Subgroups — C₁₁×#21491 #14598684

Order 2816.

1094 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₁	C₂	1	2	yes	maximal, complemented
2	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2392	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1955	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1924	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1870	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1798	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₁×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
14	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
18	C₈×D₄×C₁₁	—	2	8	no	—
19	C₈×D₄×C₁₁	—	2	4	no	—
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₁₁×#405	—	2	4	no	—
28	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
33	C₁₁×#398	C₄	1	1	yes	characteristic
34	C₁₁×#397	C₄	1	1	yes	characteristic
35	C₁₁×#396	C₄	1	2	yes	—
36	C₁₁×#394	C₄	1	2	yes	—
37	C₁₁×#394	C₄	1	1	yes	characteristic
38	C₁₁×#392	C₄	1	1	yes	characteristic
39	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₁₁×#336	C₂²	1	2	yes	—
42	C₁₁×#336	C₂²	1	2	yes	—
43	C₁₁×#336	C₂²	1	2	yes	—
44	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
48	C₂×C₁₁×M₁₆	—	2	2	no	—
49	C₂×C₁₁×M₁₆	—	2	2	no	—
50	C₂×C₁₁×M₁₆	—	2	2	no	—
51	C₂²×C₈×C₁₁	—	2	2	no	—
52	C₂²×C₈×C₁₁	—	2	2	no	—
53	C₂²×C₈×C₁₁	—	2	4	no	—
54	C₂²×C₈×C₁₁	—	2	4	no	—
55	C₂²×C₈×C₁₁	—	2	4	no	—
56	C₂²×C₈×C₁₁	D₄	1	4	yes	complemented
57	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₁₁	—	2	4	no	—
64	C₄×D₄×C₁₁	—	2	4	no	—
65	C₄×D₄×C₁₁	—	2	2	no	—
66	C₄×D₄×C₁₁	—	2	2	no	—
67	C₁₁×#117	—	2	2	no	—
68	C₁₁×#117	—	2	2	no	—
69	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
77	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
78	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
79	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
80	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
84	C₁₁×C₄⋊C₈	—	2	4	no	—
85	C₁₁×C₄⋊C₈	—	2	2	no	—
86	C₁₁×C₄⋊C₈	—	2	2	no	—
87	C₁₁×C₂²⋊C₈	—	2	4	no	—
88	C₁₁×C₂²⋊C₈	—	2	4	no	—
89	C₁₁×C₂²⋊C₈	—	2	4	no	—
90	C₁₁×C₂²⋊C₈	—	2	4	no	—
91	C₁₁×#97	—	2	2	no	—
92	C₁₁×#97	—	2	2	no	—
93	C₄×C₈×C₁₁	—	2	2	no	—
94	C₄×C₈×C₁₁	—	2	4	no	—
95	C₄×C₈×C₁₁	D₄	1	4	yes	complemented
96	C₁₁×#95	C₂×C₄	1	2	yes	—
97	C₁₁×#95	C₂×C₄	1	2	yes	—
98	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
99	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
100	#21491	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
103	C₂×D₄×C₁₁	—	2	4	no	—
104	C₂×D₄×C₁₁	—	2	4	no	—
105	C₂×D₄×C₁₁	—	2	4	no	—
106	C₂×D₄×C₁₁	—	2	2	no	—
107	C₂×D₄×C₁₁	—	2	4	no	—
108	C₂²×C₄×C₁₁	—	2	1	no	—
109	C₂²×C₄×C₁₁	—	2	1	no	—
110	C₂²×C₄×C₁₁	—	2	1	no	—
111	C₂²×C₄×C₁₁	—	2	1	no	—
112	C₂²×C₄×C₁₁	—	2	2	no	—
113	C₂²×C₄×C₁₁	—	2	2	no	—
114	C₂²×C₄×C₁₁	—	2	2	no	—
115	C₂²×C₄×C₁₁	—	2	2	no	—
116	C₂²×C₄×C₁₁	—	2	2	no	—
117	C₂²×C₄×C₁₁	—	2	2	no	—
118	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₁	#41	1	2	yes	—
128	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
129	C₁₁×M₁₆	—	2	8	no	—
130	C₂×C₈×C₁₁	—	2	8	no	—
131	C₂×C₈×C₁₁	—	2	1	no	—
132	C₂×C₈×C₁₁	—	2	1	no	—
133	C₂×C₈×C₁₁	—	2	2	no	—
134	C₂×C₈×C₁₁	—	2	2	no	—
135	C₂×C₈×C₁₁	—	2	2	no	—
136	C₂×C₈×C₁₁	—	2	1	no	—
137	C₂×C₈×C₁₁	—	2	1	no	—
138	C₂×C₈×C₁₁	—	2	1	no	—
139	C₂×C₈×C₁₁	—	2	1	no	—
140	C₂×C₈×C₁₁	—	2	2	no	—
141	C₂×C₈×C₁₁	—	2	2	no	—
142	C₂×C₈×C₁₁	—	2	2	no	—
143	C₂×C₈×C₁₁	—	4	8	no	—
144	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₁₁	#41	1	2	yes	—
149	C₂×C₈×C₁₁	#41	1	2	yes	—
150	C₁₁×C₄⋊C₄	—	2	2	no	—
151	C₁₁×C₄⋊C₄	—	2	2	no	—
152	C₁₁×C₄⋊C₄	—	2	4	no	—
153	C₁₁×C₄⋊C₄	—	2	2	no	—
154	C₁₁×C₄⋊C₄	—	2	4	no	—
155	C₁₁×C₂²⋊C₄	—	2	4	no	—
156	C₁₁×C₂²⋊C₄	—	2	4	no	—
157	C₁₁×C₂²⋊C₄	—	2	2	no	—
158	C₁₁×C₂²⋊C₄	—	2	2	no	—
159	C₁₁×C₂²⋊C₄	—	2	4	no	—
160	C₁₁×C₂²⋊C₄	—	2	4	no	—
161	C₁₁×C₂²⋊C₄	—	2	4	no	—
162	C₄²×C₁₁	—	2	1	no	—
163	C₄²×C₁₁	—	2	2	no	—
164	C₄²×C₁₁	—	2	1	no	—
165	C₄²×C₁₁	—	2	2	no	—
166	C₄²×C₁₁	C₂×D₄	1	2	yes	—
167	C₄²×C₁₁	#41	1	2	yes	—
168	C₂×C₈×D₄	C₂×C₁₁	1	2	yes	complemented
169	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
170	C₂×#405	C₂×C₁₁	1	1	yes	characteristic, complemented
171	#2392	C₂×C₁₁	1	1	yes	characteristic
172	#1955	C₂×C₁₁	1	1	yes	characteristic, complemented
173	#1940	C₂×C₁₁	1	1	yes	characteristic, complemented
174	#1924	C₂×C₁₁	1	2	yes	complemented
175	#1870	C₂×C₁₁	1	2	yes	complemented
176	#1798	C₂×C₁₁	1	1	yes	characteristic, complemented
177	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
178	C₈×C₂²⋊C₄	C₂×C₁₁	1	2	yes	complemented
179	C₂³×C₁₁	—	2	1	no	—
180	C₂³×C₁₁	—	2	2	no	—
181	C₂³×C₁₁	—	2	2	no	—
182	C₂³×C₁₁	—	2	2	no	—
183	C₂³×C₁₁	—	2	1	no	—
184	C₂³×C₁₁	—	2	2	no	—
185	C₂³×C₁₁	—	2	2	no	—
186	C₂³×C₁₁	—	2	2	no	—
187	C₂³×C₁₁	—	2	2	no	—
188	C₂³×C₁₁	—	2	2	no	—
189	C₂³×C₁₁	C₄×D₄	1	2	yes	—
190	C₂³×C₁₁	#131	1	4	yes	—
191	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
192	D₄×C₁₁	—	2	8	no	—
193	D₄×C₁₁	—	2	16	no	—
194	C₂×C₄×C₁₁	—	2	2	no	—
195	C₂×C₄×C₁₁	—	2	1	no	—
196	C₂×C₄×C₁₁	—	2	1	no	—
197	C₂×C₄×C₁₁	—	2	2	no	—
198	C₂×C₄×C₁₁	—	2	2	no	—
199	C₂×C₄×C₁₁	—	2	2	no	—
200	C₂×C₄×C₁₁	—	2	2	no	—
201	C₂×C₄×C₁₁	—	2	2	no	—
202	C₂×C₄×C₁₁	—	2	2	no	—
203	C₂×C₄×C₁₁	—	2	2	no	—
204	C₂×C₄×C₁₁	—	2	2	no	—
205	C₂×C₄×C₁₁	—	2	1	no	—
206	C₂×C₄×C₁₁	—	2	1	no	—
207	C₂×C₄×C₁₁	—	2	2	no	—
208	C₂×C₄×C₁₁	—	2	2	no	—
209	C₂×C₄×C₁₁	—	2	2	no	—
210	C₂×C₄×C₁₁	—	2	2	no	—
211	C₂×C₄×C₁₁	—	2	2	no	—
212	C₂×C₄×C₁₁	—	2	2	no	—
213	C₂×C₄×C₁₁	—	2	2	no	—
214	C₂×C₄×C₁₁	—	4	2	no	—
215	C₂×C₄×C₁₁	—	4	2	no	—
216	C₂×C₄×C₁₁	—	4	2	no	—
217	C₂×C₄×C₁₁	—	4	2	no	—
218	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
219	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
221	C₂×C₄×C₁₁	#131	1	4	yes	—
222	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
228	C₈×C₁₁	—	2	2	no	—
229	C₈×C₁₁	—	2	2	no	—
230	C₈×C₁₁	—	2	2	no	—
231	C₈×C₁₁	—	4	2	no	—
232	C₈×C₁₁	—	4	2	no	—
233	C₈×C₁₁	#121	1	4	yes	—
234	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
235	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
236	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
237	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
238	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
239	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
240	C₈×D₄	—	2	8	no	—
241	C₈×D₄	—	2	4	no	—
242	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
245	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
246	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
247	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
248	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
249	#405	—	2	4	no	—
250	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
251	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
252	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
253	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
254	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
255	#398	C₄×C₁₁	1	1	yes	characteristic
256	#397	C₄×C₁₁	1	1	yes	characteristic
257	#396	C₄×C₁₁	1	2	yes	—
258	#394	C₄×C₁₁	1	2	yes	—
259	#394	C₄×C₁₁	1	1	yes	characteristic
260	#392	C₄×C₁₁	1	1	yes	characteristic
261	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
262	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
263	#336	C₂²×C₁₁	1	2	yes	—
264	#336	C₂²×C₁₁	1	2	yes	—
265	#336	C₂²×C₁₁	1	2	yes	—
266	C₂²×C₁₁	—	2	4	no	—
267	C₂²×C₁₁	—	2	4	no	—
268	C₂²×C₁₁	—	2	4	no	—
269	C₂²×C₁₁	—	2	4	no	—
270	C₂²×C₁₁	—	2	2	no	—
271	C₂²×C₁₁	—	4	1	no	—
272	C₂²×C₁₁	—	4	2	no	—
273	C₂²×C₁₁	—	4	1	no	—
274	C₂²×C₁₁	—	4	2	no	—
275	C₂²×C₁₁	—	4	2	no	—
276	C₂²×C₁₁	—	4	2	no	—
277	C₂²×C₁₁	—	4	2	no	—
278	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
280	C₂²×C₁₁	C₄×#41	1	1	yes	characteristic
281	C₂²×C₁₁	C₂×#131	1	2	yes	—
282	C₂²×C₁₁	C₂×#131	1	2	yes	—
283	C₄×C₁₁	—	2	2	no	—
284	C₄×C₁₁	—	2	4	no	—
285	C₄×C₁₁	—	2	2	no	—
286	C₄×C₁₁	—	2	2	no	—
287	C₄×C₁₁	—	4	2	no	—
288	C₄×C₁₁	—	4	1	no	—
289	C₄×C₁₁	—	4	1	no	—
290	C₄×C₁₁	—	4	2	no	—
291	C₄×C₁₁	C₂×#121	1	1	yes	characteristic
292	C₄×C₁₁	#525	1	1	yes	characteristic
293	C₄×C₁₁	#529	1	1	yes	characteristic
294	C₄×C₁₁	#532	1	1	yes	characteristic
295	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
296	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
297	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
298	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂²×C₈	—	2	2	no	—
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	—	2	4	no	—
305	C₂²×C₈	—	2	4	no	—
306	C₂²×C₈	—	2	4	no	—
307	C₂²×C₈	D₄×C₁₁	1	4	yes	complemented
308	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
309	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
310	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	—	2	4	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	—	2	2	no	—
318	#117	—	2	2	no	—
319	#117	—	2	2	no	—
320	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
323	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
328	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
329	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
330	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
331	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
332	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
334	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
335	C₄⋊C₈	—	2	4	no	—
336	C₄⋊C₈	—	2	2	no	—
337	C₄⋊C₈	—	2	2	no	—
338	C₂²⋊C₈	—	2	4	no	—
339	C₂²⋊C₈	—	2	4	no	—
340	C₂²⋊C₈	—	2	4	no	—
341	C₂²⋊C₈	—	2	4	no	—
342	#97	—	2	2	no	—
343	#97	—	2	2	no	—
344	C₄×C₈	—	2	2	no	—
345	C₄×C₈	—	2	4	no	—
346	C₄×C₈	D₄×C₁₁	1	4	yes	complemented
347	#95	C₂×C₄×C₁₁	1	2	yes	—
348	#95	C₂×C₄×C₁₁	1	2	yes	—
349	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
350	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
351	C₂×C₁₁	—	4	2	no	—
352	C₂×C₁₁	—	4	4	no	—
353	C₂×C₁₁	C₄×#121	1	1	yes	characteristic
354	C₂×C₁₁	#2929	1	1	yes	characteristic
355	C₂×C₁₁	#2929	1	2	yes	—
356	C₂×C₁₁	#2931	1	1	yes	characteristic
357	C₂×C₁₁	#2966	1	2	yes	—
358	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
359	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
376	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
377	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
378	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
379	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
383	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
384	C₂²×C₄	C₁₁×#41	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
386	M₁₆	—	2	8	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	8	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	4	8	no	—
401	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
402	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
403	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
404	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
405	C₂×C₈	C₁₁×#41	1	2	yes	—
406	C₂×C₈	C₁₁×#41	1	2	yes	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	2	no	—
423	C₄²	C₂×D₄×C₁₁	1	2	yes	—
424	C₄²	C₁₁×#41	1	2	yes	—
425	C₁₁	#21491	1	1	yes	characteristic, direct product factor, Sylow
426	C₂³	—	2	1	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	C₄×D₄×C₁₁	1	2	yes	—
437	C₂³	C₁₁×#131	1	4	yes	—
438	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
439	D₄	—	2	8	no	—
440	D₄	—	2	16	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
466	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
467	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
468	C₂×C₄	C₁₁×#131	1	4	yes	—
469	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
471	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
472	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
473	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
474	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	4	2	no	—
479	C₈	—	4	2	no	—
480	C₈	C₁₁×#121	1	4	yes	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
494	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
495	C₂²	C₄×C₁₁×#41	1	1	yes	characteristic
496	C₂²	C₂×C₁₁×#131	1	2	yes	—
497	C₂²	C₂×C₁₁×#131	1	2	yes	—
498	C₄	—	2	2	no	—
499	C₄	—	2	4	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	1	no	—
505	C₄	—	4	2	no	—
506	C₄	C₂×C₁₁×#121	1	1	yes	characteristic
507	C₄	C₁₁×#525	1	1	yes	characteristic
508	C₄	C₁₁×#529	1	1	yes	characteristic
509	C₄	C₁₁×#532	1	1	yes	characteristic
510	C₂	—	4	2	no	—
511	C₂	—	4	4	no	—
512	C₂	C₄×C₁₁×#121	1	1	yes	characteristic
513	C₂	C₁₁×#2929	1	1	yes	characteristic
514	C₂	C₁₁×#2929	1	2	yes	—
515	C₂	C₁₁×#2931	1	1	yes	characteristic
516	C₂	C₁₁×#2966	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₁	C₂³
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂³×C₁₁	C₂³×C₄
prime radical	C₁₁×#392	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×D₄×C₁₁	C₂	semidirect
2. C₂×C₈×D₄×C₁₁	C₂	semidirect
3. C₂×C₁₁×#405	C₂	semidirect
5. C₁₁×#1955	C₂	semidirect
6. C₁₁×#1940	C₂	semidirect
7. C₁₁×#1924	C₂	semidirect
8. C₁₁×#1870	C₂	semidirect
9. C₁₁×#1798	C₂	semidirect
10. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
11. C₈×C₁₁×C₂²⋊C₄	C₂	semidirect
56. C₂²×C₈×C₁₁	D₄	semidirect
95. C₄×C₈×C₁₁	D₄	semidirect
100. #21491	C₁₁	direct (N × H)
168. C₂×C₈×D₄	C₂×C₁₁	semidirect
169. C₂×C₈×D₄	C₂×C₁₁	semidirect
170. C₂×#405	C₂×C₁₁	semidirect
172. #1955	C₂×C₁₁	semidirect
173. #1940	C₂×C₁₁	semidirect
174. #1924	C₂×C₁₁	semidirect
175. #1870	C₂×C₁₁	semidirect
176. #1798	C₂×C₁₁	semidirect
177. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
178. C₈×C₂²⋊C₄	C₂×C₁₁	semidirect
307. C₂²×C₈	D₄×C₁₁	semidirect
346. C₄×C₈	D₄×C₁₁	semidirect
425. C₁₁	#21491	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×C₈×D₄×C₁₁	2
C₂×C₁₁×#405	2
C₁₁×#2392	2
C₁₁×#1955	2
C₁₁×#1940	2
C₁₁×#1924	2
C₁₁×#1870	2
C₁₁×#1798	2
C₈×C₁₁×C₄⋊C₄	2
C₈×C₁₁×C₂²⋊C₄	2
#21491	11

Subgroups — C11×#21491 #14598684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21491 #14598684