Subgroups — #13082037

Order 1408.

1140 conjugacy classes of subgroups.

The subgroup lattice has 680 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	#10623241	C₂	1	2	yes	maximal, complemented
3	#10623235	C₂	1	2	yes	maximal, complemented
4	#10623229	C₂	1	1	yes	maximal, characteristic, complemented
5	#10623220	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623213	C₂	1	1	yes	maximal, characteristic, complemented
7	#10623205	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623194	C₂	1	2	yes	maximal, complemented
9	#10623188	C₂	1	2	yes	maximal, complemented
10	#10623174	C₂	1	1	yes	maximal, characteristic, complemented
11	#10623160	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623150	C₂	1	1	yes	maximal, characteristic, complemented
13	#10623138	C₂	1	1	yes	maximal, characteristic, complemented
14	#10623111	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#4343	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623079	C₂	1	2	yes	maximal, complemented
17	#10623079	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623078	C₂	1	2	yes	maximal, complemented
19	C₄×D₄×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623059	C₂	1	2	yes	maximal, complemented
21	#10623055	C₂	1	2	yes	maximal, complemented
22	#10623008	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#4339	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#4343	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
26	C₂×#4339	C₂²	1	1	yes	characteristic
27	C₂×#4339	C₂²	1	2	yes	complemented
28	C₂×#4339	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₁₁	C₂²	1	2	yes	—
30	C₁₁×#126	C₂²	1	2	yes	complemented
31	C₁₁×#125	C₂²	1	1	yes	characteristic, complemented
32	C₁₁×#124	C₂²	1	1	yes	characteristic
33	C₁₁×#123	C₂²	1	2	yes	complemented
34	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₁×#121	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₁₁	C₂²	1	2	yes	complemented
39	C₁₁×#117	C₂²	1	2	yes	complemented
40	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic, complemented
41	#67000	C₂²	1	1	yes	characteristic
42	#66999	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
44	#66993	C₂²	1	2	yes	—
45	#66993	C₂²	1	1	yes	characteristic
46	#66992	C₂²	1	2	yes	complemented
47	#66991	C₂²	1	1	yes	characteristic
48	#66991	C₂²	1	2	yes	complemented
49	#66990	C₂²	1	2	yes	—
50	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
51	#66983	C₂²	1	1	yes	characteristic
52	#66983	C₂²	1	1	yes	characteristic, complemented
53	#66983	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
57	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
60	#66979	C₂²	1	1	yes	characteristic, complemented
61	#66951	C₂²	1	2	yes	complemented
62	#66951	C₂²	1	2	yes	complemented
63	#66950	C₂²	1	2	yes	—
64	#66950	C₂²	1	2	yes	complemented
65	#66949	C₂²	1	2	yes	—
66	#66949	C₂²	1	2	yes	complemented
67	#66948	C₂²	1	2	yes	—
68	#66948	C₂²	1	1	yes	characteristic
69	#66948	C₂²	1	2	yes	complemented
70	#66948	C₂²	1	2	yes	complemented
71	#66948	C₂²	1	1	yes	characteristic, complemented
72	#66947	C₂²	1	2	yes	complemented
73	#66947	C₂²	1	2	yes	complemented
74	#66947	C₂²	1	2	yes	complemented
75	#66946	C₂²	1	2	yes	—
76	#66946	C₂²	1	1	yes	characteristic
77	#66946	C₂²	1	1	yes	characteristic, complemented
78	#66945	C₂²	1	1	yes	characteristic
79	#66945	C₂²	1	2	yes	complemented
80	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
81	#66943	C₂²	1	1	yes	characteristic, complemented
82	#66942	C₂²	1	2	yes	complemented
83	#66941	C₂²	1	2	yes	complemented
84	#66941	C₂²	1	1	yes	characteristic, complemented
85	#66939	C₂²	1	2	yes	complemented
86	#66939	C₂²	1	2	yes	complemented
87	#66938	C₂²	1	2	yes	—
88	#66938	C₂²	1	2	yes	complemented
89	#66938	C₂²	1	2	yes	complemented
90	#66938	C₂²	1	2	yes	complemented
91	#66937	C₂²	1	2	yes	—
92	#66937	C₂²	1	2	yes	—
93	#66937	C₂²	1	2	yes	—
94	#66937	C₂²	1	2	yes	complemented
95	#66937	C₂²	1	2	yes	complemented
96	#66936	C₂²	1	2	yes	complemented
97	#66936	C₂²	1	2	yes	complemented
98	#66935	C₂²	1	2	yes	—
99	#66935	C₂²	1	2	yes	—
100	#66935	C₂²	1	2	yes	—
101	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
102	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
103	#66932	C₂²	1	2	yes	complemented
104	#66931	C₂²	1	2	yes	complemented
105	#66928	C₂²	1	2	yes	complemented
106	#66927	C₂²	1	1	yes	characteristic
107	C₄×D₄₄	C₂²	1	1	yes	characteristic
108	C₄×D₄₄	C₂²	1	1	yes	characteristic
109	C₄×D₄₄	C₂²	1	1	yes	characteristic
110	C₄×D₄₄	C₂²	1	2	yes	—
111	C₄×D₄₄	C₂²	1	2	yes	complemented
112	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₄₄	C₂²	1	2	yes	complemented
114	#66925	C₂²	1	1	yes	characteristic
115	#66925	C₂²	1	1	yes	characteristic, complemented
116	#66925	C₂²	1	2	yes	complemented
117	C₄²×D₁₁	C₂²	1	1	yes	characteristic
118	C₄²×D₁₁	C₂²	1	1	yes	characteristic, complemented
119	C₄²×D₁₁	C₂²	1	2	yes	complemented
120	#66922	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	2	yes	—
127	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
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	C₂²×Dic₁₁	C₂³	1	2	yes	—
140	#4343	—	2	4	no	—
141	D₄×D₁₁	—	2	4	no	—
142	#4339	—	2	4	no	—
143	#4339	—	4	4	no	—
144	#4339	—	4	4	no	—
145	C₂×D₄₄	C₂³	1	1	yes	characteristic
146	C₂×D₄₄	C₂³	1	1	yes	characteristic
147	C₂×D₄₄	C₂³	1	2	yes	—
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×C₄×D₁₁	—	4	4	no	—
154	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
161	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₁	C₂³	1	2	yes	—
163	C₂×C₄×D₁₁	C₂³	1	2	yes	—
164	C₂×C₄×D₁₁	C₂³	1	2	yes	—
165	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
166	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
167	C₂×Dic₂₂	C₂³	1	2	yes	—
168	C₂×Dic₂₂	C₂³	1	2	yes	—
169	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
171	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
172	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
174	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
175	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₄²×C₁₁	C₂³	1	1	yes	characteristic
181	C₄²×C₁₁	C₂³	1	1	yes	characteristic
182	C₄²×C₁₁	C₂³	1	1	yes	characteristic
183	C₄²×C₁₁	C₂³	1	1	yes	characteristic
184	C₄²×C₁₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
189	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₁)⋊C₄	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	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₁	C₂³	1	2	yes	—
209	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₁₁	C₂³	1	2	yes	—
211	C₄⋊Dic₁₁	C₂³	1	2	yes	—
212	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
216	Dic₁₁⋊C₄	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	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₁	C₂³	1	2	yes	—
227	C₄×Dic₁₁	C₂³	1	2	yes	—
228	#3460	—	11	1	no	maximal, Sylow
229	C₂³×C₁₁	C₂⁴	1	2	yes	—
230	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₁	—	2	4	no	—
232	C₂²×D₁₁	—	4	2	no	—
233	C₂²×D₁₁	—	4	2	no	—
234	C₂²×D₁₁	C₂⁴	1	2	yes	—
235	C₂²×D₁₁	C₂⁴	1	2	yes	—
236	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
238	Q₈×C₁₁	—	2	2	no	—
239	D₄×C₁₁	—	2	2	no	—
240	D₄×C₁₁	—	4	2	no	—
241	C₂×C₄×C₁₁	—	2	2	no	—
242	C₂×C₄×C₁₁	—	2	4	no	—
243	C₂×C₄×C₁₁	—	2	2	no	—
244	C₂×C₄×C₁₁	—	4	1	no	—
245	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
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	C₂²⋊D₁₁	—	2	2	no	—
255	C₂²⋊D₁₁	—	2	2	no	—
256	C₂²⋊D₁₁	—	2	4	no	—
257	C₂²⋊D₁₁	—	4	2	no	—
258	C₂²⋊D₁₁	—	4	2	no	—
259	C₂²⋊D₁₁	—	4	2	no	—
260	C₂²⋊D₁₁	—	4	2	no	—
261	C₂²⋊D₁₁	—	4	2	no	—
262	C₂×Dic₁₁	—	4	2	no	—
263	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₁	C₂⁴	1	2	yes	—
268	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₁	C₂⁴	1	2	yes	—
270	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
271	D₄₄	—	2	2	no	—
272	D₄₄	—	2	4	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	C₄×D₁₁	—	2	2	no	—
280	C₄×D₁₁	—	2	2	no	—
281	C₄×D₁₁	—	2	4	no	—
282	C₄×D₁₁	—	2	2	no	—
283	C₄×D₁₁	—	2	4	no	—
284	C₄×D₁₁	—	2	4	no	—
285	C₄×D₁₁	—	4	2	no	—
286	C₄×D₁₁	—	4	2	no	—
287	C₄×D₁₁	—	4	1	no	—
288	C₄×D₁₁	—	4	2	no	—
289	C₄×D₁₁	—	4	1	no	—
290	C₄×D₁₁	#41	1	4	yes	complemented
291	Dic₂₂	—	2	2	no	—
292	Dic₂₂	—	4	2	no	—
293	Dic₂₂	—	4	2	no	—
294	#544	—	11	1	no	—
295	#542	—	11	2	no	—
296	#542	—	11	1	no	—
297	#542	—	11	1	no	—
298	#540	—	11	1	no	—
299	#540	—	11	2	no	—
300	#540	—	11	1	no	—
301	#538	—	11	2	no	—
302	#538	—	11	2	no	—
303	#537	—	11	1	no	—
304	#535	—	11	1	no	—
305	#535	—	11	1	no	—
306	#532	—	11	1	no	—
307	#532	—	11	2	no	—
308	#532	—	11	1	no	—
309	#529	—	11	1	no	—
310	#529	—	11	2	no	—
311	#529	D₁₁	1	1	yes	characteristic, complemented
312	#525	—	11	2	no	—
313	#525	—	11	2	no	—
314	C₄×#41	—	11	1	no	—
315	C₄×#41	—	11	1	no	—
316	C₂×C₄×D₄	—	11	1	no	—
317	C₂²×C₁₁	—	2	1	no	—
318	C₂²×C₁₁	—	2	2	no	—
319	C₂²×C₁₁	—	2	2	no	—
320	C₂²×C₁₁	—	2	1	no	—
321	C₂²×C₁₁	—	2	1	no	—
322	C₂²×C₁₁	—	2	2	no	—
323	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
324	C₂×D₁₁	—	2	1	no	—
325	C₂×D₁₁	—	2	1	no	—
326	C₂×D₁₁	—	2	2	no	—
327	C₂×D₁₁	—	2	2	no	—
328	C₂×D₁₁	—	2	1	no	—
329	C₂×D₁₁	—	2	2	no	—
330	C₂×D₁₁	—	2	2	no	—
331	C₂×D₁₁	—	2	1	no	—
332	C₂×D₁₁	—	2	2	no	—
333	C₂×D₁₁	—	2	1	no	—
334	C₂×D₁₁	—	2	2	no	—
335	C₂×D₁₁	—	4	8	no	—
336	C₂×D₁₁	C₂×#41	1	2	yes	—
337	C₄×C₁₁	—	2	1	no	—
338	C₄×C₁₁	—	2	2	no	—
339	C₄×C₁₁	—	2	1	no	—
340	C₄×C₁₁	—	2	2	no	—
341	C₄×C₁₁	—	2	1	no	—
342	C₄×C₁₁	—	2	1	no	—
343	C₄×C₁₁	—	2	2	no	—
344	C₄×C₁₁	C₂×#41	1	2	yes	—
345	C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
346	Dic₁₁	—	2	1	no	—
347	Dic₁₁	—	2	1	no	—
348	Dic₁₁	—	2	2	no	—
349	Dic₁₁	—	2	2	no	—
350	Dic₁₁	—	2	1	no	—
351	Dic₁₁	—	2	1	no	—
352	Dic₁₁	—	2	1	no	—
353	Dic₁₁	C₂×#41	1	2	yes	—
354	C₂×#41	—	11	1	no	—
355	C₂×#41	—	11	1	no	—
356	C₂×#41	—	11	2	no	—
357	C₂×#41	—	11	2	no	—
358	C₂²×D₄	—	11	1	no	—
359	C₂³×C₄	—	11	2	no	—
360	C₄⋊Q₈	—	11	2	no	—
361	C₄⋊Q₈	—	11	1	no	—
362	C₄⋊Q₈	—	11	1	no	—
363	#127	—	11	2	no	—
364	#127	—	11	1	no	—
365	#127	—	11	1	no	—
366	#126	—	11	2	no	—
367	#126	—	11	2	no	—
368	#126	—	11	2	no	—
369	#126	C₂×D₁₁	1	2	yes	complemented
370	#125	—	11	2	no	—
371	#125	—	11	1	no	—
372	#125	C₂×D₁₁	1	1	yes	characteristic, complemented
373	#124	—	11	1	no	—
374	#124	—	11	2	no	—
375	#124	—	11	2	no	—
376	#124	—	11	2	no	—
377	#124	—	11	2	no	—
378	#124	—	11	2	no	—
379	#124	C₂×D₁₁	1	1	yes	characteristic
380	#123	—	11	2	no	—
381	#123	—	11	2	no	—
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	C₂×D₁₁	1	2	yes	complemented
388	C₂²⋊Q₈	—	11	1	no	—
389	C₂²⋊Q₈	—	11	2	no	—
390	C₂²⋊Q₈	—	11	2	no	—
391	C₂²⋊Q₈	—	11	2	no	—
392	C₂²⋊Q₈	—	11	2	no	—
393	C₂²⋊Q₈	—	11	2	no	—
394	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
395	#121	—	11	2	no	—
396	#121	—	11	1	no	—
397	#121	—	11	2	no	—
398	#121	—	11	1	no	—
399	#121	—	11	1	no	—
400	#121	—	11	2	no	—
401	#121	—	11	2	no	—
402	#121	—	11	2	no	—
403	#121	—	11	1	no	—
404	#121	—	11	1	no	—
405	#121	—	11	2	no	—
406	#121	—	11	2	no	—
407	#121	—	11	2	no	—
408	#121	—	11	2	no	—
409	#121	—	11	2	no	—
410	#121	—	11	2	no	—
411	#121	C₂×D₁₁	1	1	yes	characteristic
412	#120	—	11	2	no	—
413	#120	—	11	2	no	—
414	#120	—	11	2	no	—
415	#120	—	11	2	no	—
416	C₄×Q₈	—	11	1	no	—
417	C₄×Q₈	—	11	1	no	—
418	C₄×Q₈	—	11	1	no	—
419	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
420	C₄×D₄	—	11	1	no	—
421	C₄×D₄	—	11	2	no	—
422	C₄×D₄	—	11	1	no	—
423	C₄×D₄	—	11	1	no	—
424	C₄×D₄	—	11	1	no	—
425	C₄×D₄	—	11	1	no	—
426	C₄×D₄	—	11	2	no	—
427	C₄×D₄	—	11	1	no	—
428	C₄×D₄	—	11	2	no	—
429	C₄×D₄	—	11	1	no	—
430	C₄×D₄	—	11	2	no	—
431	C₄×D₄	—	11	1	no	—
432	C₄×D₄	—	11	2	no	—
433	C₄×D₄	—	11	1	no	—
434	C₄×D₄	—	11	1	no	—
435	C₄×D₄	—	11	1	no	—
436	C₄×D₄	—	11	2	no	—
437	C₄×D₄	—	11	2	no	—
438	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
439	C₄×D₄	C₂×D₁₁	1	2	yes	complemented
440	#117	—	11	1	no	—
441	#117	—	11	1	no	—
442	#117	—	11	2	no	—
443	#117	—	11	1	no	—
444	#117	—	11	1	no	—
445	#117	—	11	2	no	—
446	#117	C₂×D₁₁	1	2	yes	complemented
447	C₂×C₄⋊C₄	—	11	1	no	—
448	C₂×C₂²⋊C₄	—	11	2	no	—
449	C₂×C₄²	—	11	1	no	—
450	C₂×C₄²	—	11	2	no	—
451	C₂×C₄²	—	11	1	no	—
452	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic, complemented
453	C₂×C₁₁	—	4	2	no	—
454	C₂×C₁₁	—	4	1	no	—
455	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
456	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂×C₁₁	#585	1	1	yes	characteristic
458	D₁₁	—	2	2	no	—
459	D₁₁	—	4	2	no	—
460	D₁₁	—	4	1	no	—
461	D₁₁	—	4	2	no	—
462	C₂⁴	—	11	2	no	—
463	#41	—	22	4	no	—
464	#41	—	22	4	no	—
465	#41	—	44	4	no	—
466	#41	—	44	4	no	—
467	C₂×Q₈	—	11	1	no	—
468	C₂×Q₈	—	11	2	no	—
469	C₂×Q₈	—	11	2	no	—
470	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
471	C₂×D₄	—	11	1	no	—
472	C₂×D₄	—	11	2	no	—
473	C₂×D₄	—	11	1	no	—
474	C₂×D₄	—	11	2	no	—
475	C₂×D₄	—	11	2	no	—
476	C₂×D₄	—	11	2	no	—
477	C₂×D₄	—	11	2	no	—
478	C₂×D₄	—	11	2	no	—
479	C₂×D₄	—	11	2	no	—
480	C₂×D₄	—	11	1	no	—
481	C₂×D₄	—	11	1	no	—
482	C₂×D₄	—	11	1	no	—
483	C₂×D₄	—	11	2	no	—
484	C₂×D₄	—	11	2	no	—
485	C₂×D₄	—	11	2	no	—
486	C₂×D₄	—	11	2	no	—
487	C₂×D₄	—	22	4	no	—
488	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
489	C₂×D₄	C₂²×D₁₁	1	2	yes	—
490	C₂²×C₄	—	11	1	no	—
491	C₂²×C₄	—	11	2	no	—
492	C₂²×C₄	—	11	2	no	—
493	C₂²×C₄	—	11	1	no	—
494	C₂²×C₄	—	11	1	no	—
495	C₂²×C₄	—	11	1	no	—
496	C₂²×C₄	—	11	2	no	—
497	C₂²×C₄	—	11	2	no	—
498	C₂²×C₄	—	11	1	no	—
499	C₂²×C₄	—	11	2	no	—
500	C₂²×C₄	—	11	1	no	—
501	C₂²×C₄	—	11	2	no	—
502	C₂²×C₄	—	11	2	no	—
503	C₂²×C₄	—	44	4	no	—
504	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
505	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
506	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
507	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
508	C₄⋊C₄	—	11	2	no	—
509	C₄⋊C₄	—	11	1	no	—
510	C₄⋊C₄	—	11	1	no	—
511	C₄⋊C₄	—	11	1	no	—
512	C₄⋊C₄	—	11	1	no	—
513	C₄⋊C₄	—	11	1	no	—
514	C₄⋊C₄	—	11	2	no	—
515	C₄⋊C₄	—	11	1	no	—
516	C₄⋊C₄	—	11	1	no	—
517	C₄⋊C₄	—	11	1	no	—
518	C₄⋊C₄	—	11	2	no	—
519	C₄⋊C₄	—	11	2	no	—
520	C₄⋊C₄	—	11	2	no	—
521	C₄⋊C₄	—	11	2	no	—
522	C₄⋊C₄	—	11	2	no	—
523	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
526	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
527	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
528	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
529	C₂²⋊C₄	—	11	2	no	—
530	C₂²⋊C₄	—	11	1	no	—
531	C₂²⋊C₄	—	11	1	no	—
532	C₂²⋊C₄	—	11	2	no	—
533	C₂²⋊C₄	—	11	2	no	—
534	C₂²⋊C₄	—	11	2	no	—
535	C₂²⋊C₄	—	11	1	no	—
536	C₂²⋊C₄	—	11	2	no	—
537	C₂²⋊C₄	—	11	1	no	—
538	C₂²⋊C₄	—	11	2	no	—
539	C₂²⋊C₄	—	11	1	no	—
540	C₂²⋊C₄	—	11	1	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	—	11	2	no	—
546	C₂²⋊C₄	—	11	2	no	—
547	C₂²⋊C₄	—	11	2	no	—
548	C₂²⋊C₄	—	11	2	no	—
549	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
554	C₄²	—	11	1	no	—
555	C₄²	—	11	1	no	—
556	C₄²	—	11	2	no	—
557	C₄²	—	11	1	no	—
558	C₄²	—	11	2	no	—
559	C₄²	—	11	1	no	—
560	C₄²	—	11	1	no	—
561	C₄²	—	11	1	no	—
562	C₄²	C₂²×D₁₁	1	1	yes	characteristic
563	C₄²	C₂²×D₁₁	1	1	yes	characteristic
564	C₄²	C₂²×D₁₁	1	1	yes	characteristic
565	C₄²	C₂²×D₁₁	1	2	yes	—
566	C₄²	C₂²×D₁₁	1	1	yes	characteristic
567	C₁₁	#3460	1	1	yes	characteristic, complemented, Sylow
568	C₂³	—	11	1	no	—
569	C₂³	—	11	2	no	—
570	C₂³	—	11	1	no	—
571	C₂³	—	11	2	no	—
572	C₂³	—	22	4	no	—
573	C₂³	—	44	2	no	—
574	C₂³	—	44	2	no	—
575	C₂³	C₂³×D₁₁	1	2	yes	—
576	C₂³	C₂³×D₁₁	1	1	yes	characteristic
577	Q₈	—	2	2	no	—
578	Q₈	—	22	2	no	—
579	Q₈	—	44	2	no	—
580	Q₈	—	44	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	22	2	no	—
584	D₄	—	22	4	no	—
585	D₄	—	22	4	no	—
586	D₄	—	22	2	no	—
587	D₄	—	22	2	no	—
588	D₄	—	22	2	no	—
589	D₄	—	22	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	D₄	—	44	2	no	—
598	D₄	—	44	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	11	1	no	—
604	C₂×C₄	—	11	4	no	—
605	C₂×C₄	—	11	1	no	—
606	C₂×C₄	—	11	1	no	—
607	C₂×C₄	—	11	1	no	—
608	C₂×C₄	—	11	1	no	—
609	C₂×C₄	—	11	1	no	—
610	C₂×C₄	—	11	2	no	—
611	C₂×C₄	—	11	2	no	—
612	C₂×C₄	—	22	4	no	—
613	C₂×C₄	—	22	2	no	—
614	C₂×C₄	—	22	2	no	—
615	C₂×C₄	—	22	4	no	—
616	C₂×C₄	—	22	2	no	—
617	C₂×C₄	—	22	4	no	—
618	C₂×C₄	—	44	2	no	—
619	C₂×C₄	—	44	2	no	—
620	C₂×C₄	—	44	1	no	—
621	C₂×C₄	—	44	1	no	—
622	C₂×C₄	—	44	2	no	—
623	C₂×C₄	—	44	2	no	—
624	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₁	1	2	yes	—
626	C₂×C₄	C₂³×D₁₁	1	2	yes	—
627	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₁	1	2	yes	—
631	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	11	2	no	—
640	C₂²	—	22	1	no	—
641	C₂²	—	22	1	no	—
642	C₂²	—	22	2	no	—
643	C₂²	—	22	1	no	—
644	C₂²	—	22	2	no	—
645	C₂²	—	22	2	no	—
646	C₂²	—	22	1	no	—
647	C₂²	—	22	2	no	—
648	C₂²	—	22	1	no	—
649	C₂²	—	22	2	no	—
650	C₂²	—	22	2	no	—
651	C₂²	—	44	8	no	—
652	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	2	no	—
660	C₄	—	11	2	no	—
661	C₄	—	22	1	no	—
662	C₄	—	22	1	no	—
663	C₄	—	22	2	no	—
664	C₄	—	22	1	no	—
665	C₄	—	22	2	no	—
666	C₄	—	22	1	no	—
667	C₄	—	22	1	no	—
668	C₄	#41×D₁₁	1	2	yes	—
669	C₄	#67042	1	2	yes	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	22	2	no	—
673	C₂	—	44	2	no	—
674	C₂	—	44	2	no	—
675	C₂	—	44	1	no	—
676	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
677	C₂	C₂×#67042	1	1	yes	characteristic
678	C₂	#10623453	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁
Fitting	C₁₁×#529	C₂
hypercenter	#529	D₁₁
hypocenter	C₁₁	#3460
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₁₁×#529	C₂	semidirect
2. #10623241	C₂	semidirect
3. #10623235	C₂	semidirect
4. #10623229	C₂	semidirect
5. #10623220	C₂	semidirect
6. #10623213	C₂	semidirect
7. #10623205	C₂	semidirect
8. #10623194	C₂	semidirect
9. #10623188	C₂	semidirect
10. #10623174	C₂	semidirect
11. #10623160	C₂	semidirect
12. #10623150	C₂	semidirect
13. #10623138	C₂	semidirect
14. #10623111	C₂	semidirect
15. C₄×#4343	C₂	semidirect
16. #10623079	C₂	semidirect
17. #10623079	C₂	semidirect
18. #10623078	C₂	semidirect
19. C₄×D₄×D₁₁	C₂	semidirect
20. #10623059	C₂	semidirect
21. #10623055	C₂	semidirect
22. #10623008	C₂	semidirect
23. C₄×#4339	C₂	semidirect
27. C₂×#4339	C₂²	semidirect
28. C₂×#4339	C₂²	semidirect
30. C₁₁×#126	C₂²	semidirect
31. C₁₁×#125	C₂²	semidirect
33. C₁₁×#123	C₂²	semidirect
34. C₁₁×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₁	C₂²	semidirect
38. C₄×D₄×C₁₁	C₂²	semidirect
39. C₁₁×#117	C₂²	semidirect
40. C₂×C₄²×C₁₁	C₂²	semidirect
42. #66999	C₂²	semidirect
43. Q₈×Dic₁₁	C₂²	semidirect
46. #66992	C₂²	semidirect
48. #66991	C₂²	semidirect
52. #66983	C₂²	semidirect
53. #66983	C₂²	semidirect
57. C₄×C₂²⋊D₁₁	C₂²	semidirect
58. C₄×C₂²⋊D₁₁	C₂²	semidirect
59. C₄×C₂²⋊D₁₁	C₂²	semidirect
60. #66979	C₂²	semidirect
61. #66951	C₂²	semidirect
62. #66951	C₂²	semidirect
64. #66950	C₂²	semidirect
66. #66949	C₂²	semidirect
69. #66948	C₂²	semidirect
70. #66948	C₂²	semidirect
71. #66948	C₂²	semidirect
72. #66947	C₂²	semidirect
73. #66947	C₂²	semidirect
74. #66947	C₂²	semidirect
77. #66946	C₂²	semidirect
79. #66945	C₂²	semidirect
81. #66943	C₂²	semidirect
82. #66942	C₂²	semidirect
83. #66941	C₂²	semidirect
84. #66941	C₂²	semidirect
85. #66939	C₂²	semidirect
86. #66939	C₂²	semidirect
88. #66938	C₂²	semidirect
89. #66938	C₂²	semidirect
90. #66938	C₂²	semidirect
94. #66937	C₂²	semidirect
95. #66937	C₂²	semidirect
96. #66936	C₂²	semidirect
97. #66936	C₂²	semidirect
103. #66932	C₂²	semidirect
104. #66931	C₂²	semidirect
105. #66928	C₂²	semidirect
111. C₄×D₄₄	C₂²	semidirect
112. C₄×D₄₄	C₂²	semidirect
113. C₄×D₄₄	C₂²	semidirect
115. #66925	C₂²	semidirect
116. #66925	C₂²	semidirect
118. C₄²×D₁₁	C₂²	semidirect
119. C₄²×D₁₁	C₂²	semidirect
120. #66922	C₂²	semidirect
121. C₄×Dic₂₂	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
290. C₄×D₁₁	#41	semidirect
311. #529	D₁₁	semidirect
369. #126	C₂×D₁₁	semidirect
372. #125	C₂×D₁₁	semidirect
387. #123	C₂×D₁₁	semidirect
394. C₂²⋊Q₈	C₂×D₁₁	semidirect
419. C₄×Q₈	C₂×D₁₁	semidirect
439. C₄×D₄	C₂×D₁₁	semidirect
446. #117	C₂×D₁₁	semidirect
452. C₂×C₄²	C₂×D₁₁	semidirect
567. C₁₁	#3460	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
#10623241	2
#10623235	2
#10623229	2
#10623220	2
#10623213	2
#10623205	2
#10623194	2
#10623188	2
#10623174	2
#10623160	2
#10623150	2
#10623138	2
#10623111	2
C₄×#4343	2
#10623079	2
#10623078	2
C₄×D₄×D₁₁	2
#10623059	2
#10623055	2
#10623008	2
C₄×#4339	2
#3460	11