Subgroups — #13082652

Order 1408.

1124 conjugacy classes of subgroups.

The subgroup lattice has 660 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	#10623358	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623355	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623337	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623213	C₂	1	1	yes	maximal, characteristic, complemented
7	#10623202	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623196	C₂	1	2	yes	maximal, complemented
9	#10623181	C₂	1	2	yes	maximal, complemented
10	#10623166	C₂	1	1	yes	maximal, characteristic, complemented
11	#10623153	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623142	C₂	1	1	yes	maximal, characteristic, complemented
13	#10623134	C₂	1	1	yes	maximal, characteristic, complemented
14	#10623133	C₂	1	2	yes	maximal, complemented
15	#10623129	C₂	1	2	yes	maximal, complemented
16	#10623118	C₂	1	2	yes	maximal, complemented
17	#10623117	C₂	1	2	yes	maximal, complemented
18	#10623077	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623074	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623069	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623026	C₂	1	2	yes	maximal, complemented
23	C₂×#66931	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	C₂³×Dic₁₁	C₂²	1	2	yes	—
27	C₂×#4341	C₂²	1	1	yes	characteristic
28	C₂×#4341	C₂²	1	2	yes	complemented
29	C₂²×Dic₂₂	C₂²	1	2	yes	complemented
30	C₁₁×#124	C₂²	1	1	yes	characteristic
31	C₁₁×#123	C₂²	1	2	yes	—
32	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₁×#121	C₂²	1	2	yes	—
34	C₁₁×#121	C₂²	1	1	yes	characteristic
35	C₁₁×#120	C₂²	1	2	yes	—
36	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
38	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
39	#67006	C₂²	1	2	yes	—
40	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	—
41	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	—
42	#66999	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
45	#66997	C₂²	1	1	yes	characteristic, complemented
46	#66992	C₂²	1	1	yes	characteristic
47	#66992	C₂²	1	2	yes	—
48	#66992	C₂²	1	2	yes	complemented
49	#66991	C₂²	1	1	yes	characteristic
50	#66989	C₂²	1	1	yes	characteristic
51	#66989	C₂²	1	2	yes	complemented
52	#66988	C₂²	1	1	yes	characteristic
53	#66988	C₂²	1	2	yes	—
54	#66988	C₂²	1	2	yes	complemented
55	#66988	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	2	yes	—
61	D₄×Dic₁₁	C₂²	1	2	yes	—
62	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
63	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
64	D₄×Dic₁₁	C₂²	1	2	yes	—
65	D₄×Dic₁₁	C₂²	1	2	yes	complemented
66	D₄×Dic₁₁	C₂²	1	2	yes	complemented
67	#66982	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
71	#66979	C₂²	1	2	yes	complemented
72	#66979	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic
74	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	complemented
75	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic, complemented
76	#66977	C₂²	1	1	yes	characteristic
77	#66977	C₂²	1	2	yes	complemented
78	#66977	C₂²	1	1	yes	characteristic, complemented
79	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	complemented
80	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	complemented
81	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
82	#66951	C₂²	1	1	yes	characteristic, complemented
83	#66950	C₂²	1	2	yes	complemented
84	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
85	#66943	C₂²	1	2	yes	complemented
86	#66942	C₂²	1	1	yes	characteristic, complemented
87	#66942	C₂²	1	2	yes	complemented
88	#66942	C₂²	1	2	yes	complemented
89	#66941	C₂²	1	1	yes	characteristic, complemented
90	#66941	C₂²	1	1	yes	characteristic, complemented
91	#66940	C₂²	1	1	yes	characteristic, complemented
92	#66940	C₂²	1	2	yes	complemented
93	#66939	C₂²	1	1	yes	characteristic
94	#66939	C₂²	1	2	yes	complemented
95	#66938	C₂²	1	2	yes	complemented
96	#66938	C₂²	1	1	yes	characteristic, complemented
97	#66936	C₂²	1	2	yes	complemented
98	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
99	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
100	#66932	C₂²	1	2	yes	complemented
101	#66932	C₂²	1	2	yes	complemented
102	#66932	C₂²	1	1	yes	characteristic, complemented
103	#66932	C₂²	1	2	yes	complemented
104	#66932	C₂²	1	2	yes	complemented
105	#66931	C₂²	1	1	yes	characteristic
106	#66931	C₂²	1	2	yes	—
107	#66931	C₂²	1	2	yes	—
108	#66931	C₂²	1	2	yes	—
109	#66931	C₂²	1	2	yes	complemented
110	#66931	C₂²	1	2	yes	complemented
111	#66931	C₂²	1	2	yes	complemented
112	#66931	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	2	yes	—
117	#66930	C₂²	1	2	yes	complemented
118	#66930	C₂²	1	2	yes	complemented
119	#66925	C₂²	1	1	yes	characteristic, complemented
120	#66922	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	2	yes	—
124	C₁₁×#41	—	2	4	no	—
125	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₁	—	2	4	no	—
127	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₁	C₂³	1	2	yes	—
129	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₁	C₂³	1	2	yes	—
131	C₂×D₄×C₁₁	C₂³	1	2	yes	—
132	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
141	C₂²×Dic₁₁	—	4	4	no	—
142	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
143	C₂²×Dic₁₁	C₂³	1	2	yes	—
144	C₂²×Dic₁₁	C₂³	1	2	yes	—
145	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₁	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	C₂²×Dic₁₁	C₂³	1	2	yes	—
152	#4341	—	2	4	no	—
153	#4341	—	4	4	no	—
154	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₁	C₂³	1	2	yes	—
156	C₂×Dic₂₂	—	4	4	no	—
157	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
158	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
159	C₂×Dic₂₂	C₂³	1	2	yes	—
160	C₂×Dic₂₂	C₂³	1	2	yes	—
161	C₂×Dic₂₂	C₂³	1	2	yes	—
162	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
164	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₄²×C₁₁	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₁	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	2	yes	—
190	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₁₁	C₂³	1	2	yes	—
195	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₁	C₂³	1	2	yes	—
199	C₄⋊Dic₁₁	C₂³	1	2	yes	—
200	C₄⋊Dic₁₁	C₂³	1	2	yes	—
201	C₄⋊Dic₁₁	C₂³	1	2	yes	—
202	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
203	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
204	Dic₁₁⋊C₄	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	2	yes	—
210	Dic₁₁⋊C₄	C₂³	1	2	yes	—
211	Dic₁₁⋊C₄	C₂³	1	2	yes	—
212	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
219	C₄×Dic₁₁	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	2	yes	—
225	C₄×Dic₁₁	C₂³	1	2	yes	—
226	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
228	#3520	—	11	1	no	maximal, Sylow
229	C₂³×C₁₁	—	2	4	no	—
230	C₂³×C₁₁	—	2	4	no	—
231	C₂³×C₁₁	—	4	2	no	—
232	C₂³×C₁₁	C₂⁴	1	2	yes	—
233	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
234	C₂³×C₁₁	C₂⁴	1	2	yes	—
235	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
237	Q₈×C₁₁	—	2	2	no	—
238	D₄×C₁₁	—	2	4	no	—
239	D₄×C₁₁	—	2	4	no	—
240	D₄×C₁₁	—	2	2	no	—
241	D₄×C₁₁	—	2	2	no	—
242	D₄×C₁₁	—	4	2	no	—
243	D₄×C₁₁	#41	1	4	yes	complemented
244	C₂×C₄×C₁₁	—	2	4	no	—
245	C₂×C₄×C₁₁	—	2	2	no	—
246	C₂×C₄×C₁₁	—	2	2	no	—
247	C₂×C₄×C₁₁	—	4	2	no	—
248	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₁₁	—	2	4	no	—
256	C₂²⋊D₁₁	—	2	2	no	—
257	C₂²⋊D₁₁	—	2	2	no	—
258	C₂²⋊D₁₁	—	4	2	no	—
259	C₂×Dic₁₁	—	2	4	no	—
260	C₂×Dic₁₁	—	2	2	no	—
261	C₂×Dic₁₁	—	2	4	no	—
262	C₂×Dic₁₁	—	2	4	no	—
263	C₂×Dic₁₁	—	2	2	no	—
264	C₂×Dic₁₁	—	4	2	no	—
265	C₂×Dic₁₁	—	4	2	no	—
266	C₂×Dic₁₁	—	4	2	no	—
267	C₂×Dic₁₁	—	4	2	no	—
268	C₂×Dic₁₁	—	4	2	no	—
269	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₁	C₂⁴	1	2	yes	—
272	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₁	C₂⁴	1	2	yes	—
275	C₂×Dic₁₁	C₂⁴	1	2	yes	—
276	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₁₁	C₂⁴	1	2	yes	—
279	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
280	C₄×D₁₁	—	2	2	no	—
281	C₄×D₁₁	—	4	2	no	—
282	Dic₂₂	—	2	2	no	—
283	Dic₂₂	—	2	2	no	—
284	Dic₂₂	—	2	4	no	—
285	Dic₂₂	—	4	2	no	—
286	Dic₂₂	—	4	2	no	—
287	#556	—	11	1	no	—
288	#554	—	11	1	no	—
289	#554	—	11	1	no	—
290	#552	—	11	2	no	—
291	#551	—	11	2	no	—
292	#551	—	11	2	no	—
293	D₄×Q₈	—	11	1	no	—
294	#548	—	11	2	no	—
295	#547	—	11	1	no	—
296	#547	—	11	1	no	—
297	#546	—	11	1	no	—
298	#546	D₁₁	1	1	yes	characteristic, complemented
299	#542	—	11	1	no	—
300	#542	—	11	1	no	—
301	#539	—	11	2	no	—
302	#539	—	11	2	no	—
303	#533	—	11	1	no	—
304	#529	—	11	1	no	—
305	#525	—	11	2	no	—
306	C₂×C₂²⋊Q₈	—	11	2	no	—
307	#520	—	11	1	no	—
308	#520	—	11	1	no	—
309	C₂×C₄×D₄	—	11	1	no	—
310	C₂²×C₁₁	—	2	1	no	—
311	C₂²×C₁₁	—	2	2	no	—
312	C₂²×C₁₁	—	2	1	no	—
313	C₂²×C₁₁	—	2	2	no	—
314	C₂²×C₁₁	—	2	1	no	—
315	C₂²×C₁₁	—	2	2	no	—
316	C₂²×C₁₁	—	2	1	no	—
317	C₂²×C₁₁	—	2	2	no	—
318	C₂²×C₁₁	—	2	1	no	—
319	C₂²×C₁₁	—	2	2	no	—
320	C₂²×C₁₁	—	4	8	no	—
321	C₂²×C₁₁	C₂×#41	1	4	yes	—
322	C₂²×C₁₁	2₋¹⁺⁴	1	2	yes	—
323	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
324	C₂×D₁₁	—	2	1	no	—
325	C₂×D₁₁	—	2	1	no	—
326	C₂×D₁₁	—	2	1	no	—
327	C₄×C₁₁	—	2	1	no	—
328	C₄×C₁₁	—	2	1	no	—
329	C₄×C₁₁	—	2	2	no	—
330	C₄×C₁₁	—	2	1	no	—
331	C₄×C₁₁	—	2	2	no	—
332	C₄×C₁₁	—	2	1	no	—
333	C₄×C₁₁	C₂×#41	1	2	yes	—
334	Dic₁₁	—	2	2	no	—
335	Dic₁₁	—	2	1	no	—
336	Dic₁₁	—	2	1	no	—
337	Dic₁₁	—	2	2	no	—
338	Dic₁₁	—	2	2	no	—
339	Dic₁₁	—	2	2	no	—
340	Dic₁₁	—	2	1	no	—
341	Dic₁₁	—	2	1	no	—
342	Dic₁₁	—	2	1	no	—
343	Dic₁₁	—	2	1	no	—
344	Dic₁₁	H(5,𝔽₂)	1	2	yes	—
345	C₂×#41	—	11	1	no	—
346	C₂×#41	—	11	2	no	—
347	C₂×#41	C₂×D₁₁	1	1	yes	characteristic
348	C₂²×Q₈	—	11	2	no	—
349	C₂²×D₄	C₂×D₁₁	1	1	yes	characteristic
350	C₂³×C₄	—	11	2	no	—
351	C₄⋊Q₈	—	11	1	no	—
352	C₄⋊Q₈	—	11	1	no	—
353	C₄⋊Q₈	—	11	1	no	—
354	C₄⋊Q₈	—	11	1	no	—
355	#126	—	11	1	no	—
356	#126	—	11	1	no	—
357	#126	—	11	2	no	—
358	#126	—	11	2	no	—
359	#126	—	11	2	no	—
360	#126	—	11	2	no	—
361	#125	—	11	1	no	—
362	#125	—	11	2	no	—
363	#125	—	11	2	no	—
364	#125	—	11	2	no	—
365	#124	—	11	1	no	—
366	#124	—	11	2	no	—
367	#124	—	11	1	no	—
368	#124	—	11	2	no	—
369	#124	C₂×D₁₁	1	1	yes	characteristic
370	#123	—	11	2	no	—
371	#123	—	11	1	no	—
372	#123	—	11	2	no	—
373	#123	—	11	2	no	—
374	#123	—	11	2	no	—
375	#123	—	11	2	no	—
376	#123	—	11	2	no	—
377	#123	—	11	1	no	—
378	#123	—	11	2	no	—
379	#123	C₂×D₁₁	1	2	yes	—
380	C₂²⋊Q₈	—	11	1	no	—
381	C₂²⋊Q₈	—	11	1	no	—
382	C₂²⋊Q₈	—	11	2	no	—
383	C₂²⋊Q₈	—	11	1	no	—
384	C₂²⋊Q₈	—	11	2	no	—
385	C₂²⋊Q₈	—	11	1	no	—
386	C₂²⋊Q₈	—	11	2	no	—
387	C₂²⋊Q₈	—	11	2	no	—
388	C₂²⋊Q₈	—	11	2	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	—	11	2	no	—
395	C₂²⋊Q₈	—	11	2	no	—
396	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic
397	#121	—	11	1	no	—
398	#121	—	11	2	no	—
399	#121	—	11	2	no	—
400	#121	—	11	1	no	—
401	#121	C₂×D₁₁	1	2	yes	—
402	#121	C₂×D₁₁	1	1	yes	characteristic
403	#120	—	11	2	no	—
404	#120	C₂×D₁₁	1	2	yes	—
405	C₄×Q₈	—	11	1	no	—
406	C₄×Q₈	—	11	1	no	—
407	C₄×Q₈	—	11	1	no	—
408	C₄×Q₈	—	11	2	no	—
409	C₄×Q₈	—	11	1	no	—
410	C₄×Q₈	—	11	1	no	—
411	C₄×D₄	—	11	1	no	—
412	C₄×D₄	—	11	2	no	—
413	C₄×D₄	—	11	1	no	—
414	C₄×D₄	—	11	1	no	—
415	C₄×D₄	—	11	1	no	—
416	C₄×D₄	—	11	2	no	—
417	C₄×D₄	—	11	2	no	—
418	C₄×D₄	—	11	1	no	—
419	C₄×D₄	—	11	2	no	—
420	C₄×D₄	—	11	2	no	—
421	C₄×D₄	—	11	2	no	—
422	C₄×D₄	—	11	1	no	—
423	C₄×D₄	—	11	1	no	—
424	C₄×D₄	—	11	2	no	—
425	C₄×D₄	—	11	2	no	—
426	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
427	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
428	#117	—	11	1	no	—
429	#117	—	11	2	no	—
430	#117	—	11	2	no	—
431	#117	—	11	2	no	—
432	#117	—	11	2	no	—
433	#117	—	11	1	no	—
434	C₂×C₄⋊C₄	—	11	1	no	—
435	C₂×C₄⋊C₄	—	11	2	no	—
436	C₂×C₄⋊C₄	—	11	2	no	—
437	C₂×C₄⋊C₄	—	11	1	no	—
438	C₂×C₄⋊C₄	—	11	2	no	—
439	C₂×C₄⋊C₄	—	11	1	no	—
440	C₂×C₂²⋊C₄	—	11	2	no	—
441	C₂×C₂²⋊C₄	—	11	2	no	—
442	C₂×C₂²⋊C₄	C₂×D₁₁	1	2	yes	—
443	C₂×C₄²	—	11	1	no	—
444	C₂×C₁₁	—	2	2	no	—
445	C₂×C₁₁	—	2	4	no	—
446	C₂×C₁₁	—	4	1	no	—
447	C₂×C₁₁	—	4	2	no	—
448	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
449	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
451	D₁₁	—	4	1	no	—
452	C₂⁴	C₂²×D₁₁	1	2	yes	—
453	#41	—	2	4	no	—
454	#41	—	22	4	no	—
455	#41	—	44	4	no	—
456	C₂×Q₈	—	11	1	no	—
457	C₂×Q₈	—	11	1	no	—
458	C₂×Q₈	—	11	2	no	—
459	C₂×Q₈	—	11	2	no	—
460	C₂×Q₈	—	11	2	no	—
461	C₂×Q₈	—	44	4	no	—
462	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	11	1	no	—
465	C₂×D₄	—	11	2	no	—
466	C₂×D₄	—	11	1	no	—
467	C₂×D₄	—	11	2	no	—
468	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
469	C₂×D₄	C₂²×D₁₁	1	2	yes	—
470	C₂×D₄	C₂²×D₁₁	1	2	yes	—
471	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
472	C₂×D₄	C₂²×D₁₁	1	2	yes	—
473	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
474	C₂²×C₄	—	11	1	no	—
475	C₂²×C₄	—	11	1	no	—
476	C₂²×C₄	—	11	2	no	—
477	C₂²×C₄	—	11	2	no	—
478	C₂²×C₄	—	11	2	no	—
479	C₂²×C₄	—	11	2	no	—
480	C₂²×C₄	—	11	2	no	—
481	C₂²×C₄	—	11	2	no	—
482	C₂²×C₄	—	11	2	no	—
483	C₂²×C₄	—	11	2	no	—
484	C₂²×C₄	—	11	1	no	—
485	C₂²×C₄	—	11	2	no	—
486	C₂²×C₄	—	44	4	no	—
487	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
489	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
490	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
491	C₄⋊C₄	—	11	1	no	—
492	C₄⋊C₄	—	11	1	no	—
493	C₄⋊C₄	—	11	1	no	—
494	C₄⋊C₄	—	11	2	no	—
495	C₄⋊C₄	—	11	2	no	—
496	C₄⋊C₄	—	11	1	no	—
497	C₄⋊C₄	—	11	2	no	—
498	C₄⋊C₄	—	11	2	no	—
499	C₄⋊C₄	—	11	1	no	—
500	C₄⋊C₄	—	11	1	no	—
501	C₄⋊C₄	—	11	2	no	—
502	C₄⋊C₄	—	11	2	no	—
503	C₄⋊C₄	—	11	2	no	—
504	C₄⋊C₄	—	11	2	no	—
505	C₄⋊C₄	—	11	2	no	—
506	C₄⋊C₄	—	11	2	no	—
507	C₄⋊C₄	—	11	1	no	—
508	C₄⋊C₄	—	11	1	no	—
509	C₄⋊C₄	—	11	1	no	—
510	C₄⋊C₄	—	11	2	no	—
511	C₄⋊C₄	—	11	2	no	—
512	C₄⋊C₄	—	11	2	no	—
513	C₄⋊C₄	—	11	2	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	C₂²×D₁₁	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
521	C₂²⋊C₄	—	11	1	no	—
522	C₂²⋊C₄	—	11	2	no	—
523	C₂²⋊C₄	—	11	2	no	—
524	C₂²⋊C₄	—	11	2	no	—
525	C₂²⋊C₄	—	11	2	no	—
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	1	no	—
531	C₂²⋊C₄	—	11	1	no	—
532	C₂²⋊C₄	—	11	2	no	—
533	C₂²⋊C₄	—	11	2	no	—
534	C₂²⋊C₄	—	11	1	no	—
535	C₂²⋊C₄	—	11	1	no	—
536	C₂²⋊C₄	—	11	1	no	—
537	C₂²⋊C₄	—	11	1	no	—
538	C₂²⋊C₄	—	11	2	no	—
539	C₂²⋊C₄	—	11	1	no	—
540	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
541	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
547	C₄²	—	11	1	no	—
548	C₄²	—	11	1	no	—
549	C₄²	—	11	1	no	—
550	C₄²	—	11	1	no	—
551	C₄²	—	11	2	no	—
552	C₄²	—	11	2	no	—
553	C₄²	—	11	2	no	—
554	C₄²	—	11	2	no	—
555	C₄²	—	11	1	no	—
556	C₄²	C₂²×D₁₁	1	1	yes	characteristic
557	C₁₁	#3520	1	1	yes	characteristic, complemented, Sylow
558	C₂³	—	2	4	no	—
559	C₂³	—	2	4	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	11	1	no	—
562	C₂³	C₂³×D₁₁	1	2	yes	—
563	C₂³	C₂³×D₁₁	1	1	yes	characteristic
564	C₂³	C₂³×D₁₁	1	2	yes	—
565	C₂³	C₂³×D₁₁	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	22	2	no	—
568	Q₈	—	22	4	no	—
569	Q₈	—	22	2	no	—
570	Q₈	—	44	2	no	—
571	Q₈	—	44	2	no	—
572	D₄	—	2	4	no	—
573	D₄	—	2	4	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	22	2	no	—
578	D₄	—	22	4	no	—
579	D₄	—	22	2	no	—
580	D₄	—	44	2	no	—
581	D₄	#4341	1	4	yes	complemented
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	11	1	no	—
587	C₂×C₄	—	11	1	no	—
588	C₂×C₄	—	11	1	no	—
589	C₂×C₄	—	11	1	no	—
590	C₂×C₄	—	11	2	no	—
591	C₂×C₄	—	11	1	no	—
592	C₂×C₄	—	11	2	no	—
593	C₂×C₄	—	11	1	no	—
594	C₂×C₄	—	11	2	no	—
595	C₂×C₄	—	11	1	no	—
596	C₂×C₄	—	11	2	no	—
597	C₂×C₄	—	22	2	no	—
598	C₂×C₄	—	22	4	no	—
599	C₂×C₄	—	22	4	no	—
600	C₂×C₄	—	22	4	no	—
601	C₂×C₄	—	22	2	no	—
602	C₂×C₄	—	22	2	no	—
603	C₂×C₄	—	44	2	no	—
604	C₂×C₄	—	44	2	no	—
605	C₂×C₄	—	44	2	no	—
606	C₂×C₄	—	44	2	no	—
607	C₂×C₄	—	44	2	no	—
608	C₂×C₄	—	44	2	no	—
609	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₁₁	1	2	yes	—
611	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₁	1	2	yes	—
613	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
615	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	4	8	no	—
627	C₂²	—	22	1	no	—
628	C₂²	—	22	1	no	—
629	C₂²	—	22	1	no	—
630	C₂²	C₂×#4341	1	4	yes	—
631	C₂²	#67043	1	2	yes	—
632	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	11	2	no	—
640	C₄	—	22	1	no	—
641	C₄	—	22	2	no	—
642	C₄	—	22	1	no	—
643	C₄	—	22	1	no	—
644	C₄	—	22	1	no	—
645	C₄	—	22	1	no	—
646	C₄	—	22	2	no	—
647	C₄	—	22	2	no	—
648	C₄	—	22	2	no	—
649	C₄	—	22	1	no	—
650	C₄	C₂×#4341	1	2	yes	—
651	C₂	—	2	2	no	—
652	C₂	—	2	4	no	—
653	C₂	—	4	2	no	—
654	C₂	—	4	1	no	—
655	C₂	—	44	1	no	—
656	C₂	C₂²×#4341	1	1	yes	characteristic
657	C₂	C₂×#67043	1	1	yes	characteristic
658	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	#3520
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. #10623358	C₂	semidirect
3. #10623355	C₂	semidirect
4. #10623337	C₂	semidirect
5. C₂×D₄×Dic₁₁	C₂	semidirect
6. #10623213	C₂	semidirect
7. #10623202	C₂	semidirect
8. #10623196	C₂	semidirect
9. #10623181	C₂	semidirect
10. #10623166	C₂	semidirect
11. #10623153	C₂	semidirect
12. #10623142	C₂	semidirect
13. #10623134	C₂	semidirect
14. #10623133	C₂	semidirect
15. #10623129	C₂	semidirect
16. #10623118	C₂	semidirect
17. #10623117	C₂	semidirect
18. #10623077	C₂	semidirect
19. #10623074	C₂	semidirect
20. #10623069	C₂	semidirect
21. D₄×Dic₂₂	C₂	semidirect
22. #10623026	C₂	semidirect
23. C₂×#66931	C₂	semidirect
28. C₂×#4341	C₂²	semidirect
29. C₂²×Dic₂₂	C₂²	semidirect
42. #66999	C₂²	semidirect
43. Q₈×Dic₁₁	C₂²	semidirect
44. Q₈×Dic₁₁	C₂²	semidirect
45. #66997	C₂²	semidirect
48. #66992	C₂²	semidirect
51. #66989	C₂²	semidirect
54. #66988	C₂²	semidirect
55. #66988	C₂²	semidirect
56. #66988	C₂²	semidirect
65. D₄×Dic₁₁	C₂²	semidirect
66. D₄×Dic₁₁	C₂²	semidirect
67. #66982	C₂²	semidirect
69. C₄×C₂²⋊D₁₁	C₂²	semidirect
70. C₄×C₂²⋊D₁₁	C₂²	semidirect
71. #66979	C₂²	semidirect
72. #66979	C₂²	semidirect
74. C₂×C₄⋊Dic₁₁	C₂²	semidirect
75. C₂×C₄⋊Dic₁₁	C₂²	semidirect
77. #66977	C₂²	semidirect
78. #66977	C₂²	semidirect
79. C₂×Dic₁₁⋊C₄	C₂²	semidirect
80. C₂×Dic₁₁⋊C₄	C₂²	semidirect
82. #66951	C₂²	semidirect
83. #66950	C₂²	semidirect
84. C₄⋊C₄×D₁₁	C₂²	semidirect
85. #66943	C₂²	semidirect
86. #66942	C₂²	semidirect
87. #66942	C₂²	semidirect
88. #66942	C₂²	semidirect
89. #66941	C₂²	semidirect
90. #66941	C₂²	semidirect
91. #66940	C₂²	semidirect
92. #66940	C₂²	semidirect
94. #66939	C₂²	semidirect
95. #66938	C₂²	semidirect
96. #66938	C₂²	semidirect
97. #66936	C₂²	semidirect
99. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
100. #66932	C₂²	semidirect
101. #66932	C₂²	semidirect
102. #66932	C₂²	semidirect
103. #66932	C₂²	semidirect
104. #66932	C₂²	semidirect
109. #66931	C₂²	semidirect
110. #66931	C₂²	semidirect
111. #66931	C₂²	semidirect
112. #66931	C₂²	semidirect
113. #66931	C₂²	semidirect
114. #66931	C₂²	semidirect
115. #66931	C₂²	semidirect
117. #66930	C₂²	semidirect
118. #66930	C₂²	semidirect
119. #66925	C₂²	semidirect
120. #66922	C₂²	semidirect
121. C₄×Dic₂₂	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
243. D₄×C₁₁	#41	semidirect
298. #546	D₁₁	semidirect
557. C₁₁	#3520	semidirect
581. 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
#10623358	2
#10623355	2
#10623337	2
C₂×D₄×Dic₁₁	2
#10623213	2
#10623202	2
#10623196	2
#10623181	2
#10623166	2
#10623153	2
#10623142	2
#10623134	2
#10623133	2
#10623129	2
#10623118	2
#10623117	2
#10623077	2
#10623074	2
#10623069	2
D₄×Dic₂₂	2
#10623026	2
C₂×#66931	2
#3520	11