Subgroups — C₁₁×#17943 #14595136

Order 2816.

604 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3108	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2966	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1591	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1590	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1587	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1585	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1573	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1491	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1483	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#529	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#483	C₄	1	1	yes	characteristic
15	C₁₁×#480	C₄	1	1	yes	characteristic
16	C₁₁×#479	C₄	1	2	yes	—
17	C₁₁×#464	C₄	1	2	yes	—
18	C₁₁×#451	C₄	1	1	yes	characteristic
19	C₁₁×#448	C₄	1	1	yes	characteristic
20	C₁₁×#446	—	2	1	no	—
21	C₁₁×#446	—	2	1	no	—
22	C₁₁×#446	C₂²	1	2	yes	—
23	C₁₁×#446	C₂²	1	2	yes	—
24	C₁₁×#446	C₂²	1	1	yes	characteristic
25	C₈×Q₈×C₁₁	C₂²	1	1	yes	characteristic
26	C₄×C₁₁×Q₁₆	C₂²	1	2	yes	—
27	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
28	C₁₁×#436	C₂²	1	1	yes	characteristic
29	C₁₁×#435	—	2	1	no	—
30	C₈×D₄×C₁₁	—	2	1	no	—
31	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
32	C₁₁×#433	—	2	1	no	—
33	C₁₁×#432	C₂²	1	1	yes	characteristic
34	C₁₁×#431	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
36	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₁×#405	—	2	1	no	—
38	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₁₁×#97	—	2	1	no	—
40	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
41	C₁₁×#335	C₂²	1	2	yes	—
42	C₁₁×#334	C₂²	1	2	yes	—
43	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
47	C₁₁×#322	C₂²	1	2	yes	—
48	C₈²×C₁₁	C₂²	1	2	yes	—
49	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₁₁×M₁₆	—	2	1	no	—
53	C₂×C₁₁×M₁₆	—	2	1	no	—
54	C₂²×C₈×C₁₁	—	2	1	no	—
55	C₂²×C₈×C₁₁	—	2	1	no	—
56	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
58	C₁₁×#126	—	2	1	no	—
59	C₁₁×#125	C₂×C₄	1	1	yes	characteristic
60	C₁₁×#124	C₂×C₄	1	1	yes	characteristic
61	C₁₁×#123	—	2	1	no	—
62	C₁₁×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
63	C₁₁×#121	C₂×C₄	1	1	yes	characteristic
64	C₄×Q₈×C₁₁	—	2	1	no	—
65	C₄×Q₈×C₁₁	—	2	1	no	—
66	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
67	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
68	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₁	—	2	1	no	—
70	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
71	C₁₁×#117	—	2	1	no	—
72	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₁	—	2	1	no	—
75	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
76	C₁₁×#107	C₂×C₄	1	2	yes	—
77	C₁₁×#106	C₂×C₄	1	2	yes	—
78	C₁₁×C₄⋊C₈	—	2	2	no	—
79	C₁₁×C₄⋊C₈	—	2	2	no	—
80	C₁₁×C₄⋊C₈	—	2	1	no	—
81	C₁₁×C₄⋊C₈	—	2	1	no	—
82	C₁₁×C₄⋊C₈	—	2	1	no	—
83	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
84	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
85	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₁×#103	C₂×C₄	1	2	yes	—
88	C₁₁×#103	C₂×C₄	1	2	yes	—
89	C₁₁×#103	C₂×C₄	1	2	yes	—
90	C₁₁×#102	C₂×C₄	1	2	yes	—
91	C₁₁×C₂²⋊C₈	—	2	1	no	—
92	C₁₁×C₂²⋊C₈	—	2	1	no	—
93	C₁₁×C₂²⋊C₈	—	2	1	no	—
94	C₁₁×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₁₁×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₁₁×#97	—	2	2	no	—
97	C₁₁×#97	—	2	2	no	—
98	C₁₁×#97	—	2	1	no	—
99	C₁₁×#97	—	2	1	no	—
100	C₁₁×#97	—	2	1	no	—
101	C₄×C₈×C₁₁	—	2	1	no	—
102	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
103	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
104	C₄×C₈×C₁₁	C₂³	1	2	yes	—
105	C₄×C₈×C₁₁	C₂³	1	2	yes	—
106	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
108	#17943	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂×Q₈×C₁₁	—	2	1	no	—
110	C₂×Q₈×C₁₁	—	4	2	no	—
111	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
112	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₄×C₁₁	—	2	1	no	—
114	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₁	—	2	1	no	—
116	C₂²×C₄×C₁₁	—	2	1	no	—
117	C₂²×C₄×C₁₁	—	2	1	no	—
118	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
121	C₁₁×Q₁₆	—	4	2	no	—
122	C₁₁×SD₁₆	—	4	2	no	—
123	C₁₁×M₁₆	—	2	4	no	—
124	C₁₁×M₁₆	—	4	2	no	—
125	C₂×C₈×C₁₁	—	2	2	no	—
126	C₂×C₈×C₁₁	—	2	1	no	—
127	C₂×C₈×C₁₁	—	2	1	no	—
128	C₂×C₈×C₁₁	—	2	2	no	—
129	C₂×C₈×C₁₁	—	2	2	no	—
130	C₂×C₈×C₁₁	—	4	1	no	—
131	C₂×C₈×C₁₁	—	4	2	no	—
132	C₂×C₈×C₁₁	—	4	2	no	—
133	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
139	C₁₁×C₄⋊C₄	—	2	2	no	—
140	C₁₁×C₄⋊C₄	—	2	1	no	—
141	C₁₁×C₄⋊C₄	—	2	1	no	—
142	C₁₁×C₄⋊C₄	—	2	1	no	—
143	C₁₁×C₄⋊C₄	—	2	1	no	—
144	C₁₁×C₄⋊C₄	—	2	2	no	—
145	C₁₁×C₄⋊C₄	—	2	1	no	—
146	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
147	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
148	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
149	C₁₁×C₂²⋊C₄	—	2	1	no	—
150	C₁₁×C₂²⋊C₄	—	2	1	no	—
151	C₁₁×C₂²⋊C₄	—	2	1	no	—
152	C₁₁×C₂²⋊C₄	—	2	1	no	—
153	C₁₁×C₂²⋊C₄	—	2	1	no	—
154	C₄²×C₁₁	—	2	2	no	—
155	C₄²×C₁₁	—	2	1	no	—
156	C₄²×C₁₁	—	2	2	no	—
157	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₁	#41	1	1	yes	characteristic
160	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
161	#3108	C₂×C₁₁	1	1	yes	characteristic
162	#2966	C₂×C₁₁	1	1	yes	characteristic
163	C₂×#446	C₂×C₁₁	1	1	yes	characteristic, complemented
164	#1591	C₂×C₁₁	1	2	yes	complemented
165	#1590	C₂×C₁₁	1	2	yes	complemented
166	#1587	C₂×C₁₁	1	2	yes	complemented
167	#1585	C₂×C₁₁	1	2	yes	complemented
168	#1573	C₂×C₁₁	1	1	yes	characteristic, complemented
169	#1491	C₂×C₁₁	1	1	yes	characteristic, complemented
170	#1483	C₂×C₁₁	1	1	yes	characteristic
171	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
172	C₂³×C₁₁	—	2	1	no	—
173	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
174	Q₈×C₁₁	—	2	2	no	—
175	Q₈×C₁₁	—	2	2	no	—
176	Q₈×C₁₁	—	2	2	no	—
177	Q₈×C₁₁	—	4	2	no	—
178	D₄×C₁₁	—	2	2	no	—
179	D₄×C₁₁	—	4	2	no	—
180	C₂×C₄×C₁₁	—	2	2	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	—	2	1	no	—
183	C₂×C₄×C₁₁	—	2	1	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	2	2	no	—
186	C₂×C₄×C₁₁	—	2	1	no	—
187	C₂×C₄×C₁₁	—	2	1	no	—
188	C₂×C₄×C₁₁	—	2	1	no	—
189	C₂×C₄×C₁₁	—	4	2	no	—
190	C₂×C₄×C₁₁	—	4	2	no	—
191	C₂×C₄×C₁₁	—	4	1	no	—
192	C₂×C₄×C₁₁	—	4	1	no	—
193	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
199	C₈×C₁₁	—	2	4	no	—
200	C₈×C₁₁	—	2	2	no	—
201	C₈×C₁₁	—	2	2	no	—
202	C₈×C₁₁	—	2	1	no	—
203	C₈×C₁₁	—	2	1	no	—
204	C₈×C₁₁	—	2	1	no	—
205	C₈×C₁₁	—	4	1	no	—
206	C₈×C₁₁	—	4	1	no	—
207	C₈×C₁₁	—	4	2	no	—
208	C₈×C₁₁	#137	1	2	yes	—
209	#529	C₂²×C₁₁	1	1	yes	characteristic
210	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
211	#483	C₄×C₁₁	1	1	yes	characteristic
212	#480	C₄×C₁₁	1	1	yes	characteristic
213	#479	C₄×C₁₁	1	2	yes	—
214	#464	C₄×C₁₁	1	2	yes	—
215	#451	C₄×C₁₁	1	1	yes	characteristic
216	#448	C₄×C₁₁	1	1	yes	characteristic
217	#446	—	2	1	no	—
218	#446	—	2	1	no	—
219	#446	C₂²×C₁₁	1	2	yes	—
220	#446	C₂²×C₁₁	1	2	yes	—
221	#446	C₂²×C₁₁	1	1	yes	characteristic
222	C₈×Q₈	C₂²×C₁₁	1	1	yes	characteristic
223	C₄×Q₁₆	C₂²×C₁₁	1	2	yes	—
224	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	—
225	#436	C₂²×C₁₁	1	1	yes	characteristic
226	#435	—	2	1	no	—
227	C₈×D₄	—	2	1	no	—
228	C₈×D₄	C₂²×C₁₁	1	1	yes	characteristic
229	#433	—	2	1	no	—
230	#432	C₂²×C₁₁	1	1	yes	characteristic
231	#431	C₂²×C₁₁	1	1	yes	characteristic
232	C₂×C₄⋊C₈	—	2	1	no	—
233	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
234	#405	—	2	1	no	—
235	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
236	C₂×#97	—	2	1	no	—
237	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
238	#335	C₂²×C₁₁	1	2	yes	—
239	#334	C₂²×C₁₁	1	2	yes	—
240	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	—
241	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	—
242	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	—
243	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
244	#322	C₂²×C₁₁	1	2	yes	—
245	C₈²	C₂²×C₁₁	1	2	yes	—
246	C₂²×C₁₁	—	2	1	no	—
247	C₂²×C₁₁	—	2	1	no	—
248	C₂²×C₁₁	—	4	1	no	—
249	C₂²×C₁₁	—	4	1	no	—
250	C₂²×C₁₁	—	4	1	no	—
251	C₂²×C₁₁	#443	1	2	yes	—
252	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
253	C₄×C₁₁	—	2	1	no	—
254	C₄×C₁₁	—	2	1	no	—
255	C₄×C₁₁	—	2	1	no	—
256	C₄×C₁₁	—	2	1	no	—
257	C₄×C₁₁	—	4	2	no	—
258	C₄×C₁₁	—	4	1	no	—
259	C₄×C₁₁	—	4	1	no	—
260	C₄×C₁₁	—	4	2	no	—
261	C₄×C₁₁	—	4	1	no	—
262	C₄×C₁₁	#568	1	2	yes	—
263	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
264	C₄×C₁₁	#575	1	1	yes	characteristic
265	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
266	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
267	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
273	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
274	#126	—	2	1	no	—
275	#125	C₂×C₄×C₁₁	1	1	yes	characteristic
276	#124	C₂×C₄×C₁₁	1	1	yes	characteristic
277	#123	—	2	1	no	—
278	C₂²⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
279	#121	C₂×C₄×C₁₁	1	1	yes	characteristic
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
283	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
284	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
287	#117	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
292	#107	C₂×C₄×C₁₁	1	2	yes	—
293	#106	C₂×C₄×C₁₁	1	2	yes	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
300	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
301	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
302	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
303	#103	C₂×C₄×C₁₁	1	2	yes	—
304	#103	C₂×C₄×C₁₁	1	2	yes	—
305	#103	C₂×C₄×C₁₁	1	2	yes	—
306	#102	C₂×C₄×C₁₁	1	2	yes	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	2	1	no	—
310	C₂²⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
311	C₂²⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
312	#97	—	2	2	no	—
313	#97	—	2	2	no	—
314	#97	—	2	1	no	—
315	#97	—	2	1	no	—
316	#97	—	2	1	no	—
317	C₄×C₈	—	2	1	no	—
318	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
319	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
320	C₄×C₈	C₂³×C₁₁	1	2	yes	—
321	C₄×C₈	C₂³×C₁₁	1	2	yes	—
322	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
323	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
324	C₂×C₁₁	—	2	2	no	—
325	C₂×C₁₁	—	8	1	no	—
326	C₂×C₁₁	#2930	1	1	yes	characteristic
327	C₂×C₁₁	C₄×#137	1	1	yes	characteristic
328	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
332	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
340	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
341	Q₁₆	—	4	2	no	—
342	SD₁₆	—	4	2	no	—
343	M₁₆	—	2	4	no	—
344	M₁₆	—	4	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	2	no	—
352	C₂×C₈	—	4	2	no	—
353	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
354	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
355	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
356	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
357	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
358	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
367	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
368	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	1	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	2	no	—
377	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
379	C₄²	C₁₁×#41	1	1	yes	characteristic
380	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
381	C₁₁	#17943	1	1	yes	characteristic, direct product factor, Sylow
382	C₂³	—	2	1	no	—
383	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	2	2	no	—
387	Q₈	—	4	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	4	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
404	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
405	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
406	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
408	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
409	C₈	—	2	4	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	1	no	—
413	C₈	—	2	1	no	—
414	C₈	—	2	1	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	2	no	—
418	C₈	C₁₁×#137	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	C₁₁×#443	1	2	yes	—
425	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	1	no	—
435	C₄	C₁₁×#568	1	2	yes	—
436	C₄	C₂×C₁₁×#137	1	1	yes	characteristic
437	C₄	C₁₁×#575	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	8	1	no	—
440	C₂	C₁₁×#2930	1	1	yes	characteristic
441	C₂	C₄×C₁₁×#137	1	1	yes	characteristic
442	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×#121	C₂×C₄
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
3. C₂×C₁₁×#446	C₂	semidirect
4. C₁₁×#1591	C₂	semidirect
5. C₁₁×#1590	C₂	semidirect
6. C₁₁×#1587	C₂	semidirect
7. C₁₁×#1585	C₂	semidirect
8. C₁₁×#1573	C₂	semidirect
9. C₁₁×#1491	C₂	semidirect
11. C₈×C₁₁×M₁₆	C₂	semidirect
108. #17943	C₁₁	direct (N × H)
163. C₂×#446	C₂×C₁₁	semidirect
164. #1591	C₂×C₁₁	semidirect
165. #1590	C₂×C₁₁	semidirect
166. #1587	C₂×C₁₁	semidirect
167. #1585	C₂×C₁₁	semidirect
168. #1573	C₂×C₁₁	semidirect
169. #1491	C₂×C₁₁	semidirect
171. C₈×M₁₆	C₂×C₁₁	semidirect
381. C₁₁	#17943	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×#3108	2
C₁₁×#2966	2
C₂×C₁₁×#446	2
C₁₁×#1591	2
C₁₁×#1590	2
C₁₁×#1587	2
C₁₁×#1585	2
C₁₁×#1573	2
C₁₁×#1491	2
C₁₁×#1483	2
C₈×C₁₁×M₁₆	2
#17943	11

Subgroups — C11×#17943 #14595136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#17943 #14595136