Subgroups — C₁₁×#1711 #13064549

Order 1408.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#487	C₂	1	3	yes	maximal, complemented
2	C₁₁×#486	C₂	1	3	yes	maximal
3	C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₄⋊Q₈	C₂²	1	3	yes	—
5	C₁₁×#127	C₂²	1	1	yes	characteristic
6	C₁₁×#103	—	2	6	no	—
7	C₁₁×#102	—	2	6	no	—
8	C₄×C₈×C₁₁	C₂²	1	3	yes	—
9	C₂×Q₈×C₁₁	—	2	3	no	—
10	C₂×D₄×C₁₁	—	2	3	no	—
11	C₂×C₈×C₁₁	D₄	1	6	yes	—
12	C₁₁×C₄⋊C₄	—	2	3	no	—
13	C₁₁×C₄⋊C₄	—	2	3	no	—
14	C₄²×C₁₁	C₂³	1	1	yes	characteristic
15	#1711	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂³×C₁₁	—	4	1	no	—
17	Q₈×C₁₁	—	4	6	no	—
18	D₄×C₁₁	—	4	6	no	—
19	C₂×C₄×C₁₁	—	4	3	no	—
20	C₂×C₄×C₁₁	C₂×D₄	1	3	yes	—
21	C₈×C₁₁	—	2	6	no	—
22	#487	C₂×C₁₁	1	3	yes	complemented
23	#486	C₂×C₁₁	1	3	yes	—
24	C₈²	C₂×C₁₁	1	1	yes	characteristic, complemented
25	C₂²×C₁₁	—	8	3	no	—
26	C₂²×C₁₁	#127	1	1	yes	characteristic
27	C₄×C₁₁	—	8	3	no	—
28	C₄×C₁₁	#135	1	6	yes	—
29	C₄⋊Q₈	C₂²×C₁₁	1	3	yes	—
30	#127	C₂²×C₁₁	1	1	yes	characteristic
31	#103	—	2	6	no	—
32	#102	—	2	6	no	—
33	C₄×C₈	C₂²×C₁₁	1	3	yes	—
34	C₂×C₁₁	—	16	1	no	—
35	C₂×C₁₁	#495	1	3	yes	—
36	C₂×Q₈	—	2	3	no	—
37	C₂×D₄	—	2	3	no	—
38	C₂×C₈	D₄×C₁₁	1	6	yes	—
39	C₄⋊C₄	—	2	3	no	—
40	C₄⋊C₄	—	2	3	no	—
41	C₄²	C₂³×C₁₁	1	1	yes	characteristic
42	C₁₁	#1711	1	1	yes	characteristic, direct product factor, Sylow
43	C₂³	—	4	1	no	—
44	Q₈	—	4	6	no	—
45	D₄	—	4	6	no	—
46	C₂×C₄	—	4	3	no	—
47	C₂×C₄	C₂×D₄×C₁₁	1	3	yes	—
48	C₈	—	2	6	no	—
49	C₂²	—	8	3	no	—
50	C₂²	C₁₁×#127	1	1	yes	characteristic
51	C₄	—	8	3	no	—
52	C₄	C₁₁×#135	1	6	yes	—
53	C₂	—	16	1	no	—
54	C₂	C₁₁×#495	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₁₁
prime radical	C₁₁×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#487	C₂	semidirect
3. C₈²×C₁₁	C₂	semidirect
15. #1711	C₁₁	direct (N × H)
22. #487	C₂×C₁₁	semidirect
24. C₈²	C₂×C₁₁	semidirect
42. C₁₁	#1711	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×#487	2
C₁₁×#486	2
C₈²×C₁₁	2
#1711	11

Subgroups — C11×#1711 #13064549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#1711 #13064549