Subgroups — C₁₁×#60724 #14637917

Order 2816.

1874 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3183	C₂	1	4	yes	maximal, complemented
4	C₁₁×#3179	C₂	1	4	yes	maximal, complemented
5	C₁₁×#3178	C₂	1	4	yes	maximal, complemented
6	C₁₁×#3168	C₂	1	4	yes	maximal, complemented
7	C₁₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#3153	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#3131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#488	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#3063	C₂	1	2	yes	maximal, complemented
12	C₁₁×#3062	C₂	1	2	yes	maximal, complemented
13	C₁₁×#2947	C₂	1	2	yes	maximal, complemented
14	C₁₁×#2946	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₁×#137	C₂²	1	2	yes	—
17	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
18	C₂×C₁₁×#131	C₂²	1	2	yes	—
19	C₁₁×#559	—	2	2	no	—
20	C₁₁×#556	—	2	2	no	—
21	C₁₁×#553	—	2	4	no	—
22	C₁₁×#553	—	2	2	no	—
23	C₁₁×#552	—	2	2	no	—
24	C₁₁×#551	—	2	4	no	—
25	C₁₁×#542	C₂²	1	4	yes	—
26	C₁₁×#541	C₂²	1	2	yes	complemented
27	C₁₁×#540	C₂²	1	2	yes	complemented
28	C₁₁×#537	C₂²	1	2	yes	—
29	C₁₁×#536	C₂²	1	1	yes	characteristic
30	C₁₁×#535	C₂²	1	1	yes	characteristic
31	C₁₁×#533	C₂²	1	1	yes	characteristic
32	C₁₁×#532	C₂²	1	1	yes	characteristic
33	C₁₁×#529	C₂²	1	4	yes	—
34	C₁₁×#529	C₂²	1	4	yes	complemented
35	C₂×C₁₁×#125	C₂²	1	1	yes	characteristic
36	C₂×C₁₁×#124	C₂²	1	1	yes	characteristic
37	C₁₁×#520	C₂²	1	2	yes	—
38	C₁₁×#519	C₂²	1	1	yes	characteristic
39	C₁₁×#518	C₂²	1	1	yes	characteristic
40	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
41	C₁₁×#501	C₂²	1	4	yes	complemented
42	C₁₁×#499	C₂²	1	4	yes	complemented
43	C₁₁×#497	C₂²	1	2	yes	—
44	C₁₁×#496	C₂²	1	2	yes	—
45	C₁₁×#495	C₂²	1	4	yes	—
46	C₁₁×#488	C₂²	1	2	yes	—
47	C₁₁×#488	C₂²	1	4	yes	—
48	C₁₁×#488	C₂²	1	2	yes	—
49	C₁₁×#488	C₂²	1	2	yes	complemented
50	C₁₁×#488	C₂²	1	2	yes	complemented
51	C₁₁×#487	C₂²	1	2	yes	complemented
52	C₁₁×#486	C₂²	1	2	yes	complemented
53	C₁₁×#470	C₂²	1	4	yes	complemented
54	C₁₁×#469	C₂²	1	4	yes	—
55	C₁₁×#468	C₂²	1	4	yes	—
56	C₁₁×#468	C₂²	1	4	yes	complemented
57	C₁₁×#467	C₂²	1	4	yes	complemented
58	C₁₁×#466	C₂²	1	4	yes	—
59	C₁₁×#465	C₂²	1	4	yes	—
60	C₁₁×#465	C₂²	1	4	yes	complemented
61	C₁₁×#442	C₂²	1	4	yes	—
62	C₁₁×#441	C₂²	1	4	yes	complemented
63	C₁₁×#440	C₂²	1	4	yes	—
64	C₁₁×#440	C₂²	1	4	yes	complemented
65	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	complemented
66	C₄×C₁₁×SD₁₆	C₂²	1	4	yes	—
67	C₄×C₁₁×SD₁₆	C₂²	1	4	yes	complemented
68	C₄×C₁₁×D₈	C₂²	1	4	yes	—
69	C₁₁×#428	C₂²	1	2	yes	—
70	C₁₁×#428	C₂²	1	2	yes	—
71	C₁₁×#416	C₂²	1	2	yes	—
72	C₁₁×#416	C₂²	1	2	yes	—
73	C₂×C₁₁×#103	C₂²	1	2	yes	—
74	C₂×C₁₁×#102	C₂²	1	2	yes	—
75	C₁₁×#405	C₂²	1	2	yes	—
76	C₁₁×#405	C₂²	1	4	yes	complemented
77	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
78	C₄×C₁₁×M₁₆	C₂²	1	2	yes	complemented
79	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
80	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
81	C₂×C₁₁×#41	C₂³	1	2	yes	—
82	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
85	C₁₁×#137	—	2	8	no	—
86	C₁₁×AGL(1,ℤ/8)	—	2	8	no	—
87	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
88	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
89	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
90	C₂×C₁₁×D₈	C₂³	1	4	yes	—
91	C₁₁×#131	—	2	8	no	—
92	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
93	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
94	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
95	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
96	C₁₁×C₄⋊Q₈	—	2	1	no	—
97	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
98	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₁₁×#127	—	2	1	no	—
100	C₁₁×#127	C₂³	1	1	yes	characteristic
101	C₁₁×#126	—	2	4	no	—
102	C₁₁×#126	—	2	4	no	—
103	C₁₁×#126	—	2	4	no	—
104	C₁₁×#126	—	2	4	no	—
105	C₁₁×#125	—	2	4	no	—
106	C₁₁×#125	—	2	2	no	—
107	C₁₁×#125	C₂³	1	2	yes	—
108	C₁₁×#125	C₂³	1	2	yes	—
109	C₁₁×#125	C₂³	1	2	yes	—
110	C₁₁×#124	—	2	1	no	—
111	C₁₁×#124	—	2	1	no	—
112	C₁₁×#124	—	2	4	no	—
113	C₁₁×#124	—	2	2	no	—
114	C₁₁×#124	C₂³	1	2	yes	—
115	C₁₁×#124	C₂³	1	2	yes	—
116	C₁₁×#124	C₂³	1	2	yes	—
117	C₁₁×#123	—	2	2	no	—
118	C₁₁×#123	—	2	4	no	—
119	C₁₁×#123	—	2	4	no	—
120	C₁₁×#123	—	2	4	no	—
121	C₁₁×#123	—	2	4	no	—
122	C₁₁×C₂²⋊Q₈	—	2	2	no	—
123	C₁₁×C₂²⋊Q₈	—	2	2	no	—
124	C₁₁×C₂²⋊Q₈	—	2	4	no	—
125	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
127	C₁₁×#121	—	2	2	no	—
128	C₁₁×#121	—	2	4	no	—
129	C₁₁×#121	—	2	2	no	—
130	C₁₁×#121	—	2	4	no	—
131	C₁₁×#121	C₂³	1	4	yes	—
132	C₁₁×#121	C₂³	1	4	yes	—
133	C₁₁×#120	—	2	2	no	—
134	C₄×Q₈×C₁₁	—	2	2	no	—
135	C₄×Q₈×C₁₁	—	2	2	no	—
136	C₄×Q₈×C₁₁	D₄	1	2	yes	—
137	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
138	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
139	C₄×D₄×C₁₁	—	2	4	no	—
140	C₄×D₄×C₁₁	—	2	4	no	—
141	C₄×D₄×C₁₁	—	2	2	no	—
142	C₄×D₄×C₁₁	—	2	4	no	—
143	C₄×D₄×C₁₁	—	2	2	no	—
144	C₄×D₄×C₁₁	D₄	1	4	yes	—
145	C₄×D₄×C₁₁	D₄	1	2	yes	—
146	C₄×D₄×C₁₁	C₂³	1	4	yes	—
147	C₄×D₄×C₁₁	C₂³	1	4	yes	—
148	C₁₁×#117	—	2	2	no	—
149	C₁₁×#117	—	2	2	no	—
150	C₁₁×#117	—	2	4	no	—
151	C₁₁×#117	—	2	4	no	—
152	C₁₁×#117	C₂³	1	1	yes	characteristic
153	C₁₁×#117	C₂³	1	1	yes	characteristic
154	C₁₁×#117	C₂³	1	1	yes	characteristic
155	C₁₁×#117	C₂³	1	2	yes	—
156	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
157	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
158	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
160	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
161	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
163	C₁₁×#107	C₂³	1	4	yes	—
164	C₁₁×#107	C₂³	1	4	yes	—
165	C₁₁×#106	C₂³	1	4	yes	—
166	C₁₁×#106	C₂³	1	4	yes	—
167	C₁₁×#103	C₂³	1	4	yes	—
168	C₁₁×#103	C₂³	1	4	yes	—
169	C₁₁×#103	C₂³	1	2	yes	—
170	C₁₁×#103	C₂³	1	2	yes	—
171	C₁₁×#103	C₂³	1	2	yes	—
172	C₁₁×#103	C₂³	1	2	yes	—
173	C₁₁×#102	C₂³	1	4	yes	—
174	C₁₁×#102	C₂³	1	4	yes	—
175	C₁₁×#102	C₂³	1	2	yes	—
176	C₁₁×#102	C₂³	1	2	yes	—
177	C₁₁×#102	C₂³	1	2	yes	—
178	C₁₁×#102	C₂³	1	2	yes	—
179	C₁₁×#97	C₂³	1	2	yes	—
180	C₁₁×#97	C₂³	1	4	yes	—
181	C₄×C₈×C₁₁	C₂³	1	2	yes	—
182	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
183	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
184	C₄×C₈×C₁₁	C₂³	1	2	yes	—
185	C₄×C₈×C₁₁	C₂³	1	4	yes	—
186	#60724	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂⁴×C₁₁	—	2	1	no	—
188	C₁₁×#41	—	2	4	no	—
189	C₁₁×#41	—	2	4	no	—
190	C₁₁×#41	—	2	4	no	—
191	C₂×Q₈×C₁₁	—	2	1	no	—
192	C₂×Q₈×C₁₁	—	2	2	no	—
193	C₂×Q₈×C₁₁	—	2	4	no	—
194	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
195	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
196	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
197	C₂×D₄×C₁₁	—	2	2	no	—
198	C₂×D₄×C₁₁	—	2	4	no	—
199	C₂×D₄×C₁₁	—	2	4	no	—
200	C₂×D₄×C₁₁	—	2	1	no	—
201	C₂×D₄×C₁₁	—	2	2	no	—
202	C₂×D₄×C₁₁	—	2	4	no	—
203	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
205	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
206	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₁	—	2	1	no	—
208	C₂²×C₄×C₁₁	—	2	2	no	—
209	C₂²×C₄×C₁₁	—	2	2	no	—
210	C₂²×C₄×C₁₁	—	2	4	no	—
211	C₂²×C₄×C₁₁	—	2	4	no	—
212	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
216	C₁₁×Q₁₆	—	2	8	no	—
217	C₁₁×SD₁₆	—	2	8	no	—
218	C₁₁×SD₁₆	—	2	8	no	—
219	C₁₁×D₈	—	2	8	no	—
220	C₁₁×M₁₆	—	2	8	no	—
221	C₁₁×M₁₆	#41	1	8	yes	—
222	C₂×C₈×C₁₁	—	2	8	no	—
223	C₂×C₈×C₁₁	—	2	4	no	—
224	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
225	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
226	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
227	C₁₁×C₄⋊C₄	—	2	2	no	—
228	C₁₁×C₄⋊C₄	—	2	4	no	—
229	C₁₁×C₄⋊C₄	—	2	4	no	—
230	C₁₁×C₄⋊C₄	—	2	4	no	—
231	C₁₁×C₄⋊C₄	—	2	2	no	—
232	C₁₁×C₄⋊C₄	—	2	4	no	—
233	C₁₁×C₄⋊C₄	—	2	4	no	—
234	C₁₁×C₄⋊C₄	—	2	4	no	—
235	C₁₁×C₄⋊C₄	—	2	2	no	—
236	C₁₁×C₄⋊C₄	—	2	2	no	—
237	C₁₁×C₄⋊C₄	—	2	2	no	—
238	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
239	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
240	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
241	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
242	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
243	C₁₁×C₂²⋊C₄	—	2	1	no	—
244	C₁₁×C₂²⋊C₄	—	2	1	no	—
245	C₁₁×C₂²⋊C₄	—	2	4	no	—
246	C₁₁×C₂²⋊C₄	—	2	4	no	—
247	C₁₁×C₂²⋊C₄	—	2	4	no	—
248	C₁₁×C₂²⋊C₄	—	2	4	no	—
249	C₁₁×C₂²⋊C₄	—	2	4	no	—
250	C₁₁×C₂²⋊C₄	—	2	2	no	—
251	C₁₁×C₂²⋊C₄	—	2	4	no	—
252	C₁₁×C₂²⋊C₄	—	2	4	no	—
253	C₁₁×C₂²⋊C₄	—	2	4	no	—
254	C₁₁×C₂²⋊C₄	—	2	2	no	—
255	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
256	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
257	C₄²×C₁₁	—	2	4	no	—
258	C₄²×C₁₁	—	2	4	no	—
259	C₄²×C₁₁	—	2	1	no	—
260	C₄²×C₁₁	—	2	1	no	—
261	C₄²×C₁₁	C₂×D₄	1	4	yes	—
262	C₄²×C₁₁	C₂×D₄	1	2	yes	—
263	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
264	C₄²×C₁₁	C₂⁴	1	2	yes	—
265	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
266	#3512	C₂×C₁₁	1	1	yes	characteristic, complemented
267	#3510	C₂×C₁₁	1	1	yes	characteristic, complemented
268	#3183	C₂×C₁₁	1	4	yes	complemented
269	#3179	C₂×C₁₁	1	4	yes	complemented
270	#3178	C₂×C₁₁	1	4	yes	complemented
271	#3168	C₂×C₁₁	1	4	yes	complemented
272	#3166	C₂×C₁₁	1	1	yes	characteristic, complemented
273	#3153	C₂×C₁₁	1	1	yes	characteristic, complemented
274	#3131	C₂×C₁₁	1	1	yes	characteristic, complemented
275	C₂×#488	C₂×C₁₁	1	1	yes	characteristic, complemented
276	#3063	C₂×C₁₁	1	2	yes	complemented
277	#3062	C₂×C₁₁	1	2	yes	complemented
278	#2947	C₂×C₁₁	1	2	yes	complemented
279	#2946	C₂×C₁₁	1	2	yes	complemented
280	C₄×#131	C₂×C₁₁	1	1	yes	characteristic, complemented
281	C₂³×C₁₁	—	2	2	no	—
282	C₂³×C₁₁	—	2	2	no	—
283	C₂³×C₁₁	—	4	2	no	—
284	C₂³×C₁₁	—	8	2	no	—
285	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
286	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
287	Q₈×C₁₁	—	2	2	no	—
288	Q₈×C₁₁	—	2	2	no	—
289	Q₈×C₁₁	—	2	4	no	—
290	Q₈×C₁₁	—	2	2	no	—
291	Q₈×C₁₁	—	4	2	no	—
292	Q₈×C₁₁	—	8	2	no	—
293	D₄×C₁₁	—	2	4	no	—
294	D₄×C₁₁	—	2	2	no	—
295	D₄×C₁₁	—	2	2	no	—
296	D₄×C₁₁	—	2	4	no	—
297	D₄×C₁₁	—	2	2	no	—
298	D₄×C₁₁	—	4	4	no	—
299	D₄×C₁₁	—	4	2	no	—
300	D₄×C₁₁	—	8	2	no	—
301	D₄×C₁₁	—	8	4	no	—
302	D₄×C₁₁	—	8	4	no	—
303	C₂×C₄×C₁₁	—	2	4	no	—
304	C₂×C₄×C₁₁	—	2	2	no	—
305	C₂×C₄×C₁₁	—	2	2	no	—
306	C₂×C₄×C₁₁	—	2	2	no	—
307	C₂×C₄×C₁₁	—	2	2	no	—
308	C₂×C₄×C₁₁	—	2	4	no	—
309	C₂×C₄×C₁₁	—	4	4	no	—
310	C₂×C₄×C₁₁	—	4	2	no	—
311	C₂×C₄×C₁₁	—	4	2	no	—
312	C₂×C₄×C₁₁	—	4	4	no	—
313	C₂×C₄×C₁₁	—	8	4	no	—
314	C₂×C₄×C₁₁	—	8	4	no	—
315	C₂×C₄×C₁₁	—	8	2	no	—
316	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
317	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
322	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
323	C₈×C₁₁	—	2	2	no	—
324	C₈×C₁₁	—	2	2	no	—
325	C₈×C₁₁	C₂×#41	1	8	yes	—
326	C₂×#137	C₂²×C₁₁	1	2	yes	—
327	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	2	yes	—
328	C₂×#131	C₂²×C₁₁	1	2	yes	—
329	#559	—	2	2	no	—
330	#556	—	2	2	no	—
331	#553	—	2	4	no	—
332	#553	—	2	2	no	—
333	#552	—	2	2	no	—
334	#551	—	2	4	no	—
335	#542	C₂²×C₁₁	1	4	yes	—
336	#541	C₂²×C₁₁	1	2	yes	complemented
337	#540	C₂²×C₁₁	1	2	yes	complemented
338	#537	C₂²×C₁₁	1	2	yes	—
339	#536	C₂²×C₁₁	1	1	yes	characteristic
340	#535	C₂²×C₁₁	1	1	yes	characteristic
341	#533	C₂²×C₁₁	1	1	yes	characteristic
342	#532	C₂²×C₁₁	1	1	yes	characteristic
343	#529	C₂²×C₁₁	1	4	yes	—
344	#529	C₂²×C₁₁	1	4	yes	complemented
345	C₂×#125	C₂²×C₁₁	1	1	yes	characteristic
346	C₂×#124	C₂²×C₁₁	1	1	yes	characteristic
347	#520	C₂²×C₁₁	1	2	yes	—
348	#519	C₂²×C₁₁	1	1	yes	characteristic
349	#518	C₂²×C₁₁	1	1	yes	characteristic
350	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
351	#501	C₂²×C₁₁	1	4	yes	complemented
352	#499	C₂²×C₁₁	1	4	yes	complemented
353	#497	C₂²×C₁₁	1	2	yes	—
354	#496	C₂²×C₁₁	1	2	yes	—
355	#495	C₂²×C₁₁	1	4	yes	—
356	#488	C₂²×C₁₁	1	2	yes	—
357	#488	C₂²×C₁₁	1	4	yes	—
358	#488	C₂²×C₁₁	1	2	yes	—
359	#488	C₂²×C₁₁	1	2	yes	complemented
360	#488	C₂²×C₁₁	1	2	yes	complemented
361	#487	C₂²×C₁₁	1	2	yes	complemented
362	#486	C₂²×C₁₁	1	2	yes	complemented
363	#470	C₂²×C₁₁	1	4	yes	complemented
364	#469	C₂²×C₁₁	1	4	yes	—
365	#468	C₂²×C₁₁	1	4	yes	—
366	#468	C₂²×C₁₁	1	4	yes	complemented
367	#467	C₂²×C₁₁	1	4	yes	complemented
368	#466	C₂²×C₁₁	1	4	yes	—
369	#465	C₂²×C₁₁	1	4	yes	—
370	#465	C₂²×C₁₁	1	4	yes	complemented
371	#442	C₂²×C₁₁	1	4	yes	—
372	#441	C₂²×C₁₁	1	4	yes	complemented
373	#440	C₂²×C₁₁	1	4	yes	—
374	#440	C₂²×C₁₁	1	4	yes	complemented
375	C₄×Q₁₆	C₂²×C₁₁	1	4	yes	complemented
376	C₄×SD₁₆	C₂²×C₁₁	1	4	yes	—
377	C₄×SD₁₆	C₂²×C₁₁	1	4	yes	complemented
378	C₄×D₈	C₂²×C₁₁	1	4	yes	—
379	#428	C₂²×C₁₁	1	2	yes	—
380	#428	C₂²×C₁₁	1	2	yes	—
381	#416	C₂²×C₁₁	1	2	yes	—
382	#416	C₂²×C₁₁	1	2	yes	—
383	C₂×#103	C₂²×C₁₁	1	2	yes	—
384	C₂×#102	C₂²×C₁₁	1	2	yes	—
385	#405	C₂²×C₁₁	1	2	yes	—
386	#405	C₂²×C₁₁	1	4	yes	complemented
387	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
388	C₄×M₁₆	C₂²×C₁₁	1	2	yes	complemented
389	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
390	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
391	C₂²×C₁₁	—	2	2	no	—
392	C₂²×C₁₁	—	2	4	no	—
393	C₂²×C₁₁	—	2	2	no	—
394	C₂²×C₁₁	—	4	2	no	—
395	C₂²×C₁₁	—	4	4	no	—
396	C₂²×C₁₁	—	4	2	no	—
397	C₂²×C₁₁	—	4	2	no	—
398	C₂²×C₁₁	—	4	2	no	—
399	C₂²×C₁₁	—	16	2	no	—
400	C₂²×C₁₁	#532	1	2	yes	—
401	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
402	C₄×C₁₁	—	2	2	no	—
403	C₄×C₁₁	—	2	4	no	—
404	C₄×C₁₁	—	2	2	no	—
405	C₄×C₁₁	—	2	2	no	—
406	C₄×C₁₁	—	4	4	no	—
407	C₄×C₁₁	—	4	2	no	—
408	C₄×C₁₁	—	4	2	no	—
409	C₄×C₁₁	—	4	2	no	—
410	C₄×C₁₁	—	4	2	no	—
411	C₄×C₁₁	#532	1	2	yes	—
412	C₄×C₁₁	C₂²×#41	1	2	yes	—
413	C₂×#41	C₂³×C₁₁	1	2	yes	—
414	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
415	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
416	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
417	#137	—	2	8	no	—
418	AGL(1,ℤ/8)	—	2	8	no	—
419	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
420	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
421	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
422	C₂×D₈	C₂³×C₁₁	1	4	yes	—
423	#131	—	2	8	no	—
424	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
425	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
426	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
427	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
428	C₄⋊Q₈	—	2	1	no	—
429	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
430	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
431	#127	—	2	1	no	—
432	#127	C₂³×C₁₁	1	1	yes	characteristic
433	#126	—	2	4	no	—
434	#126	—	2	4	no	—
435	#126	—	2	4	no	—
436	#126	—	2	4	no	—
437	#125	—	2	4	no	—
438	#125	—	2	2	no	—
439	#125	C₂³×C₁₁	1	2	yes	—
440	#125	C₂³×C₁₁	1	2	yes	—
441	#125	C₂³×C₁₁	1	2	yes	—
442	#124	—	2	1	no	—
443	#124	—	2	1	no	—
444	#124	—	2	4	no	—
445	#124	—	2	2	no	—
446	#124	C₂³×C₁₁	1	2	yes	—
447	#124	C₂³×C₁₁	1	2	yes	—
448	#124	C₂³×C₁₁	1	2	yes	—
449	#123	—	2	2	no	—
450	#123	—	2	4	no	—
451	#123	—	2	4	no	—
452	#123	—	2	4	no	—
453	#123	—	2	4	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	—	2	2	no	—
456	C₂²⋊Q₈	—	2	4	no	—
457	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
458	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
459	#121	—	2	2	no	—
460	#121	—	2	4	no	—
461	#121	—	2	2	no	—
462	#121	—	2	4	no	—
463	#121	C₂³×C₁₁	1	4	yes	—
464	#121	C₂³×C₁₁	1	4	yes	—
465	#120	—	2	2	no	—
466	C₄×Q₈	—	2	2	no	—
467	C₄×Q₈	—	2	2	no	—
468	C₄×Q₈	D₄×C₁₁	1	2	yes	—
469	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
470	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
471	C₄×D₄	—	2	4	no	—
472	C₄×D₄	—	2	4	no	—
473	C₄×D₄	—	2	2	no	—
474	C₄×D₄	—	2	4	no	—
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	D₄×C₁₁	1	4	yes	—
477	C₄×D₄	D₄×C₁₁	1	2	yes	—
478	C₄×D₄	C₂³×C₁₁	1	4	yes	—
479	C₄×D₄	C₂³×C₁₁	1	4	yes	—
480	#117	—	2	2	no	—
481	#117	—	2	2	no	—
482	#117	—	2	4	no	—
483	#117	—	2	4	no	—
484	#117	C₂³×C₁₁	1	1	yes	characteristic
485	#117	C₂³×C₁₁	1	1	yes	characteristic
486	#117	C₂³×C₁₁	1	1	yes	characteristic
487	#117	C₂³×C₁₁	1	2	yes	—
488	C₂×C₄⋊C₄	—	2	2	no	—
489	C₂×C₄⋊C₄	—	2	2	no	—
490	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
491	C₂×C₂²⋊C₄	—	2	2	no	—
492	C₂×C₂²⋊C₄	—	2	2	no	—
493	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
495	#107	C₂³×C₁₁	1	4	yes	—
496	#107	C₂³×C₁₁	1	4	yes	—
497	#106	C₂³×C₁₁	1	4	yes	—
498	#106	C₂³×C₁₁	1	4	yes	—
499	#103	C₂³×C₁₁	1	4	yes	—
500	#103	C₂³×C₁₁	1	4	yes	—
501	#103	C₂³×C₁₁	1	2	yes	—
502	#103	C₂³×C₁₁	1	2	yes	—
503	#103	C₂³×C₁₁	1	2	yes	—
504	#103	C₂³×C₁₁	1	2	yes	—
505	#102	C₂³×C₁₁	1	4	yes	—
506	#102	C₂³×C₁₁	1	4	yes	—
507	#102	C₂³×C₁₁	1	2	yes	—
508	#102	C₂³×C₁₁	1	2	yes	—
509	#102	C₂³×C₁₁	1	2	yes	—
510	#102	C₂³×C₁₁	1	2	yes	—
511	#97	C₂³×C₁₁	1	2	yes	—
512	#97	C₂³×C₁₁	1	4	yes	—
513	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
514	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
515	C₄×C₈	C₂³×C₁₁	1	2	yes	—
516	C₄×C₈	C₂³×C₁₁	1	2	yes	—
517	C₄×C₈	C₂³×C₁₁	1	4	yes	—
518	C₂×C₁₁	—	2	2	no	—
519	C₂×C₁₁	—	4	2	no	—
520	C₂×C₁₁	—	8	2	no	—
521	C₂×C₁₁	—	8	2	no	—
522	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
523	C₂×C₁₁	#3584	1	2	yes	—
524	C₂⁴	—	2	1	no	—
525	#41	—	2	4	no	—
526	#41	—	2	4	no	—
527	#41	—	2	4	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	—	2	4	no	—
531	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
532	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
533	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
541	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
542	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
543	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
550	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
553	Q₁₆	—	2	8	no	—
554	SD₁₆	—	2	8	no	—
555	SD₁₆	—	2	8	no	—
556	D₈	—	2	8	no	—
557	M₁₆	—	2	8	no	—
558	M₁₆	C₁₁×#41	1	8	yes	—
559	C₂×C₈	—	2	4	no	—
560	C₂×C₈	—	2	8	no	—
561	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
562	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
563	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
576	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
577	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
578	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
579	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
580	C₂²⋊C₄	—	2	1	no	—
581	C₂²⋊C₄	—	2	1	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
593	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
594	C₄²	—	2	4	no	—
595	C₄²	—	2	4	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	1	no	—
598	C₄²	C₂×D₄×C₁₁	1	4	yes	—
599	C₄²	C₂×D₄×C₁₁	1	2	yes	—
600	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
601	C₄²	C₂⁴×C₁₁	1	2	yes	—
602	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
603	C₁₁	#60724	1	1	yes	characteristic, direct product factor, Sylow
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	4	2	no	—
607	C₂³	—	8	2	no	—
608	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
609	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
610	Q₈	—	2	2	no	—
611	Q₈	—	2	2	no	—
612	Q₈	—	2	4	no	—
613	Q₈	—	2	2	no	—
614	Q₈	—	4	2	no	—
615	Q₈	—	8	2	no	—
616	D₄	—	2	4	no	—
617	D₄	—	2	2	no	—
618	D₄	—	2	2	no	—
619	D₄	—	2	4	no	—
620	D₄	—	2	2	no	—
621	D₄	—	4	4	no	—
622	D₄	—	4	2	no	—
623	D₄	—	8	2	no	—
624	D₄	—	8	4	no	—
625	D₄	—	8	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	4	4	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	4	4	no	—
636	C₂×C₄	—	8	4	no	—
637	C₂×C₄	—	8	4	no	—
638	C₂×C₄	—	8	2	no	—
639	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
640	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
641	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
642	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
643	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
644	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
645	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
646	C₈	—	2	2	no	—
647	C₈	—	2	2	no	—
648	C₈	C₂×C₁₁×#41	1	8	yes	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	4	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	16	2	no	—
658	C₂²	C₁₁×#532	1	2	yes	—
659	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	4	no	—
663	C₄	—	2	2	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	4	no	—
667	C₄	—	4	2	no	—
668	C₄	—	4	2	no	—
669	C₄	C₁₁×#532	1	2	yes	—
670	C₄	C₂²×C₁₁×#41	1	2	yes	—
671	C₂	—	2	2	no	—
672	C₂	—	4	2	no	—
673	C₂	—	8	2	no	—
674	C₂	—	8	2	no	—
675	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
676	C₂	C₁₁×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
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×#3512	C₂	semidirect
2. C₁₁×#3510	C₂	semidirect
3. C₁₁×#3183	C₂	semidirect
4. C₁₁×#3179	C₂	semidirect
5. C₁₁×#3178	C₂	semidirect
6. C₁₁×#3168	C₂	semidirect
7. C₁₁×#3166	C₂	semidirect
8. C₁₁×#3153	C₂	semidirect
9. C₁₁×#3131	C₂	semidirect
10. C₂×C₁₁×#488	C₂	semidirect
11. C₁₁×#3063	C₂	semidirect
12. C₁₁×#3062	C₂	semidirect
13. C₁₁×#2947	C₂	semidirect
14. C₁₁×#2946	C₂	semidirect
15. C₄×C₁₁×#131	C₂	semidirect
26. C₁₁×#541	C₂²	semidirect
27. C₁₁×#540	C₂²	semidirect
34. C₁₁×#529	C₂²	semidirect
41. C₁₁×#501	C₂²	semidirect
42. C₁₁×#499	C₂²	semidirect
49. C₁₁×#488	C₂²	semidirect
50. C₁₁×#488	C₂²	semidirect
51. C₁₁×#487	C₂²	semidirect
52. C₁₁×#486	C₂²	semidirect
53. C₁₁×#470	C₂²	semidirect
56. C₁₁×#468	C₂²	semidirect
57. C₁₁×#467	C₂²	semidirect
60. C₁₁×#465	C₂²	semidirect
62. C₁₁×#441	C₂²	semidirect
64. C₁₁×#440	C₂²	semidirect
65. C₄×C₁₁×Q₁₆	C₂²	semidirect
67. C₄×C₁₁×SD₁₆	C₂²	semidirect
76. C₁₁×#405	C₂²	semidirect
78. C₄×C₁₁×M₁₆	C₂²	semidirect
80. C₂×C₄×C₈×C₁₁	C₂²	semidirect
186. #60724	C₁₁	direct (N × H)
266. #3512	C₂×C₁₁	semidirect
267. #3510	C₂×C₁₁	semidirect
268. #3183	C₂×C₁₁	semidirect
269. #3179	C₂×C₁₁	semidirect
270. #3178	C₂×C₁₁	semidirect
271. #3168	C₂×C₁₁	semidirect
272. #3166	C₂×C₁₁	semidirect
273. #3153	C₂×C₁₁	semidirect
274. #3131	C₂×C₁₁	semidirect
275. C₂×#488	C₂×C₁₁	semidirect
276. #3063	C₂×C₁₁	semidirect
277. #3062	C₂×C₁₁	semidirect
278. #2947	C₂×C₁₁	semidirect
279. #2946	C₂×C₁₁	semidirect
280. C₄×#131	C₂×C₁₁	semidirect
336. #541	C₂²×C₁₁	semidirect
337. #540	C₂²×C₁₁	semidirect
344. #529	C₂²×C₁₁	semidirect
351. #501	C₂²×C₁₁	semidirect
352. #499	C₂²×C₁₁	semidirect
359. #488	C₂²×C₁₁	semidirect
360. #488	C₂²×C₁₁	semidirect
361. #487	C₂²×C₁₁	semidirect
362. #486	C₂²×C₁₁	semidirect
363. #470	C₂²×C₁₁	semidirect
366. #468	C₂²×C₁₁	semidirect
367. #467	C₂²×C₁₁	semidirect
370. #465	C₂²×C₁₁	semidirect
372. #441	C₂²×C₁₁	semidirect
374. #440	C₂²×C₁₁	semidirect
375. C₄×Q₁₆	C₂²×C₁₁	semidirect
377. C₄×SD₁₆	C₂²×C₁₁	semidirect
386. #405	C₂²×C₁₁	semidirect
388. C₄×M₁₆	C₂²×C₁₁	semidirect
390. C₂×C₄×C₈	C₂²×C₁₁	semidirect
603. C₁₁	#60724	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×#3512	2
C₁₁×#3510	2
C₁₁×#3183	2
C₁₁×#3179	2
C₁₁×#3178	2
C₁₁×#3168	2
C₁₁×#3166	2
C₁₁×#3153	2
C₁₁×#3131	2
C₂×C₁₁×#488	2
C₁₁×#3063	2
C₁₁×#3062	2
C₁₁×#2947	2
C₁₁×#2946	2
C₄×C₁₁×#131	2
#60724	11

Subgroups — C11×#60724 #14637917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60724 #14637917