Subgroups — C₁₁×#60727 #14637920

Order 2816.

1902 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3181	C₂	1	2	yes	maximal, complemented
4	C₁₁×#3180	C₂	1	2	yes	maximal, complemented
5	C₁₁×#3175	C₂	1	4	yes	maximal, complemented
6	C₁₁×#3173	C₂	1	4	yes	maximal, complemented
7	C₁₁×#3172	C₂	1	2	yes	maximal, complemented
8	C₁₁×#3171	C₂	1	2	yes	maximal, complemented
9	C₁₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#3153	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#3135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#489	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₁×#3063	C₂	1	2	yes	maximal, complemented
14	C₁₁×#3062	C₂	1	2	yes	maximal, complemented
15	C₁₁×#2947	C₂	1	2	yes	maximal, complemented
16	C₁₁×#2946	C₂	1	2	yes	maximal, complemented
17	C₁₁×#2875	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₁×#137	C₂²	1	2	yes	—
19	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₁₁×#131	C₂²	1	2	yes	—
21	C₁₁×#559	—	2	1	no	—
22	C₁₁×#559	—	2	1	no	—
23	C₁₁×#556	—	2	1	no	—
24	C₁₁×#556	—	2	1	no	—
25	C₁₁×#556	—	2	1	no	—
26	C₁₁×#555	—	2	1	no	—
27	C₁₁×#554	—	2	1	no	—
28	C₁₁×#553	—	2	2	no	—
29	C₁₁×#551	—	2	2	no	—
30	C₁₁×#551	—	2	2	no	—
31	C₁₁×#548	—	2	2	no	—
32	C₁₁×#547	—	2	1	no	—
33	C₁₁×#542	C₂²	1	2	yes	—
34	C₁₁×#542	C₂²	1	2	yes	—
35	C₁₁×#542	C₂²	1	4	yes	complemented
36	C₁₁×#537	C₂²	1	2	yes	—
37	C₁₁×#536	C₂²	1	1	yes	characteristic
38	C₁₁×#535	C₂²	1	1	yes	characteristic
39	C₁₁×#533	C₂²	1	1	yes	characteristic
40	C₁₁×#533	C₂²	1	2	yes	complemented
41	C₁₁×#532	C₂²	1	1	yes	characteristic
42	C₁₁×#532	C₂²	1	2	yes	complemented
43	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₁₁×#529	C₂²	1	2	yes	—
45	C₁₁×#529	C₂²	1	2	yes	—
46	C₂×C₁₁×#124	C₂²	1	1	yes	characteristic
47	C₁₁×#520	C₂²	1	2	yes	—
48	C₁₁×#519	C₂²	1	1	yes	characteristic
49	C₁₁×#518	C₂²	1	1	yes	characteristic
50	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
51	C₁₁×#501	C₂²	1	2	yes	complemented
52	C₁₁×#501	C₂²	1	2	yes	complemented
53	C₁₁×#500	C₂²	1	2	yes	complemented
54	C₁₁×#498	C₂²	1	2	yes	complemented
55	C₁₁×#497	C₂²	1	2	yes	—
56	C₁₁×#496	C₂²	1	2	yes	—
57	C₁₁×#495	C₂²	1	4	yes	—
58	C₁₁×#491	C₂²	1	1	yes	characteristic, complemented
59	C₁₁×#491	C₂²	1	1	yes	characteristic, complemented
60	C₁₁×#490	C₂²	1	1	yes	characteristic, complemented
61	C₁₁×#490	C₂²	1	1	yes	characteristic, complemented
62	C₁₁×#489	C₂²	1	2	yes	—
63	C₁₁×#489	C₂²	1	4	yes	—
64	C₁₁×#489	C₂²	1	2	yes	—
65	C₁₁×#489	C₂²	1	2	yes	complemented
66	C₁₁×#489	C₂²	1	2	yes	complemented
67	C₁₁×#470	C₂²	1	4	yes	complemented
68	C₁₁×#469	C₂²	1	4	yes	—
69	C₁₁×#468	C₂²	1	4	yes	—
70	C₁₁×#468	C₂²	1	4	yes	complemented
71	C₁₁×#467	C₂²	1	4	yes	complemented
72	C₁₁×#466	C₂²	1	4	yes	—
73	C₁₁×#465	C₂²	1	4	yes	—
74	C₁₁×#465	C₂²	1	4	yes	complemented
75	C₁₁×#442	C₂²	1	4	yes	—
76	C₁₁×#441	C₂²	1	4	yes	complemented
77	C₁₁×#440	C₂²	1	4	yes	—
78	C₁₁×#440	C₂²	1	4	yes	complemented
79	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	complemented
80	C₄×C₁₁×SD₁₆	C₂²	1	4	yes	—
81	C₄×C₁₁×SD₁₆	C₂²	1	4	yes	complemented
82	C₄×C₁₁×D₈	C₂²	1	4	yes	—
83	C₁₁×#428	C₂²	1	2	yes	—
84	C₁₁×#428	C₂²	1	2	yes	—
85	C₁₁×#416	C₂²	1	2	yes	—
86	C₁₁×#416	C₂²	1	2	yes	—
87	C₂×C₁₁×#103	C₂²	1	2	yes	—
88	C₂×C₁₁×#102	C₂²	1	2	yes	—
89	C₁₁×#405	C₂²	1	2	yes	—
90	C₁₁×#405	C₂²	1	4	yes	complemented
91	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
92	C₄×C₁₁×M₁₆	C₂²	1	2	yes	complemented
93	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
94	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
95	C₂×C₁₁×#41	—	2	2	no	—
96	C₂×C₁₁×#41	C₂³	1	2	yes	—
97	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₁	—	2	1	no	—
99	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
101	C₁₁×#137	—	2	8	no	—
102	C₁₁×AGL(1,ℤ/8)	—	2	8	no	—
103	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₁×D₈	C₂³	1	4	yes	—
107	C₁₁×#131	—	2	8	no	—
108	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
109	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
110	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
111	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
112	C₁₁×C₄⋊Q₈	—	2	1	no	—
113	C₁₁×C₄⋊Q₈	—	2	1	no	—
114	C₁₁×C₄⋊Q₈	—	2	1	no	—
115	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₁×#127	—	2	1	no	—
121	C₁₁×#127	C₂³	1	1	yes	characteristic
122	C₁₁×#126	—	2	2	no	—
123	C₁₁×#126	—	2	2	no	—
124	C₁₁×#126	—	2	4	no	—
125	C₁₁×#126	—	2	2	no	—
126	C₁₁×#126	—	2	2	no	—
127	C₁₁×#125	—	2	2	no	—
128	C₁₁×#125	C₂³	1	1	yes	characteristic
129	C₁₁×#125	C₂³	1	1	yes	characteristic
130	C₁₁×#124	—	2	1	no	—
131	C₁₁×#124	—	2	1	no	—
132	C₁₁×#124	—	2	2	no	—
133	C₁₁×#124	—	2	2	no	—
134	C₁₁×#124	—	2	4	no	—
135	C₁₁×#124	—	2	1	no	—
136	C₁₁×#124	—	2	1	no	—
137	C₁₁×#124	—	2	2	no	—
138	C₁₁×#124	C₂³	1	2	yes	—
139	C₁₁×#124	C₂³	1	2	yes	—
140	C₁₁×#124	C₂³	1	2	yes	—
141	C₁₁×#123	—	2	2	no	—
142	C₁₁×#123	—	2	2	no	—
143	C₁₁×#123	—	2	2	no	—
144	C₁₁×#123	—	2	2	no	—
145	C₁₁×#123	—	2	2	no	—
146	C₁₁×#123	—	2	4	no	—
147	C₁₁×C₂²⋊Q₈	—	2	2	no	—
148	C₁₁×C₂²⋊Q₈	—	2	1	no	—
149	C₁₁×C₂²⋊Q₈	—	2	1	no	—
150	C₁₁×C₂²⋊Q₈	—	2	2	no	—
151	C₁₁×C₂²⋊Q₈	—	2	2	no	—
152	C₁₁×C₂²⋊Q₈	—	2	2	no	—
153	C₁₁×C₂²⋊Q₈	—	2	4	no	—
154	C₁₁×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₁₁×C₂²⋊Q₈	C₂³	1	2	yes	—
156	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
157	C₁₁×#121	—	2	2	no	—
158	C₁₁×#121	—	2	4	no	—
159	C₁₁×#121	—	2	1	no	—
160	C₁₁×#121	—	2	1	no	—
161	C₁₁×#121	—	2	2	no	—
162	C₁₁×#121	C₂³	1	2	yes	—
163	C₁₁×#121	C₂³	1	2	yes	—
164	C₁₁×#121	C₂³	1	4	yes	—
165	C₁₁×#120	—	2	2	no	—
166	C₄×Q₈×C₁₁	—	2	1	no	—
167	C₄×Q₈×C₁₁	—	2	1	no	—
168	C₄×Q₈×C₁₁	—	2	1	no	—
169	C₄×Q₈×C₁₁	—	2	1	no	—
170	C₄×Q₈×C₁₁	—	2	2	no	—
171	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
172	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
173	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
174	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
175	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
176	C₄×D₄×C₁₁	—	2	2	no	—
177	C₄×D₄×C₁₁	—	2	2	no	—
178	C₄×D₄×C₁₁	—	2	1	no	—
179	C₄×D₄×C₁₁	—	2	1	no	—
180	C₄×D₄×C₁₁	—	2	4	no	—
181	C₄×D₄×C₁₁	—	2	1	no	—
182	C₄×D₄×C₁₁	—	2	1	no	—
183	C₄×D₄×C₁₁	—	2	2	no	—
184	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
185	C₄×D₄×C₁₁	D₄	1	2	yes	—
186	C₄×D₄×C₁₁	D₄	1	2	yes	—
187	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
188	C₄×D₄×C₁₁	C₂³	1	2	yes	—
189	C₄×D₄×C₁₁	C₂³	1	2	yes	—
190	C₄×D₄×C₁₁	C₂³	1	4	yes	—
191	C₁₁×#117	—	2	2	no	—
192	C₁₁×#117	—	2	2	no	—
193	C₁₁×#117	—	2	2	no	—
194	C₁₁×#117	—	2	2	no	—
195	C₁₁×#117	—	2	2	no	—
196	C₁₁×#117	C₂³	1	1	yes	characteristic
197	C₁₁×#117	C₂³	1	1	yes	characteristic
198	C₁₁×#117	C₂³	1	1	yes	characteristic
199	C₁₁×#117	C₂³	1	2	yes	—
200	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
201	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
202	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
204	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
205	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
208	C₁₁×#107	C₂³	1	4	yes	—
209	C₁₁×#107	C₂³	1	4	yes	—
210	C₁₁×#106	C₂³	1	4	yes	—
211	C₁₁×#106	C₂³	1	4	yes	—
212	C₁₁×#103	C₂³	1	4	yes	—
213	C₁₁×#103	C₂³	1	4	yes	—
214	C₁₁×#103	C₂³	1	2	yes	—
215	C₁₁×#103	C₂³	1	2	yes	—
216	C₁₁×#103	C₂³	1	2	yes	—
217	C₁₁×#103	C₂³	1	2	yes	—
218	C₁₁×#102	C₂³	1	4	yes	—
219	C₁₁×#102	C₂³	1	4	yes	—
220	C₁₁×#102	C₂³	1	2	yes	—
221	C₁₁×#102	C₂³	1	2	yes	—
222	C₁₁×#102	C₂³	1	2	yes	—
223	C₁₁×#102	C₂³	1	2	yes	—
224	C₁₁×#97	C₂³	1	2	yes	—
225	C₁₁×#97	C₂³	1	1	yes	characteristic
226	C₁₁×#97	C₂³	1	1	yes	characteristic
227	C₁₁×#97	C₂³	1	2	yes	—
228	C₁₁×#97	C₂³	1	4	yes	—
229	C₄×C₈×C₁₁	C₂³	1	2	yes	—
230	C₄×C₈×C₁₁	C₂³	1	4	yes	—
231	#60727	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂⁴×C₁₁	—	2	1	no	—
233	C₁₁×#41	—	2	4	no	—
234	C₁₁×#41	—	2	4	no	—
235	C₁₁×#41	—	2	4	no	—
236	C₁₁×#41	—	8	4	no	—
237	C₂×Q₈×C₁₁	—	2	1	no	—
238	C₂×Q₈×C₁₁	—	2	2	no	—
239	C₂×Q₈×C₁₁	—	2	1	no	—
240	C₂×Q₈×C₁₁	—	2	1	no	—
241	C₂×Q₈×C₁₁	—	2	2	no	—
242	C₂×Q₈×C₁₁	—	2	4	no	—
243	C₂×Q₈×C₁₁	—	8	2	no	—
244	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
247	C₂×D₄×C₁₁	—	2	2	no	—
248	C₂×D₄×C₁₁	—	2	2	no	—
249	C₂×D₄×C₁₁	—	2	2	no	—
250	C₂×D₄×C₁₁	—	2	4	no	—
251	C₂×D₄×C₁₁	—	2	1	no	—
252	C₂×D₄×C₁₁	—	2	1	no	—
253	C₂×D₄×C₁₁	—	2	1	no	—
254	C₂×D₄×C₁₁	—	2	4	no	—
255	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
258	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₁	—	2	1	no	—
260	C₂²×C₄×C₁₁	—	2	2	no	—
261	C₂²×C₄×C₁₁	—	2	2	no	—
262	C₂²×C₄×C₁₁	—	2	2	no	—
263	C₂²×C₄×C₁₁	—	2	2	no	—
264	C₂²×C₄×C₁₁	—	2	4	no	—
265	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
271	C₁₁×Q₁₆	—	2	8	no	—
272	C₁₁×SD₁₆	—	2	8	no	—
273	C₁₁×SD₁₆	—	2	8	no	—
274	C₁₁×D₈	—	2	8	no	—
275	C₁₁×M₁₆	—	2	8	no	—
276	C₁₁×M₁₆	#41	1	8	yes	complemented
277	C₂×C₈×C₁₁	—	2	8	no	—
278	C₂×C₈×C₁₁	—	2	4	no	—
279	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
280	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
281	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
282	C₁₁×C₄⋊C₄	—	2	2	no	—
283	C₁₁×C₄⋊C₄	—	2	2	no	—
284	C₁₁×C₄⋊C₄	—	2	4	no	—
285	C₁₁×C₄⋊C₄	—	2	2	no	—
286	C₁₁×C₄⋊C₄	—	2	1	no	—
287	C₁₁×C₄⋊C₄	—	2	1	no	—
288	C₁₁×C₄⋊C₄	—	2	1	no	—
289	C₁₁×C₄⋊C₄	—	2	2	no	—
290	C₁₁×C₄⋊C₄	—	2	2	no	—
291	C₁₁×C₄⋊C₄	—	2	2	no	—
292	C₁₁×C₄⋊C₄	—	2	2	no	—
293	C₁₁×C₄⋊C₄	—	2	1	no	—
294	C₁₁×C₄⋊C₄	—	2	1	no	—
295	C₁₁×C₄⋊C₄	—	2	1	no	—
296	C₁₁×C₄⋊C₄	—	2	4	no	—
297	C₁₁×C₄⋊C₄	—	2	1	no	—
298	C₁₁×C₄⋊C₄	—	2	1	no	—
299	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
300	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
301	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
303	C₁₁×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
304	C₁₁×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
305	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
306	C₁₁×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
307	C₁₁×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
308	C₁₁×C₂²⋊C₄	—	2	1	no	—
309	C₁₁×C₂²⋊C₄	—	2	1	no	—
310	C₁₁×C₂²⋊C₄	—	2	4	no	—
311	C₁₁×C₂²⋊C₄	—	2	2	no	—
312	C₁₁×C₂²⋊C₄	—	2	2	no	—
313	C₁₁×C₂²⋊C₄	—	2	2	no	—
314	C₁₁×C₂²⋊C₄	—	2	2	no	—
315	C₁₁×C₂²⋊C₄	—	2	2	no	—
316	C₁₁×C₂²⋊C₄	—	2	2	no	—
317	C₁₁×C₂²⋊C₄	—	2	2	no	—
318	C₁₁×C₂²⋊C₄	—	2	2	no	—
319	C₁₁×C₂²⋊C₄	—	2	4	no	—
320	C₁₁×C₂²⋊C₄	—	2	2	no	—
321	C₁₁×C₂²⋊C₄	—	2	2	no	—
322	C₁₁×C₂²⋊C₄	—	2	4	no	—
323	C₁₁×C₂²⋊C₄	—	2	2	no	—
324	C₁₁×C₂²⋊C₄	—	2	2	no	—
325	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
326	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
327	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
328	C₄²×C₁₁	—	2	2	no	—
329	C₄²×C₁₁	—	2	2	no	—
330	C₄²×C₁₁	—	2	4	no	—
331	C₄²×C₁₁	—	2	1	no	—
332	C₄²×C₁₁	—	2	1	no	—
333	C₄²×C₁₁	C₂×D₄	1	2	yes	—
334	C₄²×C₁₁	C₂×D₄	1	2	yes	—
335	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₁₁	C₂⁴	1	2	yes	—
338	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
339	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
340	#3511	C₂×C₁₁	1	1	yes	characteristic, complemented
341	#3510	C₂×C₁₁	1	1	yes	characteristic, complemented
342	#3181	C₂×C₁₁	1	2	yes	complemented
343	#3180	C₂×C₁₁	1	2	yes	complemented
344	#3175	C₂×C₁₁	1	4	yes	complemented
345	#3173	C₂×C₁₁	1	4	yes	complemented
346	#3172	C₂×C₁₁	1	2	yes	complemented
347	#3171	C₂×C₁₁	1	2	yes	complemented
348	#3165	C₂×C₁₁	1	1	yes	characteristic, complemented
349	#3153	C₂×C₁₁	1	1	yes	characteristic, complemented
350	#3135	C₂×C₁₁	1	1	yes	characteristic, complemented
351	C₂×#489	C₂×C₁₁	1	1	yes	characteristic, complemented
352	#3063	C₂×C₁₁	1	2	yes	complemented
353	#3062	C₂×C₁₁	1	2	yes	complemented
354	#2947	C₂×C₁₁	1	2	yes	complemented
355	#2946	C₂×C₁₁	1	2	yes	complemented
356	#2875	C₂×C₁₁	1	1	yes	characteristic, complemented
357	C₂³×C₁₁	—	2	2	no	—
358	C₂³×C₁₁	—	2	2	no	—
359	C₂³×C₁₁	—	4	2	no	—
360	C₂³×C₁₁	—	8	1	no	—
361	C₂³×C₁₁	—	8	1	no	—
362	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
363	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
364	Q₈×C₁₁	—	2	2	no	—
365	Q₈×C₁₁	—	2	2	no	—
366	Q₈×C₁₁	—	2	4	no	—
367	Q₈×C₁₁	—	2	2	no	—
368	Q₈×C₁₁	—	4	4	no	—
369	Q₈×C₁₁	—	4	2	no	—
370	Q₈×C₁₁	—	8	1	no	—
371	Q₈×C₁₁	—	8	1	no	—
372	Q₈×C₁₁	—	8	2	no	—
373	D₄×C₁₁	—	2	4	no	—
374	D₄×C₁₁	—	2	2	no	—
375	D₄×C₁₁	—	2	2	no	—
376	D₄×C₁₁	—	2	4	no	—
377	D₄×C₁₁	—	2	2	no	—
378	D₄×C₁₁	—	4	2	no	—
379	D₄×C₁₁	—	4	2	no	—
380	D₄×C₁₁	—	4	4	no	—
381	D₄×C₁₁	—	4	2	no	—
382	D₄×C₁₁	—	8	2	no	—
383	D₄×C₁₁	—	8	2	no	—
384	D₄×C₁₁	—	8	4	no	—
385	C₂×C₄×C₁₁	—	2	4	no	—
386	C₂×C₄×C₁₁	—	2	1	no	—
387	C₂×C₄×C₁₁	—	2	1	no	—
388	C₂×C₄×C₁₁	—	2	2	no	—
389	C₂×C₄×C₁₁	—	2	2	no	—
390	C₂×C₄×C₁₁	—	2	1	no	—
391	C₂×C₄×C₁₁	—	2	1	no	—
392	C₂×C₄×C₁₁	—	2	4	no	—
393	C₂×C₄×C₁₁	—	4	2	no	—
394	C₂×C₄×C₁₁	—	4	1	no	—
395	C₂×C₄×C₁₁	—	4	1	no	—
396	C₂×C₄×C₁₁	—	4	2	no	—
397	C₂×C₄×C₁₁	—	4	2	no	—
398	C₂×C₄×C₁₁	—	4	4	no	—
399	C₂×C₄×C₁₁	—	8	2	no	—
400	C₂×C₄×C₁₁	—	8	2	no	—
401	C₂×C₄×C₁₁	—	8	4	no	—
402	C₂×C₄×C₁₁	—	8	2	no	—
403	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
412	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
413	C₈×C₁₁	—	2	2	no	—
414	C₈×C₁₁	—	2	2	no	—
415	C₈×C₁₁	C₂×#41	1	8	yes	—
416	C₂×#137	C₂²×C₁₁	1	2	yes	—
417	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	2	yes	—
418	C₂×#131	C₂²×C₁₁	1	2	yes	—
419	#559	—	2	1	no	—
420	#559	—	2	1	no	—
421	#556	—	2	1	no	—
422	#556	—	2	1	no	—
423	#556	—	2	1	no	—
424	#555	—	2	1	no	—
425	#554	—	2	1	no	—
426	#553	—	2	2	no	—
427	#551	—	2	2	no	—
428	#551	—	2	2	no	—
429	#548	—	2	2	no	—
430	#547	—	2	1	no	—
431	#542	C₂²×C₁₁	1	2	yes	—
432	#542	C₂²×C₁₁	1	2	yes	—
433	#542	C₂²×C₁₁	1	4	yes	complemented
434	#537	C₂²×C₁₁	1	2	yes	—
435	#536	C₂²×C₁₁	1	1	yes	characteristic
436	#535	C₂²×C₁₁	1	1	yes	characteristic
437	#533	C₂²×C₁₁	1	1	yes	characteristic
438	#533	C₂²×C₁₁	1	2	yes	complemented
439	#532	C₂²×C₁₁	1	1	yes	characteristic
440	#532	C₂²×C₁₁	1	2	yes	complemented
441	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
442	#529	C₂²×C₁₁	1	2	yes	—
443	#529	C₂²×C₁₁	1	2	yes	—
444	C₂×#124	C₂²×C₁₁	1	1	yes	characteristic
445	#520	C₂²×C₁₁	1	2	yes	—
446	#519	C₂²×C₁₁	1	1	yes	characteristic
447	#518	C₂²×C₁₁	1	1	yes	characteristic
448	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
449	#501	C₂²×C₁₁	1	2	yes	complemented
450	#501	C₂²×C₁₁	1	2	yes	complemented
451	#500	C₂²×C₁₁	1	2	yes	complemented
452	#498	C₂²×C₁₁	1	2	yes	complemented
453	#497	C₂²×C₁₁	1	2	yes	—
454	#496	C₂²×C₁₁	1	2	yes	—
455	#495	C₂²×C₁₁	1	4	yes	—
456	#491	C₂²×C₁₁	1	1	yes	characteristic, complemented
457	#491	C₂²×C₁₁	1	1	yes	characteristic, complemented
458	#490	C₂²×C₁₁	1	1	yes	characteristic, complemented
459	#490	C₂²×C₁₁	1	1	yes	characteristic, complemented
460	#489	C₂²×C₁₁	1	2	yes	—
461	#489	C₂²×C₁₁	1	4	yes	—
462	#489	C₂²×C₁₁	1	2	yes	—
463	#489	C₂²×C₁₁	1	2	yes	complemented
464	#489	C₂²×C₁₁	1	2	yes	complemented
465	#470	C₂²×C₁₁	1	4	yes	complemented
466	#469	C₂²×C₁₁	1	4	yes	—
467	#468	C₂²×C₁₁	1	4	yes	—
468	#468	C₂²×C₁₁	1	4	yes	complemented
469	#467	C₂²×C₁₁	1	4	yes	complemented
470	#466	C₂²×C₁₁	1	4	yes	—
471	#465	C₂²×C₁₁	1	4	yes	—
472	#465	C₂²×C₁₁	1	4	yes	complemented
473	#442	C₂²×C₁₁	1	4	yes	—
474	#441	C₂²×C₁₁	1	4	yes	complemented
475	#440	C₂²×C₁₁	1	4	yes	—
476	#440	C₂²×C₁₁	1	4	yes	complemented
477	C₄×Q₁₆	C₂²×C₁₁	1	4	yes	complemented
478	C₄×SD₁₆	C₂²×C₁₁	1	4	yes	—
479	C₄×SD₁₆	C₂²×C₁₁	1	4	yes	complemented
480	C₄×D₈	C₂²×C₁₁	1	4	yes	—
481	#428	C₂²×C₁₁	1	2	yes	—
482	#428	C₂²×C₁₁	1	2	yes	—
483	#416	C₂²×C₁₁	1	2	yes	—
484	#416	C₂²×C₁₁	1	2	yes	—
485	C₂×#103	C₂²×C₁₁	1	2	yes	—
486	C₂×#102	C₂²×C₁₁	1	2	yes	—
487	#405	C₂²×C₁₁	1	2	yes	—
488	#405	C₂²×C₁₁	1	4	yes	complemented
489	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
490	C₄×M₁₆	C₂²×C₁₁	1	2	yes	complemented
491	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
492	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
493	C₂²×C₁₁	—	2	1	no	—
494	C₂²×C₁₁	—	2	1	no	—
495	C₂²×C₁₁	—	2	2	no	—
496	C₂²×C₁₁	—	2	2	no	—
497	C₂²×C₁₁	—	2	2	no	—
498	C₂²×C₁₁	—	4	2	no	—
499	C₂²×C₁₁	—	4	2	no	—
500	C₂²×C₁₁	—	4	2	no	—
501	C₂²×C₁₁	—	4	2	no	—
502	C₂²×C₁₁	—	4	2	no	—
503	C₂²×C₁₁	—	4	2	no	—
504	C₂²×C₁₁	—	16	2	no	—
505	C₂²×C₁₁	#532	1	2	yes	—
506	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
507	C₄×C₁₁	—	2	1	no	—
508	C₄×C₁₁	—	2	2	no	—
509	C₄×C₁₁	—	2	1	no	—
510	C₄×C₁₁	—	2	1	no	—
511	C₄×C₁₁	—	2	2	no	—
512	C₄×C₁₁	—	2	1	no	—
513	C₄×C₁₁	—	2	2	no	—
514	C₄×C₁₁	—	4	4	no	—
515	C₄×C₁₁	—	4	1	no	—
516	C₄×C₁₁	—	4	1	no	—
517	C₄×C₁₁	—	4	1	no	—
518	C₄×C₁₁	—	4	1	no	—
519	C₄×C₁₁	—	4	2	no	—
520	C₄×C₁₁	—	4	2	no	—
521	C₄×C₁₁	#532	1	2	yes	—
522	C₄×C₁₁	C₂²×#41	1	2	yes	—
523	C₂×#41	—	2	2	no	—
524	C₂×#41	C₂³×C₁₁	1	2	yes	—
525	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
526	C₂²×Q₈	—	2	1	no	—
527	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
529	#137	—	2	8	no	—
530	AGL(1,ℤ/8)	—	2	8	no	—
531	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
532	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
533	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
534	C₂×D₈	C₂³×C₁₁	1	4	yes	—
535	#131	—	2	8	no	—
536	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
537	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
538	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
539	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	—	2	1	no	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
544	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
545	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
546	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
547	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
548	#127	—	2	1	no	—
549	#127	C₂³×C₁₁	1	1	yes	characteristic
550	#126	—	2	2	no	—
551	#126	—	2	2	no	—
552	#126	—	2	4	no	—
553	#126	—	2	2	no	—
554	#126	—	2	2	no	—
555	#125	—	2	2	no	—
556	#125	C₂³×C₁₁	1	1	yes	characteristic
557	#125	C₂³×C₁₁	1	1	yes	characteristic
558	#124	—	2	1	no	—
559	#124	—	2	1	no	—
560	#124	—	2	2	no	—
561	#124	—	2	2	no	—
562	#124	—	2	4	no	—
563	#124	—	2	1	no	—
564	#124	—	2	1	no	—
565	#124	—	2	2	no	—
566	#124	C₂³×C₁₁	1	2	yes	—
567	#124	C₂³×C₁₁	1	2	yes	—
568	#124	C₂³×C₁₁	1	2	yes	—
569	#123	—	2	2	no	—
570	#123	—	2	2	no	—
571	#123	—	2	2	no	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	4	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₂²⋊Q₈	C₂³×C₁₁	1	2	yes	—
583	C₂²⋊Q₈	C₂³×C₁₁	1	2	yes	—
584	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
585	#121	—	2	2	no	—
586	#121	—	2	4	no	—
587	#121	—	2	1	no	—
588	#121	—	2	1	no	—
589	#121	—	2	2	no	—
590	#121	C₂³×C₁₁	1	2	yes	—
591	#121	C₂³×C₁₁	1	2	yes	—
592	#121	C₂³×C₁₁	1	4	yes	—
593	#120	—	2	2	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
600	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
602	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
603	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	4	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	D₄×C₁₁	1	1	yes	characteristic
613	C₄×D₄	D₄×C₁₁	1	2	yes	—
614	C₄×D₄	D₄×C₁₁	1	2	yes	—
615	C₄×D₄	D₄×C₁₁	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₁₁	1	2	yes	—
617	C₄×D₄	C₂³×C₁₁	1	2	yes	—
618	C₄×D₄	C₂³×C₁₁	1	4	yes	—
619	#117	—	2	2	no	—
620	#117	—	2	2	no	—
621	#117	—	2	2	no	—
622	#117	—	2	2	no	—
623	#117	—	2	2	no	—
624	#117	C₂³×C₁₁	1	1	yes	characteristic
625	#117	C₂³×C₁₁	1	1	yes	characteristic
626	#117	C₂³×C₁₁	1	1	yes	characteristic
627	#117	C₂³×C₁₁	1	2	yes	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	—	2	2	no	—
630	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	2	no	—
634	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
636	#107	C₂³×C₁₁	1	4	yes	—
637	#107	C₂³×C₁₁	1	4	yes	—
638	#106	C₂³×C₁₁	1	4	yes	—
639	#106	C₂³×C₁₁	1	4	yes	—
640	#103	C₂³×C₁₁	1	4	yes	—
641	#103	C₂³×C₁₁	1	4	yes	—
642	#103	C₂³×C₁₁	1	2	yes	—
643	#103	C₂³×C₁₁	1	2	yes	—
644	#103	C₂³×C₁₁	1	2	yes	—
645	#103	C₂³×C₁₁	1	2	yes	—
646	#102	C₂³×C₁₁	1	4	yes	—
647	#102	C₂³×C₁₁	1	4	yes	—
648	#102	C₂³×C₁₁	1	2	yes	—
649	#102	C₂³×C₁₁	1	2	yes	—
650	#102	C₂³×C₁₁	1	2	yes	—
651	#102	C₂³×C₁₁	1	2	yes	—
652	#97	C₂³×C₁₁	1	1	yes	characteristic
653	#97	C₂³×C₁₁	1	1	yes	characteristic
654	#97	C₂³×C₁₁	1	2	yes	—
655	#97	C₂³×C₁₁	1	2	yes	—
656	#97	C₂³×C₁₁	1	4	yes	—
657	C₄×C₈	C₂³×C₁₁	1	2	yes	—
658	C₄×C₈	C₂³×C₁₁	1	4	yes	—
659	C₂×C₁₁	—	2	2	no	—
660	C₂×C₁₁	—	4	2	no	—
661	C₂×C₁₁	—	8	2	no	—
662	C₂×C₁₁	—	8	2	no	—
663	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
664	C₂×C₁₁	#3585	1	1	yes	characteristic
665	C₂×C₁₁	#3586	1	1	yes	characteristic
666	C₂⁴	—	2	1	no	—
667	#41	—	2	4	no	—
668	#41	—	2	4	no	—
669	#41	—	2	4	no	—
670	#41	—	8	4	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	1	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	4	no	—
677	C₂×Q₈	—	8	2	no	—
678	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
679	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
680	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
690	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
691	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
692	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
702	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
705	Q₁₆	—	2	8	no	—
706	SD₁₆	—	2	8	no	—
707	SD₁₆	—	2	8	no	—
708	D₈	—	2	8	no	—
709	M₁₆	—	2	8	no	—
710	M₁₆	C₁₁×#41	1	8	yes	complemented
711	C₂×C₈	—	2	4	no	—
712	C₂×C₈	—	2	8	no	—
713	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
714	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
715	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
735	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₁₁	1	1	yes	characteristic
738	C₄⋊C₄	C₂⁴×C₁₁	1	1	yes	characteristic
739	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
740	C₄⋊C₄	C₂⁴×C₁₁	1	1	yes	characteristic
741	C₄⋊C₄	C₂⁴×C₁₁	1	1	yes	characteristic
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
760	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
761	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	4	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	C₂×D₄×C₁₁	1	2	yes	—
768	C₄²	C₂×D₄×C₁₁	1	2	yes	—
769	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
771	C₄²	C₂⁴×C₁₁	1	2	yes	—
772	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
773	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
774	C₁₁	#60727	1	1	yes	characteristic, direct product factor, Sylow
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	4	2	no	—
778	C₂³	—	8	1	no	—
779	C₂³	—	8	1	no	—
780	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
781	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
782	Q₈	—	2	2	no	—
783	Q₈	—	2	2	no	—
784	Q₈	—	2	4	no	—
785	Q₈	—	2	2	no	—
786	Q₈	—	4	4	no	—
787	Q₈	—	4	2	no	—
788	Q₈	—	8	1	no	—
789	Q₈	—	8	1	no	—
790	Q₈	—	8	2	no	—
791	D₄	—	2	4	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	4	no	—
795	D₄	—	2	2	no	—
796	D₄	—	4	2	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	2	no	—
800	D₄	—	8	2	no	—
801	D₄	—	8	2	no	—
802	D₄	—	8	4	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	4	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	8	2	no	—
818	C₂×C₄	—	8	2	no	—
819	C₂×C₄	—	8	4	no	—
820	C₂×C₄	—	8	2	no	—
821	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
826	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
829	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
830	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
831	C₈	—	2	2	no	—
832	C₈	—	2	2	no	—
833	C₈	C₂×C₁₁×#41	1	8	yes	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	16	2	no	—
846	C₂²	C₁₁×#532	1	2	yes	—
847	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
848	C₄	—	2	2	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	4	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	C₁₁×#532	1	2	yes	—
863	C₄	C₂²×C₁₁×#41	1	2	yes	—
864	C₂	—	2	2	no	—
865	C₂	—	4	2	no	—
866	C₂	—	8	2	no	—
867	C₂	—	8	2	no	—
868	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
869	C₂	C₁₁×#3585	1	1	yes	characteristic
870	C₂	C₁₁×#3586	1	1	yes	characteristic

	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×#3511	C₂	semidirect
2. C₁₁×#3510	C₂	semidirect
3. C₁₁×#3181	C₂	semidirect
4. C₁₁×#3180	C₂	semidirect
5. C₁₁×#3175	C₂	semidirect
6. C₁₁×#3173	C₂	semidirect
7. C₁₁×#3172	C₂	semidirect
8. C₁₁×#3171	C₂	semidirect
9. C₁₁×#3165	C₂	semidirect
10. C₁₁×#3153	C₂	semidirect
11. C₁₁×#3135	C₂	semidirect
12. C₂×C₁₁×#489	C₂	semidirect
13. C₁₁×#3063	C₂	semidirect
14. C₁₁×#3062	C₂	semidirect
15. C₁₁×#2947	C₂	semidirect
16. C₁₁×#2946	C₂	semidirect
17. C₁₁×#2875	C₂	semidirect
35. C₁₁×#542	C₂²	semidirect
40. C₁₁×#533	C₂²	semidirect
42. C₁₁×#532	C₂²	semidirect
51. C₁₁×#501	C₂²	semidirect
52. C₁₁×#501	C₂²	semidirect
53. C₁₁×#500	C₂²	semidirect
54. C₁₁×#498	C₂²	semidirect
58. C₁₁×#491	C₂²	semidirect
59. C₁₁×#491	C₂²	semidirect
60. C₁₁×#490	C₂²	semidirect
61. C₁₁×#490	C₂²	semidirect
65. C₁₁×#489	C₂²	semidirect
66. C₁₁×#489	C₂²	semidirect
67. C₁₁×#470	C₂²	semidirect
70. C₁₁×#468	C₂²	semidirect
71. C₁₁×#467	C₂²	semidirect
74. C₁₁×#465	C₂²	semidirect
76. C₁₁×#441	C₂²	semidirect
78. C₁₁×#440	C₂²	semidirect
79. C₄×C₁₁×Q₁₆	C₂²	semidirect
81. C₄×C₁₁×SD₁₆	C₂²	semidirect
90. C₁₁×#405	C₂²	semidirect
92. C₄×C₁₁×M₁₆	C₂²	semidirect
94. C₂×C₁₁×#97	C₂²	semidirect
231. #60727	C₁₁	direct (N × H)
276. C₁₁×M₁₆	#41	semidirect
340. #3511	C₂×C₁₁	semidirect
341. #3510	C₂×C₁₁	semidirect
342. #3181	C₂×C₁₁	semidirect
343. #3180	C₂×C₁₁	semidirect
344. #3175	C₂×C₁₁	semidirect
345. #3173	C₂×C₁₁	semidirect
346. #3172	C₂×C₁₁	semidirect
347. #3171	C₂×C₁₁	semidirect
348. #3165	C₂×C₁₁	semidirect
349. #3153	C₂×C₁₁	semidirect
350. #3135	C₂×C₁₁	semidirect
351. C₂×#489	C₂×C₁₁	semidirect
352. #3063	C₂×C₁₁	semidirect
353. #3062	C₂×C₁₁	semidirect
354. #2947	C₂×C₁₁	semidirect
355. #2946	C₂×C₁₁	semidirect
356. #2875	C₂×C₁₁	semidirect
433. #542	C₂²×C₁₁	semidirect
438. #533	C₂²×C₁₁	semidirect
440. #532	C₂²×C₁₁	semidirect
449. #501	C₂²×C₁₁	semidirect
450. #501	C₂²×C₁₁	semidirect
451. #500	C₂²×C₁₁	semidirect
452. #498	C₂²×C₁₁	semidirect
456. #491	C₂²×C₁₁	semidirect
457. #491	C₂²×C₁₁	semidirect
458. #490	C₂²×C₁₁	semidirect
459. #490	C₂²×C₁₁	semidirect
463. #489	C₂²×C₁₁	semidirect
464. #489	C₂²×C₁₁	semidirect
465. #470	C₂²×C₁₁	semidirect
468. #468	C₂²×C₁₁	semidirect
469. #467	C₂²×C₁₁	semidirect
472. #465	C₂²×C₁₁	semidirect
474. #441	C₂²×C₁₁	semidirect
476. #440	C₂²×C₁₁	semidirect
477. C₄×Q₁₆	C₂²×C₁₁	semidirect
479. C₄×SD₁₆	C₂²×C₁₁	semidirect
488. #405	C₂²×C₁₁	semidirect
490. C₄×M₁₆	C₂²×C₁₁	semidirect
492. C₂×#97	C₂²×C₁₁	semidirect
710. M₁₆	C₁₁×#41	semidirect
774. C₁₁	#60727	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×#3511	2
C₁₁×#3510	2
C₁₁×#3181	2
C₁₁×#3180	2
C₁₁×#3175	2
C₁₁×#3173	2
C₁₁×#3172	2
C₁₁×#3171	2
C₁₁×#3165	2
C₁₁×#3153	2
C₁₁×#3135	2
C₂×C₁₁×#489	2
C₁₁×#3063	2
C₁₁×#3062	2
C₁₁×#2947	2
C₁₁×#2946	2
C₁₁×#2875	2
#60727	11

Subgroups — C11×#60727 #14637920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60727 #14637920