Subgroups — #14722798

Order 2816.

756 conjugacy classes of subgroups.

The subgroup lattice has 514 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	C₂×#10622450	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₁₁	C₂	1	1	yes	maximal, characteristic
4	#13067382	C₂	1	2	yes	maximal, complemented
5	#13067380	C₂	1	2	yes	maximal, complemented
6	#13067373	C₂	1	2	yes	maximal, complemented
7	#13067370	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	C₂×M₁₆×D₁₁	C₄	1	1	yes	characteristic
13	C₂×M₁₆×D₁₁	C₄	1	1	yes	characteristic
14	C₂²×#4313	—	2	1	no	—
15	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#431	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
19	M₁₆×Dic₁₁	C₄	1	1	yes	characteristic
20	M₁₆×Dic₁₁	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	1	yes	characteristic
28	#10622450	C₂²	1	2	yes	—
29	#10622450	C₂²	1	1	yes	characteristic
30	#10622450	C₂²	1	2	yes	—
31	#10622448	C₂²	1	1	yes	characteristic
32	#10622448	C₂²	1	1	yes	characteristic
33	#10622339	—	2	1	no	—
34	#10622332	—	2	1	no	—
35	#10622320	C₄	1	2	yes	—
36	D₁₁×#97	C₄	1	2	yes	—
37	C₄×#4313	—	2	1	no	—
38	C₄×#4313	C₂²	1	2	yes	—
39	#10622298	—	2	1	no	—
40	C₄×C₈×D₁₁	C₂²	1	2	yes	—
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	M₁₆×D₁₁	—	2	4	no	—
63	M₁₆×D₁₁	—	2	4	no	—
64	C₂×#4313	—	2	2	no	—
65	C₂×#4313	—	2	2	no	—
66	C₂×#4313	—	2	1	no	—
67	C₂×#4313	—	2	1	no	—
68	C₂×#4313	—	4	4	no	—
69	C₂×#4313	C₂×C₄	1	2	yes	—
70	C₂×#4313	C₂×C₄	1	2	yes	—
71	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
72	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
73	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
75	C₄²×D₁₁	D₄	1	1	yes	characteristic
76	C₄²×D₁₁	D₄	1	1	yes	characteristic
77	C₄²×D₁₁	Q₈	1	1	yes	characteristic
78	C₄²×D₁₁	Q₈	1	1	yes	characteristic
79	C₄²×D₁₁	C₂³	1	1	yes	characteristic
80	C₄²×D₁₁	C₂³	1	1	yes	characteristic
81	C₁₁×C₄⋊C₈	—	2	1	no	—
82	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₁×C₂²⋊C₈	—	2	1	no	—
86	C₁₁×#97	C₂×C₄	1	2	yes	—
87	C₄×C₈×C₁₁	—	2	1	no	—
88	C₄×C₈×C₁₁	C₂³	1	2	yes	—
89	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
90	(C₂×D₁₁)⋊C₈	—	2	1	no	—
91	(C₂×D₁₁)⋊C₈	—	2	1	no	—
92	#66879	—	2	1	no	—
93	#66879	—	2	1	no	—
94	#66879	C₂×C₄	1	2	yes	—
95	#66879	C₂×C₄	1	2	yes	—
96	Dic₁₁⋊C₈	—	2	1	no	—
97	Dic₁₁⋊C₈	—	2	1	no	—
98	Dic₁₁⋊C₈	—	2	2	no	—
99	Dic₁₁⋊C₈	—	2	2	no	—
100	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
101	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
102	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
103	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
104	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
105	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
106	#66867	C₂×C₄	1	2	yes	—
107	C₄×C₁₁⋊C₈	—	2	1	no	—
108	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
109	#17796	—	11	1	no	maximal, Sylow
110	C₂³×D₁₁	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
114	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
115	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₁	—	2	2	no	—
118	C₂×C₄×D₁₁	—	2	2	no	—
119	C₂×C₄×D₁₁	—	2	2	no	—
120	C₂×C₄×D₁₁	—	2	2	no	—
121	C₂×C₄×D₁₁	—	4	2	no	—
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	C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
133	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
134	C₁₁×M₁₆	—	2	2	no	—
135	C₁₁×M₁₆	M₁₆	1	4	yes	complemented
136	C₂×C₈×C₁₁	—	2	2	no	—
137	C₂×C₈×C₁₁	—	2	1	no	—
138	C₂×C₈×C₁₁	—	2	1	no	—
139	C₂×C₈×C₁₁	—	4	2	no	—
140	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
142	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
145	C₄²×C₁₁	C₂⁴	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	C₄⋊C₄	1	1	yes	characteristic
151	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
152	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
154	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
155	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
156	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
157	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
158	#4318	—	2	2	no	—
159	#4318	M₁₆	1	4	yes	complemented
160	C₂×C₁₁⋊C₈	—	2	1	no	—
161	C₂×C₁₁⋊C₈	—	2	1	no	—
162	C₂×C₁₁⋊C₈	—	2	2	no	—
163	C₂×C₁₁⋊C₈	—	4	2	no	—
164	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
165	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
166	#4313	—	2	4	no	—
167	#4313	—	2	4	no	—
168	#4313	—	4	4	no	—
169	#4313	—	4	2	no	—
170	#4313	—	4	4	no	—
171	#4313	—	4	2	no	—
172	C₈×D₁₁	—	2	4	no	—
173	C₈×D₁₁	—	2	4	no	—
174	#2920	—	11	1	no	—
175	C₂×#423	—	11	1	no	—
176	C₂×C₄×M₁₆	—	11	1	no	—
177	#1569	—	11	2	no	—
178	#1569	—	11	2	no	—
179	#1567	—	11	2	no	—
180	#1566	—	11	2	no	—
181	#1565	—	11	1	no	—
182	#1565	—	11	1	no	—
183	#1565	—	11	1	no	—
184	#1565	D₁₁	1	1	yes	characteristic, complemented
185	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂²×D₁₁	—	2	2	no	—
187	C₂²×D₁₁	—	2	2	no	—
188	C₂²×D₁₁	—	4	1	no	—
189	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₁	—	2	1	no	—
192	C₂×C₄×C₁₁	—	2	1	no	—
193	C₂×C₄×C₁₁	—	4	1	no	—
194	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
198	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
199	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
202	C₂×Dic₁₁	—	2	2	no	—
203	C₂×Dic₁₁	—	2	2	no	—
204	C₂×Dic₁₁	—	2	2	no	—
205	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₄×D₁₁	—	2	2	no	—
212	C₄×D₁₁	—	2	1	no	—
213	C₄×D₁₁	—	2	1	no	—
214	C₄×D₁₁	—	2	1	no	—
215	C₄×D₁₁	—	2	1	no	—
216	C₄×D₁₁	—	2	1	no	—
217	C₄×D₁₁	—	2	1	no	—
218	C₄×D₁₁	—	2	2	no	—
219	C₄×D₁₁	—	2	2	no	—
220	C₄×D₁₁	—	2	2	no	—
221	C₄×D₁₁	—	2	2	no	—
222	C₄×D₁₁	—	2	2	no	—
223	C₄×D₁₁	—	4	1	no	—
224	C₄×D₁₁	—	4	1	no	—
225	C₄×D₁₁	AGL(1,ℤ/8)	1	2	yes	—
226	C₄×D₁₁	#137	1	2	yes	—
227	C₈×C₁₁	—	2	2	no	—
228	C₈×C₁₁	—	4	2	no	—
229	C₈×C₁₁	—	4	1	no	—
230	C₈×C₁₁	—	4	1	no	—
231	C₈×C₁₁	C₂×M₁₆	1	4	yes	complemented
232	C₁₁⋊C₈	—	2	2	no	—
233	C₁₁⋊C₈	—	4	2	no	—
234	C₁₁⋊C₈	—	4	1	no	—
235	C₁₁⋊C₈	—	4	1	no	—
236	C₁₁⋊C₈	C₂×M₁₆	1	4	yes	complemented
237	C₂²×M₁₆	—	11	1	no	—
238	C₂²×M₁₆	—	11	1	no	—
239	C₂²×M₁₆	—	22	1	no	—
240	C₂²×C₄²	—	11	1	no	—
241	#432	—	11	1	no	—
242	#432	—	11	1	no	—
243	#432	—	22	1	no	—
244	#431	—	11	1	no	—
245	#431	—	22	1	no	—
246	#431	C₂×D₁₁	1	1	yes	characteristic
247	#423	—	11	1	no	—
248	#423	—	11	2	no	—
249	#423	—	11	1	no	—
250	#423	—	11	2	no	—
251	#423	—	22	1	no	—
252	#423	—	22	1	no	—
253	C₂×C₄⋊C₈	—	11	1	no	—
254	C₂×C₄⋊C₈	—	22	1	no	—
255	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
256	#407	—	22	1	no	—
257	C₄×M₁₆	—	11	1	no	—
258	C₄×M₁₆	—	11	1	no	—
259	C₄×M₁₆	—	11	1	no	—
260	C₄×M₁₆	—	11	2	no	—
261	C₄×M₁₆	—	11	2	no	—
262	C₄×M₁₆	—	22	1	no	—
263	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
264	C₂×#97	—	11	2	no	—
265	C₂×C₄×C₈	—	11	2	no	—
266	#335	—	11	2	no	—
267	#335	—	11	2	no	—
268	#335	—	11	2	no	—
269	#335	C₂×D₁₁	1	2	yes	complemented
270	#334	—	11	2	no	—
271	#334	—	11	2	no	—
272	#334	—	11	2	no	—
273	#334	C₂×D₁₁	1	2	yes	complemented
274	C₂²×C₁₁	—	2	1	no	—
275	C₂²×C₁₁	—	2	1	no	—
276	C₂²×C₁₁	#423	1	2	yes	—
277	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
278	C₂×D₁₁	—	2	1	no	—
279	C₂×D₁₁	—	2	1	no	—
280	C₂×D₁₁	—	2	1	no	—
281	C₂×D₁₁	—	2	1	no	—
282	C₂×D₁₁	—	2	1	no	—
283	C₂×D₁₁	—	4	4	no	—
284	C₂×D₁₁	#428	1	2	yes	—
285	C₄×C₁₁	—	2	1	no	—
286	C₄×C₁₁	—	2	1	no	—
287	C₄×C₁₁	—	2	1	no	—
288	C₄×C₁₁	#423	1	2	yes	—
289	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
290	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
291	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
292	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
293	Dic₁₁	—	2	1	no	—
294	Dic₁₁	—	2	1	no	—
295	Dic₁₁	—	2	1	no	—
296	Dic₁₁	—	2	1	no	—
297	Dic₁₁	#428	1	2	yes	—
298	Dic₁₁	#430	1	2	yes	—
299	C₂³×C₄	—	11	1	no	—
300	C₂³×C₄	—	11	1	no	—
301	C₂³×C₄	—	11	1	no	—
302	C₂×M₁₆	—	11	1	no	—
303	C₂×M₁₆	—	11	1	no	—
304	C₂×M₁₆	—	11	2	no	—
305	C₂×M₁₆	—	11	2	no	—
306	C₂×M₁₆	—	22	2	no	—
307	C₂×M₁₆	—	22	2	no	—
308	C₂×M₁₆	—	22	1	no	—
309	C₂×M₁₆	—	22	1	no	—
310	C₂×M₁₆	—	22	4	no	—
311	C₂×M₁₆	—	22	4	no	—
312	C₂×M₁₆	—	44	4	no	—
313	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
314	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
315	C₂²×C₈	—	2	1	no	—
316	C₂²×C₈	—	11	2	no	—
317	C₂²×C₈	—	11	2	no	—
318	C₂²×C₈	—	22	1	no	—
319	C₂×C₄²	—	11	1	no	—
320	C₂×C₄²	—	11	1	no	—
321	C₂×C₄²	—	11	1	no	—
322	C₂×C₄²	—	11	1	no	—
323	C₂×C₄²	—	11	1	no	—
324	C₂×C₄²	—	11	1	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	C₂²×D₁₁	1	1	yes	characteristic
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	11	1	no	—
333	C₄⋊C₈	—	11	2	no	—
334	C₄⋊C₈	—	11	1	no	—
335	C₄⋊C₈	—	22	2	no	—
336	C₄⋊C₈	—	22	2	no	—
337	C₄⋊C₈	—	22	1	no	—
338	C₄⋊C₈	—	22	1	no	—
339	C₄⋊C₈	—	22	1	no	—
340	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
341	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
342	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
343	C₂²⋊C₈	—	2	1	no	—
344	C₂²⋊C₈	—	22	1	no	—
345	C₂²⋊C₈	—	22	1	no	—
346	C₂²⋊C₈	—	22	1	no	—
347	#97	—	11	2	no	—
348	#97	—	11	2	no	—
349	#97	—	11	2	no	—
350	#97	—	22	1	no	—
351	#97	—	22	1	no	—
352	#97	C₄×D₁₁	1	2	yes	—
353	C₄×C₈	—	2	1	no	—
354	C₄×C₈	—	11	2	no	—
355	C₄×C₈	—	11	2	no	—
356	C₄×C₈	—	11	2	no	—
357	C₄×C₈	—	22	1	no	—
358	C₄×C₈	C₂²×D₁₁	1	2	yes	—
359	C₂×C₁₁	—	2	2	no	—
360	C₂×C₁₁	C₂×#423	1	1	yes	characteristic
361	C₂×C₁₁	C₂×#428	1	1	yes	characteristic
362	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
363	D₁₁	—	2	2	no	—
364	D₁₁	—	4	1	no	—
365	C₂⁴	—	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	—	11	1	no	—
374	C₂²×C₄	—	11	1	no	—
375	C₂²×C₄	—	11	1	no	—
376	C₂²×C₄	—	11	1	no	—
377	C₂²×C₄	—	11	1	no	—
378	C₂²×C₄	—	11	1	no	—
379	C₂²×C₄	—	11	1	no	—
380	C₂²×C₄	—	11	1	no	—
381	C₂²×C₄	—	22	2	no	—
382	C₂²×C₄	—	22	2	no	—
383	C₂²×C₄	—	22	2	no	—
384	C₂²×C₄	—	22	2	no	—
385	C₂²×C₄	—	44	2	no	—
386	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
387	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
388	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
389	M₁₆	—	2	2	no	—
390	M₁₆	—	11	4	no	—
391	M₁₆	—	22	4	no	—
392	M₁₆	—	22	2	no	—
393	M₁₆	—	22	4	no	—
394	M₁₆	—	44	4	no	—
395	M₁₆	—	44	2	no	—
396	M₁₆	—	44	2	no	—
397	M₁₆	—	44	4	no	—
398	M₁₆	#4313	1	4	yes	complemented
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	4	2	no	—
403	C₂×C₈	—	11	2	no	—
404	C₂×C₈	—	11	2	no	—
405	C₂×C₈	—	22	4	no	—
406	C₂×C₈	—	22	4	no	—
407	C₂×C₈	—	22	1	no	—
408	C₂×C₈	—	22	1	no	—
409	C₂×C₈	—	22	2	no	—
410	C₂×C₈	—	44	2	no	—
411	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
412	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
413	C₄²	—	11	1	no	—
414	C₄²	—	11	1	no	—
415	C₄²	—	11	1	no	—
416	C₄²	—	11	1	no	—
417	C₄²	—	11	1	no	—
418	C₄²	—	11	1	no	—
419	C₄²	—	11	1	no	—
420	C₄²	—	11	1	no	—
421	C₄²	—	11	1	no	—
422	C₄²	—	11	1	no	—
423	C₄²	—	11	1	no	—
424	C₄²	—	11	1	no	—
425	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
426	C₄²	D₄×D₁₁	1	1	yes	characteristic
427	C₄²	Q₈×D₁₁	1	1	yes	characteristic
428	C₄²	C₂³×D₁₁	1	1	yes	characteristic
429	C₁₁	#17796	1	1	yes	characteristic, complemented, Sylow
430	C₂³	—	11	1	no	—
431	C₂³	—	11	1	no	—
432	C₂³	—	22	2	no	—
433	C₂³	—	22	2	no	—
434	C₂³	—	44	1	no	—
435	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	11	1	no	—
440	C₂×C₄	—	11	1	no	—
441	C₂×C₄	—	11	2	no	—
442	C₂×C₄	—	11	2	no	—
443	C₂×C₄	—	11	1	no	—
444	C₂×C₄	—	11	1	no	—
445	C₂×C₄	—	11	1	no	—
446	C₂×C₄	—	11	1	no	—
447	C₂×C₄	—	22	2	no	—
448	C₂×C₄	—	22	2	no	—
449	C₂×C₄	—	22	2	no	—
450	C₂×C₄	—	22	2	no	—
451	C₂×C₄	—	22	2	no	—
452	C₂×C₄	—	22	2	no	—
453	C₂×C₄	—	22	2	no	—
454	C₂×C₄	—	22	1	no	—
455	C₂×C₄	—	22	1	no	—
456	C₂×C₄	—	22	1	no	—
457	C₂×C₄	—	22	1	no	—
458	C₂×C₄	—	22	1	no	—
459	C₂×C₄	—	22	1	no	—
460	C₂×C₄	—	22	2	no	—
461	C₂×C₄	—	22	2	no	—
462	C₂×C₄	—	44	1	no	—
463	C₂×C₄	—	44	1	no	—
464	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
465	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
466	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
467	C₂×C₄	C₂×#4313	1	2	yes	—
468	C₂×C₄	M₁₆×D₁₁	1	2	yes	—
469	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
470	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
471	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
472	C₈	—	2	2	no	—
473	C₈	—	4	2	no	—
474	C₈	—	4	1	no	—
475	C₈	—	4	1	no	—
476	C₈	—	11	4	no	—
477	C₈	—	22	2	no	—
478	C₈	—	44	2	no	—
479	C₈	—	44	1	no	—
480	C₈	—	44	1	no	—
481	C₈	C₂×#4313	1	4	yes	complemented
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	11	2	no	—
485	C₂²	—	22	1	no	—
486	C₂²	—	22	1	no	—
487	C₂²	—	22	1	no	—
488	C₂²	—	22	1	no	—
489	C₂²	—	22	1	no	—
490	C₂²	—	44	4	no	—
491	C₂²	#10622450	1	2	yes	—
492	C₂²	C₂×C₄⋊C₄×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	—	11	2	no	—
498	C₄	—	22	1	no	—
499	C₄	—	22	1	no	—
500	C₄	—	22	1	no	—
501	C₄	—	22	1	no	—
502	C₄	#10622450	1	2	yes	—
503	C₄	C₂²×#4313	1	1	yes	characteristic
504	C₄	C₂×M₁₆×D₁₁	1	1	yes	characteristic
505	C₄	D₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
506	C₄	D₁₁×#137	1	1	yes	characteristic
507	C₂	—	2	2	no	—
508	C₂	—	22	2	no	—
509	C₂	—	44	1	no	—
510	C₂	C₂×#10622450	1	1	yes	characteristic
511	C₂	D₁₁×#428	1	1	yes	characteristic
512	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	#17796
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. #13067382	C₂	semidirect
5. #13067380	C₂	semidirect
6. #13067373	C₂	semidirect
7. #13067370	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
135. C₁₁×M₁₆	M₁₆	semidirect
159. #4318	M₁₆	semidirect
184. #1565	D₁₁	semidirect
231. C₈×C₁₁	C₂×M₁₆	semidirect
236. C₁₁⋊C₈	C₂×M₁₆	semidirect
269. #335	C₂×D₁₁	semidirect
273. #334	C₂×D₁₁	semidirect
398. M₁₆	#4313	semidirect
429. C₁₁	#17796	semidirect
481. C₈	C₂×#4313	semidirect

Maximal subgroups

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

subgroup	index
#13077244	2
C₂×#10622450	2
C₄×M₁₆×D₁₁	2
#13067382	2
#13067380	2
#13067373	2
#13067370	2
#13067369	2
#13067368	2
#13067366	2
C₁₁×#1565	2
#17796	11