Subgroups — C₁₁×#23188 #14600381

Order 2816.

1226 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#493	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#442	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2366	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1982	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1972	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1879	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₁×#106	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
10	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
11	C₂×C₁₁×#127	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₁	—	2	2	no	—
13	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
14	C₁₁×#493	C₄	1	8	yes	complemented
15	C₁₁×#442	—	2	8	no	—
16	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×#102	C₂²	1	4	yes	—
20	C₂×C₁₁×#102	C₂²	1	4	yes	—
21	C₂×C₁₁×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
23	C₁₁×#390	—	2	2	no	—
24	C₁₁×#390	C₂²	1	4	yes	—
25	C₁₁×#386	—	2	4	no	—
26	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
27	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₁₁×#340	C₂²	1	2	yes	—
29	C₁₁×#336	C₂²	1	2	yes	—
30	C₂²×D₄×C₁₁	—	2	2	no	—
31	C₂²×D₄×C₁₁	—	2	2	no	—
32	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
33	C₂³×C₄×C₁₁	—	2	4	no	—
34	C₂×C₁₁×D₈	—	2	4	no	—
35	C₂×C₁₁×D₈	—	2	4	no	—
36	C₂×C₁₁×D₈	—	4	2	no	—
37	C₂×C₁₁×D₈	—	4	2	no	—
38	C₂×C₁₁×D₈	C₂×C₄	1	8	yes	complemented
39	C₂×C₁₁×D₈	C₂×C₄	1	8	yes	complemented
40	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
43	C₁₁×#127	—	2	4	no	—
44	C₁₁×#127	C₂×C₄	1	8	yes	complemented
45	C₄×D₄×C₁₁	—	2	8	no	—
46	C₄×D₄×C₁₁	—	4	4	no	—
47	C₄×D₄×C₁₁	—	4	8	no	—
48	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
49	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
50	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
51	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
52	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
53	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
54	C₂×C₄²×C₁₁	—	2	2	no	—
55	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
57	C₁₁×#106	—	2	2	no	—
58	C₁₁×#106	D₄	1	4	yes	complemented
59	C₁₁×C₄⋊C₈	—	2	2	no	—
60	C₁₁×#102	—	2	8	no	—
61	C₁₁×#102	—	4	4	no	—
62	C₁₁×#97	—	2	4	no	—
63	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
64	C₁₁×#95	—	2	2	no	—
65	C₁₁×#95	D₄	1	2	yes	—
66	#23188	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂⁴×C₁₁	—	2	4	no	—
68	C₂×D₄×C₁₁	—	2	8	no	—
69	C₂×D₄×C₁₁	—	2	8	no	—
70	C₂×D₄×C₁₁	—	2	4	no	—
71	C₂×D₄×C₁₁	—	2	4	no	—
72	C₂×D₄×C₁₁	—	2	4	no	—
73	C₂×D₄×C₁₁	—	2	4	no	—
74	C₂×D₄×C₁₁	—	2	4	no	—
75	C₂×D₄×C₁₁	—	4	4	no	—
76	C₂×D₄×C₁₁	—	4	4	no	—
77	C₂×D₄×C₁₁	—	8	2	no	—
78	C₂×D₄×C₁₁	—	8	2	no	—
79	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
80	C₂²×C₄×C₁₁	—	2	2	no	—
81	C₂²×C₄×C₁₁	—	2	2	no	—
82	C₂²×C₄×C₁₁	—	4	8	no	—
83	C₂²×C₄×C₁₁	—	4	8	no	—
84	C₂²×C₄×C₁₁	—	8	4	no	—
85	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
86	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
89	C₁₁×D₈	—	2	16	no	—
90	C₁₁×D₈	—	4	8	no	—
91	C₂×C₈×C₁₁	—	2	2	no	—
92	C₂×C₈×C₁₁	—	2	2	no	—
93	C₂×C₈×C₁₁	—	2	1	no	—
94	C₂×C₈×C₁₁	—	2	1	no	—
95	C₂×C₈×C₁₁	—	2	2	no	—
96	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
99	C₂×C₈×C₁₁	#41	1	2	yes	—
100	C₁₁×C₄⋊C₄	—	2	4	no	—
101	C₁₁×C₄⋊C₄	—	2	2	no	—
102	C₁₁×C₄⋊C₄	—	2	2	no	—
103	C₁₁×C₄⋊C₄	—	2	2	no	—
104	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
105	C₁₁×C₂²⋊C₄	—	4	8	no	—
106	C₁₁×C₂²⋊C₄	—	4	8	no	—
107	C₁₁×C₂²⋊C₄	—	8	4	no	—
108	C₄²×C₁₁	—	2	2	no	—
109	C₄²×C₁₁	—	2	2	no	—
110	C₄²×C₁₁	—	4	4	no	—
111	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
112	C₄²×C₁₁	#41	1	2	yes	—
113	C₂×#493	C₂×C₁₁	1	1	yes	characteristic
114	C₂×#442	C₂×C₁₁	1	2	yes	complemented
115	#2366	C₂×C₁₁	1	2	yes	complemented
116	#1982	C₂×C₁₁	1	2	yes	complemented
117	#1972	C₂×C₁₁	1	2	yes	complemented
118	#1879	C₂×C₁₁	1	4	yes	complemented
119	C₄×#106	C₂×C₁₁	1	1	yes	characteristic, complemented
120	#1770	C₂×C₁₁	1	1	yes	characteristic, complemented
121	C₂³×C₁₁	—	2	8	no	—
122	C₂³×C₁₁	—	4	4	no	—
123	C₂³×C₁₁	—	4	4	no	—
124	C₂³×C₁₁	—	4	4	no	—
125	C₂³×C₁₁	—	4	4	no	—
126	C₂³×C₁₁	—	4	4	no	—
127	C₂³×C₁₁	—	4	4	no	—
128	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
129	D₄×C₁₁	—	2	8	no	—
130	D₄×C₁₁	—	2	8	no	—
131	D₄×C₁₁	—	4	4	no	—
132	D₄×C₁₁	—	4	4	no	—
133	D₄×C₁₁	—	4	16	no	—
134	D₄×C₁₁	—	8	8	no	—
135	C₂×C₄×C₁₁	—	2	2	no	—
136	C₂×C₄×C₁₁	—	2	4	no	—
137	C₂×C₄×C₁₁	—	2	4	no	—
138	C₂×C₄×C₁₁	—	2	4	no	—
139	C₂×C₄×C₁₁	—	2	4	no	—
140	C₂×C₄×C₁₁	—	4	2	no	—
141	C₂×C₄×C₁₁	—	4	2	no	—
142	C₂×C₄×C₁₁	—	4	2	no	—
143	C₂×C₄×C₁₁	—	4	2	no	—
144	C₂×C₄×C₁₁	—	4	2	no	—
145	C₂×C₄×C₁₁	—	8	16	no	—
146	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
147	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
148	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
149	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
155	C₈×C₁₁	—	2	2	no	—
156	C₈×C₁₁	—	4	2	no	—
157	C₈×C₁₁	C₄×D₄	1	4	yes	complemented
158	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
159	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
160	C₂×#127	C₂²×C₁₁	1	2	yes	—
161	C₂×C₄×D₄	—	2	2	no	—
162	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
163	#493	C₄×C₁₁	1	8	yes	complemented
164	#442	—	2	8	no	—
165	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
166	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
167	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
168	C₂×#102	C₂²×C₁₁	1	4	yes	—
169	C₂×#102	C₂²×C₁₁	1	4	yes	—
170	C₂×#97	C₂²×C₁₁	1	2	yes	—
171	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
172	#390	—	2	2	no	—
173	#390	C₂²×C₁₁	1	4	yes	—
174	#386	—	2	4	no	—
175	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
176	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
177	#340	C₂²×C₁₁	1	2	yes	—
178	#336	C₂²×C₁₁	1	2	yes	—
179	C₂²×C₁₁	—	4	8	no	—
180	C₂²×C₁₁	—	4	8	no	—
181	C₂²×C₁₁	—	4	8	no	—
182	C₂²×C₁₁	—	8	4	no	—
183	C₂²×C₁₁	—	8	4	no	—
184	C₂²×C₁₁	—	8	4	no	—
185	C₂²×C₁₁	—	8	4	no	—
186	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂²×C₁₁	D₄²	1	1	yes	characteristic
188	C₂²×C₁₁	#550	1	1	yes	characteristic
189	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
190	C₂²×C₁₁	#576	1	2	yes	—
191	C₄×C₁₁	—	2	2	no	—
192	C₄×C₁₁	—	4	4	no	—
193	C₄×C₁₁	—	4	4	no	—
194	C₄×C₁₁	—	8	2	no	—
195	C₄×C₁₁	#442	1	4	yes	complemented
196	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
197	C₄×C₁₁	#518	1	1	yes	characteristic
198	C₄×C₁₁	#550	1	1	yes	characteristic
199	C₄×C₁₁	#559	1	1	yes	characteristic
200	C₂²×D₄	—	2	2	no	—
201	C₂²×D₄	—	2	2	no	—
202	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
203	C₂³×C₄	—	2	4	no	—
204	C₂×D₈	—	2	4	no	—
205	C₂×D₈	—	2	4	no	—
206	C₂×D₈	—	4	2	no	—
207	C₂×D₈	—	4	2	no	—
208	C₂×D₈	C₂×C₄×C₁₁	1	8	yes	complemented
209	C₂×D₈	C₂×C₄×C₁₁	1	8	yes	complemented
210	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
211	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
213	#127	—	2	4	no	—
214	#127	C₂×C₄×C₁₁	1	8	yes	complemented
215	C₄×D₄	—	2	8	no	—
216	C₄×D₄	—	4	4	no	—
217	C₄×D₄	—	4	8	no	—
218	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
219	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
220	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
221	C₂×C₂²⋊C₄	—	2	4	no	—
222	C₂×C₂²⋊C₄	—	2	4	no	—
223	C₂×C₂²⋊C₄	—	2	4	no	—
224	C₂×C₄²	—	2	2	no	—
225	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
226	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
227	#106	—	2	2	no	—
228	#106	D₄×C₁₁	1	4	yes	complemented
229	C₄⋊C₈	—	2	2	no	—
230	#102	—	2	8	no	—
231	#102	—	4	4	no	—
232	#97	—	2	4	no	—
233	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
234	#95	—	2	2	no	—
235	#95	D₄×C₁₁	1	2	yes	—
236	C₂×C₁₁	—	8	8	no	—
237	C₂×C₁₁	#2366	1	1	yes	characteristic
238	C₂×C₁₁	C₂×#442	1	1	yes	characteristic
239	C₂×C₁₁	#2948	1	1	yes	characteristic
240	C₂×C₁₁	#3274	1	2	yes	—
241	C₂×C₁₁	#3399	1	2	yes	—
242	C₂⁴	—	2	4	no	—
243	C₂×D₄	—	2	8	no	—
244	C₂×D₄	—	2	8	no	—
245	C₂×D₄	—	2	4	no	—
246	C₂×D₄	—	2	4	no	—
247	C₂×D₄	—	2	4	no	—
248	C₂×D₄	—	2	4	no	—
249	C₂×D₄	—	2	4	no	—
250	C₂×D₄	—	4	4	no	—
251	C₂×D₄	—	4	4	no	—
252	C₂×D₄	—	8	2	no	—
253	C₂×D₄	—	8	2	no	—
254	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	4	8	no	—
258	C₂²×C₄	—	4	8	no	—
259	C₂²×C₄	—	8	4	no	—
260	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
261	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
263	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
264	D₈	—	2	16	no	—
265	D₈	—	4	8	no	—
266	C₂×C₈	—	2	1	no	—
267	C₂×C₈	—	2	1	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
272	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
273	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
274	C₂×C₈	C₁₁×#41	1	2	yes	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
280	C₂²⋊C₄	—	4	8	no	—
281	C₂²⋊C₄	—	4	8	no	—
282	C₂²⋊C₄	—	8	4	no	—
283	C₄²	—	2	2	no	—
284	C₄²	—	2	2	no	—
285	C₄²	—	4	4	no	—
286	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
287	C₄²	C₁₁×#41	1	2	yes	—
288	C₁₁	#23188	1	1	yes	characteristic, direct product factor, Sylow
289	C₂³	—	2	8	no	—
290	C₂³	—	4	4	no	—
291	C₂³	—	4	4	no	—
292	C₂³	—	4	4	no	—
293	C₂³	—	4	4	no	—
294	C₂³	—	4	4	no	—
295	C₂³	—	4	4	no	—
296	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
297	D₄	—	2	8	no	—
298	D₄	—	2	8	no	—
299	D₄	—	4	4	no	—
300	D₄	—	4	4	no	—
301	D₄	—	4	16	no	—
302	D₄	—	8	8	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	8	16	no	—
314	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
315	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
316	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	4	yes	—
317	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
318	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
319	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
320	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
321	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
323	C₈	—	2	2	no	—
324	C₈	—	4	2	no	—
325	C₈	C₄×D₄×C₁₁	1	4	yes	complemented
326	C₂²	—	4	8	no	—
327	C₂²	—	4	8	no	—
328	C₂²	—	4	8	no	—
329	C₂²	—	8	4	no	—
330	C₂²	—	8	4	no	—
331	C₂²	—	8	4	no	—
332	C₂²	—	8	4	no	—
333	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
334	C₂²	D₄²×C₁₁	1	1	yes	characteristic
335	C₂²	C₁₁×#550	1	1	yes	characteristic
336	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	2	yes	—
337	C₂²	C₁₁×#576	1	2	yes	—
338	C₄	—	2	2	no	—
339	C₄	—	4	4	no	—
340	C₄	—	4	4	no	—
341	C₄	—	8	2	no	—
342	C₄	C₁₁×#442	1	4	yes	complemented
343	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
344	C₄	C₁₁×#518	1	1	yes	characteristic
345	C₄	C₁₁×#550	1	1	yes	characteristic
346	C₄	C₁₁×#559	1	1	yes	characteristic
347	C₂	—	8	8	no	—
348	C₂	C₁₁×#2366	1	1	yes	characteristic
349	C₂	C₂×C₁₁×#442	1	1	yes	characteristic
350	C₂	C₁₁×#2948	1	1	yes	characteristic
351	C₂	C₁₁×#3274	1	2	yes	—
352	C₂	C₁₁×#3399	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#493	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄×C₁₁×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#442	C₂	semidirect
3. C₁₁×#2366	C₂	semidirect
4. C₁₁×#1982	C₂	semidirect
5. C₁₁×#1972	C₂	semidirect
6. C₁₁×#1879	C₂	semidirect
7. C₄×C₁₁×#106	C₂	semidirect
8. C₁₁×#1770	C₂	semidirect
14. C₁₁×#493	C₄	semidirect
38. C₂×C₁₁×D₈	C₂×C₄	semidirect
39. C₂×C₁₁×D₈	C₂×C₄	semidirect
44. C₁₁×#127	C₂×C₄	semidirect
58. C₁₁×#106	D₄	semidirect
63. C₄×C₈×C₁₁	C₂×C₄	semidirect
66. #23188	C₁₁	direct (N × H)
114. C₂×#442	C₂×C₁₁	semidirect
115. #2366	C₂×C₁₁	semidirect
116. #1982	C₂×C₁₁	semidirect
117. #1972	C₂×C₁₁	semidirect
118. #1879	C₂×C₁₁	semidirect
119. C₄×#106	C₂×C₁₁	semidirect
120. #1770	C₂×C₁₁	semidirect
157. C₈×C₁₁	C₄×D₄	semidirect
163. #493	C₄×C₁₁	semidirect
195. C₄×C₁₁	#442	semidirect
208. C₂×D₈	C₂×C₄×C₁₁	semidirect
209. C₂×D₈	C₂×C₄×C₁₁	semidirect
214. #127	C₂×C₄×C₁₁	semidirect
228. #106	D₄×C₁₁	semidirect
233. C₄×C₈	C₂×C₄×C₁₁	semidirect
288. C₁₁	#23188	direct (N × H)
325. C₈	C₄×D₄×C₁₁	semidirect
342. C₄	C₁₁×#442	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#493	2
C₂×C₁₁×#442	2
C₁₁×#2366	2
C₁₁×#1982	2
C₁₁×#1972	2
C₁₁×#1879	2
C₄×C₁₁×#106	2
C₁₁×#1770	2
#23188	11

Subgroups — C11×#23188 #14600381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23188 #14600381