Subgroups — #13082464

Order 1408.

1140 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623249	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623246	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623212	C₂	1	1	yes	maximal, characteristic, complemented
5	#10623209	C₂	1	2	yes	maximal, complemented
6	#10623205	C₂	1	1	yes	maximal, characteristic, complemented
7	#10623202	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623201	C₂	1	2	yes	maximal, complemented
9	#10623199	C₂	1	1	yes	maximal, characteristic, complemented
10	#10623192	C₂	1	2	yes	maximal, complemented
11	#10623188	C₂	1	2	yes	maximal, complemented
12	#10623187	C₂	1	2	yes	maximal, complemented
13	#10623186	C₂	1	2	yes	maximal, complemented
14	#10623116	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623109	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623105	C₂	1	1	yes	maximal, characteristic, complemented
17	#10623099	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623090	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623084	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623078	C₂	1	2	yes	maximal, complemented
21	#10623077	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#10623071	C₂	1	2	yes	maximal, complemented
24	C₂×#4343	C₂²	1	1	yes	characteristic
25	C₂×#4341	C₂²	1	1	yes	characteristic
26	C₂×#4341	C₂²	1	2	yes	complemented
27	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
28	C₂×#4339	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₁₁	C₂²	1	2	yes	—
30	C₁₁×#127	C₂²	1	1	yes	characteristic
31	C₁₁×#124	C₂²	1	1	yes	characteristic
32	C₁₁×#124	C₂²	1	1	yes	characteristic, complemented
33	C₁₁×#124	C₂²	1	2	yes	complemented
34	C₁₁×#123	C₂²	1	2	yes	complemented
35	C₁₁×#123	C₂²	1	2	yes	complemented
36	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
37	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
38	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₁₁	C₂²	1	2	yes	complemented
40	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
41	#67000	C₂²	1	1	yes	characteristic
42	#67000	C₂²	1	2	yes	complemented
43	#66999	C₂²	1	1	yes	characteristic
44	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
45	#66997	C₂²	1	1	yes	characteristic, complemented
46	#66997	C₂²	1	1	yes	characteristic, complemented
47	#66993	C₂²	1	1	yes	characteristic
48	#66993	C₂²	1	1	yes	characteristic
49	#66993	C₂²	1	1	yes	characteristic, complemented
50	#66992	C₂²	1	2	yes	—
51	#66992	C₂²	1	2	yes	—
52	#66992	C₂²	1	2	yes	complemented
53	#66992	C₂²	1	2	yes	complemented
54	#66991	C₂²	1	2	yes	complemented
55	#66990	C₂²	1	2	yes	—
56	#66990	C₂²	1	2	yes	—
57	#66989	C₂²	1	1	yes	characteristic
58	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
59	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
60	#66983	C₂²	1	2	yes	complemented
61	#66982	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
64	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
65	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	complemented
66	#66951	C₂²	1	2	yes	complemented
67	#66950	C₂²	1	1	yes	characteristic
68	#66949	C₂²	1	1	yes	characteristic
69	#66949	C₂²	1	1	yes	characteristic
70	#66949	C₂²	1	2	yes	complemented
71	#66947	C₂²	1	2	yes	complemented
72	#66947	C₂²	1	2	yes	complemented
73	#66946	C₂²	1	1	yes	characteristic
74	#66946	C₂²	1	2	yes	—
75	#66946	C₂²	1	1	yes	characteristic, complemented
76	#66946	C₂²	1	2	yes	complemented
77	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
78	C₄⋊C₄×D₁₁	C₂²	1	2	yes	complemented
79	#66942	C₂²	1	1	yes	characteristic, complemented
80	#66942	C₂²	1	1	yes	characteristic, complemented
81	#66941	C₂²	1	1	yes	characteristic, complemented
82	#66940	C₂²	1	1	yes	characteristic, complemented
83	#66939	C₂²	1	2	yes	complemented
84	#66938	C₂²	1	2	yes	complemented
85	#66938	C₂²	1	2	yes	complemented
86	#66937	C₂²	1	2	yes	—
87	#66937	C₂²	1	2	yes	—
88	#66937	C₂²	1	2	yes	—
89	#66937	C₂²	1	2	yes	—
90	#66937	C₂²	1	2	yes	complemented
91	#66937	C₂²	1	2	yes	complemented
92	#66936	C₂²	1	2	yes	complemented
93	#66936	C₂²	1	2	yes	complemented
94	#66935	C₂²	1	2	yes	—
95	#66935	C₂²	1	2	yes	—
96	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
97	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
98	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
100	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
101	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
102	#66932	C₂²	1	2	yes	complemented
103	#66932	C₂²	1	2	yes	complemented
104	#66931	C₂²	1	2	yes	complemented
105	#66930	C₂²	1	2	yes	complemented
106	#66930	C₂²	1	2	yes	complemented
107	#66929	C₂²	1	2	yes	complemented
108	#66928	C₂²	1	1	yes	characteristic
109	#66928	C₂²	1	1	yes	characteristic, complemented
110	#66927	C₂²	1	1	yes	characteristic
111	C₄×D₄₄	C₂²	1	1	yes	characteristic
112	C₄×D₄₄	C₂²	1	2	yes	—
113	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
114	#66925	C₂²	1	1	yes	characteristic
115	#66925	C₂²	1	1	yes	characteristic
116	#66925	C₂²	1	2	yes	complemented
117	#66925	C₂²	1	2	yes	complemented
118	C₄²×D₁₁	C₂²	1	1	yes	characteristic
119	C₄×Dic₂₂	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×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	2	yes	—
129	C₂×D₄×C₁₁	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
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	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	C₂²×Dic₁₁	C₂³	1	2	yes	—
142	C₂²×Dic₁₁	C₂³	1	2	yes	—
143	#4343	—	2	4	no	—
144	#4341	—	2	4	no	—
145	#4341	—	4	4	no	—
146	D₄×D₁₁	—	2	4	no	—
147	#4339	—	4	4	no	—
148	C₂×D₄₄	C₂³	1	1	yes	characteristic
149	C₂×D₄₄	C₂³	1	2	yes	—
150	C₂×D₄₄	C₂³	1	1	yes	characteristic
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	2	yes	—
156	C₂×C₄×D₁₁	C₂³	1	2	yes	—
157	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
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×C₄×D₁₁	C₂³	1	2	yes	—
162	C₂×C₄×D₁₁	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	1	yes	characteristic
166	C₂×Dic₂₂	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	2	yes	—
172	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₁₁×C₂²⋊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	C₄²×C₁₁	C₂³	1	1	yes	characteristic
179	C₄²×C₁₁	C₂³	1	1	yes	characteristic
180	C₄²×C₁₁	C₂³	1	1	yes	characteristic
181	C₄²×C₁₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
186	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
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	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	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
206	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
207	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₁₁⋊C₄	C₂³	1	2	yes	—
209	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	#3506	—	11	1	no	maximal, Sylow
229	C₂³×C₁₁	C₂⁴	1	2	yes	—
230	C₂³×C₁₁	C₂⁴	1	2	yes	—
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	Q₈×C₁₁	—	2	2	no	—
238	Q₈×C₁₁	—	4	1	no	—
239	D₄×C₁₁	—	2	2	no	—
240	D₄×C₁₁	—	2	2	no	—
241	D₄×C₁₁	—	4	2	no	—
242	D₄×C₁₁	—	4	2	no	—
243	C₂×C₄×C₁₁	—	4	2	no	—
244	C₂×C₄×C₁₁	—	4	2	no	—
245	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
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	C₂²⋊D₁₁	—	2	4	no	—
255	C₂²⋊D₁₁	—	2	4	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	—	2	4	no	—
263	C₂×Dic₁₁	—	2	4	no	—
264	C₂×Dic₁₁	—	4	2	no	—
265	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₁	C₂⁴	1	2	yes	—
269	C₂×Dic₁₁	C₂⁴	1	2	yes	—
270	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
274	D₄₄	—	2	4	no	—
275	D₄₄	—	2	2	no	—
276	D₄₄	—	2	2	no	—
277	D₄₄	—	4	2	no	—
278	D₄₄	—	4	2	no	—
279	C₄×D₁₁	—	2	4	no	—
280	C₄×D₁₁	—	2	2	no	—
281	C₄×D₁₁	—	2	4	no	—
282	C₄×D₁₁	—	4	2	no	—
283	C₄×D₁₁	—	4	2	no	—
284	C₄×D₁₁	—	4	1	no	—
285	C₄×D₁₁	—	4	2	no	—
286	C₄×D₁₁	—	4	2	no	—
287	C₄×D₁₁	#41	1	4	yes	complemented
288	Dic₂₂	—	2	2	no	—
289	Dic₂₂	—	2	2	no	—
290	Dic₂₂	—	2	2	no	—
291	Dic₂₂	—	4	1	no	—
292	#559	—	11	1	no	—
293	#559	—	11	1	no	—
294	#559	—	11	1	no	—
295	#559	D₁₁	1	1	yes	characteristic, complemented
296	#556	—	11	1	no	—
297	#556	—	11	1	no	—
298	#555	—	11	2	no	—
299	#553	—	11	2	no	—
300	#553	—	11	2	no	—
301	#550	—	11	1	no	—
302	#550	—	11	1	no	—
303	#547	—	11	2	no	—
304	#538	—	11	2	no	—
305	#538	—	11	2	no	—
306	#535	—	11	1	no	—
307	#535	—	11	1	no	—
308	#533	—	11	1	no	—
309	#532	—	11	1	no	—
310	#525	—	11	2	no	—
311	#525	—	11	2	no	—
312	#520	—	11	1	no	—
313	#520	—	11	1	no	—
314	C₂×C₄×D₄	—	11	1	no	—
315	C₂²×C₁₁	—	2	2	no	—
316	C₂²×C₁₁	—	2	2	no	—
317	C₂²×C₁₁	—	2	2	no	—
318	C₂²×C₁₁	—	2	2	no	—
319	C₂²×C₁₁	—	2	2	no	—
320	C₂²×C₁₁	—	2	2	no	—
321	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
322	C₂×D₁₁	—	2	1	no	—
323	C₂×D₁₁	—	2	1	no	—
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	—	4	8	no	—
331	C₂×D₁₁	C₂×#41	1	2	yes	—
332	C₄×C₁₁	—	2	2	no	—
333	C₄×C₁₁	—	2	1	no	—
334	C₄×C₁₁	—	2	1	no	—
335	C₄×C₁₁	—	2	2	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	C₂×#41	1	2	yes	—
341	Dic₁₁	—	2	2	no	—
342	Dic₁₁	—	2	1	no	—
343	Dic₁₁	—	2	1	no	—
344	Dic₁₁	—	2	2	no	—
345	Dic₁₁	—	2	1	no	—
346	Dic₁₁	—	2	1	no	—
347	Dic₁₁	—	2	1	no	—
348	Dic₁₁	C₂×#41	1	2	yes	—
349	Dic₁₁	H(5,𝔽₂)	1	2	yes	—
350	C₂×#41	—	11	1	no	—
351	C₂×#41	—	11	1	no	—
352	C₂×#41	—	11	2	no	—
353	C₂×#41	—	11	2	no	—
354	C₂²×D₄	—	11	1	no	—
355	C₂³×C₄	—	11	2	no	—
356	C₄⋊Q₈	—	11	1	no	—
357	C₄⋊Q₈	—	11	1	no	—
358	C₄⋊Q₈	—	11	1	no	—
359	#127	—	11	1	no	—
360	#127	—	11	1	no	—
361	#127	—	11	1	no	—
362	#127	—	11	1	no	—
363	#127	C₂×D₁₁	1	1	yes	characteristic
364	#126	—	11	2	no	—
365	#126	—	11	2	no	—
366	#126	—	11	2	no	—
367	#126	—	11	2	no	—
368	#125	—	11	1	no	—
369	#125	—	11	1	no	—
370	#124	—	11	1	no	—
371	#124	—	11	2	no	—
372	#124	—	11	1	no	—
373	#124	—	11	2	no	—
374	#124	—	11	2	no	—
375	#124	—	11	1	no	—
376	#124	—	11	1	no	—
377	#124	C₂×D₁₁	1	1	yes	characteristic
378	#124	C₂×D₁₁	1	1	yes	characteristic, complemented
379	#124	C₂×D₁₁	1	2	yes	complemented
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	2	yes	complemented
387	#123	C₂×D₁₁	1	2	yes	complemented
388	C₂²⋊Q₈	—	11	1	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	2	no	—
394	#121	—	11	2	no	—
395	#121	—	11	2	no	—
396	#121	—	11	2	no	—
397	#121	—	11	2	no	—
398	#121	—	11	2	no	—
399	#121	—	11	2	no	—
400	#121	—	11	2	no	—
401	#121	—	11	2	no	—
402	#121	—	11	2	no	—
403	#121	—	11	2	no	—
404	#121	—	11	2	no	—
405	#121	—	11	2	no	—
406	#120	—	11	2	no	—
407	#120	—	11	2	no	—
408	#120	—	11	2	no	—
409	#120	—	11	2	no	—
410	C₄×Q₈	—	11	1	no	—
411	C₄×Q₈	—	11	1	no	—
412	C₄×Q₈	—	11	1	no	—
413	C₄×Q₈	—	11	1	no	—
414	C₄×Q₈	—	11	1	no	—
415	C₄×Q₈	—	11	1	no	—
416	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
417	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
418	C₄×D₄	—	11	1	no	—
419	C₄×D₄	—	11	1	no	—
420	C₄×D₄	—	11	2	no	—
421	C₄×D₄	—	11	2	no	—
422	C₄×D₄	—	11	2	no	—
423	C₄×D₄	—	11	1	no	—
424	C₄×D₄	—	11	2	no	—
425	C₄×D₄	—	11	1	no	—
426	C₄×D₄	—	11	2	no	—
427	C₄×D₄	—	11	2	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	1	no	—
433	C₄×D₄	—	11	2	no	—
434	C₄×D₄	—	11	1	no	—
435	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
436	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
437	C₄×D₄	C₂×D₁₁	1	2	yes	complemented
438	#117	—	11	2	no	—
439	#117	—	11	2	no	—
440	#117	—	11	1	no	—
441	#117	—	11	1	no	—
442	#117	—	11	2	no	—
443	#117	—	11	2	no	—
444	C₂×C₄⋊C₄	—	11	2	no	—
445	C₂×C₄⋊C₄	—	11	1	no	—
446	C₂×C₄⋊C₄	—	11	2	no	—
447	C₂×C₂²⋊C₄	—	11	2	no	—
448	C₂×C₄²	—	11	1	no	—
449	C₂×C₁₁	—	4	2	no	—
450	C₂×C₁₁	—	4	2	no	—
451	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
452	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂×C₁₁	#585	1	1	yes	characteristic
454	D₁₁	—	2	2	no	—
455	D₁₁	—	4	2	no	—
456	D₁₁	—	4	2	no	—
457	C₂⁴	—	11	2	no	—
458	#41	—	22	4	no	—
459	#41	—	22	4	no	—
460	#41	—	44	4	no	—
461	#41	—	44	4	no	—
462	C₂×Q₈	—	11	1	no	—
463	C₂×Q₈	—	11	1	no	—
464	C₂×Q₈	—	11	1	no	—
465	C₂×Q₈	—	11	1	no	—
466	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
467	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
468	C₂×D₄	—	11	2	no	—
469	C₂×D₄	—	11	2	no	—
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	2	no	—
480	C₂×D₄	—	11	2	no	—
481	C₂×D₄	—	22	4	no	—
482	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₁₁	1	2	yes	—
485	C₂×D₄	C₂²×D₁₁	1	2	yes	—
486	C₂²×C₄	—	11	1	no	—
487	C₂²×C₄	—	11	2	no	—
488	C₂²×C₄	—	11	2	no	—
489	C₂²×C₄	—	11	2	no	—
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	2	no	—
495	C₂²×C₄	—	11	2	no	—
496	C₂²×C₄	—	11	2	no	—
497	C₂²×C₄	—	11	2	no	—
498	C₂²×C₄	—	44	4	no	—
499	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
500	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
501	C₄⋊C₄	—	11	2	no	—
502	C₄⋊C₄	—	11	1	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	1	no	—
509	C₄⋊C₄	—	11	1	no	—
510	C₄⋊C₄	—	11	2	no	—
511	C₄⋊C₄	—	11	1	no	—
512	C₄⋊C₄	—	11	1	no	—
513	C₄⋊C₄	—	11	1	no	—
514	C₄⋊C₄	—	11	1	no	—
515	C₄⋊C₄	—	11	2	no	—
516	C₄⋊C₄	—	11	1	no	—
517	C₄⋊C₄	—	11	1	no	—
518	C₄⋊C₄	—	11	1	no	—
519	C₄⋊C₄	—	11	1	no	—
520	C₄⋊C₄	—	11	1	no	—
521	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
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	1	no	—
533	C₂²⋊C₄	—	11	1	no	—
534	C₂²⋊C₄	—	11	1	no	—
535	C₂²⋊C₄	—	11	1	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	C₂²×D₁₁	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
550	C₄²	—	11	1	no	—
551	C₄²	—	11	1	no	—
552	C₄²	—	11	1	no	—
553	C₄²	—	11	2	no	—
554	C₄²	—	11	2	no	—
555	C₄²	—	11	2	no	—
556	C₄²	—	11	1	no	—
557	C₄²	—	11	1	no	—
558	C₄²	C₂²×D₁₁	1	1	yes	characteristic
559	C₄²	C₂²×D₁₁	1	2	yes	—
560	C₄²	C₂²×D₁₁	1	1	yes	characteristic
561	C₄²	C₂²×D₁₁	1	1	yes	characteristic
562	C₁₁	#3506	1	1	yes	characteristic, complemented, Sylow
563	C₂³	—	11	1	no	—
564	C₂³	—	11	2	no	—
565	C₂³	—	11	2	no	—
566	C₂³	—	22	4	no	—
567	C₂³	—	44	2	no	—
568	C₂³	—	44	2	no	—
569	C₂³	C₂³×D₁₁	1	2	yes	—
570	C₂³	C₂³×D₁₁	1	2	yes	—
571	Q₈	—	2	2	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	22	2	no	—
574	Q₈	—	22	2	no	—
575	Q₈	—	22	2	no	—
576	Q₈	—	44	1	no	—
577	D₄	—	2	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	22	4	no	—
582	D₄	—	22	4	no	—
583	D₄	—	22	4	no	—
584	D₄	—	22	4	no	—
585	D₄	—	22	2	no	—
586	D₄	—	22	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	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	11	1	no	—
597	C₂×C₄	—	11	1	no	—
598	C₂×C₄	—	11	4	no	—
599	C₂×C₄	—	11	1	no	—
600	C₂×C₄	—	11	1	no	—
601	C₂×C₄	—	11	2	no	—
602	C₂×C₄	—	11	1	no	—
603	C₂×C₄	—	11	2	no	—
604	C₂×C₄	—	11	1	no	—
605	C₂×C₄	—	11	1	no	—
606	C₂×C₄	—	22	2	no	—
607	C₂×C₄	—	22	4	no	—
608	C₂×C₄	—	22	4	no	—
609	C₂×C₄	—	22	4	no	—
610	C₂×C₄	—	22	4	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	—	44	1	no	—
616	C₂×C₄	—	44	2	no	—
617	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₁₁	1	2	yes	—
620	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₁	1	2	yes	—
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	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	11	2	no	—
633	C₂²	—	22	1	no	—
634	C₂²	—	22	1	no	—
635	C₂²	—	22	2	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	—	44	8	no	—
642	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
643	C₄	—	2	2	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	11	2	no	—
652	C₄	—	11	2	no	—
653	C₄	—	22	2	no	—
654	C₄	—	22	1	no	—
655	C₄	—	22	1	no	—
656	C₄	—	22	1	no	—
657	C₄	—	22	2	no	—
658	C₄	—	22	1	no	—
659	C₄	—	22	1	no	—
660	C₄	#41×D₁₁	1	2	yes	—
661	C₂	—	4	2	no	—
662	C₂	—	4	2	no	—
663	C₂	—	22	2	no	—
664	C₂	—	44	2	no	—
665	C₂	—	44	2	no	—
666	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
667	C₂	#10623453	1	1	yes	characteristic
668	C₂	D₁₁×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#559	C₂
hypercenter	#559	D₁₁
hypocenter	C₁₁	#3506
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #559

Complements

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

N	H ≅ G/N	type
1. C₁₁×#559	C₂	semidirect
2. #10623249	C₂	semidirect
3. #10623246	C₂	semidirect
4. #10623212	C₂	semidirect
5. #10623209	C₂	semidirect
6. #10623205	C₂	semidirect
7. #10623202	C₂	semidirect
8. #10623201	C₂	semidirect
9. #10623199	C₂	semidirect
10. #10623192	C₂	semidirect
11. #10623188	C₂	semidirect
12. #10623187	C₂	semidirect
13. #10623186	C₂	semidirect
14. #10623116	C₂	semidirect
15. #10623109	C₂	semidirect
16. #10623105	C₂	semidirect
17. #10623099	C₂	semidirect
18. #10623090	C₂	semidirect
19. #10623084	C₂	semidirect
20. #10623078	C₂	semidirect
21. #10623077	C₂	semidirect
22. C₄×D₄×D₁₁	C₂	semidirect
23. #10623071	C₂	semidirect
26. C₂×#4341	C₂²	semidirect
28. C₂×#4339	C₂²	semidirect
32. C₁₁×#124	C₂²	semidirect
33. C₁₁×#124	C₂²	semidirect
34. C₁₁×#123	C₂²	semidirect
35. C₁₁×#123	C₂²	semidirect
36. C₄×Q₈×C₁₁	C₂²	semidirect
37. C₄×Q₈×C₁₁	C₂²	semidirect
39. C₄×D₄×C₁₁	C₂²	semidirect
40. C₄×D₄×C₁₁	C₂²	semidirect
42. #67000	C₂²	semidirect
44. Q₈×Dic₁₁	C₂²	semidirect
45. #66997	C₂²	semidirect
46. #66997	C₂²	semidirect
49. #66993	C₂²	semidirect
52. #66992	C₂²	semidirect
53. #66992	C₂²	semidirect
54. #66991	C₂²	semidirect
59. D₄×Dic₁₁	C₂²	semidirect
60. #66983	C₂²	semidirect
61. #66982	C₂²	semidirect
64. C₄×C₂²⋊D₁₁	C₂²	semidirect
65. C₂×Dic₁₁⋊C₄	C₂²	semidirect
66. #66951	C₂²	semidirect
70. #66949	C₂²	semidirect
71. #66947	C₂²	semidirect
72. #66947	C₂²	semidirect
75. #66946	C₂²	semidirect
76. #66946	C₂²	semidirect
78. C₄⋊C₄×D₁₁	C₂²	semidirect
79. #66942	C₂²	semidirect
80. #66942	C₂²	semidirect
81. #66941	C₂²	semidirect
82. #66940	C₂²	semidirect
83. #66939	C₂²	semidirect
84. #66938	C₂²	semidirect
85. #66938	C₂²	semidirect
90. #66937	C₂²	semidirect
91. #66937	C₂²	semidirect
92. #66936	C₂²	semidirect
93. #66936	C₂²	semidirect
98. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
100. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
102. #66932	C₂²	semidirect
103. #66932	C₂²	semidirect
104. #66931	C₂²	semidirect
105. #66930	C₂²	semidirect
106. #66930	C₂²	semidirect
107. #66929	C₂²	semidirect
109. #66928	C₂²	semidirect
113. C₄×D₄₄	C₂²	semidirect
116. #66925	C₂²	semidirect
117. #66925	C₂²	semidirect
119. C₄×Dic₂₂	C₂²	semidirect
120. C₄×Dic₂₂	C₂²	semidirect
121. C₄×Dic₂₂	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
287. C₄×D₁₁	#41	semidirect
295. #559	D₁₁	semidirect
378. #124	C₂×D₁₁	semidirect
379. #124	C₂×D₁₁	semidirect
386. #123	C₂×D₁₁	semidirect
387. #123	C₂×D₁₁	semidirect
416. C₄×Q₈	C₂×D₁₁	semidirect
417. C₄×Q₈	C₂×D₁₁	semidirect
436. C₄×D₄	C₂×D₁₁	semidirect
437. C₄×D₄	C₂×D₁₁	semidirect
562. C₁₁	#3506	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#559	2
#10623249	2
#10623246	2
#10623212	2
#10623209	2
#10623205	2
#10623202	2
#10623201	2
#10623199	2
#10623192	2
#10623188	2
#10623187	2
#10623186	2
#10623116	2
#10623109	2
#10623105	2
#10623099	2
#10623090	2
#10623084	2
#10623078	2
#10623077	2
C₄×D₄×D₁₁	2
#10623071	2
#3506	11