Subgroups — #14719427

Order 2816.

836 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077244	C₂	1	1	yes	maximal, characteristic
2	D₁₁×#431	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₁₁	C₂	1	1	yes	maximal, characteristic
4	#13066913	C₂	1	1	yes	maximal, characteristic, complemented
5	#13066911	C₂	1	1	yes	maximal, characteristic, complemented
6	#13066911	C₂	1	1	yes	maximal, characteristic, complemented
7	#13066904	C₂	1	1	yes	maximal, characteristic, complemented
8	#13066904	C₂	1	1	yes	maximal, characteristic, complemented
9	#13066902	C₂	1	1	yes	maximal, characteristic, complemented
10	#13066902	C₂	1	1	yes	maximal, characteristic, complemented
11	#13066895	C₂	1	1	yes	maximal, characteristic, complemented
12	#13066895	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#4313	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×M₁₆×D₁₁	C₄	1	2	yes	—
17	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#431	C₂²	1	1	yes	characteristic
19	C₁₁×#431	C₂²	1	1	yes	characteristic
20	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
21	M₁₆×Dic₁₁	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	#10622320	C₄	1	2	yes	—
34	D₁₁×#97	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, 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	M₁₆×D₁₁	—	2	8	no	—
73	C₂×#4313	C₂×C₄	1	2	yes	—
74	C₂×#4313	C₂×C₄	1	2	yes	—
75	C₂×#4313	C₂×C₄	1	2	yes	—
76	C₂×#4313	C₂×C₄	1	2	yes	—
77	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
78	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
79	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
80	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
81	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
82	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
83	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
84	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
85	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
86	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
87	C₄²×D₁₁	C₂³	1	1	yes	characteristic
88	C₄²×D₁₁	C₂³	1	1	yes	characteristic
89	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
90	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
91	C₁₁×C₂²⋊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	C₂³	1	1	yes	characteristic
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	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
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	C₄⋊(C₁₁⋊C₈)	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	#17327	—	11	1	no	maximal, Sylow
128	C₂³×D₁₁	C₄²	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×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
133	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
134	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
135	C₂×C₄×D₁₁	—	2	4	no	—
136	C₂×C₄×D₁₁	—	2	4	no	—
137	C₂×C₄×D₁₁	—	4	2	no	—
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	C₄²	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	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
150	C₁₁×M₁₆	—	2	4	no	—
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	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
157	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₁₁	C₂⁴	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	C₄²	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	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
173	#4318	—	2	4	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	—	2	4	no	—
183	#4313	M₁₆	1	8	yes	complemented
184	C₈×D₁₁	—	2	4	no	—
185	C₈×D₁₁	—	2	4	no	—
186	C₈×D₁₁	—	4	2	no	—
187	C₈×D₁₁	—	4	2	no	—
188	#2920	—	11	1	no	—
189	C₂×#431	—	11	1	no	—
190	C₂×C₄×M₁₆	—	11	1	no	—
191	#1453	—	11	1	no	—
192	#1453	—	11	1	no	—
193	#1453	—	11	1	no	—
194	#1453	D₁₁	1	1	yes	characteristic, complemented
195	#1451	—	11	1	no	—
196	#1451	—	11	1	no	—
197	#1451	—	11	1	no	—
198	#1451	—	11	1	no	—
199	C₈×M₁₆	—	11	1	no	—
200	C₈×M₁₆	—	11	1	no	—
201	C₈×M₁₆	—	11	1	no	—
202	C₈×M₁₆	—	11	1	no	—
203	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
204	C₂²×D₁₁	—	2	2	no	—
205	C₂²×D₁₁	—	2	2	no	—
206	C₂²×D₁₁	—	4	1	no	—
207	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
208	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
209	C₂×C₄×C₁₁	—	2	2	no	—
210	C₂×C₄×C₁₁	—	2	2	no	—
211	C₂×C₄×C₁₁	—	2	2	no	—
212	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
213	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
214	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
215	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
218	C₂×Dic₁₁	—	2	2	no	—
219	C₂×Dic₁₁	—	2	2	no	—
220	C₂×Dic₁₁	—	4	1	no	—
221	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
222	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
223	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
224	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
225	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
226	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
227	C₄×D₁₁	—	2	2	no	—
228	C₄×D₁₁	—	2	2	no	—
229	C₄×D₁₁	—	2	2	no	—
230	C₄×D₁₁	—	2	2	no	—
231	C₄×D₁₁	—	2	2	no	—
232	C₄×D₁₁	—	2	2	no	—
233	C₄×D₁₁	—	2	2	no	—
234	C₄×D₁₁	—	2	2	no	—
235	C₄×D₁₁	—	4	1	no	—
236	C₄×D₁₁	—	4	1	no	—
237	C₄×D₁₁	C₂×M₁₆	1	4	yes	—
238	C₄×D₁₁	#131	1	4	yes	—
239	C₈×C₁₁	—	2	2	no	—
240	C₈×C₁₁	—	2	2	no	—
241	C₈×C₁₁	—	2	2	no	—
242	C₈×C₁₁	—	2	2	no	—
243	C₈×C₁₁	—	2	2	no	—
244	C₈×C₁₁	C₂×M₁₆	1	4	yes	—
245	C₁₁⋊C₈	—	2	2	no	—
246	C₁₁⋊C₈	—	2	2	no	—
247	C₁₁⋊C₈	—	2	2	no	—
248	C₁₁⋊C₈	—	2	2	no	—
249	C₁₁⋊C₈	—	2	2	no	—
250	C₁₁⋊C₈	C₂×M₁₆	1	4	yes	—
251	C₂²×M₁₆	—	11	2	no	—
252	C₂²×C₄²	—	11	1	no	—
253	#432	—	11	2	no	—
254	#432	—	11	2	no	—
255	#431	—	11	1	no	—
256	#431	—	11	1	no	—
257	#431	—	11	2	no	—
258	#431	—	11	2	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	C₂×C₄⋊C₈	—	11	2	no	—
267	#407	—	11	2	no	—
268	C₂×C₂²⋊C₈	—	11	2	no	—
269	C₄×M₁₆	—	11	2	no	—
270	C₄×M₁₆	—	11	1	no	—
271	C₄×M₁₆	—	11	2	no	—
272	C₄×M₁₆	—	11	1	no	—
273	C₄×M₁₆	—	11	1	no	—
274	C₄×M₁₆	—	11	1	no	—
275	C₄×M₁₆	—	11	1	no	—
276	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
277	C₂×#97	—	11	2	no	—
278	C₂×C₄×C₈	—	11	1	no	—
279	C₂×C₄×C₈	—	11	1	no	—
280	C₂×C₄×C₈	—	11	1	no	—
281	C₂×C₄×C₈	—	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	—	11	1	no	—
287	#322	—	11	1	no	—
288	#322	—	11	1	no	—
289	#322	—	11	1	no	—
290	#322	—	11	1	no	—
291	#322	C₂×D₁₁	1	1	yes	characteristic, complemented
292	#322	C₂×D₁₁	1	1	yes	characteristic, complemented
293	#322	C₂×D₁₁	1	1	yes	characteristic, complemented
294	C₈²	—	11	1	no	—
295	C₈²	—	11	1	no	—
296	C₈²	—	11	1	no	—
297	C₈²	C₂×D₁₁	1	1	yes	characteristic, complemented
298	C₂²×C₁₁	—	2	1	no	—
299	C₂²×C₁₁	—	2	1	no	—
300	C₂²×C₁₁	—	2	1	no	—
301	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
302	C₂×D₁₁	—	2	1	no	—
303	C₂×D₁₁	—	2	1	no	—
304	C₂×D₁₁	—	2	1	no	—
305	C₂×D₁₁	—	2	1	no	—
306	C₂×D₁₁	—	4	4	no	—
307	C₂×D₁₁	C₄×M₁₆	1	2	yes	—
308	C₂×D₁₁	#405	1	2	yes	—
309	C₄×C₁₁	—	2	1	no	—
310	C₄×C₁₁	—	2	1	no	—
311	C₄×C₁₁	—	2	1	no	—
312	C₄×C₁₁	C₂²×M₁₆	1	2	yes	—
313	C₄×C₁₁	C₂×#131	1	2	yes	—
314	C₄×C₁₁	#568	1	2	yes	—
315	Dic₁₁	—	2	1	no	—
316	Dic₁₁	—	2	1	no	—
317	Dic₁₁	—	2	1	no	—
318	Dic₁₁	—	2	1	no	—
319	Dic₁₁	C₄×M₁₆	1	2	yes	—
320	Dic₁₁	#405	1	2	yes	—
321	C₂³×C₄	—	11	1	no	—
322	C₂³×C₄	—	11	1	no	—
323	C₂³×C₄	—	11	1	no	—
324	C₂×M₁₆	—	11	2	no	—
325	C₂×M₁₆	—	11	2	no	—
326	C₂×M₁₆	—	11	2	no	—
327	C₂×M₁₆	—	11	2	no	—
328	C₂×M₁₆	—	11	2	no	—
329	C₂×M₁₆	—	22	8	no	—
330	C₂×M₁₆	C₄×D₁₁	1	2	yes	—
331	C₂²×C₈	—	11	2	no	—
332	C₂²×C₈	—	11	2	no	—
333	C₂²×C₈	—	11	2	no	—
334	C₂²×C₈	—	11	2	no	—
335	C₂×C₄²	—	11	1	no	—
336	C₂×C₄²	—	11	1	no	—
337	C₂×C₄²	—	11	1	no	—
338	C₂×C₄²	—	11	1	no	—
339	C₂×C₄²	—	11	1	no	—
340	C₂×C₄²	—	11	1	no	—
341	C₂×C₄²	—	11	1	no	—
342	C₂×C₄²	—	11	1	no	—
343	C₂×C₄²	—	11	1	no	—
344	C₂×C₄²	—	11	1	no	—
345	C₂×C₄²	—	11	1	no	—
346	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
347	C₄⋊C₈	—	11	2	no	—
348	C₄⋊C₈	—	11	2	no	—
349	C₄⋊C₈	—	11	2	no	—
350	C₄⋊C₈	—	11	2	no	—
351	C₄⋊C₈	—	11	2	no	—
352	C₄⋊C₈	—	11	2	no	—
353	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
354	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
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	—	11	2	no	—
360	C₂²⋊C₈	—	11	2	no	—
361	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
362	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
363	#97	—	11	2	no	—
364	#97	—	11	2	no	—
365	#97	—	11	2	no	—
366	#97	—	11	2	no	—
367	#97	—	11	2	no	—
368	#97	C₄×D₁₁	1	2	yes	—
369	C₄×C₈	—	11	2	no	—
370	C₄×C₈	—	11	2	no	—
371	C₄×C₈	—	11	2	no	—
372	C₄×C₈	—	11	2	no	—
373	C₄×C₈	—	11	1	no	—
374	C₄×C₈	—	11	1	no	—
375	C₄×C₈	—	11	1	no	—
376	C₄×C₈	—	11	1	no	—
377	C₄×C₈	—	11	1	no	—
378	C₄×C₈	—	11	1	no	—
379	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
380	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
381	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
382	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
383	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
384	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
385	C₂×C₁₁	—	4	1	no	—
386	C₂×C₁₁	C₂×C₄×M₁₆	1	1	yes	characteristic
387	C₂×C₁₁	C₂×#405	1	1	yes	characteristic
388	C₂×C₁₁	#2873	1	1	yes	characteristic
389	D₁₁	—	2	2	no	—
390	D₁₁	—	2	2	no	—
391	C₂⁴	—	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	—	11	1	no	—
402	C₂²×C₄	—	11	1	no	—
403	C₂²×C₄	—	11	1	no	—
404	C₂²×C₄	—	11	1	no	—
405	C₂²×C₄	—	11	1	no	—
406	C₂²×C₄	—	11	1	no	—
407	C₂²×C₄	—	22	4	no	—
408	C₂²×C₄	—	22	4	no	—
409	C₂²×C₄	—	44	2	no	—
410	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
411	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
412	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
413	M₁₆	—	2	4	no	—
414	M₁₆	—	11	8	no	—
415	M₁₆	—	22	4	no	—
416	M₁₆	—	22	4	no	—
417	M₁₆	—	22	4	no	—
418	M₁₆	—	22	4	no	—
419	C₂×C₈	—	11	2	no	—
420	C₂×C₈	—	11	2	no	—
421	C₂×C₈	—	11	2	no	—
422	C₂×C₈	—	11	2	no	—
423	C₂×C₈	—	11	2	no	—
424	C₂×C₈	—	11	2	no	—
425	C₂×C₈	—	22	4	no	—
426	C₂×C₈	—	22	4	no	—
427	C₂×C₈	—	44	2	no	—
428	C₂×C₈	—	44	2	no	—
429	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
430	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
431	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
432	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
433	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
434	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
435	C₄²	—	11	1	no	—
436	C₄²	—	11	1	no	—
437	C₄²	—	11	1	no	—
438	C₄²	—	11	1	no	—
439	C₄²	—	11	1	no	—
440	C₄²	—	11	1	no	—
441	C₄²	—	11	1	no	—
442	C₄²	—	11	1	no	—
443	C₄²	—	11	1	no	—
444	C₄²	—	11	1	no	—
445	C₄²	—	11	1	no	—
446	C₄²	—	11	1	no	—
447	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
448	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
449	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
450	C₄²	C₂³×D₁₁	1	1	yes	characteristic
451	C₁₁	#17327	1	1	yes	characteristic, complemented, Sylow
452	C₂³	—	11	1	no	—
453	C₂³	—	11	1	no	—
454	C₂³	—	22	2	no	—
455	C₂³	—	22	2	no	—
456	C₂³	—	44	1	no	—
457	C₂³	C₄²×D₁₁	1	1	yes	characteristic
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	11	1	no	—
462	C₂×C₄	—	11	1	no	—
463	C₂×C₄	—	11	4	no	—
464	C₂×C₄	—	11	4	no	—
465	C₂×C₄	—	11	1	no	—
466	C₂×C₄	—	11	1	no	—
467	C₂×C₄	—	11	1	no	—
468	C₂×C₄	—	11	1	no	—
469	C₂×C₄	—	22	2	no	—
470	C₂×C₄	—	22	2	no	—
471	C₂×C₄	—	22	2	no	—
472	C₂×C₄	—	22	2	no	—
473	C₂×C₄	—	22	2	no	—
474	C₂×C₄	—	22	2	no	—
475	C₂×C₄	—	22	2	no	—
476	C₂×C₄	—	22	2	no	—
477	C₂×C₄	—	22	2	no	—
478	C₂×C₄	—	22	2	no	—
479	C₂×C₄	—	44	1	no	—
480	C₂×C₄	—	44	1	no	—
481	C₂×C₄	—	44	1	no	—
482	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
483	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
484	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
487	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
488	C₈	—	2	2	no	—
489	C₈	—	2	2	no	—
490	C₈	—	2	2	no	—
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	—	11	4	no	—
494	C₈	—	22	2	no	—
495	C₈	—	22	2	no	—
496	C₈	—	22	2	no	—
497	C₈	—	22	2	no	—
498	C₈	—	22	2	no	—
499	C₈	M₁₆×D₁₁	1	4	yes	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	11	2	no	—
504	C₂²	—	11	2	no	—
505	C₂²	—	22	1	no	—
506	C₂²	—	22	1	no	—
507	C₂²	—	22	1	no	—
508	C₂²	—	22	1	no	—
509	C₂²	—	44	4	no	—
510	C₂²	C₂×C₄²×D₁₁	1	1	yes	characteristic
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	11	2	no	—
515	C₄	—	11	2	no	—
516	C₄	—	22	1	no	—
517	C₄	—	22	1	no	—
518	C₄	—	22	1	no	—
519	C₄	—	22	1	no	—
520	C₄	C₂×M₁₆×D₁₁	1	2	yes	—
521	C₄	D₁₁×#131	1	2	yes	—
522	C₄	#10623281	1	2	yes	—
523	C₂	—	4	1	no	—
524	C₂	—	22	2	no	—
525	C₂	—	22	2	no	—
526	C₂	C₄×M₁₆×D₁₁	1	1	yes	characteristic
527	C₂	D₁₁×#405	1	1	yes	characteristic
528	C₂	#13077032	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	#17327
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. #13066913	C₂	semidirect
5. #13066911	C₂	semidirect
6. #13066911	C₂	semidirect
7. #13066904	C₂	semidirect
8. #13066904	C₂	semidirect
9. #13066902	C₂	semidirect
10. #13066902	C₂	semidirect
11. #13066895	C₂	semidirect
12. #13066895	C₂	semidirect
13. C₈×#4313	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
183. #4313	M₁₆	semidirect
194. #1453	D₁₁	semidirect
291. #322	C₂×D₁₁	semidirect
292. #322	C₂×D₁₁	semidirect
293. #322	C₂×D₁₁	semidirect
297. C₈²	C₂×D₁₁	semidirect
451. C₁₁	#17327	semidirect

Maximal subgroups

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

subgroup	index
#13077244	2
D₁₁×#431	2
C₄×M₁₆×D₁₁	2
#13066913	2
#13066911	2
#13066904	2
#13066902	2
#13066895	2
C₈×#4313	2
C₁₁×#1453	2
#17327	11