Subgroups — C₁₁×#60712 #14637905

Order 2816.

1950 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3508	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#3182	C₂	1	4	yes	maximal, complemented
4	C₁₁×#3174	C₂	1	8	yes	maximal, complemented
5	C₁₁×#3167	C₂	1	4	yes	maximal, complemented
6	C₁₁×#3160	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#3057	C₂	1	4	yes	maximal, complemented
11	C₁₁×#2949	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₁×SD₁₆	C₂²	1	4	yes	—
14	C₂×C₁₁×#131	C₂²	1	2	yes	—
15	C₁₁×#559	—	2	2	no	—
16	C₁₁×#557	—	2	2	no	—
17	C₁₁×#556	—	2	2	no	—
18	C₁₁×#552	—	2	4	no	—
19	C₁₁×#550	—	2	2	no	—
20	C₁₁×#546	—	2	4	no	—
21	C₁₁×#541	C₂²	1	4	yes	complemented
22	C₁₁×#540	C₂²	1	4	yes	—
23	C₁₁×#536	C₂²	1	2	yes	—
24	C₁₁×#535	C₂²	1	2	yes	—
25	C₁₁×#533	C₂²	1	1	yes	characteristic
26	C₁₁×#533	C₂²	1	1	yes	characteristic
27	C₁₁×#533	C₂²	1	4	yes	complemented
28	C₁₁×#532	C₂²	1	4	yes	—
29	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
31	C₁₁×#519	C₂²	1	2	yes	—
32	C₁₁×#518	C₂²	1	2	yes	—
33	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
34	C₁₁×#500	C₂²	1	2	yes	complemented
35	C₁₁×#499	C₂²	1	4	yes	complemented
36	C₁₁×#498	C₂²	1	2	yes	complemented
37	C₁₁×#492	C₂²	1	2	yes	—
38	C₁₁×#492	C₂²	1	4	yes	—
39	C₁₁×#492	C₂²	1	2	yes	—
40	C₁₁×#491	C₂²	1	4	yes	complemented
41	C₁₁×#490	C₂²	1	4	yes	—
42	C₁₁×#487	C₂²	1	4	yes	complemented
43	C₁₁×#486	C₂²	1	4	yes	—
44	C₁₁×#468	C₂²	1	16	yes	complemented
45	C₁₁×#465	C₂²	1	16	yes	complemented
46	C₁₁×#440	C₂²	1	16	yes	complemented
47	C₄×C₁₁×SD₁₆	C₂²	1	16	yes	complemented
48	C₁₁×#427	C₂²	1	4	yes	—
49	C₁₁×#419	C₂²	1	4	yes	—
50	C₁₁×#418	C₂²	1	4	yes	—
51	C₁₁×#405	C₂²	1	2	yes	—
52	C₁₁×#405	C₂²	1	4	yes	complemented
53	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
54	C₄×C₁₁×M₁₆	C₂²	1	2	yes	complemented
55	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
57	C₂×C₁₁×#41	—	2	4	no	—
58	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₁	—	2	2	no	—
61	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
62	C₂×C₁₁×SD₁₆	—	2	16	no	—
63	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
64	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
65	C₁₁×#131	—	2	8	no	—
66	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
67	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
68	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
69	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
70	C₁₁×C₄⋊Q₈	—	2	2	no	—
71	C₁₁×C₄⋊Q₈	—	2	2	no	—
72	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
73	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
75	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
76	C₁₁×#127	—	2	2	no	—
77	C₁₁×#127	—	2	2	no	—
78	C₁₁×#127	C₂³	1	2	yes	—
79	C₁₁×#127	C₂³	1	2	yes	—
80	C₁₁×#126	—	2	8	no	—
81	C₁₁×#125	—	2	8	no	—
82	C₁₁×#125	—	2	4	no	—
83	C₁₁×#125	C₂³	1	2	yes	—
84	C₁₁×#125	C₂³	1	2	yes	—
85	C₁₁×#124	—	2	2	no	—
86	C₁₁×#124	—	2	2	no	—
87	C₁₁×#124	—	2	4	no	—
88	C₁₁×#123	—	2	4	no	—
89	C₁₁×#123	—	2	8	no	—
90	C₁₁×C₂²⋊Q₈	—	2	2	no	—
91	C₁₁×C₂²⋊Q₈	—	2	2	no	—
92	C₁₁×C₂²⋊Q₈	—	2	4	no	—
93	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	—
94	C₁₁×#121	—	2	4	no	—
95	C₁₁×#121	—	2	8	no	—
96	C₁₁×#121	C₂³	1	8	yes	—
97	C₁₁×#120	—	2	4	no	—
98	C₄×Q₈×C₁₁	—	2	4	no	—
99	C₄×Q₈×C₁₁	—	2	2	no	—
100	C₄×Q₈×C₁₁	—	2	2	no	—
101	C₄×Q₈×C₁₁	—	2	4	no	—
102	C₄×Q₈×C₁₁	D₄	1	2	yes	—
103	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
104	C₄×D₄×C₁₁	—	2	4	no	—
105	C₄×D₄×C₁₁	—	2	4	no	—
106	C₄×D₄×C₁₁	D₄	1	4	yes	—
107	C₄×D₄×C₁₁	D₄	1	2	yes	—
108	C₄×D₄×C₁₁	C₂³	1	8	yes	—
109	C₁₁×#117	—	2	4	no	—
110	C₁₁×#117	—	2	4	no	—
111	C₁₁×#117	C₂³	1	2	yes	—
112	C₁₁×#117	C₂³	1	2	yes	—
113	C₁₁×#117	C₂³	1	1	yes	characteristic
114	C₁₁×#117	C₂³	1	2	yes	—
115	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
116	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
117	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
119	C₁₁×#107	C₂³	1	8	yes	—
120	C₁₁×#106	C₂³	1	8	yes	—
121	C₁₁×#103	C₂³	1	16	yes	—
122	C₁₁×#102	C₂³	1	16	yes	—
123	C₁₁×#97	C₂³	1	2	yes	—
124	C₁₁×#97	C₂³	1	4	yes	—
125	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
126	C₄×C₈×C₁₁	C₂³	1	2	yes	—
127	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
128	C₄×C₈×C₁₁	C₂³	1	2	yes	—
129	C₄×C₈×C₁₁	C₂³	1	4	yes	—
130	#60712	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂⁴×C₁₁	—	2	2	no	—
132	C₁₁×#41	—	2	4	no	—
133	C₁₁×#41	—	8	8	no	—
134	C₂×Q₈×C₁₁	—	2	2	no	—
135	C₂×Q₈×C₁₁	—	2	2	no	—
136	C₂×Q₈×C₁₁	—	2	2	no	—
137	C₂×Q₈×C₁₁	—	2	8	no	—
138	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
140	C₂×D₄×C₁₁	—	2	8	no	—
141	C₂×D₄×C₁₁	—	2	2	no	—
142	C₂×D₄×C₁₁	—	2	4	no	—
143	C₂×D₄×C₁₁	—	2	4	no	—
144	C₂×D₄×C₁₁	—	2	8	no	—
145	C₂×D₄×C₁₁	—	8	4	no	—
146	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
147	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
148	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₁	—	2	2	no	—
150	C₂²×C₄×C₁₁	—	2	8	no	—
151	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
155	C₁₁×SD₁₆	—	2	16	no	—
156	C₁₁×SD₁₆	—	2	16	no	—
157	C₁₁×M₁₆	—	2	8	no	—
158	C₁₁×M₁₆	—	2	4	no	—
159	C₂×C₈×C₁₁	—	2	8	no	—
160	C₂×C₈×C₁₁	#41	1	8	yes	complemented
161	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
162	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
163	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
164	C₁₁×C₄⋊C₄	—	2	4	no	—
165	C₁₁×C₄⋊C₄	—	2	4	no	—
166	C₁₁×C₄⋊C₄	—	2	2	no	—
167	C₁₁×C₄⋊C₄	—	2	8	no	—
168	C₁₁×C₄⋊C₄	—	2	2	no	—
169	C₁₁×C₄⋊C₄	—	2	4	no	—
170	C₁₁×C₄⋊C₄	—	2	4	no	—
171	C₁₁×C₄⋊C₄	—	2	8	no	—
172	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
173	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
174	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
175	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
176	C₁₁×C₂²⋊C₄	—	2	2	no	—
177	C₁₁×C₂²⋊C₄	—	2	2	no	—
178	C₁₁×C₂²⋊C₄	—	2	8	no	—
179	C₁₁×C₂²⋊C₄	—	2	8	no	—
180	C₁₁×C₂²⋊C₄	—	2	8	no	—
181	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
182	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
183	C₄²×C₁₁	—	2	8	no	—
184	C₄²×C₁₁	—	2	2	no	—
185	C₄²×C₁₁	—	2	2	no	—
186	C₄²×C₁₁	C₂×D₄	1	4	yes	—
187	C₄²×C₁₁	C₂×D₄	1	2	yes	—
188	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
189	C₄²×C₁₁	C₂⁴	1	2	yes	—
190	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
191	#3509	C₂×C₁₁	1	1	yes	characteristic, complemented
192	#3508	C₂×C₁₁	1	1	yes	characteristic
193	#3182	C₂×C₁₁	1	4	yes	complemented
194	#3174	C₂×C₁₁	1	8	yes	complemented
195	#3167	C₂×C₁₁	1	4	yes	complemented
196	#3160	C₂×C₁₁	1	1	yes	characteristic, complemented
197	C₂×#492	C₂×C₁₁	1	1	yes	characteristic, complemented
198	#3139	C₂×C₁₁	1	1	yes	characteristic, complemented
199	#3138	C₂×C₁₁	1	1	yes	characteristic, complemented
200	#3057	C₂×C₁₁	1	4	yes	complemented
201	#2949	C₂×C₁₁	1	4	yes	complemented
202	C₄×#131	C₂×C₁₁	1	1	yes	characteristic, complemented
203	C₂³×C₁₁	—	2	4	no	—
204	C₂³×C₁₁	—	4	4	no	—
205	C₂³×C₁₁	—	8	4	no	—
206	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
207	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₁₁	—	2	2	no	—
209	Q₈×C₁₁	—	2	8	no	—
210	Q₈×C₁₁	—	4	4	no	—
211	Q₈×C₁₁	—	4	4	no	—
212	Q₈×C₁₁	—	4	4	no	—
213	D₄×C₁₁	—	2	4	no	—
214	D₄×C₁₁	—	2	2	no	—
215	D₄×C₁₁	—	2	8	no	—
216	D₄×C₁₁	—	4	4	no	—
217	D₄×C₁₁	—	4	8	no	—
218	D₄×C₁₁	—	8	4	no	—
219	D₄×C₁₁	—	8	8	no	—
220	C₂×C₄×C₁₁	—	2	4	no	—
221	C₂×C₄×C₁₁	—	2	8	no	—
222	C₂×C₄×C₁₁	—	2	4	no	—
223	C₂×C₄×C₁₁	—	2	4	no	—
224	C₂×C₄×C₁₁	—	2	4	no	—
225	C₂×C₄×C₁₁	—	2	4	no	—
226	C₂×C₄×C₁₁	—	4	4	no	—
227	C₂×C₄×C₁₁	—	8	8	no	—
228	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
229	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
234	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
235	C₈×C₁₁	—	2	4	no	—
236	C₈×C₁₁	C₂×#41	1	4	yes	—
237	C₈×C₁₁	C₂×#41	1	4	yes	—
238	C₂²×SD₁₆	C₂²×C₁₁	1	4	yes	—
239	C₂×#131	C₂²×C₁₁	1	2	yes	—
240	#559	—	2	2	no	—
241	#557	—	2	2	no	—
242	#556	—	2	2	no	—
243	#552	—	2	4	no	—
244	#550	—	2	2	no	—
245	#546	—	2	4	no	—
246	#541	C₂²×C₁₁	1	4	yes	complemented
247	#540	C₂²×C₁₁	1	4	yes	—
248	#536	C₂²×C₁₁	1	2	yes	—
249	#535	C₂²×C₁₁	1	2	yes	—
250	#533	C₂²×C₁₁	1	1	yes	characteristic
251	#533	C₂²×C₁₁	1	1	yes	characteristic
252	#533	C₂²×C₁₁	1	4	yes	complemented
253	#532	C₂²×C₁₁	1	4	yes	—
254	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
255	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
256	#519	C₂²×C₁₁	1	2	yes	—
257	#518	C₂²×C₁₁	1	2	yes	—
258	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
259	#500	C₂²×C₁₁	1	2	yes	complemented
260	#499	C₂²×C₁₁	1	4	yes	complemented
261	#498	C₂²×C₁₁	1	2	yes	complemented
262	#492	C₂²×C₁₁	1	2	yes	—
263	#492	C₂²×C₁₁	1	4	yes	—
264	#492	C₂²×C₁₁	1	2	yes	—
265	#491	C₂²×C₁₁	1	4	yes	complemented
266	#490	C₂²×C₁₁	1	4	yes	—
267	#487	C₂²×C₁₁	1	4	yes	complemented
268	#486	C₂²×C₁₁	1	4	yes	—
269	#468	C₂²×C₁₁	1	16	yes	complemented
270	#465	C₂²×C₁₁	1	16	yes	complemented
271	#440	C₂²×C₁₁	1	16	yes	complemented
272	C₄×SD₁₆	C₂²×C₁₁	1	16	yes	complemented
273	#427	C₂²×C₁₁	1	4	yes	—
274	#419	C₂²×C₁₁	1	4	yes	—
275	#418	C₂²×C₁₁	1	4	yes	—
276	#405	C₂²×C₁₁	1	2	yes	—
277	#405	C₂²×C₁₁	1	4	yes	complemented
278	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
279	C₄×M₁₆	C₂²×C₁₁	1	2	yes	complemented
280	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
281	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
282	C₂²×C₁₁	—	2	2	no	—
283	C₂²×C₁₁	—	2	2	no	—
284	C₂²×C₁₁	—	2	4	no	—
285	C₂²×C₁₁	—	4	4	no	—
286	C₂²×C₁₁	—	4	8	no	—
287	C₂²×C₁₁	—	16	4	no	—
288	C₂²×C₁₁	#532	1	2	yes	—
289	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
290	C₄×C₁₁	—	2	2	no	—
291	C₄×C₁₁	—	2	4	no	—
292	C₄×C₁₁	—	2	2	no	—
293	C₄×C₁₁	—	4	4	no	—
294	C₄×C₁₁	—	4	4	no	—
295	C₄×C₁₁	—	4	4	no	—
296	C₄×C₁₁	#532	1	2	yes	—
297	C₄×C₁₁	#577	1	4	yes	—
298	C₄×C₁₁	C₂²×#41	1	2	yes	—
299	C₂×#41	—	2	4	no	—
300	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
301	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
302	C₂²×D₄	—	2	2	no	—
303	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
304	C₂×SD₁₆	—	2	16	no	—
305	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
306	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
307	#131	—	2	8	no	—
308	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
309	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
310	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
311	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
312	C₄⋊Q₈	—	2	2	no	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
315	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
316	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
317	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
318	#127	—	2	2	no	—
319	#127	—	2	2	no	—
320	#127	C₂³×C₁₁	1	2	yes	—
321	#127	C₂³×C₁₁	1	2	yes	—
322	#126	—	2	8	no	—
323	#125	—	2	8	no	—
324	#125	—	2	4	no	—
325	#125	C₂³×C₁₁	1	2	yes	—
326	#125	C₂³×C₁₁	1	2	yes	—
327	#124	—	2	2	no	—
328	#124	—	2	2	no	—
329	#124	—	2	4	no	—
330	#123	—	2	4	no	—
331	#123	—	2	8	no	—
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	C₂²⋊Q₈	—	2	4	no	—
335	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	—
336	#121	—	2	4	no	—
337	#121	—	2	8	no	—
338	#121	C₂³×C₁₁	1	8	yes	—
339	#120	—	2	4	no	—
340	C₄×Q₈	—	2	4	no	—
341	C₄×Q₈	—	2	2	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	4	no	—
344	C₄×Q₈	D₄×C₁₁	1	2	yes	—
345	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	4	no	—
348	C₄×D₄	D₄×C₁₁	1	4	yes	—
349	C₄×D₄	D₄×C₁₁	1	2	yes	—
350	C₄×D₄	C₂³×C₁₁	1	8	yes	—
351	#117	—	2	4	no	—
352	#117	—	2	4	no	—
353	#117	C₂³×C₁₁	1	2	yes	—
354	#117	C₂³×C₁₁	1	2	yes	—
355	#117	C₂³×C₁₁	1	1	yes	characteristic
356	#117	C₂³×C₁₁	1	2	yes	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	4	no	—
359	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
360	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
361	#107	C₂³×C₁₁	1	8	yes	—
362	#106	C₂³×C₁₁	1	8	yes	—
363	#103	C₂³×C₁₁	1	16	yes	—
364	#102	C₂³×C₁₁	1	16	yes	—
365	#97	C₂³×C₁₁	1	2	yes	—
366	#97	C₂³×C₁₁	1	4	yes	—
367	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
368	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
369	C₄×C₈	C₂³×C₁₁	1	2	yes	—
370	C₄×C₈	C₂³×C₁₁	1	2	yes	—
371	C₄×C₈	C₂³×C₁₁	1	4	yes	—
372	C₂×C₁₁	—	2	2	no	—
373	C₂×C₁₁	—	4	2	no	—
374	C₂×C₁₁	—	8	4	no	—
375	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
376	C₂×C₁₁	C₂×#577	1	2	yes	—
377	C₂⁴	—	2	2	no	—
378	#41	—	2	4	no	—
379	#41	—	8	8	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	8	no	—
384	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
385	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	8	no	—
391	C₂×D₄	—	8	4	no	—
392	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
393	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
394	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	8	no	—
397	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
399	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
401	SD₁₆	—	2	16	no	—
402	SD₁₆	—	2	16	no	—
403	M₁₆	—	2	4	no	—
404	M₁₆	—	2	8	no	—
405	C₂×C₈	—	2	8	no	—
406	C₂×C₈	C₁₁×#41	1	8	yes	complemented
407	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
408	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
409	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
419	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
420	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
421	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
428	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
429	C₄²	—	2	8	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	C₂×D₄×C₁₁	1	4	yes	—
433	C₄²	C₂×D₄×C₁₁	1	2	yes	—
434	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
435	C₄²	C₂⁴×C₁₁	1	2	yes	—
436	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
437	C₁₁	#60712	1	1	yes	characteristic, direct product factor, Sylow
438	C₂³	—	2	4	no	—
439	C₂³	—	4	4	no	—
440	C₂³	—	8	4	no	—
441	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
442	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
443	Q₈	—	2	2	no	—
444	Q₈	—	2	8	no	—
445	Q₈	—	4	4	no	—
446	Q₈	—	4	4	no	—
447	Q₈	—	4	4	no	—
448	D₄	—	2	4	no	—
449	D₄	—	2	2	no	—
450	D₄	—	2	8	no	—
451	D₄	—	4	4	no	—
452	D₄	—	4	8	no	—
453	D₄	—	8	4	no	—
454	D₄	—	8	8	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	8	8	no	—
463	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
464	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
468	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
469	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
470	C₈	—	2	4	no	—
471	C₈	C₂×C₁₁×#41	1	4	yes	—
472	C₈	C₂×C₁₁×#41	1	4	yes	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	8	no	—
478	C₂²	—	16	4	no	—
479	C₂²	C₁₁×#532	1	2	yes	—
480	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
481	C₄	—	2	2	no	—
482	C₄	—	2	4	no	—
483	C₄	—	2	2	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	4	no	—
486	C₄	—	4	4	no	—
487	C₄	C₁₁×#532	1	2	yes	—
488	C₄	C₁₁×#577	1	4	yes	—
489	C₄	C₂²×C₁₁×#41	1	2	yes	—
490	C₂	—	2	2	no	—
491	C₂	—	4	2	no	—
492	C₂	—	8	4	no	—
493	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
494	C₂	C₂×C₁₁×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₁₁×#3508	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×#3509	C₂	semidirect
3. C₁₁×#3182	C₂	semidirect
4. C₁₁×#3174	C₂	semidirect
5. C₁₁×#3167	C₂	semidirect
6. C₁₁×#3160	C₂	semidirect
7. C₂×C₁₁×#492	C₂	semidirect
8. C₁₁×#3139	C₂	semidirect
9. C₁₁×#3138	C₂	semidirect
10. C₁₁×#3057	C₂	semidirect
11. C₁₁×#2949	C₂	semidirect
12. C₄×C₁₁×#131	C₂	semidirect
21. C₁₁×#541	C₂²	semidirect
27. C₁₁×#533	C₂²	semidirect
34. C₁₁×#500	C₂²	semidirect
35. C₁₁×#499	C₂²	semidirect
36. C₁₁×#498	C₂²	semidirect
40. C₁₁×#491	C₂²	semidirect
42. C₁₁×#487	C₂²	semidirect
44. C₁₁×#468	C₂²	semidirect
45. C₁₁×#465	C₂²	semidirect
46. C₁₁×#440	C₂²	semidirect
47. C₄×C₁₁×SD₁₆	C₂²	semidirect
52. C₁₁×#405	C₂²	semidirect
54. C₄×C₁₁×M₁₆	C₂²	semidirect
56. C₂×C₄×C₈×C₁₁	C₂²	semidirect
130. #60712	C₁₁	direct (N × H)
160. C₂×C₈×C₁₁	#41	semidirect
191. #3509	C₂×C₁₁	semidirect
193. #3182	C₂×C₁₁	semidirect
194. #3174	C₂×C₁₁	semidirect
195. #3167	C₂×C₁₁	semidirect
196. #3160	C₂×C₁₁	semidirect
197. C₂×#492	C₂×C₁₁	semidirect
198. #3139	C₂×C₁₁	semidirect
199. #3138	C₂×C₁₁	semidirect
200. #3057	C₂×C₁₁	semidirect
201. #2949	C₂×C₁₁	semidirect
202. C₄×#131	C₂×C₁₁	semidirect
246. #541	C₂²×C₁₁	semidirect
252. #533	C₂²×C₁₁	semidirect
259. #500	C₂²×C₁₁	semidirect
260. #499	C₂²×C₁₁	semidirect
261. #498	C₂²×C₁₁	semidirect
265. #491	C₂²×C₁₁	semidirect
267. #487	C₂²×C₁₁	semidirect
269. #468	C₂²×C₁₁	semidirect
270. #465	C₂²×C₁₁	semidirect
271. #440	C₂²×C₁₁	semidirect
272. C₄×SD₁₆	C₂²×C₁₁	semidirect
277. #405	C₂²×C₁₁	semidirect
279. C₄×M₁₆	C₂²×C₁₁	semidirect
281. C₂×C₄×C₈	C₂²×C₁₁	semidirect
406. C₂×C₈	C₁₁×#41	semidirect
437. C₁₁	#60712	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×#3509	2
C₁₁×#3508	2
C₁₁×#3182	2
C₁₁×#3174	2
C₁₁×#3167	2
C₁₁×#3160	2
C₂×C₁₁×#492	2
C₁₁×#3139	2
C₁₁×#3138	2
C₁₁×#3057	2
C₁₁×#2949	2
C₄×C₁₁×#131	2
#60712	11

Subgroups — C11×#60712 #14637905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60712 #14637905