Subgroups — #14641441

Order 2816.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066814	C₂	1	2	yes	maximal
2	C₁₁×#1311	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₁×C₁₆	C₄	1	1	yes	characteristic
4	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
5	C₈²×C₁₁	C₄	1	1	yes	characteristic
6	#10622137	—	2	2	no	—
7	C₂×C₁₁×C₁₆	C₈	1	1	yes	characteristic
8	C₂×C₁₁×C₁₆	C₈	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	—	2	1	no	—
12	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
13	C₁₁⋊C₃₂	—	4	2	no	—
14	#7456	—	11	1	no	maximal, Sylow
15	C₂×C₈×C₁₁	—	2	2	no	—
16	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
18	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
19	C₁₁×C₁₆	—	2	1	no	—
20	C₁₁×C₁₆	—	2	1	no	—
21	C₁₁×C₁₆	C₁₆	1	2	yes	—
22	C₁₁×C₁₆	SD₁₆	1	2	yes	—
23	#1422	—	11	2	no	—
24	#1311	D₁₁	1	1	yes	characteristic
25	C₂×C₄×C₁₁	—	2	1	no	—
26	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
27	C₈×C₁₁	—	4	2	no	—
28	C₈×C₁₁	#106	1	1	yes	characteristic
29	C₈×C₁₁	#108	1	1	yes	characteristic
30	C₈×C₁₁	C₂×C₁₆	1	1	yes	characteristic
31	C₈×C₁₁	M₃₂	1	1	yes	characteristic
32	M₆₄	—	22	2	no	—
33	C₄×C₁₆	Dic₁₁	1	1	yes	characteristic
34	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
35	C₈²	Dic₁₁	1	1	yes	characteristic
36	C₂²×C₁₁	#364	1	1	yes	characteristic
37	C₄×C₁₁	—	2	2	no	—
38	C₄×C₁₁	#334	1	1	yes	characteristic
39	C₄×C₁₁	C₄⋊C₁₆	1	1	yes	characteristic
40	C₂×C₁₆	C₁₁⋊C₈	1	1	yes	characteristic
41	C₂×C₁₆	C₁₁⋊C₈	1	1	yes	characteristic
42	C₂×C₁₆	Dic₂₂	1	1	yes	characteristic
43	C₂×C₁₆	D₄₄	1	1	yes	characteristic
44	C₄×C₈	—	2	1	no	—
45	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
46	C₃₂	—	44	2	no	—
47	C₂×C₁₁	—	2	1	no	—
48	C₂×C₁₁	#1367	1	1	yes	characteristic
49	C₂×C₈	—	2	2	no	—
50	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
51	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
52	C₄²	#4318	1	1	yes	characteristic
53	C₁₆	—	2	1	no	—
54	C₁₆	—	2	1	no	—
55	C₁₆	C₁₁⋊C₁₆	1	2	yes	—
56	C₁₆	#4314	1	2	yes	—
57	C₁₁	#7456	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
60	C₈	—	4	2	no	—
61	C₈	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
62	C₈	#66876	1	1	yes	characteristic
63	C₈	#66881	1	1	yes	characteristic
64	C₈	#66883	1	1	yes	characteristic
65	C₂²	#10622101	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	#10622095	1	1	yes	characteristic
68	C₄	C₄⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	#13066680	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#66881
commutator	C₈×C₁₁	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₁₁
Fitting	C₁₁×#1311	C₂
socle	C₂×C₁₁	#1367
prime radical	C₂²×C₁₁	#364
cosocle	C₄×C₁₁×C₁₆	C₂²
hypercenter	#1311	D₁₁
hypocenter	C₁₁	#7456
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ #1311

Complements

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

N	H ≅ G/N	type
57. 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
C₁₁×#1311	2
#7456	11