Subgroups — C₁₁×#22606 #14599799

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2924	C₂	1	2	yes	maximal
2	C₂×C₁₁×#427	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1945	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1922	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1826	C₂	1	2	yes	maximal
6	C₁₁×#1810	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#1772	C₂	1	2	yes	maximal, complemented
8	C₈×C₁₁×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×#117	C₂²	1	2	yes	—
11	C₁₁×#433	—	2	4	no	—
12	C₁₁×#432	—	2	2	no	—
13	C₁₁×#431	—	2	2	no	—
14	C₂×C₁₁×#108	C₂²	1	2	yes	—
15	C₁₁×#427	C₄	1	1	yes	characteristic, complemented
16	C₁₁×#427	C₄	1	1	yes	characteristic, complemented
17	C₁₁×#427	C₄	1	2	yes	complemented
18	C₁₁×#427	C₂²	1	2	yes	—
19	C₁₁×#427	C₂²	1	1	yes	characteristic
20	C₁₁×#427	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×#107	C₄	1	1	yes	characteristic, complemented
22	C₂×C₁₁×#107	C₄	1	1	yes	characteristic, complemented
23	C₂×C₁₁×#106	C₄	1	2	yes	complemented
24	C₁₁×#424	C₂²	1	4	yes	—
25	C₁₁×#407	C₂²	1	2	yes	—
26	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₁₁×#405	C₂²	1	4	yes	—
28	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
29	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₁₁×#341	C₂²	1	2	yes	—
31	C₁₁×#339	C₂²	1	4	yes	—
32	C₁₁×#339	C₂²	1	4	yes	—
33	C₁₁×#336	C₂²	1	2	yes	—
34	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
35	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
36	C₂²×C₈×C₁₁	—	2	4	no	—
37	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
44	C₁₁×#117	—	2	2	no	—
45	C₁₁×#117	—	2	2	no	—
46	C₁₁×#117	C₂×C₄	1	2	yes	—
47	C₁₁×#117	C₂×C₄	1	2	yes	—
48	C₁₁×#117	C₂³	1	2	yes	—
49	C₁₁×#117	C₂³	1	2	yes	—
50	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
53	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
54	C₂×C₄²×C₁₁	—	2	2	no	—
55	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
56	C₁₁×#108	—	2	4	no	—
57	C₁₁×#107	C₂×C₄	1	2	yes	—
58	C₁₁×#107	C₂×C₄	1	2	yes	—
59	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
60	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
61	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
62	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
63	C₁₁×#106	C₂×C₄	1	2	yes	—
64	C₁₁×#106	C₂×C₄	1	2	yes	—
65	C₁₁×#106	C₂×C₄	1	2	yes	—
66	C₁₁×#106	C₂×C₄	1	2	yes	—
67	C₁₁×C₄⋊C₈	—	2	4	no	—
68	C₁₁×C₄⋊C₈	—	2	4	no	—
69	C₁₁×C₂²⋊C₈	—	2	2	no	—
70	C₁₁×C₂²⋊C₈	—	2	2	no	—
71	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
72	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
73	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
74	C₁₁×#97	—	2	4	no	—
75	C₄×C₈×C₁₁	—	2	4	no	—
76	C₄×C₈×C₁₁	—	2	4	no	—
77	C₁₁×#95	—	2	1	no	—
78	#22606	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂⁴×C₁₁	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	—	2	2	no	—
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	—	2	2	no	—
85	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
90	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
91	C₁₁×M₁₆	—	2	4	no	—
92	C₁₁×M₁₆	—	2	4	no	—
93	C₂×C₈×C₁₁	—	2	2	no	—
94	C₂×C₈×C₁₁	—	2	2	no	—
95	C₂×C₈×C₁₁	—	2	2	no	—
96	C₂×C₈×C₁₁	—	2	2	no	—
97	C₂×C₈×C₁₁	—	2	4	no	—
98	C₂×C₈×C₁₁	—	2	2	no	—
99	C₂×C₈×C₁₁	—	2	2	no	—
100	C₂×C₈×C₁₁	—	2	2	no	—
101	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₁₁	#41	1	4	yes	—
108	C₁₁×C₄⋊C₄	—	2	2	no	—
109	C₁₁×C₄⋊C₄	—	2	2	no	—
110	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
111	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
112	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
113	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
114	C₁₁×C₂²⋊C₄	—	2	4	no	—
115	C₁₁×C₂²⋊C₄	—	2	2	no	—
116	C₁₁×C₂²⋊C₄	—	2	2	no	—
117	C₁₁×C₂²⋊C₄	—	2	2	no	—
118	C₁₁×C₂²⋊C₄	—	2	2	no	—
119	C₄²×C₁₁	—	2	2	no	—
120	C₄²×C₁₁	—	2	2	no	—
121	C₄²×C₁₁	—	2	2	no	—
122	C₄²×C₁₁	—	2	2	no	—
123	C₄²×C₁₁	—	2	2	no	—
124	C₄²×C₁₁	—	2	2	no	—
125	#2924	C₂×C₁₁	1	2	yes	—
126	C₂×#427	C₂×C₁₁	1	1	yes	characteristic
127	#1945	C₂×C₁₁	1	2	yes	complemented
128	#1922	C₂×C₁₁	1	4	yes	complemented
129	#1826	C₂×C₁₁	1	2	yes	—
130	#1810	C₂×C₁₁	1	1	yes	characteristic
131	#1772	C₂×C₁₁	1	2	yes	complemented
132	C₈×C₂²⋊C₄	C₂×C₁₁	1	1	yes	characteristic
133	C₂³×C₁₁	—	2	2	no	—
134	C₂³×C₁₁	—	2	2	no	—
135	C₂³×C₁₁	—	4	1	no	—
136	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
137	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
138	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
139	C₂×C₄×C₁₁	—	2	2	no	—
140	C₂×C₄×C₁₁	—	2	1	no	—
141	C₂×C₄×C₁₁	—	2	1	no	—
142	C₂×C₄×C₁₁	—	2	1	no	—
143	C₂×C₄×C₁₁	—	2	1	no	—
144	C₂×C₄×C₁₁	—	2	2	no	—
145	C₂×C₄×C₁₁	—	2	2	no	—
146	C₂×C₄×C₁₁	—	2	4	no	—
147	C₂×C₄×C₁₁	—	2	2	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	2	2	no	—
151	C₂×C₄×C₁₁	—	4	2	no	—
152	C₂×C₄×C₁₁	—	4	2	no	—
153	C₂×C₄×C₁₁	—	4	4	no	—
154	C₂×C₄×C₁₁	—	8	2	no	—
155	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
160	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
161	C₈×C₁₁	—	2	1	no	—
162	C₈×C₁₁	—	2	1	no	—
163	C₈×C₁₁	—	2	2	no	—
164	C₈×C₁₁	—	2	2	no	—
165	C₈×C₁₁	—	4	4	no	—
166	C₈×C₁₁	#117	1	2	yes	—
167	C₈×C₁₁	#117	1	2	yes	—
168	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
169	C₂×#117	C₂²×C₁₁	1	2	yes	—
170	#433	—	2	4	no	—
171	#432	—	2	2	no	—
172	#431	—	2	2	no	—
173	C₂×#108	C₂²×C₁₁	1	2	yes	—
174	#427	C₄×C₁₁	1	1	yes	characteristic, complemented
175	#427	C₄×C₁₁	1	1	yes	characteristic, complemented
176	#427	C₄×C₁₁	1	2	yes	complemented
177	#427	C₂²×C₁₁	1	2	yes	—
178	#427	C₂²×C₁₁	1	1	yes	characteristic
179	#427	C₂²×C₁₁	1	1	yes	characteristic
180	C₂×#107	C₄×C₁₁	1	1	yes	characteristic, complemented
181	C₂×#107	C₄×C₁₁	1	1	yes	characteristic, complemented
182	C₂×#106	C₄×C₁₁	1	2	yes	complemented
183	#424	C₂²×C₁₁	1	4	yes	—
184	#407	C₂²×C₁₁	1	2	yes	—
185	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
186	#405	C₂²×C₁₁	1	4	yes	—
187	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
188	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
189	#341	C₂²×C₁₁	1	2	yes	—
190	#339	C₂²×C₁₁	1	4	yes	—
191	#339	C₂²×C₁₁	1	4	yes	—
192	#336	C₂²×C₁₁	1	2	yes	—
193	C₂²×C₁₁	—	2	1	no	—
194	C₂²×C₁₁	—	2	1	no	—
195	C₂²×C₁₁	—	2	1	no	—
196	C₂²×C₁₁	—	2	1	no	—
197	C₂²×C₁₁	—	2	1	no	—
198	C₂²×C₁₁	—	2	1	no	—
199	C₂²×C₁₁	—	2	1	no	—
200	C₂²×C₁₁	—	4	4	no	—
201	C₂²×C₁₁	#443	1	2	yes	—
202	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂²×C₁₁	#552	1	2	yes	—
204	C₄×C₁₁	—	2	1	no	—
205	C₄×C₁₁	—	2	1	no	—
206	C₄×C₁₁	—	4	4	no	—
207	C₄×C₁₁	—	4	2	no	—
208	C₄×C₁₁	—	4	2	no	—
209	C₄×C₁₁	—	4	2	no	—
210	C₄×C₁₁	—	4	2	no	—
211	C₄×C₁₁	C₂×#117	1	1	yes	characteristic
212	C₄×C₁₁	#519	1	1	yes	characteristic
213	C₄×C₁₁	#547	1	2	yes	—
214	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
215	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
216	C₂²×C₈	—	2	4	no	—
217	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
218	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
219	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
220	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
223	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
224	#117	—	2	2	no	—
225	#117	—	2	2	no	—
226	#117	C₂×C₄×C₁₁	1	2	yes	—
227	#117	C₂×C₄×C₁₁	1	2	yes	—
228	#117	C₂³×C₁₁	1	2	yes	—
229	#117	C₂³×C₁₁	1	2	yes	—
230	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₂²⋊C₄	—	2	1	no	—
234	C₂×C₄²	—	2	2	no	—
235	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
236	#108	—	2	4	no	—
237	#107	C₂×C₄×C₁₁	1	2	yes	—
238	#107	C₂×C₄×C₁₁	1	2	yes	—
239	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
240	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
241	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
242	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
243	#106	C₂×C₄×C₁₁	1	2	yes	—
244	#106	C₂×C₄×C₁₁	1	2	yes	—
245	#106	C₂×C₄×C₁₁	1	2	yes	—
246	#106	C₂×C₄×C₁₁	1	2	yes	—
247	C₄⋊C₈	—	2	4	no	—
248	C₄⋊C₈	—	2	4	no	—
249	C₂²⋊C₈	—	2	2	no	—
250	C₂²⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	D₄×C₁₁	1	1	yes	characteristic
252	C₂²⋊C₈	D₄×C₁₁	1	1	yes	characteristic
253	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
254	#97	—	2	4	no	—
255	C₄×C₈	—	2	4	no	—
256	C₄×C₈	—	2	4	no	—
257	#95	—	2	1	no	—
258	C₂×C₁₁	—	2	2	no	—
259	C₂×C₁₁	—	2	2	no	—
260	C₂×C₁₁	—	4	1	no	—
261	C₂×C₁₁	#2344	1	1	yes	characteristic
262	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
263	C₂×C₁₁	#2957	1	1	yes	characteristic
264	C₂⁴	C₁₁×#41	1	1	yes	characteristic
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
274	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
275	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
276	M₁₆	—	2	4	no	—
277	M₁₆	—	2	4	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
287	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
288	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
289	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
290	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
291	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
292	C₂×C₈	C₁₁×#41	1	4	yes	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
296	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
297	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
298	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₁₁	#22606	1	1	yes	characteristic, direct product factor, Sylow
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	4	1	no	—
314	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
315	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
316	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	8	2	no	—
333	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
334	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
335	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
336	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
337	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
338	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
339	C₈	—	2	1	no	—
340	C₈	—	2	1	no	—
341	C₈	—	2	2	no	—
342	C₈	—	2	2	no	—
343	C₈	—	4	4	no	—
344	C₈	C₁₁×#117	1	2	yes	—
345	C₈	C₁₁×#117	1	2	yes	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	4	4	no	—
354	C₂²	C₁₁×#443	1	2	yes	—
355	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
356	C₂²	C₁₁×#552	1	2	yes	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	4	4	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	2	no	—
364	C₄	C₂×C₁₁×#117	1	1	yes	characteristic
365	C₄	C₁₁×#519	1	1	yes	characteristic
366	C₄	C₁₁×#547	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	4	1	no	—
370	C₂	C₁₁×#2344	1	1	yes	characteristic
371	C₂	C₂×C₁₁×#443	1	1	yes	characteristic
372	C₂	C₁₁×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂⁴×C₁₁	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1945	C₂	semidirect
4. C₁₁×#1922	C₂	semidirect
7. C₁₁×#1772	C₂	semidirect
15. C₁₁×#427	C₄	semidirect
16. C₁₁×#427	C₄	semidirect
17. C₁₁×#427	C₄	semidirect
21. C₂×C₁₁×#107	C₄	semidirect
22. C₂×C₁₁×#107	C₄	semidirect
23. C₂×C₁₁×#106	C₄	semidirect
78. #22606	C₁₁	direct (N × H)
127. #1945	C₂×C₁₁	semidirect
128. #1922	C₂×C₁₁	semidirect
131. #1772	C₂×C₁₁	semidirect
174. #427	C₄×C₁₁	semidirect
175. #427	C₄×C₁₁	semidirect
176. #427	C₄×C₁₁	semidirect
180. C₂×#107	C₄×C₁₁	semidirect
181. C₂×#107	C₄×C₁₁	semidirect
182. C₂×#106	C₄×C₁₁	semidirect
310. C₁₁	#22606	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×#2924	2
C₂×C₁₁×#427	2
C₁₁×#1945	2
C₁₁×#1922	2
C₁₁×#1826	2
C₁₁×#1810	2
C₁₁×#1772	2
C₈×C₁₁×C₂²⋊C₄	2
#22606	11

Subgroups — C11×#22606 #14599799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22606 #14599799