Subgroups — #13082605

Order 1408.

1012 conjugacy classes of subgroups.

The subgroup lattice has 628 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	#10623239	C₂	1	2	yes	maximal, complemented
3	#10623233	C₂	1	2	yes	maximal, complemented
4	#10623227	C₂	1	2	yes	maximal, complemented
5	#10623200	C₂	1	2	yes	maximal, complemented
6	#10623180	C₂	1	2	yes	maximal, complemented
7	#10623180	C₂	1	2	yes	maximal, complemented
8	#10623167	C₂	1	2	yes	maximal, complemented
9	#10623132	C₂	1	2	yes	maximal, complemented
10	#10623115	C₂	1	1	yes	maximal, characteristic, complemented
11	#10623098	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623096	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	#10623074	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623072	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623065	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623054	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623049	C₂	1	1	yes	maximal, characteristic, complemented
21	#10623047	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623010	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#4339	C₂²	1	1	yes	characteristic
25	C₂²×Dic₂₂	C₂²	1	1	yes	characteristic
26	C₂²×Dic₂₂	C₂²	1	1	yes	characteristic
27	C₁₁×#126	C₂²	1	1	yes	characteristic
28	C₁₁×#126	C₂²	1	1	yes	characteristic
29	C₁₁×#125	C₂²	1	1	yes	characteristic
30	C₁₁×#124	C₂²	1	1	yes	characteristic
31	C₁₁×#123	C₂²	1	1	yes	characteristic
32	C₁₁×#123	C₂²	1	1	yes	characteristic
33	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₁×#121	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
39	C₁₁×#117	C₂²	1	1	yes	characteristic
40	C₁₁×#117	C₂²	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
42	#66999	C₂²	1	2	yes	—
43	#66997	C₂²	1	2	yes	—
44	#66992	C₂²	1	2	yes	—
45	#66992	C₂²	1	2	yes	—
46	#66992	C₂²	1	2	yes	—
47	#66988	C₂²	1	2	yes	—
48	D₄×Dic₁₁	C₂²	1	2	yes	—
49	D₄×Dic₁₁	C₂²	1	2	yes	—
50	#66983	C₂²	1	1	yes	characteristic
51	#66983	C₂²	1	1	yes	characteristic
52	#66982	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
54	#66979	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic
57	#66977	C₂²	1	1	yes	characteristic
58	#66977	C₂²	1	1	yes	characteristic
59	#66977	C₂²	1	1	yes	characteristic
60	#66977	C₂²	1	1	yes	characteristic
61	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	—
62	C₂×C₄×Dic₁₁	C₂²	1	2	yes	—
63	#66951	C₂²	1	2	yes	—
64	#66951	C₂²	1	2	yes	—
65	#66951	C₂²	1	2	yes	—
66	#66951	C₂²	1	2	yes	—
67	#66949	C₂²	1	2	yes	—
68	#66949	C₂²	1	2	yes	—
69	#66949	C₂²	1	2	yes	—
70	#66945	C₂²	1	2	yes	—
71	#66945	C₂²	1	2	yes	—
72	C₄⋊C₄×D₁₁	C₂²	1	2	yes	—
73	#66943	C₂²	1	2	yes	—
74	#66942	C₂²	1	2	yes	—
75	#66942	C₂²	1	2	yes	—
76	#66942	C₂²	1	2	yes	—
77	#66942	C₂²	1	2	yes	—
78	#66942	C₂²	1	2	yes	—
79	#66941	C₂²	1	2	yes	—
80	#66940	C₂²	1	2	yes	—
81	#66940	C₂²	1	2	yes	—
82	#66940	C₂²	1	2	yes	—
83	#66938	C₂²	1	2	yes	—
84	#66938	C₂²	1	2	yes	—
85	#66938	C₂²	1	2	yes	—
86	#66936	C₂²	1	2	yes	—
87	#66936	C₂²	1	2	yes	—
88	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
89	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
90	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
91	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
92	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
93	#66932	C₂²	1	2	yes	—
94	#66932	C₂²	1	2	yes	—
95	#66932	C₂²	1	2	yes	—
96	#66931	C₂²	1	2	yes	—
97	#66931	C₂²	1	2	yes	—
98	#66931	C₂²	1	2	yes	—
99	#66931	C₂²	1	2	yes	—
100	#66930	C₂²	1	2	yes	—
101	#66930	C₂²	1	2	yes	—
102	#66930	C₂²	1	2	yes	—
103	#66929	C₂²	1	2	yes	—
104	#66928	C₂²	1	1	yes	characteristic
105	#66928	C₂²	1	1	yes	characteristic
106	C₄×D₄₄	C₂²	1	1	yes	characteristic
107	C₄×D₄₄	C₂²	1	1	yes	characteristic
108	#66925	C₂²	1	2	yes	—
109	#66923	C₂²	1	1	yes	characteristic
110	#66923	C₂²	1	1	yes	characteristic
111	#66922	C₂²	1	1	yes	characteristic
112	#66922	C₂²	1	1	yes	characteristic
113	C₄×Dic₂₂	C₂²	1	2	yes	—
114	C₄×Dic₂₂	C₂²	1	1	yes	characteristic
115	C₄×Dic₂₂	C₂²	1	1	yes	characteristic
116	C₄×Dic₂₂	C₂²	1	1	yes	characteristic
117	C₄×Dic₂₂	C₂²	1	1	yes	characteristic
118	C₄×Dic₂₂	C₂²	1	2	yes	—
119	C₄×Dic₂₂	C₂²	1	1	yes	characteristic
120	C₄×Dic₂₂	C₂²	1	1	yes	characteristic
121	C₄×Dic₂₂	C₂²	1	1	yes	characteristic
122	C₄×Dic₂₂	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
124	C₂×D₄×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	C₂²×C₄×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	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
135	C₂²×Dic₁₁	C₂³	1	2	yes	—
136	C₂²×Dic₁₁	C₂³	1	2	yes	—
137	C₂²×Dic₁₁	C₂³	1	2	yes	—
138	C₂²×Dic₁₁	C₂³	1	2	yes	—
139	#4339	—	2	4	no	—
140	C₂×D₄₄	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₁	C₂³	1	2	yes	—
142	C₂×C₄×D₁₁	C₂³	1	2	yes	—
143	C₂×C₄×D₁₁	C₂³	1	2	yes	—
144	C₂×Dic₂₂	—	2	4	no	—
145	C₂×Dic₂₂	—	2	4	no	—
146	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
147	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
148	C₂×Dic₂₂	C₂³	1	2	yes	—
149	C₂×Dic₂₂	C₂³	1	2	yes	—
150	C₂×Dic₂₂	C₂³	1	2	yes	—
151	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
152	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
164	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₄²×C₁₁	C₂³	1	1	yes	characteristic
173	C₄²×C₁₁	C₂³	1	1	yes	characteristic
174	C₄²×C₁₁	C₂³	1	1	yes	characteristic
175	C₄²×C₁₁	C₂³	1	1	yes	characteristic
176	C₄²×C₁₁	C₂³	1	1	yes	characteristic
177	C₄²×C₁₁	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
183	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
191	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₁₁	C₂³	1	2	yes	—
195	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₁₁	C₂³	1	2	yes	—
197	C₄⋊Dic₁₁	C₂³	1	2	yes	—
198	C₄⋊Dic₁₁	C₂³	1	2	yes	—
199	C₄⋊Dic₁₁	C₂³	1	2	yes	—
200	Dic₁₁⋊C₄	C₂³	1	2	yes	—
201	Dic₁₁⋊C₄	C₂³	1	2	yes	—
202	Dic₁₁⋊C₄	C₂³	1	2	yes	—
203	Dic₁₁⋊C₄	C₂³	1	2	yes	—
204	Dic₁₁⋊C₄	C₂³	1	2	yes	—
205	Dic₁₁⋊C₄	C₂³	1	2	yes	—
206	Dic₁₁⋊C₄	C₂³	1	2	yes	—
207	Dic₁₁⋊C₄	C₂³	1	2	yes	—
208	Dic₁₁⋊C₄	C₂³	1	2	yes	—
209	Dic₁₁⋊C₄	C₂³	1	2	yes	—
210	Dic₁₁⋊C₄	C₂³	1	2	yes	—
211	Dic₁₁⋊C₄	C₂³	1	2	yes	—
212	Dic₁₁⋊C₄	C₂³	1	2	yes	—
213	Dic₁₁⋊C₄	C₂³	1	2	yes	—
214	Dic₁₁⋊C₄	C₂³	1	2	yes	—
215	Dic₁₁⋊C₄	C₂³	1	2	yes	—
216	C₄×Dic₁₁	C₂³	1	2	yes	—
217	C₄×Dic₁₁	C₂³	1	2	yes	—
218	C₄×Dic₁₁	C₂³	1	2	yes	—
219	C₄×Dic₁₁	C₂³	1	2	yes	—
220	C₄×Dic₁₁	C₂³	1	2	yes	—
221	C₄×Dic₁₁	C₂³	1	2	yes	—
222	C₄×Dic₁₁	C₂³	1	2	yes	—
223	C₄×Dic₁₁	C₂³	1	2	yes	—
224	C₄×Dic₁₁	C₂³	1	2	yes	—
225	#3516	—	11	1	no	maximal, Sylow
226	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
227	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
228	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
229	C₂²×D₁₁	C₂⁴	1	2	yes	—
230	Q₈×C₁₁	—	4	1	no	—
231	D₄×C₁₁	—	2	2	no	—
232	D₄×C₁₁	—	2	2	no	—
233	D₄×C₁₁	—	4	1	no	—
234	C₂×C₄×C₁₁	—	2	2	no	—
235	C₂×C₄×C₁₁	—	2	2	no	—
236	C₂×C₄×C₁₁	—	2	2	no	—
237	C₂×C₄×C₁₁	—	2	2	no	—
238	C₂×C₄×C₁₁	—	4	1	no	—
239	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₁₁	—	2	4	no	—
252	C₂²⋊D₁₁	—	2	4	no	—
253	C₂²⋊D₁₁	—	4	2	no	—
254	C₂×Dic₁₁	—	2	4	no	—
255	C₂×Dic₁₁	—	2	4	no	—
256	C₂×Dic₁₁	—	4	2	no	—
257	C₂×Dic₁₁	—	4	2	no	—
258	C₂×Dic₁₁	C₂⁴	1	2	yes	—
259	C₂×Dic₁₁	C₂⁴	1	2	yes	—
260	C₂×Dic₁₁	C₂⁴	1	2	yes	—
261	C₂×Dic₁₁	C₂⁴	1	2	yes	—
262	C₂×Dic₁₁	C₂⁴	1	2	yes	—
263	C₂×Dic₁₁	C₂⁴	1	2	yes	—
264	C₂×Dic₁₁	C₂⁴	1	2	yes	—
265	D₄₄	—	2	2	no	—
266	C₄×D₁₁	—	2	4	no	—
267	C₄×D₁₁	—	4	2	no	—
268	C₄×D₁₁	—	4	2	no	—
269	Dic₂₂	—	2	2	no	—
270	Dic₂₂	—	2	2	no	—
271	Dic₂₂	—	2	4	no	—
272	Dic₂₂	—	2	4	no	—
273	Dic₂₂	—	4	2	no	—
274	Dic₂₂	#41	1	4	yes	—
275	#557	—	11	1	no	—
276	#556	—	11	2	no	—
277	#556	—	11	1	no	—
278	#554	—	11	2	no	—
279	#554	—	11	1	no	—
280	#553	—	11	2	no	—
281	#553	—	11	1	no	—
282	#552	—	11	2	no	—
283	#552	—	11	1	no	—
284	D₄×Q₈	—	11	1	no	—
285	#548	—	11	1	no	—
286	#548	—	11	1	no	—
287	#542	—	11	2	no	—
288	#542	—	11	1	no	—
289	#541	—	11	2	no	—
290	#541	—	11	1	no	—
291	#529	—	11	2	no	—
292	#529	—	11	2	no	—
293	#529	—	11	1	no	—
294	#529	D₁₁	1	1	yes	characteristic, complemented
295	#520	—	11	1	no	—
296	#519	—	11	1	no	—
297	C₂×C₄×Q₈	—	11	1	no	—
298	C₂²×C₁₁	—	2	1	no	—
299	C₂²×C₁₁	—	2	1	no	—
300	C₂²×C₁₁	—	2	1	no	—
301	C₂²×C₁₁	—	2	1	no	—
302	C₂²×C₁₁	—	2	1	no	—
303	C₂²×C₁₁	—	2	1	no	—
304	C₂²×C₁₁	—	2	1	no	—
305	C₂²×C₁₁	—	2	1	no	—
306	C₂²×C₁₁	2₋¹⁺⁴	1	2	yes	—
307	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
308	C₂×D₁₁	—	2	2	no	—
309	C₂×D₁₁	—	2	2	no	—
310	C₂×D₁₁	—	2	2	no	—
311	C₄×C₁₁	—	2	1	no	—
312	C₄×C₁₁	—	2	1	no	—
313	C₄×C₁₁	—	2	1	no	—
314	C₄×C₁₁	—	2	1	no	—
315	C₄×C₁₁	—	2	1	no	—
316	C₄×C₁₁	—	2	1	no	—
317	C₄×C₁₁	—	2	1	no	—
318	C₄×C₁₁	—	2	1	no	—
319	C₄×C₁₁	—	2	1	no	—
320	C₄×C₁₁	—	2	1	no	—
321	C₄×C₁₁	—	2	1	no	—
322	C₄×C₁₁	C₂×#41	1	2	yes	—
323	Dic₁₁	—	2	2	no	—
324	Dic₁₁	—	2	2	no	—
325	Dic₁₁	—	2	2	no	—
326	Dic₁₁	—	2	2	no	—
327	Dic₁₁	—	2	2	no	—
328	Dic₁₁	—	2	2	no	—
329	Dic₁₁	C₂×#41	1	4	yes	—
330	C₂×#41	—	11	1	no	—
331	C₂²×Q₈	—	11	1	no	—
332	C₂²×Q₈	—	11	1	no	—
333	C₄⋊Q₈	—	11	2	no	—
334	C₄⋊Q₈	—	11	2	no	—
335	C₄⋊Q₈	—	11	1	no	—
336	C₄⋊Q₈	—	11	1	no	—
337	#126	—	11	2	no	—
338	#126	—	11	2	no	—
339	#126	—	11	2	no	—
340	#126	—	11	2	no	—
341	#126	—	11	2	no	—
342	#126	—	11	2	no	—
343	#126	—	11	2	no	—
344	#126	—	11	2	no	—
345	#126	C₂×D₁₁	1	1	yes	characteristic
346	#126	C₂×D₁₁	1	1	yes	characteristic
347	#125	—	11	2	no	—
348	#125	—	11	2	no	—
349	#125	—	11	2	no	—
350	#125	—	11	2	no	—
351	#125	—	11	2	no	—
352	#125	—	11	2	no	—
353	#125	—	11	1	no	—
354	#125	—	11	1	no	—
355	#125	C₂×D₁₁	1	1	yes	characteristic
356	#124	—	11	2	no	—
357	#124	—	11	2	no	—
358	#124	—	11	2	no	—
359	#124	—	11	1	no	—
360	#124	—	11	1	no	—
361	#124	C₂×D₁₁	1	1	yes	characteristic
362	#123	—	11	2	no	—
363	#123	—	11	2	no	—
364	#123	—	11	2	no	—
365	#123	—	11	2	no	—
366	#123	C₂×D₁₁	1	1	yes	characteristic
367	#123	C₂×D₁₁	1	1	yes	characteristic
368	C₂²⋊Q₈	—	11	2	no	—
369	C₂²⋊Q₈	—	11	1	no	—
370	C₂²⋊Q₈	—	11	1	no	—
371	C₂²⋊Q₈	—	11	1	no	—
372	C₂²⋊Q₈	—	11	1	no	—
373	C₂²⋊Q₈	—	11	2	no	—
374	C₂²⋊Q₈	—	11	2	no	—
375	C₂²⋊Q₈	—	11	2	no	—
376	C₂²⋊Q₈	—	11	2	no	—
377	C₂²⋊Q₈	—	11	2	no	—
378	C₂²⋊Q₈	—	11	2	no	—
379	C₂²⋊Q₈	—	11	2	no	—
380	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic
381	#121	—	11	2	no	—
382	#121	—	11	2	no	—
383	#121	—	11	2	no	—
384	#121	—	11	1	no	—
385	#121	—	11	1	no	—
386	#121	C₂×D₁₁	1	1	yes	characteristic
387	C₄×Q₈	—	11	2	no	—
388	C₄×Q₈	—	11	2	no	—
389	C₄×Q₈	—	11	2	no	—
390	C₄×Q₈	—	11	1	no	—
391	C₄×Q₈	—	11	2	no	—
392	C₄×Q₈	—	11	1	no	—
393	C₄×Q₈	—	11	1	no	—
394	C₄×Q₈	—	11	1	no	—
395	C₄×Q₈	—	11	2	no	—
396	C₄×Q₈	—	11	1	no	—
397	C₄×Q₈	—	11	1	no	—
398	C₄×Q₈	—	11	1	no	—
399	C₄×Q₈	—	11	1	no	—
400	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic
401	C₄×D₄	—	11	2	no	—
402	C₄×D₄	—	11	2	no	—
403	C₄×D₄	—	11	2	no	—
404	C₄×D₄	—	11	2	no	—
405	C₄×D₄	—	11	2	no	—
406	C₄×D₄	—	11	2	no	—
407	C₄×D₄	—	11	2	no	—
408	C₄×D₄	—	11	2	no	—
409	C₄×D₄	—	11	1	no	—
410	C₄×D₄	—	11	1	no	—
411	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
412	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
413	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
414	#117	—	11	1	no	—
415	#117	—	11	2	no	—
416	#117	—	11	2	no	—
417	#117	—	11	2	no	—
418	#117	—	11	2	no	—
419	#117	—	11	2	no	—
420	#117	—	11	2	no	—
421	#117	C₂×D₁₁	1	1	yes	characteristic
422	#117	C₂×D₁₁	1	1	yes	characteristic
423	C₂×C₄⋊C₄	—	11	2	no	—
424	C₂×C₄⋊C₄	—	11	1	no	—
425	C₂×C₄⋊C₄	—	11	1	no	—
426	C₂×C₄⋊C₄	—	11	2	no	—
427	C₂×C₄²	—	11	2	no	—
428	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
429	C₂×C₁₁	—	2	2	no	—
430	C₂×C₁₁	—	4	1	no	—
431	C₂×C₁₁	—	4	1	no	—
432	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
433	C₂×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
434	C₂×C₁₁	#585	1	1	yes	characteristic
435	D₁₁	—	4	2	no	—
436	#41	—	22	4	no	—
437	C₂×Q₈	—	11	1	no	—
438	C₂×Q₈	—	11	2	no	—
439	C₂×Q₈	—	11	2	no	—
440	C₂×Q₈	—	11	1	no	—
441	C₂×Q₈	—	11	1	no	—
442	C₂×Q₈	—	11	2	no	—
443	C₂×Q₈	—	22	4	no	—
444	C₂×Q₈	—	22	4	no	—
445	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
446	C₂×D₄	—	11	2	no	—
447	C₂×D₄	—	11	2	no	—
448	C₂×D₄	—	11	2	no	—
449	C₂×D₄	—	11	1	no	—
450	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
451	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
452	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
453	C₂²×C₄	—	11	2	no	—
454	C₂²×C₄	—	11	2	no	—
455	C₂²×C₄	—	11	2	no	—
456	C₂²×C₄	—	11	2	no	—
457	C₂²×C₄	—	11	2	no	—
458	C₂²×C₄	—	11	2	no	—
459	C₂²×C₄	—	11	2	no	—
460	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
461	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
462	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
463	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
464	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
465	C₄⋊C₄	—	11	2	no	—
466	C₄⋊C₄	—	11	1	no	—
467	C₄⋊C₄	—	11	2	no	—
468	C₄⋊C₄	—	11	2	no	—
469	C₄⋊C₄	—	11	1	no	—
470	C₄⋊C₄	—	11	2	no	—
471	C₄⋊C₄	—	11	1	no	—
472	C₄⋊C₄	—	11	2	no	—
473	C₄⋊C₄	—	11	2	no	—
474	C₄⋊C₄	—	11	2	no	—
475	C₄⋊C₄	—	11	2	no	—
476	C₄⋊C₄	—	11	2	no	—
477	C₄⋊C₄	—	11	1	no	—
478	C₄⋊C₄	—	11	2	no	—
479	C₄⋊C₄	—	11	2	no	—
480	C₄⋊C₄	—	11	2	no	—
481	C₄⋊C₄	—	11	2	no	—
482	C₄⋊C₄	—	11	2	no	—
483	C₄⋊C₄	—	11	2	no	—
484	C₄⋊C₄	—	11	2	no	—
485	C₄⋊C₄	—	11	2	no	—
486	C₄⋊C₄	—	11	2	no	—
487	C₄⋊C₄	—	11	2	no	—
488	C₄⋊C₄	—	11	2	no	—
489	C₄⋊C₄	—	11	2	no	—
490	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
500	C₂²⋊C₄	—	11	2	no	—
501	C₂²⋊C₄	—	11	2	no	—
502	C₂²⋊C₄	—	11	2	no	—
503	C₂²⋊C₄	—	11	2	no	—
504	C₂²⋊C₄	—	11	2	no	—
505	C₂²⋊C₄	—	11	2	no	—
506	C₂²⋊C₄	—	11	2	no	—
507	C₂²⋊C₄	—	11	2	no	—
508	C₂²⋊C₄	—	11	2	no	—
509	C₂²⋊C₄	—	11	2	no	—
510	C₂²⋊C₄	—	11	2	no	—
511	C₂²⋊C₄	—	11	2	no	—
512	C₂²⋊C₄	—	11	2	no	—
513	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
514	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
515	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
516	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
517	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
518	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
519	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
520	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
521	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
522	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
523	C₄²	—	11	2	no	—
524	C₄²	—	11	2	no	—
525	C₄²	—	11	2	no	—
526	C₄²	—	11	2	no	—
527	C₄²	—	11	2	no	—
528	C₄²	—	11	2	no	—
529	C₄²	—	11	2	no	—
530	C₄²	—	11	2	no	—
531	C₄²	—	11	2	no	—
532	C₄²	C₂²×D₁₁	1	1	yes	characteristic
533	C₄²	C₂²×D₁₁	1	1	yes	characteristic
534	C₄²	C₂²×D₁₁	1	1	yes	characteristic
535	C₄²	C₂²×D₁₁	1	1	yes	characteristic
536	C₄²	C₂²×D₁₁	1	1	yes	characteristic
537	C₄²	C₂²×D₁₁	1	1	yes	characteristic
538	C₁₁	#3516	1	1	yes	characteristic, complemented, Sylow
539	C₂³	—	11	2	no	—
540	C₂³	C₂³×D₁₁	1	1	yes	characteristic
541	C₂³	C₂³×D₁₁	1	1	yes	characteristic
542	C₂³	C₂³×D₁₁	1	1	yes	characteristic
543	Q₈	—	4	1	no	—
544	Q₈	—	11	4	no	—
545	Q₈	—	22	4	no	—
546	Q₈	—	22	4	no	—
547	Q₈	—	22	2	no	—
548	Q₈	—	22	2	no	—
549	Q₈	—	44	2	no	—
550	D₄	—	2	2	no	—
551	D₄	—	2	2	no	—
552	D₄	—	4	1	no	—
553	D₄	—	22	4	no	—
554	D₄	—	22	4	no	—
555	D₄	—	22	2	no	—
556	D₄	—	44	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	11	2	no	—
563	C₂×C₄	—	11	2	no	—
564	C₂×C₄	—	11	2	no	—
565	C₂×C₄	—	11	2	no	—
566	C₂×C₄	—	11	2	no	—
567	C₂×C₄	—	11	2	no	—
568	C₂×C₄	—	11	2	no	—
569	C₂×C₄	—	22	4	no	—
570	C₂×C₄	—	22	4	no	—
571	C₂×C₄	—	22	4	no	—
572	C₂×C₄	—	44	2	no	—
573	C₂×C₄	—	44	2	no	—
574	C₂×C₄	—	44	2	no	—
575	C₂×C₄	—	44	2	no	—
576	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
577	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
578	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
579	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
582	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	22	2	no	—
597	C₂²	—	22	2	no	—
598	C₂²	—	22	2	no	—
599	C₂²	#67043	1	2	yes	—
600	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	11	4	no	—
613	C₄	—	22	2	no	—
614	C₄	—	22	2	no	—
615	C₄	—	22	2	no	—
616	C₄	—	22	2	no	—
617	C₄	—	22	2	no	—
618	C₄	—	22	2	no	—
619	C₄	#41×D₁₁	1	2	yes	—
620	C₂	—	2	2	no	—
621	C₂	—	4	1	no	—
622	C₂	—	4	1	no	—
623	C₂	—	44	2	no	—
624	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
625	C₂	C₂×#67043	1	1	yes	characteristic
626	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	#3516
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. #10623239	C₂	semidirect
3. #10623233	C₂	semidirect
4. #10623227	C₂	semidirect
5. #10623200	C₂	semidirect
6. #10623180	C₂	semidirect
7. #10623180	C₂	semidirect
8. #10623167	C₂	semidirect
9. #10623132	C₂	semidirect
10. #10623115	C₂	semidirect
11. #10623098	C₂	semidirect
12. #10623096	C₂	semidirect
13. #10623083	C₂	semidirect
14. #10623083	C₂	semidirect
15. #10623074	C₂	semidirect
16. #10623072	C₂	semidirect
17. D₄×Dic₂₂	C₂	semidirect
18. #10623065	C₂	semidirect
19. #10623054	C₂	semidirect
20. #10623049	C₂	semidirect
21. #10623047	C₂	semidirect
22. #10623010	C₂	semidirect
23. C₂×C₄×Dic₂₂	C₂	semidirect
294. #529	D₁₁	semidirect
538. C₁₁	#3516	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
#10623239	2
#10623233	2
#10623227	2
#10623200	2
#10623180	2
#10623167	2
#10623132	2
#10623115	2
#10623098	2
#10623096	2
#10623083	2
#10623074	2
#10623072	2
D₄×Dic₂₂	2
#10623065	2
#10623054	2
#10623049	2
#10623047	2
#10623010	2
C₂×C₄×Dic₂₂	2
#3516	11