Subgroups — C₁₁×#19162 #14596355

Order 2816.

844 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1687	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1685	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1667	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1665	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1545	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂×C₁₁×AGL(1,ℤ/8)	—	2	1	no	—
14	C₂²×C₁₁×D₈	—	2	1	no	—
15	C₂²×C₁₁×M₁₆	—	2	1	no	—
16	C₁₁×#532	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
19	C₁₁×#496	—	2	2	no	—
20	C₁₁×#493	C₂²	1	2	yes	complemented
21	C₁₁×#492	C₂²	1	2	yes	complemented
22	C₁₁×#480	—	2	1	no	—
23	C₁₁×#474	C₂²	1	1	yes	characteristic, complemented
24	C₁₁×#474	C₂²	1	1	yes	characteristic, complemented
25	C₁₁×#459	—	2	1	no	—
26	C₁₁×#459	—	2	1	no	—
27	C₁₁×#459	C₂²	1	2	yes	—
28	C₁₁×#459	C₂²	1	2	yes	—
29	C₁₁×#459	C₂²	1	1	yes	characteristic, complemented
30	C₁₁×#459	C₂²	1	1	yes	characteristic, complemented
31	C₁₁×#447	—	2	1	no	—
32	C₄×C₁₁×D₈	—	2	1	no	—
33	C₄×C₁₁×D₈	—	2	1	no	—
34	C₁₁×#436	C₂²	1	2	yes	complemented
35	C₁₁×#435	—	2	2	no	—
36	C₈×D₄×C₁₁	C₂²	1	2	yes	complemented
37	C₁₁×#431	C₂²	1	1	yes	characteristic
38	C₁₁×#423	C₂²	1	1	yes	characteristic
39	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₁×#102	—	2	1	no	—
41	C₁₁×#407	—	2	1	no	—
42	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
43	C₁₁×#335	C₂²	1	2	yes	complemented
44	C₁₁×#334	C₂²	1	2	yes	complemented
45	C₁₁×#332	C₂²	1	2	yes	complemented
46	C₁₁×#331	C₂²	1	2	yes	complemented
47	C₁₁×#331	C₂²	1	2	yes	complemented
48	C₁₁×#331	C₂²	1	2	yes	complemented
49	C₂×C₁₁×#41	—	2	1	no	—
50	C₂²×D₄×C₁₁	—	2	1	no	—
51	C₂²×D₄×C₁₁	—	2	1	no	—
52	C₂²×D₄×C₁₁	—	2	1	no	—
53	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₁	—	2	1	no	—
55	C₁₁×AGL(1,ℤ/8)	—	4	4	no	—
56	C₁₁×AGL(1,ℤ/8)	—	4	4	no	—
57	C₂×C₁₁×SD₁₆	—	2	2	no	—
58	C₂×C₁₁×SD₁₆	—	2	2	no	—
59	C₂×C₁₁×D₈	—	2	2	no	—
60	C₂×C₁₁×D₈	—	2	2	no	—
61	C₂×C₁₁×D₈	—	2	1	no	—
62	C₂×C₁₁×D₈	—	2	1	no	—
63	C₂×C₁₁×D₈	—	2	2	no	—
64	C₂×C₁₁×D₈	—	2	2	no	—
65	C₂×C₁₁×D₈	—	4	4	no	—
66	C₂×C₁₁×M₁₆	—	2	1	no	—
67	C₂×C₁₁×M₁₆	—	2	2	no	—
68	C₂×C₁₁×M₁₆	—	4	4	no	—
69	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
70	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
71	C₂²×C₈×C₁₁	—	2	1	no	—
72	C₂²×C₈×C₁₁	—	2	2	no	—
73	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
74	C₁₁×#127	—	2	1	no	—
75	C₁₁×#127	—	2	1	no	—
76	C₁₁×#127	—	2	1	no	—
77	C₁₁×#127	C₂³	1	2	yes	—
78	C₁₁×#127	C₂³	1	1	yes	characteristic
79	C₁₁×#124	—	2	1	no	—
80	C₁₁×#121	—	2	1	no	—
81	C₁₁×#121	—	2	1	no	—
82	C₄×D₄×C₁₁	—	2	1	no	—
83	C₄×D₄×C₁₁	—	2	1	no	—
84	C₄×D₄×C₁₁	—	2	1	no	—
85	C₄×D₄×C₁₁	—	2	1	no	—
86	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
87	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
88	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
89	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
90	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
91	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
93	C₁₁×#107	—	2	1	no	—
94	C₁₁×#107	—	2	1	no	—
95	C₁₁×C₄⋊C₈	—	2	1	no	—
96	C₁₁×C₄⋊C₈	—	2	1	no	—
97	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
98	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
99	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
100	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
101	C₁₁×#102	—	2	1	no	—
102	C₁₁×#102	—	2	1	no	—
103	C₁₁×#102	—	2	2	no	—
104	C₁₁×#102	—	2	2	no	—
105	C₁₁×#102	—	2	1	no	—
106	C₁₁×#102	—	2	1	no	—
107	C₁₁×C₂²⋊C₈	—	2	1	no	—
108	C₁₁×C₂²⋊C₈	—	2	2	no	—
109	C₁₁×C₂²⋊C₈	—	2	2	no	—
110	C₁₁×#97	D₄	1	2	yes	—
111	C₄×C₈×C₁₁	—	2	1	no	—
112	C₄×C₈×C₁₁	C₂³	1	2	yes	—
113	#19162	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂⁴×C₁₁	—	2	1	no	—
115	C₂⁴×C₁₁	—	4	1	no	—
116	C₁₁×#41	—	4	2	no	—
117	C₁₁×#41	—	4	2	no	—
118	C₂×Q₈×C₁₁	—	2	1	no	—
119	C₂×D₄×C₁₁	—	2	2	no	—
120	C₂×D₄×C₁₁	—	2	1	no	—
121	C₂×D₄×C₁₁	—	2	1	no	—
122	C₂×D₄×C₁₁	—	2	2	no	—
123	C₂×D₄×C₁₁	—	2	1	no	—
124	C₂×D₄×C₁₁	—	2	2	no	—
125	C₂×D₄×C₁₁	—	2	1	no	—
126	C₂×D₄×C₁₁	—	2	2	no	—
127	C₂×D₄×C₁₁	—	4	1	no	—
128	C₂×D₄×C₁₁	—	4	2	no	—
129	C₂×D₄×C₁₁	—	4	2	no	—
130	C₂×D₄×C₁₁	—	4	1	no	—
131	C₂×D₄×C₁₁	—	4	1	no	—
132	C₂×D₄×C₁₁	—	4	1	no	—
133	C₂×D₄×C₁₁	—	4	1	no	—
134	C₂×D₄×C₁₁	—	4	2	no	—
135	C₂×D₄×C₁₁	—	4	2	no	—
136	C₂×D₄×C₁₁	—	8	2	no	—
137	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
138	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₁	—	2	1	no	—
140	C₂²×C₄×C₁₁	—	2	1	no	—
141	C₂²×C₄×C₁₁	—	2	1	no	—
142	C₂²×C₄×C₁₁	—	2	1	no	—
143	C₂²×C₄×C₁₁	—	2	1	no	—
144	C₂²×C₄×C₁₁	—	4	2	no	—
145	C₂²×C₄×C₁₁	—	4	2	no	—
146	C₂²×C₄×C₁₁	—	4	1	no	—
147	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
150	C₁₁×SD₁₆	—	4	4	no	—
151	C₁₁×SD₁₆	—	4	4	no	—
152	C₁₁×D₈	—	4	2	no	—
153	C₁₁×D₈	—	4	4	no	—
154	C₁₁×D₈	—	4	4	no	—
155	C₁₁×D₈	—	4	4	no	—
156	C₁₁×D₈	—	4	2	no	—
157	C₁₁×D₈	—	4	4	no	—
158	C₁₁×M₁₆	—	2	2	no	—
159	C₁₁×M₁₆	—	4	4	no	—
160	C₁₁×M₁₆	—	4	2	no	—
161	C₁₁×M₁₆	D₈	1	4	yes	complemented
162	C₂×C₈×C₁₁	—	2	1	no	—
163	C₂×C₈×C₁₁	—	2	1	no	—
164	C₂×C₈×C₁₁	—	2	2	no	—
165	C₂×C₈×C₁₁	—	2	2	no	—
166	C₂×C₈×C₁₁	—	4	2	no	—
167	C₂×C₈×C₁₁	—	4	4	no	—
168	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
169	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
170	C₁₁×C₄⋊C₄	—	2	1	no	—
171	C₁₁×C₄⋊C₄	—	2	1	no	—
172	C₁₁×C₄⋊C₄	—	2	1	no	—
173	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
174	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
175	C₁₁×C₂²⋊C₄	—	2	1	no	—
176	C₁₁×C₂²⋊C₄	—	2	1	no	—
177	C₁₁×C₂²⋊C₄	—	2	1	no	—
178	C₁₁×C₂²⋊C₄	—	2	1	no	—
179	C₁₁×C₂²⋊C₄	—	4	1	no	—
180	C₁₁×C₂²⋊C₄	—	4	1	no	—
181	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₁	#41	1	1	yes	characteristic
184	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
185	#3151	C₂×C₁₁	1	1	yes	characteristic, complemented
186	#3100	C₂×C₁₁	1	1	yes	characteristic, complemented
187	C₂×#459	C₂×C₁₁	1	1	yes	characteristic, complemented
188	D₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
189	#1687	C₂×C₁₁	1	2	yes	complemented
190	#1685	C₂×C₁₁	1	2	yes	complemented
191	#1667	C₂×C₁₁	1	2	yes	complemented
192	#1665	C₂×C₁₁	1	2	yes	complemented
193	#1565	C₂×C₁₁	1	1	yes	characteristic, complemented
194	#1547	C₂×C₁₁	1	1	yes	characteristic, complemented
195	#1545	C₂×C₁₁	1	1	yes	characteristic, complemented
196	C₂³×C₁₁	—	2	1	no	—
197	C₂³×C₁₁	—	2	1	no	—
198	C₂³×C₁₁	—	4	2	no	—
199	C₂³×C₁₁	—	4	2	no	—
200	C₂³×C₁₁	—	4	1	no	—
201	C₂³×C₁₁	—	4	2	no	—
202	C₂³×C₁₁	—	8	1	no	—
203	C₂³×C₁₁	—	8	2	no	—
204	C₂³×C₁₁	—	8	2	no	—
205	C₂³×C₁₁	—	8	2	no	—
206	C₂³×C₁₁	#121	1	1	yes	characteristic
207	Q₈×C₁₁	—	4	1	no	—
208	Q₈×C₁₁	—	4	1	no	—
209	D₄×C₁₁	—	2	1	no	—
210	D₄×C₁₁	—	2	1	no	—
211	D₄×C₁₁	—	2	1	no	—
212	D₄×C₁₁	—	4	2	no	—
213	D₄×C₁₁	—	4	1	no	—
214	D₄×C₁₁	—	4	2	no	—
215	D₄×C₁₁	—	4	2	no	—
216	D₄×C₁₁	—	4	1	no	—
217	D₄×C₁₁	—	4	2	no	—
218	D₄×C₁₁	—	4	1	no	—
219	D₄×C₁₁	—	4	1	no	—
220	D₄×C₁₁	—	4	2	no	—
221	D₄×C₁₁	—	8	1	no	—
222	D₄×C₁₁	—	8	2	no	—
223	D₄×C₁₁	—	8	2	no	—
224	D₄×C₁₁	—	8	2	no	—
225	D₄×C₁₁	—	8	2	no	—
226	D₄×C₁₁	—	8	2	no	—
227	D₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	complemented
228	C₂×C₄×C₁₁	—	2	1	no	—
229	C₂×C₄×C₁₁	—	2	1	no	—
230	C₂×C₄×C₁₁	—	2	1	no	—
231	C₂×C₄×C₁₁	—	2	1	no	—
232	C₂×C₄×C₁₁	—	4	1	no	—
233	C₂×C₄×C₁₁	—	4	2	no	—
234	C₂×C₄×C₁₁	—	4	1	no	—
235	C₂×C₄×C₁₁	—	4	1	no	—
236	C₂×C₄×C₁₁	—	4	1	no	—
237	C₂×C₄×C₁₁	—	4	1	no	—
238	C₂×C₄×C₁₁	—	4	2	no	—
239	C₂×C₄×C₁₁	—	4	2	no	—
240	C₂×C₄×C₁₁	—	4	1	no	—
241	C₂×C₄×C₁₁	—	8	2	no	—
242	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
243	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
244	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
245	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
246	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
247	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
250	C₈×C₁₁	—	2	2	no	—
251	C₈×C₁₁	—	4	2	no	—
252	C₈×C₁₁	—	4	2	no	—
253	C₈×C₁₁	—	4	1	no	—
254	C₈×C₁₁	—	4	1	no	—
255	C₈×C₁₁	C₂×D₈	1	4	yes	complemented
256	C₂×AGL(1,ℤ/8)	—	2	1	no	—
257	C₂×AGL(1,ℤ/8)	—	2	1	no	—
258	C₂²×D₈	—	2	1	no	—
259	C₂²×M₁₆	—	2	1	no	—
260	#532	C₂²×C₁₁	1	1	yes	characteristic
261	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
263	#496	—	2	2	no	—
264	#493	C₂²×C₁₁	1	2	yes	complemented
265	#492	C₂²×C₁₁	1	2	yes	complemented
266	#480	—	2	1	no	—
267	#474	C₂²×C₁₁	1	1	yes	characteristic, complemented
268	#474	C₂²×C₁₁	1	1	yes	characteristic, complemented
269	#459	—	2	1	no	—
270	#459	—	2	1	no	—
271	#459	C₂²×C₁₁	1	2	yes	—
272	#459	C₂²×C₁₁	1	2	yes	—
273	#459	C₂²×C₁₁	1	1	yes	characteristic, complemented
274	#459	C₂²×C₁₁	1	1	yes	characteristic, complemented
275	#447	—	2	1	no	—
276	C₄×D₈	—	2	1	no	—
277	C₄×D₈	—	2	1	no	—
278	#436	C₂²×C₁₁	1	2	yes	complemented
279	#435	—	2	2	no	—
280	C₈×D₄	C₂²×C₁₁	1	2	yes	complemented
281	#431	C₂²×C₁₁	1	1	yes	characteristic
282	#423	C₂²×C₁₁	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
284	C₂×#102	—	2	1	no	—
285	#407	—	2	1	no	—
286	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
287	#335	C₂²×C₁₁	1	2	yes	complemented
288	#334	C₂²×C₁₁	1	2	yes	complemented
289	#332	C₂²×C₁₁	1	2	yes	complemented
290	#331	C₂²×C₁₁	1	2	yes	complemented
291	#331	C₂²×C₁₁	1	2	yes	complemented
292	#331	C₂²×C₁₁	1	2	yes	complemented
293	C₂²×C₁₁	—	2	1	no	—
294	C₂²×C₁₁	—	2	1	no	—
295	C₂²×C₁₁	—	2	2	no	—
296	C₂²×C₁₁	—	4	1	no	—
297	C₂²×C₁₁	—	4	1	no	—
298	C₂²×C₁₁	—	4	1	no	—
299	C₂²×C₁₁	—	4	1	no	—
300	C₂²×C₁₁	—	4	1	no	—
301	C₂²×C₁₁	—	8	4	no	—
302	C₂²×C₁₁	—	8	1	no	—
303	C₂²×C₁₁	—	8	2	no	—
304	C₂²×C₁₁	—	8	2	no	—
305	C₂²×C₁₁	—	8	1	no	—
306	C₂²×C₁₁	—	8	2	no	—
307	C₂²×C₁₁	—	8	1	no	—
308	C₂²×C₁₁	—	16	4	no	—
309	C₂²×C₁₁	#459	1	2	yes	—
310	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
311	C₄×C₁₁	—	2	1	no	—
312	C₄×C₁₁	—	2	1	no	—
313	C₄×C₁₁	—	2	1	no	—
314	C₄×C₁₁	—	4	1	no	—
315	C₄×C₁₁	—	4	1	no	—
316	C₄×C₁₁	—	8	1	no	—
317	C₄×C₁₁	#459	1	2	yes	—
318	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
319	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
320	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
321	C₄×C₁₁	#575	1	1	yes	characteristic
322	C₂×#41	—	2	1	no	—
323	C₂²×D₄	—	2	1	no	—
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
327	C₂³×C₄	—	2	1	no	—
328	AGL(1,ℤ/8)	—	4	4	no	—
329	AGL(1,ℤ/8)	—	4	4	no	—
330	C₂×SD₁₆	—	2	2	no	—
331	C₂×SD₁₆	—	2	2	no	—
332	C₂×D₈	—	2	2	no	—
333	C₂×D₈	—	2	2	no	—
334	C₂×D₈	—	2	1	no	—
335	C₂×D₈	—	2	1	no	—
336	C₂×D₈	—	2	2	no	—
337	C₂×D₈	—	2	2	no	—
338	C₂×D₈	—	4	4	no	—
339	C₂×M₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	2	no	—
341	C₂×M₁₆	—	4	4	no	—
342	C₂×M₁₆	D₄×C₁₁	1	1	yes	characteristic
343	C₂×M₁₆	D₄×C₁₁	1	1	yes	characteristic
344	C₂²×C₈	—	2	1	no	—
345	C₂²×C₈	—	2	2	no	—
346	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
347	#127	—	2	1	no	—
348	#127	—	2	1	no	—
349	#127	—	2	1	no	—
350	#127	C₂³×C₁₁	1	2	yes	—
351	#127	C₂³×C₁₁	1	1	yes	characteristic
352	#124	—	2	1	no	—
353	#121	—	2	1	no	—
354	#121	—	2	1	no	—
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	D₄×C₁₁	1	1	yes	characteristic
360	C₄×D₄	D₄×C₁₁	1	1	yes	characteristic
361	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
362	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
363	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
366	#107	—	2	1	no	—
367	#107	—	2	1	no	—
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
371	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
372	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
373	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
374	#102	—	2	1	no	—
375	#102	—	2	1	no	—
376	#102	—	2	2	no	—
377	#102	—	2	2	no	—
378	#102	—	2	1	no	—
379	#102	—	2	1	no	—
380	C₂²⋊C₈	—	2	1	no	—
381	C₂²⋊C₈	—	2	2	no	—
382	C₂²⋊C₈	—	2	2	no	—
383	#97	D₄×C₁₁	1	2	yes	—
384	C₄×C₈	—	2	1	no	—
385	C₄×C₈	C₂³×C₁₁	1	2	yes	—
386	C₂×C₁₁	—	2	2	no	—
387	C₂×C₁₁	—	4	2	no	—
388	C₂×C₁₁	—	8	1	no	—
389	C₂×C₁₁	—	16	1	no	—
390	C₂×C₁₁	—	16	2	no	—
391	C₂×C₁₁	C₂×#459	1	1	yes	characteristic
392	C₂×C₁₁	#3055	1	1	yes	characteristic
393	C₂×C₁₁	#3068	1	1	yes	characteristic
394	C₂⁴	—	2	1	no	—
395	C₂⁴	—	4	1	no	—
396	#41	—	4	2	no	—
397	#41	—	4	2	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	4	1	no	—
408	C₂×D₄	—	4	2	no	—
409	C₂×D₄	—	4	2	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	—	4	1	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	4	2	no	—
416	C₂×D₄	—	8	2	no	—
417	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
418	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	4	2	no	—
426	C₂²×C₄	—	4	1	no	—
427	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
429	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
430	SD₁₆	—	4	4	no	—
431	SD₁₆	—	4	4	no	—
432	D₈	—	4	4	no	—
433	D₈	—	4	4	no	—
434	D₈	—	4	2	no	—
435	D₈	—	4	4	no	—
436	D₈	—	4	2	no	—
437	D₈	—	4	4	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	4	2	no	—
440	M₁₆	—	4	4	no	—
441	M₁₆	C₁₁×D₈	1	4	yes	complemented
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	4	2	no	—
447	C₂×C₈	—	4	4	no	—
448	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
449	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
454	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	4	1	no	—
460	C₂²⋊C₄	—	4	1	no	—
461	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
462	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
463	C₄²	C₁₁×#41	1	1	yes	characteristic
464	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
465	C₁₁	#19162	1	1	yes	characteristic, direct product factor, Sylow
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	8	1	no	—
473	C₂³	—	8	2	no	—
474	C₂³	—	8	2	no	—
475	C₂³	—	8	2	no	—
476	C₂³	C₁₁×#121	1	1	yes	characteristic
477	Q₈	—	4	1	no	—
478	Q₈	—	4	1	no	—
479	D₄	—	2	1	no	—
480	D₄	—	2	1	no	—
481	D₄	—	2	1	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	1	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	1	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	1	no	—
490	D₄	—	4	2	no	—
491	D₄	—	8	1	no	—
492	D₄	—	8	2	no	—
493	D₄	—	8	2	no	—
494	D₄	—	8	2	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	D₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	complemented
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	8	2	no	—
512	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
513	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
514	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
515	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
516	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
517	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
519	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	4	2	no	—
522	C₈	—	4	2	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	1	no	—
525	C₈	C₂×C₁₁×D₈	1	4	yes	complemented
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	8	4	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	2	no	—
537	C₂²	—	8	2	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	2	no	—
540	C₂²	—	8	1	no	—
541	C₂²	—	16	4	no	—
542	C₂²	C₁₁×#459	1	2	yes	—
543	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	8	1	no	—
550	C₄	C₁₁×#459	1	2	yes	—
551	C₄	C₂²×C₁₁×D₈	1	1	yes	characteristic
552	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
553	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
554	C₄	C₁₁×#575	1	1	yes	characteristic
555	C₂	—	2	2	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	1	no	—
558	C₂	—	16	2	no	—
559	C₂	—	16	1	no	—
560	C₂	C₂×C₁₁×#459	1	1	yes	characteristic
561	C₂	C₁₁×#3055	1	1	yes	characteristic
562	C₂	C₁₁×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3151	C₂	semidirect
2. C₁₁×#3100	C₂	semidirect
3. C₂×C₁₁×#459	C₂	semidirect
4. D₄×C₁₁×M₁₆	C₂	semidirect
5. C₁₁×#1687	C₂	semidirect
6. C₁₁×#1685	C₂	semidirect
7. C₁₁×#1667	C₂	semidirect
8. C₁₁×#1665	C₂	semidirect
9. C₁₁×#1565	C₂	semidirect
10. C₁₁×#1547	C₂	semidirect
11. C₁₁×#1545	C₂	semidirect
20. C₁₁×#493	C₂²	semidirect
21. C₁₁×#492	C₂²	semidirect
23. C₁₁×#474	C₂²	semidirect
24. C₁₁×#474	C₂²	semidirect
29. C₁₁×#459	C₂²	semidirect
30. C₁₁×#459	C₂²	semidirect
34. C₁₁×#436	C₂²	semidirect
36. C₈×D₄×C₁₁	C₂²	semidirect
43. C₁₁×#335	C₂²	semidirect
44. C₁₁×#334	C₂²	semidirect
45. C₁₁×#332	C₂²	semidirect
46. C₁₁×#331	C₂²	semidirect
47. C₁₁×#331	C₂²	semidirect
48. C₁₁×#331	C₂²	semidirect
113. #19162	C₁₁	direct (N × H)
161. C₁₁×M₁₆	D₈	semidirect
185. #3151	C₂×C₁₁	semidirect
186. #3100	C₂×C₁₁	semidirect
187. C₂×#459	C₂×C₁₁	semidirect
188. D₄×M₁₆	C₂×C₁₁	semidirect
189. #1687	C₂×C₁₁	semidirect
190. #1685	C₂×C₁₁	semidirect
191. #1667	C₂×C₁₁	semidirect
192. #1665	C₂×C₁₁	semidirect
193. #1565	C₂×C₁₁	semidirect
194. #1547	C₂×C₁₁	semidirect
195. #1545	C₂×C₁₁	semidirect
227. D₄×C₁₁	AGL(1,ℤ/8)	semidirect
255. C₈×C₁₁	C₂×D₈	semidirect
264. #493	C₂²×C₁₁	semidirect
265. #492	C₂²×C₁₁	semidirect
267. #474	C₂²×C₁₁	semidirect
268. #474	C₂²×C₁₁	semidirect
273. #459	C₂²×C₁₁	semidirect
274. #459	C₂²×C₁₁	semidirect
278. #436	C₂²×C₁₁	semidirect
280. C₈×D₄	C₂²×C₁₁	semidirect
287. #335	C₂²×C₁₁	semidirect
288. #334	C₂²×C₁₁	semidirect
289. #332	C₂²×C₁₁	semidirect
290. #331	C₂²×C₁₁	semidirect
291. #331	C₂²×C₁₁	semidirect
292. #331	C₂²×C₁₁	semidirect
441. M₁₆	C₁₁×D₈	semidirect
465. C₁₁	#19162	direct (N × H)
497. D₄	C₁₁×AGL(1,ℤ/8)	semidirect
525. C₈	C₂×C₁₁×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#3151	2
C₁₁×#3100	2
C₂×C₁₁×#459	2
D₄×C₁₁×M₁₆	2
C₁₁×#1687	2
C₁₁×#1685	2
C₁₁×#1667	2
C₁₁×#1665	2
C₁₁×#1565	2
C₁₁×#1547	2
C₁₁×#1545	2
#19162	11

Subgroups — C11×#19162 #14596355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19162 #14596355