Subgroups — #13066558

Order 1408.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#424	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₁₁⋊C₁₆)	C₂	1	2	yes	maximal
3	C₂×C₁₁×M₁₆	C₄	1	1	yes	characteristic
4	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
5	C₁₁×#117	C₄	1	1	yes	characteristic
6	C₁₁×C₄⋊C₈	—	2	2	no	—
7	C₂×C₁₁⋊C₁₆	—	2	2	no	—
8	C₂²×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
9	C₁₁×M₁₆	—	4	1	no	—
10	C₂×C₈×C₁₁	—	2	1	no	—
11	C₂×C₈×C₁₁	—	4	1	no	—
12	C₂×C₈×C₁₁	D₄	1	2	yes	—
13	C₁₁×C₄⋊C₄	C₈	1	2	yes	—
14	C₁₁×C₂²⋊C₄	—	2	1	no	—
15	C₄²×C₁₁	—	2	1	no	—
16	C₁₁⋊C₁₆	—	4	2	no	—
17	#1323	—	11	1	no	maximal, Sylow
18	C₂³×C₁₁	M₁₆	1	1	yes	characteristic
19	C₂×C₄×C₁₁	—	2	1	no	—
20	C₂×C₄×C₁₁	—	2	1	no	—
21	C₂×C₄×C₁₁	—	2	2	no	—
22	C₂×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
24	C₈×C₁₁	—	2	2	no	—
25	C₈×C₁₁	—	4	1	no	—
26	#424	D₁₁	1	1	yes	characteristic
27	C₂²⋊C₁₆	—	11	2	no	—
28	C₂²×C₁₁	—	2	1	no	—
29	C₂²×C₁₁	—	2	2	no	—
30	C₂²×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₁₁	—	2	1	no	—
32	C₄×C₁₁	—	4	2	no	—
33	C₄×C₁₁	#99	1	1	yes	characteristic
34	C₄×C₁₁	#101	1	1	yes	characteristic
35	C₂×M₁₆	Dic₁₁	1	1	yes	characteristic
36	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
37	#117	Dic₁₁	1	1	yes	characteristic
38	C₂×C₁₆	—	22	2	no	—
39	C₄⋊C₈	—	2	2	no	—
40	C₂×C₁₁	—	4	1	no	—
41	C₂×C₁₁	#324	1	1	yes	characteristic
42	C₂×C₁₁	#350	1	2	yes	—
43	C₂²×C₄	C₂×Dic₁₁	1	1	yes	characteristic
44	M₁₆	—	4	1	no	—
45	C₂×C₈	—	2	1	no	—
46	C₂×C₈	—	4	1	no	—
47	C₂×C₈	C₂²⋊D₁₁	1	2	yes	—
48	C₄⋊C₄	C₁₁⋊C₈	1	2	yes	—
49	C₂²⋊C₄	—	2	1	no	—
50	C₄²	—	2	1	no	—
51	C₁₆	—	44	2	no	—
52	C₁₁	#1323	1	1	yes	characteristic, complemented, Sylow
53	C₂³	#4318	1	1	yes	characteristic
54	C₂×C₄	—	2	1	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
58	C₂×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
59	C₈	—	2	2	no	—
60	C₈	—	4	1	no	—
61	C₂²	—	2	1	no	—
62	C₂²	—	2	2	no	—
63	C₂²	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	4	2	no	—
66	C₄	#66898	1	1	yes	characteristic
67	C₄	#66900	1	1	yes	characteristic
68	C₂	—	4	1	no	—
69	C₂	#10622166	1	1	yes	characteristic
70	C₂	#10622199	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₁₁
commutator	C₂×C₄×C₁₁	C₂×C₈
Frattini	C₂²×C₈	C₂×D₁₁
Fitting	C₁₁×#424	C₂
socle	C₂²×C₁₁	C₂²⋊C₈
prime radical	C₂³×C₁₁	M₁₆
cosocle	C₂²×C₈×C₁₁	C₂²
hypercenter	#424	D₁₁
hypocenter	C₁₁	#1323
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #424

Complements

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

N	H ≅ G/N	type
52. C₁₁	#1323	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#424	2
C₂²⋊(C₁₁⋊C₁₆)	2
#1323	11