Subgroups — C₁₁×#18085 #14595278

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3167	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2979	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1590	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1588	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1585	C₂	1	2	yes	maximal, complemented
7	C₈×C₁₁×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1485	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1484	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#533	C₂²	1	1	yes	characteristic
13	C₁₁×#532	C₂²	1	1	yes	characteristic
14	C₁₁×#498	C₄	1	1	yes	characteristic
15	C₁₁×#492	C₄	1	1	yes	characteristic
16	C₁₁×#487	C₄	1	1	yes	characteristic
17	C₁₁×#486	C₄	1	1	yes	characteristic
18	C₁₁×#465	C₄	1	2	yes	—
19	C₁₁×#465	C₄	1	2	yes	—
20	C₁₁×#446	—	2	1	no	—
21	C₁₁×#446	C₂²	1	2	yes	—
22	C₈×Q₈×C₁₁	—	2	1	no	—
23	C₈×Q₈×C₁₁	C₂²	1	2	yes	—
24	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
25	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
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×#433	—	2	2	no	—
31	C₁₁×#431	C₂²	1	1	yes	characteristic
32	C₁₁×#431	C₂²	1	1	yes	characteristic
33	C₁₁×#431	C₂²	1	1	yes	characteristic
34	C₁₁×#408	—	2	2	no	—
35	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
37	C₁₁×#335	C₂²	1	1	yes	characteristic
38	C₁₁×#335	C₂²	1	1	yes	characteristic
39	C₁₁×#334	C₂²	1	1	yes	characteristic
40	C₁₁×#334	C₂²	1	1	yes	characteristic
41	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
42	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
44	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
45	C₁₁×#322	C₂²	1	2	yes	—
46	C₈²×C₁₁	C₂²	1	2	yes	—
47	C₂×C₁₁×#41	—	2	1	no	—
48	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₁₁×M₁₆	—	2	1	no	—
51	C₂×C₁₁×M₁₆	—	2	2	no	—
52	C₂²×C₈×C₁₁	—	2	2	no	—
53	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
55	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
56	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
57	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
58	C₁₁×#127	C₂×C₄	1	1	yes	characteristic
59	C₁₁×#125	—	2	1	no	—
60	C₁₁×#124	—	2	1	no	—
61	C₁₁×C₂²⋊Q₈	—	2	1	no	—
62	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
63	C₁₁×#121	—	2	1	no	—
64	C₁₁×#121	C₂×C₄	1	2	yes	—
65	C₄×Q₈×C₁₁	—	2	1	no	—
66	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
67	C₄×D₄×C₁₁	—	2	1	no	—
68	C₄×D₄×C₁₁	C₂³	1	2	yes	—
69	C₁₁×#117	—	2	1	no	—
70	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
71	C₁₁×#106	C₂×C₄	1	2	yes	—
72	C₁₁×#106	C₂×C₄	1	2	yes	—
73	C₁₁×C₄⋊C₈	—	2	2	no	—
74	C₁₁×C₄⋊C₈	—	2	2	no	—
75	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
76	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
77	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₁₁×#103	C₂×C₄	1	2	yes	—
82	C₁₁×#103	C₂×C₄	1	2	yes	—
83	C₁₁×#102	C₂×C₄	1	2	yes	—
84	C₁₁×#102	C₂×C₄	1	2	yes	—
85	C₁₁×C₂²⋊C₈	—	2	1	no	—
86	C₁₁×C₂²⋊C₈	—	2	1	no	—
87	C₁₁×C₂²⋊C₈	—	2	2	no	—
88	C₁₁×C₂²⋊C₈	—	2	2	no	—
89	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
90	C₁₁×#97	—	2	2	no	—
91	C₁₁×#97	—	2	1	no	—
92	C₄×C₈×C₁₁	—	2	2	no	—
93	C₄×C₈×C₁₁	—	2	1	no	—
94	C₄×C₈×C₁₁	—	2	1	no	—
95	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
97	C₄×C₈×C₁₁	C₂³	1	2	yes	—
98	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₁	C₂³	1	2	yes	—
101	#18085	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₁₁×#41	—	8	1	no	—
103	C₁₁×#41	—	8	1	no	—
104	C₂×Q₈×C₁₁	—	2	1	no	—
105	C₂×Q₈×C₁₁	—	2	1	no	—
106	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₁₁	—	2	2	no	—
108	C₂×D₄×C₁₁	—	2	1	no	—
109	C₂×D₄×C₁₁	—	2	1	no	—
110	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₁	—	2	2	no	—
112	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
115	C₁₁×SD₁₆	—	2	4	no	—
116	C₁₁×SD₁₆	—	4	2	no	—
117	C₁₁×M₁₆	—	2	4	no	—
118	C₁₁×M₁₆	—	8	2	no	—
119	C₂×C₈×C₁₁	—	2	2	no	—
120	C₂×C₈×C₁₁	—	2	1	no	—
121	C₂×C₈×C₁₁	—	2	1	no	—
122	C₂×C₈×C₁₁	—	2	1	no	—
123	C₂×C₈×C₁₁	—	2	1	no	—
124	C₂×C₈×C₁₁	—	2	2	no	—
125	C₂×C₈×C₁₁	—	4	1	no	—
126	C₂×C₈×C₁₁	—	8	2	no	—
127	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
133	C₁₁×C₄⋊C₄	—	2	1	no	—
134	C₁₁×C₄⋊C₄	—	2	1	no	—
135	C₁₁×C₄⋊C₄	—	2	1	no	—
136	C₁₁×C₄⋊C₄	—	2	1	no	—
137	C₁₁×C₄⋊C₄	—	2	2	no	—
138	C₁₁×C₄⋊C₄	—	2	2	no	—
139	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
140	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
141	C₁₁×C₂²⋊C₄	—	2	2	no	—
142	C₁₁×C₂²⋊C₄	—	2	2	no	—
143	C₁₁×C₂²⋊C₄	—	2	2	no	—
144	C₄²×C₁₁	—	2	2	no	—
145	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₁	#41	1	1	yes	characteristic
148	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
149	#3167	C₂×C₁₁	1	1	yes	characteristic
150	#2986	C₂×C₁₁	1	1	yes	characteristic, complemented
151	#2979	C₂×C₁₁	1	1	yes	characteristic
152	#1590	C₂×C₁₁	1	2	yes	complemented
153	#1588	C₂×C₁₁	1	2	yes	complemented
154	#1585	C₂×C₁₁	1	2	yes	complemented
155	C₈×SD₁₆	C₂×C₁₁	1	2	yes	complemented
156	#1564	C₂×C₁₁	1	1	yes	characteristic, complemented
157	#1485	C₂×C₁₁	1	1	yes	characteristic, complemented
158	#1484	C₂×C₁₁	1	1	yes	characteristic
159	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
160	C₂³×C₁₁	—	2	2	no	—
161	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
162	Q₈×C₁₁	—	2	2	no	—
163	Q₈×C₁₁	—	2	2	no	—
164	Q₈×C₁₁	—	4	2	no	—
165	Q₈×C₁₁	—	8	1	no	—
166	D₄×C₁₁	—	2	2	no	—
167	D₄×C₁₁	—	2	2	no	—
168	D₄×C₁₁	—	4	2	no	—
169	D₄×C₁₁	—	8	1	no	—
170	D₄×C₁₁	—	8	2	no	—
171	C₂×C₄×C₁₁	—	2	1	no	—
172	C₂×C₄×C₁₁	—	2	1	no	—
173	C₂×C₄×C₁₁	—	2	1	no	—
174	C₂×C₄×C₁₁	—	2	1	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	—	2	2	no	—
177	C₂×C₄×C₁₁	—	2	2	no	—
178	C₂×C₄×C₁₁	—	2	2	no	—
179	C₂×C₄×C₁₁	—	4	2	no	—
180	C₂×C₄×C₁₁	—	4	2	no	—
181	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
187	C₈×C₁₁	—	2	4	no	—
188	C₈×C₁₁	—	2	1	no	—
189	C₈×C₁₁	—	2	1	no	—
190	C₈×C₁₁	—	2	1	no	—
191	C₈×C₁₁	—	2	2	no	—
192	C₈×C₁₁	—	2	2	no	—
193	C₈×C₁₁	—	4	1	no	—
194	C₈×C₁₁	—	4	1	no	—
195	C₈×C₁₁	—	4	1	no	—
196	C₈×C₁₁	—	4	1	no	—
197	C₈×C₁₁	#131	1	2	yes	—
198	#533	C₂²×C₁₁	1	1	yes	characteristic
199	#532	C₂²×C₁₁	1	1	yes	characteristic
200	#498	C₄×C₁₁	1	1	yes	characteristic
201	#492	C₄×C₁₁	1	1	yes	characteristic
202	#487	C₄×C₁₁	1	1	yes	characteristic
203	#486	C₄×C₁₁	1	1	yes	characteristic
204	#465	C₄×C₁₁	1	2	yes	—
205	#465	C₄×C₁₁	1	2	yes	—
206	#446	—	2	1	no	—
207	#446	C₂²×C₁₁	1	2	yes	—
208	C₈×Q₈	—	2	1	no	—
209	C₈×Q₈	C₂²×C₁₁	1	2	yes	—
210	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	—
211	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	—
212	#436	—	2	1	no	—
213	#436	C₂²×C₁₁	1	2	yes	—
214	C₈×D₄	—	2	1	no	—
215	C₈×D₄	C₂²×C₁₁	1	2	yes	—
216	#433	—	2	2	no	—
217	#431	C₂²×C₁₁	1	1	yes	characteristic
218	#431	C₂²×C₁₁	1	1	yes	characteristic
219	#431	C₂²×C₁₁	1	1	yes	characteristic
220	#408	—	2	2	no	—
221	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
223	#335	C₂²×C₁₁	1	1	yes	characteristic
224	#335	C₂²×C₁₁	1	1	yes	characteristic
225	#334	C₂²×C₁₁	1	1	yes	characteristic
226	#334	C₂²×C₁₁	1	1	yes	characteristic
227	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	—
228	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	—
229	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
230	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
231	#322	C₂²×C₁₁	1	2	yes	—
232	C₈²	C₂²×C₁₁	1	2	yes	—
233	C₂²×C₁₁	—	2	1	no	—
234	C₂²×C₁₁	—	2	1	no	—
235	C₂²×C₁₁	—	2	1	no	—
236	C₂²×C₁₁	—	4	2	no	—
237	C₂²×C₁₁	—	4	2	no	—
238	C₂²×C₁₁	—	4	2	no	—
239	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₁₁	—	2	1	no	—
241	C₄×C₁₁	—	2	1	no	—
242	C₄×C₁₁	—	2	1	no	—
243	C₄×C₁₁	—	4	2	no	—
244	C₄×C₁₁	—	4	2	no	—
245	C₄×C₁₁	—	4	2	no	—
246	C₄×C₁₁	#443	1	2	yes	—
247	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
248	C₄×C₁₁	#568	1	1	yes	characteristic
249	C₄×C₁₁	#577	1	1	yes	characteristic
250	C₄×C₁₁	#577	1	1	yes	characteristic
251	C₂×#41	—	2	1	no	—
252	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
253	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
258	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
259	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
260	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
261	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
262	#127	C₂×C₄×C₁₁	1	1	yes	characteristic
263	#125	—	2	1	no	—
264	#124	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
267	#121	—	2	1	no	—
268	#121	C₂×C₄×C₁₁	1	2	yes	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	C₂³×C₁₁	1	2	yes	—
273	#117	—	2	1	no	—
274	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
275	#106	C₂×C₄×C₁₁	1	2	yes	—
276	#106	C₂×C₄×C₁₁	1	2	yes	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
280	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
281	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
282	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
283	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
284	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
285	#103	C₂×C₄×C₁₁	1	2	yes	—
286	#103	C₂×C₄×C₁₁	1	2	yes	—
287	#102	C₂×C₄×C₁₁	1	2	yes	—
288	#102	C₂×C₄×C₁₁	1	2	yes	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	2	2	no	—
292	C₂²⋊C₈	—	2	2	no	—
293	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
294	#97	—	2	2	no	—
295	#97	—	2	1	no	—
296	C₄×C₈	—	2	2	no	—
297	C₄×C₈	—	2	1	no	—
298	C₄×C₈	—	2	1	no	—
299	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
300	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
301	C₄×C₈	C₂³×C₁₁	1	2	yes	—
302	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
303	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
304	C₄×C₈	C₂³×C₁₁	1	2	yes	—
305	C₂×C₁₁	—	4	1	no	—
306	C₂×C₁₁	—	8	2	no	—
307	C₂×C₁₁	#2935	1	1	yes	characteristic
308	C₂×C₁₁	#2949	1	1	yes	characteristic
309	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
310	#41	—	8	1	no	—
311	#41	—	8	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
322	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
323	SD₁₆	—	2	4	no	—
324	SD₁₆	—	4	2	no	—
325	M₁₆	—	2	4	no	—
326	M₁₆	—	8	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	8	2	no	—
335	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
336	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
337	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
338	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
339	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
340	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
348	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
354	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
355	C₄²	C₁₁×#41	1	1	yes	characteristic
356	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
357	C₁₁	#18085	1	1	yes	characteristic, direct product factor, Sylow
358	C₂³	—	2	2	no	—
359	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	8	1	no	—
364	D₄	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	8	1	no	—
368	D₄	—	8	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
380	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
381	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
382	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
384	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
385	C₈	—	2	4	no	—
386	C₈	—	2	1	no	—
387	C₈	—	2	1	no	—
388	C₈	—	2	1	no	—
389	C₈	—	2	2	no	—
390	C₈	—	2	2	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	1	no	—
395	C₈	C₁₁×#131	1	2	yes	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	C₁₁×#443	1	2	yes	—
410	C₄	C₂×C₁₁×#131	1	1	yes	characteristic
411	C₄	C₁₁×#568	1	1	yes	characteristic
412	C₄	C₁₁×#577	1	1	yes	characteristic
413	C₄	C₁₁×#577	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	8	2	no	—
416	C₂	C₁₁×#2935	1	1	yes	characteristic
417	C₂	C₁₁×#2949	1	1	yes	characteristic
418	C₂	C₂×C₁₁×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₁₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2986	C₂	semidirect
4. C₁₁×#1590	C₂	semidirect
5. C₁₁×#1588	C₂	semidirect
6. C₁₁×#1585	C₂	semidirect
7. C₈×C₁₁×SD₁₆	C₂	semidirect
8. C₁₁×#1564	C₂	semidirect
9. C₁₁×#1485	C₂	semidirect
11. C₈×C₁₁×M₁₆	C₂	semidirect
101. #18085	C₁₁	direct (N × H)
150. #2986	C₂×C₁₁	semidirect
152. #1590	C₂×C₁₁	semidirect
153. #1588	C₂×C₁₁	semidirect
154. #1585	C₂×C₁₁	semidirect
155. C₈×SD₁₆	C₂×C₁₁	semidirect
156. #1564	C₂×C₁₁	semidirect
157. #1485	C₂×C₁₁	semidirect
159. C₈×M₁₆	C₂×C₁₁	semidirect
357. C₁₁	#18085	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×#3167	2
C₁₁×#2986	2
C₁₁×#2979	2
C₁₁×#1590	2
C₁₁×#1588	2
C₁₁×#1585	2
C₈×C₁₁×SD₁₆	2
C₁₁×#1564	2
C₁₁×#1485	2
C₁₁×#1484	2
C₈×C₁₁×M₁₆	2
#18085	11

Subgroups — C11×#18085 #14595278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#18085 #14595278