Subgroups — C₁₁×#11414 #14588607

Order 2816.

248 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2163	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1313	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1313	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×M₃₂	C₄	1	2	yes	—
7	C₁₁×#431	C₄	1	1	yes	characteristic
8	C₄×C₁₁×M₁₆	C₄	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₁₁×C₄⋊C₁₆	C₄	1	2	yes	—
11	C₁₁×C₂²⋊C₁₆	C₄	1	2	yes	—
12	C₁₁×#346	C₂²	1	2	yes	—
13	C₁₁×#346	C₂²	1	1	yes	characteristic
14	C₁₁×#346	C₂²	1	1	yes	characteristic
15	C₄×C₁₁×C₁₆	C₄	1	2	yes	—
16	C₁₁×#322	C₄	1	2	yes	—
17	C₁₁×#322	C₂²	1	2	yes	—
18	C₂×C₁₁×M₁₆	—	2	1	no	—
19	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₁₁×M₃₂	—	2	4	no	—
23	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
24	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
25	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
26	C₁₁×C₄⋊C₈	—	2	1	no	—
27	C₁₁×C₂²⋊C₈	—	2	1	no	—
28	C₁₁×#97	—	2	1	no	—
29	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
32	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
33	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
35	#11414	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
37	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
38	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
39	C₁₁×M₁₆	—	4	2	no	—
40	C₂×C₈×C₁₁	—	2	2	no	—
41	C₂×C₈×C₁₁	—	2	2	no	—
42	C₂×C₈×C₁₁	—	2	2	no	—
43	C₂×C₈×C₁₁	—	2	2	no	—
44	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
45	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
46	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
48	C₄²×C₁₁	C₄²	1	1	yes	characteristic
49	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
50	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
51	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
52	C₁₁×C₁₆	—	2	2	no	—
53	C₁₁×C₁₆	—	2	4	no	—
54	C₁₁×C₁₆	M₁₆	1	4	yes	complemented
55	#2163	C₂×C₁₁	1	1	yes	characteristic
56	C₄×M₃₂	C₂×C₁₁	1	1	yes	characteristic
57	#1451	C₂×C₁₁	1	1	yes	characteristic
58	#1313	C₂×C₁₁	1	2	yes	complemented
59	#1313	C₂×C₁₁	1	2	yes	complemented
60	C₂³×C₁₁	#97	1	1	yes	characteristic
61	C₂×C₄×C₁₁	—	2	2	no	—
62	C₂×C₄×C₁₁	—	2	1	no	—
63	C₂×C₄×C₁₁	—	2	1	no	—
64	C₂×C₄×C₁₁	—	4	1	no	—
65	C₂×C₄×C₁₁	#97	1	1	yes	characteristic
66	C₂×C₄×C₁₁	#97	1	1	yes	characteristic
67	C₂×C₄×C₁₁	#97	1	1	yes	characteristic
68	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
69	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
70	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
71	C₈×C₁₁	—	2	1	no	—
72	C₈×C₁₁	—	2	1	no	—
73	C₈×C₁₁	—	4	2	no	—
74	C₈×C₁₁	—	4	2	no	—
75	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
76	C₈×C₁₁	#131	1	2	yes	—
77	C₂×M₃₂	C₄×C₁₁	1	2	yes	—
78	#431	C₄×C₁₁	1	1	yes	characteristic
79	C₄×M₁₆	C₄×C₁₁	1	1	yes	characteristic
80	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
81	C₄⋊C₁₆	C₄×C₁₁	1	2	yes	—
82	C₂²⋊C₁₆	C₄×C₁₁	1	2	yes	—
83	#346	C₂²×C₁₁	1	1	yes	characteristic
84	#346	C₂²×C₁₁	1	1	yes	characteristic
85	#346	C₂²×C₁₁	1	2	yes	—
86	C₄×C₁₆	C₄×C₁₁	1	2	yes	—
87	#322	C₄×C₁₁	1	2	yes	—
88	#322	C₂²×C₁₁	1	2	yes	—
89	C₂²×C₁₁	—	2	1	no	—
90	C₂²×C₁₁	—	2	1	no	—
91	C₂²×C₁₁	—	2	1	no	—
92	C₂²×C₁₁	C₂×#97	1	1	yes	characteristic
93	C₄×C₁₁	—	2	1	no	—
94	C₄×C₁₁	—	2	1	no	—
95	C₄×C₁₁	—	2	1	no	—
96	C₄×C₁₁	—	2	1	no	—
97	C₄×C₁₁	#347	1	2	yes	—
98	C₄×C₁₁	C₄×M₁₆	1	1	yes	characteristic
99	C₄×C₁₁	#405	1	1	yes	characteristic
100	C₂×M₁₆	—	2	1	no	—
101	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
102	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
103	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
104	M₃₂	—	2	4	no	—
105	C₂×C₁₆	C₂×C₄×C₁₁	1	2	yes	—
106	C₂×C₁₆	C₂×C₄×C₁₁	1	4	yes	—
107	C₂×C₁₆	C₂×C₄×C₁₁	1	2	yes	—
108	C₄⋊C₈	—	2	1	no	—
109	C₂²⋊C₈	—	2	1	no	—
110	#97	—	2	1	no	—
111	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
112	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
113	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
114	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
115	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
116	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
117	C₂×C₁₁	—	4	1	no	—
118	C₂×C₁₁	#1451	1	1	yes	characteristic
119	C₂×C₁₁	C₂×#347	1	1	yes	characteristic
120	C₂×C₁₁	#2110	1	1	yes	characteristic
121	C₂²×C₄	C₄²×C₁₁	1	1	yes	characteristic
122	C₂²×C₄	C₁₁×M₁₆	1	1	yes	characteristic
123	C₂²×C₄	C₁₁×M₁₆	1	1	yes	characteristic
124	M₁₆	—	4	2	no	—
125	C₂×C₈	—	2	2	no	—
126	C₂×C₈	—	2	2	no	—
127	C₂×C₈	—	2	2	no	—
128	C₂×C₈	—	2	2	no	—
129	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
130	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
131	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
132	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
133	C₄²	C₄²×C₁₁	1	1	yes	characteristic
134	C₄²	C₁₁×M₁₆	1	1	yes	characteristic
135	C₄²	C₁₁×M₁₆	1	1	yes	characteristic
136	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
137	C₁₆	—	2	2	no	—
138	C₁₆	—	2	4	no	—
139	C₁₆	C₁₁×M₁₆	1	4	yes	complemented
140	C₁₁	#11414	1	1	yes	characteristic, direct product factor, Sylow
141	C₂³	C₁₁×#97	1	1	yes	characteristic
142	C₂×C₄	—	2	2	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	4	1	no	—
146	C₂×C₄	C₁₁×#97	1	1	yes	characteristic
147	C₂×C₄	C₁₁×#97	1	1	yes	characteristic
148	C₂×C₄	C₁₁×#97	1	1	yes	characteristic
149	C₂×C₄	C₂×C₄²×C₁₁	1	1	yes	characteristic
150	C₂×C₄	C₂×C₁₁×M₁₆	1	1	yes	characteristic
151	C₂×C₄	C₂×C₁₁×M₁₆	1	1	yes	characteristic
152	C₈	—	2	1	no	—
153	C₈	—	2	1	no	—
154	C₈	—	4	2	no	—
155	C₈	—	4	2	no	—
156	C₈	C₂×C₁₁×M₁₆	1	2	yes	—
157	C₈	C₁₁×#131	1	2	yes	—
158	C₂²	—	2	1	no	—
159	C₂²	—	2	1	no	—
160	C₂²	—	2	1	no	—
161	C₂²	C₂×C₁₁×#97	1	1	yes	characteristic
162	C₄	—	2	1	no	—
163	C₄	—	2	1	no	—
164	C₄	—	2	1	no	—
165	C₄	—	2	1	no	—
166	C₄	C₁₁×#347	1	2	yes	—
167	C₄	C₄×C₁₁×M₁₆	1	1	yes	characteristic
168	C₄	C₁₁×#405	1	1	yes	characteristic
169	C₂	—	4	1	no	—
170	C₂	C₁₁×#1451	1	1	yes	characteristic
171	C₂	C₂×C₁₁×#347	1	1	yes	characteristic
172	C₂	C₁₁×#2110	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×#97
prime radical	C₂³×C₁₁	#97
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₁×#1313	C₂	semidirect
5. C₁₁×#1313	C₂	semidirect
35. #11414	C₁₁	direct (N × H)
54. C₁₁×C₁₆	M₁₆	semidirect
58. #1313	C₂×C₁₁	semidirect
59. #1313	C₂×C₁₁	semidirect
139. C₁₆	C₁₁×M₁₆	semidirect
140. C₁₁	#11414	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×#2163	2
C₄×C₁₁×M₃₂	2
C₁₁×#1451	2
C₁₁×#1313	2
#11414	11

Subgroups — C11×#11414 #14588607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11414 #14588607