Subgroups — C₁₁×#19101 #14596294

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 396 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, complemented
2	C₁₁×#3100	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1669	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1667	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1665	C₂	1	4	yes	maximal, complemented
7	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1540	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₁×#135	—	2	1	no	—
10	C₂×C₁₁×#135	—	2	1	no	—
11	C₂³×C₈×C₁₁	—	2	1	no	—
12	C₁₁×#532	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#495	—	2	1	no	—
15	C₁₁×#495	—	2	1	no	—
16	C₁₁×#494	C₂²	1	1	yes	characteristic, complemented
17	C₁₁×#493	C₂²	1	1	yes	characteristic, complemented
18	C₁₁×#492	C₂²	1	2	yes	complemented
19	C₁₁×#480	—	2	2	no	—
20	C₁₁×#474	C₂²	1	4	yes	—
21	C₁₁×#459	C₂²	1	4	yes	—
22	C₁₁×#447	—	2	2	no	—
23	C₄×C₁₁×D₈	—	2	4	no	—
24	C₈×D₄×C₁₁	—	2	1	no	—
25	C₈×D₄×C₁₁	—	2	1	no	—
26	C₈×D₄×C₁₁	C₂²	1	2	yes	—
27	C₈×D₄×C₁₁	C₂²	1	2	yes	—
28	C₁₁×#431	C₂²	1	2	yes	—
29	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₁₁×#335	C₂²	1	2	yes	complemented
33	C₁₁×#334	C₂²	1	2	yes	complemented
34	C₁₁×#332	C₂²	1	4	yes	complemented
35	C₁₁×#331	C₂²	1	4	yes	complemented
36	C₂×C₁₁×#41	—	2	2	no	—
37	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₁	—	2	1	no	—
39	C₁₁×#135	—	4	4	no	—
40	C₁₁×#135	—	4	4	no	—
41	C₂×C₁₁×Q₁₆	—	2	1	no	—
42	C₂×C₁₁×Q₁₆	—	2	1	no	—
43	C₂×C₁₁×SD₁₆	—	2	2	no	—
44	C₂×C₁₁×SD₁₆	—	2	2	no	—
45	C₂×C₁₁×D₈	—	2	4	no	—
46	C₂×C₁₁×D₈	—	2	1	no	—
47	C₂×C₁₁×D₈	—	2	1	no	—
48	C₂²×C₈×C₁₁	—	2	1	no	—
49	C₂²×C₈×C₁₁	—	2	2	no	—
50	C₂²×C₈×C₁₁	—	2	2	no	—
51	C₂²×C₈×C₁₁	—	4	4	no	—
52	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
54	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₁₁×#127	C₂³	1	2	yes	—
56	C₁₁×#124	—	2	2	no	—
57	C₁₁×#121	—	2	2	no	—
58	C₁₁×#121	—	2	2	no	—
59	C₄×D₄×C₁₁	—	2	1	no	—
60	C₄×D₄×C₁₁	—	2	2	no	—
61	C₄×D₄×C₁₁	—	2	1	no	—
62	C₄×D₄×C₁₁	—	2	2	no	—
63	C₄×D₄×C₁₁	D₄	1	2	yes	—
64	C₄×D₄×C₁₁	C₂³	1	2	yes	—
65	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
68	C₁₁×#107	—	2	4	no	—
69	C₁₁×C₄⋊C₈	—	2	1	no	—
70	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
71	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
72	C₁₁×#102	—	2	4	no	—
73	C₁₁×#102	—	2	4	no	—
74	C₁₁×C₂²⋊C₈	—	2	2	no	—
75	C₁₁×C₂²⋊C₈	—	2	2	no	—
76	C₁₁×C₂²⋊C₈	—	2	2	no	—
77	C₄×C₈×C₁₁	—	2	2	no	—
78	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
80	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
82	#19101	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₁	—	2	1	no	—
84	C₁₁×#41	—	4	4	no	—
85	C₁₁×#41	—	4	4	no	—
86	C₂×Q₈×C₁₁	—	2	2	no	—
87	C₂×D₄×C₁₁	—	2	4	no	—
88	C₂×D₄×C₁₁	—	2	1	no	—
89	C₂×D₄×C₁₁	—	2	2	no	—
90	C₂×D₄×C₁₁	—	2	2	no	—
91	C₂×D₄×C₁₁	—	2	2	no	—
92	C₂×D₄×C₁₁	—	4	2	no	—
93	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₁	—	2	1	no	—
95	C₂²×C₄×C₁₁	—	2	2	no	—
96	C₂²×C₄×C₁₁	—	2	2	no	—
97	C₂²×C₄×C₁₁	—	4	2	no	—
98	C₂²×C₄×C₁₁	—	4	2	no	—
99	C₂²×C₄×C₁₁	—	4	2	no	—
100	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
103	C₁₁×Q₁₆	—	4	2	no	—
104	C₁₁×Q₁₆	—	4	2	no	—
105	C₁₁×SD₁₆	—	4	4	no	—
106	C₁₁×SD₁₆	—	4	4	no	—
107	C₁₁×D₈	—	4	2	no	—
108	C₁₁×D₈	—	4	2	no	—
109	C₁₁×D₈	—	4	8	no	—
110	C₂×C₈×C₁₁	—	2	2	no	—
111	C₂×C₈×C₁₁	—	2	4	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	4	4	no	—
114	C₂×C₈×C₁₁	—	4	4	no	—
115	C₂×C₈×C₁₁	—	4	2	no	—
116	C₂×C₈×C₁₁	D₈	1	4	yes	complemented
117	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
121	C₁₁×C₄⋊C₄	—	2	1	no	—
122	C₁₁×C₄⋊C₄	—	2	2	no	—
123	C₁₁×C₄⋊C₄	—	2	2	no	—
124	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
125	C₁₁×C₂²⋊C₄	—	2	2	no	—
126	C₁₁×C₂²⋊C₄	—	2	2	no	—
127	C₁₁×C₂²⋊C₄	—	4	2	no	—
128	C₁₁×C₂²⋊C₄	—	4	2	no	—
129	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₁	#41	1	1	yes	characteristic
132	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
133	#3147	C₂×C₁₁	1	1	yes	characteristic, complemented
134	#3100	C₂×C₁₁	1	2	yes	complemented
135	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
136	#1669	C₂×C₁₁	1	2	yes	complemented
137	#1667	C₂×C₁₁	1	2	yes	complemented
138	#1665	C₂×C₁₁	1	4	yes	complemented
139	#1564	C₂×C₁₁	1	1	yes	characteristic, complemented
140	#1540	C₂×C₁₁	1	2	yes	complemented
141	C₂³×C₁₁	—	2	4	no	—
142	C₂³×C₁₁	—	2	2	no	—
143	C₂³×C₁₁	—	4	2	no	—
144	C₂³×C₁₁	—	4	2	no	—
145	C₂³×C₁₁	—	4	2	no	—
146	C₂³×C₁₁	#121	1	1	yes	characteristic
147	Q₈×C₁₁	—	4	2	no	—
148	Q₈×C₁₁	—	4	2	no	—
149	D₄×C₁₁	—	2	4	no	—
150	D₄×C₁₁	—	2	2	no	—
151	D₄×C₁₁	—	4	2	no	—
152	D₄×C₁₁	—	4	4	no	—
153	D₄×C₁₁	—	4	2	no	—
154	D₄×C₁₁	—	8	2	no	—
155	D₄×C₁₁	—	8	4	no	—
156	D₄×C₁₁	#135	1	4	yes	complemented
157	C₂×C₄×C₁₁	—	2	2	no	—
158	C₂×C₄×C₁₁	—	2	2	no	—
159	C₂×C₄×C₁₁	—	4	1	no	—
160	C₂×C₄×C₁₁	—	4	2	no	—
161	C₂×C₄×C₁₁	—	4	2	no	—
162	C₂×C₄×C₁₁	—	4	2	no	—
163	C₂×C₄×C₁₁	—	4	4	no	—
164	C₂×C₄×C₁₁	—	4	2	no	—
165	C₂×C₄×C₁₁	—	8	4	no	—
166	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
167	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
168	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
169	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
170	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
171	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
174	C₈×C₁₁	—	2	1	no	—
175	C₈×C₁₁	—	2	1	no	—
176	C₈×C₁₁	—	4	2	no	—
177	C₈×C₁₁	—	4	4	no	—
178	C₈×C₁₁	C₂×D₈	1	2	yes	—
179	C₈×C₁₁	C₂×D₈	1	2	yes	—
180	C₂×#135	—	2	1	no	—
181	C₂×#135	—	2	1	no	—
182	C₂³×C₈	—	2	1	no	—
183	#532	C₂²×C₁₁	1	2	yes	—
184	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
185	#495	—	2	1	no	—
186	#495	—	2	1	no	—
187	#494	C₂²×C₁₁	1	1	yes	characteristic, complemented
188	#493	C₂²×C₁₁	1	1	yes	characteristic, complemented
189	#492	C₂²×C₁₁	1	2	yes	complemented
190	#480	—	2	2	no	—
191	#474	C₂²×C₁₁	1	4	yes	—
192	#459	C₂²×C₁₁	1	4	yes	—
193	#447	—	2	2	no	—
194	C₄×D₈	—	2	4	no	—
195	C₈×D₄	—	2	1	no	—
196	C₈×D₄	—	2	1	no	—
197	C₈×D₄	C₂²×C₁₁	1	2	yes	—
198	C₈×D₄	C₂²×C₁₁	1	2	yes	—
199	#431	C₂²×C₁₁	1	2	yes	—
200	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
201	C₂×C₂²⋊C₈	—	2	1	no	—
202	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
203	#335	C₂²×C₁₁	1	2	yes	complemented
204	#334	C₂²×C₁₁	1	2	yes	complemented
205	#332	C₂²×C₁₁	1	4	yes	complemented
206	#331	C₂²×C₁₁	1	4	yes	complemented
207	C₂²×C₁₁	—	2	1	no	—
208	C₂²×C₁₁	—	2	1	no	—
209	C₂²×C₁₁	—	2	4	no	—
210	C₂²×C₁₁	—	4	8	no	—
211	C₂²×C₁₁	—	4	2	no	—
212	C₂²×C₁₁	—	4	2	no	—
213	C₂²×C₁₁	—	8	2	no	—
214	C₂²×C₁₁	—	8	2	no	—
215	C₂²×C₁₁	—	8	2	no	—
216	C₂²×C₁₁	#459	1	2	yes	—
217	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
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	—	8	2	no	—
223	C₄×C₁₁	#459	1	2	yes	—
224	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
225	C₄×C₁₁	C₂×#135	1	2	yes	—
226	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₂×#41	—	2	2	no	—
228	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
229	C₂³×C₄	—	2	1	no	—
230	#135	—	4	4	no	—
231	#135	—	4	4	no	—
232	C₂×Q₁₆	—	2	1	no	—
233	C₂×Q₁₆	—	2	1	no	—
234	C₂×SD₁₆	—	2	2	no	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×D₈	—	2	4	no	—
237	C₂×D₈	—	2	1	no	—
238	C₂×D₈	—	2	1	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	4	4	no	—
243	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
244	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
245	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
246	#127	C₂³×C₁₁	1	2	yes	—
247	#124	—	2	2	no	—
248	#121	—	2	2	no	—
249	#121	—	2	2	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	D₄×C₁₁	1	2	yes	—
255	C₄×D₄	C₂³×C₁₁	1	2	yes	—
256	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
259	#107	—	2	4	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
262	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
263	#102	—	2	4	no	—
264	#102	—	2	4	no	—
265	C₂²⋊C₈	—	2	2	no	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₄×C₈	—	2	2	no	—
269	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
270	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
273	C₂×C₁₁	—	2	2	no	—
274	C₂×C₁₁	—	4	4	no	—
275	C₂×C₁₁	—	16	2	no	—
276	C₂×C₁₁	C₂×#459	1	1	yes	characteristic
277	C₂×C₁₁	#3050	1	1	yes	characteristic
278	C₂×C₁₁	#3067	1	1	yes	characteristic
279	C₂⁴	—	2	1	no	—
280	#41	—	4	4	no	—
281	#41	—	4	4	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
298	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
299	Q₁₆	—	4	2	no	—
300	Q₁₆	—	4	2	no	—
301	SD₁₆	—	4	4	no	—
302	SD₁₆	—	4	4	no	—
303	D₈	—	4	2	no	—
304	D₈	—	4	8	no	—
305	D₈	—	4	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	—	4	4	no	—
311	C₂×C₈	—	4	4	no	—
312	C₂×C₈	C₁₁×D₈	1	4	yes	complemented
313	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
314	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
316	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
327	C₄²	C₁₁×#41	1	1	yes	characteristic
328	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
329	C₁₁	#19101	1	1	yes	characteristic, direct product factor, Sylow
330	C₂³	—	2	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	C₁₁×#121	1	1	yes	characteristic
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	D₄	—	2	4	no	—
339	D₄	—	2	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	2	no	—
343	D₄	—	8	2	no	—
344	D₄	—	8	4	no	—
345	D₄	C₁₁×#135	1	4	yes	complemented
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	8	4	no	—
355	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
356	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
357	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
358	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
359	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
360	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
361	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
362	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	4	no	—
367	C₈	C₂×C₁₁×D₈	1	2	yes	—
368	C₈	C₂×C₁₁×D₈	1	2	yes	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	C₁₁×#459	1	2	yes	—
379	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	2	no	—
385	C₄	C₁₁×#459	1	2	yes	—
386	C₄	C₂²×C₁₁×D₈	1	1	yes	characteristic
387	C₄	C₂×C₁₁×#135	1	2	yes	—
388	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	4	4	no	—
391	C₂	—	16	2	no	—
392	C₂	C₂×C₁₁×#459	1	1	yes	characteristic
393	C₂	C₁₁×#3050	1	1	yes	characteristic
394	C₂	C₁₁×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×#121
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3147	C₂	semidirect
2. C₁₁×#3100	C₂	semidirect
3. C₂×C₈×D₄×C₁₁	C₂	semidirect
4. C₁₁×#1669	C₂	semidirect
5. C₁₁×#1667	C₂	semidirect
6. C₁₁×#1665	C₂	semidirect
7. C₁₁×#1564	C₂	semidirect
8. C₁₁×#1540	C₂	semidirect
16. C₁₁×#494	C₂²	semidirect
17. C₁₁×#493	C₂²	semidirect
18. C₁₁×#492	C₂²	semidirect
32. C₁₁×#335	C₂²	semidirect
33. C₁₁×#334	C₂²	semidirect
34. C₁₁×#332	C₂²	semidirect
35. C₁₁×#331	C₂²	semidirect
82. #19101	C₁₁	direct (N × H)
116. C₂×C₈×C₁₁	D₈	semidirect
133. #3147	C₂×C₁₁	semidirect
134. #3100	C₂×C₁₁	semidirect
135. C₂×C₈×D₄	C₂×C₁₁	semidirect
136. #1669	C₂×C₁₁	semidirect
137. #1667	C₂×C₁₁	semidirect
138. #1665	C₂×C₁₁	semidirect
139. #1564	C₂×C₁₁	semidirect
140. #1540	C₂×C₁₁	semidirect
156. D₄×C₁₁	#135	semidirect
187. #494	C₂²×C₁₁	semidirect
188. #493	C₂²×C₁₁	semidirect
189. #492	C₂²×C₁₁	semidirect
203. #335	C₂²×C₁₁	semidirect
204. #334	C₂²×C₁₁	semidirect
205. #332	C₂²×C₁₁	semidirect
206. #331	C₂²×C₁₁	semidirect
312. C₂×C₈	C₁₁×D₈	semidirect
329. C₁₁	#19101	direct (N × H)
345. D₄	C₁₁×#135	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
C₁₁×#3100	2
C₂×C₈×D₄×C₁₁	2
C₁₁×#1669	2
C₁₁×#1667	2
C₁₁×#1665	2
C₁₁×#1564	2
C₁₁×#1540	2
#19101	11

Subgroups — C11×#19101 #14596294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19101 #14596294