Subgroups — C₁₁×#19197 #14596390

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3226	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#3206	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1699	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1679	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×#1546	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×#500	—	2	1	no	—
15	C₁₁×#492	—	2	1	no	—
16	C₁₁×#487	—	2	1	no	—
17	C₁₁×#487	—	2	1	no	—
18	C₁₁×#487	—	2	1	no	—
19	C₁₁×#487	C₂²	1	2	yes	—
20	C₁₁×#487	C₂²	1	2	yes	—
21	C₁₁×#486	—	2	1	no	—
22	C₁₁×#480	—	2	2	no	—
23	C₁₁×#474	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	C₁₁×#423	C₂²	1	1	yes	characteristic
33	C₂×C₁₁×#103	—	2	1	no	—
34	C₂×C₁₁×#103	—	2	1	no	—
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×#332	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×#107	—	2	4	no	—
72	C₁₁×C₄⋊C₈	—	2	1	no	—
73	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
74	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
75	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
76	C₁₁×#103	—	2	2	no	—
77	C₁₁×#103	—	2	2	no	—
78	C₁₁×#103	—	2	2	no	—
79	C₁₁×#103	—	2	2	no	—
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	#19197	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	—	4	2	no	—
101	C₂×Q₈×C₁₁	—	4	2	no	—
102	C₂×Q₈×C₁₁	—	8	2	no	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	—	2	1	no	—
105	C₂×D₄×C₁₁	—	2	1	no	—
106	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₁	—	2	2	no	—
108	C₂²×C₄×C₁₁	—	4	1	no	—
109	C₂²×C₄×C₁₁	—	4	1	no	—
110	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
113	C₁₁×SD₁₆	—	8	4	no	—
114	C₁₁×M₁₆	—	4	4	no	—
115	C₁₁×M₁₆	—	4	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	—	2	2	no	—
120	C₂×C₈×C₁₁	—	2	2	no	—
121	C₂×C₈×C₁₁	—	4	4	no	—
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	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
126	C₁₁×C₄⋊C₄	—	2	1	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	—	2	2	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	—	4	1	no	—
135	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
136	C₁₁×C₂²⋊C₄	—	2	2	no	—
137	C₁₁×C₂²⋊C₄	—	2	2	no	—
138	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₁	#41	1	1	yes	characteristic
141	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
142	#3226	C₂×C₁₁	1	1	yes	characteristic
143	#3206	C₂×C₁₁	1	1	yes	characteristic
144	C₂×#487	C₂×C₁₁	1	1	yes	characteristic, complemented
145	#2931	C₂×C₁₁	1	1	yes	characteristic
146	#1699	C₂×C₁₁	1	4	yes	complemented
147	#1679	C₂×C₁₁	1	4	yes	complemented
148	#1564	C₂×C₁₁	1	1	yes	characteristic, complemented
149	#1549	C₂×C₁₁	1	1	yes	characteristic, complemented
150	#1546	C₂×C₁₁	1	1	yes	characteristic, complemented
151	C₂³×C₁₁	—	2	2	no	—
152	C₂³×C₁₁	#121	1	1	yes	characteristic
153	Q₈×C₁₁	—	4	2	no	—
154	Q₈×C₁₁	—	4	2	no	—
155	Q₈×C₁₁	—	4	2	no	—
156	Q₈×C₁₁	—	4	4	no	—
157	Q₈×C₁₁	—	8	2	no	—
158	Q₈×C₁₁	—	8	2	no	—
159	D₄×C₁₁	—	2	4	no	—
160	D₄×C₁₁	—	4	4	no	—
161	D₄×C₁₁	—	4	2	no	—
162	D₄×C₁₁	—	4	2	no	—
163	C₂×C₄×C₁₁	—	2	2	no	—
164	C₂×C₄×C₁₁	—	2	2	no	—
165	C₂×C₄×C₁₁	—	2	2	no	—
166	C₂×C₄×C₁₁	—	4	2	no	—
167	C₂×C₄×C₁₁	—	4	2	no	—
168	C₂×C₄×C₁₁	—	4	2	no	—
169	C₂×C₄×C₁₁	—	4	2	no	—
170	C₂×C₄×C₁₁	—	8	2	no	—
171	C₂×C₄×C₁₁	—	8	2	no	—
172	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₁	#135	1	2	yes	—
176	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
180	C₈×C₁₁	—	2	1	no	—
181	C₈×C₁₁	—	2	1	no	—
182	C₈×C₁₁	—	2	1	no	—
183	C₈×C₁₁	—	2	1	no	—
184	C₈×C₁₁	—	4	2	no	—
185	C₈×C₁₁	—	4	2	no	—
186	C₈×C₁₁	—	4	2	no	—
187	C₂×#131	—	2	1	no	—
188	#532	C₂²×C₁₁	1	1	yes	characteristic
189	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
190	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
191	#500	—	2	1	no	—
192	#492	—	2	1	no	—
193	#487	—	2	1	no	—
194	#487	—	2	1	no	—
195	#487	—	2	1	no	—
196	#487	C₂²×C₁₁	1	2	yes	—
197	#487	C₂²×C₁₁	1	2	yes	—
198	#486	—	2	1	no	—
199	#480	—	2	2	no	—
200	#474	C₂²×C₁₁	1	4	yes	—
201	#461	C₂²×C₁₁	1	4	yes	—
202	#448	—	2	2	no	—
203	#436	—	2	1	no	—
204	#436	C₂²×C₁₁	1	2	yes	—
205	C₈×D₄	—	2	1	no	—
206	C₈×D₄	C₂²×C₁₁	1	2	yes	—
207	#431	C₂²×C₁₁	1	1	yes	characteristic
208	#431	C₂²×C₁₁	1	1	yes	characteristic
209	#423	C₂²×C₁₁	1	1	yes	characteristic
210	C₂×#103	—	2	1	no	—
211	C₂×#103	—	2	1	no	—
212	#408	—	2	1	no	—
213	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
214	#335	C₂²×C₁₁	1	2	yes	—
215	#334	C₂²×C₁₁	1	2	yes	—
216	#332	C₂²×C₁₁	1	4	yes	—
217	#332	C₂²×C₁₁	1	4	yes	—
218	C₂²×C₁₁	—	2	1	no	—
219	C₂²×C₁₁	—	2	1	no	—
220	C₂²×C₁₁	—	4	2	no	—
221	C₂²×C₁₁	—	4	2	no	—
222	C₂²×C₁₁	—	4	2	no	—
223	C₂²×C₁₁	#463	1	2	yes	—
224	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
225	C₄×C₁₁	—	2	1	no	—
226	C₄×C₁₁	—	2	1	no	—
227	C₄×C₁₁	—	4	2	no	—
228	C₄×C₁₁	—	8	2	no	—
229	C₄×C₁₁	—	8	2	no	—
230	C₄×C₁₁	#463	1	2	yes	—
231	C₄×C₁₁	#473	1	2	yes	—
232	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
233	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₄×C₁₁	#577	1	2	yes	—
235	C₂×#41	—	2	1	no	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	—	2	1	no	—
238	C₂×SD₁₆	—	2	4	no	—
239	#131	—	4	4	no	—
240	C₂×M₁₆	—	2	1	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
244	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
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	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	D₄×C₁₁	1	1	yes	characteristic
252	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
253	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
254	#127	D₄×C₁₁	1	1	yes	characteristic
255	#124	—	2	1	no	—
256	#121	—	2	1	no	—
257	#121	D₄×C₁₁	1	2	yes	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	C₂³×C₁₁	1	2	yes	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
265	#107	—	2	4	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
268	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
269	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
270	#103	—	2	2	no	—
271	#103	—	2	2	no	—
272	#103	—	2	2	no	—
273	#103	—	2	2	no	—
274	#103	—	2	4	no	—
275	#102	—	2	4	no	—
276	C₂²⋊C₈	—	2	1	no	—
277	C₂²⋊C₈	—	2	1	no	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₂²⋊C₈	—	2	2	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
283	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
286	C₂×C₁₁	—	2	2	no	—
287	C₂×C₁₁	—	8	2	no	—
288	C₂×C₁₁	C₂×#463	1	1	yes	characteristic
289	C₂×C₁₁	#3057	1	1	yes	characteristic
290	C₂×C₁₁	C₂×#473	1	1	yes	characteristic
291	#41	—	4	2	no	—
292	#41	—	4	2	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	—	8	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
310	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
311	SD₁₆	—	8	4	no	—
312	M₁₆	—	4	4	no	—
313	M₁₆	—	4	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	4	4	no	—
320	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
321	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
322	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
323	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
337	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
338	C₄²	C₁₁×#41	1	1	yes	characteristic
339	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
340	C₁₁	#19197	1	1	yes	characteristic, direct product factor, Sylow
341	C₂³	—	2	2	no	—
342	C₂³	C₁₁×#121	1	1	yes	characteristic
343	Q₈	—	4	2	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	4	4	no	—
347	Q₈	—	8	2	no	—
348	Q₈	—	8	2	no	—
349	D₄	—	2	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
363	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
364	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
365	C₂×C₄	C₁₁×#135	1	2	yes	—
366	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
369	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	2	1	no	—
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₈	—	4	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	C₁₁×#463	1	2	yes	—
383	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	8	2	no	—
388	C₄	—	8	2	no	—
389	C₄	C₁₁×#463	1	2	yes	—
390	C₄	C₁₁×#473	1	2	yes	—
391	C₄	C₂×C₁₁×#135	1	1	yes	characteristic
392	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₄	C₁₁×#577	1	2	yes	—
394	C₂	—	2	2	no	—
395	C₂	—	8	2	no	—
396	C₂	C₂×C₁₁×#463	1	1	yes	characteristic
397	C₂	C₁₁×#3057	1	1	yes	characteristic
398	C₂	C₂×C₁₁×#473	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×#487	C₂	semidirect
5. C₁₁×#1699	C₂	semidirect
6. C₁₁×#1679	C₂	semidirect
7. C₁₁×#1564	C₂	semidirect
8. C₁₁×#1549	C₂	semidirect
9. C₁₁×#1546	C₂	semidirect
92. #19197	C₁₁	direct (N × H)
144. C₂×#487	C₂×C₁₁	semidirect
146. #1699	C₂×C₁₁	semidirect
147. #1679	C₂×C₁₁	semidirect
148. #1564	C₂×C₁₁	semidirect
149. #1549	C₂×C₁₁	semidirect
150. #1546	C₂×C₁₁	semidirect
340. C₁₁	#19197	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×#3226	2
C₁₁×#3206	2
C₂×C₁₁×#487	2
C₁₁×#2931	2
C₁₁×#1699	2
C₁₁×#1679	2
C₁₁×#1564	2
C₁₁×#1549	2
C₁₁×#1546	2
#19197	11

Subgroups — C11×#19197 #14596390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19197 #14596390