Subgroups — C₁₁×#1328 #13064166

Order 1408.

90 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	C₁₁×#349	C₂	1	2	yes	maximal
3	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
4	C₂²×C₈×C₁₁	C₄	1	1	yes	characteristic
5	C₁₁×#117	C₄	1	1	yes	characteristic
6	C₁₁×M₃₂	—	2	2	no	—
7	C₁₁×C₄⋊C₈	—	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	—	2	1	no	—
14	C₁₁×C₂²⋊C₄	C₈	1	2	yes	—
15	C₄²×C₁₁	—	2	1	no	—
16	C₁₁×C₁₆	—	4	2	no	—
17	#1328	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂³×C₁₁	C₂×C₈	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	M₁₆	1	1	yes	characteristic
24	C₈×C₁₁	—	2	2	no	—
25	C₈×C₁₁	—	4	1	no	—
26	#424	C₂×C₁₁	1	1	yes	characteristic
27	#349	C₂×C₁₁	1	2	yes	—
28	C₂²×C₁₁	—	2	1	no	—
29	C₂²×C₁₁	—	4	1	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	C₂²×C₁₁	1	1	yes	characteristic
36	C₂²×C₈	C₄×C₁₁	1	1	yes	characteristic
37	#117	C₄×C₁₁	1	1	yes	characteristic
38	M₃₂	—	2	2	no	—
39	C₄⋊C₈	—	2	2	no	—
40	C₂×C₁₁	—	2	1	no	—
41	C₂×C₁₁	—	4	1	no	—
42	C₂×C₁₁	#324	1	1	yes	characteristic
43	C₂²×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
44	M₁₆	—	4	1	no	—
45	C₂×C₈	—	2	1	no	—
46	C₂×C₈	—	4	1	no	—
47	C₂×C₈	D₄×C₁₁	1	2	yes	—
48	C₄⋊C₄	—	2	1	no	—
49	C₂²⋊C₄	C₈×C₁₁	1	2	yes	—
50	C₄²	—	2	1	no	—
51	C₁₆	—	4	2	no	—
52	C₁₁	#1328	1	1	yes	characteristic, direct product factor, Sylow
53	C₂³	C₂×C₈×C₁₁	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	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₄	C₁₁×M₁₆	1	1	yes	characteristic
59	C₈	—	2	2	no	—
60	C₈	—	4	1	no	—
61	C₂²	—	2	1	no	—
62	C₂²	—	4	1	no	—
63	C₂²	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	4	2	no	—
66	C₄	C₁₁×#99	1	1	yes	characteristic
67	C₄	C₁₁×#101	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	C₁₁×#324	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁	#99
commutator	C₂³	C₂×C₈×C₁₁
Frattini, cosocle	C₂×M₁₆	C₂²×C₁₁
socle	C₂×C₁₁	#324
prime radical	C₂³×C₁₁	C₂×C₈
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
17. #1328	C₁₁	direct (N × H)
52. C₁₁	#1328	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#424	2
C₁₁×#349	2
#1328	11

Subgroups — C11×#1328 #13064166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#1328 #13064166