Subgroups — #14670195

Order 2816.

278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070382	C₂	1	3	yes	maximal
2	#13070375	C₂	1	3	yes	maximal
3	C₁₁×#1747	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#405	C₂²	1	3	yes	—
5	C₂×#66876	C₂²	1	3	yes	—
6	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
7	C₁₁×#338	C₄	1	1	yes	characteristic
8	C₁₁×H(3,ℤ/4)	C₄	1	3	yes	—
9	#10622101	—	2	6	no	—
10	C₄⋊(C₁₁⋊C₁₆)	—	2	6	no	—
11	C₂×C₁₁×M₁₆	C₂×C₄	1	3	yes	—
12	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
13	C₁₁×#117	C₂×C₄	1	3	yes	—
14	C₁₁×#97	Q₈	1	6	yes	—
15	C₄×C₈×C₁₁	D₄	1	6	yes	—
16	#66876	—	2	6	no	—
17	C₂×C₁₁⋊C₁₆	—	2	3	no	—
18	C₂×C₁₁⋊C₁₆	—	2	3	no	—
19	#12902	—	11	1	no	maximal, Sylow
20	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
21	C₁₁×M₁₆	—	2	6	no	—
22	C₂×C₈×C₁₁	C₄⋊C₄	1	6	yes	—
23	C₂×C₈×C₁₁	C₂×D₄	1	3	yes	—
24	C₂×C₈×C₁₁	C₂×Q₈	1	3	yes	—
25	C₁₁×C₄⋊C₄	—	2	3	no	—
26	C₁₁×C₂²⋊C₄	—	2	3	no	—
27	C₄²×C₁₁	C₄⋊C₄	1	6	yes	—
28	C₁₁⋊C₁₆	—	4	1	no	—
29	C₁₁⋊C₁₆	—	4	3	no	—
30	#2153	—	11	3	no	—
31	#2151	—	11	3	no	—
32	#1747	D₁₁	1	1	yes	characteristic
33	C₂³×C₁₁	#131	1	1	yes	characteristic
34	C₂×C₄×C₁₁	—	2	6	no	—
35	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
36	C₂×C₄×C₁₁	#131	1	3	yes	—
37	C₈×C₁₁	—	2	6	no	—
38	C₈×C₁₁	#127	1	1	yes	characteristic
39	C₈×C₁₁	C₄⋊Q₈	1	3	yes	—
40	C₂×M₃₂	—	11	3	no	—
41	C₂²×C₁₆	—	11	1	no	—
42	#405	C₂×D₁₁	1	3	yes	—
43	#364	—	22	6	no	—
44	C₄⋊C₁₆	—	22	6	no	—
45	#338	Dic₁₁	1	1	yes	characteristic
46	H(3,ℤ/4)	Dic₁₁	1	3	yes	—
47	C₂²×C₁₁	—	4	1	no	—
48	C₂²×C₁₁	#424	1	3	yes	—
49	C₄×C₁₁	—	4	6	no	—
50	C₄×C₁₁	#384	1	1	yes	characteristic
51	C₄×C₁₁	#424	1	3	yes	—
52	C₂×M₁₆	C₂×Dic₁₁	1	3	yes	—
53	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
54	#117	C₂×Dic₁₁	1	3	yes	—
55	M₃₂	—	22	6	no	—
56	C₂×C₁₆	—	22	3	no	—
57	C₂×C₁₆	—	22	3	no	—
58	#97	Dic₂₂	1	6	yes	—
59	C₄×C₈	D₄₄	1	6	yes	—
60	C₂×C₁₁	—	2	3	no	—
61	C₂×C₁₁	#1843	1	1	yes	characteristic
62	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
63	M₁₆	—	2	6	no	—
64	C₂×C₈	C₄⋊Dic₁₁	1	6	yes	—
65	C₂×C₈	C₂×Dic₂₂	1	3	yes	—
66	C₂×C₈	C₂×D₄₄	1	3	yes	—
67	C₄⋊C₄	—	2	3	no	—
68	C₂²⋊C₄	—	2	3	no	—
69	C₄²	C₄⋊Dic₁₁	1	6	yes	—
70	C₁₆	—	44	1	no	—
71	C₁₆	—	44	3	no	—
72	C₁₁	#12902	1	1	yes	characteristic, complemented, Sylow
73	C₂³	#67001	1	1	yes	characteristic
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	C₂×C₄⋊Dic₁₁	1	3	yes	—
76	C₂×C₄	#67001	1	3	yes	—
77	C₈	—	2	6	no	—
78	C₈	#66922	1	3	yes	—
79	C₈	#66927	1	1	yes	characteristic
80	C₂²	—	4	1	no	—
81	C₂²	#10622612	1	3	yes	—
82	C₄	—	4	6	no	—
83	C₄	#10622548	1	1	yes	characteristic
84	C₄	#10622612	1	3	yes	—
85	C₂	—	2	3	no	—
86	C₂	#13068770	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#66927
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1747	C₂
socle	C₂×C₁₁	#1843
prime radical	C₂³×C₁₁	#131
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1747	D₁₁
hypocenter	C₁₁	#12902
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #1747

Complements

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

N	H ≅ G/N	type
72. C₁₁	#12902	semidirect

Maximal subgroups

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

subgroup	index
#13070382	2
#13070375	2
C₁₁×#1747	2
#12902	11