Subgroups — C₁₁×#490 #10622977

Order 704.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#127	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#102	C₂	1	4	yes	maximal, complemented
4	C₁₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×C₁₁	—	2	2	no	—
6	C₂×D₄×C₁₁	C₂²	1	2	yes	—
7	C₂×C₈×C₁₁	C₂²	1	2	yes	—
8	C₁₁×C₄⋊C₄	—	2	2	no	—
9	C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
10	C₄²×C₁₁	C₂²	1	1	yes	characteristic
11	C₂³×C₁₁	—	2	2	no	—
12	D₄×C₁₁	—	2	4	no	—
13	D₄×C₁₁	—	4	4	no	—
14	C₂×C₄×C₁₁	—	2	2	no	—
15	C₂×C₄×C₁₁	D₄	1	2	yes	—
16	C₂×C₄×C₁₁	C₂³	1	1	yes	characteristic
17	C₈×C₁₁	—	2	2	no	—
18	#490	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₁₁	—	4	2	no	—
20	C₂²×C₁₁	—	4	4	no	—
21	C₂²×C₁₁	C₂×D₄	1	1	yes	characteristic
22	C₄×C₁₁	—	2	2	no	—
23	C₄×C₁₁	—	4	2	no	—
24	C₄×C₁₁	#41	1	2	yes	—
25	#127	C₂×C₁₁	1	1	yes	characteristic
26	#125	C₂×C₁₁	1	1	yes	characteristic, complemented
27	#102	C₂×C₁₁	1	4	yes	complemented
28	#97	C₂×C₁₁	1	1	yes	characteristic, complemented
29	C₂×C₁₁	—	8	2	no	—
30	C₂×C₁₁	#124	1	1	yes	characteristic
31	C₂×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
32	C₂×D₄	—	2	2	no	—
33	C₂×D₄	C₂²×C₁₁	1	2	yes	—
34	C₂×C₈	C₂²×C₁₁	1	2	yes	—
35	C₄⋊C₄	—	2	2	no	—
36	C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
37	C₄²	C₂²×C₁₁	1	1	yes	characteristic
38	C₁₁	#490	1	1	yes	characteristic, direct product factor, Sylow
39	C₂³	—	2	2	no	—
40	D₄	—	2	4	no	—
41	D₄	—	4	4	no	—
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	D₄×C₁₁	1	2	yes	—
44	C₂×C₄	C₂³×C₁₁	1	1	yes	characteristic
45	C₈	—	2	2	no	—
46	C₂²	—	4	2	no	—
47	C₂²	—	4	4	no	—
48	C₂²	C₂×D₄×C₁₁	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	4	2	no	—
51	C₄	C₁₁×#41	1	2	yes	—
52	C₂	—	8	2	no	—
53	C₂	C₁₁×#124	1	1	yes	characteristic
54	C₂	C₁₁×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₁₁
prime radical	C₁₁×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#125	C₂	semidirect
3. C₁₁×#102	C₂	semidirect
4. C₁₁×#97	C₂	semidirect
18. #490	C₁₁	direct (N × H)
26. #125	C₂×C₁₁	semidirect
27. #102	C₂×C₁₁	semidirect
28. #97	C₂×C₁₁	semidirect
38. C₁₁	#490	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×#127	2
C₁₁×#125	2
C₁₁×#102	2
C₁₁×#97	2
#490	11

Subgroups — C11×#490 #10622977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#490 #10622977