Subgroups — C₁₁×#18075 #14595268

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3168	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2969	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1594	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1588	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1585	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1580	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1579	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1482	C₂	1	2	yes	maximal, complemented
11	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#529	C₂²	1	2	yes	—
13	C₁₁×#499	C₄	1	1	yes	characteristic
14	C₁₁×#495	C₄	1	1	yes	characteristic
15	C₁₁×#488	C₄	1	2	yes	—
16	C₁₁×#467	C₄	1	1	yes	characteristic
17	C₁₁×#466	C₄	1	1	yes	characteristic
18	C₁₁×#465	C₄	1	2	yes	—
19	C₁₁×#446	C₂²	1	2	yes	—
20	C₈×Q₈×C₁₁	C₂²	1	2	yes	—
21	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
22	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
23	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
24	C₁₁×#436	—	2	2	no	—
25	C₁₁×#436	C₂²	1	2	yes	—
26	C₁₁×#435	—	2	2	no	—
27	C₈×D₄×C₁₁	C₂²	1	2	yes	—
28	C₁₁×#433	—	2	2	no	—
29	C₁₁×#431	C₂²	1	2	yes	—
30	C₁₁×#431	C₂²	1	1	yes	characteristic
31	C₁₁×#405	—	2	2	no	—
32	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
34	C₁₁×#335	C₂²	1	2	yes	—
35	C₁₁×#334	C₂²	1	1	yes	characteristic
36	C₁₁×#334	C₂²	1	1	yes	characteristic
37	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
40	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
41	C₁₁×#322	C₂²	1	1	yes	characteristic
42	C₁₁×#322	C₂²	1	1	yes	characteristic
43	C₁₁×#322	C₂²	1	1	yes	characteristic
44	C₁₁×#322	C₂²	1	1	yes	characteristic
45	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
46	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
47	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₁×M₁₆	—	2	2	no	—
49	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
50	C₂²×C₈×C₁₁	—	2	2	no	—
51	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
53	C₁₁×#126	—	2	2	no	—
54	C₁₁×#125	C₂×C₄	1	2	yes	—
55	C₁₁×#124	C₂×C₄	1	2	yes	—
56	C₁₁×#123	—	2	2	no	—
57	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
58	C₁₁×#121	C₂×C₄	1	2	yes	—
59	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
60	C₄×D₄×C₁₁	—	2	2	no	—
61	C₄×D₄×C₁₁	C₂³	1	2	yes	—
62	C₁₁×#117	—	2	2	no	—
63	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
64	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
65	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
66	C₁₁×#106	C₂×C₄	1	2	yes	—
67	C₁₁×C₄⋊C₈	—	2	2	no	—
68	C₁₁×C₄⋊C₈	—	2	2	no	—
69	C₁₁×C₄⋊C₈	—	2	1	no	—
70	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
71	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₁×#103	C₂×C₄	1	2	yes	—
73	C₁₁×#103	C₂×C₄	1	2	yes	—
74	C₁₁×#102	C₂×C₄	1	2	yes	—
75	C₁₁×#102	C₂×C₄	1	2	yes	—
76	C₁₁×C₂²⋊C₈	—	2	2	no	—
77	C₁₁×C₂²⋊C₈	—	2	1	no	—
78	C₁₁×C₂²⋊C₈	—	2	2	no	—
79	C₁₁×C₂²⋊C₈	—	2	2	no	—
80	C₁₁×#97	—	2	2	no	—
81	C₁₁×#97	D₄	1	2	yes	—
82	C₄×C₈×C₁₁	—	2	2	no	—
83	C₄×C₈×C₁₁	—	2	2	no	—
84	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
85	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
86	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
92	#18075	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
94	C₂×D₄×C₁₁	—	2	2	no	—
95	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₁	—	2	2	no	—
97	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
100	C₁₁×Q₁₆	—	2	2	no	—
101	C₁₁×SD₁₆	—	4	2	no	—
102	C₁₁×D₈	—	2	2	no	—
103	C₁₁×M₁₆	—	4	2	no	—
104	C₁₁×M₁₆	—	4	4	no	—
105	C₂×C₈×C₁₁	—	2	2	no	—
106	C₂×C₈×C₁₁	—	2	2	no	—
107	C₂×C₈×C₁₁	—	2	2	no	—
108	C₂×C₈×C₁₁	—	2	1	no	—
109	C₂×C₈×C₁₁	—	2	1	no	—
110	C₂×C₈×C₁₁	—	4	1	no	—
111	C₂×C₈×C₁₁	—	4	4	no	—
112	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
118	C₁₁×C₄⋊C₄	—	2	2	no	—
119	C₁₁×C₄⋊C₄	—	2	2	no	—
120	C₁₁×C₄⋊C₄	—	2	2	no	—
121	C₁₁×C₄⋊C₄	—	2	2	no	—
122	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
123	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
124	C₁₁×C₂²⋊C₄	—	2	2	no	—
125	C₁₁×C₂²⋊C₄	—	2	2	no	—
126	C₁₁×C₂²⋊C₄	—	2	2	no	—
127	C₁₁×C₂²⋊C₄	—	2	2	no	—
128	C₁₁×C₂²⋊C₄	—	2	2	no	—
129	C₄²×C₁₁	—	2	2	no	—
130	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₁	#41	1	1	yes	characteristic
133	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
134	#3168	C₂×C₁₁	1	1	yes	characteristic
135	#2969	C₂×C₁₁	1	2	yes	complemented
136	#1594	C₂×C₁₁	1	1	yes	characteristic, complemented
137	#1593	C₂×C₁₁	1	1	yes	characteristic, complemented
138	#1588	C₂×C₁₁	1	2	yes	complemented
139	#1585	C₂×C₁₁	1	2	yes	complemented
140	#1580	C₂×C₁₁	1	1	yes	characteristic, complemented
141	#1579	C₂×C₁₁	1	1	yes	characteristic, complemented
142	#1564	C₂×C₁₁	1	1	yes	characteristic, complemented
143	#1482	C₂×C₁₁	1	2	yes	complemented
144	#1451	C₂×C₁₁	1	1	yes	characteristic, complemented
145	C₂³×C₁₁	—	2	2	no	—
146	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
147	Q₈×C₁₁	—	2	2	no	—
148	Q₈×C₁₁	—	2	2	no	—
149	D₄×C₁₁	—	2	2	no	—
150	D₄×C₁₁	—	2	2	no	—
151	D₄×C₁₁	—	8	2	no	—
152	C₂×C₄×C₁₁	—	2	1	no	—
153	C₂×C₄×C₁₁	—	2	1	no	—
154	C₂×C₄×C₁₁	—	2	2	no	—
155	C₂×C₄×C₁₁	—	2	2	no	—
156	C₂×C₄×C₁₁	—	2	2	no	—
157	C₂×C₄×C₁₁	—	2	2	no	—
158	C₂×C₄×C₁₁	—	4	1	no	—
159	C₂×C₄×C₁₁	—	4	2	no	—
160	C₂×C₄×C₁₁	—	4	2	no	—
161	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
167	C₈×C₁₁	—	2	1	no	—
168	C₈×C₁₁	—	2	1	no	—
169	C₈×C₁₁	—	2	1	no	—
170	C₈×C₁₁	—	2	2	no	—
171	C₈×C₁₁	—	2	2	no	—
172	C₈×C₁₁	—	4	1	no	—
173	C₈×C₁₁	—	4	1	no	—
174	C₈×C₁₁	—	4	2	no	—
175	C₈×C₁₁	—	4	2	no	—
176	C₈×C₁₁	#131	1	2	yes	—
177	#529	C₂²×C₁₁	1	2	yes	—
178	#499	C₄×C₁₁	1	1	yes	characteristic
179	#495	C₄×C₁₁	1	1	yes	characteristic
180	#488	C₄×C₁₁	1	2	yes	—
181	#467	C₄×C₁₁	1	1	yes	characteristic
182	#466	C₄×C₁₁	1	1	yes	characteristic
183	#465	C₄×C₁₁	1	2	yes	—
184	#446	C₂²×C₁₁	1	2	yes	—
185	C₈×Q₈	C₂²×C₁₁	1	2	yes	—
186	C₄×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
187	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	—
188	C₄×D₈	C₂²×C₁₁	1	1	yes	characteristic
189	#436	—	2	2	no	—
190	#436	C₂²×C₁₁	1	2	yes	—
191	#435	—	2	2	no	—
192	C₈×D₄	C₂²×C₁₁	1	2	yes	—
193	#433	—	2	2	no	—
194	#431	C₂²×C₁₁	1	2	yes	—
195	#431	C₂²×C₁₁	1	1	yes	characteristic
196	#405	—	2	2	no	—
197	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
198	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
199	#335	C₂²×C₁₁	1	2	yes	—
200	#334	C₂²×C₁₁	1	1	yes	characteristic
201	#334	C₂²×C₁₁	1	1	yes	characteristic
202	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	—
203	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	—
204	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
205	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
206	#322	C₂²×C₁₁	1	1	yes	characteristic
207	#322	C₂²×C₁₁	1	1	yes	characteristic
208	#322	C₂²×C₁₁	1	1	yes	characteristic
209	#322	C₂²×C₁₁	1	1	yes	characteristic
210	C₂²×C₁₁	—	2	1	no	—
211	C₂²×C₁₁	—	2	1	no	—
212	C₂²×C₁₁	—	2	1	no	—
213	C₂²×C₁₁	—	4	2	no	—
214	C₂²×C₁₁	—	4	2	no	—
215	C₂²×C₁₁	—	4	2	no	—
216	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
217	C₄×C₁₁	—	2	1	no	—
218	C₄×C₁₁	—	2	1	no	—
219	C₄×C₁₁	—	2	1	no	—
220	C₄×C₁₁	—	2	1	no	—
221	C₄×C₁₁	—	4	2	no	—
222	C₄×C₁₁	—	4	2	no	—
223	C₄×C₁₁	—	4	2	no	—
224	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
225	C₄×C₁₁	#568	1	1	yes	characteristic
226	C₄×C₁₁	#575	1	2	yes	—
227	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
228	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
229	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
234	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
235	#126	—	2	2	no	—
236	#125	C₂×C₄×C₁₁	1	2	yes	—
237	#124	C₂×C₄×C₁₁	1	2	yes	—
238	#123	—	2	2	no	—
239	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
240	#121	C₂×C₄×C₁₁	1	2	yes	—
241	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	C₂³×C₁₁	1	2	yes	—
244	#117	—	2	2	no	—
245	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
246	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
247	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
248	#106	C₂×C₄×C₁₁	1	2	yes	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
253	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
254	#103	C₂×C₄×C₁₁	1	2	yes	—
255	#103	C₂×C₄×C₁₁	1	2	yes	—
256	#102	C₂×C₄×C₁₁	1	2	yes	—
257	#102	C₂×C₄×C₁₁	1	2	yes	—
258	C₂²⋊C₈	—	2	2	no	—
259	C₂²⋊C₈	—	2	1	no	—
260	C₂²⋊C₈	—	2	2	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	#97	—	2	2	no	—
263	#97	D₄×C₁₁	1	2	yes	—
264	C₄×C₈	—	2	2	no	—
265	C₄×C₈	—	2	2	no	—
266	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
267	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
268	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
269	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
274	C₂×C₁₁	—	4	1	no	—
275	C₂×C₁₁	—	8	2	no	—
276	C₂×C₁₁	#2935	1	1	yes	characteristic
277	C₂×C₁₁	#2943	1	1	yes	characteristic
278	C₂×C₁₁	#2957	1	1	yes	characteristic
279	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
285	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
286	Q₁₆	—	2	2	no	—
287	SD₁₆	—	4	2	no	—
288	D₈	—	2	2	no	—
289	M₁₆	—	4	2	no	—
290	M₁₆	—	4	4	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	4	4	no	—
298	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
299	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
300	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
302	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
303	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
309	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
317	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
318	C₄²	C₁₁×#41	1	1	yes	characteristic
319	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
320	C₁₁	#18075	1	1	yes	characteristic, direct product factor, Sylow
321	C₂³	—	2	2	no	—
322	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	2	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	8	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
338	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
339	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
340	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
342	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	—	2	1	no	—
346	C₈	—	2	2	no	—
347	C₈	—	2	2	no	—
348	C₈	—	4	1	no	—
349	C₈	—	4	1	no	—
350	C₈	—	4	2	no	—
351	C₈	—	4	2	no	—
352	C₈	C₁₁×#131	1	2	yes	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	C₂×C₁₁×#131	1	1	yes	characteristic
368	C₄	C₁₁×#568	1	1	yes	characteristic
369	C₄	C₁₁×#575	1	2	yes	—
370	C₂	—	4	1	no	—
371	C₂	—	8	2	no	—
372	C₂	C₁₁×#2935	1	1	yes	characteristic
373	C₂	C₁₁×#2943	1	1	yes	characteristic
374	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	C₁₁×#466	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
2. C₁₁×#2969	C₂	semidirect
3. C₁₁×#1594	C₂	semidirect
4. C₁₁×#1593	C₂	semidirect
5. C₁₁×#1588	C₂	semidirect
6. C₁₁×#1585	C₂	semidirect
7. C₁₁×#1580	C₂	semidirect
8. C₁₁×#1579	C₂	semidirect
9. C₁₁×#1564	C₂	semidirect
10. C₁₁×#1482	C₂	semidirect
11. C₁₁×#1451	C₂	semidirect
92. #18075	C₁₁	direct (N × H)
135. #2969	C₂×C₁₁	semidirect
136. #1594	C₂×C₁₁	semidirect
137. #1593	C₂×C₁₁	semidirect
138. #1588	C₂×C₁₁	semidirect
139. #1585	C₂×C₁₁	semidirect
140. #1580	C₂×C₁₁	semidirect
141. #1579	C₂×C₁₁	semidirect
142. #1564	C₂×C₁₁	semidirect
143. #1482	C₂×C₁₁	semidirect
144. #1451	C₂×C₁₁	semidirect
320. C₁₁	#18075	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×#3168	2
C₁₁×#2969	2
C₁₁×#1594	2
C₁₁×#1593	2
C₁₁×#1588	2
C₁₁×#1585	2
C₁₁×#1580	2
C₁₁×#1579	2
C₁₁×#1564	2
C₁₁×#1482	2
C₁₁×#1451	2
#18075	11

Subgroups — C11×#18075 #14595268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#18075 #14595268