Subgroups — C₁₁×#18045 #14595238

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2970	C₂	1	2	yes	maximal, complemented
2	C₄×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1593	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1585	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1580	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1488	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#135	C₄	1	1	yes	characteristic
10	C₄×C₁₁×#41	C₂²	1	2	yes	—
11	C₁₁×#446	C₂²	1	4	yes	—
12	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic
13	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
14	C₄×C₁₁×SD₁₆	C₄	1	2	yes	—
15	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
16	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic
17	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
18	C₁₁×#435	—	2	4	no	—
19	C₈×D₄×C₁₁	C₂²	1	4	yes	—
20	C₁₁×#432	—	2	2	no	—
21	C₁₁×#432	C₂²	1	2	yes	—
22	C₁₁×#431	C₂²	1	1	yes	characteristic
23	C₁₁×#427	C₄	1	1	yes	characteristic
24	C₁₁×#416	C₄	1	2	yes	—
25	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×#97	—	2	2	no	—
27	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₁₁×#335	C₂²	1	2	yes	—
29	C₁₁×#334	C₂²	1	2	yes	—
30	C₁₁×Q₈⋊C₈	C₂²	1	4	yes	—
31	C₁₁×D₄⋊C₈	C₂²	1	4	yes	—
32	C₁₁×#322	C₂²	1	2	yes	—
33	C₁₁×#322	C₂²	1	2	yes	—
34	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
35	C₁₁×#135	—	2	4	no	—
36	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
37	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
38	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
40	C₂²×C₈×C₁₁	—	2	4	no	—
41	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
44	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
45	C₄×D₄×C₁₁	—	2	2	no	—
46	C₄×D₄×C₁₁	—	2	2	no	—
47	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
48	C₄×D₄×C₁₁	C₂³	1	2	yes	—
49	C₁₁×#117	—	2	2	no	—
50	C₁₁×#117	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₁	—	2	2	no	—
52	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
53	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
54	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
55	C₁₁×#106	C₂×C₄	1	2	yes	—
56	C₁₁×C₄⋊C₈	—	2	4	no	—
57	C₁₁×C₄⋊C₈	—	2	1	no	—
58	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
59	C₁₁×#103	C₂×C₄	1	2	yes	—
60	C₁₁×#103	C₂×C₄	1	2	yes	—
61	C₁₁×#102	C₂×C₄	1	2	yes	—
62	C₁₁×#102	C₂×C₄	1	2	yes	—
63	C₁₁×C₂²⋊C₈	—	2	2	no	—
64	C₁₁×C₂²⋊C₈	—	2	1	no	—
65	C₁₁×C₂²⋊C₈	—	2	4	no	—
66	C₁₁×#97	—	2	4	no	—
67	C₁₁×#97	—	2	2	no	—
68	C₁₁×#97	D₄	1	2	yes	—
69	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₁₁	C₂³	1	2	yes	—
72	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₁₁	C₂³	1	2	yes	—
75	#18045	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₁₁×#41	—	2	4	no	—
77	C₁₁×#41	—	4	2	no	—
78	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
79	C₂×D₄×C₁₁	—	2	2	no	—
80	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₁	—	2	2	no	—
82	C₂²×C₄×C₁₁	—	2	2	no	—
83	C₂²×C₄×C₁₁	—	2	2	no	—
84	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
87	C₁₁×Q₁₆	—	2	2	no	—
88	C₁₁×SD₁₆	—	2	4	no	—
89	C₁₁×D₈	M₁₆	1	4	yes	complemented
90	C₁₁×M₁₆	—	4	2	no	—
91	C₂×C₈×C₁₁	—	2	2	no	—
92	C₂×C₈×C₁₁	—	2	4	no	—
93	C₂×C₈×C₁₁	—	2	2	no	—
94	C₂×C₈×C₁₁	—	4	1	no	—
95	C₂×C₈×C₁₁	—	4	8	no	—
96	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
101	C₁₁×C₄⋊C₄	—	2	2	no	—
102	C₁₁×C₄⋊C₄	—	2	2	no	—
103	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
104	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
105	C₁₁×C₂²⋊C₄	—	2	2	no	—
106	C₁₁×C₂²⋊C₄	—	2	2	no	—
107	C₁₁×C₂²⋊C₄	—	2	2	no	—
108	C₄²×C₁₁	—	2	2	no	—
109	C₄²×C₁₁	—	2	2	no	—
110	C₄²×C₁₁	—	2	2	no	—
111	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₁₁	#41	1	1	yes	characteristic
114	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
115	#2970	C₂×C₁₁	1	2	yes	complemented
116	C₄×#135	C₂×C₁₁	1	1	yes	characteristic
117	#1593	C₂×C₁₁	1	2	yes	complemented
118	#1585	C₂×C₁₁	1	4	yes	complemented
119	#1580	C₂×C₁₁	1	2	yes	complemented
120	#1568	C₂×C₁₁	1	1	yes	characteristic, complemented
121	#1488	C₂×C₁₁	1	2	yes	complemented
122	#1451	C₂×C₁₁	1	1	yes	characteristic, complemented
123	C₂³×C₁₁	—	2	2	no	—
124	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
125	Q₈×C₁₁	—	2	2	no	—
126	Q₈×C₁₁	—	2	2	no	—
127	D₄×C₁₁	—	2	2	no	—
128	D₄×C₁₁	—	4	4	no	—
129	D₄×C₁₁	C₂×M₁₆	1	4	yes	—
130	C₂×C₄×C₁₁	—	2	1	no	—
131	C₂×C₄×C₁₁	—	2	1	no	—
132	C₂×C₄×C₁₁	—	2	2	no	—
133	C₂×C₄×C₁₁	—	2	2	no	—
134	C₂×C₄×C₁₁	—	2	2	no	—
135	C₂×C₄×C₁₁	—	2	2	no	—
136	C₂×C₄×C₁₁	—	4	1	no	—
137	C₂×C₄×C₁₁	—	4	4	no	—
138	C₂×C₄×C₁₁	—	4	4	no	—
139	C₂×C₄×C₁₁	—	8	2	no	—
140	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
146	C₈×C₁₁	—	2	1	no	—
147	C₈×C₁₁	—	2	1	no	—
148	C₈×C₁₁	—	2	1	no	—
149	C₈×C₁₁	—	2	4	no	—
150	C₈×C₁₁	—	4	2	no	—
151	C₈×C₁₁	—	4	4	no	—
152	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
153	C₂×#135	C₄×C₁₁	1	1	yes	characteristic
154	C₄×#41	C₂²×C₁₁	1	2	yes	—
155	#446	C₂²×C₁₁	1	4	yes	—
156	C₄×Q₁₆	C₄×C₁₁	1	1	yes	characteristic
157	C₄×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
158	C₄×SD₁₆	C₄×C₁₁	1	2	yes	—
159	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	—
160	C₄×D₈	C₄×C₁₁	1	1	yes	characteristic
161	C₄×D₈	C₂²×C₁₁	1	1	yes	characteristic
162	#435	—	2	4	no	—
163	C₈×D₄	C₂²×C₁₁	1	4	yes	—
164	#432	—	2	2	no	—
165	#432	C₂²×C₁₁	1	2	yes	—
166	#431	C₂²×C₁₁	1	1	yes	characteristic
167	#427	C₄×C₁₁	1	1	yes	characteristic
168	#416	C₄×C₁₁	1	2	yes	—
169	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
170	C₂×#97	—	2	2	no	—
171	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
172	#335	C₂²×C₁₁	1	2	yes	—
173	#334	C₂²×C₁₁	1	2	yes	—
174	Q₈⋊C₈	C₂²×C₁₁	1	4	yes	—
175	D₄⋊C₈	C₂²×C₁₁	1	4	yes	—
176	#322	C₂²×C₁₁	1	2	yes	—
177	#322	C₂²×C₁₁	1	2	yes	—
178	C₂²×C₁₁	—	2	1	no	—
179	C₂²×C₁₁	—	2	4	no	—
180	C₂²×C₁₁	—	2	1	no	—
181	C₂²×C₁₁	—	2	1	no	—
182	C₂²×C₁₁	—	4	2	no	—
183	C₂²×C₁₁	—	4	2	no	—
184	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
185	C₄×C₁₁	—	2	1	no	—
186	C₄×C₁₁	—	2	1	no	—
187	C₄×C₁₁	—	2	1	no	—
188	C₄×C₁₁	—	2	1	no	—
189	C₄×C₁₁	—	4	2	no	—
190	C₄×C₁₁	—	4	2	no	—
191	C₄×C₁₁	—	4	2	no	—
192	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
193	C₄×C₁₁	#568	1	1	yes	characteristic
194	C₄×C₁₁	#575	1	2	yes	—
195	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
196	#135	—	2	4	no	—
197	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
198	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
199	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
200	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
201	C₂²×C₈	—	2	4	no	—
202	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
203	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
204	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
205	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
206	C₄×D₄	—	2	2	no	—
207	C₄×D₄	—	2	2	no	—
208	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
209	C₄×D₄	C₂³×C₁₁	1	2	yes	—
210	#117	—	2	2	no	—
211	#117	C₂×C₄×C₁₁	1	2	yes	—
212	C₂×C₄²	—	2	2	no	—
213	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
214	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
215	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
216	#106	C₂×C₄×C₁₁	1	2	yes	—
217	C₄⋊C₈	—	2	4	no	—
218	C₄⋊C₈	—	2	1	no	—
219	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
220	#103	C₂×C₄×C₁₁	1	2	yes	—
221	#103	C₂×C₄×C₁₁	1	2	yes	—
222	#102	C₂×C₄×C₁₁	1	2	yes	—
223	#102	C₂×C₄×C₁₁	1	2	yes	—
224	C₂²⋊C₈	—	2	2	no	—
225	C₂²⋊C₈	—	2	1	no	—
226	C₂²⋊C₈	—	2	4	no	—
227	#97	—	2	4	no	—
228	#97	—	2	2	no	—
229	#97	D₄×C₁₁	1	2	yes	—
230	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
231	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
232	C₄×C₈	C₂³×C₁₁	1	2	yes	—
233	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
234	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
235	C₄×C₈	C₂³×C₁₁	1	2	yes	—
236	C₂×C₁₁	—	4	1	no	—
237	C₂×C₁₁	—	4	4	no	—
238	C₂×C₁₁	D₄×M₁₆	1	1	yes	characteristic
239	C₂×C₁₁	#2943	1	1	yes	characteristic
240	C₂×C₁₁	#2957	1	1	yes	characteristic
241	#41	—	2	4	no	—
242	#41	—	4	2	no	—
243	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
244	C₂×D₄	—	2	2	no	—
245	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
250	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
251	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
252	Q₁₆	—	2	2	no	—
253	SD₁₆	—	2	4	no	—
254	D₈	C₁₁×M₁₆	1	4	yes	complemented
255	M₁₆	—	4	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	4	1	no	—
260	C₂×C₈	—	4	8	no	—
261	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
262	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
263	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
264	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
265	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
269	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
270	C₂²⋊C₄	—	2	2	no	—
271	C₂²⋊C₄	—	2	2	no	—
272	C₂²⋊C₄	—	2	2	no	—
273	C₄²	—	2	2	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
277	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
278	C₄²	C₁₁×#41	1	1	yes	characteristic
279	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
280	C₁₁	#18045	1	1	yes	characteristic, direct product factor, Sylow
281	C₂³	—	2	2	no	—
282	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
283	Q₈	—	2	2	no	—
284	Q₈	—	2	2	no	—
285	D₄	—	2	2	no	—
286	D₄	—	4	4	no	—
287	D₄	C₂×C₁₁×M₁₆	1	4	yes	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	4	1	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	8	2	no	—
298	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
299	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
300	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
301	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
302	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
303	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
304	C₈	—	2	1	no	—
305	C₈	—	2	1	no	—
306	C₈	—	2	1	no	—
307	C₈	—	2	4	no	—
308	C₈	—	4	2	no	—
309	C₈	—	4	4	no	—
310	C₈	C₂×C₁₁×M₁₆	1	2	yes	—
311	C₂²	—	2	1	no	—
312	C₂²	—	2	4	no	—
313	C₂²	—	2	1	no	—
314	C₂²	—	2	1	no	—
315	C₂²	—	4	2	no	—
316	C₂²	—	4	2	no	—
317	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
318	C₄	—	2	1	no	—
319	C₄	—	2	1	no	—
320	C₄	—	2	1	no	—
321	C₄	—	2	1	no	—
322	C₄	—	4	2	no	—
323	C₄	—	4	2	no	—
324	C₄	—	4	2	no	—
325	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
326	C₄	C₁₁×#568	1	1	yes	characteristic
327	C₄	C₁₁×#575	1	2	yes	—
328	C₂	—	4	1	no	—
329	C₂	—	4	4	no	—
330	C₂	D₄×C₁₁×M₁₆	1	1	yes	characteristic
331	C₂	C₁₁×#2943	1	1	yes	characteristic
332	C₂	C₁₁×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#135	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₁₁×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#2970	C₂	semidirect
3. C₁₁×#1593	C₂	semidirect
4. C₁₁×#1585	C₂	semidirect
5. C₁₁×#1580	C₂	semidirect
6. C₁₁×#1568	C₂	semidirect
7. C₁₁×#1488	C₂	semidirect
8. C₁₁×#1451	C₂	semidirect
75. #18045	C₁₁	direct (N × H)
89. C₁₁×D₈	M₁₆	semidirect
115. #2970	C₂×C₁₁	semidirect
117. #1593	C₂×C₁₁	semidirect
118. #1585	C₂×C₁₁	semidirect
119. #1580	C₂×C₁₁	semidirect
120. #1568	C₂×C₁₁	semidirect
121. #1488	C₂×C₁₁	semidirect
122. #1451	C₂×C₁₁	semidirect
254. D₈	C₁₁×M₁₆	semidirect
280. C₁₁	#18045	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×#2970	2
C₄×C₁₁×#135	2
C₁₁×#1593	2
C₁₁×#1585	2
C₁₁×#1580	2
C₁₁×#1568	2
C₁₁×#1488	2
C₁₁×#1451	2
#18045	11

Subgroups — C11×#18045 #14595238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#18045 #14595238