Subgroups — C₁₁×#22234 #14599427

Order 2816.

714 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×#3131	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1962	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1929	C₂	1	4	yes	maximal, complemented
7	C₁₁×#1866	C₂	1	4	yes	maximal, complemented
8	C₁₁×#1848	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#131	C₂²	1	2	yes	—
11	C₁₁×#533	C₂²	1	1	yes	characteristic
12	C₁₁×#532	C₂²	1	1	yes	characteristic
13	C₁₁×#488	C₄	1	4	yes	complemented
14	C₁₁×#487	C₄	1	1	yes	characteristic, complemented
15	C₁₁×#487	C₄	1	1	yes	characteristic, complemented
16	C₁₁×#486	C₄	1	1	yes	characteristic, complemented
17	C₁₁×#486	C₄	1	1	yes	characteristic, complemented
18	C₁₁×#446	—	2	1	no	—
19	C₁₁×#446	—	2	1	no	—
20	C₈×Q₈×C₁₁	—	2	1	no	—
21	C₈×Q₈×C₁₁	—	2	1	no	—
22	C₁₁×#436	—	2	1	no	—
23	C₁₁×#436	—	2	1	no	—
24	C₈×D₄×C₁₁	—	2	1	no	—
25	C₈×D₄×C₁₁	—	2	1	no	—
26	C₂×C₁₁×#108	C₂²	1	4	yes	—
27	C₁₁×#424	C₂²	1	2	yes	—
28	C₁₁×#423	C₂²	1	1	yes	characteristic
29	C₁₁×#423	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×#104	C₂²	1	4	yes	—
31	C₁₁×#416	C₂²	1	4	yes	—
32	C₁₁×#408	C₂²	1	2	yes	—
33	C₁₁×#405	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
36	C₄³×C₁₁	C₂²	1	1	yes	characteristic
37	C₁₁×#339	C₂²	1	4	yes	—
38	C₁₁×#336	C₂²	1	2	yes	—
39	C₁₁×#336	C₂²	1	2	yes	—
40	C₂×C₁₁×#41	C₂³	1	2	yes	—
41	C₁₁×#131	—	4	4	no	—
42	C₂×C₁₁×M₁₆	—	2	2	no	—
43	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
44	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₁	—	2	2	no	—
46	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
49	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
50	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
51	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₁₁×#127	C₂×C₄	1	1	yes	characteristic
53	C₁₁×#125	C₂×C₄	1	2	yes	—
54	C₁₁×#124	C₂×C₄	1	2	yes	—
55	C₁₁×C₂²⋊Q₈	—	2	1	no	—
56	C₁₁×C₂²⋊Q₈	—	2	1	no	—
57	C₁₁×#121	—	2	1	no	—
58	C₁₁×#121	—	2	1	no	—
59	C₄×Q₈×C₁₁	—	2	1	no	—
60	C₄×Q₈×C₁₁	—	2	1	no	—
61	C₄×D₄×C₁₁	—	2	1	no	—
62	C₄×D₄×C₁₁	—	2	1	no	—
63	C₁₁×#117	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₁	—	2	1	no	—
65	C₂×C₄²×C₁₁	—	2	1	no	—
66	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
68	C₁₁×#108	—	4	4	no	—
69	C₁₁×C₄⋊C₈	—	2	2	no	—
70	C₁₁×C₄⋊C₈	—	2	2	no	—
71	C₁₁×C₄⋊C₈	—	2	1	no	—
72	C₁₁×C₄⋊C₈	—	2	1	no	—
73	C₁₁×C₄⋊C₈	—	2	1	no	—
74	C₁₁×C₄⋊C₈	—	2	1	no	—
75	C₁₁×#104	—	4	4	no	—
76	C₁₁×#103	C₂×C₄	1	4	yes	—
77	C₁₁×#103	C₂×C₄	1	4	yes	—
78	C₁₁×#102	C₂×C₄	1	4	yes	—
79	C₁₁×#102	C₂×C₄	1	4	yes	—
80	C₁₁×C₂²⋊C₈	—	2	2	no	—
81	C₁₁×C₂²⋊C₈	—	2	2	no	—
82	C₁₁×#97	—	2	2	no	—
83	C₄×C₈×C₁₁	—	2	2	no	—
84	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
85	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
86	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
87	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
88	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
89	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
90	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
91	#22234	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₁₁×#41	—	2	4	no	—
93	C₁₁×#41	—	2	4	no	—
94	C₂×Q₈×C₁₁	—	2	1	no	—
95	C₂×Q₈×C₁₁	—	2	1	no	—
96	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
97	C₂×D₄×C₁₁	—	2	2	no	—
98	C₂×D₄×C₁₁	—	2	1	no	—
99	C₂×D₄×C₁₁	—	2	1	no	—
100	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₁	—	2	2	no	—
102	C₂²×C₄×C₁₁	—	2	2	no	—
103	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
104	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
106	C₁₁×M₁₆	—	2	4	no	—
107	C₁₁×M₁₆	—	2	4	no	—
108	C₁₁×M₁₆	—	4	4	no	—
109	C₂×C₈×C₁₁	—	2	2	no	—
110	C₂×C₈×C₁₁	—	2	2	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	2	2	no	—
114	C₂×C₈×C₁₁	—	2	2	no	—
115	C₂×C₈×C₁₁	—	4	4	no	—
116	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
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	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
122	C₁₁×C₄⋊C₄	—	2	1	no	—
123	C₁₁×C₄⋊C₄	—	2	1	no	—
124	C₁₁×C₄⋊C₄	—	2	2	no	—
125	C₁₁×C₄⋊C₄	—	2	2	no	—
126	C₁₁×C₄⋊C₄	—	2	1	no	—
127	C₁₁×C₄⋊C₄	—	2	1	no	—
128	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
129	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
130	C₁₁×C₂²⋊C₄	—	2	2	no	—
131	C₁₁×C₂²⋊C₄	—	2	2	no	—
132	C₁₁×C₂²⋊C₄	—	2	2	no	—
133	C₄²×C₁₁	—	2	4	no	—
134	C₄²×C₁₁	—	2	2	no	—
135	C₄²×C₁₁	—	2	2	no	—
136	C₄²×C₁₁	—	2	2	no	—
137	C₄²×C₁₁	—	4	2	no	—
138	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
142	#3131	C₂×C₁₁	1	1	yes	characteristic
143	#2960	C₂×C₁₁	1	1	yes	characteristic, complemented
144	#2931	C₂×C₁₁	1	1	yes	characteristic
145	#1994	C₂×C₁₁	1	1	yes	characteristic, complemented
146	#1962	C₂×C₁₁	1	1	yes	characteristic
147	#1929	C₂×C₁₁	1	4	yes	complemented
148	#1866	C₂×C₁₁	1	4	yes	complemented
149	#1848	C₂×C₁₁	1	1	yes	characteristic, complemented
150	#1744	C₂×C₁₁	1	1	yes	characteristic, complemented
151	C₂³×C₁₁	—	2	2	no	—
152	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
153	Q₈×C₁₁	—	2	4	no	—
154	Q₈×C₁₁	—	4	2	no	—
155	Q₈×C₁₁	—	4	2	no	—
156	D₄×C₁₁	—	2	4	no	—
157	D₄×C₁₁	—	4	4	no	—
158	D₄×C₁₁	—	4	2	no	—
159	D₄×C₁₁	—	4	2	no	—
160	C₂×C₄×C₁₁	—	2	2	no	—
161	C₂×C₄×C₁₁	—	2	2	no	—
162	C₂×C₄×C₁₁	—	2	4	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	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
177	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
178	C₈×C₁₁	—	2	2	no	—
179	C₈×C₁₁	—	2	2	no	—
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	C₂×#131	C₂²×C₁₁	1	2	yes	—
187	#533	C₂²×C₁₁	1	1	yes	characteristic
188	#532	C₂²×C₁₁	1	1	yes	characteristic
189	#488	C₄×C₁₁	1	4	yes	complemented
190	#487	C₄×C₁₁	1	1	yes	characteristic, complemented
191	#487	C₄×C₁₁	1	1	yes	characteristic, complemented
192	#486	C₄×C₁₁	1	1	yes	characteristic, complemented
193	#486	C₄×C₁₁	1	1	yes	characteristic, complemented
194	#446	—	2	1	no	—
195	#446	—	2	1	no	—
196	C₈×Q₈	—	2	1	no	—
197	C₈×Q₈	—	2	1	no	—
198	#436	—	2	1	no	—
199	#436	—	2	1	no	—
200	C₈×D₄	—	2	1	no	—
201	C₈×D₄	—	2	1	no	—
202	C₂×#108	C₂²×C₁₁	1	4	yes	—
203	#424	C₂²×C₁₁	1	2	yes	—
204	#423	C₂²×C₁₁	1	1	yes	characteristic
205	#423	C₂²×C₁₁	1	1	yes	characteristic
206	C₂×#104	C₂²×C₁₁	1	4	yes	—
207	#416	C₂²×C₁₁	1	4	yes	—
208	#408	C₂²×C₁₁	1	2	yes	—
209	#405	C₂²×C₁₁	1	2	yes	—
210	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
211	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
212	C₄³	C₂²×C₁₁	1	1	yes	characteristic
213	#339	C₂²×C₁₁	1	4	yes	—
214	#336	C₂²×C₁₁	1	2	yes	—
215	#336	C₂²×C₁₁	1	2	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	C₂×C₄×D₄	1	1	yes	characteristic
222	C₂²×C₁₁	#542	1	2	yes	—
223	C₄×C₁₁	—	2	1	no	—
224	C₄×C₁₁	—	2	1	no	—
225	C₄×C₁₁	—	4	4	no	—
226	C₄×C₁₁	—	4	2	no	—
227	C₄×C₁₁	—	4	2	no	—
228	C₄×C₁₁	—	4	2	no	—
229	C₄×C₁₁	#443	1	2	yes	—
230	C₄×C₁₁	#444	1	2	yes	—
231	C₄×C₁₁	#520	1	2	yes	—
232	C₄×C₁₁	#535	1	1	yes	characteristic
233	C₄×C₁₁	#536	1	1	yes	characteristic
234	C₂×#41	C₂³×C₁₁	1	2	yes	—
235	#131	—	4	4	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
238	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
241	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
243	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
244	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
245	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
246	#127	C₂×C₄×C₁₁	1	1	yes	characteristic
247	#125	C₂×C₄×C₁₁	1	2	yes	—
248	#124	C₂×C₄×C₁₁	1	2	yes	—
249	C₂²⋊Q₈	—	2	1	no	—
250	C₂²⋊Q₈	—	2	1	no	—
251	#121	—	2	1	no	—
252	#121	—	2	1	no	—
253	C₄×Q₈	—	2	1	no	—
254	C₄×Q₈	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	#117	C₂³×C₁₁	1	2	yes	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	—	2	1	no	—
260	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
261	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
262	#108	—	4	4	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	2	1	no	—
269	#104	—	4	4	no	—
270	#103	C₂×C₄×C₁₁	1	4	yes	—
271	#103	C₂×C₄×C₁₁	1	4	yes	—
272	#102	C₂×C₄×C₁₁	1	4	yes	—
273	#102	C₂×C₄×C₁₁	1	4	yes	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	—	2	2	no	—
276	#97	—	2	2	no	—
277	C₄×C₈	—	2	2	no	—
278	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
279	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
280	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
281	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
282	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
283	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
284	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
285	C₂×C₁₁	—	2	2	no	—
286	C₂×C₁₁	—	8	2	no	—
287	C₂×C₁₁	#2326	1	1	yes	characteristic
288	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
289	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
290	#41	—	2	4	no	—
291	#41	—	2	4	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
302	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
303	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
304	M₁₆	—	2	4	no	—
305	M₁₆	—	2	4	no	—
306	M₁₆	—	4	4	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	4	4	no	—
314	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
315	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
316	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
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	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
327	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₄²	—	2	4	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	4	2	no	—
336	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
337	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
338	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
340	C₁₁	#22234	1	1	yes	characteristic, direct product factor, Sylow
341	C₂³	—	2	2	no	—
342	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
343	Q₈	—	2	4	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	2	no	—
346	D₄	—	2	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	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	C₄×D₄×C₁₁	1	1	yes	characteristic
361	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
362	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
363	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
364	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
365	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
366	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
367	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
368	C₈	—	2	2	no	—
369	C₈	—	2	2	no	—
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	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
382	C₂²	C₁₁×#542	1	2	yes	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	4	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	2	no	—
389	C₄	C₁₁×#443	1	2	yes	—
390	C₄	C₁₁×#444	1	2	yes	—
391	C₄	C₁₁×#520	1	2	yes	—
392	C₄	C₁₁×#535	1	1	yes	characteristic
393	C₄	C₁₁×#536	1	1	yes	characteristic
394	C₂	—	2	2	no	—
395	C₂	—	8	2	no	—
396	C₂	C₁₁×#2326	1	1	yes	characteristic
397	C₂	C₂×C₁₁×#443	1	1	yes	characteristic
398	C₂	C₂×C₁₁×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2960	C₂	semidirect
4. C₁₁×#1994	C₂	semidirect
6. C₁₁×#1929	C₂	semidirect
7. C₁₁×#1866	C₂	semidirect
8. C₁₁×#1848	C₂	semidirect
9. C₁₁×#1744	C₂	semidirect
13. C₁₁×#488	C₄	semidirect
14. C₁₁×#487	C₄	semidirect
15. C₁₁×#487	C₄	semidirect
16. C₁₁×#486	C₄	semidirect
17. C₁₁×#486	C₄	semidirect
91. #22234	C₁₁	direct (N × H)
143. #2960	C₂×C₁₁	semidirect
145. #1994	C₂×C₁₁	semidirect
147. #1929	C₂×C₁₁	semidirect
148. #1866	C₂×C₁₁	semidirect
149. #1848	C₂×C₁₁	semidirect
150. #1744	C₂×C₁₁	semidirect
189. #488	C₄×C₁₁	semidirect
190. #487	C₄×C₁₁	semidirect
191. #487	C₄×C₁₁	semidirect
192. #486	C₄×C₁₁	semidirect
193. #486	C₄×C₁₁	semidirect
340. C₁₁	#22234	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×#3131	2
C₁₁×#2960	2
C₁₁×#2931	2
C₁₁×#1994	2
C₁₁×#1962	2
C₁₁×#1929	2
C₁₁×#1866	2
C₁₁×#1848	2
C₁₁×#1744	2
#22234	11

Subgroups — C11×#22234 #14599427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22234 #14599427