Subgroups — C₁₁×#60725 #14637918

Order 2816.

1962 conjugacy classes of subgroups.

The subgroup lattice has 562 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×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3180	C₂	1	4	yes	maximal, complemented
4	C₁₁×#3176	C₂	1	4	yes	maximal, complemented
5	C₁₁×#3174	C₂	1	4	yes	maximal, complemented
6	C₁₁×#3171	C₂	1	4	yes	maximal, complemented
7	C₁₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#3135	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#490	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#3062	C₂	1	4	yes	maximal, complemented
12	C₁₁×#2946	C₂	1	4	yes	maximal, complemented
13	C₁₁×#2875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	4	yes	—
15	C₂×C₁₁×#131	C₂²	1	2	yes	—
16	C₁₁×#559	—	2	2	no	—
17	C₁₁×#553	—	2	4	no	—
18	C₁₁×#553	—	2	2	no	—
19	C₁₁×#552	—	2	2	no	—
20	C₁₁×#550	—	2	2	no	—
21	C₁₁×#546	—	2	4	no	—
22	C₁₁×#541	C₂²	1	2	yes	complemented
23	C₁₁×#540	C₂²	1	4	yes	—
24	C₁₁×#540	C₂²	1	2	yes	complemented
25	C₁₁×#537	C₂²	1	2	yes	—
26	C₁₁×#535	C₂²	1	2	yes	—
27	C₁₁×#533	C₂²	1	1	yes	characteristic
28	C₁₁×#532	C₂²	1	1	yes	characteristic
29	C₁₁×#532	C₂²	1	4	yes	—
30	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
31	C₁₁×#529	C₂²	1	4	yes	complemented
32	C₂×C₁₁×#125	C₂²	1	1	yes	characteristic
33	C₁₁×#520	C₂²	1	2	yes	—
34	C₁₁×#518	C₂²	1	2	yes	—
35	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
36	C₁₁×#501	C₂²	1	4	yes	complemented
37	C₁₁×#499	C₂²	1	4	yes	complemented
38	C₁₁×#496	C₂²	1	4	yes	—
39	C₁₁×#493	C₂²	1	2	yes	—
40	C₁₁×#492	C₂²	1	2	yes	—
41	C₁₁×#491	C₂²	1	2	yes	complemented
42	C₁₁×#490	C₂²	1	2	yes	—
43	C₁₁×#490	C₂²	1	4	yes	—
44	C₁₁×#490	C₂²	1	2	yes	—
45	C₁₁×#490	C₂²	1	2	yes	complemented
46	C₁₁×#489	C₂²	1	2	yes	complemented
47	C₁₁×#489	C₂²	1	2	yes	complemented
48	C₁₁×#469	C₂²	1	8	yes	complemented
49	C₁₁×#468	C₂²	1	8	yes	complemented
50	C₁₁×#466	C₂²	1	8	yes	complemented
51	C₁₁×#465	C₂²	1	8	yes	complemented
52	C₁₁×#442	C₂²	1	8	yes	complemented
53	C₁₁×#440	C₂²	1	8	yes	complemented
54	C₄×C₁₁×SD₁₆	C₂²	1	8	yes	complemented
55	C₄×C₁₁×D₈	C₂²	1	8	yes	complemented
56	C₁₁×#428	C₂²	1	4	yes	—
57	C₁₁×#416	C₂²	1	4	yes	—
58	C₂×C₁₁×#102	C₂²	1	4	yes	—
59	C₁₁×#405	C₂²	1	2	yes	—
60	C₁₁×#405	C₂²	1	4	yes	complemented
61	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
62	C₄×C₁₁×M₁₆	C₂²	1	2	yes	complemented
63	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
64	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
65	C₂×C₁₁×#41	—	2	4	no	—
66	C₂×C₁₁×#41	C₂³	1	2	yes	—
67	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₁	—	2	2	no	—
69	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
70	C₁₁×AGL(1,ℤ/8)	—	2	16	no	—
71	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
72	C₂×C₁₁×D₈	C₂³	1	8	yes	—
73	C₁₁×#131	—	2	8	no	—
74	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
75	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
76	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
77	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
78	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
80	C₁₁×#127	—	2	2	no	—
81	C₁₁×#127	—	2	2	no	—
82	C₁₁×#127	C₂³	1	2	yes	—
83	C₁₁×#127	C₂³	1	2	yes	—
84	C₁₁×#127	C₂³	1	1	yes	characteristic
85	C₁₁×#126	—	2	4	no	—
86	C₁₁×#126	—	2	4	no	—
87	C₁₁×#125	—	2	4	no	—
88	C₁₁×#125	—	2	2	no	—
89	C₁₁×#125	C₂³	1	2	yes	—
90	C₁₁×#125	C₂³	1	2	yes	—
91	C₁₁×#125	C₂³	1	2	yes	—
92	C₁₁×#124	—	2	2	no	—
93	C₁₁×#124	—	2	4	no	—
94	C₁₁×#124	C₂³	1	2	yes	—
95	C₁₁×#123	—	2	4	no	—
96	C₁₁×#123	—	2	8	no	—
97	C₁₁×#123	—	2	4	no	—
98	C₁₁×C₂²⋊Q₈	—	2	2	no	—
99	C₁₁×C₂²⋊Q₈	—	2	2	no	—
100	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
101	C₁₁×#121	—	2	2	no	—
102	C₁₁×#121	—	2	4	no	—
103	C₁₁×#121	—	2	4	no	—
104	C₁₁×#121	—	2	2	no	—
105	C₁₁×#121	—	2	8	no	—
106	C₁₁×#121	—	2	4	no	—
107	C₁₁×#121	C₂³	1	4	yes	—
108	C₁₁×#121	C₂³	1	8	yes	—
109	C₁₁×#120	—	2	4	no	—
110	C₄×Q₈×C₁₁	—	2	2	no	—
111	C₄×Q₈×C₁₁	D₄	1	2	yes	—
112	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
113	C₄×D₄×C₁₁	—	2	4	no	—
114	C₄×D₄×C₁₁	—	2	4	no	—
115	C₄×D₄×C₁₁	—	2	4	no	—
116	C₄×D₄×C₁₁	—	2	4	no	—
117	C₄×D₄×C₁₁	—	2	2	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	C₄×D₄×C₁₁	C₂³	1	4	yes	—
122	C₁₁×#117	—	2	2	no	—
123	C₁₁×#117	—	2	4	no	—
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×C₄⋊C₄	—	2	2	no	—
128	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
129	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
131	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
133	C₁₁×#107	C₂³	1	8	yes	—
134	C₁₁×#106	C₂³	1	8	yes	—
135	C₁₁×#103	C₂³	1	4	yes	—
136	C₁₁×#103	C₂³	1	4	yes	—
137	C₁₁×#102	C₂³	1	4	yes	—
138	C₁₁×#102	C₂³	1	4	yes	—
139	C₁₁×#102	C₂³	1	8	yes	—
140	C₁₁×#102	C₂³	1	8	yes	—
141	C₁₁×#97	C₂³	1	1	yes	characteristic
142	C₁₁×#97	C₂³	1	1	yes	characteristic
143	C₁₁×#97	C₂³	1	2	yes	—
144	C₁₁×#97	C₂³	1	2	yes	—
145	C₁₁×#97	C₂³	1	4	yes	—
146	C₄×C₈×C₁₁	C₂³	1	2	yes	—
147	C₄×C₈×C₁₁	C₂³	1	4	yes	—
148	#60725	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂⁴×C₁₁	—	2	2	no	—
150	C₁₁×#41	—	2	4	no	—
151	C₁₁×#41	—	2	8	no	—
152	C₁₁×#41	—	8	8	no	—
153	C₂×Q₈×C₁₁	—	2	2	no	—
154	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
156	C₂×D₄×C₁₁	—	2	2	no	—
157	C₂×D₄×C₁₁	—	2	4	no	—
158	C₂×D₄×C₁₁	—	2	8	no	—
159	C₂×D₄×C₁₁	—	2	2	no	—
160	C₂×D₄×C₁₁	—	2	4	no	—
161	C₂×D₄×C₁₁	—	2	2	no	—
162	C₂×D₄×C₁₁	—	2	4	no	—
163	C₂×D₄×C₁₁	—	2	8	no	—
164	C₂×D₄×C₁₁	—	8	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	2	yes	—
168	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₁	—	2	2	no	—
170	C₂²×C₄×C₁₁	—	2	2	no	—
171	C₂²×C₄×C₁₁	—	2	8	no	—
172	C₂²×C₄×C₁₁	—	2	4	no	—
173	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
177	C₁₁×SD₁₆	—	2	16	no	—
178	C₁₁×D₈	—	2	16	no	—
179	C₁₁×M₁₆	—	2	8	no	—
180	C₁₁×M₁₆	#41	1	8	yes	complemented
181	C₂×C₈×C₁₁	—	2	8	no	—
182	C₂×C₈×C₁₁	—	2	4	no	—
183	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
184	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
185	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
186	C₁₁×C₄⋊C₄	—	2	2	no	—
187	C₁₁×C₄⋊C₄	—	2	4	no	—
188	C₁₁×C₄⋊C₄	—	2	4	no	—
189	C₁₁×C₄⋊C₄	—	2	4	no	—
190	C₁₁×C₄⋊C₄	—	2	4	no	—
191	C₁₁×C₄⋊C₄	—	2	2	no	—
192	C₁₁×C₄⋊C₄	—	2	2	no	—
193	C₁₁×C₄⋊C₄	—	2	4	no	—
194	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
195	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
196	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
197	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
198	C₁₁×C₂²⋊C₄	—	2	2	no	—
199	C₁₁×C₂²⋊C₄	—	2	4	no	—
200	C₁₁×C₂²⋊C₄	—	2	8	no	—
201	C₁₁×C₂²⋊C₄	—	2	2	no	—
202	C₁₁×C₂²⋊C₄	—	2	4	no	—
203	C₁₁×C₂²⋊C₄	—	2	4	no	—
204	C₁₁×C₂²⋊C₄	—	2	2	no	—
205	C₁₁×C₂²⋊C₄	—	2	8	no	—
206	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
207	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
208	C₄²×C₁₁	—	2	4	no	—
209	C₄²×C₁₁	—	2	2	no	—
210	C₄²×C₁₁	C₂×D₄	1	4	yes	—
211	C₄²×C₁₁	C₂×D₄	1	2	yes	—
212	C₄²×C₁₁	C₂⁴	1	2	yes	—
213	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
214	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
215	#3512	C₂×C₁₁	1	1	yes	characteristic, complemented
216	#3508	C₂×C₁₁	1	1	yes	characteristic, complemented
217	#3180	C₂×C₁₁	1	4	yes	complemented
218	#3176	C₂×C₁₁	1	4	yes	complemented
219	#3174	C₂×C₁₁	1	4	yes	complemented
220	#3171	C₂×C₁₁	1	4	yes	complemented
221	#3166	C₂×C₁₁	1	1	yes	characteristic, complemented
222	#3151	C₂×C₁₁	1	1	yes	characteristic, complemented
223	#3135	C₂×C₁₁	1	1	yes	characteristic, complemented
224	C₂×#490	C₂×C₁₁	1	1	yes	characteristic, complemented
225	#3062	C₂×C₁₁	1	4	yes	complemented
226	#2946	C₂×C₁₁	1	4	yes	complemented
227	#2875	C₂×C₁₁	1	1	yes	characteristic, complemented
228	C₂³×C₁₁	—	2	2	no	—
229	C₂³×C₁₁	—	2	4	no	—
230	C₂³×C₁₁	—	4	4	no	—
231	C₂³×C₁₁	—	8	4	no	—
232	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
233	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₁₁	—	2	2	no	—
235	Q₈×C₁₁	—	2	4	no	—
236	Q₈×C₁₁	—	4	4	no	—
237	D₄×C₁₁	—	2	4	no	—
238	D₄×C₁₁	—	2	2	no	—
239	D₄×C₁₁	—	2	4	no	—
240	D₄×C₁₁	—	2	8	no	—
241	D₄×C₁₁	—	4	8	no	—
242	D₄×C₁₁	—	4	4	no	—
243	D₄×C₁₁	—	4	4	no	—
244	D₄×C₁₁	—	8	2	no	—
245	D₄×C₁₁	—	8	4	no	—
246	D₄×C₁₁	—	8	4	no	—
247	D₄×C₁₁	—	8	8	no	—
248	C₂×C₄×C₁₁	—	2	4	no	—
249	C₂×C₄×C₁₁	—	2	2	no	—
250	C₂×C₄×C₁₁	—	2	4	no	—
251	C₂×C₄×C₁₁	—	2	4	no	—
252	C₂×C₄×C₁₁	—	4	2	no	—
253	C₂×C₄×C₁₁	—	4	4	no	—
254	C₂×C₄×C₁₁	—	4	4	no	—
255	C₂×C₄×C₁₁	—	8	4	no	—
256	C₂×C₄×C₁₁	—	8	8	no	—
257	C₂×C₄×C₁₁	—	8	2	no	—
258	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
259	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
264	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
265	C₈×C₁₁	—	2	2	no	—
266	C₈×C₁₁	—	2	2	no	—
267	C₈×C₁₁	C₂×#41	1	8	yes	—
268	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	4	yes	—
269	C₂×#131	C₂²×C₁₁	1	2	yes	—
270	#559	—	2	2	no	—
271	#553	—	2	4	no	—
272	#553	—	2	2	no	—
273	#552	—	2	2	no	—
274	#550	—	2	2	no	—
275	#546	—	2	4	no	—
276	#541	C₂²×C₁₁	1	2	yes	complemented
277	#540	C₂²×C₁₁	1	4	yes	—
278	#540	C₂²×C₁₁	1	2	yes	complemented
279	#537	C₂²×C₁₁	1	2	yes	—
280	#535	C₂²×C₁₁	1	2	yes	—
281	#533	C₂²×C₁₁	1	1	yes	characteristic
282	#532	C₂²×C₁₁	1	1	yes	characteristic
283	#532	C₂²×C₁₁	1	4	yes	—
284	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
285	#529	C₂²×C₁₁	1	4	yes	complemented
286	C₂×#125	C₂²×C₁₁	1	1	yes	characteristic
287	#520	C₂²×C₁₁	1	2	yes	—
288	#518	C₂²×C₁₁	1	2	yes	—
289	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
290	#501	C₂²×C₁₁	1	4	yes	complemented
291	#499	C₂²×C₁₁	1	4	yes	complemented
292	#496	C₂²×C₁₁	1	4	yes	—
293	#493	C₂²×C₁₁	1	2	yes	—
294	#492	C₂²×C₁₁	1	2	yes	—
295	#491	C₂²×C₁₁	1	2	yes	complemented
296	#490	C₂²×C₁₁	1	2	yes	—
297	#490	C₂²×C₁₁	1	4	yes	—
298	#490	C₂²×C₁₁	1	2	yes	—
299	#490	C₂²×C₁₁	1	2	yes	complemented
300	#489	C₂²×C₁₁	1	2	yes	complemented
301	#489	C₂²×C₁₁	1	2	yes	complemented
302	#469	C₂²×C₁₁	1	8	yes	complemented
303	#468	C₂²×C₁₁	1	8	yes	complemented
304	#466	C₂²×C₁₁	1	8	yes	complemented
305	#465	C₂²×C₁₁	1	8	yes	complemented
306	#442	C₂²×C₁₁	1	8	yes	complemented
307	#440	C₂²×C₁₁	1	8	yes	complemented
308	C₄×SD₁₆	C₂²×C₁₁	1	8	yes	complemented
309	C₄×D₈	C₂²×C₁₁	1	8	yes	complemented
310	#428	C₂²×C₁₁	1	4	yes	—
311	#416	C₂²×C₁₁	1	4	yes	—
312	C₂×#102	C₂²×C₁₁	1	4	yes	—
313	#405	C₂²×C₁₁	1	2	yes	—
314	#405	C₂²×C₁₁	1	4	yes	complemented
315	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
316	C₄×M₁₆	C₂²×C₁₁	1	2	yes	complemented
317	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
318	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
319	C₂²×C₁₁	—	2	2	no	—
320	C₂²×C₁₁	—	2	4	no	—
321	C₂²×C₁₁	—	2	2	no	—
322	C₂²×C₁₁	—	4	2	no	—
323	C₂²×C₁₁	—	4	8	no	—
324	C₂²×C₁₁	—	4	2	no	—
325	C₂²×C₁₁	—	4	2	no	—
326	C₂²×C₁₁	—	4	4	no	—
327	C₂²×C₁₁	—	16	4	no	—
328	C₂²×C₁₁	#532	1	2	yes	—
329	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
330	C₄×C₁₁	—	2	2	no	—
331	C₄×C₁₁	—	2	4	no	—
332	C₄×C₁₁	—	2	2	no	—
333	C₄×C₁₁	—	2	2	no	—
334	C₄×C₁₁	—	4	4	no	—
335	C₄×C₁₁	—	4	4	no	—
336	C₄×C₁₁	—	4	2	no	—
337	C₄×C₁₁	#532	1	2	yes	—
338	C₄×C₁₁	C₂²×#41	1	2	yes	—
339	C₂×#41	—	2	4	no	—
340	C₂×#41	C₂³×C₁₁	1	2	yes	—
341	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
344	AGL(1,ℤ/8)	—	2	16	no	—
345	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
346	C₂×D₈	C₂³×C₁₁	1	8	yes	—
347	#131	—	2	8	no	—
348	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
349	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
350	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
351	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
352	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
353	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
354	#127	—	2	2	no	—
355	#127	—	2	2	no	—
356	#127	C₂³×C₁₁	1	2	yes	—
357	#127	C₂³×C₁₁	1	2	yes	—
358	#127	C₂³×C₁₁	1	1	yes	characteristic
359	#126	—	2	4	no	—
360	#126	—	2	4	no	—
361	#125	—	2	4	no	—
362	#125	—	2	2	no	—
363	#125	C₂³×C₁₁	1	2	yes	—
364	#125	C₂³×C₁₁	1	2	yes	—
365	#125	C₂³×C₁₁	1	2	yes	—
366	#124	—	2	2	no	—
367	#124	—	2	4	no	—
368	#124	C₂³×C₁₁	1	2	yes	—
369	#123	—	2	4	no	—
370	#123	—	2	8	no	—
371	#123	—	2	4	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
375	#121	—	2	2	no	—
376	#121	—	2	4	no	—
377	#121	—	2	4	no	—
378	#121	—	2	2	no	—
379	#121	—	2	8	no	—
380	#121	—	2	4	no	—
381	#121	C₂³×C₁₁	1	4	yes	—
382	#121	C₂³×C₁₁	1	8	yes	—
383	#120	—	2	4	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	D₄×C₁₁	1	2	yes	—
386	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
387	C₄×D₄	—	2	4	no	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	4	no	—
390	C₄×D₄	—	2	4	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	D₄×C₁₁	1	4	yes	—
393	C₄×D₄	D₄×C₁₁	1	2	yes	—
394	C₄×D₄	C₂³×C₁₁	1	8	yes	—
395	C₄×D₄	C₂³×C₁₁	1	4	yes	—
396	#117	—	2	2	no	—
397	#117	—	2	4	no	—
398	#117	C₂³×C₁₁	1	2	yes	—
399	#117	C₂³×C₁₁	1	1	yes	characteristic
400	#117	C₂³×C₁₁	1	2	yes	—
401	C₂×C₄⋊C₄	—	2	2	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
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	8	yes	—
408	#106	C₂³×C₁₁	1	8	yes	—
409	#103	C₂³×C₁₁	1	4	yes	—
410	#103	C₂³×C₁₁	1	4	yes	—
411	#102	C₂³×C₁₁	1	8	yes	—
412	#102	C₂³×C₁₁	1	8	yes	—
413	#102	C₂³×C₁₁	1	4	yes	—
414	#102	C₂³×C₁₁	1	4	yes	—
415	#97	C₂³×C₁₁	1	1	yes	characteristic
416	#97	C₂³×C₁₁	1	1	yes	characteristic
417	#97	C₂³×C₁₁	1	2	yes	—
418	#97	C₂³×C₁₁	1	2	yes	—
419	#97	C₂³×C₁₁	1	4	yes	—
420	C₄×C₈	C₂³×C₁₁	1	2	yes	—
421	C₄×C₈	C₂³×C₁₁	1	4	yes	—
422	C₂×C₁₁	—	2	2	no	—
423	C₂×C₁₁	—	4	2	no	—
424	C₂×C₁₁	—	8	2	no	—
425	C₂×C₁₁	—	8	4	no	—
426	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
427	C₂×C₁₁	#3585	1	2	yes	—
428	C₂⁴	—	2	2	no	—
429	#41	—	2	4	no	—
430	#41	—	2	8	no	—
431	#41	—	8	8	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
434	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	8	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	8	no	—
443	C₂×D₄	—	8	4	no	—
444	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
445	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
446	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
447	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	8	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
453	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
455	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
456	SD₁₆	—	2	16	no	—
457	D₈	—	2	16	no	—
458	M₁₆	—	2	8	no	—
459	M₁₆	C₁₁×#41	1	8	yes	complemented
460	C₂×C₈	—	2	4	no	—
461	C₂×C₈	—	2	8	no	—
462	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
463	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
464	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
474	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
475	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
476	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	8	no	—
485	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
486	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
487	C₄²	—	2	4	no	—
488	C₄²	—	2	2	no	—
489	C₄²	C₂×D₄×C₁₁	1	4	yes	—
490	C₄²	C₂×D₄×C₁₁	1	2	yes	—
491	C₄²	C₂⁴×C₁₁	1	2	yes	—
492	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
493	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
494	C₁₁	#60725	1	1	yes	characteristic, direct product factor, Sylow
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	4	4	no	—
498	C₂³	—	8	4	no	—
499	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
500	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
501	Q₈	—	2	2	no	—
502	Q₈	—	2	4	no	—
503	Q₈	—	4	4	no	—
504	D₄	—	2	4	no	—
505	D₄	—	2	2	no	—
506	D₄	—	2	4	no	—
507	D₄	—	2	8	no	—
508	D₄	—	4	8	no	—
509	D₄	—	4	4	no	—
510	D₄	—	4	4	no	—
511	D₄	—	8	2	no	—
512	D₄	—	8	4	no	—
513	D₄	—	8	4	no	—
514	D₄	—	8	8	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	8	4	no	—
523	C₂×C₄	—	8	8	no	—
524	C₂×C₄	—	8	2	no	—
525	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
526	C₂×C₄	C₂²×D₄×C₁₁	1	2	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	1	yes	characteristic
530	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
531	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
532	C₈	—	2	2	no	—
533	C₈	—	2	2	no	—
534	C₈	C₂×C₁₁×#41	1	8	yes	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	8	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	16	4	no	—
544	C₂²	C₁₁×#532	1	2	yes	—
545	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	4	no	—
549	C₄	—	2	2	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	4	no	—
553	C₄	C₁₁×#532	1	2	yes	—
554	C₄	C₂²×C₁₁×#41	1	2	yes	—
555	C₂	—	2	2	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	4	no	—
558	C₂	—	8	2	no	—
559	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
560	C₂	C₁₁×#3585	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×#3508	C₂	semidirect
3. C₁₁×#3180	C₂	semidirect
4. C₁₁×#3176	C₂	semidirect
5. C₁₁×#3174	C₂	semidirect
6. C₁₁×#3171	C₂	semidirect
7. C₁₁×#3166	C₂	semidirect
8. C₁₁×#3151	C₂	semidirect
9. C₁₁×#3135	C₂	semidirect
10. C₂×C₁₁×#490	C₂	semidirect
11. C₁₁×#3062	C₂	semidirect
12. C₁₁×#2946	C₂	semidirect
13. C₁₁×#2875	C₂	semidirect
22. C₁₁×#541	C₂²	semidirect
24. C₁₁×#540	C₂²	semidirect
31. C₁₁×#529	C₂²	semidirect
36. C₁₁×#501	C₂²	semidirect
37. C₁₁×#499	C₂²	semidirect
41. C₁₁×#491	C₂²	semidirect
45. C₁₁×#490	C₂²	semidirect
46. C₁₁×#489	C₂²	semidirect
47. C₁₁×#489	C₂²	semidirect
48. C₁₁×#469	C₂²	semidirect
49. C₁₁×#468	C₂²	semidirect
50. C₁₁×#466	C₂²	semidirect
51. C₁₁×#465	C₂²	semidirect
52. C₁₁×#442	C₂²	semidirect
53. C₁₁×#440	C₂²	semidirect
54. C₄×C₁₁×SD₁₆	C₂²	semidirect
55. C₄×C₁₁×D₈	C₂²	semidirect
60. C₁₁×#405	C₂²	semidirect
62. C₄×C₁₁×M₁₆	C₂²	semidirect
64. C₂×C₁₁×#97	C₂²	semidirect
148. #60725	C₁₁	direct (N × H)
180. C₁₁×M₁₆	#41	semidirect
215. #3512	C₂×C₁₁	semidirect
216. #3508	C₂×C₁₁	semidirect
217. #3180	C₂×C₁₁	semidirect
218. #3176	C₂×C₁₁	semidirect
219. #3174	C₂×C₁₁	semidirect
220. #3171	C₂×C₁₁	semidirect
221. #3166	C₂×C₁₁	semidirect
222. #3151	C₂×C₁₁	semidirect
223. #3135	C₂×C₁₁	semidirect
224. C₂×#490	C₂×C₁₁	semidirect
225. #3062	C₂×C₁₁	semidirect
226. #2946	C₂×C₁₁	semidirect
227. #2875	C₂×C₁₁	semidirect
276. #541	C₂²×C₁₁	semidirect
278. #540	C₂²×C₁₁	semidirect
285. #529	C₂²×C₁₁	semidirect
290. #501	C₂²×C₁₁	semidirect
291. #499	C₂²×C₁₁	semidirect
295. #491	C₂²×C₁₁	semidirect
299. #490	C₂²×C₁₁	semidirect
300. #489	C₂²×C₁₁	semidirect
301. #489	C₂²×C₁₁	semidirect
302. #469	C₂²×C₁₁	semidirect
303. #468	C₂²×C₁₁	semidirect
304. #466	C₂²×C₁₁	semidirect
305. #465	C₂²×C₁₁	semidirect
306. #442	C₂²×C₁₁	semidirect
307. #440	C₂²×C₁₁	semidirect
308. C₄×SD₁₆	C₂²×C₁₁	semidirect
309. C₄×D₈	C₂²×C₁₁	semidirect
314. #405	C₂²×C₁₁	semidirect
316. C₄×M₁₆	C₂²×C₁₁	semidirect
318. C₂×#97	C₂²×C₁₁	semidirect
459. M₁₆	C₁₁×#41	semidirect
494. C₁₁	#60725	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×#3508	2
C₁₁×#3180	2
C₁₁×#3176	2
C₁₁×#3174	2
C₁₁×#3171	2
C₁₁×#3166	2
C₁₁×#3151	2
C₁₁×#3135	2
C₂×C₁₁×#490	2
C₁₁×#3062	2
C₁₁×#2946	2
C₁₁×#2875	2
#60725	11

Subgroups — C11×#60725 #14637918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60725 #14637918