Subgroups — C₂×C₁₁×#1281 #14585110

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#431	C₂	1	2	yes	maximal
2	C₂²×C₁₁×#97	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1281	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₈×C₁₁	C₄	1	2	yes	—
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×#431	—	2	2	no	—
7	C₁₁×#431	—	2	2	no	—
8	C₁₁×#431	C₄	1	4	yes	—
9	C₁₁×#431	C₂²	1	4	yes	—
10	C₂×C₁₁×C₄⋊C₈	—	2	2	no	—
11	C₂×C₁₁×C₂²⋊C₈	C₄	1	4	yes	—
12	C₂×C₁₁×#97	—	2	2	no	—
13	C₂×C₁₁×#97	—	2	2	no	—
14	C₂×C₁₁×#97	C₄	1	2	yes	—
15	C₂×C₁₁×#97	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₁	—	2	2	no	—
17	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
18	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₁	—	2	2	no	—
20	C₂²×C₈×C₁₁	—	2	2	no	—
21	C₂²×C₈×C₁₁	—	2	4	no	—
22	C₂²×C₈×C₁₁	—	2	4	no	—
23	C₂²×C₈×C₁₁	C₈	1	8	yes	complemented
24	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₁	D₄	1	2	yes	—
28	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₁	D₄	1	2	yes	—
31	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
34	C₁₁×C₄⋊C₈	—	2	4	no	—
35	C₁₁×C₄⋊C₈	—	2	4	no	—
36	C₁₁×C₂²⋊C₈	—	2	4	no	—
37	C₁₁×C₂²⋊C₈	C₂×C₄	1	8	yes	—
38	C₁₁×#97	—	2	4	no	—
39	C₁₁×#97	—	2	4	no	—
40	C₄×C₈×C₁₁	—	2	4	no	—
41	C₄×C₈×C₁₁	—	2	4	no	—
42	C₂×#1281	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂⁴×C₁₁	C₄²	1	1	yes	characteristic
44	C₂²×C₄×C₁₁	—	4	4	no	—
45	C₂²×C₄×C₁₁	C₄²	1	2	yes	—
46	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
52	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
56	C₂²×C₄×C₁₁	M₁₆	1	4	yes	—
57	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
58	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₁₁	—	2	8	no	—
60	C₂×C₈×C₁₁	—	2	8	no	—
61	C₂×C₈×C₁₁	—	2	4	no	—
62	C₂×C₈×C₁₁	—	2	8	no	—
63	C₂×C₈×C₁₁	—	2	4	no	—
64	C₂×C₈×C₁₁	—	4	8	no	—
65	C₂×C₈×C₁₁	C₂×C₈	1	8	yes	complemented
66	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
67	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
68	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
69	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
70	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
71	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
72	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
73	C₄²×C₁₁	C₂×D₄	1	2	yes	—
74	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
76	C₂×#431	C₂×C₁₁	1	2	yes	—
77	C₂²×#97	C₂×C₁₁	1	1	yes	characteristic
78	#1281	C₂×C₁₁	1	4	yes	direct product factor
79	C₂³×C₁₁	—	2	4	no	—
80	C₂³×C₁₁	#95	1	1	yes	characteristic
81	C₂³×C₁₁	#95	1	1	yes	characteristic
82	C₂³×C₁₁	C₄×C₈	1	2	yes	—
83	C₂³×C₁₁	#97	1	2	yes	—
84	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
85	C₂×C₄×C₁₁	—	2	4	no	—
86	C₂×C₄×C₁₁	—	2	4	no	—
87	C₂×C₄×C₁₁	—	4	2	no	—
88	C₂×C₄×C₁₁	—	4	2	no	—
89	C₂×C₄×C₁₁	—	4	2	no	—
90	C₂×C₄×C₁₁	—	4	2	no	—
91	C₂×C₄×C₁₁	#95	1	2	yes	—
92	C₂×C₄×C₁₁	#95	1	2	yes	—
93	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
94	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
95	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
96	C₂×C₄×C₁₁	#97	1	2	yes	—
97	C₂×C₄×C₁₁	C₂²⋊C₈	1	4	yes	—
98	C₂×C₄×C₁₁	C₂²⋊C₈	1	4	yes	—
99	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
100	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
101	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
102	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
104	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
106	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
107	C₈×C₁₁	—	2	8	no	—
108	C₈×C₁₁	—	4	8	no	—
109	C₂³×C₈	C₄×C₁₁	1	2	yes	—
110	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
111	#431	—	2	2	no	—
112	#431	—	2	2	no	—
113	#431	C₄×C₁₁	1	4	yes	—
114	#431	C₂²×C₁₁	1	4	yes	—
115	C₂×C₄⋊C₈	—	2	2	no	—
116	C₂×C₂²⋊C₈	C₄×C₁₁	1	4	yes	—
117	C₂×#97	—	2	2	no	—
118	C₂×#97	—	2	2	no	—
119	C₂×#97	C₄×C₁₁	1	2	yes	—
120	C₂×#97	C₂²×C₁₁	1	2	yes	—
121	C₂×C₄×C₈	—	2	2	no	—
122	C₂²×C₁₁	—	2	4	no	—
123	C₂²×C₁₁	—	2	4	no	—
124	C₂²×C₁₁	—	2	2	no	—
125	C₂²×C₁₁	—	2	2	no	—
126	C₂²×C₁₁	#336	1	2	yes	—
127	C₂²×C₁₁	#336	1	2	yes	—
128	C₂²×C₁₁	#344	1	4	yes	—
129	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
130	C₂²×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
131	C₂²×C₁₁	C₂×#97	1	1	yes	characteristic
132	C₄×C₁₁	—	2	2	no	—
133	C₄×C₁₁	—	2	2	no	—
134	C₄×C₁₁	—	2	2	no	—
135	C₄×C₁₁	—	2	2	no	—
136	C₄×C₁₁	#336	1	2	yes	—
137	C₄×C₁₁	#336	1	2	yes	—
138	C₄×C₁₁	C₂×C₂²⋊C₈	1	2	yes	—
139	C₄×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
140	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
141	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
142	C₂²×C₈	—	2	2	no	—
143	C₂²×C₈	—	2	2	no	—
144	C₂²×C₈	—	2	4	no	—
145	C₂²×C₈	—	2	4	no	—
146	C₂²×C₈	C₈×C₁₁	1	8	yes	complemented
147	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
148	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
149	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
150	C₂×C₄²	D₄×C₁₁	1	2	yes	—
151	C₂×C₄²	D₄×C₁₁	1	2	yes	—
152	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
153	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
154	C₂×C₄²	Q₈×C₁₁	1	1	yes	characteristic
155	C₂×C₄²	Q₈×C₁₁	1	1	yes	characteristic
156	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
157	C₄⋊C₈	—	2	4	no	—
158	C₄⋊C₈	—	2	4	no	—
159	C₂²⋊C₈	—	2	4	no	—
160	C₂²⋊C₈	C₂×C₄×C₁₁	1	8	yes	—
161	#97	—	2	4	no	—
162	#97	—	2	4	no	—
163	C₄×C₈	—	2	4	no	—
164	C₄×C₈	—	2	4	no	—
165	C₂×C₁₁	—	2	2	no	—
166	C₂×C₁₁	—	2	1	no	—
167	C₂×C₁₁	—	2	1	no	—
168	C₂×C₁₁	#1281	1	4	yes	direct product factor
169	C₂×C₁₁	C₂×#336	1	1	yes	characteristic
170	C₂×C₁₁	C₂×#344	1	2	yes	—
171	C₂⁴	C₄²×C₁₁	1	1	yes	characteristic
172	C₂²×C₄	—	4	4	no	—
173	C₂²×C₄	C₄²×C₁₁	1	2	yes	—
174	C₂²×C₄	C₄²×C₁₁	1	1	yes	characteristic
175	C₂²×C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
176	C₂²×C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
177	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
178	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
180	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
181	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
182	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×C₄	C₂×C₈×C₁₁	1	4	yes	—
184	C₂²×C₄	C₁₁×M₁₆	1	4	yes	—
185	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
186	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
187	C₂×C₈	—	2	8	no	—
188	C₂×C₈	—	2	8	no	—
189	C₂×C₈	—	2	4	no	—
190	C₂×C₈	—	2	4	no	—
191	C₂×C₈	—	2	8	no	—
192	C₂×C₈	—	4	8	no	—
193	C₂×C₈	C₂×C₈×C₁₁	1	8	yes	complemented
194	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
195	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
196	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
197	C₄²	C₁₁×C₄⋊C₄	1	1	yes	characteristic
198	C₄²	C₁₁×C₄⋊C₄	1	1	yes	characteristic
199	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
200	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
201	C₄²	C₂×D₄×C₁₁	1	2	yes	—
202	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
203	C₄²	C₂×Q₈×C₁₁	1	1	yes	characteristic
204	C₁₁	C₂×#1281	1	1	yes	characteristic, direct product factor, Sylow
205	C₂³	—	2	4	no	—
206	C₂³	C₁₁×#95	1	1	yes	characteristic
207	C₂³	C₁₁×#95	1	1	yes	characteristic
208	C₂³	C₄×C₈×C₁₁	1	2	yes	—
209	C₂³	C₁₁×#97	1	2	yes	—
210	C₂³	C₂×C₄²×C₁₁	1	1	yes	characteristic
211	C₂×C₄	—	2	4	no	—
212	C₂×C₄	—	2	4	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	C₁₁×#95	1	2	yes	—
218	C₂×C₄	C₁₁×#95	1	2	yes	—
219	C₂×C₄	C₁₁×#95	1	1	yes	characteristic
220	C₂×C₄	C₁₁×#95	1	1	yes	characteristic
221	C₂×C₄	C₄×C₈×C₁₁	1	2	yes	—
222	C₂×C₄	C₁₁×#97	1	2	yes	—
223	C₂×C₄	C₁₁×C₂²⋊C₈	1	4	yes	—
224	C₂×C₄	C₁₁×C₂²⋊C₈	1	4	yes	—
225	C₂×C₄	C₁₁×C₄⋊C₈	1	4	yes	—
226	C₂×C₄	C₁₁×C₄⋊C₈	1	4	yes	—
227	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
228	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
230	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
232	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
233	C₈	—	2	8	no	—
234	C₈	—	4	8	no	—
235	C₂²	—	2	2	no	—
236	C₂²	—	2	2	no	—
237	C₂²	—	2	4	no	—
238	C₂²	—	2	4	no	—
239	C₂²	C₁₁×#336	1	2	yes	—
240	C₂²	C₁₁×#336	1	2	yes	—
241	C₂²	C₁₁×#344	1	4	yes	—
242	C₂²	C₂×C₁₁×#95	1	1	yes	characteristic
243	C₂²	C₂×C₄×C₈×C₁₁	1	1	yes	characteristic
244	C₂²	C₂×C₁₁×#97	1	1	yes	characteristic
245	C₄	—	2	2	no	—
246	C₄	—	2	2	no	—
247	C₄	—	2	2	no	—
248	C₄	—	2	2	no	—
249	C₄	C₁₁×#336	1	2	yes	—
250	C₄	C₁₁×#336	1	2	yes	—
251	C₄	C₂×C₁₁×C₂²⋊C₈	1	2	yes	—
252	C₄	C₂×C₁₁×C₄⋊C₈	1	2	yes	—
253	C₂	—	2	2	no	—
254	C₂	—	2	1	no	—
255	C₂	—	2	1	no	—
256	C₂	C₁₁×#1281	1	4	yes	direct product factor
257	C₂	C₂×C₁₁×#336	1	1	yes	characteristic
258	C₂	C₂×C₁₁×#344	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂²⋊C₄
commutator	C₂²	C₂×C₄×C₈×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂³×C₁₁	#95
prime radical	C₂⁴×C₁₁	C₄²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1281	C₂	direct (N × H)
23. C₂²×C₈×C₁₁	C₈	semidirect
42. C₂×#1281	C₁₁	direct (N × H)
65. C₂×C₈×C₁₁	C₂×C₈	semidirect
78. #1281	C₂×C₁₁	direct (N × H)
146. C₂²×C₈	C₈×C₁₁	semidirect
168. C₂×C₁₁	#1281	direct (N × H)
193. C₂×C₈	C₂×C₈×C₁₁	semidirect
204. C₁₁	C₂×#1281	direct (N × H)
256. C₂	C₁₁×#1281	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×#431	2
C₂²×C₁₁×#97	2
C₁₁×#1281	2
C₂×#1281	11

Subgroups — C2×C11×#1281 #14585110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#1281 #14585110