Subgroups — C₁₁×#60713 #14637906

Order 2816.

1878 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×#3510	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3183	C₂	1	4	yes	maximal, complemented
3	C₁₁×#3175	C₂	1	4	yes	maximal, complemented
4	C₁₁×#3173	C₂	1	4	yes	maximal, complemented
5	C₁₁×#3168	C₂	1	4	yes	maximal, complemented
6	C₁₁×#3160	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#3140	C₂	1	2	yes	maximal, complemented
9	C₁₁×#3059	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#3058	C₂	1	1	yes	maximal, characteristic
11	C₁₁×#3057	C₂	1	2	yes	maximal, complemented
12	C₁₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₁×#2949	C₂	1	2	yes	maximal, complemented
14	C₁₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
18	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
21	C₁₁×#559	—	2	4	no	—
22	C₁₁×#556	—	2	4	no	—
23	C₁₁×#551	—	2	8	no	—
24	C₁₁×#542	C₂²	1	8	yes	complemented
25	C₁₁×#536	C₂²	1	2	yes	—
26	C₁₁×#535	C₂²	1	2	yes	—
27	C₁₁×#533	C₂²	1	2	yes	—
28	C₁₁×#529	C₂²	1	8	yes	complemented
29	C₂×C₁₁×#124	C₂²	1	2	yes	—
30	C₁₁×#519	C₂²	1	2	yes	—
31	C₁₁×#518	C₂²	1	2	yes	—
32	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
33	C₁₁×#500	C₂²	1	2	yes	complemented
34	C₁₁×#499	C₂²	1	2	yes	complemented
35	C₁₁×#499	C₂²	1	2	yes	complemented
36	C₁₁×#498	C₂²	1	2	yes	complemented
37	C₁₁×#495	C₂²	1	2	yes	—
38	C₁₁×#495	C₂²	1	2	yes	—
39	C₁₁×#495	C₂²	1	2	yes	—
40	C₁₁×#495	C₂²	1	2	yes	—
41	C₁₁×#489	C₂²	1	8	yes	complemented
42	C₁₁×#488	C₂²	1	8	yes	complemented
43	C₁₁×#470	C₂²	1	4	yes	complemented
44	C₁₁×#469	C₂²	1	4	yes	—
45	C₁₁×#468	C₂²	1	8	yes	complemented
46	C₁₁×#467	C₂²	1	4	yes	complemented
47	C₁₁×#466	C₂²	1	4	yes	—
48	C₁₁×#465	C₂²	1	8	yes	complemented
49	C₁₁×#442	C₂²	1	4	yes	—
50	C₁₁×#441	C₂²	1	4	yes	complemented
51	C₁₁×#440	C₂²	1	8	yes	complemented
52	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	complemented
53	C₄×C₁₁×SD₁₆	C₂²	1	8	yes	complemented
54	C₄×C₁₁×D₈	C₂²	1	4	yes	—
55	C₁₁×#427	C₂²	1	1	yes	characteristic
56	C₁₁×#427	C₂²	1	2	yes	—
57	C₁₁×#427	C₂²	1	1	yes	characteristic
58	C₁₁×#419	C₂²	1	2	yes	—
59	C₁₁×#419	C₂²	1	2	yes	—
60	C₁₁×#418	C₂²	1	2	yes	—
61	C₁₁×#418	C₂²	1	2	yes	—
62	C₁₁×#405	C₂²	1	1	yes	characteristic
63	C₁₁×#405	C₂²	1	1	yes	characteristic
64	C₁₁×#405	C₂²	1	2	yes	complemented
65	C₁₁×#405	C₂²	1	2	yes	complemented
66	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
67	C₄×C₁₁×M₁₆	C₂²	1	2	yes	complemented
68	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
69	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
70	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
73	C₂×C₁₁×Q₁₆	—	2	4	no	—
74	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
75	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
76	C₂×C₁₁×SD₁₆	—	2	8	no	—
77	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
78	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
79	C₂×C₁₁×D₈	—	2	4	no	—
80	C₂×C₁₁×D₈	C₂³	1	2	yes	—
81	C₂×C₁₁×D₈	C₂³	1	2	yes	—
82	C₁₁×#131	—	2	4	no	—
83	C₁₁×#131	—	2	4	no	—
84	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
87	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
88	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
89	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
90	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
92	C₁₁×C₄⋊Q₈	—	2	2	no	—
93	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
94	C₁₁×#127	—	2	2	no	—
95	C₁₁×#126	—	2	8	no	—
96	C₁₁×#126	—	2	8	no	—
97	C₁₁×#125	C₂³	1	4	yes	—
98	C₁₁×#124	—	2	2	no	—
99	C₁₁×#124	—	2	2	no	—
100	C₁₁×#124	—	2	8	no	—
101	C₁₁×#124	—	2	4	no	—
102	C₁₁×#124	C₂³	1	4	yes	—
103	C₁₁×#124	C₂³	1	4	yes	—
104	C₁₁×#123	—	2	4	no	—
105	C₁₁×#123	—	2	8	no	—
106	C₁₁×#123	—	2	8	no	—
107	C₁₁×C₂²⋊Q₈	—	2	4	no	—
108	C₁₁×C₂²⋊Q₈	—	2	8	no	—
109	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	—
110	C₁₁×#121	C₂³	1	8	yes	—
111	C₁₁×#120	—	2	4	no	—
112	C₄×Q₈×C₁₁	—	2	4	no	—
113	C₄×Q₈×C₁₁	—	2	4	no	—
114	C₄×Q₈×C₁₁	D₄	1	2	yes	—
115	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
116	C₄×D₄×C₁₁	—	2	8	no	—
117	C₄×D₄×C₁₁	—	2	4	no	—
118	C₄×D₄×C₁₁	D₄	1	4	yes	—
119	C₄×D₄×C₁₁	D₄	1	2	yes	—
120	C₄×D₄×C₁₁	C₂³	1	8	yes	—
121	C₁₁×#117	—	2	4	no	—
122	C₁₁×#117	—	2	8	no	—
123	C₁₁×#117	C₂³	1	2	yes	—
124	C₁₁×#117	C₂³	1	2	yes	—
125	C₁₁×#117	C₂³	1	1	yes	characteristic
126	C₁₁×#117	C₂³	1	2	yes	—
127	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
128	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
129	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
131	C₁₁×#107	C₂³	1	2	yes	—
132	C₁₁×#107	C₂³	1	2	yes	—
133	C₁₁×#107	C₂³	1	4	yes	—
134	C₁₁×#106	C₂³	1	4	yes	—
135	C₁₁×#106	C₂³	1	2	yes	—
136	C₁₁×#106	C₂³	1	2	yes	—
137	C₁₁×#103	C₂³	1	8	yes	—
138	C₁₁×#103	C₂³	1	8	yes	—
139	C₁₁×#102	C₂³	1	8	yes	—
140	C₁₁×#102	C₂³	1	8	yes	—
141	C₁₁×#97	C₂³	1	2	yes	—
142	C₁₁×#97	C₂³	1	2	yes	—
143	C₁₁×#97	C₂³	1	2	yes	—
144	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
146	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
147	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
148	C₄×C₈×C₁₁	C₂³	1	2	yes	—
149	C₄×C₈×C₁₁	C₂³	1	2	yes	—
150	C₄×C₈×C₁₁	C₂³	1	2	yes	—
151	#60713	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂⁴×C₁₁	—	2	2	no	—
153	C₁₁×#41	—	2	2	no	—
154	C₁₁×#41	—	2	2	no	—
155	C₂×Q₈×C₁₁	—	2	2	no	—
156	C₂×Q₈×C₁₁	—	2	4	no	—
157	C₂×Q₈×C₁₁	—	2	4	no	—
158	C₂×Q₈×C₁₁	—	2	4	no	—
159	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
160	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
161	C₂×D₄×C₁₁	—	2	8	no	—
162	C₂×D₄×C₁₁	—	2	2	no	—
163	C₂×D₄×C₁₁	—	2	4	no	—
164	C₂×D₄×C₁₁	—	2	4	no	—
165	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
166	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₁	—	2	2	no	—
169	C₂²×C₄×C₁₁	—	2	8	no	—
170	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
174	C₁₁×Q₁₆	—	2	4	no	—
175	C₁₁×Q₁₆	—	2	4	no	—
176	C₁₁×SD₁₆	—	2	8	no	—
177	C₁₁×SD₁₆	—	2	8	no	—
178	C₁₁×D₈	—	2	4	no	—
179	C₁₁×D₈	—	2	4	no	—
180	C₁₁×M₁₆	—	2	4	no	—
181	C₁₁×M₁₆	—	2	4	no	—
182	C₁₁×M₁₆	—	2	2	no	—
183	C₁₁×M₁₆	—	2	2	no	—
184	C₂×C₈×C₁₁	—	2	4	no	—
185	C₂×C₈×C₁₁	—	2	4	no	—
186	C₂×C₈×C₁₁	#41	1	4	yes	—
187	C₂×C₈×C₁₁	#41	1	4	yes	—
188	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
189	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
190	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
191	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
192	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
193	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
194	C₁₁×C₄⋊C₄	—	2	4	no	—
195	C₁₁×C₄⋊C₄	—	2	8	no	—
196	C₁₁×C₄⋊C₄	—	2	8	no	—
197	C₁₁×C₄⋊C₄	—	2	4	no	—
198	C₁₁×C₄⋊C₄	—	2	4	no	—
199	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
200	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
201	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
202	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
203	C₁₁×C₂²⋊C₄	—	2	2	no	—
204	C₁₁×C₂²⋊C₄	—	2	2	no	—
205	C₁₁×C₂²⋊C₄	—	2	8	no	—
206	C₁₁×C₂²⋊C₄	—	2	8	no	—
207	C₁₁×C₂²⋊C₄	—	2	8	no	—
208	C₁₁×C₂²⋊C₄	—	2	8	no	—
209	C₁₁×C₂²⋊C₄	—	2	8	no	—
210	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
211	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
212	C₄²×C₁₁	—	2	8	no	—
213	C₄²×C₁₁	—	2	2	no	—
214	C₄²×C₁₁	—	2	2	no	—
215	C₄²×C₁₁	C₂×D₄	1	4	yes	—
216	C₄²×C₁₁	C₂×D₄	1	2	yes	—
217	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
218	C₄²×C₁₁	C₂⁴	1	2	yes	—
219	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
220	#3510	C₂×C₁₁	1	2	yes	complemented
221	#3183	C₂×C₁₁	1	4	yes	complemented
222	#3175	C₂×C₁₁	1	4	yes	complemented
223	#3173	C₂×C₁₁	1	4	yes	complemented
224	#3168	C₂×C₁₁	1	4	yes	complemented
225	#3160	C₂×C₁₁	1	1	yes	characteristic, complemented
226	C₂×#495	C₂×C₁₁	1	1	yes	characteristic, complemented
227	#3140	C₂×C₁₁	1	2	yes	complemented
228	#3059	C₂×C₁₁	1	1	yes	characteristic, complemented
229	#3058	C₂×C₁₁	1	1	yes	characteristic
230	#3057	C₂×C₁₁	1	2	yes	complemented
231	#2950	C₂×C₁₁	1	1	yes	characteristic, complemented
232	#2949	C₂×C₁₁	1	2	yes	complemented
233	#2948	C₂×C₁₁	1	1	yes	characteristic, complemented
234	C₄×#131	C₂×C₁₁	1	1	yes	characteristic, complemented
235	C₂³×C₁₁	—	2	4	no	—
236	C₂³×C₁₁	—	4	4	no	—
237	C₂³×C₁₁	—	8	4	no	—
238	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
239	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
240	Q₈×C₁₁	—	2	2	no	—
241	Q₈×C₁₁	—	2	4	no	—
242	Q₈×C₁₁	—	2	4	no	—
243	Q₈×C₁₁	—	4	4	no	—
244	Q₈×C₁₁	—	8	4	no	—
245	D₄×C₁₁	—	2	4	no	—
246	D₄×C₁₁	—	2	2	no	—
247	D₄×C₁₁	—	2	4	no	—
248	D₄×C₁₁	—	2	4	no	—
249	D₄×C₁₁	—	4	4	no	—
250	D₄×C₁₁	—	8	8	no	—
251	C₂×C₄×C₁₁	—	2	2	no	—
252	C₂×C₄×C₁₁	—	2	2	no	—
253	C₂×C₄×C₁₁	—	2	4	no	—
254	C₂×C₄×C₁₁	—	2	4	no	—
255	C₂×C₄×C₁₁	—	2	4	no	—
256	C₂×C₄×C₁₁	—	4	4	no	—
257	C₂×C₄×C₁₁	—	4	2	no	—
258	C₂×C₄×C₁₁	—	4	4	no	—
259	C₂×C₄×C₁₁	—	8	8	no	—
260	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
261	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
266	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
267	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
268	C₈×C₁₁	—	2	2	no	—
269	C₈×C₁₁	—	2	2	no	—
270	C₈×C₁₁	C₂×#41	1	2	yes	—
271	C₈×C₁₁	C₂×#41	1	2	yes	—
272	C₈×C₁₁	C₂×#41	1	2	yes	—
273	C₈×C₁₁	C₂×#41	1	2	yes	—
274	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
275	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
276	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
277	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
278	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
279	#559	—	2	4	no	—
280	#556	—	2	4	no	—
281	#551	—	2	8	no	—
282	#542	C₂²×C₁₁	1	8	yes	complemented
283	#536	C₂²×C₁₁	1	2	yes	—
284	#535	C₂²×C₁₁	1	2	yes	—
285	#533	C₂²×C₁₁	1	2	yes	—
286	#529	C₂²×C₁₁	1	8	yes	complemented
287	C₂×#124	C₂²×C₁₁	1	2	yes	—
288	#519	C₂²×C₁₁	1	2	yes	—
289	#518	C₂²×C₁₁	1	2	yes	—
290	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
291	#500	C₂²×C₁₁	1	2	yes	complemented
292	#499	C₂²×C₁₁	1	2	yes	complemented
293	#499	C₂²×C₁₁	1	2	yes	complemented
294	#498	C₂²×C₁₁	1	2	yes	complemented
295	#495	C₂²×C₁₁	1	2	yes	—
296	#495	C₂²×C₁₁	1	2	yes	—
297	#495	C₂²×C₁₁	1	2	yes	—
298	#495	C₂²×C₁₁	1	2	yes	—
299	#489	C₂²×C₁₁	1	8	yes	complemented
300	#488	C₂²×C₁₁	1	8	yes	complemented
301	#470	C₂²×C₁₁	1	4	yes	complemented
302	#469	C₂²×C₁₁	1	4	yes	—
303	#468	C₂²×C₁₁	1	8	yes	complemented
304	#467	C₂²×C₁₁	1	4	yes	complemented
305	#466	C₂²×C₁₁	1	4	yes	—
306	#465	C₂²×C₁₁	1	8	yes	complemented
307	#442	C₂²×C₁₁	1	4	yes	—
308	#441	C₂²×C₁₁	1	4	yes	complemented
309	#440	C₂²×C₁₁	1	8	yes	complemented
310	C₄×Q₁₆	C₂²×C₁₁	1	4	yes	complemented
311	C₄×SD₁₆	C₂²×C₁₁	1	8	yes	complemented
312	C₄×D₈	C₂²×C₁₁	1	4	yes	—
313	#427	C₂²×C₁₁	1	1	yes	characteristic
314	#427	C₂²×C₁₁	1	2	yes	—
315	#427	C₂²×C₁₁	1	1	yes	characteristic
316	#419	C₂²×C₁₁	1	2	yes	—
317	#419	C₂²×C₁₁	1	2	yes	—
318	#418	C₂²×C₁₁	1	2	yes	—
319	#418	C₂²×C₁₁	1	2	yes	—
320	#405	C₂²×C₁₁	1	1	yes	characteristic
321	#405	C₂²×C₁₁	1	1	yes	characteristic
322	#405	C₂²×C₁₁	1	2	yes	complemented
323	#405	C₂²×C₁₁	1	2	yes	complemented
324	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
325	C₄×M₁₆	C₂²×C₁₁	1	2	yes	complemented
326	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
327	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
328	C₂²×C₁₁	—	2	2	no	—
329	C₂²×C₁₁	—	2	4	no	—
330	C₂²×C₁₁	—	2	2	no	—
331	C₂²×C₁₁	—	4	8	no	—
332	C₂²×C₁₁	—	4	4	no	—
333	C₂²×C₁₁	—	16	4	no	—
334	C₂²×C₁₁	#532	1	2	yes	—
335	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
336	C₄×C₁₁	—	2	2	no	—
337	C₄×C₁₁	—	2	4	no	—
338	C₄×C₁₁	—	2	2	no	—
339	C₄×C₁₁	—	2	2	no	—
340	C₄×C₁₁	—	4	4	no	—
341	C₄×C₁₁	—	4	4	no	—
342	C₄×C₁₁	—	4	4	no	—
343	C₄×C₁₁	#532	1	2	yes	—
344	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
345	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
346	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
347	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
348	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
349	C₂×Q₁₆	—	2	4	no	—
350	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
351	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
352	C₂×SD₁₆	—	2	8	no	—
353	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
354	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
355	C₂×D₈	—	2	4	no	—
356	C₂×D₈	C₂³×C₁₁	1	2	yes	—
357	C₂×D₈	C₂³×C₁₁	1	2	yes	—
358	#131	—	2	4	no	—
359	#131	—	2	4	no	—
360	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
361	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
362	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
363	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
364	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
365	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
366	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
368	C₄⋊Q₈	—	2	2	no	—
369	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
370	#127	—	2	2	no	—
371	#126	—	2	8	no	—
372	#126	—	2	8	no	—
373	#125	C₂³×C₁₁	1	4	yes	—
374	#124	—	2	2	no	—
375	#124	—	2	2	no	—
376	#124	—	2	8	no	—
377	#124	—	2	4	no	—
378	#124	C₂³×C₁₁	1	4	yes	—
379	#124	C₂³×C₁₁	1	4	yes	—
380	#123	—	2	4	no	—
381	#123	—	2	8	no	—
382	#123	—	2	8	no	—
383	C₂²⋊Q₈	—	2	4	no	—
384	C₂²⋊Q₈	—	2	8	no	—
385	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	—
386	#121	C₂³×C₁₁	1	8	yes	—
387	#120	—	2	4	no	—
388	C₄×Q₈	—	2	4	no	—
389	C₄×Q₈	—	2	4	no	—
390	C₄×Q₈	D₄×C₁₁	1	2	yes	—
391	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
392	C₄×D₄	—	2	8	no	—
393	C₄×D₄	—	2	4	no	—
394	C₄×D₄	D₄×C₁₁	1	4	yes	—
395	C₄×D₄	D₄×C₁₁	1	2	yes	—
396	C₄×D₄	C₂³×C₁₁	1	8	yes	—
397	#117	—	2	4	no	—
398	#117	—	2	8	no	—
399	#117	C₂³×C₁₁	1	2	yes	—
400	#117	C₂³×C₁₁	1	2	yes	—
401	#117	C₂³×C₁₁	1	1	yes	characteristic
402	#117	C₂³×C₁₁	1	2	yes	—
403	C₂×C₂²⋊C₄	—	2	4	no	—
404	C₂×C₂²⋊C₄	—	2	4	no	—
405	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
407	#107	C₂³×C₁₁	1	2	yes	—
408	#107	C₂³×C₁₁	1	2	yes	—
409	#107	C₂³×C₁₁	1	4	yes	—
410	#106	C₂³×C₁₁	1	4	yes	—
411	#106	C₂³×C₁₁	1	2	yes	—
412	#106	C₂³×C₁₁	1	2	yes	—
413	#103	C₂³×C₁₁	1	8	yes	—
414	#103	C₂³×C₁₁	1	8	yes	—
415	#102	C₂³×C₁₁	1	8	yes	—
416	#102	C₂³×C₁₁	1	8	yes	—
417	#97	C₂³×C₁₁	1	2	yes	—
418	#97	C₂³×C₁₁	1	2	yes	—
419	#97	C₂³×C₁₁	1	2	yes	—
420	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
421	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
422	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
423	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
424	C₄×C₈	C₂³×C₁₁	1	2	yes	—
425	C₄×C₈	C₂³×C₁₁	1	2	yes	—
426	C₄×C₈	C₂³×C₁₁	1	2	yes	—
427	C₂×C₁₁	—	2	2	no	—
428	C₂×C₁₁	—	4	2	no	—
429	C₂×C₁₁	—	8	4	no	—
430	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
431	C₂×C₁₁	#3584	1	2	yes	—
432	C₂⁴	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	4	no	—
437	C₂×Q₈	—	2	4	no	—
438	C₂×Q₈	—	2	4	no	—
439	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
440	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
446	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
447	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	8	no	—
450	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
451	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
454	Q₁₆	—	2	4	no	—
455	Q₁₆	—	2	4	no	—
456	SD₁₆	—	2	8	no	—
457	SD₁₆	—	2	8	no	—
458	D₈	—	2	4	no	—
459	D₈	—	2	4	no	—
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	2	4	no	—
463	M₁₆	—	2	4	no	—
464	C₂×C₈	—	2	4	no	—
465	C₂×C₈	—	2	4	no	—
466	C₂×C₈	C₁₁×#41	1	4	yes	—
467	C₂×C₈	C₁₁×#41	1	4	yes	—
468	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
469	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
470	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
471	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
472	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
473	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	8	no	—
476	C₄⋊C₄	—	2	8	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
480	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
481	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
482	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	8	no	—
486	C₂²⋊C₄	—	2	8	no	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
491	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
492	C₄²	—	2	8	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₄²	C₂×D₄×C₁₁	1	4	yes	—
496	C₄²	C₂×D₄×C₁₁	1	2	yes	—
497	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
498	C₄²	C₂⁴×C₁₁	1	2	yes	—
499	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
500	C₁₁	#60713	1	1	yes	characteristic, direct product factor, Sylow
501	C₂³	—	2	4	no	—
502	C₂³	—	4	4	no	—
503	C₂³	—	8	4	no	—
504	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
505	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
506	Q₈	—	2	2	no	—
507	Q₈	—	2	4	no	—
508	Q₈	—	2	4	no	—
509	Q₈	—	4	4	no	—
510	Q₈	—	8	4	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	4	no	—
514	D₄	—	2	4	no	—
515	D₄	—	4	4	no	—
516	D₄	—	8	8	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	8	8	no	—
526	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
527	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
528	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
530	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
531	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
532	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
533	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
534	C₈	—	2	2	no	—
535	C₈	—	2	2	no	—
536	C₈	C₂×C₁₁×#41	1	2	yes	—
537	C₈	C₂×C₁₁×#41	1	2	yes	—
538	C₈	C₂×C₁₁×#41	1	2	yes	—
539	C₈	C₂×C₁₁×#41	1	2	yes	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	8	no	—
545	C₂²	—	16	4	no	—
546	C₂²	C₁₁×#532	1	2	yes	—
547	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	4	no	—
551	C₄	—	2	2	no	—
552	C₄	—	4	4	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	4	no	—
555	C₄	C₁₁×#532	1	2	yes	—
556	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
557	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
558	C₂	—	2	2	no	—
559	C₂	—	4	2	no	—
560	C₂	—	8	4	no	—
561	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
562	C₂	C₁₁×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₁₁×#3058	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄×C₁₁×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3510	C₂	semidirect
2. C₁₁×#3183	C₂	semidirect
3. C₁₁×#3175	C₂	semidirect
4. C₁₁×#3173	C₂	semidirect
5. C₁₁×#3168	C₂	semidirect
6. C₁₁×#3160	C₂	semidirect
7. C₂×C₁₁×#495	C₂	semidirect
8. C₁₁×#3140	C₂	semidirect
9. C₁₁×#3059	C₂	semidirect
11. C₁₁×#3057	C₂	semidirect
12. C₁₁×#2950	C₂	semidirect
13. C₁₁×#2949	C₂	semidirect
14. C₁₁×#2948	C₂	semidirect
15. C₄×C₁₁×#131	C₂	semidirect
24. C₁₁×#542	C₂²	semidirect
28. C₁₁×#529	C₂²	semidirect
33. C₁₁×#500	C₂²	semidirect
34. C₁₁×#499	C₂²	semidirect
35. C₁₁×#499	C₂²	semidirect
36. C₁₁×#498	C₂²	semidirect
41. C₁₁×#489	C₂²	semidirect
42. C₁₁×#488	C₂²	semidirect
43. C₁₁×#470	C₂²	semidirect
45. C₁₁×#468	C₂²	semidirect
46. C₁₁×#467	C₂²	semidirect
48. C₁₁×#465	C₂²	semidirect
50. C₁₁×#441	C₂²	semidirect
51. C₁₁×#440	C₂²	semidirect
52. C₄×C₁₁×Q₁₆	C₂²	semidirect
53. C₄×C₁₁×SD₁₆	C₂²	semidirect
64. C₁₁×#405	C₂²	semidirect
65. C₁₁×#405	C₂²	semidirect
67. C₄×C₁₁×M₁₆	C₂²	semidirect
69. C₂×C₄×C₈×C₁₁	C₂²	semidirect
151. #60713	C₁₁	direct (N × H)
220. #3510	C₂×C₁₁	semidirect
221. #3183	C₂×C₁₁	semidirect
222. #3175	C₂×C₁₁	semidirect
223. #3173	C₂×C₁₁	semidirect
224. #3168	C₂×C₁₁	semidirect
225. #3160	C₂×C₁₁	semidirect
226. C₂×#495	C₂×C₁₁	semidirect
227. #3140	C₂×C₁₁	semidirect
228. #3059	C₂×C₁₁	semidirect
230. #3057	C₂×C₁₁	semidirect
231. #2950	C₂×C₁₁	semidirect
232. #2949	C₂×C₁₁	semidirect
233. #2948	C₂×C₁₁	semidirect
234. C₄×#131	C₂×C₁₁	semidirect
282. #542	C₂²×C₁₁	semidirect
286. #529	C₂²×C₁₁	semidirect
291. #500	C₂²×C₁₁	semidirect
292. #499	C₂²×C₁₁	semidirect
293. #499	C₂²×C₁₁	semidirect
294. #498	C₂²×C₁₁	semidirect
299. #489	C₂²×C₁₁	semidirect
300. #488	C₂²×C₁₁	semidirect
301. #470	C₂²×C₁₁	semidirect
303. #468	C₂²×C₁₁	semidirect
304. #467	C₂²×C₁₁	semidirect
306. #465	C₂²×C₁₁	semidirect
308. #441	C₂²×C₁₁	semidirect
309. #440	C₂²×C₁₁	semidirect
310. C₄×Q₁₆	C₂²×C₁₁	semidirect
311. C₄×SD₁₆	C₂²×C₁₁	semidirect
322. #405	C₂²×C₁₁	semidirect
323. #405	C₂²×C₁₁	semidirect
325. C₄×M₁₆	C₂²×C₁₁	semidirect
327. C₂×C₄×C₈	C₂²×C₁₁	semidirect
500. C₁₁	#60713	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3510	2
C₁₁×#3183	2
C₁₁×#3175	2
C₁₁×#3173	2
C₁₁×#3168	2
C₁₁×#3160	2
C₂×C₁₁×#495	2
C₁₁×#3140	2
C₁₁×#3059	2
C₁₁×#3058	2
C₁₁×#3057	2
C₁₁×#2950	2
C₁₁×#2949	2
C₁₁×#2948	2
C₄×C₁₁×#131	2
#60713	11

Subgroups — C11×#60713 #14637906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60713 #14637906