Subgroups — C₁₁×#23371 #14600564

Order 2816.

604 conjugacy classes of subgroups.

The subgroup lattice has 376 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×#1940	C₂	1	2	yes	maximal
3	C₁₁×#1939	C₂	1	2	yes	maximal
4	C₁₁×#1917	C₂	1	2	yes	maximal
5	C₁₁×#1917	C₂	1	2	yes	maximal
6	C₁₁×#1916	C₂	1	2	yes	maximal
7	C₁₁×#1916	C₂	1	2	yes	maximal
8	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₁×#125	C₄	1	1	yes	characteristic
11	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×#97	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
19	C₁₁×#389	C₄	1	1	yes	characteristic
20	C₁₁×#389	C₄	1	1	yes	characteristic
21	C₁₁×#387	C₄	1	2	yes	—
22	C₁₁×#387	C₄	1	2	yes	—
23	C₁₁×#382	C₄	1	1	yes	characteristic
24	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
26	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
28	C₄³×C₁₁	C₂²	1	1	yes	characteristic
29	C₁₁×#336	C₂²	1	2	yes	—
30	C₁₁×#336	C₂²	1	2	yes	—
31	C₁₁×#336	C₂²	1	2	yes	—
32	C₁₁×#336	C₂²	1	2	yes	—
33	C₁₁×#336	C₂²	1	2	yes	—
34	C₁₁×#336	C₂²	1	2	yes	—
35	C₁₁×#336	C₂²	1	2	yes	—
36	C₁₁×#336	C₂²	1	2	yes	—
37	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
41	C₁₁×#125	—	2	4	no	—
42	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
43	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
44	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
45	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
46	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
58	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
59	C₁₁×C₄⋊C₈	—	4	2	no	—
60	C₁₁×C₄⋊C₈	—	4	2	no	—
61	C₁₁×C₄⋊C₈	—	4	1	no	—
62	C₁₁×C₄⋊C₈	—	4	1	no	—
63	C₁₁×C₄⋊C₈	—	4	1	no	—
64	C₁₁×C₄⋊C₈	—	4	1	no	—
65	C₁₁×#97	—	4	2	no	—
66	C₄×C₈×C₁₁	—	4	2	no	—
67	C₁₁×#95	C₂×C₄	1	2	yes	—
68	C₁₁×#95	C₂×C₄	1	2	yes	—
69	C₁₁×#95	C₂×C₄	1	2	yes	—
70	C₁₁×#95	C₂×C₄	1	2	yes	—
71	C₁₁×#95	C₂×C₄	1	2	yes	—
72	C₁₁×#95	C₂×C₄	1	2	yes	—
73	#23371	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
85	C₂×C₈×C₁₁	—	2	2	no	—
86	C₂×C₈×C₁₁	—	2	2	no	—
87	C₂×C₈×C₁₁	—	2	2	no	—
88	C₂×C₈×C₁₁	—	2	2	no	—
89	C₂×C₈×C₁₁	—	2	2	no	—
90	C₂×C₈×C₁₁	—	2	2	no	—
91	C₂×C₈×C₁₁	—	2	2	no	—
92	C₂×C₈×C₁₁	—	2	2	no	—
93	C₂×C₈×C₁₁	—	2	2	no	—
94	C₂×C₈×C₁₁	—	2	2	no	—
95	C₂×C₈×C₁₁	—	2	2	no	—
96	C₂×C₈×C₁₁	—	2	2	no	—
97	C₁₁×C₄⋊C₄	—	2	4	no	—
98	C₁₁×C₄⋊C₄	—	2	4	no	—
99	C₁₁×C₄⋊C₄	—	2	2	no	—
100	C₁₁×C₄⋊C₄	—	2	4	no	—
101	C₁₁×C₄⋊C₄	—	2	4	no	—
102	C₁₁×C₄⋊C₄	—	4	1	no	—
103	C₁₁×C₄⋊C₄	—	4	1	no	—
104	C₁₁×C₄⋊C₄	M₁₆	1	4	yes	—
105	C₄²×C₁₁	—	2	2	no	—
106	C₄²×C₁₁	—	2	2	no	—
107	C₄²×C₁₁	—	2	2	no	—
108	C₄²×C₁₁	—	2	2	no	—
109	C₄²×C₁₁	—	2	2	no	—
110	C₄²×C₁₁	—	2	1	no	—
111	C₄²×C₁₁	—	2	1	no	—
112	C₄²×C₁₁	—	2	1	no	—
113	C₄²×C₁₁	—	2	1	no	—
114	C₄²×C₁₁	—	2	1	no	—
115	C₄²×C₁₁	—	2	1	no	—
116	C₄²×C₁₁	—	2	2	no	—
117	C₄²×C₁₁	—	2	2	no	—
118	C₄²×C₁₁	—	4	1	no	—
119	C₄×#125	C₂×C₁₁	1	1	yes	characteristic
120	#1940	C₂×C₁₁	1	2	yes	—
121	#1939	C₂×C₁₁	1	2	yes	—
122	#1917	C₂×C₁₁	1	2	yes	—
123	#1917	C₂×C₁₁	1	2	yes	—
124	#1916	C₂×C₁₁	1	2	yes	—
125	#1916	C₂×C₁₁	1	2	yes	—
126	#1831	C₂×C₁₁	1	1	yes	characteristic
127	#1831	C₂×C₁₁	1	1	yes	characteristic
128	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₁	—	2	1	no	—
130	C₂×C₄×C₁₁	—	2	2	no	—
131	C₂×C₄×C₁₁	—	2	1	no	—
132	C₂×C₄×C₁₁	—	2	1	no	—
133	C₂×C₄×C₁₁	—	2	2	no	—
134	C₂×C₄×C₁₁	—	2	1	no	—
135	C₂×C₄×C₁₁	—	2	1	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	1	no	—
141	C₂×C₄×C₁₁	—	2	2	no	—
142	C₂×C₄×C₁₁	—	2	2	no	—
143	C₂×C₄×C₁₁	—	2	1	no	—
144	C₂×C₄×C₁₁	—	2	1	no	—
145	C₂×C₄×C₁₁	—	2	2	no	—
146	C₂×C₄×C₁₁	—	2	1	no	—
147	C₂×C₄×C₁₁	—	2	1	no	—
148	C₂×C₄×C₁₁	—	2	1	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	2	no	—
153	C₂×C₄×C₁₁	—	2	2	no	—
154	C₂×C₄×C₁₁	—	2	2	no	—
155	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
156	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
157	C₂×C₄×C₁₁	#131	1	2	yes	—
158	C₂×C₄×C₁₁	#131	1	2	yes	—
159	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
160	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
162	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
163	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
164	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
165	C₈×C₁₁	—	4	2	no	—
166	C₈×C₁₁	—	4	2	no	—
167	C₈×C₁₁	—	4	2	no	—
168	C₈×C₁₁	—	4	2	no	—
169	C₂×#125	C₄×C₁₁	1	1	yes	characteristic
170	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
171	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
172	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
173	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
174	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
175	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
176	C₂×#97	C₂²×C₁₁	1	2	yes	—
177	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
178	#389	C₄×C₁₁	1	1	yes	characteristic
179	#389	C₄×C₁₁	1	1	yes	characteristic
180	#387	C₄×C₁₁	1	2	yes	—
181	#387	C₄×C₁₁	1	2	yes	—
182	#382	C₄×C₁₁	1	1	yes	characteristic
183	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
184	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
185	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
186	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
187	C₄³	C₂²×C₁₁	1	1	yes	characteristic
188	#336	C₂²×C₁₁	1	2	yes	—
189	#336	C₂²×C₁₁	1	2	yes	—
190	#336	C₂²×C₁₁	1	2	yes	—
191	#336	C₂²×C₁₁	1	2	yes	—
192	#336	C₂²×C₁₁	1	2	yes	—
193	#336	C₂²×C₁₁	1	2	yes	—
194	#336	C₂²×C₁₁	1	2	yes	—
195	#336	C₂²×C₁₁	1	2	yes	—
196	C₂²×C₁₁	#519	1	1	yes	characteristic
197	C₂²×C₁₁	#520	1	1	yes	characteristic
198	C₂²×C₁₁	#520	1	1	yes	characteristic
199	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
200	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
201	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
202	C₂²×C₁₁	#568	1	1	yes	characteristic
203	C₄×C₁₁	—	2	2	no	—
204	C₄×C₁₁	—	2	4	no	—
205	C₄×C₁₁	—	2	2	no	—
206	C₄×C₁₁	—	2	2	no	—
207	C₄×C₁₁	—	4	1	no	—
208	C₄×C₁₁	—	4	1	no	—
209	C₄×C₁₁	—	4	1	no	—
210	C₄×C₁₁	—	4	2	no	—
211	C₄×C₁₁	—	4	2	no	—
212	C₄×C₁₁	—	4	2	no	—
213	C₄×C₁₁	#562	1	1	yes	characteristic
214	C₄×C₁₁	#563	1	1	yes	characteristic
215	C₄×C₁₁	#563	1	1	yes	characteristic
216	C₄×C₁₁	#564	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
218	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
219	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
220	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
221	#125	—	2	4	no	—
222	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
223	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
224	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
226	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
227	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
230	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
234	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
238	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
239	C₄⋊C₈	—	4	2	no	—
240	C₄⋊C₈	—	4	2	no	—
241	C₄⋊C₈	—	4	1	no	—
242	C₄⋊C₈	—	4	1	no	—
243	C₄⋊C₈	—	4	1	no	—
244	C₄⋊C₈	—	4	1	no	—
245	#97	—	4	2	no	—
246	C₄×C₈	—	4	2	no	—
247	#95	C₂×C₄×C₁₁	1	2	yes	—
248	#95	C₂×C₄×C₁₁	1	2	yes	—
249	#95	C₂×C₄×C₁₁	1	2	yes	—
250	#95	C₂×C₄×C₁₁	1	2	yes	—
251	#95	C₂×C₄×C₁₁	1	2	yes	—
252	#95	C₂×C₄×C₁₁	1	2	yes	—
253	C₂×C₁₁	#2382	1	1	yes	characteristic
254	C₂×C₁₁	#2983	1	1	yes	characteristic
255	C₂×C₁₁	#2986	1	1	yes	characteristic
256	C₂×C₁₁	#2990	1	1	yes	characteristic
257	C₂×C₁₁	#2991	1	1	yes	characteristic
258	C₂×C₁₁	#2992	1	1	yes	characteristic
259	C₂×C₁₁	#2992	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
266	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
267	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
270	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₄⋊C₄	—	2	4	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄⋊C₄	C₁₁×M₁₆	1	4	yes	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	2	1	no	—
301	C₄²	—	2	1	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	4	1	no	—
305	C₁₁	#23371	1	1	yes	characteristic, direct product factor, Sylow
306	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
334	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
335	C₂×C₄	C₁₁×#131	1	2	yes	—
336	C₂×C₄	C₁₁×#131	1	2	yes	—
337	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
340	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
341	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
342	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
343	C₈	—	4	2	no	—
344	C₈	—	4	2	no	—
345	C₈	—	4	2	no	—
346	C₈	—	4	2	no	—
347	C₂²	C₁₁×#519	1	1	yes	characteristic
348	C₂²	C₁₁×#520	1	1	yes	characteristic
349	C₂²	C₁₁×#520	1	1	yes	characteristic
350	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
351	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
352	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
353	C₂²	C₁₁×#568	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	2	no	—
364	C₄	C₁₁×#562	1	1	yes	characteristic
365	C₄	C₁₁×#563	1	1	yes	characteristic
366	C₄	C₁₁×#563	1	1	yes	characteristic
367	C₄	C₁₁×#564	1	1	yes	characteristic
368	C₂	C₁₁×#2382	1	1	yes	characteristic
369	C₂	C₁₁×#2983	1	1	yes	characteristic
370	C₂	C₁₁×#2986	1	1	yes	characteristic
371	C₂	C₁₁×#2990	1	1	yes	characteristic
372	C₂	C₁₁×#2991	1	1	yes	characteristic
373	C₂	C₁₁×#2992	1	1	yes	characteristic
374	C₂	C₁₁×#2992	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
73. #23371	C₁₁	direct (N × H)
305. C₁₁	#23371	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×#1940	2
C₁₁×#1939	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1831	2
#23371	11

Subgroups — C11×#23371 #14600564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23371 #14600564