Subgroups — #13082221

Order 1408.

1242 conjugacy classes of subgroups.

The subgroup lattice has 690 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	#10623360	C₂	1	1	yes	maximal, characteristic, complemented
3	#41×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623212	C₂	1	1	yes	maximal, characteristic, complemented
7	#10623211	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623189	C₂	1	2	yes	maximal, complemented
9	#10623180	C₂	1	2	yes	maximal, complemented
10	#10623166	C₂	1	1	yes	maximal, characteristic, complemented
11	#10623155	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623145	C₂	1	1	yes	maximal, characteristic, complemented
13	#10623137	C₂	1	2	yes	maximal, complemented
14	#10623132	C₂	1	2	yes	maximal, complemented
15	#10623127	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623122	C₂	1	2	yes	maximal, complemented
17	#10623117	C₂	1	2	yes	maximal, complemented
18	#10623096	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₄×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623070	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#4341	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623026	C₂	1	2	yes	maximal, complemented
23	C₂×(C₂²⋊D₁₁)⋊C₄	C₂	1	2	yes	maximal, complemented
24	C₂×C₁₁×#41	C₂²	1	1	yes	characteristic
25	C₂²×D₄×C₁₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₁₁	C₂²	1	2	yes	—
27	C₂³×Dic₁₁	C₂²	1	2	yes	complemented
28	C₂×#4341	C₂²	1	1	yes	characteristic
29	C₂×#4341	C₂²	1	2	yes	complemented
30	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₁₁	C₂²	1	2	yes	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	complemented
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	#67000	C₂²	1	1	yes	characteristic, complemented
44	#66999	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
46	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
47	#66993	C₂²	1	1	yes	characteristic
48	#66992	C₂²	1	2	yes	—
49	#66992	C₂²	1	2	yes	complemented
50	#66992	C₂²	1	2	yes	complemented
51	#66992	C₂²	1	2	yes	complemented
52	#66991	C₂²	1	1	yes	characteristic
53	#66991	C₂²	1	2	yes	complemented
54	#66990	C₂²	1	2	yes	—
55	#66990	C₂²	1	2	yes	complemented
56	#66988	C₂²	1	2	yes	complemented
57	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
58	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
59	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
60	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
61	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
62	D₄×Dic₁₁	C₂²	1	2	yes	complemented
63	D₄×Dic₁₁	C₂²	1	2	yes	complemented
64	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
65	D₄×Dic₁₁	C₂²	1	2	yes	complemented
66	D₄×Dic₁₁	C₂²	1	2	yes	complemented
67	#66983	C₂²	1	1	yes	characteristic
68	#66983	C₂²	1	1	yes	characteristic, complemented
69	#66982	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
73	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	complemented
74	#66979	C₂²	1	2	yes	complemented
75	#66979	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic, complemented
77	#66977	C₂²	1	2	yes	complemented
78	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	complemented
79	C₂×C₄×Dic₁₁	C₂²	1	2	yes	complemented
80	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
82	#66951	C₂²	1	2	yes	complemented
83	#66951	C₂²	1	2	yes	complemented
84	#66950	C₂²	1	2	yes	complemented
85	#66946	C₂²	1	1	yes	characteristic, complemented
86	#66945	C₂²	1	1	yes	characteristic, complemented
87	#66945	C₂²	1	2	yes	complemented
88	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
89	#66943	C₂²	1	1	yes	characteristic, complemented
90	#66942	C₂²	1	2	yes	complemented
91	#66941	C₂²	1	1	yes	characteristic, complemented
92	#66940	C₂²	1	1	yes	characteristic, complemented
93	#66939	C₂²	1	2	yes	complemented
94	#66939	C₂²	1	2	yes	complemented
95	#66938	C₂²	1	2	yes	complemented
96	#66938	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	—
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	2	yes	complemented
106	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
107	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
108	(C₂²⋊D₁₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
109	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	complemented
111	#66932	C₂²	1	2	yes	complemented
112	#66932	C₂²	1	2	yes	complemented
113	#66931	C₂²	1	2	yes	complemented
114	#66931	C₂²	1	2	yes	complemented
115	#66931	C₂²	1	2	yes	complemented
116	#66930	C₂²	1	1	yes	characteristic, complemented
117	#66930	C₂²	1	1	yes	characteristic, 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	2	yes	—
125	C₁₁×#41	—	2	4	no	—
126	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₁	—	2	4	no	—
128	C₂×D₄×C₁₁	C₂³	1	2	yes	—
129	C₂×D₄×C₁₁	C₂³	1	2	yes	—
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	1	yes	characteristic
134	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₁	—	2	8	no	—
139	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
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	1	yes	characteristic
147	C₂²×Dic₁₁	—	4	4	no	—
148	C₂²×Dic₁₁	C₂³	1	2	yes	—
149	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
150	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
151	C₂²×Dic₁₁	C₂³	1	2	yes	—
152	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
153	C₂²×Dic₁₁	C₂³	1	2	yes	—
154	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
155	C₂²×Dic₁₁	C₂³	1	2	yes	—
156	C₂²×Dic₁₁	C₂³	1	2	yes	—
157	C₂²×Dic₁₁	C₂³	1	2	yes	—
158	#4341	—	2	4	no	—
159	#4341	—	4	4	no	—
160	D₄×D₁₁	—	2	4	no	—
161	C₂×D₄₄	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₁	—	4	4	no	—
163	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₁₁	C₂³	1	2	yes	—
167	C₂×C₄×D₁₁	C₂³	1	2	yes	—
168	C₂×C₄×D₁₁	C₂³	1	2	yes	—
169	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
170	C₂×Dic₂₂	C₂³	1	2	yes	—
171	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
174	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
179	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₄²×C₁₁	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
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	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
209	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
214	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₁₁⋊C₄	C₂³	1	2	yes	—
216	Dic₁₁⋊C₄	C₂³	1	2	yes	—
217	Dic₁₁⋊C₄	C₂³	1	2	yes	—
218	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
228	C₄×Dic₁₁	C₂³	1	2	yes	—
229	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
230	#3481	—	11	1	no	maximal, Sylow
231	C₂³×C₁₁	—	2	4	no	—
232	C₂³×C₁₁	—	2	4	no	—
233	C₂³×C₁₁	—	4	2	no	—
234	C₂³×C₁₁	C₂⁴	1	2	yes	—
235	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
236	C₂³×C₁₁	C₂⁴	1	2	yes	—
237	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₁	—	2	4	no	—
239	C₂²×D₁₁	—	2	4	no	—
240	C₂²×D₁₁	—	4	2	no	—
241	C₂²×D₁₁	C₂⁴	1	2	yes	—
242	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
243	Q₈×C₁₁	—	2	2	no	—
244	D₄×C₁₁	—	2	2	no	—
245	D₄×C₁₁	—	2	4	no	—
246	D₄×C₁₁	—	2	4	no	—
247	D₄×C₁₁	—	2	2	no	—
248	D₄×C₁₁	—	4	2	no	—
249	D₄×C₁₁	#41	1	4	yes	complemented
250	C₂×C₄×C₁₁	—	2	4	no	—
251	C₂×C₄×C₁₁	—	2	2	no	—
252	C₂×C₄×C₁₁	—	2	2	no	—
253	C₂×C₄×C₁₁	—	4	2	no	—
254	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
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	2	yes	—
260	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
261	C₂²⋊D₁₁	—	2	4	no	—
262	C₂²⋊D₁₁	—	2	4	no	—
263	C₂²⋊D₁₁	—	2	2	no	—
264	C₂²⋊D₁₁	—	2	4	no	—
265	C₂²⋊D₁₁	—	2	4	no	—
266	C₂²⋊D₁₁	—	4	2	no	—
267	C₂²⋊D₁₁	—	4	2	no	—
268	C₂²⋊D₁₁	#41	1	4	yes	complemented
269	C₂×Dic₁₁	—	2	2	no	—
270	C₂×Dic₁₁	—	2	2	no	—
271	C₂×Dic₁₁	—	2	4	no	—
272	C₂×Dic₁₁	—	2	4	no	—
273	C₂×Dic₁₁	—	2	2	no	—
274	C₂×Dic₁₁	—	2	4	no	—
275	C₂×Dic₁₁	—	2	2	no	—
276	C₂×Dic₁₁	—	4	2	no	—
277	C₂×Dic₁₁	—	4	2	no	—
278	C₂×Dic₁₁	—	4	2	no	—
279	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₁₁	C₂⁴	1	2	yes	—
282	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₁₁	C₂⁴	1	2	yes	—
286	C₂×Dic₁₁	C₂⁴	1	2	yes	—
287	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
289	D₄₄	—	2	2	no	—
290	C₄×D₁₁	—	2	2	no	—
291	C₄×D₁₁	—	2	2	no	—
292	C₄×D₁₁	—	2	2	no	—
293	C₄×D₁₁	—	2	4	no	—
294	C₄×D₁₁	—	4	2	no	—
295	C₄×D₁₁	—	4	2	no	—
296	Dic₂₂	—	2	2	no	—
297	Dic₂₂	—	4	2	no	—
298	#559	—	11	1	no	—
299	#554	—	11	1	no	—
300	#554	—	11	1	no	—
301	#553	—	11	2	no	—
302	#553	—	11	1	no	—
303	#553	—	11	1	no	—
304	#551	—	11	2	no	—
305	#551	—	11	2	no	—
306	#546	—	11	1	no	—
307	#546	—	11	2	no	—
308	#546	D₁₁	1	1	yes	characteristic, complemented
309	D₄²	—	11	1	no	—
310	#532	—	11	1	no	—
311	#529	—	11	1	no	—
312	#529	—	11	2	no	—
313	#529	—	11	1	no	—
314	#525	—	11	2	no	—
315	#525	—	11	2	no	—
316	C₄×#41	—	11	1	no	—
317	C₄×#41	—	11	1	no	—
318	C₂×C₄×D₄	—	11	1	no	—
319	C₂×C₄×D₄	—	11	1	no	—
320	C₂×C₄×D₄	—	11	2	no	—
321	C₂²×C₁₁	—	2	1	no	—
322	C₂²×C₁₁	—	2	2	no	—
323	C₂²×C₁₁	—	2	2	no	—
324	C₂²×C₁₁	—	2	1	no	—
325	C₂²×C₁₁	—	2	1	no	—
326	C₂²×C₁₁	—	2	2	no	—
327	C₂²×C₁₁	—	2	1	no	—
328	C₂²×C₁₁	—	2	2	no	—
329	C₂²×C₁₁	—	2	1	no	—
330	C₂²×C₁₁	—	2	2	no	—
331	C₂²×C₁₁	—	4	8	no	—
332	C₂²×C₁₁	C₂×#41	1	4	yes	—
333	C₂²×C₁₁	C₂×#41	1	2	yes	—
334	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
335	C₂×D₁₁	—	2	1	no	—
336	C₂×D₁₁	—	2	1	no	—
337	C₂×D₁₁	—	2	2	no	—
338	C₂×D₁₁	—	2	2	no	—
339	C₂×D₁₁	—	2	2	no	—
340	C₂×D₁₁	—	4	8	no	—
341	C₂×D₁₁	C₂×#41	1	2	yes	—
342	C₄×C₁₁	—	2	1	no	—
343	C₄×C₁₁	—	2	1	no	—
344	C₄×C₁₁	—	2	2	no	—
345	C₄×C₁₁	—	2	1	no	—
346	C₄×C₁₁	—	2	1	no	—
347	C₄×C₁₁	—	2	2	no	—
348	C₄×C₁₁	C₂×#41	1	2	yes	—
349	Dic₁₁	—	2	1	no	—
350	Dic₁₁	—	2	1	no	—
351	Dic₁₁	—	2	1	no	—
352	Dic₁₁	—	2	2	no	—
353	Dic₁₁	—	2	1	no	—
354	Dic₁₁	—	2	2	no	—
355	Dic₁₁	—	2	2	no	—
356	Dic₁₁	—	2	1	no	—
357	Dic₁₁	C₂×#41	1	2	yes	—
358	Dic₁₁	H(5,𝔽₂)	1	2	yes	—
359	C₂×#41	—	11	1	no	—
360	C₂×#41	—	11	2	no	—
361	C₂×#41	C₂×D₁₁	1	1	yes	characteristic
362	C₂²×D₄	—	11	2	no	—
363	C₂²×D₄	—	11	1	no	—
364	C₂²×D₄	C₂×D₁₁	1	1	yes	characteristic
365	C₂³×C₄	—	11	2	no	—
366	C₂³×C₄	—	11	2	no	—
367	C₄⋊Q₈	—	11	1	no	—
368	#127	—	11	1	no	—
369	#126	—	11	2	no	—
370	#126	—	11	2	no	—
371	#126	—	11	2	no	—
372	#126	—	11	2	no	—
373	#125	—	11	2	no	—
374	#125	—	11	1	no	—
375	#125	—	11	1	no	—
376	#124	—	11	1	no	—
377	#124	—	11	2	no	—
378	#124	—	11	2	no	—
379	#124	C₂×D₁₁	1	1	yes	characteristic, 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	—	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	2	no	—
397	#121	—	11	2	no	—
398	#121	—	11	1	no	—
399	#121	—	11	2	no	—
400	#121	—	11	2	no	—
401	#121	—	11	1	no	—
402	#121	—	11	1	no	—
403	#121	C₂×D₁₁	1	2	yes	complemented
404	#121	C₂×D₁₁	1	1	yes	characteristic, complemented
405	#120	—	11	2	no	—
406	#120	—	11	2	no	—
407	#120	—	11	2	no	—
408	#120	C₂×D₁₁	1	2	yes	complemented
409	C₄×Q₈	—	11	1	no	—
410	C₄×Q₈	—	11	1	no	—
411	C₄×Q₈	—	11	1	no	—
412	C₄×Q₈	—	11	1	no	—
413	C₄×D₄	—	11	1	no	—
414	C₄×D₄	—	11	2	no	—
415	C₄×D₄	—	11	1	no	—
416	C₄×D₄	—	11	1	no	—
417	C₄×D₄	—	11	2	no	—
418	C₄×D₄	—	11	1	no	—
419	C₄×D₄	—	11	2	no	—
420	C₄×D₄	—	11	1	no	—
421	C₄×D₄	—	11	1	no	—
422	C₄×D₄	—	11	2	no	—
423	C₄×D₄	—	11	2	no	—
424	C₄×D₄	—	11	1	no	—
425	C₄×D₄	—	11	1	no	—
426	C₄×D₄	—	11	1	no	—
427	C₄×D₄	—	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	2	no	—
436	C₄×D₄	—	11	1	no	—
437	C₄×D₄	—	11	1	no	—
438	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
439	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
440	#117	—	11	2	no	—
441	#117	—	11	1	no	—
442	#117	—	11	1	no	—
443	#117	—	11	2	no	—
444	#117	—	11	1	no	—
445	#117	—	11	1	no	—
446	#117	—	11	2	no	—
447	C₂×C₄⋊C₄	—	11	2	no	—
448	C₂×C₄⋊C₄	—	11	1	no	—
449	C₂×C₄⋊C₄	—	11	1	no	—
450	C₂×C₂²⋊C₄	—	11	2	no	—
451	C₂×C₂²⋊C₄	—	11	2	no	—
452	C₂×C₂²⋊C₄	—	11	2	no	—
453	C₂×C₂²⋊C₄	C₂×D₁₁	1	2	yes	complemented
454	C₂×C₄²	—	11	1	no	—
455	C₂×C₄²	—	11	2	no	—
456	C₂×C₄²	—	11	1	no	—
457	C₂×C₄²	—	11	1	no	—
458	C₂×C₁₁	—	2	4	no	—
459	C₂×C₁₁	—	2	2	no	—
460	C₂×C₁₁	—	4	1	no	—
461	C₂×C₁₁	—	4	2	no	—
462	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
463	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
464	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
465	D₁₁	—	2	2	no	—
466	D₁₁	—	4	2	no	—
467	C₂⁴	—	11	2	no	—
468	C₂⁴	C₂²×D₁₁	1	2	yes	—
469	#41	—	2	4	no	—
470	#41	—	22	4	no	—
471	#41	—	44	4	no	—
472	C₂×Q₈	—	11	1	no	—
473	C₂×Q₈	—	11	2	no	—
474	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	11	1	no	—
477	C₂×D₄	—	11	1	no	—
478	C₂×D₄	—	11	2	no	—
479	C₂×D₄	—	11	2	no	—
480	C₂×D₄	—	11	2	no	—
481	C₂×D₄	—	11	2	no	—
482	C₂×D₄	—	11	2	no	—
483	C₂×D₄	—	11	2	no	—
484	C₂×D₄	—	11	1	no	—
485	C₂×D₄	—	22	8	no	—
486	C₂×D₄	—	22	4	no	—
487	C₂×D₄	C₂²×D₁₁	1	2	yes	—
488	C₂×D₄	C₂²×D₁₁	1	2	yes	—
489	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
490	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
491	C₂×D₄	C₂²×D₁₁	1	2	yes	—
492	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
493	C₂²×C₄	—	11	1	no	—
494	C₂²×C₄	—	11	2	no	—
495	C₂²×C₄	—	11	1	no	—
496	C₂²×C₄	—	11	2	no	—
497	C₂²×C₄	—	11	1	no	—
498	C₂²×C₄	—	11	1	no	—
499	C₂²×C₄	—	11	2	no	—
500	C₂²×C₄	—	11	2	no	—
501	C₂²×C₄	—	11	2	no	—
502	C₂²×C₄	—	11	2	no	—
503	C₂²×C₄	—	11	1	no	—
504	C₂²×C₄	—	11	1	no	—
505	C₂²×C₄	—	11	1	no	—
506	C₂²×C₄	—	11	2	no	—
507	C₂²×C₄	—	11	2	no	—
508	C₂²×C₄	—	11	2	no	—
509	C₂²×C₄	—	44	4	no	—
510	C₂²×C₄	—	44	4	no	—
511	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
512	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
514	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
515	C₄⋊C₄	—	11	1	no	—
516	C₄⋊C₄	—	11	1	no	—
517	C₄⋊C₄	—	11	2	no	—
518	C₄⋊C₄	—	11	1	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	—	11	1	no	—
524	C₄⋊C₄	—	11	1	no	—
525	C₄⋊C₄	—	11	1	no	—
526	C₄⋊C₄	—	11	2	no	—
527	C₄⋊C₄	—	11	1	no	—
528	C₄⋊C₄	—	11	1	no	—
529	C₄⋊C₄	—	11	2	no	—
530	C₄⋊C₄	—	11	2	no	—
531	C₄⋊C₄	—	11	2	no	—
532	C₄⋊C₄	—	11	2	no	—
533	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
534	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
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	1	no	—
542	C₂²⋊C₄	—	11	2	no	—
543	C₂²⋊C₄	—	11	1	no	—
544	C₂²⋊C₄	—	11	2	no	—
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	C₂²×D₁₁	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
556	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
561	C₄²	—	11	1	no	—
562	C₄²	—	11	1	no	—
563	C₄²	—	11	1	no	—
564	C₄²	—	11	1	no	—
565	C₄²	—	11	2	no	—
566	C₄²	—	11	1	no	—
567	C₄²	—	11	1	no	—
568	C₄²	—	11	1	no	—
569	C₄²	—	11	2	no	—
570	C₄²	—	11	2	no	—
571	C₄²	—	11	1	no	—
572	C₄²	—	11	1	no	—
573	C₄²	C₂²×D₁₁	1	1	yes	characteristic
574	C₁₁	#3481	1	1	yes	characteristic, complemented, Sylow
575	C₂³	—	2	4	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	11	1	no	—
579	C₂³	—	11	2	no	—
580	C₂³	—	22	4	no	—
581	C₂³	—	22	4	no	—
582	C₂³	—	44	2	no	—
583	C₂³	C₂³×D₁₁	1	2	yes	—
584	C₂³	C₂³×D₁₁	1	1	yes	characteristic
585	C₂³	C₂³×D₁₁	1	2	yes	—
586	C₂³	C₂³×D₁₁	1	1	yes	characteristic
587	Q₈	—	2	2	no	—
588	Q₈	—	22	2	no	—
589	Q₈	—	44	2	no	—
590	D₄	—	2	4	no	—
591	D₄	—	2	4	no	—
592	D₄	—	2	2	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	11	4	no	—
596	D₄	—	22	4	no	—
597	D₄	—	22	4	no	—
598	D₄	—	22	2	no	—
599	D₄	—	22	4	no	—
600	D₄	—	22	4	no	—
601	D₄	—	22	2	no	—
602	D₄	—	44	2	no	—
603	D₄	—	44	2	no	—
604	D₄	#4341	1	4	yes	complemented
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	11	1	no	—
610	C₂×C₄	—	11	1	no	—
611	C₂×C₄	—	11	1	no	—
612	C₂×C₄	—	11	1	no	—
613	C₂×C₄	—	11	1	no	—
614	C₂×C₄	—	11	2	no	—
615	C₂×C₄	—	11	2	no	—
616	C₂×C₄	—	11	1	no	—
617	C₂×C₄	—	11	1	no	—
618	C₂×C₄	—	11	2	no	—
619	C₂×C₄	—	22	2	no	—
620	C₂×C₄	—	22	4	no	—
621	C₂×C₄	—	22	2	no	—
622	C₂×C₄	—	22	4	no	—
623	C₂×C₄	—	22	2	no	—
624	C₂×C₄	—	22	4	no	—
625	C₂×C₄	—	22	4	no	—
626	C₂×C₄	—	22	2	no	—
627	C₂×C₄	—	22	2	no	—
628	C₂×C₄	—	22	2	no	—
629	C₂×C₄	—	22	2	no	—
630	C₂×C₄	—	44	2	no	—
631	C₂×C₄	—	44	2	no	—
632	C₂×C₄	—	44	2	no	—
633	C₂×C₄	—	44	2	no	—
634	C₂×C₄	—	44	2	no	—
635	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₁	1	2	yes	—
637	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
640	C₂×C₄	C₂³×D₁₁	1	2	yes	—
641	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	4	8	no	—
653	C₂²	—	11	2	no	—
654	C₂²	—	22	1	no	—
655	C₂²	—	22	1	no	—
656	C₂²	—	22	2	no	—
657	C₂²	—	22	2	no	—
658	C₂²	—	22	2	no	—
659	C₂²	—	44	8	no	—
660	C₂²	C₂×#4341	1	4	yes	—
661	C₂²	#41×D₁₁	1	2	yes	—
662	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	11	2	no	—
670	C₄	—	11	2	no	—
671	C₄	—	22	1	no	—
672	C₄	—	22	1	no	—
673	C₄	—	22	2	no	—
674	C₄	—	22	1	no	—
675	C₄	—	22	2	no	—
676	C₄	—	22	1	no	—
677	C₄	—	22	2	no	—
678	C₄	—	22	1	no	—
679	C₄	C₂×#4341	1	2	yes	—
680	C₂	—	2	2	no	—
681	C₂	—	2	4	no	—
682	C₂	—	4	2	no	—
683	C₂	—	4	1	no	—
684	C₂	—	22	2	no	—
685	C₂	—	44	2	no	—
686	C₂	C₂²×#4341	1	1	yes	characteristic
687	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
688	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×#546	C₂
hypercenter	#546	D₁₁
hypocenter	C₁₁	#3481
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. #10623360	C₂	semidirect
3. #41×Dic₁₁	C₂	semidirect
4. D₄×C₂²⋊D₁₁	C₂	semidirect
5. C₂×D₄×Dic₁₁	C₂	semidirect
6. #10623212	C₂	semidirect
7. #10623211	C₂	semidirect
8. #10623189	C₂	semidirect
9. #10623180	C₂	semidirect
10. #10623166	C₂	semidirect
11. #10623155	C₂	semidirect
12. #10623145	C₂	semidirect
13. #10623137	C₂	semidirect
14. #10623132	C₂	semidirect
15. #10623127	C₂	semidirect
16. #10623122	C₂	semidirect
17. #10623117	C₂	semidirect
18. #10623096	C₂	semidirect
19. C₄×D₄×D₁₁	C₂	semidirect
20. #10623070	C₂	semidirect
21. C₄×#4341	C₂	semidirect
22. #10623026	C₂	semidirect
23. C₂×(C₂²⋊D₁₁)⋊C₄	C₂	semidirect
27. C₂³×Dic₁₁	C₂²	semidirect
29. 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
37. C₁₁×#120	C₂²	semidirect
39. C₄×D₄×C₁₁	C₂²	semidirect
40. C₂×C₁₁×C₂²⋊C₄	C₂²	semidirect
42. C₂×C₂²⋊Dic₁₁	C₂²	semidirect
43. #67000	C₂²	semidirect
44. #66999	C₂²	semidirect
45. Q₈×Dic₁₁	C₂²	semidirect
46. Q₈×Dic₁₁	C₂²	semidirect
49. #66992	C₂²	semidirect
50. #66992	C₂²	semidirect
51. #66992	C₂²	semidirect
53. #66991	C₂²	semidirect
55. #66990	C₂²	semidirect
56. #66988	C₂²	semidirect
60. D₄×Dic₁₁	C₂²	semidirect
61. D₄×Dic₁₁	C₂²	semidirect
62. D₄×Dic₁₁	C₂²	semidirect
63. D₄×Dic₁₁	C₂²	semidirect
64. D₄×Dic₁₁	C₂²	semidirect
65. D₄×Dic₁₁	C₂²	semidirect
66. D₄×Dic₁₁	C₂²	semidirect
68. #66983	C₂²	semidirect
69. #66982	C₂²	semidirect
71. C₄×C₂²⋊D₁₁	C₂²	semidirect
72. C₄×C₂²⋊D₁₁	C₂²	semidirect
73. C₂×(C₂×D₁₁)⋊C₄	C₂²	semidirect
74. #66979	C₂²	semidirect
75. #66979	C₂²	semidirect
76. C₂×C₄⋊Dic₁₁	C₂²	semidirect
77. #66977	C₂²	semidirect
78. C₂×Dic₁₁⋊C₄	C₂²	semidirect
79. C₂×C₄×Dic₁₁	C₂²	semidirect
80. C₂×C₄×Dic₁₁	C₂²	semidirect
81. C₂×C₄×Dic₁₁	C₂²	semidirect
82. #66951	C₂²	semidirect
83. #66951	C₂²	semidirect
84. #66950	C₂²	semidirect
85. #66946	C₂²	semidirect
86. #66945	C₂²	semidirect
87. #66945	C₂²	semidirect
88. C₄⋊C₄×D₁₁	C₂²	semidirect
89. #66943	C₂²	semidirect
90. #66942	C₂²	semidirect
91. #66941	C₂²	semidirect
92. #66940	C₂²	semidirect
93. #66939	C₂²	semidirect
94. #66939	C₂²	semidirect
95. #66938	C₂²	semidirect
96. #66938	C₂²	semidirect
97. #66936	C₂²	semidirect
98. #66936	C₂²	semidirect
99. #66936	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
106. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
107. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
108. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
109. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
110. C₂²⋊C₄×D₁₁	C₂²	semidirect
111. #66932	C₂²	semidirect
112. #66932	C₂²	semidirect
113. #66931	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
249. D₄×C₁₁	#41	semidirect
268. C₂²⋊D₁₁	#41	semidirect
308. #546	D₁₁	semidirect
379. #124	C₂×D₁₁	semidirect
387. #123	C₂×D₁₁	semidirect
394. C₂²⋊Q₈	C₂×D₁₁	semidirect
403. #121	C₂×D₁₁	semidirect
404. #121	C₂×D₁₁	semidirect
408. #120	C₂×D₁₁	semidirect
439. C₄×D₄	C₂×D₁₁	semidirect
453. C₂×C₂²⋊C₄	C₂×D₁₁	semidirect
574. C₁₁	#3481	semidirect
604. D₄	#4341	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
#10623360	2
#41×Dic₁₁	2
D₄×C₂²⋊D₁₁	2
C₂×D₄×Dic₁₁	2
#10623212	2
#10623211	2
#10623189	2
#10623180	2
#10623166	2
#10623155	2
#10623145	2
#10623137	2
#10623132	2
#10623127	2
#10623122	2
#10623117	2
#10623096	2
C₄×D₄×D₁₁	2
#10623070	2
C₄×#4341	2
#10623026	2
C₂×(C₂²⋊D₁₁)⋊C₄	2
#3481	11