Subgroups — C₁₁×#13551 #14590744

Order 2816.

214 conjugacy classes of subgroups.

The subgroup lattice has 118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×M₆₄	C₂	1	2	yes	maximal
2	C₁₁×#2108	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1398	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₁×M₃₂	C₄	1	1	yes	characteristic
5	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
6	C₁₁×#405	C₄	1	1	yes	characteristic
7	C₁₁×M₆₄	C₄	1	4	yes	complemented
8	C₁₁×M₆₄	C₂²	1	4	yes	—
9	C₂×C₁₁×C₃₂	C₄	1	4	yes	complemented
10	C₁₁×#346	C₂²	1	2	yes	—
11	C₄×C₁₁×C₁₆	C₄	1	2	yes	—
12	C₂×C₁₁×M₁₆	C₈	1	1	yes	characteristic
13	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
14	C₁₁×#117	C₈	1	1	yes	characteristic
15	C₁₁×M₃₂	C₈	1	4	yes	—
16	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
18	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
19	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
20	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
21	C₁₁×#97	C₈	1	2	yes	—
22	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
23	C₁₁×C₃₂	C₂×C₄	1	8	yes	—
24	#13551	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
26	C₁₁×M₁₆	—	2	2	no	—
27	C₂×C₈×C₁₁	C₄²	1	2	yes	—
28	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
29	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
30	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
31	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
32	C₁₁×C₄⋊C₄	—	2	1	no	—
33	C₁₁×C₂²⋊C₄	—	2	1	no	—
34	C₄²×C₁₁	C₂×C₈	1	2	yes	—
35	C₁₁×C₁₆	C₄²	1	1	yes	characteristic
36	C₁₁×C₁₆	C₄²	1	1	yes	characteristic
37	C₁₁×C₁₆	C₂×C₈	1	4	yes	—
38	C₁₁×C₁₆	C₂²×C₄	1	2	yes	—
39	C₂×M₆₄	C₂×C₁₁	1	2	yes	—
40	#2108	C₂×C₁₁	1	1	yes	characteristic
41	#1398	C₂×C₁₁	1	4	yes	complemented
42	C₂³×C₁₁	M₃₂	1	1	yes	characteristic
43	C₂×C₄×C₁₁	—	2	2	no	—
44	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
45	C₂×C₄×C₁₁	M₃₂	1	1	yes	characteristic
46	C₂×C₄×C₁₁	M₃₂	1	2	yes	—
47	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
48	C₈×C₁₁	—	2	2	no	—
49	C₈×C₁₁	C₄×C₈	1	2	yes	—
50	C₈×C₁₁	C₂×C₄²	1	1	yes	characteristic
51	C₈×C₁₁	C₂²×C₈	1	1	yes	characteristic
52	C₂×M₃₂	C₄×C₁₁	1	1	yes	characteristic
53	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
54	#405	C₄×C₁₁	1	1	yes	characteristic
55	M₆₄	C₄×C₁₁	1	4	yes	complemented
56	M₆₄	C₂²×C₁₁	1	4	yes	—
57	C₂×C₃₂	C₄×C₁₁	1	4	yes	complemented
58	#346	C₂²×C₁₁	1	2	yes	—
59	C₄×C₁₆	C₄×C₁₁	1	2	yes	—
60	C₂²×C₁₁	—	4	1	no	—
61	C₂²×C₁₁	#346	1	2	yes	—
62	C₂²×C₁₁	C₂×M₃₂	1	1	yes	characteristic
63	C₄×C₁₁	—	4	2	no	—
64	C₄×C₁₁	#346	1	2	yes	—
65	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
66	C₄×C₁₁	C₂×M₃₂	1	1	yes	characteristic
67	C₂×M₁₆	C₈×C₁₁	1	1	yes	characteristic
68	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
69	#117	C₈×C₁₁	1	1	yes	characteristic
70	M₃₂	C₈×C₁₁	1	4	yes	—
71	C₂×C₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
72	C₂×C₁₆	C₂×C₄×C₁₁	1	2	yes	—
73	C₂×C₁₆	C₂×C₄×C₁₁	1	2	yes	—
74	C₂×C₁₆	C₂×C₄×C₁₁	1	2	yes	—
75	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
76	#97	C₈×C₁₁	1	2	yes	—
77	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
78	C₃₂	C₂×C₄×C₁₁	1	8	yes	—
79	C₂×C₁₁	—	2	1	no	—
80	C₂×C₁₁	—	2	2	no	—
81	C₂×C₁₁	C₂×#346	1	1	yes	characteristic
82	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
83	M₁₆	—	2	2	no	—
84	C₂×C₈	C₄²×C₁₁	1	2	yes	—
85	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
86	C₂×C₈	C₂×C₈×C₁₁	1	1	yes	characteristic
87	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
88	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
89	C₄⋊C₄	—	2	1	no	—
90	C₂²⋊C₄	—	2	1	no	—
91	C₄²	C₂×C₈×C₁₁	1	2	yes	—
92	C₁₆	C₄²×C₁₁	1	1	yes	characteristic
93	C₁₆	C₄²×C₁₁	1	1	yes	characteristic
94	C₁₆	C₂×C₈×C₁₁	1	4	yes	—
95	C₁₆	C₂²×C₄×C₁₁	1	2	yes	—
96	C₁₁	#13551	1	1	yes	characteristic, direct product factor, Sylow
97	C₂³	C₁₁×M₃₂	1	1	yes	characteristic
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	C₄×C₈×C₁₁	1	2	yes	—
100	C₂×C₄	C₁₁×M₃₂	1	2	yes	—
101	C₂×C₄	C₁₁×M₃₂	1	1	yes	characteristic
102	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
103	C₈	—	2	2	no	—
104	C₈	C₄×C₈×C₁₁	1	2	yes	—
105	C₈	C₂×C₄²×C₁₁	1	1	yes	characteristic
106	C₈	C₂²×C₈×C₁₁	1	1	yes	characteristic
107	C₂²	—	4	1	no	—
108	C₂²	C₁₁×#346	1	2	yes	—
109	C₂²	C₂×C₁₁×M₃₂	1	1	yes	characteristic
110	C₄	—	4	2	no	—
111	C₄	C₁₁×#346	1	2	yes	—
112	C₄	C₂×C₄×C₈×C₁₁	1	1	yes	characteristic
113	C₄	C₂×C₁₁×M₃₂	1	1	yes	characteristic
114	C₂	—	2	1	no	—
115	C₂	—	2	2	no	—
116	C₂	C₂×C₁₁×#346	1	1	yes	characteristic

	subgroup	G/H
center	C₁₁×C₁₆	C₄²
commutator	C₄	C₂×C₄×C₈×C₁₁
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₁
socle	C₂×C₁₁	C₂×#346
prime radical	C₂³×C₁₁	M₃₂
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₁₁×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1398	C₂	semidirect
7. C₁₁×M₆₄	C₄	semidirect
9. C₂×C₁₁×C₃₂	C₄	semidirect
24. #13551	C₁₁	direct (N × H)
41. #1398	C₂×C₁₁	semidirect
55. M₆₄	C₄×C₁₁	semidirect
57. C₂×C₃₂	C₄×C₁₁	semidirect
96. C₁₁	#13551	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×M₆₄	2
C₁₁×#2108	2
C₁₁×#1398	2
#13551	11

Subgroups — C11×#13551 #14590744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13551 #14590744