Subgroups — C₁₁×#8138 #14585331

Order 2816.

354 conjugacy classes of subgroups.

The subgroup lattice has 138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#1726	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1450	C₂	1	2	yes	maximal
3	C₁₁×#1275	C₂	1	2	yes	maximal
4	C₁₁×#1274	C₂	1	2	yes	maximal
5	C₁₁×#431	C₂²	1	4	yes	—
6	C₂×C₁₁×#97	C₄	1	2	yes	—
7	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₁₁×#376	C₂²	1	1	yes	characteristic
11	C₁₁×#322	C₄	1	4	yes	complemented
12	C₈²×C₁₁	C₄	1	4	yes	complemented
13	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
14	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
18	C₁₁×C₄⋊C₈	—	2	4	no	—
19	C₁₁×C₂²⋊C₈	—	2	4	no	—
20	C₁₁×#97	—	2	2	no	—
21	C₁₁×#97	C₈	1	8	yes	complemented
22	C₄×C₈×C₁₁	—	2	4	no	—
23	C₄×C₈×C₁₁	C₂×C₄	1	8	yes	—
24	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
26	C₁₁×#95	—	2	2	no	—
27	#8138	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₄×C₁₁	—	2	2	no	—
29	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₁	#41	1	2	yes	—
31	C₂×C₈×C₁₁	—	2	2	no	—
32	C₂×C₈×C₁₁	—	2	8	no	—
33	C₂×C₈×C₁₁	—	2	2	no	—
34	C₂×C₈×C₁₁	C₄²	1	2	yes	—
35	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
36	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
37	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
38	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
39	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
40	C₄²×C₁₁	—	2	2	no	—
41	C₄²×C₁₁	C₂×C₈	1	4	yes	—
42	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
43	C₄²×C₁₁	#41	1	2	yes	—
44	#1726	C₂×C₁₁	1	1	yes	characteristic
45	#1450	C₂×C₁₁	1	2	yes	—
46	#1275	C₂×C₁₁	1	2	yes	—
47	#1274	C₂×C₁₁	1	2	yes	—
48	C₂³×C₁₁	#117	1	1	yes	characteristic
49	C₂×C₄×C₁₁	—	2	4	no	—
50	C₂×C₄×C₁₁	—	4	2	no	—
51	C₂×C₄×C₁₁	—	4	4	no	—
52	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
53	C₂×C₄×C₁₁	#117	1	4	yes	—
54	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
55	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
56	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
57	C₈×C₁₁	—	2	4	no	—
58	C₈×C₁₁	—	4	8	no	—
59	C₈×C₁₁	C₄×C₈	1	4	yes	—
60	C₈×C₁₁	#97	1	2	yes	—
61	C₈×C₁₁	#97	1	2	yes	—
62	#431	C₂²×C₁₁	1	4	yes	—
63	C₂×#97	C₄×C₁₁	1	2	yes	—
64	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
65	C₂×C₄×C₈	C₄×C₁₁	1	2	yes	—
66	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
67	#376	C₂²×C₁₁	1	1	yes	characteristic
68	#322	C₄×C₁₁	1	4	yes	complemented
69	C₈²	C₄×C₁₁	1	4	yes	complemented
70	C₂²×C₁₁	—	2	2	no	—
71	C₂²×C₁₁	#376	1	1	yes	characteristic
72	C₂²×C₁₁	#431	1	2	yes	—
73	C₄×C₁₁	—	2	4	no	—
74	C₄×C₁₁	—	4	4	no	—
75	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
76	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
77	C₄×C₁₁	#431	1	2	yes	—
78	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
79	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
80	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
81	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
82	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
83	C₄⋊C₈	—	2	4	no	—
84	C₂²⋊C₈	—	2	4	no	—
85	#97	—	2	2	no	—
86	#97	C₈×C₁₁	1	8	yes	complemented
87	C₄×C₈	—	2	4	no	—
88	C₄×C₈	C₂×C₄×C₁₁	1	8	yes	—
89	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
90	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
91	#95	—	2	2	no	—
92	C₂×C₁₁	—	2	2	no	—
93	C₂×C₁₁	#1744	1	1	yes	characteristic
94	C₂×C₁₁	#1747	1	2	yes	—
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
97	C₂²×C₄	C₁₁×#41	1	2	yes	—
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	—	2	8	no	—
101	C₂×C₈	C₄²×C₁₁	1	2	yes	—
102	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
103	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
104	C₂×C₈	C₂×C₈×C₁₁	1	4	yes	—
105	C₂×C₈	C₂×C₈×C₁₁	1	4	yes	—
106	C₂×C₈	C₁₁×M₁₆	1	4	yes	—
107	C₄²	—	2	2	no	—
108	C₄²	C₂×C₈×C₁₁	1	4	yes	—
109	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
110	C₄²	C₁₁×#41	1	2	yes	—
111	C₁₁	#8138	1	1	yes	characteristic, direct product factor, Sylow
112	C₂³	C₁₁×#117	1	1	yes	characteristic
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	4	2	no	—
115	C₂×C₄	—	4	4	no	—
116	C₂×C₄	C₂×C₄²×C₁₁	1	1	yes	characteristic
117	C₂×C₄	C₁₁×#117	1	4	yes	—
118	C₂×C₄	C₁₁×#117	1	1	yes	characteristic
119	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
120	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
121	C₈	—	2	4	no	—
122	C₈	—	4	8	no	—
123	C₈	C₄×C₈×C₁₁	1	4	yes	—
124	C₈	C₁₁×#97	1	2	yes	—
125	C₈	C₁₁×#97	1	2	yes	—
126	C₂²	—	2	2	no	—
127	C₂²	C₁₁×#376	1	1	yes	characteristic
128	C₂²	C₁₁×#431	1	2	yes	—
129	C₄	—	2	4	no	—
130	C₄	—	4	4	no	—
131	C₄	C₂×C₄×C₈×C₁₁	1	1	yes	characteristic
132	C₄	C₂×C₁₁×#97	1	1	yes	characteristic
133	C₄	C₁₁×#431	1	2	yes	—
134	C₂	—	2	2	no	—
135	C₂	C₁₁×#1744	1	1	yes	characteristic
136	C₂	C₁₁×#1747	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₁₁	C₄²
commutator	C₄	C₂×C₄×C₈×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#376
prime radical	C₂³×C₁₁	#117
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₁₁×#322	C₄	semidirect
12. C₈²×C₁₁	C₄	semidirect
21. C₁₁×#97	C₈	semidirect
27. #8138	C₁₁	direct (N × H)
68. #322	C₄×C₁₁	semidirect
69. C₈²	C₄×C₁₁	semidirect
86. #97	C₈×C₁₁	semidirect
111. C₁₁	#8138	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×#1726	2
C₁₁×#1450	2
C₁₁×#1275	2
C₁₁×#1274	2
#8138	11

Subgroups — C11×#8138 #14585331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#8138 #14585331