Subgroups — C₁₁×#2840 #13065678

Order 1408.

580 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#393	C₂	1	12	yes	maximal, complemented
2	C₁₁×#379	C₂	1	3	yes	maximal
3	C₂⁵×C₁₁	C₂²	1	1	yes	characteristic
4	C₂²×Q₈×C₁₁	C₂²	1	4	yes	complemented
5	C₂×C₁₁×C₂²⋊C₄	C₂²	1	18	yes	—
6	C₁₁×#95	C₂²	1	12	yes	complemented
7	C₂⁴×C₁₁	—	4	6	no	—
8	C₂⁴×C₁₁	Q₈	1	4	yes	complemented
9	C₂⁴×C₁₁	C₂³	1	3	yes	—
10	C₂×Q₈×C₁₁	—	4	12	no	—
11	C₂²×C₄×C₁₁	C₂³	1	12	yes	—
12	C₁₁×C₂²⋊C₄	—	4	18	no	—
13	#2840	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂³×C₁₁	—	2	18	no	—
15	C₂³×C₁₁	—	4	12	no	—
16	C₂³×C₁₁	—	4	16	no	—
17	C₂³×C₁₁	C₂×Q₈	1	6	yes	—
18	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
19	Q₈×C₁₁	—	4	16	no	—
20	C₂×C₄×C₁₁	—	2	36	no	—
21	#393	C₂×C₁₁	1	12	yes	complemented
22	#379	C₂×C₁₁	1	3	yes	—
23	C₂²×C₁₁	—	2	18	no	—
24	C₂²×C₁₁	—	4	16	no	—
25	C₂²×C₁₁	—	4	12	no	—
26	C₂²×C₁₁	C₂²×Q₈	1	1	yes	characteristic
27	C₂²×C₁₁	H(5,𝔽₂)	1	6	yes	—
28	C₄×C₁₁	—	4	12	no	—
29	C₂⁵	C₂²×C₁₁	1	1	yes	characteristic
30	C₂²×Q₈	C₂²×C₁₁	1	4	yes	complemented
31	C₂×C₂²⋊C₄	C₂²×C₁₁	1	18	yes	—
32	#95	C₂²×C₁₁	1	12	yes	complemented
33	C₂×C₁₁	—	4	6	no	—
34	C₂×C₁₁	#543	1	3	yes	—
35	C₂×C₁₁	H(3,𝔽₄)	1	4	yes	—
36	C₂⁴	—	4	6	no	—
37	C₂⁴	Q₈×C₁₁	1	4	yes	complemented
38	C₂⁴	C₂³×C₁₁	1	3	yes	—
39	C₂×Q₈	—	4	12	no	—
40	C₂²×C₄	C₂³×C₁₁	1	12	yes	—
41	C₂²⋊C₄	—	4	18	no	—
42	C₁₁	#2840	1	1	yes	characteristic, direct product factor, Sylow
43	C₂³	—	2	18	no	—
44	C₂³	—	4	12	no	—
45	C₂³	—	4	16	no	—
46	C₂³	C₂×Q₈×C₁₁	1	6	yes	—
47	C₂³	C₂⁴×C₁₁	1	1	yes	characteristic
48	Q₈	—	4	16	no	—
49	C₂×C₄	—	2	36	no	—
50	C₂²	—	2	18	no	—
51	C₂²	—	4	16	no	—
52	C₂²	—	4	12	no	—
53	C₂²	C₂²×Q₈×C₁₁	1	1	yes	characteristic
54	C₂²	C₁₁×H(5,𝔽₂)	1	6	yes	—
55	C₄	—	4	12	no	—
56	C₂	—	4	6	no	—
57	C₂	C₁₁×#543	1	3	yes	—
58	C₂	C₁₁×H(3,𝔽₄)	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₁
prime radical	C₂⁵×C₁₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#393	C₂	semidirect
4. C₂²×Q₈×C₁₁	C₂²	semidirect
6. C₁₁×#95	C₂²	semidirect
8. C₂⁴×C₁₁	Q₈	semidirect
13. #2840	C₁₁	direct (N × H)
21. #393	C₂×C₁₁	semidirect
30. C₂²×Q₈	C₂²×C₁₁	semidirect
32. #95	C₂²×C₁₁	semidirect
37. C₂⁴	Q₈×C₁₁	semidirect
42. C₁₁	#2840	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×#393	2
C₁₁×#379	2
#2840	11

Subgroups — C11×#2840 #13065678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#2840 #13065678