1	no	—
28	#1422	D₁₁	1	1	yes	characteristic
29	#1311	—	11	1	no	—
30	C₂×C₄×C₁₁	—	2	1	no	—
31	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
32	C₈×C₁₁	#106	1	1	yes	characteristic
33	C₈×C₁₁	#108	1	1	yes	characteristic
34	C₈×C₁₁	C₂×C₁₆	1	1	yes	characteristic
35	C₈×C₁₁	M₃₂	1	1	yes	characteristic
36	C₁₁⋊C₈	—	4	2	no	—
37	M₆₄	—	2	1	no	—
38	M₆₄	—	22	1	no	—
39	C₄×C₁₆	—	11	1	no	—
40	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
41	C₈²	—	11	1	no	—
42	C₂²×C₁₁	#364	1	1	yes	characteristic
43	C₄×C₁₁	—	2	2	no	—
44	C₄×C₁₁	#334	1	1	yes	characteristic
45	C₄×C₁₁	C₄⋊C₁₆	1	1	yes	characteristic
46	C₂×C₁₆	—	11	1	no	—
47	C₂×C₁₆	—	11	1	no	—
48	C₂×C₁₆	Dic₂₂	1	1	yes	characteristic
49	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
50	C₄×C₈	—	22	1	no	—
51	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
52	C₃₂	—	4	1	no	—
53	C₃₂	—	44	1	no	—
54	C₂×C₁₁	—	2	1	no	—
55	C₂×C₁₁	#1367	1	1	yes	characteristic
56	C₂×C₈	—	22	2	no	—
57	C₂×C₈	C₈×D₁₁	1	1	yes	characteristic
58	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
59	C₄²	#4313	1	1	yes	characteristic
60	C₁₆	—	2	1	no	—
61	C₁₆	—	11	2	no	—
62	C₁₆	—	22	1	no	—
63	C₁₆	#4324	1	1	yes	characteristic
64	C₁₆	#4325	1	1	yes	characteristic
65	C₁₁	#7456	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	Dic₁₁⋊C₈	1	1	yes	characteristic
68	C₈	—	44	2	no	—
69	C₈	C₁₆×D₁₁	1	1	yes	characteristic
70	C₈	#66862	1	1	yes	characteristic
71	C₈	#66872	1	1	yes	characteristic
72	C₈	#66886	1	1	yes	characteristic
73	C₂²	#10622149	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	#10622118	1	1	yes	characteristic
76	C₄	Dic₁₁⋊C₁₆	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	#13066679	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#66872
commutator	C₈×C₁₁	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₁₁
Fitting	C₁₁×#1422	C₂
socle	C₂×C₁₁	#1367
prime radical	C₂²×C₁₁	#364
cosocle	C₄×C₁₁×C₁₆	C₂²
hypercenter	#1422	D₁₁
hypocenter	C₁₁	#7456
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ #1422

Complements

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

N	H ≅ G/N	type
65. C₁₁	#7456	semidirect

Maximal subgroups

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

subgroup	index
#13066814	2
#13066532	2
C₁₁×#1422	2
#7456	11