Subgroups — C₁₁×#11411 #14588604

Order 2816.

290 conjugacy classes of subgroups.

The subgroup lattice has 154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2162	C₂	1	2	yes	maximal
2	C₂×C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1312	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1311	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₁₁×C₄⋊C₁₆	C₄	1	4	yes	—
9	C₁₁×C₂²⋊C₁₆	C₄	1	4	yes	—
10	C₄×C₁₁×C₁₆	C₂²	1	4	yes	—
11	C₈²×C₁₁	C₄	1	1	yes	characteristic
12	C₈²×C₁₁	C₄	1	1	yes	characteristic
13	C₈²×C₁₁	C₂²	1	1	yes	characteristic
14	C₈²×C₁₁	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₁₁	C₈	1	2	yes	—
16	C₂²×C₈×C₁₁	C₈	1	2	yes	—
17	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₁×C₁₆	C₂×C₄	1	8	yes	—
20	C₄×C₈×C₁₁	C₈	1	2	yes	—
21	C₄×C₈×C₁₁	C₈	1	2	yes	—
22	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
29	#11411	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
31	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
32	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
33	C₂×C₈×C₁₁	—	2	4	no	—
34	C₂×C₈×C₁₁	—	2	4	no	—
35	C₂×C₈×C₁₁	—	2	4	no	—
36	C₂×C₈×C₁₁	C₄²	1	2	yes	—
37	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
38	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
39	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
40	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
41	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
42	C₄²×C₁₁	C₄²	1	1	yes	characteristic
43	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
44	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
45	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
46	C₁₁×C₁₆	—	2	8	no	—
47	#2162	C₂×C₁₁	1	2	yes	—
48	C₂×C₈²	C₂×C₁₁	1	1	yes	characteristic
49	#1312	C₂×C₁₁	1	2	yes	complemented
50	#1311	C₂×C₁₁	1	2	yes	complemented
51	C₂³×C₁₁	C₄×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₁	—	2	2	no	—
53	C₂×C₄×C₁₁	—	2	2	no	—
54	C₂×C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₁	M₃₂	1	4	yes	—
58	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
59	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
61	C₈×C₁₁	—	2	2	no	—
62	C₈×C₁₁	—	2	2	no	—
63	C₈×C₁₁	—	2	2	no	—
64	C₈×C₁₁	—	2	2	no	—
65	C₈×C₁₁	M₃₂	1	4	yes	—
66	C₈×C₁₁	#131	1	4	yes	—
67	C₂×C₄×C₈	C₄×C₁₁	1	1	yes	characteristic
68	C₂×C₄×C₈	C₄×C₁₁	1	1	yes	characteristic
69	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
70	C₄⋊C₁₆	C₄×C₁₁	1	4	yes	—
71	C₂²⋊C₁₆	C₄×C₁₁	1	4	yes	—
72	C₄×C₁₆	C₂²×C₁₁	1	4	yes	—
73	C₈²	C₄×C₁₁	1	1	yes	characteristic
74	C₈²	C₄×C₁₁	1	1	yes	characteristic
75	C₈²	C₂²×C₁₁	1	1	yes	characteristic
76	C₈²	C₂²×C₁₁	1	1	yes	characteristic
77	C₂²×C₁₁	—	2	1	no	—
78	C₂²×C₁₁	—	2	1	no	—
79	C₂²×C₁₁	#346	1	2	yes	—
80	C₂²×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
81	C₄×C₁₁	—	2	1	no	—
82	C₄×C₁₁	—	2	1	no	—
83	C₄×C₁₁	#346	1	2	yes	—
84	C₄×C₁₁	#405	1	2	yes	—
85	C₄×C₁₁	C₂×M₃₂	1	2	yes	—
86	C₄×C₁₁	C₂×M₃₂	1	2	yes	—
87	C₂²×C₈	C₈×C₁₁	1	2	yes	—
88	C₂²×C₈	C₈×C₁₁	1	2	yes	—
89	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
90	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
91	C₂×C₁₆	C₂×C₄×C₁₁	1	8	yes	—
92	C₄×C₈	C₈×C₁₁	1	2	yes	—
93	C₄×C₈	C₈×C₁₁	1	2	yes	—
94	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
95	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
96	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
97	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
98	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
99	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
100	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
101	C₂×C₁₁	—	2	2	no	—
102	C₂×C₁₁	#1450	1	1	yes	characteristic
103	C₂×C₁₁	C₂×#346	1	1	yes	characteristic
104	C₂×C₁₁	C₄×M₃₂	1	1	yes	characteristic
105	C₂²×C₄	C₄²×C₁₁	1	1	yes	characteristic
106	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
107	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
108	C₂×C₈	—	2	4	no	—
109	C₂×C₈	—	2	4	no	—
110	C₂×C₈	—	2	4	no	—
111	C₂×C₈	C₄²×C₁₁	1	2	yes	—
112	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
113	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
114	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
115	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
116	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
117	C₄²	C₄²×C₁₁	1	1	yes	characteristic
118	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
119	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
120	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
121	C₁₆	—	2	8	no	—
122	C₁₁	#11411	1	1	yes	characteristic, direct product factor, Sylow
123	C₂³	C₄×C₈×C₁₁	1	1	yes	characteristic
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	C₄×C₈×C₁₁	1	1	yes	characteristic
127	C₂×C₄	C₄×C₈×C₁₁	1	1	yes	characteristic
128	C₂×C₄	C₄×C₈×C₁₁	1	1	yes	characteristic
129	C₂×C₄	C₁₁×M₃₂	1	4	yes	—
130	C₂×C₄	C₂×C₄²×C₁₁	1	1	yes	characteristic
131	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
132	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
133	C₈	—	2	2	no	—
134	C₈	—	2	2	no	—
135	C₈	—	2	2	no	—
136	C₈	—	2	2	no	—
137	C₈	C₁₁×M₃₂	1	4	yes	—
138	C₈	C₁₁×#131	1	4	yes	—
139	C₂²	—	2	1	no	—
140	C₂²	—	2	1	no	—
141	C₂²	C₁₁×#346	1	2	yes	—
142	C₂²	C₂×C₄×C₈×C₁₁	1	1	yes	characteristic
143	C₄	—	2	1	no	—
144	C₄	—	2	1	no	—
145	C₄	C₁₁×#346	1	2	yes	—
146	C₄	C₁₁×#405	1	2	yes	—
147	C₄	C₂×C₁₁×M₃₂	1	2	yes	—
148	C₄	C₂×C₁₁×M₃₂	1	2	yes	—
149	C₂	—	2	2	no	—
150	C₂	C₁₁×#1450	1	1	yes	characteristic
151	C₂	C₂×C₁₁×#346	1	1	yes	characteristic
152	C₂	C₄×C₁₁×M₃₂	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1312	C₂	semidirect
4. C₁₁×#1311	C₂	semidirect
29. #11411	C₁₁	direct (N × H)
49. #1312	C₂×C₁₁	semidirect
50. #1311	C₂×C₁₁	semidirect
122. C₁₁	#11411	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×#2162	2
C₂×C₈²×C₁₁	2
C₁₁×#1312	2
C₁₁×#1311	2
#11411	11

Subgroups — C11×#11411 #14588604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11411 #14588604