Subgroups — C₁₁×#22835 #14600028

Order 2816.

924 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1954	C₂	1	2	yes	maximal
3	C₁₁×#1923	C₂	1	4	yes	maximal, complemented
4	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1817	C₂	1	2	yes	maximal, complemented
6	C₈×C₁₁×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₁₁×C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×D₄×C₁₁	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₁	C₄	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₁	C₂²	1	2	yes	—
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
16	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
17	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₁	C₂²	1	4	yes	—
19	C₄×C₁₁×C₄⋊C₄	C₄	1	1	yes	characteristic
20	C₄×C₁₁×C₄⋊C₄	C₄	1	1	yes	characteristic
21	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₄×C₁₁×C₂²⋊C₄	C₄	1	2	yes	—
23	C₄×C₁₁×C₂²⋊C₄	C₄	1	2	yes	—
24	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₄³×C₁₁	C₂²	1	1	yes	characteristic
26	C₁₁×#336	C₂²	1	2	yes	—
27	C₁₁×#336	C₂²	1	4	yes	—
28	C₁₁×#336	C₂²	1	1	yes	characteristic
29	C₁₁×#336	C₂²	1	2	yes	—
30	C₁₁×#336	C₂²	1	1	yes	characteristic
31	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
35	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
36	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
37	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
38	C₄×D₄×C₁₁	—	2	4	no	—
39	C₄×D₄×C₁₁	—	2	2	no	—
40	C₄×D₄×C₁₁	—	2	2	no	—
41	C₄×D₄×C₁₁	C₈	1	8	yes	complemented
42	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
46	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₁	—	4	4	no	—
49	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
59	C₁₁×C₄⋊C₈	—	2	4	no	—
60	C₁₁×C₄⋊C₈	—	2	4	no	—
61	C₁₁×C₂²⋊C₈	—	2	8	no	—
62	C₁₁×C₂²⋊C₈	—	4	4	no	—
63	C₄×C₈×C₁₁	—	2	4	no	—
64	C₄×C₈×C₁₁	—	4	4	no	—
65	C₁₁×#95	C₂×C₄	1	2	yes	—
66	C₁₁×#95	C₂×C₄	1	2	yes	—
67	C₁₁×#95	C₂×C₄	1	2	yes	—
68	#22835	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
70	C₂×D₄×C₁₁	—	2	2	no	—
71	C₂×D₄×C₁₁	—	2	2	no	—
72	C₂×D₄×C₁₁	C₂×C₈	1	4	yes	—
73	C₂²×C₄×C₁₁	—	2	4	no	—
74	C₂²×C₄×C₁₁	—	2	4	no	—
75	C₂²×C₄×C₁₁	—	2	4	no	—
76	C₂²×C₄×C₁₁	—	2	2	no	—
77	C₂²×C₄×C₁₁	—	2	2	no	—
78	C₂²×C₄×C₁₁	—	2	4	no	—
79	C₂²×C₄×C₁₁	—	4	2	no	—
80	C₂²×C₄×C₁₁	—	4	2	no	—
81	C₂²×C₄×C₁₁	—	4	2	no	—
82	C₂²×C₄×C₁₁	C₂×C₈	1	8	yes	—
83	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
93	C₂×C₈×C₁₁	—	2	2	no	—
94	C₂×C₈×C₁₁	—	2	2	no	—
95	C₂×C₈×C₁₁	—	2	4	no	—
96	C₂×C₈×C₁₁	—	2	2	no	—
97	C₂×C₈×C₁₁	—	2	4	no	—
98	C₂×C₈×C₁₁	—	2	2	no	—
99	C₂×C₈×C₁₁	—	2	4	no	—
100	C₂×C₈×C₁₁	—	2	2	no	—
101	C₂×C₈×C₁₁	#41	1	4	yes	—
102	C₁₁×C₄⋊C₄	—	2	2	no	—
103	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	—
104	C₁₁×C₄⋊C₄	M₁₆	1	4	yes	—
105	C₁₁×C₂²⋊C₄	—	2	4	no	—
106	C₁₁×C₂²⋊C₄	—	2	4	no	—
107	C₁₁×C₂²⋊C₄	C₂×C₈	1	8	yes	—
108	C₄²×C₁₁	—	2	2	no	—
109	C₄²×C₁₁	—	2	2	no	—
110	C₄²×C₁₁	—	2	2	no	—
111	C₄²×C₁₁	—	2	4	no	—
112	C₄²×C₁₁	—	2	2	no	—
113	C₄²×C₁₁	—	4	2	no	—
114	C₄²×C₁₁	—	4	2	no	—
115	C₄²×C₁₁	—	4	1	no	—
116	C₄²×C₁₁	C₂×C₈	1	4	yes	—
117	C₄²×C₁₁	#41	1	2	yes	—
118	C₄²×C₁₁	#41	1	2	yes	—
119	C₄²×D₄	C₂×C₁₁	1	1	yes	characteristic
120	#1954	C₂×C₁₁	1	2	yes	—
121	#1923	C₂×C₁₁	1	4	yes	complemented
122	#1831	C₂×C₁₁	1	1	yes	characteristic, complemented
123	#1817	C₂×C₁₁	1	2	yes	complemented
124	C₈×C₄⋊C₄	C₂×C₁₁	1	2	yes	complemented
125	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
126	C₄×C₂²⋊C₈	C₂×C₁₁	1	2	yes	complemented
127	C₂³×C₁₁	—	2	2	no	—
128	C₂³×C₁₁	—	2	2	no	—
129	C₂³×C₁₁	—	2	2	no	—
130	C₂³×C₁₁	—	2	2	no	—
131	C₂³×C₁₁	—	2	2	no	—
132	C₂³×C₁₁	—	2	2	no	—
133	C₂³×C₁₁	C₂²×C₈	1	4	yes	—
134	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
135	D₄×C₁₁	—	2	8	no	—
136	C₂×C₄×C₁₁	—	2	1	no	—
137	C₂×C₄×C₁₁	—	2	1	no	—
138	C₂×C₄×C₁₁	—	2	1	no	—
139	C₂×C₄×C₁₁	—	2	2	no	—
140	C₂×C₄×C₁₁	—	2	2	no	—
141	C₂×C₄×C₁₁	—	2	1	no	—
142	C₂×C₄×C₁₁	—	2	1	no	—
143	C₂×C₄×C₁₁	—	2	1	no	—
144	C₂×C₄×C₁₁	—	2	2	no	—
145	C₂×C₄×C₁₁	—	2	1	no	—
146	C₂×C₄×C₁₁	—	2	1	no	—
147	C₂×C₄×C₁₁	—	2	2	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	2	1	no	—
150	C₂×C₄×C₁₁	—	2	2	no	—
151	C₂×C₄×C₁₁	—	2	2	no	—
152	C₂×C₄×C₁₁	—	2	1	no	—
153	C₂×C₄×C₁₁	—	2	1	no	—
154	C₂×C₄×C₁₁	—	4	8	no	—
155	C₂×C₄×C₁₁	—	4	8	no	—
156	C₂×C₄×C₁₁	—	4	4	no	—
157	C₂×C₄×C₁₁	—	4	4	no	—
158	C₂×C₄×C₁₁	#117	1	2	yes	—
159	C₂×C₄×C₁₁	#117	1	2	yes	—
160	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
161	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
162	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
163	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
164	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
165	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
166	C₂×C₄×C₁₁	#131	1	2	yes	—
167	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
169	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
171	C₈×C₁₁	—	2	4	no	—
172	C₈×C₁₁	—	4	2	no	—
173	C₈×C₁₁	—	4	4	no	—
174	C₂×C₄×D₄	C₄×C₁₁	1	1	yes	characteristic
175	C₂×C₄×D₄	C₄×C₁₁	1	1	yes	characteristic
176	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
177	C₂²×C₄²	C₂²×C₁₁	1	2	yes	—
178	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
179	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
180	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
181	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
182	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
183	C₂×C₄×C₈	C₂²×C₁₁	1	4	yes	—
184	C₄×C₄⋊C₄	C₄×C₁₁	1	1	yes	characteristic
185	C₄×C₄⋊C₄	C₄×C₁₁	1	1	yes	characteristic
186	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
187	C₄×C₂²⋊C₄	C₄×C₁₁	1	2	yes	—
188	C₄×C₂²⋊C₄	C₄×C₁₁	1	2	yes	—
189	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
190	C₄³	C₂²×C₁₁	1	1	yes	characteristic
191	#336	C₂²×C₁₁	1	1	yes	characteristic
192	#336	C₂²×C₁₁	1	2	yes	—
193	#336	C₂²×C₁₁	1	4	yes	—
194	#336	C₂²×C₁₁	1	2	yes	—
195	#336	C₂²×C₁₁	1	1	yes	characteristic
196	C₂²×C₁₁	—	2	4	no	—
197	C₂²×C₁₁	—	2	4	no	—
198	C₂²×C₁₁	—	2	4	no	—
199	C₂²×C₁₁	—	4	2	no	—
200	C₂²×C₁₁	—	4	2	no	—
201	C₂²×C₁₁	—	4	2	no	—
202	C₂²×C₁₁	—	4	2	no	—
203	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
204	C₂²×C₁₁	C₄×#41	1	1	yes	characteristic
205	C₂²×C₁₁	#518	1	1	yes	characteristic
206	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
207	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
208	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
209	C₂²×C₁₁	#568	1	1	yes	characteristic
210	C₄×C₁₁	—	2	2	no	—
211	C₄×C₁₁	—	2	2	no	—
212	C₄×C₁₁	—	2	2	no	—
213	C₄×C₁₁	—	2	4	no	—
214	C₄×C₁₁	—	2	2	no	—
215	C₄×C₁₁	—	2	4	no	—
216	C₄×C₁₁	—	4	2	no	—
217	C₄×C₁₁	—	4	1	no	—
218	C₄×C₁₁	#431	1	4	yes	—
219	C₄×C₁₁	#553	1	2	yes	—
220	C₄×C₁₁	#559	1	2	yes	—
221	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
222	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
223	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
224	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
225	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
226	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
227	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
228	C₄×D₄	—	2	4	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	C₈×C₁₁	1	8	yes	complemented
232	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
236	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
237	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
238	C₂×C₄²	—	4	4	no	—
239	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
240	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
242	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
243	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
244	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
248	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
249	C₄⋊C₈	—	2	4	no	—
250	C₄⋊C₈	—	2	4	no	—
251	C₂²⋊C₈	—	2	8	no	—
252	C₂²⋊C₈	—	4	4	no	—
253	C₄×C₈	—	2	4	no	—
254	C₄×C₈	—	4	4	no	—
255	#95	C₂×C₄×C₁₁	1	2	yes	—
256	#95	C₂×C₄×C₁₁	1	2	yes	—
257	#95	C₂×C₄×C₁₁	1	2	yes	—
258	C₂×C₁₁	—	4	4	no	—
259	C₂×C₁₁	#2357	1	1	yes	characteristic
260	C₂×C₁₁	C₂×#431	1	1	yes	characteristic
261	C₂×C₁₁	#2925	1	1	yes	characteristic
262	C₂×C₁₁	C₈×#41	1	1	yes	characteristic
263	C₂×C₁₁	#2971	1	1	yes	characteristic
264	C₂×C₁₁	#2972	1	1	yes	characteristic
265	C₂×C₁₁	#2974	1	1	yes	characteristic
266	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	C₂×C₈×C₁₁	1	4	yes	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	C₂×C₈×C₁₁	1	8	yes	—
280	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
289	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	C₁₁×#41	1	4	yes	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	C₂×C₈×C₁₁	1	4	yes	—
301	C₄⋊C₄	C₁₁×M₁₆	1	4	yes	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	C₂×C₈×C₁₁	1	8	yes	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	4	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	4	2	no	—
311	C₄²	—	4	2	no	—
312	C₄²	—	4	1	no	—
313	C₄²	C₂×C₈×C₁₁	1	4	yes	—
314	C₄²	C₁₁×#41	1	2	yes	—
315	C₄²	C₁₁×#41	1	2	yes	—
316	C₁₁	#22835	1	1	yes	characteristic, direct product factor, Sylow
317	C₂³	—	2	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	C₂²×C₈×C₁₁	1	4	yes	—
324	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
325	D₄	—	2	8	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	4	8	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	C₁₁×#117	1	2	yes	—
349	C₂×C₄	C₁₁×#117	1	2	yes	—
350	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
351	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
352	C₂×C₄	C₂²×C₈×C₁₁	1	4	yes	—
353	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
354	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
355	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
356	C₂×C₄	C₁₁×#131	1	2	yes	—
357	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
358	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
359	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
360	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
361	C₈	—	2	4	no	—
362	C₈	—	4	2	no	—
363	C₈	—	4	4	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
372	C₂²	C₄×C₁₁×#41	1	1	yes	characteristic
373	C₂²	C₁₁×#518	1	1	yes	characteristic
374	C₂²	C₂³×C₈×C₁₁	1	1	yes	characteristic
375	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
376	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
377	C₂²	C₁₁×#568	1	1	yes	characteristic
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	4	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	4	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	2	no	—
386	C₄	C₁₁×#431	1	4	yes	—
387	C₄	C₁₁×#553	1	2	yes	—
388	C₄	C₁₁×#559	1	2	yes	—
389	C₂	—	4	4	no	—
390	C₂	C₁₁×#2357	1	1	yes	characteristic
391	C₂	C₂×C₁₁×#431	1	1	yes	characteristic
392	C₂	C₁₁×#2925	1	1	yes	characteristic
393	C₂	C₈×C₁₁×#41	1	1	yes	characteristic
394	C₂	C₁₁×#2971	1	1	yes	characteristic
395	C₂	C₁₁×#2972	1	1	yes	characteristic
396	C₂	C₁₁×#2974	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1923	C₂	semidirect
4. C₁₁×#1831	C₂	semidirect
5. C₁₁×#1817	C₂	semidirect
6. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
7. C₄×C₁₁×C₄⋊C₈	C₂	semidirect
8. C₄×C₁₁×C₂²⋊C₈	C₂	semidirect
41. C₄×D₄×C₁₁	C₈	semidirect
68. #22835	C₁₁	direct (N × H)
121. #1923	C₂×C₁₁	semidirect
122. #1831	C₂×C₁₁	semidirect
123. #1817	C₂×C₁₁	semidirect
124. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
125. C₄×C₄⋊C₈	C₂×C₁₁	semidirect
126. C₄×C₂²⋊C₈	C₂×C₁₁	semidirect
231. C₄×D₄	C₈×C₁₁	semidirect
316. C₁₁	#22835	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×D₄×C₁₁	2
C₁₁×#1954	2
C₁₁×#1923	2
C₁₁×#1831	2
C₁₁×#1817	2
C₈×C₁₁×C₄⋊C₄	2
C₄×C₁₁×C₄⋊C₈	2
C₄×C₁₁×C₂²⋊C₈	2
#22835	11

Subgroups — C11×#22835 #14600028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22835 #14600028