Subgroups — C₁₁×#23180 #14600373

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3147	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#444	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2935	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1980	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1975	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1876	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₁×#108	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#135	C₂²	1	2	yes	—
10	C₂×C₁₁×#135	C₂²	1	2	yes	—
11	C₂×C₁₁×#131	C₂²	1	4	yes	—
12	C₁₁×#532	C₂²	1	2	yes	—
13	C₁₁×#495	C₄	1	2	yes	complemented
14	C₁₁×#495	C₄	1	2	yes	complemented
15	C₁₁×#494	C₄	1	1	yes	characteristic, complemented
16	C₁₁×#493	C₄	1	1	yes	characteristic, complemented
17	C₁₁×#492	C₄	1	2	yes	complemented
18	C₁₁×#444	—	2	8	no	—
19	C₁₁×#436	—	2	2	no	—
20	C₁₁×#435	—	2	4	no	—
21	C₈×D₄×C₁₁	—	2	2	no	—
22	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×#104	C₂²	1	4	yes	—
26	C₂×C₁₁×#104	C₂²	1	4	yes	—
27	C₁₁×#408	C₂²	1	4	yes	—
28	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
29	C₂×C₁₁×#97	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
31	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₁₁×#341	C₂²	1	2	yes	—
33	C₁₁×#336	C₂²	1	2	yes	—
34	C₂×C₁₁×#41	C₂³	1	4	yes	—
35	C₁₁×#135	—	2	4	no	—
36	C₁₁×#135	—	2	4	no	—
37	C₁₁×#135	—	4	2	no	—
38	C₁₁×#135	—	4	2	no	—
39	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
40	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
41	C₂×C₁₁×SD₁₆	C₂×C₄	1	4	yes	—
42	C₂×C₁₁×SD₁₆	C₂×C₄	1	4	yes	—
43	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
44	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
45	C₁₁×#131	—	2	8	no	—
46	C₁₁×#131	—	4	4	no	—
47	C₂×C₁₁×M₁₆	—	2	4	no	—
48	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
49	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₁	—	2	4	no	—
51	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
54	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
55	C₁₁×#127	C₂×C₄	1	2	yes	—
56	C₁₁×#124	C₂×C₄	1	4	yes	—
57	C₁₁×#121	—	2	2	no	—
58	C₁₁×#121	—	2	2	no	—
59	C₄×D₄×C₁₁	—	2	2	no	—
60	C₄×D₄×C₁₁	—	2	2	no	—
61	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
62	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
64	C₁₁×#108	—	2	2	no	—
65	C₁₁×#108	D₄	1	4	yes	complemented
66	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
67	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
68	C₁₁×#104	—	2	8	no	—
69	C₁₁×#104	—	4	4	no	—
70	C₁₁×C₂²⋊C₈	—	2	4	no	—
71	C₁₁×C₂²⋊C₈	—	2	4	no	—
72	C₁₁×#97	—	2	4	no	—
73	C₁₁×#97	—	2	2	no	—
74	C₄×C₈×C₁₁	—	2	2	no	—
75	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
79	C₁₁×#95	—	2	1	no	—
80	#23180	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₁₁×#41	—	2	4	no	—
82	C₁₁×#41	—	2	4	no	—
83	C₁₁×#41	—	2	4	no	—
84	C₁₁×#41	—	2	4	no	—
85	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
86	C₂×D₄×C₁₁	—	2	4	no	—
87	C₂×D₄×C₁₁	—	2	2	no	—
88	C₂×D₄×C₁₁	—	2	2	no	—
89	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₁₁	—	2	4	no	—
91	C₂²×C₄×C₁₁	—	2	2	no	—
92	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
93	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
95	C₁₁×Q₁₆	—	2	4	no	—
96	C₁₁×Q₁₆	—	4	2	no	—
97	C₁₁×SD₁₆	—	2	8	no	—
98	C₁₁×SD₁₆	—	4	4	no	—
99	C₁₁×D₈	—	2	4	no	—
100	C₁₁×D₈	—	4	2	no	—
101	C₁₁×M₁₆	—	2	2	no	—
102	C₁₁×M₁₆	—	2	2	no	—
103	C₁₁×M₁₆	—	2	2	no	—
104	C₁₁×M₁₆	—	4	8	no	—
105	C₁₁×M₁₆	C₂×D₄	1	4	yes	—
106	C₂×C₈×C₁₁	—	2	2	no	—
107	C₂×C₈×C₁₁	—	2	2	no	—
108	C₂×C₈×C₁₁	—	2	2	no	—
109	C₂×C₈×C₁₁	—	2	2	no	—
110	C₂×C₈×C₁₁	—	2	1	no	—
111	C₂×C₈×C₁₁	—	2	1	no	—
112	C₂×C₈×C₁₁	—	4	8	no	—
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	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
119	C₂×C₈×C₁₁	#41	1	2	yes	—
120	C₁₁×C₄⋊C₄	—	2	2	no	—
121	C₁₁×C₄⋊C₄	—	2	2	no	—
122	C₁₁×C₄⋊C₄	—	4	2	no	—
123	C₁₁×C₂²⋊C₄	—	2	4	no	—
124	C₁₁×C₂²⋊C₄	—	2	4	no	—
125	C₄²×C₁₁	—	2	2	no	—
126	C₄²×C₁₁	—	2	2	no	—
127	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
131	#3147	C₂×C₁₁	1	1	yes	characteristic
132	C₂×#444	C₂×C₁₁	1	2	yes	complemented
133	#2935	C₂×C₁₁	1	2	yes	complemented
134	#1980	C₂×C₁₁	1	2	yes	complemented
135	#1975	C₂×C₁₁	1	2	yes	complemented
136	#1876	C₂×C₁₁	1	4	yes	complemented
137	C₄×#108	C₂×C₁₁	1	1	yes	characteristic, complemented
138	#1770	C₂×C₁₁	1	1	yes	characteristic, complemented
139	C₂³×C₁₁	—	2	4	no	—
140	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
141	Q₈×C₁₁	—	2	4	no	—
142	Q₈×C₁₁	—	2	4	no	—
143	D₄×C₁₁	—	2	4	no	—
144	D₄×C₁₁	—	2	4	no	—
145	D₄×C₁₁	—	4	4	no	—
146	D₄×C₁₁	—	4	4	no	—
147	D₄×C₁₁	—	4	4	no	—
148	D₄×C₁₁	—	8	2	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	2	4	no	—
151	C₂×C₄×C₁₁	—	4	1	no	—
152	C₂×C₄×C₁₁	—	4	4	no	—
153	C₂×C₄×C₁₁	—	4	4	no	—
154	C₂×C₄×C₁₁	—	4	2	no	—
155	C₂×C₄×C₁₁	—	4	2	no	—
156	C₂×C₄×C₁₁	—	4	2	no	—
157	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
167	C₈×C₁₁	—	2	1	no	—
168	C₈×C₁₁	—	2	1	no	—
169	C₈×C₁₁	—	2	4	no	—
170	C₈×C₁₁	—	2	4	no	—
171	C₈×C₁₁	—	4	2	no	—
172	C₈×C₁₁	C₄×D₄	1	2	yes	—
173	C₈×C₁₁	C₄×D₄	1	2	yes	—
174	C₂×#135	C₂²×C₁₁	1	2	yes	—
175	C₂×#135	C₂²×C₁₁	1	2	yes	—
176	C₂×#131	C₂²×C₁₁	1	4	yes	—
177	#532	C₂²×C₁₁	1	2	yes	—
178	#495	C₄×C₁₁	1	2	yes	complemented
179	#495	C₄×C₁₁	1	2	yes	complemented
180	#494	C₄×C₁₁	1	1	yes	characteristic, complemented
181	#493	C₄×C₁₁	1	1	yes	characteristic, complemented
182	#492	C₄×C₁₁	1	2	yes	complemented
183	#444	—	2	8	no	—
184	#436	—	2	2	no	—
185	#435	—	2	4	no	—
186	C₈×D₄	—	2	2	no	—
187	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
188	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
189	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
190	C₂×#104	C₂²×C₁₁	1	4	yes	—
191	C₂×#104	C₂²×C₁₁	1	4	yes	—
192	#408	C₂²×C₁₁	1	4	yes	—
193	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
194	C₂×#97	C₂²×C₁₁	1	2	yes	—
195	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
196	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
197	#341	C₂²×C₁₁	1	2	yes	—
198	#336	C₂²×C₁₁	1	2	yes	—
199	C₂²×C₁₁	—	2	1	no	—
200	C₂²×C₁₁	—	2	1	no	—
201	C₂²×C₁₁	—	4	4	no	—
202	C₂²×C₁₁	—	4	4	no	—
203	C₂²×C₁₁	—	4	4	no	—
204	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂²×C₁₁	#550	1	1	yes	characteristic
206	C₂²×C₁₁	#559	1	1	yes	characteristic
207	C₄×C₁₁	—	2	1	no	—
208	C₄×C₁₁	—	2	1	no	—
209	C₄×C₁₁	—	2	1	no	—
210	C₄×C₁₁	—	4	4	no	—
211	C₄×C₁₁	—	8	2	no	—
212	C₄×C₁₁	#444	1	2	yes	complemented
213	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
214	C₄×C₁₁	#518	1	1	yes	characteristic
215	C₄×C₁₁	D₄²	1	1	yes	characteristic
216	C₄×C₁₁	#550	1	1	yes	characteristic
217	C₂×#41	C₂³×C₁₁	1	4	yes	—
218	#135	—	2	4	no	—
219	#135	—	2	4	no	—
220	#135	—	4	2	no	—
221	#135	—	4	2	no	—
222	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
223	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
224	C₂×SD₁₆	C₂×C₄×C₁₁	1	4	yes	—
225	C₂×SD₁₆	C₂×C₄×C₁₁	1	4	yes	—
226	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
227	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
228	#131	—	2	8	no	—
229	#131	—	4	4	no	—
230	C₂×M₁₆	—	2	4	no	—
231	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
232	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
233	C₂²×C₈	—	2	4	no	—
234	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
236	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
237	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
238	#127	C₂×C₄×C₁₁	1	2	yes	—
239	#124	C₂×C₄×C₁₁	1	4	yes	—
240	#121	—	2	2	no	—
241	#121	—	2	2	no	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
246	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
247	#108	—	2	2	no	—
248	#108	D₄×C₁₁	1	4	yes	complemented
249	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
250	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
251	#104	—	2	8	no	—
252	#104	—	4	4	no	—
253	C₂²⋊C₈	—	2	4	no	—
254	C₂²⋊C₈	—	2	4	no	—
255	#97	—	2	4	no	—
256	#97	—	2	2	no	—
257	C₄×C₈	—	2	2	no	—
258	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
259	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
260	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
261	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
262	#95	—	2	1	no	—
263	C₂×C₁₁	—	2	1	no	—
264	C₂×C₁₁	—	2	1	no	—
265	C₂×C₁₁	—	8	4	no	—
266	C₂×C₁₁	#2366	1	1	yes	characteristic
267	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
268	C₂×C₁₁	#2957	1	1	yes	characteristic
269	#41	—	2	4	no	—
270	#41	—	2	4	no	—
271	#41	—	2	4	no	—
272	#41	—	2	4	no	—
273	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
281	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
282	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
283	Q₁₆	—	2	4	no	—
284	Q₁₆	—	4	2	no	—
285	SD₁₆	—	2	8	no	—
286	SD₁₆	—	4	4	no	—
287	D₈	—	2	4	no	—
288	D₈	—	4	2	no	—
289	M₁₆	—	2	2	no	—
290	M₁₆	—	2	2	no	—
291	M₁₆	—	2	2	no	—
292	M₁₆	—	4	8	no	—
293	M₁₆	C₂×D₄×C₁₁	1	4	yes	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	4	8	no	—
301	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
302	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
303	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
304	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
306	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
307	C₂×C₈	C₁₁×#41	1	2	yes	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
316	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
317	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
319	C₁₁	#23180	1	1	yes	characteristic, direct product factor, Sylow
320	C₂³	—	2	4	no	—
321	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
322	Q₈	—	2	4	no	—
323	Q₈	—	2	4	no	—
324	D₄	—	2	4	no	—
325	D₄	—	2	4	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	4	no	—
328	D₄	—	4	4	no	—
329	D₄	—	8	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
339	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
340	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
341	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
342	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
345	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
346	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
348	C₈	—	2	1	no	—
349	C₈	—	2	1	no	—
350	C₈	—	2	4	no	—
351	C₈	—	2	4	no	—
352	C₈	—	4	2	no	—
353	C₈	C₄×D₄×C₁₁	1	2	yes	—
354	C₈	C₄×D₄×C₁₁	1	2	yes	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	4	4	no	—
358	C₂²	—	4	4	no	—
359	C₂²	—	4	4	no	—
360	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
361	C₂²	C₁₁×#550	1	1	yes	characteristic
362	C₂²	C₁₁×#559	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	4	no	—
367	C₄	—	8	2	no	—
368	C₄	C₁₁×#444	1	2	yes	complemented
369	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
370	C₄	C₁₁×#518	1	1	yes	characteristic
371	C₄	D₄²×C₁₁	1	1	yes	characteristic
372	C₄	C₁₁×#550	1	1	yes	characteristic
373	C₂	—	2	1	no	—
374	C₂	—	2	1	no	—
375	C₂	—	8	4	no	—
376	C₂	C₁₁×#2366	1	1	yes	characteristic
377	C₂	C₂×C₁₁×#444	1	1	yes	characteristic
378	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	C₁₁×#3147	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#444	C₂	semidirect
3. C₁₁×#2935	C₂	semidirect
4. C₁₁×#1980	C₂	semidirect
5. C₁₁×#1975	C₂	semidirect
6. C₁₁×#1876	C₂	semidirect
7. C₄×C₁₁×#108	C₂	semidirect
8. C₁₁×#1770	C₂	semidirect
13. C₁₁×#495	C₄	semidirect
14. C₁₁×#495	C₄	semidirect
15. C₁₁×#494	C₄	semidirect
16. C₁₁×#493	C₄	semidirect
17. C₁₁×#492	C₄	semidirect
65. C₁₁×#108	D₄	semidirect
80. #23180	C₁₁	direct (N × H)
132. C₂×#444	C₂×C₁₁	semidirect
133. #2935	C₂×C₁₁	semidirect
134. #1980	C₂×C₁₁	semidirect
135. #1975	C₂×C₁₁	semidirect
136. #1876	C₂×C₁₁	semidirect
137. C₄×#108	C₂×C₁₁	semidirect
138. #1770	C₂×C₁₁	semidirect
178. #495	C₄×C₁₁	semidirect
179. #495	C₄×C₁₁	semidirect
180. #494	C₄×C₁₁	semidirect
181. #493	C₄×C₁₁	semidirect
182. #492	C₄×C₁₁	semidirect
212. C₄×C₁₁	#444	semidirect
248. #108	D₄×C₁₁	semidirect
319. C₁₁	#23180	direct (N × H)
368. C₄	C₁₁×#444	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×#3147	2
C₂×C₁₁×#444	2
C₁₁×#2935	2
C₁₁×#1980	2
C₁₁×#1975	2
C₁₁×#1876	2
C₄×C₁₁×#108	2
C₁₁×#1770	2
#23180	11

Subgroups — C11×#23180 #14600373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23180 #14600373