Subgroups — #13082443

Order 1408.

1152 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623362	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623359	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623337	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#66991	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623211	C₂	1	1	yes	maximal, characteristic, complemented
7	#10623208	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623192	C₂	1	2	yes	maximal, complemented
9	#10623191	C₂	1	2	yes	maximal, complemented
10	#10623173	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623145	C₂	1	1	yes	maximal, characteristic, complemented
13	#10623145	C₂	1	2	yes	maximal, complemented
14	#10623144	C₂	1	2	yes	maximal, complemented
15	#10623137	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623120	C₂	1	2	yes	maximal, complemented
17	#10623118	C₂	1	2	yes	maximal, complemented
18	#10623089	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623088	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×D₄×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
21	#10623072	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623026	C₂	1	2	yes	maximal, complemented
23	#10623017	C₂	1	2	yes	maximal, complemented
24	C₂×C₁₁×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂²×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂²⋊D₁₁	C₂²	1	2	yes	—
27	C₂×Q₈×D₁₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×#4341	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
32	C₁₁×#124	C₂²	1	1	yes	characteristic, complemented
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, complemented
36	C₁₁×#121	C₂²	1	2	yes	complemented
37	C₁₁×#120	C₂²	1	2	yes	—
38	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	complemented
41	#67006	C₂²	1	2	yes	—
42	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	complemented
43	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	complemented
44	#66999	C₂²	1	1	yes	characteristic, complemented
45	#66999	C₂²	1	1	yes	characteristic, complemented
46	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
47	#66992	C₂²	1	2	yes	complemented
48	#66991	C₂²	1	1	yes	characteristic
49	#66991	C₂²	1	1	yes	characteristic
50	#66991	C₂²	1	2	yes	—
51	#66991	C₂²	1	1	yes	characteristic, complemented
52	#66991	C₂²	1	2	yes	complemented
53	#66991	C₂²	1	1	yes	characteristic, complemented
54	#66991	C₂²	1	1	yes	characteristic, complemented
55	#66991	C₂²	1	2	yes	complemented
56	#66991	C₂²	1	2	yes	complemented
57	#66990	C₂²	1	2	yes	complemented
58	#66990	C₂²	1	2	yes	complemented
59	#66989	C₂²	1	1	yes	characteristic, complemented
60	#66989	C₂²	1	2	yes	complemented
61	#66988	C₂²	1	2	yes	—
62	#66988	C₂²	1	2	yes	complemented
63	#66988	C₂²	1	2	yes	complemented
64	#66988	C₂²	1	2	yes	complemented
65	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
66	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
67	D₄×Dic₁₁	C₂²	1	2	yes	complemented
68	#66982	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
76	#66979	C₂²	1	2	yes	complemented
77	#66979	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic, complemented
79	#66977	C₂²	1	2	yes	complemented
80	#66977	C₂²	1	1	yes	characteristic, complemented
81	#66977	C₂²	1	1	yes	characteristic, complemented
82	#66951	C₂²	1	2	yes	complemented
83	#66950	C₂²	1	1	yes	characteristic, complemented
84	#66949	C₂²	1	2	yes	complemented
85	#66946	C₂²	1	1	yes	characteristic, complemented
86	#66945	C₂²	1	1	yes	characteristic, complemented
87	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
88	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
89	C₄⋊C₄×D₁₁	C₂²	1	2	yes	complemented
90	#66943	C₂²	1	1	yes	characteristic, complemented
91	#66943	C₂²	1	2	yes	complemented
92	#66942	C₂²	1	2	yes	complemented
93	#66939	C₂²	1	2	yes	—
94	#66938	C₂²	1	2	yes	complemented
95	#66937	C₂²	1	2	yes	complemented
96	#66937	C₂²	1	2	yes	complemented
97	#66936	C₂²	1	2	yes	complemented
98	#66936	C₂²	1	2	yes	complemented
99	#66936	C₂²	1	2	yes	complemented
100	(C₂²⋊D₁₁)⋊C₄	C₂²	1	1	yes	characteristic
101	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
102	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
103	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
104	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
105	(C₂²⋊D₁₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₂²⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
109	#66932	C₂²	1	2	yes	complemented
110	#66932	C₂²	1	2	yes	complemented
111	#66932	C₂²	1	2	yes	complemented
112	#66932	C₂²	1	2	yes	complemented
113	#66932	C₂²	1	2	yes	complemented
114	#66931	C₂²	1	2	yes	complemented
115	#66931	C₂²	1	2	yes	complemented
116	#66930	C₂²	1	2	yes	complemented
117	#66930	C₂²	1	2	yes	complemented
118	#66930	C₂²	1	2	yes	complemented
119	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₁₁	C₂²	1	1	yes	characteristic, complemented
121	#66923	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₁	C₂³	1	2	yes	—
124	C₂³×D₁₁	C₂³	1	1	yes	characteristic
125	C₂³×D₁₁	C₂³	1	1	yes	characteristic
126	C₁₁×#41	—	4	2	no	—
127	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₁	—	4	2	no	—
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	2	yes	—
133	C₂×D₄×C₁₁	C₂³	1	2	yes	—
134	C₂×D₄×C₁₁	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
138	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₁	—	2	8	no	—
140	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
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	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
148	C₂²×Dic₁₁	C₂³	1	2	yes	—
149	C₂²×Dic₁₁	C₂³	1	2	yes	—
150	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
151	C₂²×Dic₁₁	C₂³	1	2	yes	—
152	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
153	Q₈×D₁₁	—	4	2	no	—
154	#4341	—	4	2	no	—
155	D₄×D₁₁	—	2	4	no	—
156	C₂×D₄₄	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₁	—	4	2	no	—
158	C₂×C₄×D₁₁	—	4	2	no	—
159	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₁₁	C₂³	1	2	yes	—
166	C₂×C₄×D₁₁	C₂³	1	2	yes	—
167	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
170	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
171	C₂×Dic₂₂	C₂³	1	2	yes	—
172	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
175	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₄²×C₁₁	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
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	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
195	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
196	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
204	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
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	2	yes	—
210	C₄⋊Dic₁₁	C₂³	1	2	yes	—
211	C₄⋊Dic₁₁	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	1	yes	characteristic
221	Dic₁₁⋊C₄	C₂³	1	2	yes	—
222	Dic₁₁⋊C₄	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	1	yes	characteristic
227	C₄×Dic₁₁	C₂³	1	2	yes	—
228	C₄×Dic₁₁	C₂³	1	2	yes	—
229	C₄×Dic₁₁	C₂³	1	2	yes	—
230	#3505	—	11	1	no	maximal, Sylow
231	C₂³×C₁₁	—	2	4	no	—
232	C₂³×C₁₁	—	4	2	no	—
233	C₂³×C₁₁	—	4	2	no	—
234	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
235	C₂³×C₁₁	C₂⁴	1	2	yes	—
236	C₂³×C₁₁	C₂⁴	1	2	yes	—
237	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₁	—	2	2	no	—
239	C₂²×D₁₁	—	4	1	no	—
240	C₂²×D₁₁	—	4	1	no	—
241	C₂²×D₁₁	—	4	1	no	—
242	C₂²×D₁₁	—	4	1	no	—
243	C₂²×D₁₁	#41	1	4	yes	complemented
244	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
245	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
246	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
247	Q₈×C₁₁	—	2	2	no	—
248	D₄×C₁₁	—	2	2	no	—
249	D₄×C₁₁	—	2	2	no	—
250	D₄×C₁₁	—	2	2	no	—
251	D₄×C₁₁	—	4	2	no	—
252	D₄×C₁₁	—	4	2	no	—
253	D₄×C₁₁	—	4	2	no	—
254	C₂×C₄×C₁₁	—	2	2	no	—
255	C₂×C₄×C₁₁	—	2	2	no	—
256	C₂×C₄×C₁₁	—	4	2	no	—
257	C₂×C₄×C₁₁	—	4	2	no	—
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	2	yes	—
262	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
263	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
265	C₂²⋊D₁₁	—	2	2	no	—
266	C₂²⋊D₁₁	—	2	2	no	—
267	C₂²⋊D₁₁	—	2	4	no	—
268	C₂²⋊D₁₁	—	2	4	no	—
269	C₂²⋊D₁₁	—	2	4	no	—
270	C₂²⋊D₁₁	—	2	4	no	—
271	C₂²⋊D₁₁	—	4	2	no	—
272	C₂²⋊D₁₁	—	4	2	no	—
273	C₂×Dic₁₁	—	2	4	no	—
274	C₂×Dic₁₁	—	4	1	no	—
275	C₂×Dic₁₁	—	4	1	no	—
276	C₂×Dic₁₁	—	4	2	no	—
277	C₂×Dic₁₁	—	4	2	no	—
278	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₁	C₂⁴	1	2	yes	—
280	C₂×Dic₁₁	C₂⁴	1	2	yes	—
281	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₁₁	C₂⁴	1	2	yes	—
285	C₂×Dic₁₁	C₂⁴	1	2	yes	—
286	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
287	D₄₄	—	2	2	no	—
288	C₄×D₁₁	—	2	2	no	—
289	C₄×D₁₁	—	2	2	no	—
290	C₄×D₁₁	—	2	2	no	—
291	C₄×D₁₁	—	2	2	no	—
292	C₄×D₁₁	—	4	1	no	—
293	C₄×D₁₁	—	4	1	no	—
294	C₄×D₁₁	—	4	1	no	—
295	C₄×D₁₁	—	4	1	no	—
296	C₄×D₁₁	—	4	1	no	—
297	C₄×D₁₁	—	4	2	no	—
298	C₄×D₁₁	—	4	2	no	—
299	Dic₂₂	—	2	2	no	—
300	Dic₂₂	—	4	2	no	—
301	#553	—	11	2	no	—
302	#553	—	11	1	no	—
303	#553	—	11	2	no	—
304	#553	—	11	1	no	—
305	#552	—	11	1	no	—
306	#552	—	11	1	no	—
307	#551	—	11	2	no	—
308	#551	—	11	2	no	—
309	#548	—	11	1	no	—
310	#548	—	11	1	no	—
311	#546	—	11	1	no	—
312	#546	D₁₁	1	1	yes	characteristic, complemented
313	#539	—	11	2	no	—
314	#538	—	11	2	no	—
315	#534	—	11	2	no	—
316	#529	—	11	1	no	—
317	#529	—	11	1	no	—
318	#525	—	11	1	no	—
319	#525	—	11	1	no	—
320	C₂×C₂²⋊Q₈	—	11	1	no	—
321	C₂×#121	—	11	1	no	—
322	#518	—	11	2	no	—
323	C₂×C₄×D₄	—	11	1	no	—
324	C₂²×C₁₁	—	2	1	no	—
325	C₂²×C₁₁	—	2	1	no	—
326	C₂²×C₁₁	—	2	1	no	—
327	C₂²×C₁₁	—	2	2	no	—
328	C₂²×C₁₁	—	2	2	no	—
329	C₂²×C₁₁	—	2	1	no	—
330	C₂²×C₁₁	—	2	2	no	—
331	C₂²×C₁₁	—	2	2	no	—
332	C₂²×C₁₁	—	2	2	no	—
333	C₂²×C₁₁	—	2	1	no	—
334	C₂²×C₁₁	—	2	2	no	—
335	C₂²×C₁₁	—	8	4	no	—
336	C₂²×C₁₁	C₂×#41	1	2	yes	—
337	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
338	C₂×D₁₁	—	2	1	no	—
339	C₂×D₁₁	—	2	1	no	—
340	C₂×D₁₁	—	2	1	no	—
341	C₂×D₁₁	—	2	1	no	—
342	C₂×D₁₁	—	2	1	no	—
343	C₂×D₁₁	—	2	1	no	—
344	C₂×D₁₁	—	2	1	no	—
345	C₂×D₁₁	—	4	4	no	—
346	C₂×D₁₁	—	4	4	no	—
347	C₂×D₁₁	C₂×#41	1	2	yes	—
348	C₂×D₁₁	C₂×#41	1	2	yes	—
349	C₄×C₁₁	—	2	1	no	—
350	C₄×C₁₁	—	2	1	no	—
351	C₄×C₁₁	—	2	1	no	—
352	C₄×C₁₁	—	2	2	no	—
353	C₄×C₁₁	—	2	1	no	—
354	C₄×C₁₁	—	2	2	no	—
355	C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
356	Dic₁₁	—	2	1	no	—
357	Dic₁₁	—	2	2	no	—
358	Dic₁₁	—	2	2	no	—
359	Dic₁₁	—	2	2	no	—
360	Dic₁₁	—	2	1	no	—
361	Dic₁₁	—	2	1	no	—
362	Dic₁₁	—	2	1	no	—
363	Dic₁₁	—	2	1	no	—
364	Dic₁₁	—	2	2	no	—
365	C₂×#41	—	11	1	no	—
366	C₂×#41	C₂×D₁₁	1	1	yes	characteristic, complemented
367	C₂²×Q₈	—	11	1	no	—
368	C₂²×D₄	—	11	2	no	—
369	C₂²×D₄	—	11	1	no	—
370	C₂²×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
371	C₂³×C₄	—	11	1	no	—
372	C₂³×C₄	—	11	1	no	—
373	#126	—	11	2	no	—
374	#126	—	11	2	no	—
375	#126	—	11	2	no	—
376	#126	—	11	2	no	—
377	#126	—	11	2	no	—
378	#126	—	11	2	no	—
379	#125	—	11	1	no	—
380	#125	—	11	2	no	—
381	#125	—	11	2	no	—
382	#125	—	11	1	no	—
383	#124	—	11	1	no	—
384	#124	—	11	2	no	—
385	#124	—	11	2	no	—
386	#124	C₂×D₁₁	1	1	yes	characteristic, complemented
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	—	11	2	no	—
394	#123	—	11	2	no	—
395	#123	—	11	2	no	—
396	#123	C₂×D₁₁	1	2	yes	complemented
397	C₂²⋊Q₈	—	11	1	no	—
398	C₂²⋊Q₈	—	11	1	no	—
399	C₂²⋊Q₈	—	11	1	no	—
400	C₂²⋊Q₈	—	11	1	no	—
401	C₂²⋊Q₈	—	11	2	no	—
402	C₂²⋊Q₈	—	11	1	no	—
403	C₂²⋊Q₈	—	11	2	no	—
404	C₂²⋊Q₈	—	11	2	no	—
405	C₂²⋊Q₈	—	11	2	no	—
406	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
407	#121	—	11	1	no	—
408	#121	—	11	1	no	—
409	#121	—	11	2	no	—
410	#121	—	11	1	no	—
411	#121	—	11	1	no	—
412	#121	—	11	2	no	—
413	#121	—	11	1	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	C₂×D₁₁	1	1	yes	characteristic, complemented
420	#121	C₂×D₁₁	1	2	yes	complemented
421	#120	—	11	2	no	—
422	#120	—	11	2	no	—
423	#120	—	11	2	no	—
424	#120	C₂×D₁₁	1	2	yes	—
425	C₄×Q₈	—	11	1	no	—
426	C₄×Q₈	—	11	1	no	—
427	C₄×D₄	—	11	1	no	—
428	C₄×D₄	—	11	2	no	—
429	C₄×D₄	—	11	1	no	—
430	C₄×D₄	—	11	1	no	—
431	C₄×D₄	—	11	1	no	—
432	C₄×D₄	—	11	2	no	—
433	C₄×D₄	—	11	2	no	—
434	C₄×D₄	—	11	2	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	—	11	1	no	—
440	C₄×D₄	—	11	2	no	—
441	C₄×D₄	—	11	2	no	—
442	C₄×D₄	—	11	2	no	—
443	C₄×D₄	—	11	2	no	—
444	C₄×D₄	—	11	1	no	—
445	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
446	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
447	#117	—	11	1	no	—
448	#117	—	11	2	no	—
449	#117	—	11	1	no	—
450	#117	—	11	2	no	—
451	#117	—	11	2	no	—
452	#117	—	11	2	no	—
453	C₂×C₄⋊C₄	—	11	1	no	—
454	C₂×C₄⋊C₄	—	11	1	no	—
455	C₂×C₄⋊C₄	—	11	1	no	—
456	C₂×C₄⋊C₄	—	11	2	no	—
457	C₂×C₂²⋊C₄	—	11	2	no	—
458	C₂×C₂²⋊C₄	—	11	2	no	—
459	C₂×C₂²⋊C₄	—	11	1	no	—
460	C₂×C₂²⋊C₄	—	11	1	no	—
461	C₂×C₂²⋊C₄	—	11	2	no	—
462	C₂×C₂²⋊C₄	C₂×D₁₁	1	2	yes	complemented
463	C₂×C₄²	—	11	1	no	—
464	C₂×C₁₁	—	2	2	no	—
465	C₂×C₁₁	—	4	1	no	—
466	C₂×C₁₁	—	4	2	no	—
467	C₂×C₁₁	—	4	2	no	—
468	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
469	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂×C₁₁	#585	1	1	yes	characteristic
471	D₁₁	—	2	2	no	—
472	D₁₁	—	2	2	no	—
473	D₁₁	—	4	1	no	—
474	C₂⁴	—	11	1	no	—
475	C₂⁴	—	11	1	no	—
476	C₂⁴	C₂²×D₁₁	1	2	yes	—
477	#41	—	4	2	no	—
478	#41	—	44	2	no	—
479	C₂×Q₈	—	11	1	no	—
480	C₂×Q₈	—	11	2	no	—
481	C₂×Q₈	—	44	2	no	—
482	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
483	C₂×D₄	—	4	2	no	—
484	C₂×D₄	—	11	1	no	—
485	C₂×D₄	—	11	2	no	—
486	C₂×D₄	—	11	2	no	—
487	C₂×D₄	—	11	1	no	—
488	C₂×D₄	—	11	2	no	—
489	C₂×D₄	—	11	2	no	—
490	C₂×D₄	—	11	2	no	—
491	C₂×D₄	—	11	2	no	—
492	C₂×D₄	—	11	1	no	—
493	C₂×D₄	—	22	4	no	—
494	C₂×D₄	—	22	8	no	—
495	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
496	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
497	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
498	C₂×D₄	C₂²×D₁₁	1	2	yes	—
499	C₂×D₄	C₂²×D₁₁	1	2	yes	—
500	C₂×D₄	C₂²×D₁₁	1	2	yes	—
501	C₂²×C₄	—	11	2	no	—
502	C₂²×C₄	—	11	1	no	—
503	C₂²×C₄	—	11	2	no	—
504	C₂²×C₄	—	11	2	no	—
505	C₂²×C₄	—	11	1	no	—
506	C₂²×C₄	—	11	1	no	—
507	C₂²×C₄	—	11	1	no	—
508	C₂²×C₄	—	11	1	no	—
509	C₂²×C₄	—	11	1	no	—
510	C₂²×C₄	—	11	1	no	—
511	C₂²×C₄	—	11	2	no	—
512	C₂²×C₄	—	11	1	no	—
513	C₂²×C₄	—	11	2	no	—
514	C₂²×C₄	—	11	1	no	—
515	C₂²×C₄	—	11	1	no	—
516	C₂²×C₄	—	11	1	no	—
517	C₂²×C₄	—	44	2	no	—
518	C₂²×C₄	—	44	2	no	—
519	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
520	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
521	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
522	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
523	C₄⋊C₄	—	11	1	no	—
524	C₄⋊C₄	—	11	2	no	—
525	C₄⋊C₄	—	11	2	no	—
526	C₄⋊C₄	—	11	1	no	—
527	C₄⋊C₄	—	11	1	no	—
528	C₄⋊C₄	—	11	1	no	—
529	C₄⋊C₄	—	11	1	no	—
530	C₄⋊C₄	—	11	1	no	—
531	C₄⋊C₄	—	11	2	no	—
532	C₄⋊C₄	—	11	2	no	—
533	C₄⋊C₄	—	11	2	no	—
534	C₄⋊C₄	—	11	2	no	—
535	C₄⋊C₄	—	11	2	no	—
536	C₄⋊C₄	—	11	2	no	—
537	C₄⋊C₄	—	11	2	no	—
538	C₄⋊C₄	—	11	2	no	—
539	C₄⋊C₄	—	11	2	no	—
540	C₄⋊C₄	—	11	2	no	—
541	C₄⋊C₄	—	11	2	no	—
542	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
545	C₂²⋊C₄	—	11	1	no	—
546	C₂²⋊C₄	—	11	2	no	—
547	C₂²⋊C₄	—	11	2	no	—
548	C₂²⋊C₄	—	11	2	no	—
549	C₂²⋊C₄	—	11	2	no	—
550	C₂²⋊C₄	—	11	2	no	—
551	C₂²⋊C₄	—	11	1	no	—
552	C₂²⋊C₄	—	11	2	no	—
553	C₂²⋊C₄	—	11	2	no	—
554	C₂²⋊C₄	—	11	2	no	—
555	C₂²⋊C₄	—	11	2	no	—
556	C₂²⋊C₄	—	11	2	no	—
557	C₂²⋊C₄	—	11	2	no	—
558	C₂²⋊C₄	—	11	1	no	—
559	C₂²⋊C₄	—	11	1	no	—
560	C₂²⋊C₄	—	11	2	no	—
561	C₂²⋊C₄	—	11	2	no	—
562	C₂²⋊C₄	—	11	1	no	—
563	C₂²⋊C₄	—	11	1	no	—
564	C₂²⋊C₄	—	11	2	no	—
565	C₂²⋊C₄	—	11	2	no	—
566	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
567	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
568	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
569	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
571	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
573	C₄²	—	11	1	no	—
574	C₄²	—	11	1	no	—
575	C₄²	—	11	1	no	—
576	C₄²	—	11	2	no	—
577	C₄²	—	11	2	no	—
578	C₄²	—	11	2	no	—
579	C₄²	—	11	2	no	—
580	C₄²	C₂²×D₁₁	1	1	yes	characteristic
581	C₁₁	#3505	1	1	yes	characteristic, complemented, Sylow
582	C₂³	—	2	4	no	—
583	C₂³	—	4	2	no	—
584	C₂³	—	4	2	no	—
585	C₂³	—	11	1	no	—
586	C₂³	—	11	1	no	—
587	C₂³	—	11	4	no	—
588	C₂³	—	11	1	no	—
589	C₂³	—	22	2	no	—
590	C₂³	—	44	1	no	—
591	C₂³	—	44	1	no	—
592	C₂³	—	44	1	no	—
593	C₂³	—	44	1	no	—
594	C₂³	C₂³×D₁₁	1	1	yes	characteristic
595	C₂³	C₂³×D₁₁	1	2	yes	—
596	C₂³	C₂³×D₁₁	1	2	yes	—
597	C₂³	C₂³×D₁₁	1	1	yes	characteristic
598	Q₈	—	2	2	no	—
599	Q₈	—	22	2	no	—
600	Q₈	—	44	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	2	2	no	—
603	D₄	—	2	2	no	—
604	D₄	—	4	2	no	—
605	D₄	—	4	2	no	—
606	D₄	—	4	2	no	—
607	D₄	—	22	2	no	—
608	D₄	—	22	2	no	—
609	D₄	—	22	4	no	—
610	D₄	—	22	4	no	—
611	D₄	—	22	4	no	—
612	D₄	—	22	4	no	—
613	D₄	—	22	2	no	—
614	D₄	—	44	2	no	—
615	D₄	—	44	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	11	1	no	—
621	C₂×C₄	—	11	1	no	—
622	C₂×C₄	—	11	2	no	—
623	C₂×C₄	—	11	2	no	—
624	C₂×C₄	—	11	1	no	—
625	C₂×C₄	—	11	1	no	—
626	C₂×C₄	—	11	2	no	—
627	C₂×C₄	—	11	2	no	—
628	C₂×C₄	—	11	1	no	—
629	C₂×C₄	—	22	2	no	—
630	C₂×C₄	—	22	4	no	—
631	C₂×C₄	—	22	2	no	—
632	C₂×C₄	—	22	2	no	—
633	C₂×C₄	—	22	2	no	—
634	C₂×C₄	—	44	1	no	—
635	C₂×C₄	—	44	1	no	—
636	C₂×C₄	—	44	1	no	—
637	C₂×C₄	—	44	1	no	—
638	C₂×C₄	—	44	2	no	—
639	C₂×C₄	—	44	1	no	—
640	C₂×C₄	—	44	2	no	—
641	C₂×C₄	—	44	1	no	—
642	C₂×C₄	—	44	1	no	—
643	C₂×C₄	—	44	2	no	—
644	C₂×C₄	—	44	2	no	—
645	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₁₁	1	2	yes	—
649	C₂×C₄	C₂³×D₁₁	1	2	yes	—
650	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	8	4	no	—
664	C₂²	—	11	2	no	—
665	C₂²	—	11	2	no	—
666	C₂²	—	22	1	no	—
667	C₂²	—	22	1	no	—
668	C₂²	—	22	1	no	—
669	C₂²	—	22	1	no	—
670	C₂²	—	22	1	no	—
671	C₂²	—	22	1	no	—
672	C₂²	—	22	1	no	—
673	C₂²	—	44	4	no	—
674	C₂²	—	44	4	no	—
675	C₂²	#41×D₁₁	1	2	yes	—
676	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	22	1	no	—
684	C₄	—	22	1	no	—
685	C₄	—	22	1	no	—
686	C₄	—	22	2	no	—
687	C₄	—	22	1	no	—
688	C₄	—	22	2	no	—
689	C₄	—	22	2	no	—
690	C₄	—	22	1	no	—
691	C₄	—	22	2	no	—
692	C₄	#67037	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	2	no	—
695	C₂	—	4	2	no	—
696	C₂	—	4	1	no	—
697	C₂	—	22	2	no	—
698	C₂	—	22	2	no	—
699	C₂	—	44	1	no	—
700	C₂	C₂×#67037	1	1	yes	characteristic
701	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
702	C₂	#10623455	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#546	C₂
hypercenter	#546	D₁₁
hypocenter	C₁₁	#3505
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₁₁×#546	C₂	semidirect
2. #10623362	C₂	semidirect
3. #10623359	C₂	semidirect
4. #10623337	C₂	semidirect
5. C₂×#66991	C₂	semidirect
6. #10623211	C₂	semidirect
7. #10623208	C₂	semidirect
8. #10623192	C₂	semidirect
9. #10623191	C₂	semidirect
10. #10623173	C₂	semidirect
11. D₁₁×C₂²⋊Q₈	C₂	semidirect
12. #10623145	C₂	semidirect
13. #10623145	C₂	semidirect
14. #10623144	C₂	semidirect
15. #10623137	C₂	semidirect
16. #10623120	C₂	semidirect
17. #10623118	C₂	semidirect
18. #10623089	C₂	semidirect
19. #10623088	C₂	semidirect
20. C₄×D₄×D₁₁	C₂	semidirect
21. #10623072	C₂	semidirect
22. #10623026	C₂	semidirect
23. #10623017	C₂	semidirect
24. C₂×C₁₁×#41	C₂²	semidirect
25. C₂²×D₄×C₁₁	C₂²	semidirect
27. C₂×Q₈×D₁₁	C₂²	semidirect
28. C₂×#4341	C₂²	semidirect
31. C₂²×C₄×D₁₁	C₂²	semidirect
32. C₁₁×#124	C₂²	semidirect
33. C₁₁×#123	C₂²	semidirect
34. C₁₁×C₂²⋊Q₈	C₂²	semidirect
35. C₁₁×#121	C₂²	semidirect
36. C₁₁×#121	C₂²	semidirect
39. C₄×D₄×C₁₁	C₂²	semidirect
40. C₂×C₁₁×C₂²⋊C₄	C₂²	semidirect
42. C₂×C₂²⋊Dic₁₁	C₂²	semidirect
43. C₂×C₂²⋊Dic₁₁	C₂²	semidirect
44. #66999	C₂²	semidirect
45. #66999	C₂²	semidirect
46. Q₈×Dic₁₁	C₂²	semidirect
47. #66992	C₂²	semidirect
51. #66991	C₂²	semidirect
52. #66991	C₂²	semidirect
53. #66991	C₂²	semidirect
54. #66991	C₂²	semidirect
55. #66991	C₂²	semidirect
56. #66991	C₂²	semidirect
57. #66990	C₂²	semidirect
58. #66990	C₂²	semidirect
59. #66989	C₂²	semidirect
60. #66989	C₂²	semidirect
62. #66988	C₂²	semidirect
63. #66988	C₂²	semidirect
64. #66988	C₂²	semidirect
66. D₄×Dic₁₁	C₂²	semidirect
67. D₄×Dic₁₁	C₂²	semidirect
68. #66982	C₂²	semidirect
70. C₄×C₂²⋊D₁₁	C₂²	semidirect
71. C₄×C₂²⋊D₁₁	C₂²	semidirect
72. C₄×C₂²⋊D₁₁	C₂²	semidirect
73. C₄×C₂²⋊D₁₁	C₂²	semidirect
74. C₄×C₂²⋊D₁₁	C₂²	semidirect
75. C₄×C₂²⋊D₁₁	C₂²	semidirect
76. #66979	C₂²	semidirect
77. #66979	C₂²	semidirect
78. C₂×C₄⋊Dic₁₁	C₂²	semidirect
79. #66977	C₂²	semidirect
80. #66977	C₂²	semidirect
81. #66977	C₂²	semidirect
82. #66951	C₂²	semidirect
83. #66950	C₂²	semidirect
84. #66949	C₂²	semidirect
85. #66946	C₂²	semidirect
86. #66945	C₂²	semidirect
87. C₄⋊C₄×D₁₁	C₂²	semidirect
88. C₄⋊C₄×D₁₁	C₂²	semidirect
89. C₄⋊C₄×D₁₁	C₂²	semidirect
90. #66943	C₂²	semidirect
91. #66943	C₂²	semidirect
92. #66942	C₂²	semidirect
94. #66938	C₂²	semidirect
95. #66937	C₂²	semidirect
96. #66937	C₂²	semidirect
97. #66936	C₂²	semidirect
98. #66936	C₂²	semidirect
99. #66936	C₂²	semidirect
101. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
102. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
103. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
104. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
105. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
108. C₂²⋊C₄×D₁₁	C₂²	semidirect
109. #66932	C₂²	semidirect
110. #66932	C₂²	semidirect
111. #66932	C₂²	semidirect
112. #66932	C₂²	semidirect
113. #66932	C₂²	semidirect
114. #66931	C₂²	semidirect
115. #66931	C₂²	semidirect
116. #66930	C₂²	semidirect
117. #66930	C₂²	semidirect
118. #66930	C₂²	semidirect
119. C₄×D₄₄	C₂²	semidirect
120. C₄²×D₁₁	C₂²	semidirect
121. #66923	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
243. C₂²×D₁₁	#41	semidirect
312. #546	D₁₁	semidirect
366. C₂×#41	C₂×D₁₁	semidirect
370. C₂²×D₄	C₂×D₁₁	semidirect
386. #124	C₂×D₁₁	semidirect
396. #123	C₂×D₁₁	semidirect
406. C₂²⋊Q₈	C₂×D₁₁	semidirect
419. #121	C₂×D₁₁	semidirect
420. #121	C₂×D₁₁	semidirect
446. C₄×D₄	C₂×D₁₁	semidirect
462. C₂×C₂²⋊C₄	C₂×D₁₁	semidirect
581. C₁₁	#3505	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#546	2
#10623362	2
#10623359	2
#10623337	2
C₂×#66991	2
#10623211	2
#10623208	2
#10623192	2
#10623191	2
#10623173	2
D₁₁×C₂²⋊Q₈	2
#10623145	2
#10623144	2
#10623137	2
#10623120	2
#10623118	2
#10623089	2
#10623088	2
C₄×D₄×D₁₁	2
#10623072	2
#10623026	2
#10623017	2
#3505	11