Subgroups — C₁₁×#22589 #14599782

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×#117	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1916	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1916	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1850	C₂	1	2	yes	maximal
5	C₁₁×#1839	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1817	C₂	1	1	yes	maximal, characteristic
8	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₁₁×C₂²⋊C₄	C₂	1	2	yes	maximal
10	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₁×#336	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
13	C₂×C₁₁×#117	C₄	1	1	yes	characteristic
14	C₂×C₁₁×#117	C₄	1	1	yes	characteristic
15	C₂²×C₄²×C₁₁	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×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
21	C₄×C₁₁×C₄⋊C₄	C₄	1	1	yes	characteristic
22	C₄×C₁₁×C₄⋊C₄	C₄	1	1	yes	characteristic
23	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₄×C₁₁×C₂²⋊C₄	C₄	1	1	yes	characteristic
26	C₄×C₁₁×C₂²⋊C₄	C₄	1	1	yes	characteristic
27	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₁₁×#376	C₄	1	1	yes	characteristic
30	C₁₁×#376	C₄	1	1	yes	characteristic
31	C₄³×C₁₁	C₂²	1	1	yes	characteristic
32	C₄³×C₁₁	C₂²	1	1	yes	characteristic
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	C₁₁×#336	C₂²	1	2	yes	—
38	C₁₁×#336	C₂²	1	2	yes	—
39	C₁₁×#336	C₂²	1	1	yes	characteristic
40	C₁₁×#336	C₂²	1	1	yes	characteristic
41	C₁₁×#336	C₂²	1	1	yes	characteristic
42	C₁₁×#336	C₂²	1	1	yes	characteristic
43	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₁	—	2	4	no	—
47	C₂²×C₈×C₁₁	—	2	4	no	—
48	C₂²×C₈×C₁₁	—	4	2	no	—
49	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
53	C₁₁×#117	—	2	4	no	—
54	C₁₁×#117	C₈	1	8	yes	complemented
55	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₁	—	2	4	no	—
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	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
80	C₁₁×C₄⋊C₈	—	2	4	no	—
81	C₁₁×C₄⋊C₈	—	4	2	no	—
82	C₁₁×C₂²⋊C₈	—	2	4	no	—
83	C₄×C₈×C₁₁	—	2	4	no	—
84	C₄×C₈×C₁₁	—	4	2	no	—
85	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
86	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
87	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
88	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
89	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
90	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
91	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
92	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
93	#22589	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₁	—	2	2	no	—
96	C₂²×C₄×C₁₁	—	2	2	no	—
97	C₂²×C₄×C₁₁	—	2	2	no	—
98	C₂²×C₄×C₁₁	—	2	1	no	—
99	C₂²×C₄×C₁₁	—	2	1	no	—
100	C₂²×C₄×C₁₁	—	2	2	no	—
101	C₂²×C₄×C₁₁	—	2	2	no	—
102	C₂²×C₄×C₁₁	—	4	1	no	—
103	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
104	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	#41	1	4	yes	—
118	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₁₁	—	2	2	no	—
120	C₂×C₈×C₁₁	—	2	2	no	—
121	C₂×C₈×C₁₁	—	2	2	no	—
122	C₂×C₈×C₁₁	—	2	2	no	—
123	C₂×C₈×C₁₁	—	2	2	no	—
124	C₂×C₈×C₁₁	—	2	2	no	—
125	C₂×C₈×C₁₁	—	2	2	no	—
126	C₂×C₈×C₁₁	—	2	2	no	—
127	C₂×C₈×C₁₁	—	2	2	no	—
128	C₂×C₈×C₁₁	—	2	2	no	—
129	C₂×C₈×C₁₁	—	2	2	no	—
130	C₂×C₈×C₁₁	—	4	8	no	—
131	C₂×C₈×C₁₁	#41	1	4	yes	—
132	C₁₁×C₄⋊C₄	—	2	2	no	—
133	C₁₁×C₄⋊C₄	—	2	2	no	—
134	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	complemented
135	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	complemented
136	C₁₁×C₂²⋊C₄	—	2	2	no	—
137	C₁₁×C₂²⋊C₄	C₂×C₈	1	4	yes	—
138	C₁₁×C₂²⋊C₄	C₂×C₈	1	4	yes	—
139	C₁₁×C₂²⋊C₄	M₁₆	1	4	yes	—
140	C₄²×C₁₁	—	2	2	no	—
141	C₄²×C₁₁	—	2	2	no	—
142	C₄²×C₁₁	—	2	2	no	—
143	C₄²×C₁₁	—	2	2	no	—
144	C₄²×C₁₁	—	2	2	no	—
145	C₄²×C₁₁	—	2	2	no	—
146	C₄²×C₁₁	—	2	2	no	—
147	C₄²×C₁₁	—	2	2	no	—
148	C₄²×C₁₁	—	2	2	no	—
149	C₄²×C₁₁	—	2	2	no	—
150	C₄²×C₁₁	—	2	1	no	—
151	C₄²×C₁₁	—	2	1	no	—
152	C₄²×C₁₁	—	2	1	no	—
153	C₄²×C₁₁	—	2	1	no	—
154	C₄²×C₁₁	—	4	1	no	—
155	C₄²×C₁₁	—	4	1	no	—
156	C₄²×C₁₁	C₂×C₈	1	4	yes	complemented
157	C₄²×C₁₁	C₂×C₈	1	4	yes	complemented
158	C₄×#117	C₂×C₁₁	1	1	yes	characteristic
159	#1916	C₂×C₁₁	1	2	yes	complemented
160	#1916	C₂×C₁₁	1	2	yes	complemented
161	#1850	C₂×C₁₁	1	2	yes	—
162	#1839	C₂×C₁₁	1	1	yes	characteristic, complemented
163	#1831	C₂×C₁₁	1	1	yes	characteristic, complemented
164	#1817	C₂×C₁₁	1	1	yes	characteristic
165	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
166	C₈×C₂²⋊C₄	C₂×C₁₁	1	2	yes	—
167	#1744	C₂×C₁₁	1	1	yes	characteristic, complemented
168	C₂×#336	C₂×C₁₁	1	1	yes	characteristic
169	C₂³×C₁₁	—	2	1	no	—
170	C₂³×C₁₁	—	2	1	no	—
171	C₂³×C₁₁	—	2	1	no	—
172	C₂³×C₁₁	—	2	1	no	—
173	C₂³×C₁₁	#117	1	2	yes	—
174	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
175	C₂³×C₁₁	C₂×M₁₆	1	2	yes	—
176	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	—	2	1	no	—
178	C₂×C₄×C₁₁	—	2	1	no	—
179	C₂×C₄×C₁₁	—	2	1	no	—
180	C₂×C₄×C₁₁	—	2	1	no	—
181	C₂×C₄×C₁₁	—	2	1	no	—
182	C₂×C₄×C₁₁	—	2	1	no	—
183	C₂×C₄×C₁₁	—	2	1	no	—
184	C₂×C₄×C₁₁	—	2	1	no	—
185	C₂×C₄×C₁₁	—	2	1	no	—
186	C₂×C₄×C₁₁	—	2	1	no	—
187	C₂×C₄×C₁₁	—	2	1	no	—
188	C₂×C₄×C₁₁	—	2	1	no	—
189	C₂×C₄×C₁₁	—	2	1	no	—
190	C₂×C₄×C₁₁	—	2	1	no	—
191	C₂×C₄×C₁₁	—	2	1	no	—
192	C₂×C₄×C₁₁	—	2	1	no	—
193	C₂×C₄×C₁₁	—	2	1	no	—
194	C₂×C₄×C₁₁	—	2	1	no	—
195	C₂×C₄×C₁₁	—	2	1	no	—
196	C₂×C₄×C₁₁	—	2	1	no	—
197	C₂×C₄×C₁₁	—	2	8	no	—
198	C₂×C₄×C₁₁	—	2	4	no	—
199	C₂×C₄×C₁₁	—	2	4	no	—
200	C₂×C₄×C₁₁	—	2	1	no	—
201	C₂×C₄×C₁₁	—	2	1	no	—
202	C₂×C₄×C₁₁	—	2	1	no	—
203	C₂×C₄×C₁₁	—	2	1	no	—
204	C₂×C₄×C₁₁	—	2	1	no	—
205	C₂×C₄×C₁₁	—	2	1	no	—
206	C₂×C₄×C₁₁	—	2	1	no	—
207	C₂×C₄×C₁₁	—	2	1	no	—
208	C₂×C₄×C₁₁	—	2	1	no	—
209	C₂×C₄×C₁₁	—	4	4	no	—
210	C₂×C₄×C₁₁	#117	1	2	yes	—
211	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
212	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
213	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
214	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
215	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
216	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
217	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
218	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
219	C₂×C₄×C₁₁	#131	1	2	yes	—
220	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
221	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
222	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
224	C₈×C₁₁	—	2	4	no	—
225	C₈×C₁₁	—	4	2	no	—
226	C₈×C₁₁	—	4	2	no	—
227	C₈×C₁₁	—	4	2	no	—
228	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
229	C₂×#117	C₄×C₁₁	1	1	yes	characteristic
230	C₂×#117	C₄×C₁₁	1	1	yes	characteristic
231	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
233	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
234	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
235	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
236	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
237	C₄×C₄⋊C₄	C₄×C₁₁	1	1	yes	characteristic
238	C₄×C₄⋊C₄	C₄×C₁₁	1	1	yes	characteristic
239	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
240	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
241	C₄×C₂²⋊C₄	C₄×C₁₁	1	1	yes	characteristic
242	C₄×C₂²⋊C₄	C₄×C₁₁	1	1	yes	characteristic
243	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
244	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
245	#376	C₄×C₁₁	1	1	yes	characteristic
246	#376	C₄×C₁₁	1	1	yes	characteristic
247	C₄³	C₂²×C₁₁	1	1	yes	characteristic
248	C₄³	C₂²×C₁₁	1	1	yes	characteristic
249	#336	C₂²×C₁₁	1	1	yes	characteristic
250	#336	C₂²×C₁₁	1	1	yes	characteristic
251	#336	C₂²×C₁₁	1	2	yes	—
252	#336	C₂²×C₁₁	1	1	yes	characteristic
253	#336	C₂²×C₁₁	1	2	yes	—
254	#336	C₂²×C₁₁	1	2	yes	—
255	#336	C₂²×C₁₁	1	2	yes	—
256	#336	C₂²×C₁₁	1	2	yes	—
257	#336	C₂²×C₁₁	1	2	yes	—
258	#336	C₂²×C₁₁	1	1	yes	characteristic
259	C₂²×C₁₁	—	2	2	no	—
260	C₂²×C₁₁	—	2	2	no	—
261	C₂²×C₁₁	—	2	2	no	—
262	C₂²×C₁₁	—	2	2	no	—
263	C₂²×C₁₁	—	2	2	no	—
264	C₂²×C₁₁	—	2	2	no	—
265	C₂²×C₁₁	#431	1	4	yes	—
266	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
267	C₂²×C₁₁	C₄×#41	1	1	yes	characteristic
268	C₂²×C₁₁	#520	1	1	yes	characteristic
269	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
270	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
271	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
272	C₂²×C₁₁	#568	1	1	yes	characteristic
273	C₄×C₁₁	—	2	2	no	—
274	C₄×C₁₁	—	2	2	no	—
275	C₄×C₁₁	—	2	2	no	—
276	C₄×C₁₁	—	2	2	no	—
277	C₄×C₁₁	—	2	2	no	—
278	C₄×C₁₁	—	2	2	no	—
279	C₄×C₁₁	—	2	2	no	—
280	C₄×C₁₁	—	2	2	no	—
281	C₄×C₁₁	—	2	2	no	—
282	C₄×C₁₁	—	2	2	no	—
283	C₄×C₁₁	—	4	1	no	—
284	C₄×C₁₁	—	4	1	no	—
285	C₄×C₁₁	—	4	1	no	—
286	C₄×C₁₁	#551	1	2	yes	—
287	C₄×C₁₁	#552	1	2	yes	—
288	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
289	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
291	C₂²×C₈	—	2	4	no	—
292	C₂²×C₈	—	2	4	no	—
293	C₂²×C₈	—	4	2	no	—
294	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
295	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
296	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
297	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
298	#117	—	2	4	no	—
299	#117	C₈×C₁₁	1	8	yes	complemented
300	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
308	C₂×C₄²	—	2	4	no	—
309	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
310	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
311	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
312	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
313	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
314	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
315	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
316	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
317	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
318	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
325	C₄⋊C₈	—	2	4	no	—
326	C₄⋊C₈	—	4	2	no	—
327	C₂²⋊C₈	—	2	4	no	—
328	C₄×C₈	—	2	4	no	—
329	C₄×C₈	—	4	2	no	—
330	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
331	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
332	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
333	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
334	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
335	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
336	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
337	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
338	C₂×C₁₁	—	2	4	no	—
339	C₂×C₁₁	#2343	1	1	yes	characteristic
340	C₂×C₁₁	C₂×#431	1	1	yes	characteristic
341	C₂×C₁₁	#2924	1	1	yes	characteristic
342	C₂×C₁₁	C₈×#41	1	1	yes	characteristic
343	C₂×C₁₁	#2970	1	1	yes	characteristic
344	C₂×C₁₁	#2988	1	1	yes	characteristic
345	C₂×C₁₁	#2990	1	1	yes	characteristic
346	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	C₂×C₈×C₁₁	1	4	yes	—
356	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
357	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
359	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
361	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
362	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
364	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
365	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
366	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
367	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
369	C₂²×C₄	C₁₁×#41	1	4	yes	—
370	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	4	8	no	—
383	C₂×C₈	C₁₁×#41	1	4	yes	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	C₂×C₈×C₁₁	1	4	yes	complemented
387	C₄⋊C₄	C₂×C₈×C₁₁	1	4	yes	complemented
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	C₂×C₈×C₁₁	1	4	yes	—
390	C₂²⋊C₄	C₂×C₈×C₁₁	1	4	yes	—
391	C₂²⋊C₄	C₁₁×M₁₆	1	4	yes	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	4	1	no	—
407	C₄²	—	4	1	no	—
408	C₄²	C₂×C₈×C₁₁	1	4	yes	complemented
409	C₄²	C₂×C₈×C₁₁	1	4	yes	complemented
410	C₁₁	#22589	1	1	yes	characteristic, direct product factor, Sylow
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	C₁₁×#117	1	2	yes	—
416	C₂³	C₂²×C₈×C₁₁	1	2	yes	—
417	C₂³	C₂×C₁₁×M₁₆	1	2	yes	—
418	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	C₁₁×#117	1	2	yes	—
453	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
454	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
455	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
456	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
457	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
458	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
459	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
460	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
461	C₂×C₄	C₁₁×#131	1	2	yes	—
462	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
463	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
464	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
465	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
466	C₈	—	2	4	no	—
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₈	—	4	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	C₁₁×#431	1	4	yes	—
477	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
478	C₂²	C₄×C₁₁×#41	1	1	yes	characteristic
479	C₂²	C₁₁×#520	1	1	yes	characteristic
480	C₂²	C₂³×C₈×C₁₁	1	1	yes	characteristic
481	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
482	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
483	C₂²	C₁₁×#568	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	C₁₁×#551	1	2	yes	—
498	C₄	C₁₁×#552	1	2	yes	—
499	C₂	—	2	4	no	—
500	C₂	C₁₁×#2343	1	1	yes	characteristic
501	C₂	C₂×C₁₁×#431	1	1	yes	characteristic
502	C₂	C₁₁×#2924	1	1	yes	characteristic
503	C₂	C₈×C₁₁×#41	1	1	yes	characteristic
504	C₂	C₁₁×#2970	1	1	yes	characteristic
505	C₂	C₁₁×#2988	1	1	yes	characteristic
506	C₂	C₁₁×#2990	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	C₂⁴×C₁₁	C₂²×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
2. C₁₁×#1916	C₂	semidirect
3. C₁₁×#1916	C₂	semidirect
5. C₁₁×#1839	C₂	semidirect
6. C₁₁×#1831	C₂	semidirect
8. C₄×C₁₁×C₄⋊C₈	C₂	semidirect
10. C₁₁×#1744	C₂	semidirect
54. C₁₁×#117	C₈	semidirect
93. #22589	C₁₁	direct (N × H)
134. C₁₁×C₄⋊C₄	C₂×C₈	semidirect
135. C₁₁×C₄⋊C₄	C₂×C₈	semidirect
156. C₄²×C₁₁	C₂×C₈	semidirect
157. C₄²×C₁₁	C₂×C₈	semidirect
159. #1916	C₂×C₁₁	semidirect
160. #1916	C₂×C₁₁	semidirect
162. #1839	C₂×C₁₁	semidirect
163. #1831	C₂×C₁₁	semidirect
165. C₄×C₄⋊C₈	C₂×C₁₁	semidirect
167. #1744	C₂×C₁₁	semidirect
299. #117	C₈×C₁₁	semidirect
386. C₄⋊C₄	C₂×C₈×C₁₁	semidirect
387. C₄⋊C₄	C₂×C₈×C₁₁	semidirect
408. C₄²	C₂×C₈×C₁₁	semidirect
409. C₄²	C₂×C₈×C₁₁	semidirect
410. C₁₁	#22589	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×#117	2
C₁₁×#1916	2
C₁₁×#1850	2
C₁₁×#1839	2
C₁₁×#1831	2
C₁₁×#1817	2
C₄×C₁₁×C₄⋊C₈	2
C₈×C₁₁×C₂²⋊C₄	2
C₁₁×#1744	2
C₂×C₁₁×#336	2
#22589	11

Subgroups — C11×#22589 #14599782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22589 #14599782