Subgroups — #14719405

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077247	C₂	1	1	yes	maximal, characteristic
2	#13077244	C₂	1	1	yes	maximal, characteristic
3	D₁₁×#431	C₂	1	1	yes	maximal, characteristic
4	#13066917	C₂	1	1	yes	maximal, characteristic, complemented
5	#13066917	C₂	1	1	yes	maximal, characteristic, complemented
6	#13066917	C₂	1	1	yes	maximal, characteristic, complemented
7	#13066915	C₂	1	1	yes	maximal, characteristic, complemented
8	#13066913	C₂	1	1	yes	maximal, characteristic, complemented
9	#13066911	C₂	1	1	yes	maximal, characteristic, complemented
10	#13066911	C₂	1	1	yes	maximal, characteristic, complemented
11	#13066904	C₂	1	1	yes	maximal, characteristic, complemented
12	#13066902	C₂	1	1	yes	maximal, characteristic, complemented
13	#13066895	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#4313	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
17	C₁₁×#431	C₂²	1	1	yes	characteristic
18	C₁₁×#431	C₂²	1	1	yes	characteristic
19	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
20	#10622739	C₄	1	2	yes	—
21	#10622731	C₄	1	2	yes	—
22	#10622538	C₂²	1	1	yes	characteristic
23	#10622538	C₂²	1	1	yes	characteristic
24	C₄×#4318	C₂²	1	1	yes	characteristic
25	#10622450	C₄	1	2	yes	—
26	#10622448	C₄	1	2	yes	—
27	#10622446	C₄	1	2	yes	—
28	D₁₁×C₄⋊C₈	C₄	1	2	yes	—
29	#10622339	C₄	1	2	yes	—
30	D₁₁×C₂²⋊C₈	C₄	1	2	yes	—
31	#10622332	C₄	1	2	yes	—
32	#10622331	C₄	1	2	yes	—
33	#10622318	C₄	1	2	yes	—
34	#10622318	C₄	1	2	yes	—
35	C₄×#4313	C₂²	1	1	yes	characteristic
36	C₄×#4313	C₂²	1	1	yes	characteristic
37	#10622298	C₂²	1	1	yes	characteristic
38	#10622298	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	#10622298	C₂²	1	1	yes	characteristic
44	#10622298	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, complemented
48	C₁₁×#322	C₂²	1	1	yes	characteristic, complemented
49	C₁₁×#322	C₂²	1	1	yes	characteristic, complemented
50	C₈²×C₁₁	C₂²	1	1	yes	characteristic, complemented
51	#10622093	C₂²	1	1	yes	characteristic, complemented
52	#10622093	C₂²	1	1	yes	characteristic, complemented
53	#10622093	C₂²	1	1	yes	characteristic, complemented
54	#10622092	C₂²	1	1	yes	characteristic, complemented
55	#10622092	C₂²	1	1	yes	characteristic, complemented
56	#10622092	C₂²	1	1	yes	characteristic, complemented
57	#10622092	C₂²	1	1	yes	characteristic, complemented
58	#10622092	C₂²	1	1	yes	characteristic, complemented
59	#10622092	C₂²	1	1	yes	characteristic, complemented
60	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
68	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
71	C₂×#4318	C₂×C₄	1	2	yes	—
72	C₂×#4313	C₂×C₄	1	2	yes	—
73	C₂×#4313	C₂×C₄	1	2	yes	—
74	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
75	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
76	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
77	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
78	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
79	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
80	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
81	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
82	C₄²×D₁₁	C₂³	1	1	yes	characteristic
83	C₄²×D₁₁	C₂³	1	1	yes	characteristic
84	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
85	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
86	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
87	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
88	C₁₁×#97	C₂×C₄	1	2	yes	—
89	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
95	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
96	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
97	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
98	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
99	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
100	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
101	(C₂×D₁₁)⋊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	#66879	C₂×C₄	1	2	yes	—
106	#66879	C₂×C₄	1	2	yes	—
107	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
108	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
109	Dic₁₁⋊C₈	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	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
115	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
116	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
117	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
118	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
119	#66867	C₂×C₄	1	2	yes	—
120	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
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	#17324	—	11	1	no	maximal, Sylow
127	C₂³×D₁₁	C₄²	1	1	yes	characteristic
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	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
132	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
133	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
134	C₂×C₄×D₁₁	—	2	4	no	—
135	C₂×C₄×D₁₁	—	4	2	no	—
136	C₂×C₄×D₁₁	—	4	2	no	—
137	C₂×C₄×D₁₁	C₄²	1	1	yes	characteristic
138	C₂×C₄×D₁₁	C₄²	1	1	yes	characteristic
139	C₂×C₄×D₁₁	C₄²	1	1	yes	characteristic
140	C₂×C₄×D₁₁	C₄²	1	1	yes	characteristic
141	C₂×C₄×D₁₁	C₄²	1	1	yes	characteristic
142	C₂×C₄×D₁₁	C₄²	1	1	yes	characteristic
143	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
149	C₁₁×M₁₆	—	4	2	no	—
150	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
156	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
160	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
161	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
162	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
163	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
164	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
165	C₄×Dic₁₁	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	—	4	2	no	—
173	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
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	#4313	—	2	4	no	—
180	#4313	—	2	4	no	—
181	C₈×D₁₁	—	4	2	no	—
182	C₈×D₁₁	—	4	2	no	—
183	#2920	—	11	1	no	—
184	#2920	—	11	1	no	—
185	C₂×#431	—	11	1	no	—
186	#1454	—	11	1	no	—
187	#1454	—	11	1	no	—
188	#1454	—	11	1	no	—
189	#1454	—	11	1	no	—
190	#1453	—	11	1	no	—
191	#1453	—	11	1	no	—
192	#1453	—	11	1	no	—
193	#1453	D₁₁	1	1	yes	characteristic, complemented
194	#1451	—	11	1	no	—
195	#1451	—	11	1	no	—
196	C₈×M₁₆	—	11	1	no	—
197	C₈×M₁₆	—	11	1	no	—
198	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
199	C₂²×D₁₁	—	2	2	no	—
200	C₂²×D₁₁	—	4	1	no	—
201	C₂²×D₁₁	—	4	1	no	—
202	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
203	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
204	C₂×C₄×C₁₁	—	2	2	no	—
205	C₂×C₄×C₁₁	—	2	2	no	—
206	C₂×C₄×C₁₁	—	2	2	no	—
207	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
208	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
209	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
210	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
213	C₂×Dic₁₁	—	2	2	no	—
214	C₂×Dic₁₁	—	4	1	no	—
215	C₂×Dic₁₁	—	4	1	no	—
216	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
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	C₄×D₁₁	—	2	2	no	—
223	C₄×D₁₁	—	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	—	4	1	no	—
230	C₄×D₁₁	—	4	1	no	—
231	C₄×D₁₁	—	4	1	no	—
232	C₄×D₁₁	—	4	1	no	—
233	C₄×D₁₁	#131	1	4	yes	—
234	C₈×C₁₁	—	2	2	no	—
235	C₈×C₁₁	—	2	2	no	—
236	C₈×C₁₁	—	2	2	no	—
237	C₈×C₁₁	—	2	2	no	—
238	C₈×C₁₁	—	2	2	no	—
239	C₈×C₁₁	—	2	2	no	—
240	C₁₁⋊C₈	—	2	2	no	—
241	C₁₁⋊C₈	—	2	2	no	—
242	C₁₁⋊C₈	—	2	2	no	—
243	C₁₁⋊C₈	—	2	2	no	—
244	C₁₁⋊C₈	—	2	2	no	—
245	C₁₁⋊C₈	—	2	2	no	—
246	C₂²×C₄²	—	11	1	no	—
247	#432	—	11	2	no	—
248	#432	—	11	2	no	—
249	#432	—	11	2	no	—
250	#432	—	11	2	no	—
251	#431	—	11	1	no	—
252	#431	—	11	1	no	—
253	#431	—	11	2	no	—
254	#431	—	11	2	no	—
255	#431	—	11	1	no	—
256	#431	—	11	1	no	—
257	#431	—	11	1	no	—
258	#431	—	11	1	no	—
259	#431	—	11	1	no	—
260	#431	—	11	1	no	—
261	#431	—	11	1	no	—
262	#431	—	11	1	no	—
263	#431	C₂×D₁₁	1	1	yes	characteristic
264	#431	C₂×D₁₁	1	1	yes	characteristic
265	#423	—	11	2	no	—
266	#423	—	11	2	no	—
267	C₂×C₄⋊C₈	—	11	2	no	—
268	#407	—	11	2	no	—
269	#407	—	11	2	no	—
270	C₂×C₂²⋊C₈	—	11	2	no	—
271	C₄×M₁₆	—	11	1	no	—
272	C₄×M₁₆	—	11	1	no	—
273	C₄×M₁₆	—	11	1	no	—
274	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
275	C₂×C₄×C₈	—	11	1	no	—
276	C₂×C₄×C₈	—	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	—	11	1	no	—
285	#322	—	11	1	no	—
286	#322	C₂×D₁₁	1	1	yes	characteristic, complemented
287	#322	C₂×D₁₁	1	1	yes	characteristic, complemented
288	#322	C₂×D₁₁	1	1	yes	characteristic, complemented
289	C₈²	—	11	1	no	—
290	C₈²	—	11	1	no	—
291	C₈²	—	11	1	no	—
292	C₈²	C₂×D₁₁	1	1	yes	characteristic, complemented
293	C₂²×C₁₁	—	2	1	no	—
294	C₂²×C₁₁	—	2	1	no	—
295	C₂²×C₁₁	—	2	1	no	—
296	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
297	C₂×D₁₁	—	2	1	no	—
298	C₂×D₁₁	—	2	1	no	—
299	C₂×D₁₁	—	2	1	no	—
300	C₂×D₁₁	—	2	1	no	—
301	C₂×D₁₁	—	2	1	no	—
302	C₂×D₁₁	—	4	4	no	—
303	C₂×D₁₁	#405	1	2	yes	—
304	C₄×C₁₁	—	2	1	no	—
305	C₄×C₁₁	—	2	1	no	—
306	C₄×C₁₁	—	2	1	no	—
307	C₄×C₁₁	C₂×#131	1	2	yes	—
308	C₄×C₁₁	#568	1	2	yes	—
309	C₄×C₁₁	#568	1	2	yes	—
310	Dic₁₁	—	2	1	no	—
311	Dic₁₁	—	2	1	no	—
312	Dic₁₁	—	2	1	no	—
313	Dic₁₁	—	2	1	no	—
314	Dic₁₁	—	2	1	no	—
315	Dic₁₁	#405	1	2	yes	—
316	C₂³×C₄	—	11	1	no	—
317	C₂³×C₄	—	11	1	no	—
318	C₂³×C₄	—	11	1	no	—
319	C₂×M₁₆	—	11	2	no	—
320	C₂×M₁₆	—	11	2	no	—
321	C₂×M₁₆	—	11	2	no	—
322	C₂×M₁₆	C₄×D₁₁	1	2	yes	—
323	C₂²×C₈	—	11	2	no	—
324	C₂²×C₈	—	11	2	no	—
325	C₂×C₄²	—	11	1	no	—
326	C₂×C₄²	—	11	1	no	—
327	C₂×C₄²	—	11	1	no	—
328	C₂×C₄²	—	11	1	no	—
329	C₂×C₄²	—	11	1	no	—
330	C₂×C₄²	—	11	1	no	—
331	C₂×C₄²	—	11	1	no	—
332	C₂×C₄²	—	11	1	no	—
333	C₂×C₄²	—	11	1	no	—
334	C₂×C₄²	—	11	1	no	—
335	C₂×C₄²	—	11	1	no	—
336	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
337	C₄⋊C₈	—	11	2	no	—
338	C₄⋊C₈	—	11	2	no	—
339	C₄⋊C₈	—	11	2	no	—
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	—	11	2	no	—
346	C₄⋊C₈	—	11	2	no	—
347	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
348	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
349	C₂²⋊C₈	—	11	2	no	—
350	C₂²⋊C₈	—	11	2	no	—
351	C₂²⋊C₈	—	11	2	no	—
352	C₂²⋊C₈	—	11	2	no	—
353	C₂²⋊C₈	—	11	2	no	—
354	C₂²⋊C₈	—	11	2	no	—
355	C₂²⋊C₈	—	11	2	no	—
356	C₂²⋊C₈	—	11	2	no	—
357	C₂²⋊C₈	—	11	2	no	—
358	C₂²⋊C₈	—	11	2	no	—
359	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
360	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
361	#97	—	11	2	no	—
362	#97	—	11	2	no	—
363	#97	—	11	2	no	—
364	#97	C₄×D₁₁	1	2	yes	—
365	C₄×C₈	—	11	2	no	—
366	C₄×C₈	—	11	2	no	—
367	C₄×C₈	—	11	1	no	—
368	C₄×C₈	—	11	1	no	—
369	C₄×C₈	—	11	1	no	—
370	C₄×C₈	—	11	1	no	—
371	C₄×C₈	—	11	1	no	—
372	C₄×C₈	—	11	1	no	—
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	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
377	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
378	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
379	C₂×C₁₁	—	4	1	no	—
380	C₂×C₁₁	C₂×#405	1	1	yes	characteristic
381	C₂×C₁₁	#2873	1	1	yes	characteristic
382	C₂×C₁₁	#2873	1	1	yes	characteristic
383	D₁₁	—	2	2	no	—
384	D₁₁	—	4	1	no	—
385	C₂⁴	—	11	1	no	—
386	C₂²×C₄	—	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	—	11	1	no	—
394	C₂²×C₄	—	11	1	no	—
395	C₂²×C₄	—	11	1	no	—
396	C₂²×C₄	—	11	1	no	—
397	C₂²×C₄	—	11	1	no	—
398	C₂²×C₄	—	11	1	no	—
399	C₂²×C₄	—	11	1	no	—
400	C₂²×C₄	—	11	1	no	—
401	C₂²×C₄	—	22	4	no	—
402	C₂²×C₄	—	44	2	no	—
403	C₂²×C₄	—	44	2	no	—
404	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
405	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
406	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
407	M₁₆	—	4	2	no	—
408	M₁₆	—	22	4	no	—
409	M₁₆	—	22	4	no	—
410	M₁₆	—	44	2	no	—
411	C₂×C₈	—	11	2	no	—
412	C₂×C₈	—	11	2	no	—
413	C₂×C₈	—	11	2	no	—
414	C₂×C₈	—	11	2	no	—
415	C₂×C₈	—	11	2	no	—
416	C₂×C₈	—	11	2	no	—
417	C₂×C₈	—	44	2	no	—
418	C₂×C₈	—	44	2	no	—
419	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
420	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
421	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
422	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
423	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
424	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
425	C₄²	—	11	1	no	—
426	C₄²	—	11	1	no	—
427	C₄²	—	11	1	no	—
428	C₄²	—	11	1	no	—
429	C₄²	—	11	1	no	—
430	C₄²	—	11	1	no	—
431	C₄²	—	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	C₂×C₄×D₁₁	1	1	yes	characteristic
438	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
439	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
440	C₄²	C₂³×D₁₁	1	1	yes	characteristic
441	C₁₁	#17324	1	1	yes	characteristic, complemented, Sylow
442	C₂³	—	11	1	no	—
443	C₂³	—	11	1	no	—
444	C₂³	—	22	2	no	—
445	C₂³	—	44	1	no	—
446	C₂³	—	44	1	no	—
447	C₂³	C₄²×D₁₁	1	1	yes	characteristic
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	11	1	no	—
452	C₂×C₄	—	11	4	no	—
453	C₂×C₄	—	11	1	no	—
454	C₂×C₄	—	11	1	no	—
455	C₂×C₄	—	11	1	no	—
456	C₂×C₄	—	11	1	no	—
457	C₂×C₄	—	11	1	no	—
458	C₂×C₄	—	22	2	no	—
459	C₂×C₄	—	22	2	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	—	22	2	no	—
466	C₂×C₄	—	44	1	no	—
467	C₂×C₄	—	44	1	no	—
468	C₂×C₄	—	44	1	no	—
469	C₂×C₄	—	44	1	no	—
470	C₂×C₄	—	44	1	no	—
471	C₂×C₄	—	44	1	no	—
472	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
473	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
474	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
475	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
476	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
477	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₈	—	2	2	no	—
481	C₈	—	2	2	no	—
482	C₈	—	2	2	no	—
483	C₈	—	2	2	no	—
484	C₈	—	22	2	no	—
485	C₈	—	22	2	no	—
486	C₈	—	22	2	no	—
487	C₈	—	22	2	no	—
488	C₈	—	22	2	no	—
489	C₈	—	22	2	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	11	2	no	—
494	C₂²	—	22	1	no	—
495	C₂²	—	22	1	no	—
496	C₂²	—	22	1	no	—
497	C₂²	—	22	1	no	—
498	C₂²	—	22	1	no	—
499	C₂²	—	44	4	no	—
500	C₂²	C₂×C₄²×D₁₁	1	1	yes	characteristic
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	11	2	no	—
505	C₄	—	22	1	no	—
506	C₄	—	22	1	no	—
507	C₄	—	22	1	no	—
508	C₄	—	22	1	no	—
509	C₄	—	22	1	no	—
510	C₄	#10623276	1	2	yes	—
511	C₄	D₁₁×#131	1	2	yes	—
512	C₄	#10623281	1	2	yes	—
513	C₂	—	4	1	no	—
514	C₂	—	22	2	no	—
515	C₂	—	44	1	no	—
516	C₂	D₁₁×#405	1	1	yes	characteristic
517	C₂	#13077032	1	1	yes	characteristic
518	C₂	#13077033	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂²×C₄²
Fitting	C₁₁×#1453	C₂
prime radical	C₂³×D₁₁	C₄²
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1453	D₁₁
hypocenter	C₁₁	#17324
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ #1453

Complements

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

N	H ≅ G/N	type
4. #13066917	C₂	semidirect
5. #13066917	C₂	semidirect
6. #13066917	C₂	semidirect
7. #13066915	C₂	semidirect
8. #13066913	C₂	semidirect
9. #13066911	C₂	semidirect
10. #13066911	C₂	semidirect
11. #13066904	C₂	semidirect
12. #13066902	C₂	semidirect
13. #13066895	C₂	semidirect
14. C₈×#4313	C₂	semidirect
15. C₁₁×#1453	C₂	semidirect
47. C₁₁×#322	C₂²	semidirect
48. C₁₁×#322	C₂²	semidirect
49. C₁₁×#322	C₂²	semidirect
50. C₈²×C₁₁	C₂²	semidirect
51. #10622093	C₂²	semidirect
52. #10622093	C₂²	semidirect
53. #10622093	C₂²	semidirect
54. #10622092	C₂²	semidirect
55. #10622092	C₂²	semidirect
56. #10622092	C₂²	semidirect
57. #10622092	C₂²	semidirect
58. #10622092	C₂²	semidirect
59. #10622092	C₂²	semidirect
60. C₈×C₁₁⋊C₈	C₂²	semidirect
61. C₈×C₁₁⋊C₈	C₂²	semidirect
62. C₈×C₁₁⋊C₈	C₂²	semidirect
193. #1453	D₁₁	semidirect
286. #322	C₂×D₁₁	semidirect
287. #322	C₂×D₁₁	semidirect
288. #322	C₂×D₁₁	semidirect
292. C₈²	C₂×D₁₁	semidirect
441. C₁₁	#17324	semidirect

Maximal subgroups

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

subgroup	index
#13077247	2
#13077244	2
D₁₁×#431	2
#13066917	2
#13066915	2
#13066913	2
#13066911	2
#13066904	2
#13066902	2
#13066895	2
C₈×#4313	2
C₁₁×#1453	2
#17324	11