Subgroups — C₁₁×#17935 #14595128

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3100	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1594	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1586	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1570	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#131	—	2	1	no	—
11	C₂²×C₁₁×M₁₆	—	2	1	no	—
12	C₁₁×#532	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#480	C₄	1	2	yes	—
15	C₁₁×#474	C₄	1	2	yes	—
16	C₁₁×#459	C₄	1	2	yes	—
17	C₁₁×#447	C₄	1	2	yes	—
18	C₄×C₁₁×D₈	C₂²	1	4	yes	—
19	C₁₁×#436	—	2	1	no	—
20	C₁₁×#436	—	2	1	no	—
21	C₁₁×#436	—	2	1	no	—
22	C₁₁×#436	C₂²	1	2	yes	—
23	C₁₁×#436	C₂²	1	2	yes	—
24	C₁₁×#436	C₂²	1	2	yes	complemented
25	C₈×D₄×C₁₁	—	2	1	no	—
26	C₈×D₄×C₁₁	C₂²	1	2	yes	complemented
27	C₁₁×#431	C₂²	1	1	yes	characteristic
28	C₁₁×#431	C₂²	1	1	yes	characteristic
29	C₁₁×#423	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₁₁×#408	—	2	1	no	—
32	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
33	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
34	C₁₁×#334	C₂²	1	4	yes	complemented
35	C₁₁×D₄⋊C₈	C₂²	1	4	yes	—
36	C₁₁×D₄⋊C₈	C₂²	1	4	yes	complemented
37	C₁₁×#322	C₂²	1	2	yes	complemented
38	C₁₁×#322	C₂²	1	2	yes	complemented
39	C₂×C₁₁×#41	—	2	1	no	—
40	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₁	—	2	1	no	—
42	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
43	C₁₁×#131	—	4	4	no	—
44	C₂×C₁₁×M₁₆	—	2	1	no	—
45	C₂×C₁₁×M₁₆	—	2	2	no	—
46	C₂×C₁₁×M₁₆	—	2	2	no	—
47	C₂×C₁₁×M₁₆	—	2	2	no	—
48	C₂×C₁₁×M₁₆	—	4	4	no	—
49	C₂²×C₈×C₁₁	—	2	1	no	—
50	C₂²×C₈×C₁₁	—	2	2	no	—
51	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
53	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₁×#127	C₂×C₄	1	1	yes	characteristic
55	C₁₁×#124	—	2	1	no	—
56	C₁₁×#121	—	2	1	no	—
57	C₁₁×#121	C₂×C₄	1	2	yes	—
58	C₄×D₄×C₁₁	—	2	1	no	—
59	C₄×D₄×C₁₁	—	2	1	no	—
60	C₄×D₄×C₁₁	—	2	1	no	—
61	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
62	C₄×D₄×C₁₁	C₂³	1	2	yes	—
63	C₄×D₄×C₁₁	C₂³	1	2	yes	—
64	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
67	C₁₁×#107	C₂×C₄	1	4	yes	—
68	C₁₁×C₄⋊C₈	—	2	1	no	—
69	C₁₁×C₄⋊C₈	—	2	1	no	—
70	C₁₁×C₄⋊C₈	—	2	1	no	—
71	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
72	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
74	C₁₁×#102	C₂×C₄	1	4	yes	—
75	C₁₁×#102	C₂×C₄	1	4	yes	—
76	C₁₁×C₂²⋊C₈	—	2	1	no	—
77	C₁₁×C₂²⋊C₈	—	2	2	no	—
78	C₁₁×C₂²⋊C₈	—	2	2	no	—
79	C₁₁×C₂²⋊C₈	—	2	2	no	—
80	C₁₁×C₂²⋊C₈	—	2	2	no	—
81	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
82	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₁	C₂³	1	2	yes	—
85	C₄×C₈×C₁₁	C₂³	1	2	yes	—
86	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
88	#17935	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₁	—	2	1	no	—
90	C₁₁×#41	—	4	2	no	—
91	C₁₁×#41	—	4	2	no	—
92	C₂×Q₈×C₁₁	—	2	1	no	—
93	C₂×D₄×C₁₁	—	2	2	no	—
94	C₂×D₄×C₁₁	—	2	1	no	—
95	C₂×D₄×C₁₁	—	2	1	no	—
96	C₂×D₄×C₁₁	—	2	1	no	—
97	C₂×D₄×C₁₁	—	4	2	no	—
98	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
99	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₁	—	2	1	no	—
101	C₂²×C₄×C₁₁	—	2	2	no	—
102	C₂²×C₄×C₁₁	—	2	2	no	—
103	C₂²×C₄×C₁₁	—	2	2	no	—
104	C₂²×C₄×C₁₁	—	4	2	no	—
105	C₂²×C₄×C₁₁	—	4	2	no	—
106	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
109	C₁₁×D₈	—	4	4	no	—
110	C₁₁×M₁₆	—	4	4	no	—
111	C₁₁×M₁₆	—	4	4	no	—
112	C₁₁×M₁₆	—	4	4	no	—
113	C₁₁×M₁₆	—	4	2	no	—
114	C₂×C₈×C₁₁	—	2	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	—	4	2	no	—
121	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
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	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	C₁₁×C₂²⋊C₄	—	2	2	no	—
134	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₁	#41	1	1	yes	characteristic
137	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
138	#3100	C₂×C₁₁	1	1	yes	characteristic
139	#2931	C₂×C₁₁	1	1	yes	characteristic, complemented
140	C₂×#436	C₂×C₁₁	1	1	yes	characteristic, complemented
141	#1594	C₂×C₁₁	1	4	yes	complemented
142	#1586	C₂×C₁₁	1	4	yes	complemented
143	#1570	C₂×C₁₁	1	1	yes	characteristic, complemented
144	#1486	C₂×C₁₁	1	1	yes	characteristic, complemented
145	#1480	C₂×C₁₁	1	1	yes	characteristic, complemented
146	#1452	C₂×C₁₁	1	1	yes	characteristic, complemented
147	C₂³×C₁₁	—	2	2	no	—
148	C₂³×C₁₁	—	2	2	no	—
149	C₂³×C₁₁	—	4	2	no	—
150	C₂³×C₁₁	—	4	2	no	—
151	C₂³×C₁₁	—	4	2	no	—
152	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
153	Q₈×C₁₁	—	4	2	no	—
154	D₄×C₁₁	—	2	2	no	—
155	D₄×C₁₁	—	2	4	no	—
156	D₄×C₁₁	—	2	2	no	—
157	D₄×C₁₁	—	4	2	no	—
158	D₄×C₁₁	—	4	2	no	—
159	D₄×C₁₁	—	4	4	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	1	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	—	4	2	no	—
169	C₂×C₄×C₁₁	—	4	2	no	—
170	C₂×C₄×C₁₁	—	4	4	no	—
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	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
176	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
179	C₈×C₁₁	—	2	4	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	C₈×C₁₁	—	4	2	no	—
187	C₂×#131	—	2	1	no	—
188	C₂²×M₁₆	—	2	1	no	—
189	#532	C₂²×C₁₁	1	1	yes	characteristic
190	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
191	#480	C₄×C₁₁	1	2	yes	—
192	#474	C₄×C₁₁	1	2	yes	—
193	#459	C₄×C₁₁	1	2	yes	—
194	#447	C₄×C₁₁	1	2	yes	—
195	C₄×D₈	C₂²×C₁₁	1	4	yes	—
196	#436	—	2	1	no	—
197	#436	—	2	1	no	—
198	#436	—	2	1	no	—
199	#436	C₂²×C₁₁	1	2	yes	—
200	#436	C₂²×C₁₁	1	2	yes	—
201	#436	C₂²×C₁₁	1	2	yes	complemented
202	C₈×D₄	—	2	1	no	—
203	C₈×D₄	C₂²×C₁₁	1	2	yes	complemented
204	#431	C₂²×C₁₁	1	1	yes	characteristic
205	#431	C₂²×C₁₁	1	1	yes	characteristic
206	#423	C₂²×C₁₁	1	1	yes	characteristic
207	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
208	#408	—	2	1	no	—
209	C₂×C₂²⋊C₈	—	2	1	no	—
210	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
211	#334	C₂²×C₁₁	1	4	yes	complemented
212	D₄⋊C₈	C₂²×C₁₁	1	4	yes	—
213	D₄⋊C₈	C₂²×C₁₁	1	4	yes	complemented
214	#322	C₂²×C₁₁	1	2	yes	complemented
215	#322	C₂²×C₁₁	1	2	yes	complemented
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	—	4	2	no	—
222	C₂²×C₁₁	—	4	2	no	—
223	C₂²×C₁₁	—	4	2	no	—
224	C₂²×C₁₁	—	8	4	no	—
225	C₂²×C₁₁	#442	1	2	yes	—
226	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
227	C₄×C₁₁	—	2	1	no	—
228	C₄×C₁₁	—	2	1	no	—
229	C₄×C₁₁	—	2	1	no	—
230	C₄×C₁₁	—	4	2	no	—
231	C₄×C₁₁	—	4	2	no	—
232	C₄×C₁₁	#442	1	2	yes	—
233	C₄×C₁₁	#568	1	2	yes	—
234	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₂×#41	—	2	1	no	—
237	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
238	C₂³×C₄	—	2	1	no	—
239	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
240	#131	—	4	4	no	—
241	C₂×M₁₆	—	2	1	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	4	4	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
249	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
250	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
251	#127	C₂×C₄×C₁₁	1	1	yes	characteristic
252	#124	—	2	1	no	—
253	#121	—	2	1	no	—
254	#121	C₂×C₄×C₁₁	1	2	yes	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
259	C₄×D₄	C₂³×C₁₁	1	2	yes	—
260	C₄×D₄	C₂³×C₁₁	1	2	yes	—
261	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
264	#107	C₂×C₄×C₁₁	1	4	yes	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
269	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
270	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
271	#102	C₂×C₄×C₁₁	1	4	yes	—
272	#102	C₂×C₄×C₁₁	1	4	yes	—
273	C₂²⋊C₈	—	2	1	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	—	2	2	no	—
276	C₂²⋊C₈	—	2	2	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	C₂²⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
279	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
280	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
281	C₄×C₈	C₂³×C₁₁	1	2	yes	—
282	C₄×C₈	C₂³×C₁₁	1	2	yes	—
283	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
285	C₂×C₁₁	—	2	2	no	—
286	C₂×C₁₁	—	8	2	no	—
287	C₂×C₁₁	—	8	2	no	—
288	C₂×C₁₁	#2930	1	1	yes	characteristic
289	C₂×C₁₁	C₂×#442	1	1	yes	characteristic
290	C₂×C₁₁	#2955	1	1	yes	characteristic
291	C₂⁴	—	2	1	no	—
292	#41	—	4	2	no	—
293	#41	—	4	2	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
301	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	C₂²×C₄×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	D₈	—	4	4	no	—
312	M₁₆	—	4	4	no	—
313	M₁₆	—	4	4	no	—
314	M₁₆	—	4	4	no	—
315	M₁₆	—	4	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	4	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
324	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
325	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
331	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₄²	C₂²×C₄×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	#17935	1	1	yes	characteristic, direct product factor, Sylow
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
347	Q₈	—	4	2	no	—
348	D₄	—	2	2	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	4	no	—
354	D₄	—	4	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
366	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
367	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
368	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
369	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
370	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
372	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
373	C₈	—	2	4	no	—
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	8	4	no	—
390	C₂²	C₁₁×#442	1	2	yes	—
391	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	C₁₁×#442	1	2	yes	—
398	C₄	C₁₁×#568	1	2	yes	—
399	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	8	2	no	—
403	C₂	—	8	2	no	—
404	C₂	C₁₁×#2930	1	1	yes	characteristic
405	C₂	C₂×C₁₁×#442	1	1	yes	characteristic
406	C₂	C₁₁×#2955	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×#3100	C₂
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×#2931	C₂	semidirect
3. C₂×C₁₁×#436	C₂	semidirect
4. C₁₁×#1594	C₂	semidirect
5. C₁₁×#1586	C₂	semidirect
6. C₁₁×#1570	C₂	semidirect
7. C₁₁×#1486	C₂	semidirect
8. C₁₁×#1480	C₂	semidirect
9. C₁₁×#1452	C₂	semidirect
24. C₁₁×#436	C₂²	semidirect
26. C₈×D₄×C₁₁	C₂²	semidirect
34. C₁₁×#334	C₂²	semidirect
36. C₁₁×D₄⋊C₈	C₂²	semidirect
37. C₁₁×#322	C₂²	semidirect
38. C₁₁×#322	C₂²	semidirect
88. #17935	C₁₁	direct (N × H)
139. #2931	C₂×C₁₁	semidirect
140. C₂×#436	C₂×C₁₁	semidirect
141. #1594	C₂×C₁₁	semidirect
142. #1586	C₂×C₁₁	semidirect
143. #1570	C₂×C₁₁	semidirect
144. #1486	C₂×C₁₁	semidirect
145. #1480	C₂×C₁₁	semidirect
146. #1452	C₂×C₁₁	semidirect
201. #436	C₂²×C₁₁	semidirect
203. C₈×D₄	C₂²×C₁₁	semidirect
211. #334	C₂²×C₁₁	semidirect
213. D₄⋊C₈	C₂²×C₁₁	semidirect
214. #322	C₂²×C₁₁	semidirect
215. #322	C₂²×C₁₁	semidirect
340. C₁₁	#17935	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×#3100	2
C₁₁×#2931	2
C₂×C₁₁×#436	2
C₁₁×#1594	2
C₁₁×#1586	2
C₁₁×#1570	2
C₁₁×#1486	2
C₁₁×#1480	2
C₁₁×#1452	2
#17935	11

Subgroups — C11×#17935 #14595128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#17935 #14595128