Subgroups — #13083204

Order 1408.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623240	C₂	1	2	yes	maximal, complemented
3	#10623236	C₂	1	2	yes	maximal, complemented
4	#10623223	C₂	1	2	yes	maximal, complemented
5	#10623209	C₂	1	2	yes	maximal, complemented
6	#10623194	C₂	1	2	yes	maximal, complemented
7	#10623188	C₂	1	2	yes	maximal, complemented
8	#10623178	C₂	1	2	yes	maximal, complemented
9	#10623151	C₂	1	2	yes	maximal, complemented
10	#10623116	C₂	1	1	yes	maximal, characteristic, complemented
11	#10623115	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623084	C₂	1	1	yes	maximal, characteristic, complemented
13	#10623083	C₂	1	1	yes	maximal, characteristic, complemented
14	#10623083	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623082	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623081	C₂	1	1	yes	maximal, characteristic, complemented
17	#10623081	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623066	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623057	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623056	C₂	1	1	yes	maximal, characteristic, complemented
21	#10623049	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623010	C₂	1	1	yes	maximal, characteristic, complemented
23	#10623008	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#4339	C₂²	1	1	yes	characteristic
25	C₂×#4339	C₂²	1	1	yes	characteristic
26	C₂×#4339	C₂²	1	1	yes	characteristic
27	C₂×#4339	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₄₄	C₂²	1	1	yes	characteristic
29	C₂²×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
30	C₁₁×#126	C₂²	1	1	yes	characteristic
31	C₁₁×#126	C₂²	1	1	yes	characteristic, complemented
32	C₁₁×#125	C₂²	1	1	yes	characteristic, complemented
33	C₁₁×#124	C₂²	1	1	yes	characteristic
34	C₁₁×#123	C₂²	1	1	yes	characteristic
35	C₁₁×#123	C₂²	1	1	yes	characteristic, complemented
36	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₁₁×#121	C₂²	1	1	yes	characteristic
38	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
40	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
41	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
42	C₁₁×#117	C₂²	1	1	yes	characteristic
43	C₁₁×#117	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic, complemented
45	#67000	C₂²	1	2	yes	complemented
46	#66999	C₂²	1	2	yes	complemented
47	#66993	C₂²	1	2	yes	complemented
48	#66992	C₂²	1	2	yes	—
49	#66992	C₂²	1	2	yes	complemented
50	#66991	C₂²	1	2	yes	—
51	#66990	C₂²	1	2	yes	—
52	#66990	C₂²	1	2	yes	—
53	#66983	C₂²	1	1	yes	characteristic
54	#66983	C₂²	1	1	yes	characteristic
55	#66983	C₂²	1	2	yes	complemented
56	#66983	C₂²	1	2	yes	complemented
57	#66983	C₂²	1	1	yes	characteristic, complemented
58	#66982	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
60	#66977	C₂²	1	1	yes	characteristic
61	#66977	C₂²	1	1	yes	characteristic
62	#66977	C₂²	1	1	yes	characteristic, complemented
63	#66951	C₂²	1	2	yes	complemented
64	#66951	C₂²	1	2	yes	complemented
65	#66950	C₂²	1	2	yes	complemented
66	#66950	C₂²	1	2	yes	complemented
67	#66949	C₂²	1	2	yes	complemented
68	#66949	C₂²	1	2	yes	complemented
69	#66948	C₂²	1	2	yes	—
70	#66948	C₂²	1	2	yes	—
71	#66947	C₂²	1	2	yes	—
72	#66947	C₂²	1	2	yes	—
73	#66947	C₂²	1	2	yes	complemented
74	#66947	C₂²	1	2	yes	complemented
75	#66947	C₂²	1	2	yes	complemented
76	#66947	C₂²	1	2	yes	complemented
77	#66946	C₂²	1	2	yes	complemented
78	#66946	C₂²	1	2	yes	complemented
79	#66945	C₂²	1	2	yes	complemented
80	C₄⋊C₄×D₁₁	C₂²	1	2	yes	complemented
81	#66942	C₂²	1	2	yes	complemented
82	#66942	C₂²	1	2	yes	complemented
83	#66939	C₂²	1	2	yes	complemented
84	#66939	C₂²	1	2	yes	complemented
85	#66938	C₂²	1	2	yes	—
86	#66938	C₂²	1	2	yes	complemented
87	#66937	C₂²	1	2	yes	—
88	#66937	C₂²	1	2	yes	—
89	#66937	C₂²	1	2	yes	complemented
90	#66937	C₂²	1	2	yes	complemented
91	#66937	C₂²	1	2	yes	complemented
92	#66937	C₂²	1	2	yes	complemented
93	#66936	C₂²	1	2	yes	—
94	#66936	C₂²	1	2	yes	complemented
95	#66935	C₂²	1	2	yes	—
96	#66935	C₂²	1	2	yes	—
97	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
98	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
99	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
100	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
101	#66932	C₂²	1	2	yes	—
102	#66932	C₂²	1	2	yes	—
103	#66929	C₂²	1	2	yes	complemented
104	#66928	C₂²	1	1	yes	characteristic
105	#66928	C₂²	1	1	yes	characteristic
106	#66928	C₂²	1	1	yes	characteristic
107	#66928	C₂²	1	1	yes	characteristic
108	#66928	C₂²	1	1	yes	characteristic, complemented
109	#66927	C₂²	1	1	yes	characteristic
110	#66927	C₂²	1	1	yes	characteristic
111	C₄×D₄₄	C₂²	1	1	yes	characteristic
112	C₄×D₄₄	C₂²	1	1	yes	characteristic
113	C₄×D₄₄	C₂²	1	2	yes	complemented
114	C₄×D₄₄	C₂²	1	2	yes	complemented
115	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
116	#66925	C₂²	1	2	yes	complemented
117	#66923	C₂²	1	1	yes	characteristic, complemented
118	#66922	C₂²	1	1	yes	characteristic, complemented
119	#66922	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₁	C₂³	1	2	yes	—
124	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
140	C₂²×Dic₁₁	C₂³	1	2	yes	—
141	#4339	—	4	2	no	—
142	#4339	—	4	2	no	—
143	#4339	—	4	2	no	—
144	#4339	—	4	2	no	—
145	C₂×D₄₄	—	4	2	no	—
146	C₂×D₄₄	C₂³	1	1	yes	characteristic
147	C₂×D₄₄	C₂³	1	1	yes	characteristic
148	C₂×D₄₄	C₂³	1	1	yes	characteristic
149	C₂×D₄₄	C₂³	1	2	yes	—
150	C₂×D₄₄	C₂³	1	2	yes	—
151	C₂×D₄₄	C₂³	1	2	yes	—
152	C₂×D₄₄	C₂³	1	2	yes	—
153	C₂×D₄₄	C₂³	1	2	yes	—
154	C₂×C₄×D₁₁	C₂³	1	2	yes	—
155	C₂×C₄×D₁₁	C₂³	1	2	yes	—
156	C₂×C₄×D₁₁	C₂³	1	2	yes	—
157	C₂×C₄×D₁₁	C₂³	1	2	yes	—
158	C₂×C₄×D₁₁	C₂³	1	2	yes	—
159	C₂×C₄×D₁₁	C₂³	1	2	yes	—
160	C₂×C₄×D₁₁	C₂³	1	2	yes	—
161	C₂×Dic₂₂	—	4	2	no	—
162	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
163	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
164	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
165	C₂×Dic₂₂	C₂³	1	2	yes	—
166	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₄²×C₁₁	C₂³	1	1	yes	characteristic
187	C₄²×C₁₁	C₂³	1	1	yes	characteristic
188	C₄²×C₁₁	C₂³	1	1	yes	characteristic
189	C₄²×C₁₁	C₂³	1	1	yes	characteristic
190	C₄²×C₁₁	C₂³	1	1	yes	characteristic
191	C₄²×C₁₁	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
193	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
194	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
195	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
209	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
211	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₁₁	C₂³	1	2	yes	—
214	C₄⋊Dic₁₁	C₂³	1	2	yes	—
215	C₄⋊Dic₁₁	C₂³	1	2	yes	—
216	C₄⋊Dic₁₁	C₂³	1	2	yes	—
217	Dic₁₁⋊C₄	C₂³	1	2	yes	—
218	Dic₁₁⋊C₄	C₂³	1	2	yes	—
219	Dic₁₁⋊C₄	C₂³	1	2	yes	—
220	Dic₁₁⋊C₄	C₂³	1	2	yes	—
221	Dic₁₁⋊C₄	C₂³	1	2	yes	—
222	Dic₁₁⋊C₄	C₂³	1	2	yes	—
223	Dic₁₁⋊C₄	C₂³	1	2	yes	—
224	Dic₁₁⋊C₄	C₂³	1	2	yes	—
225	C₄×Dic₁₁	C₂³	1	2	yes	—
226	C₄×Dic₁₁	C₂³	1	2	yes	—
227	C₄×Dic₁₁	C₂³	1	2	yes	—
228	#3562	—	11	1	no	maximal, Sylow
229	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
231	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₁	—	4	2	no	—
233	C₂²×D₁₁	—	4	2	no	—
234	C₂²×D₁₁	—	4	2	no	—
235	C₂²×D₁₁	C₂⁴	1	2	yes	—
236	C₂²×D₁₁	C₂⁴	1	2	yes	—
237	C₂²×D₁₁	C₂⁴	1	2	yes	—
238	Q₈×C₁₁	—	4	1	no	—
239	D₄×C₁₁	—	4	1	no	—
240	D₄×C₁₁	—	4	1	no	—
241	D₄×C₁₁	—	4	1	no	—
242	C₂×C₄×C₁₁	—	2	2	no	—
243	C₂×C₄×C₁₁	—	2	2	no	—
244	C₂×C₄×C₁₁	—	2	2	no	—
245	C₂×C₄×C₁₁	—	4	1	no	—
246	C₂×C₄×C₁₁	—	4	1	no	—
247	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
259	C₂²⋊D₁₁	—	4	2	no	—
260	C₂²⋊D₁₁	—	4	2	no	—
261	C₂²⋊D₁₁	—	4	2	no	—
262	C₂²⋊D₁₁	—	4	2	no	—
263	C₂²⋊D₁₁	—	4	2	no	—
264	C₂²⋊D₁₁	—	4	2	no	—
265	C₂²⋊D₁₁	—	4	2	no	—
266	C₂×Dic₁₁	—	4	2	no	—
267	C₂×Dic₁₁	C₂⁴	1	2	yes	—
268	C₂×Dic₁₁	C₂⁴	1	2	yes	—
269	C₂×Dic₁₁	C₂⁴	1	2	yes	—
270	C₂×Dic₁₁	C₂⁴	1	2	yes	—
271	C₂×Dic₁₁	C₂⁴	1	2	yes	—
272	D₄₄	—	2	2	no	—
273	D₄₄	—	2	2	no	—
274	D₄₄	—	2	2	no	—
275	D₄₄	—	4	2	no	—
276	D₄₄	—	4	2	no	—
277	D₄₄	—	4	2	no	—
278	D₄₄	—	4	2	no	—
279	D₄₄	—	4	2	no	—
280	C₄×D₁₁	—	4	2	no	—
281	C₄×D₁₁	—	4	2	no	—
282	C₄×D₁₁	—	4	2	no	—
283	C₄×D₁₁	—	4	2	no	—
284	C₄×D₁₁	—	4	2	no	—
285	C₄×D₁₁	—	4	2	no	—
286	C₄×D₁₁	—	4	2	no	—
287	Dic₂₂	—	2	2	no	—
288	Dic₂₂	—	2	2	no	—
289	Dic₂₂	—	2	2	no	—
290	Dic₂₂	—	4	2	no	—
291	#562	—	11	2	no	—
292	#560	—	11	2	no	—
293	#559	—	11	1	no	—
294	#556	—	11	1	no	—
295	#553	—	11	2	no	—
296	#551	—	11	2	no	—
297	#550	—	11	1	no	—
298	#548	—	11	1	no	—
299	#548	—	11	1	no	—
300	#547	—	11	1	no	—
301	#546	—	11	1	no	—
302	#546	—	11	1	no	—
303	#541	—	11	1	no	—
304	#540	—	11	2	no	—
305	#540	—	11	1	no	—
306	#539	—	11	2	no	—
307	#538	—	11	2	no	—
308	#538	—	11	2	no	—
309	#536	—	11	1	no	—
310	#535	—	11	1	no	—
311	#532	—	11	1	no	—
312	#529	—	11	1	no	—
313	#529	D₁₁	1	1	yes	characteristic, complemented
314	C₂²×C₁₁	—	2	1	no	—
315	C₂²×C₁₁	—	2	1	no	—
316	C₂²×C₁₁	—	2	1	no	—
317	C₂²×C₁₁	—	2	1	no	—
318	C₂²×C₁₁	—	2	1	no	—
319	C₂²×C₁₁	—	2	1	no	—
320	C₂²×C₁₁	—	2	1	no	—
321	C₂²×C₁₁	—	2	1	no	—
322	C₂²×C₁₁	—	2	1	no	—
323	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
324	C₂×D₁₁	—	2	2	no	—
325	C₂×D₁₁	—	2	2	no	—
326	C₂×D₁₁	—	2	2	no	—
327	C₂×D₁₁	—	2	2	no	—
328	C₂×D₁₁	—	2	2	no	—
329	C₂×D₁₁	—	2	2	no	—
330	C₂×D₁₁	—	2	2	no	—
331	C₂×D₁₁	—	2	2	no	—
332	C₂×D₁₁	—	2	2	no	—
333	C₂×D₁₁	—	8	4	no	—
334	C₄×C₁₁	—	2	1	no	—
335	C₄×C₁₁	—	2	1	no	—
336	C₄×C₁₁	—	2	1	no	—
337	C₄×C₁₁	—	2	1	no	—
338	C₄×C₁₁	—	2	1	no	—
339	C₄×C₁₁	—	2	1	no	—
340	C₄×C₁₁	—	2	1	no	—
341	C₄×C₁₁	—	2	1	no	—
342	C₄×C₁₁	—	2	1	no	—
343	C₄×C₁₁	—	2	1	no	—
344	C₄×C₁₁	—	2	1	no	—
345	C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
346	Dic₁₁	—	2	2	no	—
347	Dic₁₁	—	2	2	no	—
348	Dic₁₁	—	2	2	no	—
349	Dic₁₁	—	2	2	no	—
350	Dic₁₁	—	2	2	no	—
351	C₂×#41	—	11	1	no	—
352	C₂×#41	—	11	1	no	—
353	C₂×#41	—	11	1	no	—
354	C₂×#41	—	11	1	no	—
355	C₂²×Q₈	—	11	1	no	—
356	C₂²×D₄	—	11	1	no	—
357	C₄⋊Q₈	—	11	1	no	—
358	C₄⋊Q₈	—	11	1	no	—
359	#127	—	11	2	no	—
360	#127	—	11	1	no	—
361	#127	—	11	1	no	—
362	#126	—	11	2	no	—
363	#126	—	11	2	no	—
364	#126	—	11	2	no	—
365	#126	—	11	2	no	—
366	#126	—	11	2	no	—
367	#126	C₂×D₁₁	1	1	yes	characteristic
368	#126	C₂×D₁₁	1	1	yes	characteristic, complemented
369	#125	—	11	2	no	—
370	#125	—	11	2	no	—
371	#125	—	11	1	no	—
372	#125	C₂×D₁₁	1	1	yes	characteristic, complemented
373	#124	—	11	2	no	—
374	#124	—	11	2	no	—
375	#124	—	11	2	no	—
376	#124	—	11	1	no	—
377	#124	—	11	1	no	—
378	#124	—	11	1	no	—
379	#124	—	11	1	no	—
380	#124	—	11	1	no	—
381	#124	C₂×D₁₁	1	1	yes	characteristic
382	#123	—	11	2	no	—
383	#123	—	11	2	no	—
384	#123	—	11	2	no	—
385	#123	—	11	2	no	—
386	#123	—	11	2	no	—
387	#123	—	11	2	no	—
388	#123	—	11	2	no	—
389	#123	—	11	2	no	—
390	#123	—	11	2	no	—
391	#123	—	11	2	no	—
392	#123	—	11	2	no	—
393	#123	C₂×D₁₁	1	1	yes	characteristic
394	#123	C₂×D₁₁	1	1	yes	characteristic, complemented
395	C₂²⋊Q₈	—	11	2	no	—
396	C₂²⋊Q₈	—	11	1	no	—
397	C₂²⋊Q₈	—	11	1	no	—
398	C₂²⋊Q₈	—	11	1	no	—
399	C₂²⋊Q₈	—	11	2	no	—
400	C₂²⋊Q₈	—	11	2	no	—
401	C₂²⋊Q₈	—	11	2	no	—
402	C₂²⋊Q₈	—	11	2	no	—
403	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
404	#121	—	11	2	no	—
405	#121	—	11	2	no	—
406	#121	—	11	2	no	—
407	#121	—	11	1	no	—
408	#121	—	11	2	no	—
409	#121	—	11	2	no	—
410	#121	—	11	1	no	—
411	#121	—	11	1	no	—
412	#121	—	11	2	no	—
413	#121	—	11	2	no	—
414	#121	—	11	2	no	—
415	#121	—	11	2	no	—
416	#121	—	11	2	no	—
417	#121	—	11	2	no	—
418	#121	—	11	2	no	—
419	#121	—	11	2	no	—
420	#121	C₂×D₁₁	1	1	yes	characteristic
421	#120	—	11	2	no	—
422	#120	—	11	2	no	—
423	#120	—	11	2	no	—
424	#120	—	11	2	no	—
425	C₄×Q₈	—	11	1	no	—
426	C₄×Q₈	—	11	1	no	—
427	C₄×Q₈	—	11	1	no	—
428	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
429	C₄×D₄	—	11	2	no	—
430	C₄×D₄	—	11	2	no	—
431	C₄×D₄	—	11	2	no	—
432	C₄×D₄	—	11	2	no	—
433	C₄×D₄	—	11	2	no	—
434	C₄×D₄	—	11	1	no	—
435	C₄×D₄	—	11	2	no	—
436	C₄×D₄	—	11	2	no	—
437	C₄×D₄	—	11	1	no	—
438	C₄×D₄	—	11	1	no	—
439	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
440	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
441	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
442	#117	—	11	2	no	—
443	#117	—	11	2	no	—
444	#117	C₂×D₁₁	1	1	yes	characteristic
445	#117	C₂×D₁₁	1	1	yes	characteristic, complemented
446	C₂×C₄⋊C₄	—	11	2	no	—
447	C₂×C₂²⋊C₄	—	11	2	no	—
448	C₂×C₂²⋊C₄	—	11	2	no	—
449	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic, complemented
450	C₂×C₁₁	—	4	1	no	—
451	C₂×C₁₁	—	4	1	no	—
452	C₂×C₁₁	—	4	1	no	—
453	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
454	C₂×C₁₁	#585	1	1	yes	characteristic
455	C₂×C₁₁	#585	1	1	yes	characteristic
456	D₁₁	—	4	2	no	—
457	D₁₁	—	4	2	no	—
458	D₁₁	—	4	2	no	—
459	C₂⁴	—	11	2	no	—
460	#41	—	44	2	no	—
461	#41	—	44	2	no	—
462	#41	—	44	2	no	—
463	#41	—	44	2	no	—
464	C₂×Q₈	—	11	1	no	—
465	C₂×Q₈	—	11	1	no	—
466	C₂×Q₈	—	11	1	no	—
467	C₂×Q₈	—	11	2	no	—
468	C₂×Q₈	—	44	2	no	—
469	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
470	C₂×D₄	—	11	2	no	—
471	C₂×D₄	—	11	2	no	—
472	C₂×D₄	—	11	2	no	—
473	C₂×D₄	—	11	2	no	—
474	C₂×D₄	—	11	2	no	—
475	C₂×D₄	—	11	2	no	—
476	C₂×D₄	—	11	2	no	—
477	C₂×D₄	—	11	1	no	—
478	C₂×D₄	—	11	1	no	—
479	C₂×D₄	—	11	1	no	—
480	C₂×D₄	—	11	2	no	—
481	C₂×D₄	—	11	2	no	—
482	C₂×D₄	—	11	2	no	—
483	C₂×D₄	—	11	2	no	—
484	C₂×D₄	—	11	2	no	—
485	C₂×D₄	—	44	2	no	—
486	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
487	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
488	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
489	C₂²×C₄	—	11	2	no	—
490	C₂²×C₄	—	11	2	no	—
491	C₂²×C₄	—	11	2	no	—
492	C₂²×C₄	—	11	2	no	—
493	C₂²×C₄	—	11	2	no	—
494	C₂²×C₄	—	11	2	no	—
495	C₂²×C₄	—	11	2	no	—
496	C₂²×C₄	—	11	2	no	—
497	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
502	C₄⋊C₄	—	11	2	no	—
503	C₄⋊C₄	—	11	2	no	—
504	C₄⋊C₄	—	11	2	no	—
505	C₄⋊C₄	—	11	2	no	—
506	C₄⋊C₄	—	11	2	no	—
507	C₄⋊C₄	—	11	1	no	—
508	C₄⋊C₄	—	11	1	no	—
509	C₄⋊C₄	—	11	2	no	—
510	C₄⋊C₄	—	11	2	no	—
511	C₄⋊C₄	—	11	2	no	—
512	C₄⋊C₄	—	11	2	no	—
513	C₄⋊C₄	—	11	2	no	—
514	C₄⋊C₄	—	11	2	no	—
515	C₄⋊C₄	—	11	2	no	—
516	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
526	C₂²⋊C₄	—	11	2	no	—
527	C₂²⋊C₄	—	11	2	no	—
528	C₂²⋊C₄	—	11	2	no	—
529	C₂²⋊C₄	—	11	2	no	—
530	C₂²⋊C₄	—	11	2	no	—
531	C₂²⋊C₄	—	11	2	no	—
532	C₂²⋊C₄	—	11	2	no	—
533	C₂²⋊C₄	—	11	2	no	—
534	C₂²⋊C₄	—	11	2	no	—
535	C₂²⋊C₄	—	11	2	no	—
536	C₂²⋊C₄	—	11	2	no	—
537	C₂²⋊C₄	—	11	2	no	—
538	C₂²⋊C₄	—	11	2	no	—
539	C₂²⋊C₄	—	11	2	no	—
540	C₂²⋊C₄	—	11	2	no	—
541	C₂²⋊C₄	—	11	2	no	—
542	C₂²⋊C₄	—	11	2	no	—
543	C₂²⋊C₄	—	11	2	no	—
544	C₂²⋊C₄	—	11	2	no	—
545	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
547	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
548	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
549	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
550	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
551	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
555	C₄²	—	11	2	no	—
556	C₄²	—	11	2	no	—
557	C₄²	—	11	2	no	—
558	C₄²	C₂²×D₁₁	1	1	yes	characteristic
559	C₄²	C₂²×D₁₁	1	1	yes	characteristic
560	C₄²	C₂²×D₁₁	1	1	yes	characteristic
561	C₄²	C₂²×D₁₁	1	1	yes	characteristic
562	C₄²	C₂²×D₁₁	1	1	yes	characteristic
563	C₄²	C₂²×D₁₁	1	1	yes	characteristic
564	C₁₁	#3562	1	1	yes	characteristic, complemented, Sylow
565	C₂³	—	11	2	no	—
566	C₂³	—	11	2	no	—
567	C₂³	—	11	2	no	—
568	C₂³	—	44	2	no	—
569	C₂³	—	44	2	no	—
570	C₂³	—	44	2	no	—
571	C₂³	C₂³×D₁₁	1	1	yes	characteristic
572	C₂³	C₂³×D₁₁	1	1	yes	characteristic
573	C₂³	C₂³×D₁₁	1	1	yes	characteristic
574	Q₈	—	4	1	no	—
575	Q₈	—	22	2	no	—
576	Q₈	—	22	2	no	—
577	Q₈	—	22	2	no	—
578	Q₈	—	44	2	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	—	4	1	no	—
582	D₄	—	22	2	no	—
583	D₄	—	22	2	no	—
584	D₄	—	22	2	no	—
585	D₄	—	44	2	no	—
586	D₄	—	44	2	no	—
587	D₄	—	44	2	no	—
588	D₄	—	44	2	no	—
589	D₄	—	44	2	no	—
590	D₄	—	44	2	no	—
591	D₄	—	44	2	no	—
592	D₄	—	44	2	no	—
593	D₄	—	44	2	no	—
594	D₄	—	44	2	no	—
595	D₄	—	44	2	no	—
596	D₄	—	44	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	11	2	no	—
603	C₂×C₄	—	11	2	no	—
604	C₂×C₄	—	11	2	no	—
605	C₂×C₄	—	11	2	no	—
606	C₂×C₄	—	11	2	no	—
607	C₂×C₄	—	44	2	no	—
608	C₂×C₄	—	44	2	no	—
609	C₂×C₄	—	44	2	no	—
610	C₂×C₄	—	44	2	no	—
611	C₂×C₄	—	44	2	no	—
612	C₂×C₄	—	44	2	no	—
613	C₂×C₄	—	44	2	no	—
614	C₂×C₄	—	44	2	no	—
615	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	22	2	no	—
637	C₂²	—	22	2	no	—
638	C₂²	—	22	2	no	—
639	C₂²	—	22	2	no	—
640	C₂²	—	22	2	no	—
641	C₂²	—	22	2	no	—
642	C₂²	—	22	2	no	—
643	C₂²	—	22	2	no	—
644	C₂²	—	22	2	no	—
645	C₂²	—	88	4	no	—
646	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	22	2	no	—
659	C₄	—	22	2	no	—
660	C₄	—	22	2	no	—
661	C₄	—	22	2	no	—
662	C₄	—	22	2	no	—
663	C₄	#67042	1	2	yes	—
664	C₂	—	4	1	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	1	no	—
667	C₂	—	44	2	no	—
668	C₂	—	44	2	no	—
669	C₂	—	44	2	no	—
670	C₂	C₂×#67042	1	1	yes	characteristic
671	C₂	#10623453	1	1	yes	characteristic
672	C₂	#10623453	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#529	C₂
hypercenter	#529	D₁₁
hypocenter	C₁₁	#3562
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₁₁×#529	C₂	semidirect
2. #10623240	C₂	semidirect
3. #10623236	C₂	semidirect
4. #10623223	C₂	semidirect
5. #10623209	C₂	semidirect
6. #10623194	C₂	semidirect
7. #10623188	C₂	semidirect
8. #10623178	C₂	semidirect
9. #10623151	C₂	semidirect
10. #10623116	C₂	semidirect
11. #10623115	C₂	semidirect
12. #10623084	C₂	semidirect
13. #10623083	C₂	semidirect
14. #10623083	C₂	semidirect
15. #10623082	C₂	semidirect
16. #10623081	C₂	semidirect
17. #10623081	C₂	semidirect
18. #10623066	C₂	semidirect
19. #10623057	C₂	semidirect
20. #10623056	C₂	semidirect
21. #10623049	C₂	semidirect
22. #10623010	C₂	semidirect
23. #10623008	C₂	semidirect
27. C₂×#4339	C₂²	semidirect
29. C₂²×Dic₂₂	C₂²	semidirect
31. C₁₁×#126	C₂²	semidirect
32. C₁₁×#125	C₂²	semidirect
35. C₁₁×#123	C₂²	semidirect
36. C₁₁×C₂²⋊Q₈	C₂²	semidirect
38. C₄×Q₈×C₁₁	C₂²	semidirect
41. C₄×D₄×C₁₁	C₂²	semidirect
43. C₁₁×#117	C₂²	semidirect
44. C₂×C₄²×C₁₁	C₂²	semidirect
45. #67000	C₂²	semidirect
46. #66999	C₂²	semidirect
47. #66993	C₂²	semidirect
49. #66992	C₂²	semidirect
55. #66983	C₂²	semidirect
56. #66983	C₂²	semidirect
57. #66983	C₂²	semidirect
58. #66982	C₂²	semidirect
59. C₄×C₂²⋊D₁₁	C₂²	semidirect
62. #66977	C₂²	semidirect
63. #66951	C₂²	semidirect
64. #66951	C₂²	semidirect
65. #66950	C₂²	semidirect
66. #66950	C₂²	semidirect
67. #66949	C₂²	semidirect
68. #66949	C₂²	semidirect
73. #66947	C₂²	semidirect
74. #66947	C₂²	semidirect
75. #66947	C₂²	semidirect
76. #66947	C₂²	semidirect
77. #66946	C₂²	semidirect
78. #66946	C₂²	semidirect
79. #66945	C₂²	semidirect
80. C₄⋊C₄×D₁₁	C₂²	semidirect
81. #66942	C₂²	semidirect
82. #66942	C₂²	semidirect
83. #66939	C₂²	semidirect
84. #66939	C₂²	semidirect
86. #66938	C₂²	semidirect
89. #66937	C₂²	semidirect
90. #66937	C₂²	semidirect
91. #66937	C₂²	semidirect
92. #66937	C₂²	semidirect
94. #66936	C₂²	semidirect
97. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
98. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
103. #66929	C₂²	semidirect
108. #66928	C₂²	semidirect
113. C₄×D₄₄	C₂²	semidirect
114. C₄×D₄₄	C₂²	semidirect
115. C₄×D₄₄	C₂²	semidirect
116. #66925	C₂²	semidirect
117. #66923	C₂²	semidirect
118. #66922	C₂²	semidirect
119. #66922	C₂²	semidirect
120. C₄×Dic₂₂	C₂²	semidirect
121. C₄×Dic₂₂	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
313. #529	D₁₁	semidirect
368. #126	C₂×D₁₁	semidirect
372. #125	C₂×D₁₁	semidirect
394. #123	C₂×D₁₁	semidirect
403. C₂²⋊Q₈	C₂×D₁₁	semidirect
428. C₄×Q₈	C₂×D₁₁	semidirect
441. C₄×D₄	C₂×D₁₁	semidirect
445. #117	C₂×D₁₁	semidirect
449. C₂×C₄²	C₂×D₁₁	semidirect
564. C₁₁	#3562	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#529	2
#10623240	2
#10623236	2
#10623223	2
#10623209	2
#10623194	2
#10623188	2
#10623178	2
#10623151	2
#10623116	2
#10623115	2
#10623084	2
#10623083	2
#10623082	2
#10623081	2
#10623066	2
#10623057	2
#10623056	2
#10623049	2
#10623010	2
#10623008	2
#3562	11