Subgroups — #13082909

Order 1408.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623364	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623356	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623322	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#66977	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623193	C₂	1	2	yes	maximal, complemented
7	#10623191	C₂	1	2	yes	maximal, complemented
8	#10623177	C₂	1	2	yes	maximal, complemented
9	#10623167	C₂	1	2	yes	maximal, complemented
10	#10623152	C₂	1	2	yes	maximal, complemented
11	#10623132	C₂	1	2	yes	maximal, complemented
12	#10623124	C₂	1	2	yes	maximal, complemented
13	#10623124	C₂	1	2	yes	maximal, complemented
14	#10623096	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623083	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623083	C₂	1	1	yes	maximal, characteristic, complemented
17	#10623082	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623074	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623073	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623072	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623065	C₂	1	1	yes	maximal, characteristic, complemented
23	#10623049	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₁×#41	C₂²	1	1	yes	characteristic
25	C₂³×C₄×C₁₁	C₂²	1	1	yes	characteristic
26	C₂×#4339	C₂²	1	1	yes	characteristic
27	C₂×#4339	C₂²	1	1	yes	characteristic, complemented
28	C₂²×Dic₂₂	C₂²	1	1	yes	characteristic
29	C₂²×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
30	C₁₁×#123	C₂²	1	1	yes	characteristic
31	C₁₁×#123	C₂²	1	1	yes	characteristic
32	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₁×#121	C₂²	1	1	yes	characteristic
35	C₁₁×#121	C₂²	1	1	yes	characteristic
36	C₁₁×#120	C₂²	1	1	yes	characteristic
37	C₁₁×#120	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
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
42	C₁₁×#117	C₂²	1	1	yes	characteristic
43	#67006	C₂²	1	2	yes	—
44	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	—
45	#66999	C₂²	1	2	yes	complemented
46	#66997	C₂²	1	2	yes	complemented
47	#66992	C₂²	1	2	yes	—
48	#66992	C₂²	1	2	yes	—
49	#66992	C₂²	1	2	yes	—
50	#66992	C₂²	1	2	yes	—
51	#66992	C₂²	1	2	yes	complemented
52	#66991	C₂²	1	2	yes	—
53	#66991	C₂²	1	2	yes	—
54	#66989	C₂²	1	2	yes	—
55	#66989	C₂²	1	2	yes	—
56	#66988	C₂²	1	2	yes	—
57	#66988	C₂²	1	2	yes	—
58	#66988	C₂²	1	2	yes	complemented
59	D₄×Dic₁₁	C₂²	1	2	yes	—
60	D₄×Dic₁₁	C₂²	1	2	yes	—
61	#66983	C₂²	1	1	yes	characteristic
62	#66983	C₂²	1	1	yes	characteristic
63	#66983	C₂²	1	1	yes	characteristic, complemented
64	#66982	C₂²	1	2	yes	—
65	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
66	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
67	#66979	C₂²	1	1	yes	characteristic
68	#66979	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic
70	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic, complemented
71	#66977	C₂²	1	1	yes	characteristic
72	#66977	C₂²	1	1	yes	characteristic
73	#66977	C₂²	1	1	yes	characteristic
74	#66977	C₂²	1	1	yes	characteristic
75	#66977	C₂²	1	1	yes	characteristic
76	#66977	C₂²	1	2	yes	—
77	#66977	C₂²	1	2	yes	—
78	#66977	C₂²	1	1	yes	characteristic
79	#66977	C₂²	1	1	yes	characteristic, complemented
80	#66977	C₂²	1	1	yes	characteristic, complemented
81	#66977	C₂²	1	1	yes	characteristic, complemented
82	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	—
83	#66951	C₂²	1	2	yes	complemented
84	#66951	C₂²	1	2	yes	complemented
85	#66949	C₂²	1	2	yes	complemented
86	#66949	C₂²	1	2	yes	complemented
87	#66949	C₂²	1	2	yes	complemented
88	C₄⋊C₄×D₁₁	C₂²	1	2	yes	complemented
89	#66943	C₂²	1	2	yes	complemented
90	#66942	C₂²	1	2	yes	complemented
91	#66942	C₂²	1	2	yes	complemented
92	#66942	C₂²	1	2	yes	complemented
93	#66941	C₂²	1	2	yes	complemented
94	#66940	C₂²	1	2	yes	complemented
95	#66938	C₂²	1	2	yes	—
96	#66938	C₂²	1	2	yes	—
97	#66938	C₂²	1	2	yes	complemented
98	#66936	C₂²	1	2	yes	—
99	#66936	C₂²	1	2	yes	—
100	#66936	C₂²	1	2	yes	complemented
101	#66936	C₂²	1	2	yes	complemented
102	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
103	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
104	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
105	#66932	C₂²	1	2	yes	—
106	#66932	C₂²	1	2	yes	—
107	#66932	C₂²	1	2	yes	—
108	#66932	C₂²	1	2	yes	—
109	#66932	C₂²	1	2	yes	complemented
110	#66931	C₂²	1	2	yes	—
111	#66931	C₂²	1	2	yes	—
112	#66931	C₂²	1	2	yes	complemented
113	#66931	C₂²	1	2	yes	complemented
114	#66930	C₂²	1	2	yes	complemented
115	#66928	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₄₄	C₂²	1	1	yes	characteristic, 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	C₂⁴×C₁₁	C₂³	1	1	yes	characteristic
124	C₁₁×#41	—	4	2	no	—
125	C₂×Q₈×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	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₁	—	4	2	no	—
134	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
147	C₂²×Dic₁₁	C₂³	1	2	yes	—
148	C₂²×Dic₁₁	C₂³	1	2	yes	—
149	C₂²×Dic₁₁	C₂³	1	2	yes	—
150	C₂²×Dic₁₁	C₂³	1	2	yes	—
151	#4339	—	4	2	no	—
152	#4339	—	4	2	no	—
153	C₂×D₄₄	C₂³	1	1	yes	characteristic
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×Dic₂₂	—	4	2	no	—
158	C₂×Dic₂₂	—	4	2	no	—
159	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
160	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
161	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
162	C₂×Dic₂₂	C₂³	1	2	yes	—
163	C₂×Dic₂₂	C₂³	1	2	yes	—
164	C₂×Dic₂₂	C₂³	1	2	yes	—
165	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₁₁×C₂²⋊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	C₄²×C₁₁	C₂³	1	1	yes	characteristic
182	C₄²×C₁₁	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
191	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
192	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
193	C₂²⋊Dic₁₁	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	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₁	C₂³	1	2	yes	—
205	C₄⋊Dic₁₁	C₂³	1	2	yes	—
206	C₄⋊Dic₁₁	C₂³	1	2	yes	—
207	C₄⋊Dic₁₁	C₂³	1	2	yes	—
208	C₄⋊Dic₁₁	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	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	Dic₁₁⋊C₄	C₂³	1	2	yes	—
221	Dic₁₁⋊C₄	C₂³	1	2	yes	—
222	Dic₁₁⋊C₄	C₂³	1	2	yes	—
223	C₄×Dic₁₁	C₂³	1	2	yes	—
224	C₄×Dic₁₁	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	#3541	—	11	1	no	maximal, Sylow
229	C₂³×C₁₁	—	2	2	no	—
230	C₂³×C₁₁	—	4	1	no	—
231	C₂³×C₁₁	—	4	1	no	—
232	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
234	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
235	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
236	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₁	C₂⁴	1	2	yes	—
238	Q₈×C₁₁	—	4	1	no	—
239	D₄×C₁₁	—	2	2	no	—
240	D₄×C₁₁	—	2	2	no	—
241	D₄×C₁₁	—	4	1	no	—
242	D₄×C₁₁	—	4	1	no	—
243	D₄×C₁₁	—	4	1	no	—
244	D₄×C₁₁	—	4	1	no	—
245	D₄×C₁₁	—	4	1	no	—
246	C₂×C₄×C₁₁	—	2	2	no	—
247	C₂×C₄×C₁₁	—	2	2	no	—
248	C₂×C₄×C₁₁	—	2	2	no	—
249	C₂×C₄×C₁₁	—	2	2	no	—
250	C₂×C₄×C₁₁	—	2	2	no	—
251	C₂×C₄×C₁₁	—	4	1	no	—
252	C₂×C₄×C₁₁	—	4	1	no	—
253	C₂×C₄×C₁₁	—	4	1	no	—
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	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
264	C₂²⋊D₁₁	—	2	4	no	—
265	C₂²⋊D₁₁	—	4	2	no	—
266	C₂²⋊D₁₁	—	4	2	no	—
267	C₂²⋊D₁₁	—	4	2	no	—
268	C₂²⋊D₁₁	—	4	2	no	—
269	C₂×Dic₁₁	—	4	2	no	—
270	C₂×Dic₁₁	—	4	2	no	—
271	C₂×Dic₁₁	—	4	2	no	—
272	C₂×Dic₁₁	—	4	2	no	—
273	C₂×Dic₁₁	C₂⁴	1	2	yes	—
274	C₂×Dic₁₁	C₂⁴	1	2	yes	—
275	C₂×Dic₁₁	C₂⁴	1	2	yes	—
276	C₂×Dic₁₁	C₂⁴	1	2	yes	—
277	C₂×Dic₁₁	C₂⁴	1	2	yes	—
278	C₂×Dic₁₁	C₂⁴	1	2	yes	—
279	C₂×Dic₁₁	C₂⁴	1	2	yes	—
280	D₄₄	—	2	2	no	—
281	C₄×D₁₁	—	4	2	no	—
282	C₄×D₁₁	—	4	2	no	—
283	C₄×D₁₁	—	4	2	no	—
284	Dic₂₂	—	2	2	no	—
285	Dic₂₂	—	2	2	no	—
286	Dic₂₂	—	2	2	no	—
287	Dic₂₂	—	4	2	no	—
288	Dic₂₂	—	4	2	no	—
289	Dic₂₂	—	4	2	no	—
290	#563	—	11	2	no	—
291	#562	—	11	2	no	—
292	#556	—	11	1	no	—
293	#554	—	11	2	no	—
294	#554	—	11	1	no	—
295	#553	—	11	2	no	—
296	#553	—	11	1	no	—
297	#552	—	11	1	no	—
298	D₄×Q₈	—	11	1	no	—
299	#548	—	11	1	no	—
300	#548	—	11	1	no	—
301	#547	—	11	1	no	—
302	#542	—	11	2	no	—
303	#542	—	11	1	no	—
304	#541	—	11	1	no	—
305	#539	—	11	2	no	—
306	#538	—	11	2	no	—
307	#538	—	11	2	no	—
308	#537	—	11	1	no	—
309	#536	—	11	1	no	—
310	#525	—	11	1	no	—
311	#525	D₁₁	1	1	yes	characteristic, complemented
312	C₂×C₂²⋊Q₈	—	11	1	no	—
313	C₂²×C₁₁	—	2	1	no	—
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	—	2	1	no	—
324	C₂²×C₁₁	—	2	1	no	—
325	C₂²×C₁₁	—	2	1	no	—
326	C₂²×C₁₁	—	2	1	no	—
327	C₂²×C₁₁	—	4	4	no	—
328	C₂²×C₁₁	2₋¹⁺⁴	1	2	yes	—
329	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
330	C₂×D₁₁	—	2	2	no	—
331	C₂×D₁₁	—	2	2	no	—
332	C₂×D₁₁	—	2	2	no	—
333	C₄×C₁₁	—	2	1	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	H(5,𝔽₂)	1	2	yes	—
343	Dic₁₁	—	2	2	no	—
344	Dic₁₁	—	2	2	no	—
345	Dic₁₁	—	2	2	no	—
346	Dic₁₁	—	2	2	no	—
347	Dic₁₁	—	2	2	no	—
348	Dic₁₁	—	2	2	no	—
349	Dic₁₁	—	2	2	no	—
350	C₂×#41	—	11	1	no	—
351	C₂×#41	—	11	1	no	—
352	C₂×#41	C₂×D₁₁	1	1	yes	characteristic
353	C₂²×Q₈	—	11	1	no	—
354	C₂²×Q₈	—	11	1	no	—
355	C₂³×C₄	C₂×D₁₁	1	1	yes	characteristic
356	C₄⋊Q₈	—	11	2	no	—
357	C₄⋊Q₈	—	11	2	no	—
358	C₄⋊Q₈	—	11	1	no	—
359	C₄⋊Q₈	—	11	1	no	—
360	#126	—	11	2	no	—
361	#126	—	11	2	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	#125	—	11	2	no	—
368	#125	—	11	2	no	—
369	#125	—	11	2	no	—
370	#125	—	11	2	no	—
371	#125	—	11	1	no	—
372	#124	—	11	2	no	—
373	#124	—	11	2	no	—
374	#124	—	11	2	no	—
375	#124	—	11	2	no	—
376	#124	—	11	2	no	—
377	#124	—	11	1	no	—
378	#123	—	11	2	no	—
379	#123	—	11	2	no	—
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	C₂×D₁₁	1	1	yes	characteristic
387	#123	C₂×D₁₁	1	1	yes	characteristic
388	C₂²⋊Q₈	—	11	2	no	—
389	C₂²⋊Q₈	—	11	1	no	—
390	C₂²⋊Q₈	—	11	1	no	—
391	C₂²⋊Q₈	—	11	2	no	—
392	C₂²⋊Q₈	—	11	1	no	—
393	C₂²⋊Q₈	—	11	1	no	—
394	C₂²⋊Q₈	—	11	2	no	—
395	C₂²⋊Q₈	—	11	1	no	—
396	C₂²⋊Q₈	—	11	1	no	—
397	C₂²⋊Q₈	—	11	1	no	—
398	C₂²⋊Q₈	—	11	1	no	—
399	C₂²⋊Q₈	—	11	1	no	—
400	C₂²⋊Q₈	—	11	2	no	—
401	C₂²⋊Q₈	—	11	2	no	—
402	C₂²⋊Q₈	—	11	2	no	—
403	C₂²⋊Q₈	—	11	2	no	—
404	C₂²⋊Q₈	—	11	2	no	—
405	C₂²⋊Q₈	—	11	2	no	—
406	C₂²⋊Q₈	—	11	2	no	—
407	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic
408	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic
409	#121	—	11	2	no	—
410	#121	—	11	2	no	—
411	#121	—	11	2	no	—
412	#121	—	11	2	no	—
413	#121	—	11	2	no	—
414	#121	—	11	2	no	—
415	#121	—	11	2	no	—
416	#121	—	11	1	no	—
417	#121	—	11	1	no	—
418	#121	—	11	1	no	—
419	#121	C₂×D₁₁	1	1	yes	characteristic
420	#121	C₂×D₁₁	1	1	yes	characteristic
421	#120	—	11	2	no	—
422	#120	C₂×D₁₁	1	1	yes	characteristic
423	#120	C₂×D₁₁	1	1	yes	characteristic
424	C₄×Q₈	—	11	2	no	—
425	C₄×Q₈	—	11	1	no	—
426	C₄×Q₈	—	11	1	no	—
427	C₄×Q₈	—	11	1	no	—
428	C₄×D₄	—	11	2	no	—
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	2	no	—
435	C₄×D₄	—	11	1	no	—
436	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
437	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
438	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
439	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
440	#117	—	11	1	no	—
441	#117	—	11	1	no	—
442	#117	—	11	2	no	—
443	#117	C₂×D₁₁	1	1	yes	characteristic
444	C₂×C₄⋊C₄	—	11	2	no	—
445	C₂×C₄⋊C₄	—	11	1	no	—
446	C₂×C₄⋊C₄	—	11	1	no	—
447	C₂×C₄⋊C₄	—	11	2	no	—
448	C₂×C₂²⋊C₄	—	11	2	no	—
449	C₂×C₁₁	—	2	2	no	—
450	C₂×C₁₁	—	4	1	no	—
451	C₂×C₁₁	—	4	1	no	—
452	C₂×C₁₁	—	4	1	no	—
453	C₂×C₁₁	—	4	1	no	—
454	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
455	C₂×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
456	C₂×C₁₁	#585	1	1	yes	characteristic
457	D₁₁	—	4	2	no	—
458	C₂⁴	C₂²×D₁₁	1	1	yes	characteristic
459	#41	—	4	2	no	—
460	#41	—	44	2	no	—
461	#41	—	44	2	no	—
462	C₂×Q₈	—	11	1	no	—
463	C₂×Q₈	—	11	1	no	—
464	C₂×Q₈	—	11	1	no	—
465	C₂×Q₈	—	11	2	no	—
466	C₂×Q₈	—	11	2	no	—
467	C₂×Q₈	—	11	2	no	—
468	C₂×Q₈	—	44	2	no	—
469	C₂×Q₈	—	44	2	no	—
470	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
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	1	no	—
477	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
478	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
479	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
480	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
481	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
482	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	—	11	2	no	—
486	C₂²×C₄	—	11	2	no	—
487	C₂²×C₄	—	11	2	no	—
488	C₂²×C₄	—	11	2	no	—
489	C₂²×C₄	—	11	2	no	—
490	C₂²×C₄	—	11	2	no	—
491	C₂²×C₄	—	11	2	no	—
492	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
493	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
494	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
495	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
496	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
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	C₄⋊C₄	—	11	1	no	—
501	C₄⋊C₄	—	11	2	no	—
502	C₄⋊C₄	—	11	2	no	—
503	C₄⋊C₄	—	11	1	no	—
504	C₄⋊C₄	—	11	1	no	—
505	C₄⋊C₄	—	11	2	no	—
506	C₄⋊C₄	—	11	2	no	—
507	C₄⋊C₄	—	11	2	no	—
508	C₄⋊C₄	—	11	2	no	—
509	C₄⋊C₄	—	11	2	no	—
510	C₄⋊C₄	—	11	2	no	—
511	C₄⋊C₄	—	11	1	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	—	11	2	no	—
517	C₄⋊C₄	—	11	2	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	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
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	—	11	2	no	—
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	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
556	C₄²	—	11	2	no	—
557	C₄²	—	11	2	no	—
558	C₄²	—	11	2	no	—
559	C₄²	—	11	2	no	—
560	C₄²	—	11	2	no	—
561	C₄²	C₂²×D₁₁	1	1	yes	characteristic
562	C₄²	C₂²×D₁₁	1	1	yes	characteristic
563	C₁₁	#3541	1	1	yes	characteristic, complemented, Sylow
564	C₂³	—	2	2	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	11	2	no	—
568	C₂³	C₂³×D₁₁	1	1	yes	characteristic
569	C₂³	C₂³×D₁₁	1	1	yes	characteristic
570	C₂³	C₂³×D₁₁	1	1	yes	characteristic
571	C₂³	C₂³×D₁₁	1	1	yes	characteristic
572	C₂³	C₂³×D₁₁	1	1	yes	characteristic
573	Q₈	—	4	1	no	—
574	Q₈	—	22	2	no	—
575	Q₈	—	22	2	no	—
576	Q₈	—	22	2	no	—
577	Q₈	—	44	2	no	—
578	Q₈	—	44	2	no	—
579	Q₈	—	44	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	1	no	—
583	D₄	—	4	1	no	—
584	D₄	—	4	1	no	—
585	D₄	—	4	1	no	—
586	D₄	—	4	1	no	—
587	D₄	—	22	4	no	—
588	D₄	—	22	2	no	—
589	D₄	—	44	2	no	—
590	D₄	—	44	2	no	—
591	D₄	—	44	2	no	—
592	D₄	—	44	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	11	2	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	—	11	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	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
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	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	4	4	no	—
640	C₂²	—	22	2	no	—
641	C₂²	—	22	2	no	—
642	C₂²	—	22	2	no	—
643	C₂²	#67043	1	2	yes	—
644	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
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	—	22	2	no	—
655	C₄	—	22	2	no	—
656	C₄	—	22	2	no	—
657	C₄	—	22	2	no	—
658	C₄	—	22	2	no	—
659	C₄	—	22	2	no	—
660	C₄	—	22	2	no	—
661	C₄	#67037	1	2	yes	—
662	C₂	—	2	2	no	—
663	C₂	—	4	1	no	—
664	C₂	—	4	1	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	1	no	—
667	C₂	—	44	2	no	—
668	C₂	C₂×#67037	1	1	yes	characteristic
669	C₂	C₂×#67043	1	1	yes	characteristic
670	C₂	#10623453	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#525	C₂
hypercenter	#525	D₁₁
hypocenter	C₁₁	#3541
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₁₁×#525	C₂	semidirect
2. #10623364	C₂	semidirect
3. #10623356	C₂	semidirect
4. #10623322	C₂	semidirect
5. C₂×#66977	C₂	semidirect
6. #10623193	C₂	semidirect
7. #10623191	C₂	semidirect
8. #10623177	C₂	semidirect
9. #10623167	C₂	semidirect
10. #10623152	C₂	semidirect
11. #10623132	C₂	semidirect
12. #10623124	C₂	semidirect
13. #10623124	C₂	semidirect
14. #10623096	C₂	semidirect
15. #10623083	C₂	semidirect
16. #10623083	C₂	semidirect
17. #10623082	C₂	semidirect
18. #10623074	C₂	semidirect
19. #10623073	C₂	semidirect
20. #10623072	C₂	semidirect
21. D₄×Dic₂₂	C₂	semidirect
22. #10623065	C₂	semidirect
23. #10623049	C₂	semidirect
27. C₂×#4339	C₂²	semidirect
29. C₂²×Dic₂₂	C₂²	semidirect
45. #66999	C₂²	semidirect
46. #66997	C₂²	semidirect
51. #66992	C₂²	semidirect
58. #66988	C₂²	semidirect
63. #66983	C₂²	semidirect
68. #66979	C₂²	semidirect
70. C₂×C₄⋊Dic₁₁	C₂²	semidirect
79. #66977	C₂²	semidirect
80. #66977	C₂²	semidirect
81. #66977	C₂²	semidirect
83. #66951	C₂²	semidirect
84. #66951	C₂²	semidirect
85. #66949	C₂²	semidirect
86. #66949	C₂²	semidirect
87. #66949	C₂²	semidirect
88. C₄⋊C₄×D₁₁	C₂²	semidirect
89. #66943	C₂²	semidirect
90. #66942	C₂²	semidirect
91. #66942	C₂²	semidirect
92. #66942	C₂²	semidirect
93. #66941	C₂²	semidirect
94. #66940	C₂²	semidirect
97. #66938	C₂²	semidirect
100. #66936	C₂²	semidirect
101. #66936	C₂²	semidirect
104. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
109. #66932	C₂²	semidirect
112. #66931	C₂²	semidirect
113. #66931	C₂²	semidirect
114. #66930	C₂²	semidirect
115. #66928	C₂²	semidirect
116. C₄×D₄₄	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
311. #525	D₁₁	semidirect
563. C₁₁	#3541	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#525	2
#10623364	2
#10623356	2
#10623322	2
C₂×#66977	2
#10623193	2
#10623191	2
#10623177	2
#10623167	2
#10623152	2
#10623132	2
#10623124	2
#10623096	2
#10623083	2
#10623082	2
#10623074	2
#10623073	2
#10623072	2
D₄×Dic₂₂	2
#10623065	2
#10623049	2
#3541	11