Subgroups — #14722881

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 502 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	D₁₁×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622450	C₂	1	1	yes	maximal, characteristic
4	#13067406	C₂	1	2	yes	maximal, complemented
5	#13067403	C₂	1	2	yes	maximal, complemented
6	#13067389	C₂	1	2	yes	maximal, complemented
7	#13067385	C₂	1	2	yes	maximal, complemented
8	#13067369	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067368	C₂	1	1	yes	maximal, characteristic, complemented
10	#13067366	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#4313	—	2	1	no	—
13	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#431	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	#10622739	C₄	1	1	yes	characteristic
18	#10622739	C₄	1	1	yes	characteristic
19	#10622731	C₄	1	1	yes	characteristic
20	#10622731	C₄	1	1	yes	characteristic
21	C₂×Dic₁₁⋊C₈	—	2	1	no	—
22	#10622538	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
24	C₄×#4318	C₂²	1	1	yes	characteristic
25	#10622450	—	2	1	no	—
26	#10622450	—	2	1	no	—
27	#10622450	C₂²	1	2	yes	—
28	#10622450	C₂²	1	2	yes	—
29	#10622446	C₂²	1	1	yes	characteristic
30	#10622446	C₂²	1	1	yes	characteristic
31	D₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	D₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	D₁₁×C₂²⋊C₈	—	2	1	no	—
34	#10622331	—	2	1	no	—
35	#10622318	C₄	1	2	yes	—
36	#10622318	C₄	1	2	yes	—
37	#10622298	—	2	1	no	—
38	#10622298	C₂²	1	2	yes	—
39	#10622298	C₂²	1	2	yes	—
40	C₄×C₈×D₁₁	—	2	1	no	—
41	C₁₁×#335	C₂²	1	2	yes	complemented
42	C₁₁×#334	C₂²	1	2	yes	complemented
43	#10622118	C₂²	1	2	yes	complemented
44	#10622118	C₂²	1	2	yes	complemented
45	#10622117	C₂²	1	2	yes	complemented
46	#10622117	C₂²	1	2	yes	complemented
47	#10622096	C₂²	1	2	yes	complemented
48	#10622095	C₂²	1	2	yes	complemented
49	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₁₁	D₄	1	1	yes	characteristic
51	C₂²×C₄×D₁₁	Q₈	1	1	yes	characteristic
52	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₁	—	2	1	no	—
55	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₁	Q₈	1	1	yes	characteristic
59	C₂×#4318	C₂×C₄	1	1	yes	characteristic
60	C₂×#4318	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₁₁⋊C₈	—	2	1	no	—
62	C₂×#4313	—	2	2	no	—
63	C₂×#4313	—	2	2	no	—
64	C₂×#4313	—	4	4	no	—
65	C₂×C₈×D₁₁	—	2	1	no	—
66	C₂×C₈×D₁₁	—	2	1	no	—
67	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₁₁	D₄	1	1	yes	characteristic
70	C₄²×D₁₁	D₄	1	1	yes	characteristic
71	C₄²×D₁₁	Q₈	1	1	yes	characteristic
72	C₄²×D₁₁	Q₈	1	1	yes	characteristic
73	C₄²×D₁₁	C₂³	1	1	yes	characteristic
74	C₄²×D₁₁	C₂³	1	1	yes	characteristic
75	C₁₁×C₄⋊C₈	—	2	1	no	—
76	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
78	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₁₁×C₂²⋊C₈	—	2	1	no	—
80	C₁₁×#97	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₁₁	—	2	1	no	—
82	C₄×C₈×C₁₁	C₂³	1	2	yes	—
83	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
84	(C₂×D₁₁)⋊C₈	—	2	1	no	—
85	(C₂×D₁₁)⋊C₈	—	2	1	no	—
86	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
87	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
88	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
89	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
90	Dic₁₁⋊C₈	—	2	1	no	—
91	Dic₁₁⋊C₈	—	2	1	no	—
92	Dic₁₁⋊C₈	—	2	2	no	—
93	Dic₁₁⋊C₈	—	2	2	no	—
94	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
95	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
96	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
97	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
98	C₈×Dic₁₁	—	2	1	no	—
99	C₈×Dic₁₁	—	2	1	no	—
100	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
101	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
102	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
103	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
104	#66867	C₂×C₄	1	2	yes	—
105	C₄×C₁₁⋊C₈	—	2	1	no	—
106	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
107	#17809	—	11	1	no	maximal, Sylow
108	C₂³×D₁₁	C₄⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
112	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
113	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
114	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₁	—	2	2	no	—
116	C₂×C₄×D₁₁	—	2	2	no	—
117	C₂×C₄×D₁₁	—	2	2	no	—
118	C₂×C₄×D₁₁	—	2	2	no	—
119	C₂×C₄×D₁₁	—	4	2	no	—
120	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
131	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
132	C₁₁×M₁₆	—	2	2	no	—
133	C₁₁×M₁₆	—	2	2	no	—
134	C₂×C₈×C₁₁	—	2	1	no	—
135	C₂×C₈×C₁₁	—	2	1	no	—
136	C₂×C₈×C₁₁	—	2	2	no	—
137	C₂×C₈×C₁₁	—	4	2	no	—
138	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
140	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
143	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
144	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
145	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
146	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
147	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
148	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
149	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
150	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
153	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
154	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
155	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
156	#4318	—	2	2	no	—
157	#4318	—	2	2	no	—
158	C₂×C₁₁⋊C₈	—	2	1	no	—
159	C₂×C₁₁⋊C₈	—	2	1	no	—
160	C₂×C₁₁⋊C₈	—	2	2	no	—
161	C₂×C₁₁⋊C₈	—	4	2	no	—
162	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
163	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
164	#4313	—	4	4	no	—
165	#4313	—	4	4	no	—
166	C₈×D₁₁	—	4	2	no	—
167	C₈×D₁₁	—	4	2	no	—
168	#2920	—	11	1	no	—
169	C₂×#431	—	11	1	no	—
170	C₂×#423	—	11	1	no	—
171	#1574	—	11	2	no	—
172	#1574	—	11	2	no	—
173	#1571	—	11	2	no	—
174	#1570	—	11	2	no	—
175	#1565	—	11	1	no	—
176	#1565	—	11	1	no	—
177	#1565	—	11	1	no	—
178	#1565	D₁₁	1	1	yes	characteristic, complemented
179	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂²×D₁₁	—	2	2	no	—
181	C₂²×D₁₁	—	2	2	no	—
182	C₂²×D₁₁	—	4	1	no	—
183	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₁	—	2	1	no	—
186	C₂×C₄×C₁₁	—	2	1	no	—
187	C₂×C₄×C₁₁	—	4	1	no	—
188	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₁	#131	1	2	yes	—
192	C₂×C₄×C₁₁	#131	1	2	yes	—
193	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
196	C₂×Dic₁₁	—	2	2	no	—
197	C₂×Dic₁₁	—	2	2	no	—
198	C₂×Dic₁₁	—	2	2	no	—
199	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₄×D₁₁	—	2	2	no	—
206	C₄×D₁₁	—	2	1	no	—
207	C₄×D₁₁	—	2	1	no	—
208	C₄×D₁₁	—	2	1	no	—
209	C₄×D₁₁	—	2	1	no	—
210	C₄×D₁₁	—	2	1	no	—
211	C₄×D₁₁	—	2	1	no	—
212	C₄×D₁₁	—	2	2	no	—
213	C₄×D₁₁	—	2	2	no	—
214	C₄×D₁₁	—	2	2	no	—
215	C₄×D₁₁	—	2	2	no	—
216	C₄×D₁₁	—	2	2	no	—
217	C₄×D₁₁	—	4	1	no	—
218	C₄×D₁₁	—	4	1	no	—
219	C₄×D₁₁	AGL(1,ℤ/8)	1	2	yes	—
220	C₄×D₁₁	#137	1	2	yes	—
221	C₈×C₁₁	—	2	2	no	—
222	C₈×C₁₁	—	2	2	no	—
223	C₈×C₁₁	—	4	1	no	—
224	C₈×C₁₁	—	4	2	no	—
225	C₈×C₁₁	—	4	1	no	—
226	C₁₁⋊C₈	—	2	2	no	—
227	C₁₁⋊C₈	—	2	2	no	—
228	C₁₁⋊C₈	—	4	1	no	—
229	C₁₁⋊C₈	—	4	2	no	—
230	C₁₁⋊C₈	—	4	1	no	—
231	C₂²×M₁₆	—	22	1	no	—
232	C₂²×C₄²	—	11	1	no	—
233	#432	—	11	2	no	—
234	#432	—	11	2	no	—
235	#431	—	11	2	no	—
236	#431	—	11	2	no	—
237	#431	—	11	1	no	—
238	#431	—	11	1	no	—
239	#431	—	11	1	no	—
240	#431	—	22	1	no	—
241	#431	—	22	1	no	—
242	#431	C₂×D₁₁	1	1	yes	characteristic
243	#423	—	11	1	no	—
244	#423	—	11	1	no	—
245	#423	—	11	2	no	—
246	#423	—	11	2	no	—
247	#423	—	22	1	no	—
248	#423	—	22	1	no	—
249	C₂×C₄⋊C₈	—	11	1	no	—
250	C₂×C₄⋊C₈	—	11	1	no	—
251	C₂×C₄⋊C₈	—	11	1	no	—
252	C₂×C₄⋊C₈	—	22	1	no	—
253	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
254	#407	—	11	1	no	—
255	#407	—	11	1	no	—
256	C₂×C₂²⋊C₈	—	22	1	no	—
257	C₄×M₁₆	—	11	1	no	—
258	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
259	C₂×C₄×C₈	—	22	1	no	—
260	#335	—	11	2	no	—
261	#335	—	11	2	no	—
262	#335	—	11	2	no	—
263	#335	C₂×D₁₁	1	2	yes	complemented
264	#334	—	11	2	no	—
265	#334	—	11	2	no	—
266	#334	—	11	2	no	—
267	#334	C₂×D₁₁	1	2	yes	complemented
268	C₂²×C₁₁	—	2	1	no	—
269	C₂²×C₁₁	—	2	1	no	—
270	C₂²×C₁₁	#424	1	2	yes	—
271	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
272	C₂×D₁₁	—	2	1	no	—
273	C₂×D₁₁	—	2	1	no	—
274	C₂×D₁₁	—	2	1	no	—
275	C₂×D₁₁	—	2	1	no	—
276	C₂×D₁₁	—	2	1	no	—
277	C₂×D₁₁	—	4	4	no	—
278	C₂×D₁₁	#428	1	2	yes	—
279	C₄×C₁₁	—	2	1	no	—
280	C₄×C₁₁	—	2	1	no	—
281	C₄×C₁₁	—	2	1	no	—
282	C₄×C₁₁	#424	1	2	yes	—
283	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
284	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
285	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
287	Dic₁₁	—	2	1	no	—
288	Dic₁₁	—	2	1	no	—
289	Dic₁₁	—	2	1	no	—
290	Dic₁₁	—	2	1	no	—
291	Dic₁₁	#428	1	2	yes	—
292	Dic₁₁	#430	1	2	yes	—
293	C₂³×C₄	—	11	1	no	—
294	C₂³×C₄	—	11	1	no	—
295	C₂³×C₄	—	11	1	no	—
296	C₂×M₁₆	—	11	1	no	—
297	C₂×M₁₆	—	11	1	no	—
298	C₂×M₁₆	—	22	2	no	—
299	C₂×M₁₆	—	22	2	no	—
300	C₂×M₁₆	—	44	4	no	—
301	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
302	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	—	22	1	no	—
305	C₂²×C₈	—	22	1	no	—
306	C₂²×C₈	—	22	1	no	—
307	C₂×C₄²	—	11	1	no	—
308	C₂×C₄²	—	11	1	no	—
309	C₂×C₄²	—	11	1	no	—
310	C₂×C₄²	—	11	1	no	—
311	C₂×C₄²	—	11	1	no	—
312	C₂×C₄²	—	11	1	no	—
313	C₂×C₄²	—	11	1	no	—
314	C₂×C₄²	—	11	1	no	—
315	C₂×C₄²	—	11	1	no	—
316	C₂×C₄²	—	11	1	no	—
317	C₂×C₄²	—	11	1	no	—
318	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	—	11	2	no	—
321	C₄⋊C₈	—	11	2	no	—
322	C₄⋊C₈	—	11	2	no	—
323	C₄⋊C₈	—	11	2	no	—
324	C₄⋊C₈	—	11	1	no	—
325	C₄⋊C₈	—	11	2	no	—
326	C₄⋊C₈	—	11	1	no	—
327	C₄⋊C₈	—	22	1	no	—
328	C₄⋊C₈	—	22	1	no	—
329	C₄⋊C₈	—	22	2	no	—
330	C₄⋊C₈	—	22	2	no	—
331	C₄⋊C₈	—	22	1	no	—
332	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
333	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
334	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	—	11	2	no	—
337	C₂²⋊C₈	—	11	2	no	—
338	C₂²⋊C₈	—	11	2	no	—
339	C₂²⋊C₈	—	11	2	no	—
340	C₂²⋊C₈	—	22	1	no	—
341	C₂²⋊C₈	—	22	1	no	—
342	C₂²⋊C₈	—	22	1	no	—
343	#97	—	11	2	no	—
344	#97	C₄×D₁₁	1	2	yes	—
345	C₄×C₈	—	2	1	no	—
346	C₄×C₈	—	11	2	no	—
347	C₄×C₈	—	22	1	no	—
348	C₄×C₈	—	22	1	no	—
349	C₄×C₈	—	22	1	no	—
350	C₄×C₈	C₂²×D₁₁	1	2	yes	—
351	C₂×C₁₁	—	2	2	no	—
352	C₂×C₁₁	C₂×#424	1	1	yes	characteristic
353	C₂×C₁₁	C₂×#428	1	1	yes	characteristic
354	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
355	D₁₁	—	2	2	no	—
356	D₁₁	—	4	1	no	—
357	C₂⁴	—	11	1	no	—
358	C₂²×C₄	—	11	1	no	—
359	C₂²×C₄	—	11	1	no	—
360	C₂²×C₄	—	11	1	no	—
361	C₂²×C₄	—	11	1	no	—
362	C₂²×C₄	—	11	1	no	—
363	C₂²×C₄	—	11	1	no	—
364	C₂²×C₄	—	11	1	no	—
365	C₂²×C₄	—	11	1	no	—
366	C₂²×C₄	—	11	1	no	—
367	C₂²×C₄	—	11	1	no	—
368	C₂²×C₄	—	11	1	no	—
369	C₂²×C₄	—	11	1	no	—
370	C₂²×C₄	—	11	1	no	—
371	C₂²×C₄	—	11	1	no	—
372	C₂²×C₄	—	11	1	no	—
373	C₂²×C₄	—	22	2	no	—
374	C₂²×C₄	—	22	2	no	—
375	C₂²×C₄	—	22	2	no	—
376	C₂²×C₄	—	22	2	no	—
377	C₂²×C₄	—	44	2	no	—
378	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
379	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
380	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
381	M₁₆	—	2	2	no	—
382	M₁₆	—	2	2	no	—
383	M₁₆	—	22	2	no	—
384	M₁₆	—	22	2	no	—
385	M₁₆	—	44	4	no	—
386	M₁₆	—	44	4	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	4	2	no	—
391	C₂×C₈	—	11	2	no	—
392	C₂×C₈	—	11	2	no	—
393	C₂×C₈	—	22	1	no	—
394	C₂×C₈	—	22	1	no	—
395	C₂×C₈	—	22	2	no	—
396	C₂×C₈	—	44	2	no	—
397	C₂×C₈	—	44	2	no	—
398	C₂×C₈	—	44	2	no	—
399	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
400	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
401	C₄²	—	11	1	no	—
402	C₄²	—	11	1	no	—
403	C₄²	—	11	1	no	—
404	C₄²	—	11	1	no	—
405	C₄²	—	11	1	no	—
406	C₄²	—	11	1	no	—
407	C₄²	—	11	1	no	—
408	C₄²	—	11	1	no	—
409	C₄²	—	11	1	no	—
410	C₄²	—	11	1	no	—
411	C₄²	—	11	1	no	—
412	C₄²	—	11	1	no	—
413	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
414	C₄²	D₄×D₁₁	1	1	yes	characteristic
415	C₄²	Q₈×D₁₁	1	1	yes	characteristic
416	C₄²	C₂³×D₁₁	1	1	yes	characteristic
417	C₁₁	#17809	1	1	yes	characteristic, complemented, Sylow
418	C₂³	—	11	1	no	—
419	C₂³	—	11	1	no	—
420	C₂³	—	22	2	no	—
421	C₂³	—	22	2	no	—
422	C₂³	—	44	1	no	—
423	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	11	1	no	—
428	C₂×C₄	—	11	1	no	—
429	C₂×C₄	—	11	2	no	—
430	C₂×C₄	—	11	2	no	—
431	C₂×C₄	—	11	1	no	—
432	C₂×C₄	—	11	1	no	—
433	C₂×C₄	—	11	1	no	—
434	C₂×C₄	—	11	1	no	—
435	C₂×C₄	—	22	2	no	—
436	C₂×C₄	—	22	2	no	—
437	C₂×C₄	—	22	2	no	—
438	C₂×C₄	—	22	2	no	—
439	C₂×C₄	—	22	2	no	—
440	C₂×C₄	—	22	2	no	—
441	C₂×C₄	—	22	2	no	—
442	C₂×C₄	—	22	1	no	—
443	C₂×C₄	—	22	1	no	—
444	C₂×C₄	—	22	1	no	—
445	C₂×C₄	—	22	1	no	—
446	C₂×C₄	—	22	1	no	—
447	C₂×C₄	—	22	1	no	—
448	C₂×C₄	—	22	2	no	—
449	C₂×C₄	—	22	2	no	—
450	C₂×C₄	—	44	1	no	—
451	C₂×C₄	—	44	1	no	—
452	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
453	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
454	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
455	C₂×C₄	#66954	1	2	yes	—
456	C₂×C₄	#66960	1	2	yes	—
457	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
458	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
459	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
460	C₈	—	2	2	no	—
461	C₈	—	2	2	no	—
462	C₈	—	4	2	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	1	no	—
465	C₈	—	22	2	no	—
466	C₈	—	22	2	no	—
467	C₈	—	44	2	no	—
468	C₈	—	44	1	no	—
469	C₈	—	44	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	11	2	no	—
473	C₂²	—	22	1	no	—
474	C₂²	—	22	1	no	—
475	C₂²	—	22	1	no	—
476	C₂²	—	22	1	no	—
477	C₂²	—	22	1	no	—
478	C₂²	—	44	4	no	—
479	C₂²	#10622452	1	2	yes	—
480	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	11	2	no	—
485	C₄	—	11	2	no	—
486	C₄	—	22	1	no	—
487	C₄	—	22	1	no	—
488	C₄	—	22	1	no	—
489	C₄	—	22	1	no	—
490	C₄	#10622452	1	2	yes	—
491	C₄	C₂×#66954	1	1	yes	characteristic
492	C₄	C₂×#66960	1	1	yes	characteristic
493	C₄	D₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
494	C₄	D₁₁×#137	1	1	yes	characteristic
495	C₂	—	2	2	no	—
496	C₂	—	22	2	no	—
497	C₂	—	44	1	no	—
498	C₂	C₂×#10622452	1	1	yes	characteristic
499	C₂	D₁₁×#428	1	1	yes	characteristic
500	C₂	D₁₁×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#1565	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1565	D₁₁
hypocenter	C₁₁	#17809
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
4. #13067406	C₂	semidirect
5. #13067403	C₂	semidirect
6. #13067389	C₂	semidirect
7. #13067385	C₂	semidirect
8. #13067369	C₂	semidirect
9. #13067368	C₂	semidirect
10. #13067366	C₂	semidirect
11. C₁₁×#1565	C₂	semidirect
41. C₁₁×#335	C₂²	semidirect
42. C₁₁×#334	C₂²	semidirect
43. #10622118	C₂²	semidirect
44. #10622118	C₂²	semidirect
45. #10622117	C₂²	semidirect
46. #10622117	C₂²	semidirect
47. #10622096	C₂²	semidirect
48. #10622095	C₂²	semidirect
178. #1565	D₁₁	semidirect
263. #335	C₂×D₁₁	semidirect
267. #334	C₂×D₁₁	semidirect
417. C₁₁	#17809	semidirect

Maximal subgroups

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

subgroup	index
#13077247	2
D₁₁×#431	2
C₂×#10622450	2
#13067406	2
#13067403	2
#13067389	2
#13067385	2
#13067369	2
#13067368	2
#13067366	2
C₁₁×#1565	2
#17809	11