Subgroups — C₁₁×#22265 #14599458

Order 2816.

962 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#436	C₂	1	2	yes	maximal, complemented
2	C₁₁×#2397	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1955	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1870	C₂	1	8	yes	maximal, complemented
5	C₁₁×#1832	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₁×M₁₆	C₂²	1	4	yes	—
8	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
9	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
10	C₁₁×#436	—	2	8	no	—
11	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
12	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
13	C₂×C₁₁×C₂²⋊C₈	C₂²	1	8	yes	—
14	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#399	C₄	1	4	yes	—
17	C₁₁×#392	C₄	1	4	yes	—
18	C₁₁×#376	C₂²	1	1	yes	characteristic
19	C₁₁×#336	C₂²	1	4	yes	—
20	C₁₁×#336	C₂²	1	4	yes	—
21	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
22	C₂²×D₄×C₁₁	C₂×C₄	1	4	yes	—
23	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
24	C₂×C₁₁×M₁₆	—	2	8	no	—
25	C₂×C₁₁×M₁₆	—	4	8	no	—
26	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
27	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
28	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
29	C₄×D₄×C₁₁	—	2	4	no	—
30	C₄×D₄×C₁₁	—	2	4	no	—
31	C₄×D₄×C₁₁	—	4	8	no	—
32	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
33	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
34	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
35	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	8	yes	—
36	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
37	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
38	C₁₁×C₄⋊C₈	—	2	4	no	—
39	C₁₁×C₂²⋊C₈	—	2	8	no	—
40	C₁₁×C₂²⋊C₈	—	4	8	no	—
41	C₁₁×#97	—	2	2	no	—
42	C₄×C₈×C₁₁	D₄	1	4	yes	complemented
43	C₁₁×#95	C₂×C₄	1	4	yes	—
44	#22265	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂⁴×C₁₁	C₂²×C₄	1	4	yes	—
46	C₂×D₄×C₁₁	—	2	4	no	—
47	C₂×D₄×C₁₁	—	4	4	no	—
48	C₂×D₄×C₁₁	—	4	4	no	—
49	C₂×D₄×C₁₁	—	4	8	no	—
50	C₂²×C₄×C₁₁	—	2	4	no	—
51	C₂²×C₄×C₁₁	—	2	4	no	—
52	C₂²×C₄×C₁₁	—	2	8	no	—
53	C₂²×C₄×C₁₁	—	2	8	no	—
54	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
55	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
56	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
57	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
58	C₁₁×M₁₆	—	4	16	no	—
59	C₂×C₈×C₁₁	—	2	4	no	—
60	C₂×C₈×C₁₁	—	2	2	no	—
61	C₂×C₈×C₁₁	—	2	4	no	—
62	C₂×C₈×C₁₁	—	2	4	no	—
63	C₂×C₈×C₁₁	—	2	8	no	—
64	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
65	C₁₁×C₄⋊C₄	—	2	4	no	—
66	C₁₁×C₄⋊C₄	—	4	4	no	—
67	C₁₁×C₂²⋊C₄	—	2	8	no	—
68	C₁₁×C₂²⋊C₄	—	4	8	no	—
69	C₄²×C₁₁	—	2	4	no	—
70	C₄²×C₁₁	C₂×D₄	1	2	yes	—
71	C₄²×C₁₁	#41	1	2	yes	—
72	C₂×#436	C₂×C₁₁	1	2	yes	complemented
73	#2397	C₂×C₁₁	1	1	yes	characteristic
74	#1955	C₂×C₁₁	1	2	yes	complemented
75	#1870	C₂×C₁₁	1	8	yes	complemented
76	#1832	C₂×C₁₁	1	1	yes	characteristic, complemented
77	#1746	C₂×C₁₁	1	1	yes	characteristic, complemented
78	C₂³×C₁₁	—	2	4	no	—
79	C₂³×C₁₁	—	2	8	no	—
80	C₂³×C₁₁	—	2	4	no	—
81	C₂³×C₁₁	—	2	4	no	—
82	C₂³×C₁₁	—	2	8	no	—
83	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
84	D₄×C₁₁	—	4	8	no	—
85	D₄×C₁₁	—	4	16	no	—
86	C₂×C₄×C₁₁	—	2	4	no	—
87	C₂×C₄×C₁₁	—	2	4	no	—
88	C₂×C₄×C₁₁	—	2	4	no	—
89	C₂×C₄×C₁₁	—	2	8	no	—
90	C₂×C₄×C₁₁	—	2	8	no	—
91	C₂×C₄×C₁₁	—	4	4	no	—
92	C₂×C₄×C₁₁	—	4	4	no	—
93	C₂×C₄×C₁₁	—	4	8	no	—
94	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
95	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
96	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
97	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
98	C₈×C₁₁	—	2	4	no	—
99	C₈×C₁₁	—	4	4	no	—
100	C₈×C₁₁	—	4	2	no	—
101	C₂²×M₁₆	C₂²×C₁₁	1	4	yes	—
102	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
103	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
104	#436	—	2	8	no	—
105	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
106	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
107	C₂×C₂²⋊C₈	C₂²×C₁₁	1	8	yes	—
108	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
109	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
110	#399	C₄×C₁₁	1	4	yes	—
111	#392	C₄×C₁₁	1	4	yes	—
112	#376	C₂²×C₁₁	1	1	yes	characteristic
113	#336	C₂²×C₁₁	1	4	yes	—
114	#336	C₂²×C₁₁	1	4	yes	—
115	C₂²×C₁₁	—	4	4	no	—
116	C₂²×C₁₁	—	4	4	no	—
117	C₂²×C₁₁	—	4	4	no	—
118	C₂²×C₁₁	—	4	8	no	—
119	C₂²×C₁₁	—	4	8	no	—
120	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
121	C₂²×C₁₁	#518	1	2	yes	—
122	C₂²×C₁₁	#568	1	4	yes	—
123	C₄×C₁₁	—	2	4	no	—
124	C₄×C₁₁	—	4	4	no	—
125	C₄×C₁₁	—	4	4	no	—
126	C₄×C₁₁	#535	1	2	yes	—
127	C₄×C₁₁	#540	1	2	yes	—
128	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
129	C₂²×D₄	C₂×C₄×C₁₁	1	4	yes	—
130	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
131	C₂×M₁₆	—	2	8	no	—
132	C₂×M₁₆	—	4	8	no	—
133	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
134	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
135	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
136	C₄×D₄	—	2	4	no	—
137	C₄×D₄	—	2	4	no	—
138	C₄×D₄	—	4	8	no	—
139	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
140	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
141	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
142	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	8	yes	—
143	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
144	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
145	C₄⋊C₈	—	2	4	no	—
146	C₂²⋊C₈	—	2	8	no	—
147	C₂²⋊C₈	—	4	8	no	—
148	#97	—	2	2	no	—
149	C₄×C₈	D₄×C₁₁	1	4	yes	complemented
150	#95	C₂×C₄×C₁₁	1	4	yes	—
151	C₂×C₁₁	—	8	4	no	—
152	C₂×C₁₁	#2328	1	1	yes	characteristic
153	C₂×C₁₁	#2930	1	2	yes	—
154	C₂×C₁₁	#2978	1	4	yes	—
155	C₂⁴	C₂²×C₄×C₁₁	1	4	yes	—
156	C₂×D₄	—	2	4	no	—
157	C₂×D₄	—	4	4	no	—
158	C₂×D₄	—	4	4	no	—
159	C₂×D₄	—	4	8	no	—
160	C₂²×C₄	—	2	4	no	—
161	C₂²×C₄	—	2	4	no	—
162	C₂²×C₄	—	2	8	no	—
163	C₂²×C₄	—	2	8	no	—
164	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
165	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
166	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
167	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
168	M₁₆	—	4	16	no	—
169	C₂×C₈	—	2	4	no	—
170	C₂×C₈	—	2	4	no	—
171	C₂×C₈	—	2	2	no	—
172	C₂×C₈	—	2	4	no	—
173	C₂×C₈	—	2	8	no	—
174	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	4	4	no	—
177	C₂²⋊C₄	—	2	8	no	—
178	C₂²⋊C₄	—	4	8	no	—
179	C₄²	—	2	4	no	—
180	C₄²	C₂×D₄×C₁₁	1	2	yes	—
181	C₄²	C₁₁×#41	1	2	yes	—
182	C₁₁	#22265	1	1	yes	characteristic, direct product factor, Sylow
183	C₂³	—	2	4	no	—
184	C₂³	—	2	8	no	—
185	C₂³	—	2	4	no	—
186	C₂³	—	2	4	no	—
187	C₂³	—	2	8	no	—
188	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
189	D₄	—	4	8	no	—
190	D₄	—	4	16	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	2	4	no	—
194	C₂×C₄	—	2	8	no	—
195	C₂×C₄	—	2	8	no	—
196	C₂×C₄	—	4	4	no	—
197	C₂×C₄	—	4	4	no	—
198	C₂×C₄	—	4	8	no	—
199	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
200	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
201	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
202	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
203	C₈	—	2	4	no	—
204	C₈	—	4	4	no	—
205	C₈	—	4	2	no	—
206	C₂²	—	4	4	no	—
207	C₂²	—	4	4	no	—
208	C₂²	—	4	8	no	—
209	C₂²	—	4	8	no	—
210	C₂²	—	4	4	no	—
211	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
212	C₂²	C₁₁×#518	1	2	yes	—
213	C₂²	C₁₁×#568	1	4	yes	—
214	C₄	—	2	4	no	—
215	C₄	—	4	4	no	—
216	C₄	—	4	4	no	—
217	C₄	C₁₁×#535	1	2	yes	—
218	C₄	C₁₁×#540	1	2	yes	—
219	C₂	—	8	4	no	—
220	C₂	C₁₁×#2328	1	1	yes	characteristic
221	C₂	C₁₁×#2930	1	2	yes	—
222	C₂	C₁₁×#2978	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂³×C₁₁	C₂³×C₄
prime radical	C₁₁×#2397	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#436	C₂	semidirect
3. C₁₁×#1955	C₂	semidirect
4. C₁₁×#1870	C₂	semidirect
5. C₁₁×#1832	C₂	semidirect
6. C₁₁×#1746	C₂	semidirect
42. C₄×C₈×C₁₁	D₄	semidirect
44. #22265	C₁₁	direct (N × H)
72. C₂×#436	C₂×C₁₁	semidirect
74. #1955	C₂×C₁₁	semidirect
75. #1870	C₂×C₁₁	semidirect
76. #1832	C₂×C₁₁	semidirect
77. #1746	C₂×C₁₁	semidirect
149. C₄×C₈	D₄×C₁₁	semidirect
182. C₁₁	#22265	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×#436	2
C₁₁×#2397	2
C₁₁×#1955	2
C₁₁×#1870	2
C₁₁×#1832	2
C₁₁×#1746	2
#22265	11

Subgroups — C11×#22265 #14599458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22265 #14599458