Subgroups — C₁₁×#23185 #14600378

Order 2816.

1238 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	C₂×C₁₁×#493	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₁×D₈	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×#1970	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1879	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₁×#107	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×C₁₁×C₄⋊C₄	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	C₄×C₁₁×D₈	—	2	8	no	—
16	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×#107	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×C₄×C₈×C₁₁	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	1	yes	characteristic
49	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
50	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
51	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
52	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
53	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
54	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
55	C₂×C₄²×C₁₁	—	2	2	no	—
56	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
58	C₁₁×#107	—	2	2	no	—
59	C₁₁×#107	D₄	1	4	yes	complemented
60	C₁₁×C₄⋊C₈	—	2	2	no	—
61	C₁₁×#102	—	2	8	no	—
62	C₁₁×#102	—	4	4	no	—
63	C₄×C₈×C₁₁	—	2	4	no	—
64	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
65	C₁₁×#95	—	2	2	no	—
66	C₁₁×#95	D₄	1	2	yes	—
67	#23185	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁴×C₁₁	—	2	4	no	—
69	C₂×D₄×C₁₁	—	2	8	no	—
70	C₂×D₄×C₁₁	—	2	8	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	—	2	4	no	—
76	C₂×D₄×C₁₁	—	4	4	no	—
77	C₂×D₄×C₁₁	—	4	4	no	—
78	C₂×D₄×C₁₁	—	8	2	no	—
79	C₂×D₄×C₁₁	—	8	2	no	—
80	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
81	C₂²×C₄×C₁₁	—	2	2	no	—
82	C₂²×C₄×C₁₁	—	2	2	no	—
83	C₂²×C₄×C₁₁	—	4	8	no	—
84	C₂²×C₄×C₁₁	—	4	8	no	—
85	C₂²×C₄×C₁₁	—	8	4	no	—
86	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
91	C₁₁×D₈	—	2	16	no	—
92	C₁₁×D₈	—	4	8	no	—
93	C₂×C₈×C₁₁	—	2	2	no	—
94	C₂×C₈×C₁₁	—	2	2	no	—
95	C₂×C₈×C₁₁	—	2	1	no	—
96	C₂×C₈×C₁₁	—	2	1	no	—
97	C₂×C₈×C₁₁	—	2	2	no	—
98	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
101	C₂×C₈×C₁₁	#41	1	2	yes	—
102	C₁₁×C₄⋊C₄	—	2	2	no	—
103	C₁₁×C₄⋊C₄	—	2	2	no	—
104	C₁₁×C₄⋊C₄	—	2	2	no	—
105	C₁₁×C₄⋊C₄	—	2	2	no	—
106	C₁₁×C₄⋊C₄	D₈	1	4	yes	complemented
107	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
108	C₁₁×C₂²⋊C₄	—	4	8	no	—
109	C₁₁×C₂²⋊C₄	—	4	8	no	—
110	C₁₁×C₂²⋊C₄	—	8	4	no	—
111	C₄²×C₁₁	—	2	2	no	—
112	C₄²×C₁₁	—	2	2	no	—
113	C₄²×C₁₁	—	4	4	no	—
114	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
115	C₄²×C₁₁	#41	1	2	yes	—
116	C₂×#493	C₂×C₁₁	1	1	yes	characteristic
117	C₂×C₄×D₈	C₂×C₁₁	1	2	yes	complemented
118	#2366	C₂×C₁₁	1	2	yes	complemented
119	#1982	C₂×C₁₁	1	2	yes	complemented
120	#1970	C₂×C₁₁	1	2	yes	complemented
121	#1879	C₂×C₁₁	1	4	yes	complemented
122	C₄×#107	C₂×C₁₁	1	1	yes	characteristic, complemented
123	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
124	C₂³×C₁₁	—	2	8	no	—
125	C₂³×C₁₁	—	4	4	no	—
126	C₂³×C₁₁	—	4	4	no	—
127	C₂³×C₁₁	—	4	4	no	—
128	C₂³×C₁₁	—	4	4	no	—
129	C₂³×C₁₁	—	4	4	no	—
130	C₂³×C₁₁	—	4	4	no	—
131	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
132	D₄×C₁₁	—	2	8	no	—
133	D₄×C₁₁	—	2	8	no	—
134	D₄×C₁₁	—	4	4	no	—
135	D₄×C₁₁	—	4	4	no	—
136	D₄×C₁₁	—	4	16	no	—
137	D₄×C₁₁	—	8	8	no	—
138	C₂×C₄×C₁₁	—	2	2	no	—
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	2	no	—
143	C₂×C₄×C₁₁	—	2	4	no	—
144	C₂×C₄×C₁₁	—	2	2	no	—
145	C₂×C₄×C₁₁	—	2	2	no	—
146	C₂×C₄×C₁₁	—	4	2	no	—
147	C₂×C₄×C₁₁	—	4	2	no	—
148	C₂×C₄×C₁₁	—	4	2	no	—
149	C₂×C₄×C₁₁	—	4	2	no	—
150	C₂×C₄×C₁₁	—	4	2	no	—
151	C₂×C₄×C₁₁	—	8	16	no	—
152	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
155	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
156	C₂×C₄×C₁₁	#135	1	2	yes	—
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	1	yes	characteristic
160	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
162	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
163	C₈×C₁₁	—	2	2	no	—
164	C₈×C₁₁	—	4	2	no	—
165	C₈×C₁₁	C₄×D₄	1	4	yes	complemented
166	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
167	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
168	C₂×#127	C₂²×C₁₁	1	2	yes	—
169	C₂×C₄×D₄	—	2	2	no	—
170	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
171	#493	C₄×C₁₁	1	8	yes	complemented
172	C₄×D₈	—	2	8	no	—
173	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
174	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
175	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
176	C₂×#102	C₂²×C₁₁	1	4	yes	—
177	C₂×#102	C₂²×C₁₁	1	4	yes	—
178	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
179	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
180	#390	—	2	2	no	—
181	#390	C₂²×C₁₁	1	4	yes	—
182	#386	—	2	4	no	—
183	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
184	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
185	#340	C₂²×C₁₁	1	2	yes	—
186	#336	C₂²×C₁₁	1	2	yes	—
187	C₂²×C₁₁	—	4	8	no	—
188	C₂²×C₁₁	—	4	8	no	—
189	C₂²×C₁₁	—	4	8	no	—
190	C₂²×C₁₁	—	8	4	no	—
191	C₂²×C₁₁	—	8	4	no	—
192	C₂²×C₁₁	—	8	4	no	—
193	C₂²×C₁₁	—	8	4	no	—
194	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂²×C₁₁	D₄²	1	1	yes	characteristic
196	C₂²×C₁₁	#550	1	1	yes	characteristic
197	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
198	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
199	C₂²×C₁₁	#576	1	1	yes	characteristic
200	C₂²×C₁₁	#576	1	1	yes	characteristic
201	C₄×C₁₁	—	2	2	no	—
202	C₄×C₁₁	—	2	4	no	—
203	C₄×C₁₁	—	4	4	no	—
204	C₄×C₁₁	—	4	2	no	—
205	C₄×C₁₁	—	8	2	no	—
206	C₄×C₁₁	C₄×D₈	1	4	yes	complemented
207	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
208	C₄×C₁₁	#518	1	1	yes	characteristic
209	C₄×C₁₁	#550	1	1	yes	characteristic
210	C₄×C₁₁	#559	1	1	yes	characteristic
211	C₂²×D₄	—	2	2	no	—
212	C₂²×D₄	—	2	2	no	—
213	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
214	C₂³×C₄	—	2	4	no	—
215	C₂×D₈	—	2	4	no	—
216	C₂×D₈	—	2	4	no	—
217	C₂×D₈	—	4	2	no	—
218	C₂×D₈	—	4	2	no	—
219	C₂×D₈	C₂×C₄×C₁₁	1	8	yes	complemented
220	C₂×D₈	C₂×C₄×C₁₁	1	8	yes	complemented
221	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
222	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
224	#127	—	2	4	no	—
225	#127	C₂×C₄×C₁₁	1	8	yes	complemented
226	C₄×D₄	—	2	8	no	—
227	C₄×D₄	—	4	4	no	—
228	C₄×D₄	—	4	8	no	—
229	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
230	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
232	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
233	C₂×C₂²⋊C₄	—	2	4	no	—
234	C₂×C₂²⋊C₄	—	2	4	no	—
235	C₂×C₂²⋊C₄	—	2	4	no	—
236	C₂×C₄²	—	2	2	no	—
237	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
238	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
239	#107	—	2	2	no	—
240	#107	D₄×C₁₁	1	4	yes	complemented
241	C₄⋊C₈	—	2	2	no	—
242	#102	—	2	8	no	—
243	#102	—	4	4	no	—
244	C₄×C₈	—	2	4	no	—
245	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
246	#95	—	2	2	no	—
247	#95	D₄×C₁₁	1	2	yes	—
248	C₂×C₁₁	—	8	8	no	—
249	C₂×C₁₁	#2366	1	1	yes	characteristic
250	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
251	C₂×C₁₁	#2948	1	1	yes	characteristic
252	C₂×C₁₁	D₄×D₈	1	1	yes	characteristic
253	C₂×C₁₁	#3287	1	1	yes	characteristic
254	C₂×C₁₁	#3391	1	1	yes	characteristic
255	C₂×C₁₁	#3396	1	1	yes	characteristic
256	C₂⁴	—	2	4	no	—
257	C₂×D₄	—	2	8	no	—
258	C₂×D₄	—	2	8	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	4	4	no	—
265	C₂×D₄	—	4	4	no	—
266	C₂×D₄	—	8	2	no	—
267	C₂×D₄	—	8	2	no	—
268	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	4	8	no	—
272	C₂²×C₄	—	4	8	no	—
273	C₂²×C₄	—	8	4	no	—
274	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
275	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
278	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
279	D₈	—	2	16	no	—
280	D₈	—	4	8	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
287	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
288	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
289	C₂×C₈	C₁₁×#41	1	2	yes	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	C₁₁×D₈	1	4	yes	complemented
295	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
296	C₂²⋊C₄	—	4	8	no	—
297	C₂²⋊C₄	—	4	8	no	—
298	C₂²⋊C₄	—	8	4	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	4	4	no	—
302	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
303	C₄²	C₁₁×#41	1	2	yes	—
304	C₁₁	#23185	1	1	yes	characteristic, direct product factor, Sylow
305	C₂³	—	2	8	no	—
306	C₂³	—	4	4	no	—
307	C₂³	—	4	4	no	—
308	C₂³	—	4	4	no	—
309	C₂³	—	4	4	no	—
310	C₂³	—	4	4	no	—
311	C₂³	—	4	4	no	—
312	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
313	D₄	—	2	8	no	—
314	D₄	—	2	8	no	—
315	D₄	—	4	4	no	—
316	D₄	—	4	4	no	—
317	D₄	—	4	16	no	—
318	D₄	—	8	8	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	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	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	8	16	no	—
333	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
334	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
335	C₂×C₄	C₂×C₁₁×D₈	1	4	yes	—
336	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
337	C₂×C₄	C₁₁×#135	1	2	yes	—
338	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
340	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
341	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
342	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
343	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
344	C₈	—	2	2	no	—
345	C₈	—	4	2	no	—
346	C₈	C₄×D₄×C₁₁	1	4	yes	complemented
347	C₂²	—	4	8	no	—
348	C₂²	—	4	8	no	—
349	C₂²	—	4	8	no	—
350	C₂²	—	8	4	no	—
351	C₂²	—	8	4	no	—
352	C₂²	—	8	4	no	—
353	C₂²	—	8	4	no	—
354	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
355	C₂²	D₄²×C₁₁	1	1	yes	characteristic
356	C₂²	C₁₁×#550	1	1	yes	characteristic
357	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
358	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
359	C₂²	C₁₁×#576	1	1	yes	characteristic
360	C₂²	C₁₁×#576	1	1	yes	characteristic
361	C₄	—	2	2	no	—
362	C₄	—	2	4	no	—
363	C₄	—	4	4	no	—
364	C₄	—	4	2	no	—
365	C₄	—	8	2	no	—
366	C₄	C₄×C₁₁×D₈	1	4	yes	complemented
367	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
368	C₄	C₁₁×#518	1	1	yes	characteristic
369	C₄	C₁₁×#550	1	1	yes	characteristic
370	C₄	C₁₁×#559	1	1	yes	characteristic
371	C₂	—	8	8	no	—
372	C₂	C₁₁×#2366	1	1	yes	characteristic
373	C₂	C₂×C₄×C₁₁×D₈	1	1	yes	characteristic
374	C₂	C₁₁×#2948	1	1	yes	characteristic
375	C₂	D₄×C₁₁×D₈	1	1	yes	characteristic
376	C₂	C₁₁×#3287	1	1	yes	characteristic
377	C₂	C₁₁×#3391	1	1	yes	characteristic
378	C₂	C₁₁×#3396	1	1	yes	characteristic

	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×C₄×C₁₁×D₈	C₂	semidirect
3. C₁₁×#2366	C₂	semidirect
4. C₁₁×#1982	C₂	semidirect
5. C₁₁×#1970	C₂	semidirect
6. C₁₁×#1879	C₂	semidirect
7. C₄×C₁₁×#107	C₂	semidirect
8. C₈×C₁₁×C₄⋊C₄	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
59. C₁₁×#107	D₄	semidirect
64. C₄×C₈×C₁₁	C₂×C₄	semidirect
67. #23185	C₁₁	direct (N × H)
106. C₁₁×C₄⋊C₄	D₈	semidirect
117. C₂×C₄×D₈	C₂×C₁₁	semidirect
118. #2366	C₂×C₁₁	semidirect
119. #1982	C₂×C₁₁	semidirect
120. #1970	C₂×C₁₁	semidirect
121. #1879	C₂×C₁₁	semidirect
122. C₄×#107	C₂×C₁₁	semidirect
123. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
165. C₈×C₁₁	C₄×D₄	semidirect
171. #493	C₄×C₁₁	semidirect
206. C₄×C₁₁	C₄×D₈	semidirect
219. C₂×D₈	C₂×C₄×C₁₁	semidirect
220. C₂×D₈	C₂×C₄×C₁₁	semidirect
225. #127	C₂×C₄×C₁₁	semidirect
240. #107	D₄×C₁₁	semidirect
245. C₄×C₈	C₂×C₄×C₁₁	semidirect
294. C₄⋊C₄	C₁₁×D₈	semidirect
304. C₁₁	#23185	direct (N × H)
346. C₈	C₄×D₄×C₁₁	semidirect
366. C₄	C₄×C₁₁×D₈	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×C₄×C₁₁×D₈	2
C₁₁×#2366	2
C₁₁×#1982	2
C₁₁×#1970	2
C₁₁×#1879	2
C₄×C₁₁×#107	2
C₈×C₁₁×C₄⋊C₄	2
#23185	11

Subgroups — C11×#23185 #14600378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23185 #14600378