Subgroups — C₁₁×#23150 #14600343

Order 2816.

780 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1984	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1984	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1940	C₂	1	2	yes	maximal
7	C₁₁×#1917	C₂	1	2	yes	maximal
8	C₁₁×#1916	C₂	1	2	yes	maximal
9	C₁₁×#1771	C₂	1	2	yes	maximal
10	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#446	—	2	4	no	—
16	C₈×Q₈×C₁₁	—	2	4	no	—
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×#97	C₂²	1	2	yes	—
24	C₂×C₁₁×#97	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₁₁×#391	C₄	1	1	yes	characteristic
29	C₁₁×#391	C₄	1	1	yes	characteristic
30	C₁₁×#389	C₄	1	2	yes	—
31	C₁₁×#389	C₄	1	2	yes	—
32	C₁₁×#384	C₄	1	1	yes	characteristic
33	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
35	C₄³×C₁₁	C₂²	1	1	yes	characteristic
36	C₁₁×#336	C₂²	1	1	yes	characteristic
37	C₁₁×#336	C₂²	1	2	yes	—
38	C₁₁×#336	C₂²	1	2	yes	—
39	C₁₁×#336	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	1	yes	characteristic
41	C₁₁×#336	C₂²	1	2	yes	—
42	C₁₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
51	C₁₁×C₄⋊Q₈	—	2	4	no	—
52	C₄×Q₈×C₁₁	—	2	2	no	—
53	C₄×Q₈×C₁₁	—	2	2	no	—
54	C₄×Q₈×C₁₁	—	2	2	no	—
55	C₄×Q₈×C₁₁	—	2	2	no	—
56	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
73	C₁₁×C₄⋊C₈	—	2	4	no	—
74	C₁₁×C₄⋊C₈	—	2	4	no	—
75	C₁₁×C₄⋊C₈	—	2	2	no	—
76	C₁₁×C₄⋊C₈	—	2	2	no	—
77	C₁₁×C₄⋊C₈	D₄	1	4	yes	—
78	C₁₁×C₄⋊C₈	Q₈	1	4	yes	complemented
79	C₁₁×#97	—	2	4	no	—
80	C₁₁×#97	—	2	4	no	—
81	C₄×C₈×C₁₁	—	2	4	no	—
82	C₄×C₈×C₁₁	—	2	2	no	—
83	C₄×C₈×C₁₁	—	2	2	no	—
84	C₁₁×#95	C₂×C₄	1	2	yes	—
85	C₁₁×#95	C₂×C₄	1	2	yes	—
86	C₁₁×#95	C₂×C₄	1	2	yes	—
87	C₁₁×#95	C₂×C₄	1	2	yes	—
88	#23150	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂×Q₈×C₁₁	—	2	2	no	—
90	C₂×Q₈×C₁₁	—	2	2	no	—
91	C₂×Q₈×C₁₁	—	2	2	no	—
92	C₂×Q₈×C₁₁	—	2	2	no	—
93	C₂×Q₈×C₁₁	—	2	2	no	—
94	C₂×Q₈×C₁₁	M₁₆	1	4	yes	—
95	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₁₁	—	2	1	no	—
107	C₂×C₈×C₁₁	—	2	1	no	—
108	C₂×C₈×C₁₁	—	2	1	no	—
109	C₂×C₈×C₁₁	—	2	1	no	—
110	C₂×C₈×C₁₁	—	2	2	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	2	1	no	—
113	C₂×C₈×C₁₁	—	2	1	no	—
114	C₂×C₈×C₁₁	—	2	2	no	—
115	C₂×C₈×C₁₁	—	2	2	no	—
116	C₂×C₈×C₁₁	—	2	1	no	—
117	C₂×C₈×C₁₁	—	2	1	no	—
118	C₂×C₈×C₁₁	—	2	1	no	—
119	C₂×C₈×C₁₁	—	2	1	no	—
120	C₂×C₈×C₁₁	—	2	2	no	—
121	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
122	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
123	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
124	C₁₁×C₄⋊C₄	—	2	4	no	—
125	C₁₁×C₄⋊C₄	—	2	2	no	—
126	C₁₁×C₄⋊C₄	—	2	2	no	—
127	C₁₁×C₄⋊C₄	—	2	4	no	—
128	C₁₁×C₄⋊C₄	—	2	4	no	—
129	C₁₁×C₄⋊C₄	—	2	4	no	—
130	C₁₁×C₄⋊C₄	—	2	4	no	—
131	C₁₁×C₄⋊C₄	—	4	2	no	—
132	C₄²×C₁₁	—	2	2	no	—
133	C₄²×C₁₁	—	2	2	no	—
134	C₄²×C₁₁	—	2	2	no	—
135	C₄²×C₁₁	—	2	2	no	—
136	C₄²×C₁₁	—	2	2	no	—
137	C₄²×C₁₁	—	2	2	no	—
138	C₄²×C₁₁	—	2	2	no	—
139	C₄²×C₁₁	—	2	1	no	—
140	C₄²×C₁₁	—	2	1	no	—
141	C₄²×C₁₁	—	4	1	no	—
142	C₄²×C₁₁	C₂×D₄	1	2	yes	—
143	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
144	C₄²×C₁₁	#41	1	2	yes	—
145	C₄²×C₁₁	#41	1	2	yes	—
146	C₂×#446	C₂×C₁₁	1	1	yes	characteristic
147	C₂×C₈×Q₈	C₂×C₁₁	1	1	yes	characteristic
148	C₄×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
149	#1984	C₂×C₁₁	1	1	yes	characteristic
150	#1984	C₂×C₁₁	1	1	yes	characteristic
151	#1940	C₂×C₁₁	1	2	yes	—
152	#1917	C₂×C₁₁	1	2	yes	—
153	#1916	C₂×C₁₁	1	2	yes	—
154	#1771	C₂×C₁₁	1	2	yes	—
155	#1767	C₂×C₁₁	1	1	yes	characteristic
156	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic
157	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
158	Q₈×C₁₁	—	2	8	no	—
159	Q₈×C₁₁	—	4	4	no	—
160	C₂×C₄×C₁₁	—	2	2	no	—
161	C₂×C₄×C₁₁	—	2	1	no	—
162	C₂×C₄×C₁₁	—	2	1	no	—
163	C₂×C₄×C₁₁	—	2	1	no	—
164	C₂×C₄×C₁₁	—	2	1	no	—
165	C₂×C₄×C₁₁	—	2	1	no	—
166	C₂×C₄×C₁₁	—	2	1	no	—
167	C₂×C₄×C₁₁	—	2	2	no	—
168	C₂×C₄×C₁₁	—	2	1	no	—
169	C₂×C₄×C₁₁	—	2	1	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	2	1	no	—
174	C₂×C₄×C₁₁	—	2	2	no	—
175	C₂×C₄×C₁₁	—	2	1	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	—	2	1	no	—
180	C₂×C₄×C₁₁	—	2	2	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
185	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
186	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
187	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
188	C₂×C₄×C₁₁	#131	1	2	yes	—
189	C₂×C₄×C₁₁	#131	1	2	yes	—
190	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
195	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
196	C₈×C₁₁	—	2	4	no	—
197	C₈×C₁₁	—	2	2	no	—
198	C₈×C₁₁	—	2	2	no	—
199	C₈×C₁₁	—	4	1	no	—
200	C₈×C₁₁	—	4	1	no	—
201	C₈×C₁₁	—	4	2	no	—
202	C₂×C₄⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
203	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
204	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
205	#446	—	2	4	no	—
206	C₈×Q₈	—	2	4	no	—
207	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
208	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
209	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
210	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
213	C₂×#97	C₂²×C₁₁	1	2	yes	—
214	C₂×#97	C₂²×C₁₁	1	2	yes	—
215	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
216	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
217	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
218	#391	C₄×C₁₁	1	1	yes	characteristic
219	#391	C₄×C₁₁	1	1	yes	characteristic
220	#389	C₄×C₁₁	1	2	yes	—
221	#389	C₄×C₁₁	1	2	yes	—
222	#384	C₄×C₁₁	1	1	yes	characteristic
223	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
224	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
225	C₄³	C₂²×C₁₁	1	1	yes	characteristic
226	#336	C₂²×C₁₁	1	1	yes	characteristic
227	#336	C₂²×C₁₁	1	2	yes	—
228	#336	C₂²×C₁₁	1	2	yes	—
229	#336	C₂²×C₁₁	1	2	yes	—
230	#336	C₂²×C₁₁	1	1	yes	characteristic
231	#336	C₂²×C₁₁	1	2	yes	—
232	#336	C₂²×C₁₁	1	2	yes	—
233	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
234	C₂²×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
235	C₂²×C₁₁	#519	1	1	yes	characteristic
236	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
237	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
238	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
239	C₂²×C₁₁	#568	1	1	yes	characteristic
240	C₄×C₁₁	—	2	4	no	—
241	C₄×C₁₁	—	2	2	no	—
242	C₄×C₁₁	—	2	2	no	—
243	C₄×C₁₁	—	2	2	no	—
244	C₄×C₁₁	—	2	2	no	—
245	C₄×C₁₁	—	4	2	no	—
246	C₄×C₁₁	—	4	2	no	—
247	C₄×C₁₁	—	4	2	no	—
248	C₄×C₁₁	—	4	1	no	—
249	C₄×C₁₁	#435	1	4	yes	—
250	C₄×C₁₁	#547	1	1	yes	characteristic
251	C₄×C₁₁	D₄×Q₈	1	1	yes	characteristic
252	C₄×C₁₁	#556	1	1	yes	characteristic
253	C₄×C₁₁	#557	1	1	yes	characteristic
254	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
255	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
257	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
260	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
262	C₄⋊Q₈	—	2	4	no	—
263	C₄×Q₈	—	2	2	no	—
264	C₄×Q₈	—	2	2	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
270	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
271	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
272	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
273	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
274	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
275	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
276	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
277	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
278	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
279	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
280	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
281	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
284	C₄⋊C₈	—	2	4	no	—
285	C₄⋊C₈	—	2	4	no	—
286	C₄⋊C₈	—	2	2	no	—
287	C₄⋊C₈	—	2	2	no	—
288	C₄⋊C₈	D₄×C₁₁	1	4	yes	—
289	C₄⋊C₈	Q₈×C₁₁	1	4	yes	complemented
290	#97	—	2	4	no	—
291	#97	—	2	4	no	—
292	C₄×C₈	—	2	4	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	2	2	no	—
295	#95	C₂×C₄×C₁₁	1	2	yes	—
296	#95	C₂×C₄×C₁₁	1	2	yes	—
297	#95	C₂×C₄×C₁₁	1	2	yes	—
298	#95	C₂×C₄×C₁₁	1	2	yes	—
299	C₂×C₁₁	#2365	1	1	yes	characteristic
300	C₂×C₁₁	C₂×#435	1	1	yes	characteristic
301	C₂×C₁₁	#2935	1	1	yes	characteristic
302	C₂×C₁₁	#2960	1	1	yes	characteristic
303	C₂×C₁₁	Q₈×M₁₆	1	1	yes	characteristic
304	C₂×C₁₁	#2984	1	1	yes	characteristic
305	C₂×C₁₁	#2985	1	1	yes	characteristic
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	C₁₁×M₁₆	1	4	yes	—
312	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
313	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
316	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
320	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
321	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
322	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
339	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
340	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	4	1	no	—
359	C₄²	C₂×D₄×C₁₁	1	2	yes	—
360	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
361	C₄²	C₁₁×#41	1	2	yes	—
362	C₄²	C₁₁×#41	1	2	yes	—
363	C₁₁	#23150	1	1	yes	characteristic, direct product factor, Sylow
364	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
365	Q₈	—	2	8	no	—
366	Q₈	—	4	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	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	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
390	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
391	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
392	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
393	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
394	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
395	C₂×C₄	C₁₁×#131	1	2	yes	—
396	C₂×C₄	C₁₁×#131	1	2	yes	—
397	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
398	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
399	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
400	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
401	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
402	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
403	C₈	—	2	4	no	—
404	C₈	—	2	2	no	—
405	C₈	—	2	2	no	—
406	C₈	—	4	1	no	—
407	C₈	—	4	1	no	—
408	C₈	—	4	2	no	—
409	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
410	C₂²	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
411	C₂²	C₁₁×#519	1	1	yes	characteristic
412	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
413	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
414	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
415	C₂²	C₁₁×#568	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	1	no	—
425	C₄	C₁₁×#435	1	4	yes	—
426	C₄	C₁₁×#547	1	1	yes	characteristic
427	C₄	D₄×Q₈×C₁₁	1	1	yes	characteristic
428	C₄	C₁₁×#556	1	1	yes	characteristic
429	C₄	C₁₁×#557	1	1	yes	characteristic
430	C₂	C₁₁×#2365	1	1	yes	characteristic
431	C₂	C₂×C₁₁×#435	1	1	yes	characteristic
432	C₂	C₁₁×#2935	1	1	yes	characteristic
433	C₂	C₁₁×#2960	1	1	yes	characteristic
434	C₂	Q₈×C₁₁×M₁₆	1	1	yes	characteristic
435	C₂	C₁₁×#2984	1	1	yes	characteristic
436	C₂	C₁₁×#2985	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
78. C₁₁×C₄⋊C₈	Q₈	semidirect
88. #23150	C₁₁	direct (N × H)
289. C₄⋊C₈	Q₈×C₁₁	semidirect
363. C₁₁	#23150	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₁×#446	2
C₂×C₈×Q₈×C₁₁	2
C₄×C₁₁×C₄⋊Q₈	2
C₁₁×#1984	2
C₁₁×#1940	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1771	2
C₁₁×#1767	2
C₄×C₁₁×C₄⋊C₈	2
#23150	11

Subgroups — C11×#23150 #14600343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23150 #14600343