Subgroups — C₁₁×#23253 #14600446

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×#125	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1939	C₂	1	2	yes	maximal
4	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1916	C₂	1	2	yes	maximal
6	C₁₁×#1916	C₂	1	2	yes	maximal
7	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
8	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₈×C₁₁×C₄⋊C₄	C₂	1	2	yes	maximal
10	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₁×#125	C₄	1	1	yes	characteristic
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
24	C₁₁×#389	C₄	1	1	yes	characteristic
25	C₁₁×#389	C₄	1	1	yes	characteristic
26	C₁₁×#387	C₄	1	2	yes	—
27	C₁₁×#387	C₄	1	2	yes	—
28	C₁₁×#382	C₄	1	1	yes	characteristic
29	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
30	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
31	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄³×C₁₁	C₂²	1	1	yes	characteristic
34	C₁₁×#336	C₂²	1	2	yes	—
35	C₁₁×#336	C₂²	1	1	yes	characteristic
36	C₁₁×#336	C₂²	1	2	yes	—
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	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
47	C₁₁×#125	C₈	1	8	yes	complemented
48	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
65	C₁₁×C₄⋊C₈	—	2	2	no	—
66	C₁₁×C₄⋊C₈	—	2	2	no	—
67	C₁₁×C₄⋊C₈	—	2	4	no	—
68	C₁₁×C₄⋊C₈	—	2	2	no	—
69	C₁₁×C₄⋊C₈	—	4	2	no	—
70	C₁₁×C₄⋊C₈	Q₈	1	4	yes	—
71	C₄×C₈×C₁₁	—	2	4	no	—
72	C₄×C₈×C₁₁	—	2	2	no	—
73	C₄×C₈×C₁₁	—	2	2	no	—
74	C₄×C₈×C₁₁	—	4	2	no	—
75	C₄×C₈×C₁₁	—	4	2	no	—
76	C₁₁×#95	C₂×C₄	1	2	yes	—
77	C₁₁×#95	C₂×C₄	1	2	yes	—
78	C₁₁×#95	C₂×C₄	1	2	yes	—
79	C₁₁×#95	C₂×C₄	1	2	yes	—
80	C₁₁×#95	C₂×C₄	1	2	yes	—
81	C₁₁×#95	C₂×C₄	1	2	yes	—
82	#23253	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
91	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
94	C₂×C₈×C₁₁	—	2	1	no	—
95	C₂×C₈×C₁₁	—	2	1	no	—
96	C₂×C₈×C₁₁	—	2	2	no	—
97	C₂×C₈×C₁₁	—	2	1	no	—
98	C₂×C₈×C₁₁	—	2	1	no	—
99	C₂×C₈×C₁₁	—	2	2	no	—
100	C₂×C₈×C₁₁	—	2	1	no	—
101	C₂×C₈×C₁₁	—	2	1	no	—
102	C₂×C₈×C₁₁	—	2	2	no	—
103	C₂×C₈×C₁₁	—	2	1	no	—
104	C₂×C₈×C₁₁	—	2	2	no	—
105	C₂×C₈×C₁₁	—	2	2	no	—
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	C₂×Q₈	1	4	yes	—
110	C₂×C₈×C₁₁	#41	1	2	yes	—
111	C₂×C₈×C₁₁	#41	1	2	yes	—
112	C₁₁×C₄⋊C₄	—	2	4	no	—
113	C₁₁×C₄⋊C₄	—	2	2	no	—
114	C₁₁×C₄⋊C₄	—	2	2	no	—
115	C₁₁×C₄⋊C₄	—	4	2	no	—
116	C₁₁×C₄⋊C₄	C₂×C₈	1	8	yes	—
117	C₁₁×C₄⋊C₄	C₂×C₈	1	8	yes	—
118	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	—
119	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	—
120	C₄²×C₁₁	—	2	2	no	—
121	C₄²×C₁₁	—	2	2	no	—
122	C₄²×C₁₁	—	2	2	no	—
123	C₄²×C₁₁	—	2	1	no	—
124	C₄²×C₁₁	—	2	1	no	—
125	C₄²×C₁₁	—	2	2	no	—
126	C₄²×C₁₁	—	2	1	no	—
127	C₄²×C₁₁	—	2	2	no	—
128	C₄²×C₁₁	—	2	1	no	—
129	C₄²×C₁₁	—	2	2	no	—
130	C₄²×C₁₁	—	4	1	no	—
131	C₄²×C₁₁	C₂×C₈	1	4	yes	—
132	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
133	C₄²×C₁₁	#41	1	2	yes	—
134	C₄×#125	C₂×C₁₁	1	1	yes	characteristic
135	#1939	C₂×C₁₁	1	1	yes	characteristic
136	#1939	C₂×C₁₁	1	2	yes	—
137	#1939	C₂×C₁₁	1	1	yes	characteristic
138	#1916	C₂×C₁₁	1	2	yes	—
139	#1916	C₂×C₁₁	1	2	yes	—
140	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic
141	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic
142	C₈×C₄⋊C₄	C₂×C₁₁	1	2	yes	—
143	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic
144	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic
145	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₁	—	2	2	no	—
147	C₂×C₄×C₁₁	—	2	1	no	—
148	C₂×C₄×C₁₁	—	2	1	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	2	1	no	—
151	C₂×C₄×C₁₁	—	2	1	no	—
152	C₂×C₄×C₁₁	—	2	1	no	—
153	C₂×C₄×C₁₁	—	2	1	no	—
154	C₂×C₄×C₁₁	—	2	2	no	—
155	C₂×C₄×C₁₁	—	2	1	no	—
156	C₂×C₄×C₁₁	—	2	1	no	—
157	C₂×C₄×C₁₁	—	2	2	no	—
158	C₂×C₄×C₁₁	—	2	2	no	—
159	C₂×C₄×C₁₁	—	2	1	no	—
160	C₂×C₄×C₁₁	—	2	2	no	—
161	C₂×C₄×C₁₁	—	2	1	no	—
162	C₂×C₄×C₁₁	—	2	2	no	—
163	C₂×C₄×C₁₁	—	2	2	no	—
164	C₂×C₄×C₁₁	—	2	2	no	—
165	C₂×C₄×C₁₁	—	2	1	no	—
166	C₂×C₄×C₁₁	—	2	2	no	—
167	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
168	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
169	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
170	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
171	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
172	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
173	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
174	C₂×C₄×C₁₁	#131	1	2	yes	—
175	C₂×C₄×C₁₁	#131	1	2	yes	—
176	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
182	C₈×C₁₁	—	2	2	no	—
183	C₈×C₁₁	—	2	2	no	—
184	C₈×C₁₁	—	2	4	no	—
185	C₈×C₁₁	—	4	1	no	—
186	C₈×C₁₁	—	4	1	no	—
187	C₈×C₁₁	—	4	2	no	—
188	C₂×#125	C₄×C₁₁	1	1	yes	characteristic
189	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
190	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
191	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
193	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
196	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
197	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
198	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
199	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
200	#389	C₄×C₁₁	1	1	yes	characteristic
201	#389	C₄×C₁₁	1	1	yes	characteristic
202	#387	C₄×C₁₁	1	2	yes	—
203	#387	C₄×C₁₁	1	2	yes	—
204	#382	C₄×C₁₁	1	1	yes	characteristic
205	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
206	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
207	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
208	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
209	C₄³	C₂²×C₁₁	1	1	yes	characteristic
210	#336	C₂²×C₁₁	1	2	yes	—
211	#336	C₂²×C₁₁	1	1	yes	characteristic
212	#336	C₂²×C₁₁	1	2	yes	—
213	#336	C₂²×C₁₁	1	2	yes	—
214	#336	C₂²×C₁₁	1	2	yes	—
215	#336	C₂²×C₁₁	1	2	yes	—
216	#336	C₂²×C₁₁	1	1	yes	characteristic
217	C₂²×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
218	C₂²×C₁₁	C₄×#41	1	1	yes	characteristic
219	C₂²×C₁₁	#520	1	1	yes	characteristic
220	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
221	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
222	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
223	C₂²×C₁₁	#568	1	1	yes	characteristic
224	C₄×C₁₁	—	2	2	no	—
225	C₄×C₁₁	—	2	2	no	—
226	C₄×C₁₁	—	2	4	no	—
227	C₄×C₁₁	—	2	2	no	—
228	C₄×C₁₁	—	2	4	no	—
229	C₄×C₁₁	—	2	2	no	—
230	C₄×C₁₁	—	4	1	no	—
231	C₄×C₁₁	—	4	2	no	—
232	C₄×C₁₁	—	4	2	no	—
233	C₄×C₁₁	C₈×Q₈	1	4	yes	—
234	C₄×C₁₁	#552	1	1	yes	characteristic
235	C₄×C₁₁	#553	1	1	yes	characteristic
236	C₄×C₁₁	#554	1	1	yes	characteristic
237	C₄×C₁₁	#557	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
241	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
244	#125	C₈×C₁₁	1	8	yes	complemented
245	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
248	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
249	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
250	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
251	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
253	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
254	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
255	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
256	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
260	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
261	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	4	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	4	2	no	—
267	C₄⋊C₈	Q₈×C₁₁	1	4	yes	—
268	C₄×C₈	—	2	4	no	—
269	C₄×C₈	—	2	2	no	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	—	4	2	no	—
272	C₄×C₈	—	4	2	no	—
273	#95	C₂×C₄×C₁₁	1	2	yes	—
274	#95	C₂×C₄×C₁₁	1	2	yes	—
275	#95	C₂×C₄×C₁₁	1	2	yes	—
276	#95	C₂×C₄×C₁₁	1	2	yes	—
277	#95	C₂×C₄×C₁₁	1	2	yes	—
278	#95	C₂×C₄×C₁₁	1	2	yes	—
279	C₂×C₁₁	#2370	1	1	yes	characteristic
280	C₂×C₁₁	C₂×C₈×Q₈	1	1	yes	characteristic
281	C₂×C₁₁	#2962	1	1	yes	characteristic
282	C₂×C₁₁	C₈×#41	1	1	yes	characteristic
283	C₂×C₁₁	#2969	1	1	yes	characteristic
284	C₂×C₁₁	#2988	1	1	yes	characteristic
285	C₂×C₁₁	#2994	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
296	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	C₂×Q₈×C₁₁	1	4	yes	—
313	C₂×C₈	C₁₁×#41	1	2	yes	—
314	C₂×C₈	C₁₁×#41	1	2	yes	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	C₂×C₈×C₁₁	1	8	yes	—
320	C₄⋊C₄	C₂×C₈×C₁₁	1	8	yes	—
321	C₄⋊C₄	C₂×C₈×C₁₁	1	4	yes	—
322	C₄⋊C₄	C₂×C₈×C₁₁	1	4	yes	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	4	1	no	—
334	C₄²	C₂×C₈×C₁₁	1	4	yes	—
335	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
336	C₄²	C₁₁×#41	1	2	yes	—
337	C₁₁	#23253	1	1	yes	characteristic, direct product factor, Sylow
338	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
361	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
362	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
363	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
364	C₂×C₄	C₂²×C₈×C₁₁	1	4	yes	—
365	C₂×C₄	C₂²×C₈×C₁₁	1	4	yes	—
366	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
367	C₂×C₄	C₁₁×#131	1	2	yes	—
368	C₂×C₄	C₁₁×#131	1	2	yes	—
369	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
370	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
371	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
372	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
373	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	2	2	no	—
377	C₈	—	2	4	no	—
378	C₈	—	4	1	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	2	no	—
381	C₂²	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
382	C₂²	C₄×C₁₁×#41	1	1	yes	characteristic
383	C₂²	C₁₁×#520	1	1	yes	characteristic
384	C₂²	C₂³×C₈×C₁₁	1	1	yes	characteristic
385	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
386	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
387	C₂²	C₁₁×#568	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	4	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	4	no	—
393	C₄	—	2	2	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	C₈×Q₈×C₁₁	1	4	yes	—
398	C₄	C₁₁×#552	1	1	yes	characteristic
399	C₄	C₁₁×#553	1	1	yes	characteristic
400	C₄	C₁₁×#554	1	1	yes	characteristic
401	C₄	C₁₁×#557	1	1	yes	characteristic
402	C₂	C₁₁×#2370	1	1	yes	characteristic
403	C₂	C₂×C₈×Q₈×C₁₁	1	1	yes	characteristic
404	C₂	C₁₁×#2962	1	1	yes	characteristic
405	C₂	C₈×C₁₁×#41	1	1	yes	characteristic
406	C₂	C₁₁×#2969	1	1	yes	characteristic
407	C₂	C₁₁×#2988	1	1	yes	characteristic
408	C₂	C₁₁×#2994	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle, prime radical	C₂³×C₁₁	C₂³×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
47. C₁₁×#125	C₈	semidirect
82. #23253	C₁₁	direct (N × H)
244. #125	C₈×C₁₁	semidirect
337. C₁₁	#23253	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₁×#125	2
C₁₁×#1939	2
C₁₁×#1916	2
C₈×C₁₁×C₄⋊C₄	2
C₄×C₁₁×C₄⋊C₈	2
#23253	11

Subgroups — C11×#23253 #14600446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23253 #14600446