Subgroups — C₂²×C₁₁×#401 #14611741

Order 2816.

2942 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#401	C₂	1	24	yes	maximal, direct product factor
2	C₂²×C₁₁×#95	C₂	1	7	yes	maximal
3	C₂⁴×C₄×C₁₁	C₂²	1	7	yes	—
4	C₁₁×#401	C₂²	1	64	yes	direct product factor
5	C₂×C₁₁×#95	C₂²	1	84	yes	—
6	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
7	C₂³×C₄×C₁₁	—	2	84	no	—
8	C₂³×C₄×C₁₁	C₂³	1	42	yes	—
9	C₁₁×#95	C₂³	1	112	yes	—
10	C₂²×#401	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂⁴×C₁₁	#41	1	28	yes	—
12	C₂⁴×C₁₁	C₂⁴	1	3	yes	—
13	C₂²×C₄×C₁₁	—	2	252	no	—
14	C₂²×C₄×C₁₁	—	4	112	no	—
15	C₂²×C₄×C₁₁	C₂⁴	1	28	yes	—
16	C₂×#401	C₂×C₁₁	1	24	yes	direct product factor
17	C₂²×#95	C₂×C₁₁	1	7	yes	—
18	C₂³×C₁₁	#126	1	112	yes	—
19	C₂³×C₁₁	C₂×#41	1	42	yes	—
20	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
21	C₂×C₄×C₁₁	—	2	84	no	—
22	C₂×C₄×C₁₁	—	4	168	no	—
23	C₂⁴×C₄	C₂²×C₁₁	1	7	yes	—
24	#401	C₂²×C₁₁	1	64	yes	direct product factor
25	C₂×#95	C₂²×C₁₁	1	84	yes	—
26	C₂²×C₁₁	#401	1	64	yes	direct product factor
27	C₂²×C₁₁	C₂×#126	1	84	yes	—
28	C₂²×C₁₁	C₂²×#41	1	7	yes	—
29	C₄×C₁₁	—	4	28	no	—
30	C₂⁵	C₂³×C₁₁	1	1	yes	characteristic
31	C₂³×C₄	—	2	84	no	—
32	C₂³×C₄	C₂³×C₁₁	1	42	yes	—
33	#95	C₂³×C₁₁	1	112	yes	—
34	C₂×C₁₁	C₂×#401	1	24	yes	direct product factor
35	C₂×C₁₁	C₂²×#126	1	7	yes	—
36	C₂⁴	C₁₁×#41	1	28	yes	—
37	C₂⁴	C₂⁴×C₁₁	1	3	yes	—
38	C₂²×C₄	—	2	252	no	—
39	C₂²×C₄	—	4	112	no	—
40	C₂²×C₄	C₂⁴×C₁₁	1	28	yes	—
41	C₁₁	C₂²×#401	1	1	yes	characteristic, direct product factor, Sylow
42	C₂³	C₁₁×#126	1	112	yes	—
43	C₂³	C₂×C₁₁×#41	1	42	yes	—
44	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
45	C₂×C₄	—	2	84	no	—
46	C₂×C₄	—	4	168	no	—
47	C₂²	C₁₁×#401	1	64	yes	direct product factor
48	C₂²	C₂×C₁₁×#126	1	84	yes	—
49	C₂²	C₂²×C₁₁×#41	1	7	yes	—
50	C₄	—	4	28	no	—
51	C₂	C₂×C₁₁×#401	1	24	yes	direct product factor
52	C₂	C₂²×C₁₁×#126	1	7	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#401	C₂	direct (N × H)
4. C₁₁×#401	C₂²	direct (N × H)
10. C₂²×#401	C₁₁	direct (N × H)
16. C₂×#401	C₂×C₁₁	direct (N × H)
24. #401	C₂²×C₁₁	direct (N × H)
26. C₂²×C₁₁	#401	direct (N × H)
34. C₂×C₁₁	C₂×#401	direct (N × H)
41. C₁₁	C₂²×#401	direct (N × H)
47. C₂²	C₁₁×#401	direct (N × H)
51. C₂	C₂×C₁₁×#401	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×#401	2
C₂²×C₁₁×#95	2
C₂²×#401	11

Subgroups — C22×C11×#401 #14611741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#401 #14611741