Subgroups — #14719500

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077580	C₂	1	1	yes	maximal, characteristic
2	#13077578	C₂	1	1	yes	maximal, characteristic
3	C₄×#66954	C₂	1	1	yes	maximal, characteristic
4	#13066920	C₂	1	1	yes	maximal, characteristic, complemented
5	#13066919	C₂	1	1	yes	maximal, characteristic, complemented
6	#13066912	C₂	1	1	yes	maximal, characteristic, complemented
7	#13066911	C₂	1	1	yes	maximal, characteristic, complemented
8	#13066905	C₂	1	1	yes	maximal, characteristic, complemented
9	#13066904	C₂	1	1	yes	maximal, characteristic, complemented
10	#13066902	C₂	1	1	yes	maximal, characteristic, complemented
11	#13066902	C₂	1	1	yes	maximal, characteristic, complemented
12	#13066902	C₂	1	1	yes	maximal, characteristic, complemented
13	#13066901	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₁×#322	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#66954	C₄	1	2	yes	—
17	C₄×#4339	C₂²	1	1	yes	characteristic
18	C₁₁×#431	C₂²	1	1	yes	characteristic
19	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
21	#10622741	C₄	1	2	yes	—
22	#10622740	C₄	1	2	yes	—
23	#10622714	C₄	1	2	yes	—
24	#10622538	C₂²	1	1	yes	characteristic
25	C₄×#4318	C₂²	1	1	yes	characteristic
26	C₄×#4318	C₂²	1	1	yes	characteristic
27	#10622449	C₄	1	2	yes	—
28	#10622441	C₄	1	2	yes	—
29	#10622342	C₄	1	2	yes	—
30	#10622341	C₄	1	2	yes	—
31	#10622319	C₄	1	2	yes	—
32	#10622314	C₄	1	2	yes	—
33	#10622302	C₄	1	2	yes	—
34	#10622302	C₄	1	2	yes	—
35	C₄×#4313	C₂²	1	1	yes	characteristic
36	C₄×#4313	C₂²	1	1	yes	characteristic
37	C₄×#4313	C₂²	1	1	yes	characteristic
38	C₄×#4313	C₂²	1	1	yes	characteristic
39	#10622298	C₂²	1	1	yes	characteristic
40	#10622298	C₂²	1	1	yes	characteristic
41	#10622298	C₂²	1	1	yes	characteristic
42	#10622298	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
47	C₁₁×#322	C₂²	1	1	yes	characteristic
48	C₁₁×#322	C₂²	1	1	yes	characteristic
49	C₁₁×#322	C₂²	1	1	yes	characteristic
50	C₁₁×#322	C₂²	1	1	yes	characteristic
51	#10622093	C₂²	1	1	yes	characteristic
52	#10622093	C₂²	1	1	yes	characteristic
53	#10622093	C₂²	1	1	yes	characteristic
54	#10622093	C₂²	1	1	yes	characteristic
55	#10622092	C₂²	1	1	yes	characteristic
56	#10622092	C₂²	1	1	yes	characteristic
57	#10622092	C₂²	1	1	yes	characteristic
58	#10622092	C₂²	1	1	yes	characteristic
59	#10622092	C₂²	1	1	yes	characteristic
60	#10622092	C₂²	1	1	yes	characteristic
61	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
62	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
63	C₂×#4339	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
65	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
70	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
71	#66979	C₂×C₄	1	1	yes	characteristic
72	C₂×#4318	C₂×C₄	1	2	yes	—
73	C₂×#4318	C₂×C₄	1	2	yes	—
74	#66954	—	2	8	no	—
75	C₂×#4313	C₂×C₄	1	2	yes	—
76	C₂×#4313	C₂×C₄	1	2	yes	—
77	C₂×#4313	C₂×C₄	1	2	yes	—
78	C₂×#4313	C₂×C₄	1	2	yes	—
79	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
80	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
81	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
82	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
83	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
84	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
85	#66925	C₂×C₄	1	1	yes	characteristic
86	#66925	C₂×C₄	1	1	yes	characteristic
87	C₄²×D₁₁	C₂³	1	1	yes	characteristic
88	C₄²×D₁₁	C₂³	1	1	yes	characteristic
89	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
90	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
91	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
92	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
93	C₁₁×#97	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
101	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
102	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
103	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
104	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
105	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
106	#66879	C₂×C₄	1	2	yes	—
107	#66879	C₂×C₄	1	2	yes	—
108	#66879	C₂×C₄	1	2	yes	—
109	#66879	C₂×C₄	1	2	yes	—
110	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
111	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
112	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
113	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
114	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
115	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
116	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
117	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
118	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
119	#66867	C₂×C₄	1	2	yes	—
120	#66867	C₂×C₄	1	2	yes	—
121	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
126	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
127	#17336	—	11	1	no	maximal, Sylow
128	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₁	C₄²	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₁	C₄²	1	1	yes	characteristic
133	#4339	—	2	4	no	—
134	C₂×D₄₄	C₄²	1	1	yes	characteristic
135	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
141	C₂×Dic₂₂	C₄²	1	1	yes	characteristic
142	C₁₁×M₁₆	—	4	2	no	—
143	C₂×C₈×C₁₁	—	2	4	no	—
144	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
149	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
150	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
154	C₂²⋊Dic₁₁	C₄²	1	1	yes	characteristic
155	C₂²⋊Dic₁₁	C₄²	1	1	yes	characteristic
156	(C₂×D₁₁)⋊C₄	C₄²	1	1	yes	characteristic
157	(C₂×D₁₁)⋊C₄	C₄²	1	1	yes	characteristic
158	(C₂×D₁₁)⋊C₄	C₄²	1	1	yes	characteristic
159	(C₂×D₁₁)⋊C₄	C₄²	1	1	yes	characteristic
160	C₄⋊Dic₁₁	C₄²	1	1	yes	characteristic
161	C₄⋊Dic₁₁	C₄²	1	1	yes	characteristic
162	Dic₁₁⋊C₄	C₄²	1	1	yes	characteristic
163	Dic₁₁⋊C₄	C₄²	1	1	yes	characteristic
164	Dic₁₁⋊C₄	C₄²	1	1	yes	characteristic
165	Dic₁₁⋊C₄	C₄²	1	1	yes	characteristic
166	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
167	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
168	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
169	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
170	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
171	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
172	#4318	—	2	4	no	—
173	#4318	—	4	2	no	—
174	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
175	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
176	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
177	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
178	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
179	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
180	#4313	—	2	4	no	—
181	#4313	—	2	4	no	—
182	#4313	—	4	2	no	—
183	#4313	—	4	2	no	—
184	C₈×D₁₁	—	2	4	no	—
185	C₈×D₁₁	—	4	2	no	—
186	C₈×D₁₁	—	4	2	no	—
187	C₈×D₁₁	M₁₆	1	8	yes	complemented
188	#2965	—	11	1	no	—
189	#2965	—	11	1	no	—
190	C₄×#131	—	11	1	no	—
191	#1455	—	11	1	no	—
192	#1455	—	11	1	no	—
193	#1453	—	11	1	no	—
194	#1453	—	11	1	no	—
195	#1451	—	11	1	no	—
196	#1451	—	11	1	no	—
197	#1451	—	11	1	no	—
198	#1451	—	11	1	no	—
199	#1451	—	11	1	no	—
200	#1451	D₁₁	1	1	yes	characteristic, complemented
201	#1450	—	11	1	no	—
202	C₂×#322	—	11	1	no	—
203	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
204	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
205	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
206	C₂×C₄×C₁₁	—	2	2	no	—
207	C₂×C₄×C₁₁	—	2	2	no	—
208	C₂×C₄×C₁₁	—	2	2	no	—
209	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
210	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
211	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
212	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
215	C₂²⋊D₁₁	—	2	2	no	—
216	C₂²⋊D₁₁	—	2	2	no	—
217	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
218	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
219	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
220	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
221	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
222	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
223	D₄₄	—	2	2	no	—
224	C₄×D₁₁	—	2	2	no	—
225	C₄×D₁₁	—	2	2	no	—
226	C₄×D₁₁	—	2	2	no	—
227	C₄×D₁₁	—	2	2	no	—
228	C₄×D₁₁	—	2	2	no	—
229	C₄×D₁₁	C₂×M₁₆	1	4	yes	—
230	Dic₂₂	—	2	2	no	—
231	C₈×C₁₁	—	2	2	no	—
232	C₈×C₁₁	—	2	2	no	—
233	C₈×C₁₁	—	2	2	no	—
234	C₈×C₁₁	—	2	2	no	—
235	C₈×C₁₁	—	2	2	no	—
236	C₈×C₁₁	C₂×M₁₆	1	4	yes	—
237	C₁₁⋊C₈	—	2	2	no	—
238	C₁₁⋊C₈	—	2	2	no	—
239	C₁₁⋊C₈	—	2	2	no	—
240	C₁₁⋊C₈	—	2	2	no	—
241	C₁₁⋊C₈	—	2	2	no	—
242	C₁₁⋊C₈	C₂×M₁₆	1	4	yes	—
243	C₂×#131	—	11	2	no	—
244	C₄×#41	—	11	1	no	—
245	#446	—	11	2	no	—
246	#446	—	11	2	no	—
247	#436	—	11	2	no	—
248	#436	—	11	2	no	—
249	#435	—	11	2	no	—
250	#435	—	11	2	no	—
251	#435	—	11	2	no	—
252	#435	—	11	2	no	—
253	#431	—	11	1	no	—
254	#431	—	11	1	no	—
255	#431	—	11	1	no	—
256	#431	—	11	1	no	—
257	#431	—	11	1	no	—
258	#431	C₂×D₁₁	1	1	yes	characteristic
259	#405	—	11	2	no	—
260	#405	—	11	2	no	—
261	#405	—	11	2	no	—
262	C₄×M₁₆	—	11	1	no	—
263	C₄×M₁₆	—	11	1	no	—
264	C₄×M₁₆	—	11	1	no	—
265	C₄×M₁₆	—	11	1	no	—
266	C₄×M₁₆	—	11	1	no	—
267	C₄×M₁₆	—	11	1	no	—
268	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
269	C₂×C₄×C₈	—	11	1	no	—
270	C₂×C₄×C₈	—	11	1	no	—
271	C₂×C₄×C₈	—	11	1	no	—
272	C₂×C₄×C₈	—	11	1	no	—
273	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
274	#322	—	11	1	no	—
275	#322	—	11	1	no	—
276	#322	—	11	1	no	—
277	#322	—	11	1	no	—
278	#322	—	11	1	no	—
279	#322	—	11	1	no	—
280	#322	—	11	1	no	—
281	#322	—	11	1	no	—
282	#322	—	11	1	no	—
283	#322	—	11	1	no	—
284	#322	C₂×D₁₁	1	1	yes	characteristic
285	#322	C₂×D₁₁	1	1	yes	characteristic
286	#322	C₂×D₁₁	1	1	yes	characteristic
287	#322	C₂×D₁₁	1	1	yes	characteristic
288	C₈²	—	11	1	no	—
289	C₈²	—	11	1	no	—
290	C₂²×C₁₁	—	2	1	no	—
291	C₂²×C₁₁	—	2	1	no	—
292	C₂²×C₁₁	—	2	1	no	—
293	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
294	C₂×D₁₁	—	2	1	no	—
295	C₂×D₁₁	—	2	1	no	—
296	C₂×D₁₁	—	2	1	no	—
297	C₂×D₁₁	—	2	1	no	—
298	C₂×D₁₁	—	2	1	no	—
299	C₂×D₁₁	C₄×M₁₆	1	2	yes	—
300	C₄×C₁₁	—	2	1	no	—
301	C₄×C₁₁	—	2	1	no	—
302	C₄×C₁₁	—	2	1	no	—
303	C₄×C₁₁	C₂²×M₁₆	1	2	yes	—
304	C₄×C₁₁	#568	1	2	yes	—
305	C₄×C₁₁	#568	1	2	yes	—
306	Dic₁₁	—	2	1	no	—
307	Dic₁₁	—	2	1	no	—
308	Dic₁₁	—	2	1	no	—
309	Dic₁₁	—	2	1	no	—
310	Dic₁₁	—	2	1	no	—
311	Dic₁₁	C₄×M₁₆	1	2	yes	—
312	C₂×#41	—	11	1	no	—
313	#131	—	22	8	no	—
314	C₂×M₁₆	—	11	2	no	—
315	C₂×M₁₆	—	11	2	no	—
316	C₂×M₁₆	—	11	2	no	—
317	C₂×M₁₆	—	11	2	no	—
318	C₂×M₁₆	—	11	2	no	—
319	C₂×M₁₆	—	11	2	no	—
320	C₂×M₁₆	C₄×D₁₁	1	2	yes	—
321	C₂²×C₈	—	11	2	no	—
322	C₂²×C₈	—	11	2	no	—
323	C₂²×C₈	—	11	2	no	—
324	C₂²×C₈	—	11	2	no	—
325	C₂²×C₈	C₄×D₁₁	1	2	yes	—
326	C₄×Q₈	—	11	1	no	—
327	C₄×Q₈	—	11	1	no	—
328	C₄×D₄	—	11	1	no	—
329	C₄×D₄	—	11	1	no	—
330	C₄×D₄	—	11	1	no	—
331	C₄×D₄	—	11	1	no	—
332	C₄×D₄	—	11	1	no	—
333	C₄×D₄	—	11	1	no	—
334	#117	—	11	1	no	—
335	#117	—	11	1	no	—
336	#117	—	11	1	no	—
337	C₂×C₄²	—	11	1	no	—
338	C₂×C₄²	—	11	1	no	—
339	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
340	C₄⋊C₈	—	11	2	no	—
341	C₄⋊C₈	—	11	2	no	—
342	C₄⋊C₈	—	11	2	no	—
343	C₄⋊C₈	—	11	2	no	—
344	C₄⋊C₈	—	11	2	no	—
345	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
346	C₂²⋊C₈	—	11	2	no	—
347	C₂²⋊C₈	—	11	2	no	—
348	C₂²⋊C₈	—	11	2	no	—
349	C₂²⋊C₈	—	11	2	no	—
350	C₂²⋊C₈	—	11	2	no	—
351	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
352	#97	—	11	2	no	—
353	#97	—	11	2	no	—
354	#97	—	11	2	no	—
355	#97	—	11	2	no	—
356	#97	—	11	2	no	—
357	#97	—	11	2	no	—
358	#97	C₄×D₁₁	1	2	yes	—
359	C₄×C₈	—	11	2	no	—
360	C₄×C₈	—	11	2	no	—
361	C₄×C₈	—	11	2	no	—
362	C₄×C₈	—	11	2	no	—
363	C₄×C₈	—	11	1	no	—
364	C₄×C₈	—	11	1	no	—
365	C₄×C₈	—	11	1	no	—
366	C₄×C₈	—	11	1	no	—
367	C₄×C₈	—	11	1	no	—
368	C₄×C₈	—	11	1	no	—
369	C₄×C₈	C₄×D₁₁	1	2	yes	—
370	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
371	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
372	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
373	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
374	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
375	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
376	C₂×C₁₁	—	4	1	no	—
377	C₂×C₁₁	C₂×C₄×M₁₆	1	1	yes	characteristic
378	C₂×C₁₁	#2875	1	1	yes	characteristic
379	C₂×C₁₁	#2875	1	1	yes	characteristic
380	D₁₁	—	2	2	no	—
381	D₁₁	—	4	1	no	—
382	#41	—	22	4	no	—
383	C₂×Q₈	—	11	1	no	—
384	C₂×D₄	—	11	1	no	—
385	C₂×D₄	—	11	1	no	—
386	C₂×D₄	—	11	1	no	—
387	C₂²×C₄	—	11	1	no	—
388	C₂²×C₄	—	11	1	no	—
389	C₂²×C₄	—	11	1	no	—
390	C₂²×C₄	—	11	1	no	—
391	C₂²×C₄	—	11	1	no	—
392	C₂²×C₄	—	11	1	no	—
393	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
396	M₁₆	—	4	2	no	—
397	M₁₆	—	22	4	no	—
398	M₁₆	—	22	4	no	—
399	M₁₆	—	22	4	no	—
400	M₁₆	—	44	2	no	—
401	M₁₆	—	44	2	no	—
402	M₁₆	—	44	2	no	—
403	C₂×C₈	—	2	4	no	—
404	C₂×C₈	—	11	2	no	—
405	C₂×C₈	—	11	8	no	—
406	C₂×C₈	—	11	2	no	—
407	C₂×C₈	—	11	2	no	—
408	C₂×C₈	—	11	2	no	—
409	C₂×C₈	—	11	2	no	—
410	C₂×C₈	—	11	2	no	—
411	C₂×C₈	—	22	4	no	—
412	C₂×C₈	—	44	2	no	—
413	C₂×C₈	—	44	2	no	—
414	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
415	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
416	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
417	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
418	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
419	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
420	C₄⋊C₄	—	11	1	no	—
421	C₄⋊C₄	—	11	1	no	—
422	C₄⋊C₄	—	11	1	no	—
423	C₄⋊C₄	—	11	1	no	—
424	C₄⋊C₄	—	11	1	no	—
425	C₄⋊C₄	—	11	1	no	—
426	C₂²⋊C₄	—	11	1	no	—
427	C₂²⋊C₄	—	11	1	no	—
428	C₂²⋊C₄	—	11	1	no	—
429	C₂²⋊C₄	—	11	1	no	—
430	C₂²⋊C₄	—	11	1	no	—
431	C₂²⋊C₄	—	11	1	no	—
432	C₄²	—	11	1	no	—
433	C₄²	—	11	1	no	—
434	C₄²	—	11	1	no	—
435	C₄²	—	11	1	no	—
436	C₄²	—	11	1	no	—
437	C₄²	—	11	1	no	—
438	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
439	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
440	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
441	C₄²	C₂³×D₁₁	1	1	yes	characteristic
442	C₁₁	#17336	1	1	yes	characteristic, complemented, Sylow
443	C₂³	—	11	1	no	—
444	C₂³	—	11	1	no	—
445	C₂³	C₄²×D₁₁	1	1	yes	characteristic
446	Q₈	—	22	2	no	—
447	D₄	—	22	2	no	—
448	D₄	—	22	2	no	—
449	D₄	—	22	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	11	1	no	—
454	C₂×C₄	—	11	4	no	—
455	C₂×C₄	—	11	1	no	—
456	C₂×C₄	—	11	1	no	—
457	C₂×C₄	—	11	1	no	—
458	C₂×C₄	—	11	1	no	—
459	C₂×C₄	—	11	1	no	—
460	C₂×C₄	—	22	2	no	—
461	C₂×C₄	—	22	2	no	—
462	C₂×C₄	—	22	2	no	—
463	C₂×C₄	—	22	2	no	—
464	C₂×C₄	—	22	2	no	—
465	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
466	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
467	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
468	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
470	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
471	C₈	—	2	2	no	—
472	C₈	—	2	2	no	—
473	C₈	—	2	2	no	—
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	11	4	no	—
477	C₈	—	22	2	no	—
478	C₈	—	22	2	no	—
479	C₈	—	22	2	no	—
480	C₈	—	22	2	no	—
481	C₈	—	22	2	no	—
482	C₈	M₁₆×D₁₁	1	4	yes	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	11	2	no	—
487	C₂²	—	22	1	no	—
488	C₂²	—	22	1	no	—
489	C₂²	—	22	1	no	—
490	C₂²	—	22	1	no	—
491	C₂²	—	22	1	no	—
492	C₂²	C₂×C₄²×D₁₁	1	1	yes	characteristic
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	11	2	no	—
497	C₄	—	22	1	no	—
498	C₄	—	22	1	no	—
499	C₄	—	22	1	no	—
500	C₄	—	22	1	no	—
501	C₄	—	22	1	no	—
502	C₄	C₂×M₁₆×D₁₁	1	2	yes	—
503	C₄	#10623276	1	2	yes	—
504	C₄	#10623281	1	2	yes	—
505	C₂	—	4	1	no	—
506	C₂	—	22	2	no	—
507	C₂	—	44	1	no	—
508	C₂	C₄×M₁₆×D₁₁	1	1	yes	characteristic
509	C₂	#13077041	1	1	yes	characteristic
510	C₂	#13077043	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂²×C₄²
Fitting	C₁₁×#1451	C₂
prime radical	C₂×#4339	C₂×C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1451	D₁₁
hypocenter	C₁₁	#17336
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ #1451

Complements

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

N	H ≅ G/N	type
4. #13066920	C₂	semidirect
5. #13066919	C₂	semidirect
6. #13066912	C₂	semidirect
7. #13066911	C₂	semidirect
8. #13066905	C₂	semidirect
9. #13066904	C₂	semidirect
10. #13066902	C₂	semidirect
11. #13066902	C₂	semidirect
12. #13066902	C₂	semidirect
13. #13066901	C₂	semidirect
14. D₁₁×#322	C₂	semidirect
15. C₁₁×#1451	C₂	semidirect
187. C₈×D₁₁	M₁₆	semidirect
200. #1451	D₁₁	semidirect
442. C₁₁	#17336	semidirect

Maximal subgroups

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

subgroup	index
#13077580	2
#13077578	2
C₄×#66954	2
#13066920	2
#13066919	2
#13066912	2
#13066911	2
#13066905	2
#13066904	2
#13066902	2
#13066901	2
D₁₁×#322	2
C₁₁×#1451	2
#17336	11