Subgroups — C₁₁×#19191 #14596384

Order 2816.

662 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×#3227	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#3206	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1691	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1671	C₂	1	4	yes	maximal, complemented
7	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#131	—	2	1	no	—
11	C₁₁×#532	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₁₁×#498	—	2	1	no	—
15	C₁₁×#498	—	2	1	no	—
16	C₁₁×#498	—	2	1	no	—
17	C₁₁×#498	C₂²	1	2	yes	—
18	C₁₁×#498	C₂²	1	2	yes	—
19	C₁₁×#492	—	2	1	no	—
20	C₁₁×#487	—	2	1	no	—
21	C₁₁×#486	—	2	1	no	—
22	C₁₁×#481	—	2	2	no	—
23	C₁₁×#476	C₂²	1	4	yes	—
24	C₁₁×#461	C₂²	1	4	yes	—
25	C₁₁×#448	—	2	2	no	—
26	C₁₁×#436	—	2	1	no	—
27	C₁₁×#436	C₂²	1	2	yes	—
28	C₈×D₄×C₁₁	—	2	1	no	—
29	C₈×D₄×C₁₁	C₂²	1	2	yes	—
30	C₁₁×#431	C₂²	1	1	yes	characteristic
31	C₁₁×#431	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×#106	—	2	1	no	—
33	C₂×C₁₁×#106	—	2	1	no	—
34	C₁₁×#423	C₂²	1	1	yes	characteristic
35	C₁₁×#408	—	2	1	no	—
36	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
37	C₁₁×#335	C₂²	1	2	yes	—
38	C₁₁×#334	C₂²	1	2	yes	—
39	C₁₁×#333	C₂²	1	4	yes	—
40	C₁₁×#332	C₂²	1	4	yes	—
41	C₂×C₁₁×#41	—	2	1	no	—
42	C₂²×Q₈×C₁₁	—	2	1	no	—
43	C₂²×Q₈×C₁₁	—	2	1	no	—
44	C₂×C₁₁×SD₁₆	—	2	4	no	—
45	C₁₁×#131	—	4	4	no	—
46	C₂×C₁₁×M₁₆	—	2	1	no	—
47	C₂×C₁₁×M₁₆	—	2	2	no	—
48	C₂²×C₈×C₁₁	—	2	2	no	—
49	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
51	C₁₁×C₄⋊Q₈	—	2	1	no	—
52	C₁₁×C₄⋊Q₈	—	2	1	no	—
53	C₁₁×C₄⋊Q₈	—	2	1	no	—
54	C₁₁×C₄⋊Q₈	—	2	1	no	—
55	C₁₁×C₄⋊Q₈	—	2	1	no	—
56	C₁₁×C₄⋊Q₈	—	2	1	no	—
57	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₁₁×#127	D₄	1	1	yes	characteristic
61	C₁₁×#124	—	2	1	no	—
62	C₁₁×#121	—	2	1	no	—
63	C₁₁×#121	D₄	1	2	yes	—
64	C₄×D₄×C₁₁	—	2	1	no	—
65	C₄×D₄×C₁₁	C₂³	1	2	yes	—
66	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
70	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
71	C₁₁×#106	—	2	2	no	—
72	C₁₁×#106	—	2	2	no	—
73	C₁₁×#106	—	2	2	no	—
74	C₁₁×#106	—	2	2	no	—
75	C₁₁×#106	—	2	4	no	—
76	C₁₁×C₄⋊C₈	—	2	1	no	—
77	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
78	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
79	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
80	C₁₁×#103	—	2	4	no	—
81	C₁₁×#102	—	2	4	no	—
82	C₁₁×C₂²⋊C₈	—	2	1	no	—
83	C₁₁×C₂²⋊C₈	—	2	1	no	—
84	C₁₁×C₂²⋊C₈	—	2	2	no	—
85	C₁₁×C₂²⋊C₈	—	2	2	no	—
86	C₄×C₈×C₁₁	—	2	1	no	—
87	C₄×C₈×C₁₁	—	2	1	no	—
88	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
89	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
90	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
92	#19191	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₁₁×#41	—	4	2	no	—
94	C₁₁×#41	—	4	2	no	—
95	C₂×Q₈×C₁₁	—	2	1	no	—
96	C₂×Q₈×C₁₁	—	2	2	no	—
97	C₂×Q₈×C₁₁	—	2	2	no	—
98	C₂×Q₈×C₁₁	—	4	1	no	—
99	C₂×Q₈×C₁₁	—	4	1	no	—
100	C₂×Q₈×C₁₁	—	8	2	no	—
101	C₂×Q₈×C₁₁	—	8	2	no	—
102	C₂×D₄×C₁₁	—	2	2	no	—
103	C₂×D₄×C₁₁	—	2	1	no	—
104	C₂×D₄×C₁₁	—	2	1	no	—
105	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₁	—	2	2	no	—
107	C₂²×C₄×C₁₁	—	4	1	no	—
108	C₂²×C₄×C₁₁	—	4	1	no	—
109	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
112	C₁₁×SD₁₆	—	8	4	no	—
113	C₁₁×M₁₆	—	4	4	no	—
114	C₁₁×M₁₆	—	4	2	no	—
115	C₂×C₈×C₁₁	—	2	2	no	—
116	C₂×C₈×C₁₁	—	2	2	no	—
117	C₂×C₈×C₁₁	—	2	2	no	—
118	C₂×C₈×C₁₁	—	2	2	no	—
119	C₂×C₈×C₁₁	—	4	4	no	—
120	C₂×C₈×C₁₁	SD₁₆	1	4	yes	complemented
121	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
125	C₁₁×C₄⋊C₄	—	2	1	no	—
126	C₁₁×C₄⋊C₄	—	2	2	no	—
127	C₁₁×C₄⋊C₄	—	2	2	no	—
128	C₁₁×C₄⋊C₄	—	2	2	no	—
129	C₁₁×C₄⋊C₄	—	2	2	no	—
130	C₁₁×C₄⋊C₄	—	4	1	no	—
131	C₁₁×C₄⋊C₄	—	4	1	no	—
132	C₁₁×C₄⋊C₄	—	4	1	no	—
133	C₁₁×C₄⋊C₄	—	4	1	no	—
134	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
135	C₁₁×C₂²⋊C₄	—	2	2	no	—
136	C₁₁×C₂²⋊C₄	—	2	2	no	—
137	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₁	#41	1	1	yes	characteristic
140	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
141	#3227	C₂×C₁₁	1	1	yes	characteristic
142	#3206	C₂×C₁₁	1	1	yes	characteristic
143	C₂×#498	C₂×C₁₁	1	1	yes	characteristic, complemented
144	#2931	C₂×C₁₁	1	1	yes	characteristic
145	#1691	C₂×C₁₁	1	4	yes	complemented
146	#1671	C₂×C₁₁	1	4	yes	complemented
147	#1564	C₂×C₁₁	1	1	yes	characteristic, complemented
148	#1549	C₂×C₁₁	1	1	yes	characteristic, complemented
149	#1548	C₂×C₁₁	1	1	yes	characteristic, complemented
150	C₂³×C₁₁	—	2	2	no	—
151	C₂³×C₁₁	#121	1	1	yes	characteristic
152	Q₈×C₁₁	—	4	2	no	—
153	Q₈×C₁₁	—	4	4	no	—
154	Q₈×C₁₁	—	8	2	no	—
155	Q₈×C₁₁	—	8	2	no	—
156	Q₈×C₁₁	—	8	2	no	—
157	D₄×C₁₁	—	2	4	no	—
158	D₄×C₁₁	—	4	4	no	—
159	D₄×C₁₁	—	4	2	no	—
160	D₄×C₁₁	—	4	2	no	—
161	C₂×C₄×C₁₁	—	2	2	no	—
162	C₂×C₄×C₁₁	—	2	2	no	—
163	C₂×C₄×C₁₁	—	2	2	no	—
164	C₂×C₄×C₁₁	—	4	2	no	—
165	C₂×C₄×C₁₁	—	4	2	no	—
166	C₂×C₄×C₁₁	—	4	2	no	—
167	C₂×C₄×C₁₁	—	4	2	no	—
168	C₂×C₄×C₁₁	—	8	2	no	—
169	C₂×C₄×C₁₁	—	8	2	no	—
170	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
174	C₂×C₄×C₁₁	#137	1	2	yes	—
175	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
178	C₈×C₁₁	—	2	1	no	—
179	C₈×C₁₁	—	2	1	no	—
180	C₈×C₁₁	—	4	2	no	—
181	C₈×C₁₁	—	4	2	no	—
182	C₈×C₁₁	—	4	2	no	—
183	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
184	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
185	C₂×#131	—	2	1	no	—
186	#532	C₂²×C₁₁	1	1	yes	characteristic
187	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
188	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
189	#498	—	2	1	no	—
190	#498	—	2	1	no	—
191	#498	—	2	1	no	—
192	#498	C₂²×C₁₁	1	2	yes	—
193	#498	C₂²×C₁₁	1	2	yes	—
194	#492	—	2	1	no	—
195	#487	—	2	1	no	—
196	#486	—	2	1	no	—
197	#481	—	2	2	no	—
198	#476	C₂²×C₁₁	1	4	yes	—
199	#461	C₂²×C₁₁	1	4	yes	—
200	#448	—	2	2	no	—
201	#436	—	2	1	no	—
202	#436	C₂²×C₁₁	1	2	yes	—
203	C₈×D₄	—	2	1	no	—
204	C₈×D₄	C₂²×C₁₁	1	2	yes	—
205	#431	C₂²×C₁₁	1	1	yes	characteristic
206	#431	C₂²×C₁₁	1	1	yes	characteristic
207	C₂×#106	—	2	1	no	—
208	C₂×#106	—	2	1	no	—
209	#423	C₂²×C₁₁	1	1	yes	characteristic
210	#408	—	2	1	no	—
211	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
212	#335	C₂²×C₁₁	1	2	yes	—
213	#334	C₂²×C₁₁	1	2	yes	—
214	#333	C₂²×C₁₁	1	4	yes	—
215	#332	C₂²×C₁₁	1	4	yes	—
216	C₂²×C₁₁	—	2	1	no	—
217	C₂²×C₁₁	—	2	1	no	—
218	C₂²×C₁₁	—	4	2	no	—
219	C₂²×C₁₁	—	4	2	no	—
220	C₂²×C₁₁	—	4	2	no	—
221	C₂²×C₁₁	#461	1	2	yes	—
222	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
223	C₄×C₁₁	—	2	1	no	—
224	C₄×C₁₁	—	2	1	no	—
225	C₄×C₁₁	—	4	2	no	—
226	C₄×C₁₁	—	8	2	no	—
227	C₄×C₁₁	—	8	2	no	—
228	C₄×C₁₁	#461	1	2	yes	—
229	C₄×C₁₁	#471	1	2	yes	—
230	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
231	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
232	C₄×C₁₁	#577	1	2	yes	—
233	C₂×#41	—	2	1	no	—
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	—	2	1	no	—
236	C₂×SD₁₆	—	2	4	no	—
237	#131	—	4	4	no	—
238	C₂×M₁₆	—	2	1	no	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
242	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	D₄×C₁₁	1	1	yes	characteristic
250	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
251	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
252	#127	D₄×C₁₁	1	1	yes	characteristic
253	#124	—	2	1	no	—
254	#121	—	2	1	no	—
255	#121	D₄×C₁₁	1	2	yes	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	C₂³×C₁₁	1	2	yes	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
263	#106	—	2	2	no	—
264	#106	—	2	2	no	—
265	#106	—	2	2	no	—
266	#106	—	2	2	no	—
267	#106	—	2	4	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
270	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
271	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
272	#103	—	2	4	no	—
273	#102	—	2	4	no	—
274	C₂²⋊C₈	—	2	1	no	—
275	C₂²⋊C₈	—	2	1	no	—
276	C₂²⋊C₈	—	2	2	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
281	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
284	C₂×C₁₁	—	2	2	no	—
285	C₂×C₁₁	—	8	2	no	—
286	C₂×C₁₁	C₂×#461	1	1	yes	characteristic
287	C₂×C₁₁	#3057	1	1	yes	characteristic
288	C₂×C₁₁	C₂×#471	1	1	yes	characteristic
289	#41	—	4	2	no	—
290	#41	—	4	2	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	8	2	no	—
297	C₂×Q₈	—	8	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
307	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
308	SD₁₆	—	8	4	no	—
309	M₁₆	—	4	2	no	—
310	M₁₆	—	4	4	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	C₁₁×SD₁₆	1	4	yes	complemented
317	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
334	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
335	C₄²	C₁₁×#41	1	1	yes	characteristic
336	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
337	C₁₁	#19191	1	1	yes	characteristic, direct product factor, Sylow
338	C₂³	—	2	2	no	—
339	C₂³	C₁₁×#121	1	1	yes	characteristic
340	Q₈	—	4	2	no	—
341	Q₈	—	4	4	no	—
342	Q₈	—	8	2	no	—
343	Q₈	—	8	2	no	—
344	Q₈	—	8	2	no	—
345	D₄	—	2	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	8	2	no	—
357	C₂×C₄	—	8	2	no	—
358	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
359	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
360	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
361	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
362	C₂×C₄	C₁₁×#137	1	2	yes	—
363	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
364	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
365	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	4	2	no	—
369	C₈	—	4	2	no	—
370	C₈	—	4	2	no	—
371	C₈	C₂×C₁₁×SD₁₆	1	2	yes	—
372	C₈	C₂×C₁₁×SD₁₆	1	2	yes	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	C₁₁×#461	1	2	yes	—
379	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	2	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	2	no	—
385	C₄	C₁₁×#461	1	2	yes	—
386	C₄	C₁₁×#471	1	2	yes	—
387	C₄	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
388	C₄	C₂×C₁₁×#137	1	1	yes	characteristic
389	C₄	C₁₁×#577	1	2	yes	—
390	C₂	—	2	2	no	—
391	C₂	—	8	2	no	—
392	C₂	C₂×C₁₁×#461	1	1	yes	characteristic
393	C₂	C₁₁×#3057	1	1	yes	characteristic
394	C₂	C₂×C₁₁×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₁×#498	C₂	semidirect
5. C₁₁×#1691	C₂	semidirect
6. C₁₁×#1671	C₂	semidirect
7. C₁₁×#1564	C₂	semidirect
8. C₁₁×#1549	C₂	semidirect
9. C₁₁×#1548	C₂	semidirect
92. #19191	C₁₁	direct (N × H)
120. C₂×C₈×C₁₁	SD₁₆	semidirect
143. C₂×#498	C₂×C₁₁	semidirect
145. #1691	C₂×C₁₁	semidirect
146. #1671	C₂×C₁₁	semidirect
147. #1564	C₂×C₁₁	semidirect
148. #1549	C₂×C₁₁	semidirect
149. #1548	C₂×C₁₁	semidirect
316. C₂×C₈	C₁₁×SD₁₆	semidirect
337. C₁₁	#19191	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×#3227	2
C₁₁×#3206	2
C₂×C₁₁×#498	2
C₁₁×#2931	2
C₁₁×#1691	2
C₁₁×#1671	2
C₁₁×#1564	2
C₁₁×#1549	2
C₁₁×#1548	2
#19191	11

Subgroups — C11×#19191 #14596384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19191 #14596384