Subgroups — C₁₁×#137 #67030

Order 352.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×Q₁₆	C₂	1	2	yes	maximal, complemented
4	C₁₁×SD₁₆	C₂	1	2	yes	maximal, complemented
5	C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₁₁	—	2	1	no	—
7	Q₈×C₁₁	C₂²	1	2	yes	—
8	Q₈×C₁₁	C₂²	1	1	yes	characteristic
9	D₄×C₁₁	—	2	1	no	—
10	D₄×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₁	—	2	1	no	—
12	C₂×C₄×C₁₁	—	2	1	no	—
13	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
14	C₈×C₁₁	C₂²	1	2	yes	—
15	C₂²×C₁₁	—	2	1	no	—
16	C₂²×C₁₁	D₄	1	1	yes	characteristic
17	C₄×C₁₁	—	2	1	no	—
18	C₄×C₁₁	—	2	2	no	—
19	C₄×C₁₁	D₄	1	1	yes	characteristic
20	C₄×C₁₁	C₂³	1	1	yes	characteristic
21	#137	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂×C₁₁	—	2	1	no	—
23	C₂×C₁₁	—	4	1	no	—
24	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
25	#41	C₂×C₁₁	1	1	yes	characteristic
26	C₂×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
27	Q₁₆	C₂×C₁₁	1	2	yes	complemented
28	SD₁₆	C₂×C₁₁	1	2	yes	complemented
29	M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
30	C₁₁	#137	1	1	yes	characteristic, direct product factor, Sylow
31	Q₈	—	2	1	no	—
32	Q₈	C₂²×C₁₁	1	2	yes	—
33	Q₈	C₂²×C₁₁	1	1	yes	characteristic
34	D₄	—	2	1	no	—
35	D₄	C₂²×C₁₁	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	C₂²×C₁₁	1	1	yes	characteristic
39	C₈	C₂²×C₁₁	1	2	yes	—
40	C₂²	—	2	1	no	—
41	C₂²	D₄×C₁₁	1	1	yes	characteristic
42	C₄	—	2	1	no	—
43	C₄	—	2	2	no	—
44	C₄	D₄×C₁₁	1	1	yes	characteristic
45	C₄	C₂³×C₁₁	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂×D₄×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂³×C₁₁
prime radical	C₁₁×#41	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈×C₁₁	C₂	semidirect
3. C₁₁×Q₁₆	C₂	semidirect
4. C₁₁×SD₁₆	C₂	semidirect
5. C₁₁×M₁₆	C₂	semidirect
21. #137	C₁₁	direct (N × H)
26. C₂×Q₈	C₂×C₁₁	semidirect
27. Q₁₆	C₂×C₁₁	semidirect
28. SD₁₆	C₂×C₁₁	semidirect
29. M₁₆	C₂×C₁₁	semidirect
30. C₁₁	#137	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×#41	2
C₂×Q₈×C₁₁	2
C₁₁×Q₁₆	2
C₁₁×SD₁₆	2
C₁₁×M₁₆	2
#137	11

Subgroups — C11×#137 #67030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#137 #67030