Subgroups — C₁₁×#1423 #13064261

Order 1408.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#366	C₂	1	2	yes	maximal
3	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
4	C₁₁×#107	—	2	2	no	—
5	C₁₁×C₃₂	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
7	C₁₁×C₄⋊C₄	—	4	2	no	—
8	C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₁₁×C₁₆	Q₈	1	1	yes	characteristic
10	#1423	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂×C₄×C₁₁	—	8	2	no	—
12	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
13	C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
14	C₈×C₁₁	Q₁₆	1	1	yes	characteristic
15	C₂×C₃₂	C₂×C₁₁	1	1	yes	characteristic
16	#366	C₂×C₁₁	1	2	yes	—
17	C₂²×C₁₁	D₁₆	1	1	yes	characteristic
18	C₄×C₁₁	—	16	2	no	—
19	C₄×C₁₁	#107	1	1	yes	characteristic
20	C₄×C₁₁	Q₃₂	1	1	yes	characteristic
21	C₂×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
22	#107	—	2	2	no	—
23	C₃₂	C₄×C₁₁	1	2	yes	complemented
24	C₂×C₁₁	#366	1	1	yes	characteristic
25	C₂×C₁₁	D₃₂	1	1	yes	characteristic
26	C₂×C₁₁	Q₆₄	1	1	yes	characteristic
27	C₂×C₈	D₄×C₁₁	1	1	yes	characteristic
28	C₄⋊C₄	—	4	2	no	—
29	C₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
30	C₁₆	Q₈×C₁₁	1	1	yes	characteristic
31	C₁₁	#1423	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₄	—	8	2	no	—
33	C₂×C₄	C₁₁×D₈	1	1	yes	characteristic
34	C₈	C₁₁×C₄⋊C₄	1	1	yes	characteristic
35	C₈	C₁₁×Q₁₆	1	1	yes	characteristic
36	C₂²	C₁₁×D₁₆	1	1	yes	characteristic
37	C₄	—	16	2	no	—
38	C₄	C₁₁×#107	1	1	yes	characteristic
39	C₄	C₁₁×Q₃₂	1	1	yes	characteristic
40	C₂	C₁₁×#366	1	1	yes	characteristic
41	C₂	C₁₁×D₃₂	1	1	yes	characteristic
42	C₂	C₁₁×Q₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁	D₁₆
commutator	C₁₆	C₂×C₄×C₁₁
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₁
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₁₁×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₁×C₃₂	C₄	semidirect
10. #1423	C₁₁	direct (N × H)
23. C₃₂	C₄×C₁₁	semidirect
31. C₁₁	#1423	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×C₃₂	2
C₁₁×#366	2
#1423	11

Subgroups — C11×#1423 #13064261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#1423 #13064261