Subgroups — C₁₁×#23209 #14600402

Order 2816.

888 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₁×#124	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1984	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1954	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1924	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1924	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1850	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1752	C₂	1	2	yes	maximal, complemented
12	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
13	C₂×C₁₁×#124	C₄	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#446	—	2	4	no	—
17	C₈×D₄×C₁₁	—	2	4	no	—
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×#97	C₂²	1	2	yes	—
27	C₂×C₁₁×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#391	C₄	1	1	yes	characteristic
31	C₁₁×#390	C₄	1	1	yes	characteristic
32	C₁₁×#388	C₄	1	2	yes	—
33	C₁₁×#388	C₄	1	2	yes	—
34	C₁₁×#382	C₄	1	1	yes	characteristic
35	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₄³×C₁₁	C₂²	1	1	yes	characteristic
38	C₁₁×#336	C₂²	1	2	yes	—
39	C₁₁×#336	C₂²	1	1	yes	characteristic
40	C₁₁×#336	C₂²	1	2	yes	—
41	C₁₁×#336	C₂²	1	2	yes	—
42	C₁₁×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
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	1	yes	characteristic
50	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
55	C₁₁×#124	—	2	4	no	—
56	C₄×Q₈×C₁₁	—	2	2	no	—
57	C₄×Q₈×C₁₁	—	2	2	no	—
58	C₄×D₄×C₁₁	—	2	2	no	—
59	C₄×D₄×C₁₁	—	2	2	no	—
60	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
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	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
76	C₁₁×C₄⋊C₈	—	2	4	no	—
77	C₁₁×C₄⋊C₈	—	2	2	no	—
78	C₁₁×C₄⋊C₈	—	2	2	no	—
79	C₁₁×C₄⋊C₈	—	2	2	no	—
80	C₁₁×C₄⋊C₈	D₄	1	4	yes	—
81	C₁₁×C₂²⋊C₈	—	2	4	no	—
82	C₁₁×C₂²⋊C₈	—	2	4	no	—
83	C₁₁×C₂²⋊C₈	—	4	2	no	—
84	C₁₁×#97	—	2	4	no	—
85	C₁₁×#97	—	4	2	no	—
86	C₄×C₈×C₁₁	—	2	2	no	—
87	C₄×C₈×C₁₁	—	2	2	no	—
88	C₁₁×#95	C₂×C₄	1	2	yes	—
89	C₁₁×#95	C₂×C₄	1	2	yes	—
90	C₁₁×#95	C₂×C₄	1	2	yes	—
91	C₁₁×#95	C₂×C₄	1	2	yes	—
92	#23209	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
94	C₂×Q₈×C₁₁	—	2	2	no	—
95	C₂×Q₈×C₁₁	—	2	2	no	—
96	C₂×Q₈×C₁₁	—	2	2	no	—
97	C₂×D₄×C₁₁	—	2	2	no	—
98	C₂×D₄×C₁₁	—	2	2	no	—
99	C₂×D₄×C₁₁	M₁₆	1	4	yes	—
100	C₂²×C₄×C₁₁	—	2	2	no	—
101	C₂²×C₄×C₁₁	—	2	2	no	—
102	C₂²×C₄×C₁₁	—	2	2	no	—
103	C₂²×C₄×C₁₁	—	2	2	no	—
104	C₂²×C₄×C₁₁	—	2	2	no	—
105	C₂²×C₄×C₁₁	—	2	2	no	—
106	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
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	2	yes	—
111	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₁₁	—	2	1	no	—
117	C₂×C₈×C₁₁	—	2	1	no	—
118	C₂×C₈×C₁₁	—	2	1	no	—
119	C₂×C₈×C₁₁	—	2	1	no	—
120	C₂×C₈×C₁₁	—	2	2	no	—
121	C₂×C₈×C₁₁	—	2	2	no	—
122	C₂×C₈×C₁₁	—	2	1	no	—
123	C₂×C₈×C₁₁	—	2	1	no	—
124	C₂×C₈×C₁₁	—	2	2	no	—
125	C₂×C₈×C₁₁	—	2	2	no	—
126	C₂×C₈×C₁₁	—	2	1	no	—
127	C₂×C₈×C₁₁	—	2	2	no	—
128	C₂×C₈×C₁₁	—	2	1	no	—
129	C₂×C₈×C₁₁	—	2	1	no	—
130	C₂×C₈×C₁₁	—	2	1	no	—
131	C₂×C₈×C₁₁	—	4	8	no	—
132	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
133	C₂×C₈×C₁₁	#41	1	2	yes	—
134	C₂×C₈×C₁₁	#41	1	2	yes	—
135	C₁₁×C₄⋊C₄	—	2	2	no	—
136	C₁₁×C₄⋊C₄	—	2	2	no	—
137	C₁₁×C₄⋊C₄	—	2	4	no	—
138	C₁₁×C₂²⋊C₄	—	2	4	no	—
139	C₁₁×C₂²⋊C₄	—	2	4	no	—
140	C₁₁×C₂²⋊C₄	—	2	4	no	—
141	C₁₁×C₂²⋊C₄	—	2	4	no	—
142	C₁₁×C₂²⋊C₄	—	4	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	1	no	—
148	C₄²×C₁₁	—	2	1	no	—
149	C₄²×C₁₁	—	2	2	no	—
150	C₄²×C₁₁	—	2	1	no	—
151	C₄²×C₁₁	—	2	1	no	—
152	C₄²×C₁₁	—	4	1	no	—
153	C₄²×C₁₁	C₂×D₄	1	2	yes	—
154	C₄²×C₁₁	#41	1	2	yes	—
155	C₂×#446	C₂×C₁₁	1	1	yes	characteristic, complemented
156	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic
157	C₄×#124	C₂×C₁₁	1	1	yes	characteristic
158	#1984	C₂×C₁₁	1	1	yes	characteristic, complemented
159	#1954	C₂×C₁₁	1	1	yes	characteristic
160	#1924	C₂×C₁₁	1	2	yes	complemented
161	#1924	C₂×C₁₁	1	2	yes	complemented
162	#1850	C₂×C₁₁	1	2	yes	complemented
163	#1767	C₂×C₁₁	1	1	yes	characteristic, complemented
164	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
165	#1752	C₂×C₁₁	1	2	yes	complemented
166	C₂³×C₁₁	—	2	2	no	—
167	C₂³×C₁₁	—	2	2	no	—
168	C₂³×C₁₁	—	2	2	no	—
169	C₂³×C₁₁	—	2	2	no	—
170	C₂³×C₁₁	—	2	2	no	—
171	C₂³×C₁₁	—	2	2	no	—
172	C₂³×C₁₁	C₂×M₁₆	1	4	yes	—
173	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
174	Q₈×C₁₁	—	4	4	no	—
175	D₄×C₁₁	—	2	8	no	—
176	C₂×C₄×C₁₁	—	2	1	no	—
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	2	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	—	2	2	no	—
183	C₂×C₄×C₁₁	—	2	1	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	2	1	no	—
186	C₂×C₄×C₁₁	—	2	1	no	—
187	C₂×C₄×C₁₁	—	2	2	no	—
188	C₂×C₄×C₁₁	—	2	1	no	—
189	C₂×C₄×C₁₁	—	2	1	no	—
190	C₂×C₄×C₁₁	—	2	2	no	—
191	C₂×C₄×C₁₁	—	2	1	no	—
192	C₂×C₄×C₁₁	—	2	1	no	—
193	C₂×C₄×C₁₁	—	2	2	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	—	4	2	no	—
199	C₂×C₄×C₁₁	—	4	2	no	—
200	C₂×C₄×C₁₁	—	4	2	no	—
201	C₂×C₄×C₁₁	—	4	2	no	—
202	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
205	C₂×C₄×C₁₁	#131	1	2	yes	—
206	C₂×C₄×C₁₁	#131	1	2	yes	—
207	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
213	C₈×C₁₁	—	2	2	no	—
214	C₈×C₁₁	—	2	4	no	—
215	C₈×C₁₁	—	2	2	no	—
216	C₈×C₁₁	—	4	1	no	—
217	C₈×C₁₁	—	4	1	no	—
218	C₈×C₁₁	—	4	2	no	—
219	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
220	C₂×#124	C₄×C₁₁	1	1	yes	characteristic
221	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
222	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
223	#446	—	2	4	no	—
224	C₈×D₄	—	2	4	no	—
225	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
227	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
230	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
231	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
232	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
233	C₂×#97	C₂²×C₁₁	1	2	yes	—
234	C₂×#97	C₂²×C₁₁	1	2	yes	—
235	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
236	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
237	#391	C₄×C₁₁	1	1	yes	characteristic
238	#390	C₄×C₁₁	1	1	yes	characteristic
239	#388	C₄×C₁₁	1	2	yes	—
240	#388	C₄×C₁₁	1	2	yes	—
241	#382	C₄×C₁₁	1	1	yes	characteristic
242	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
243	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
244	C₄³	C₂²×C₁₁	1	1	yes	characteristic
245	#336	C₂²×C₁₁	1	2	yes	—
246	#336	C₂²×C₁₁	1	2	yes	—
247	#336	C₂²×C₁₁	1	2	yes	—
248	#336	C₂²×C₁₁	1	1	yes	characteristic
249	#336	C₂²×C₁₁	1	1	yes	characteristic
250	C₂²×C₁₁	—	2	4	no	—
251	C₂²×C₁₁	—	2	4	no	—
252	C₂²×C₁₁	—	2	4	no	—
253	C₂²×C₁₁	—	4	2	no	—
254	C₂²×C₁₁	—	4	2	no	—
255	C₂²×C₁₁	—	4	2	no	—
256	C₂²×C₁₁	—	4	2	no	—
257	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂²×C₁₁	C₄×#41	1	1	yes	characteristic
259	C₂²×C₁₁	#520	1	1	yes	characteristic
260	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
261	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
262	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
263	C₂²×C₁₁	#568	1	1	yes	characteristic
264	C₄×C₁₁	—	2	2	no	—
265	C₄×C₁₁	—	2	2	no	—
266	C₄×C₁₁	—	4	2	no	—
267	C₄×C₁₁	—	4	2	no	—
268	C₄×C₁₁	—	4	2	no	—
269	C₄×C₁₁	—	4	1	no	—
270	C₄×C₁₁	—	4	1	no	—
271	C₄×C₁₁	—	4	1	no	—
272	C₄×C₁₁	#435	1	4	yes	—
273	C₄×C₁₁	#546	1	1	yes	characteristic
274	C₄×C₁₁	#548	1	1	yes	characteristic
275	C₄×C₁₁	#556	1	1	yes	characteristic
276	C₄×C₁₁	#559	1	1	yes	characteristic
277	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
278	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
280	C₂²×C₈	—	2	4	no	—
281	C₂²×C₈	—	2	4	no	—
282	C₂²×C₈	—	4	2	no	—
283	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
285	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
287	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
289	#124	—	2	4	no	—
290	C₄×Q₈	—	2	2	no	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
299	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
301	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
302	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
303	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
304	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
305	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
307	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
310	C₄⋊C₈	—	2	4	no	—
311	C₄⋊C₈	—	2	2	no	—
312	C₄⋊C₈	—	2	2	no	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	D₄×C₁₁	1	4	yes	—
315	C₂²⋊C₈	—	2	4	no	—
316	C₂²⋊C₈	—	2	4	no	—
317	C₂²⋊C₈	—	4	2	no	—
318	#97	—	2	4	no	—
319	#97	—	4	2	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	—	2	2	no	—
322	#95	C₂×C₄×C₁₁	1	2	yes	—
323	#95	C₂×C₄×C₁₁	1	2	yes	—
324	#95	C₂×C₄×C₁₁	1	2	yes	—
325	#95	C₂×C₄×C₁₁	1	2	yes	—
326	C₂×C₁₁	—	4	4	no	—
327	C₂×C₁₁	#2367	1	1	yes	characteristic
328	C₂×C₁₁	C₂×#435	1	1	yes	characteristic
329	C₂×C₁₁	#2935	1	1	yes	characteristic
330	C₂×C₁₁	#2966	1	1	yes	characteristic
331	C₂×C₁₁	#2970	1	1	yes	characteristic
332	C₂×C₁₁	#2990	1	1	yes	characteristic
333	C₂×C₁₁	#2993	1	1	yes	characteristic
334	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	C₁₁×M₁₆	1	4	yes	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
348	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
353	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	4	8	no	—
373	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
374	C₂×C₈	C₁₁×#41	1	2	yes	—
375	C₂×C₈	C₁₁×#41	1	2	yes	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	4	1	no	—
394	C₄²	C₂×D₄×C₁₁	1	2	yes	—
395	C₄²	C₁₁×#41	1	2	yes	—
396	C₁₁	#23209	1	1	yes	characteristic, direct product factor, Sylow
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	C₂×C₁₁×M₁₆	1	4	yes	—
404	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
405	Q₈	—	4	4	no	—
406	D₄	—	2	8	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
434	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
435	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
436	C₂×C₄	C₁₁×#131	1	2	yes	—
437	C₂×C₄	C₁₁×#131	1	2	yes	—
438	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
439	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
440	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
441	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
442	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
443	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
444	C₈	—	2	2	no	—
445	C₈	—	2	4	no	—
446	C₈	—	2	2	no	—
447	C₈	—	4	1	no	—
448	C₈	—	4	1	no	—
449	C₈	—	4	2	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	4	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
458	C₂²	C₄×C₁₁×#41	1	1	yes	characteristic
459	C₂²	C₁₁×#520	1	1	yes	characteristic
460	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
461	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
462	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
463	C₂²	C₁₁×#568	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	1	no	—
471	C₄	—	4	2	no	—
472	C₄	C₁₁×#435	1	4	yes	—
473	C₄	C₁₁×#546	1	1	yes	characteristic
474	C₄	C₁₁×#548	1	1	yes	characteristic
475	C₄	C₁₁×#556	1	1	yes	characteristic
476	C₄	C₁₁×#559	1	1	yes	characteristic
477	C₂	—	4	4	no	—
478	C₂	C₁₁×#2367	1	1	yes	characteristic
479	C₂	C₂×C₁₁×#435	1	1	yes	characteristic
480	C₂	C₁₁×#2935	1	1	yes	characteristic
481	C₂	C₁₁×#2966	1	1	yes	characteristic
482	C₂	C₁₁×#2970	1	1	yes	characteristic
483	C₂	C₁₁×#2990	1	1	yes	characteristic
484	C₂	C₁₁×#2993	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂³×C₁₁	C₂³×C₄
prime radical	C₂²×D₄×C₁₁	C₂×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
1. C₂×C₁₁×#446	C₂	semidirect
4. C₁₁×#1984	C₂	semidirect
6. C₁₁×#1924	C₂	semidirect
7. C₁₁×#1924	C₂	semidirect
8. C₁₁×#1850	C₂	semidirect
9. C₁₁×#1767	C₂	semidirect
10. C₄×C₁₁×C₄⋊C₈	C₂	semidirect
11. C₁₁×#1752	C₂	semidirect
92. #23209	C₁₁	direct (N × H)
155. C₂×#446	C₂×C₁₁	semidirect
158. #1984	C₂×C₁₁	semidirect
160. #1924	C₂×C₁₁	semidirect
161. #1924	C₂×C₁₁	semidirect
162. #1850	C₂×C₁₁	semidirect
163. #1767	C₂×C₁₁	semidirect
164. C₄×C₄⋊C₈	C₂×C₁₁	semidirect
165. #1752	C₂×C₁₁	semidirect
396. C₁₁	#23209	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×C₁₁×#446	2
C₂×C₈×D₄×C₁₁	2
C₄×C₁₁×#124	2
C₁₁×#1984	2
C₁₁×#1954	2
C₁₁×#1924	2
C₁₁×#1850	2
C₁₁×#1767	2
C₄×C₁₁×C₄⋊C₈	2
C₁₁×#1752	2
#23209	11

Subgroups — C11×#23209 #14600402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23209 #14600402