Subgroups — C₁₁×#1384 #13064222

Order 1408.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#427	C₂	1	2	yes	maximal
3	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
4	C₁₁×#117	—	2	2	no	—
5	C₁₁×M₃₂	—	2	2	no	—
6	C₂×C₁₁×C₁₆	C₄	1	2	yes	complemented
7	C₁₁×#107	—	2	2	no	—
8	C₁₁×#106	C₄	1	4	yes	complemented
9	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
10	C₂×C₈×C₁₁	C₂×C₄	1	2	yes	—
11	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₁₁	D₄	1	2	yes	—
13	C₂×C₈×C₁₁	Q₈	1	1	yes	characteristic
14	C₁₁×C₄⋊C₄	—	2	4	no	—
15	C₁₁×C₂²⋊C₄	—	4	2	no	—
16	C₄²×C₁₁	—	4	2	no	—
17	C₁₁×C₁₆	—	2	2	no	—
18	#1384	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₁₁	D₈	1	1	yes	characteristic
20	C₂×C₄×C₁₁	—	4	4	no	—
21	C₂×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
22	C₂×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₁	SD₁₆	1	2	yes	—
24	C₂×C₄×C₁₁	Q₁₆	1	1	yes	characteristic
25	C₈×C₁₁	C₄²	1	1	yes	characteristic
26	C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₈×C₁₁	C₄⋊C₄	1	2	yes	—
28	C₂×M₃₂	C₂×C₁₁	1	1	yes	characteristic
29	#427	C₂×C₁₁	1	2	yes	—
30	C₂²×C₁₁	—	4	1	no	—
31	C₂²×C₁₁	#102	1	2	yes	—
32	C₂²×C₁₁	#107	1	1	yes	characteristic
33	C₄×C₁₁	—	8	4	no	—
34	C₄×C₁₁	#95	1	1	yes	characteristic
35	C₄×C₁₁	#103	1	2	yes	—
36	C₄×C₁₁	#106	1	1	yes	characteristic
37	C₂²×C₈	C₂²×C₁₁	1	1	yes	characteristic
38	#117	—	2	2	no	—
39	M₃₂	—	2	2	no	—
40	C₂×C₁₆	C₄×C₁₁	1	2	yes	complemented
41	#107	—	2	2	no	—
42	#106	C₄×C₁₁	1	4	yes	complemented
43	C₂×C₁₁	—	2	2	no	—
44	C₂×C₁₁	—	2	1	no	—
45	C₂×C₁₁	#340	1	1	yes	characteristic
46	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
47	C₂×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
48	C₂×C₈	C₂×C₄×C₁₁	1	2	yes	—
49	C₂×C₈	D₄×C₁₁	1	2	yes	—
50	C₂×C₈	Q₈×C₁₁	1	1	yes	characteristic
51	C₄⋊C₄	—	2	4	no	—
52	C₂²⋊C₄	—	4	2	no	—
53	C₄²	—	4	2	no	—
54	C₁₆	—	2	2	no	—
55	C₁₁	#1384	1	1	yes	characteristic, direct product factor, Sylow
56	C₂³	C₁₁×D₈	1	1	yes	characteristic
57	C₂×C₄	—	4	4	no	—
58	C₂×C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
59	C₂×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₄	C₁₁×SD₁₆	1	2	yes	—
61	C₂×C₄	C₁₁×Q₁₆	1	1	yes	characteristic
62	C₈	C₄²×C₁₁	1	1	yes	characteristic
63	C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
64	C₈	C₁₁×C₄⋊C₄	1	2	yes	—
65	C₂²	—	4	1	no	—
66	C₂²	C₁₁×#102	1	2	yes	—
67	C₂²	C₁₁×#107	1	1	yes	characteristic
68	C₄	—	8	4	no	—
69	C₄	C₁₁×#95	1	1	yes	characteristic
70	C₄	C₁₁×#103	1	2	yes	—
71	C₄	C₁₁×#106	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	C₁₁×#340	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁	#106
commutator	C₈	C₄²×C₁₁
Frattini, cosocle	C₂²×C₈	C₂²×C₁₁
socle	C₂×C₁₁	#340
prime radical	C₂³×C₁₁	D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂²×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₂×C₁₁×C₁₆	C₄	semidirect
8. C₁₁×#106	C₄	semidirect
18. #1384	C₁₁	direct (N × H)
40. C₂×C₁₆	C₄×C₁₁	semidirect
42. #106	C₄×C₁₁	semidirect
55. C₁₁	#1384	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×M₃₂	2
C₁₁×#427	2
#1384	11

Subgroups — C11×#1384 #13064222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#1384 #13064222