Finite Group Databasebeta

← #15617700

Subgroups — #15617700

Order 2816.

2862 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623281C211yesmaximal, characteristic, complemented
2C22×M16×D11C211yesmaximal, characteristic, complemented
3D11×#525C211yesmaximal, characteristic
4#13077352C214yesmaximal, complemented
5#13077349C214yesmaximal, complemented
6#13077345C214yesmaximal, complemented
7#13077339C214yesmaximal, complemented
8#13077320C211yesmaximal, characteristic, complemented
9#13077319C211yesmaximal, characteristic, complemented
10#13077315C211yesmaximal, characteristic, complemented
11#13077313C211yesmaximal, characteristic, complemented
12#13077312C211yesmaximal, characteristic, complemented
13#13077309C211yesmaximal, characteristic, complemented
14#13077308C211yesmaximal, characteristic, complemented
15#13077177C211yesmaximal, characteristic, complemented
16#13077058C211yesmaximal, characteristic, complemented
17D11×#407C211yesmaximal, characteristic, complemented
18#13077032C211yesmaximal, characteristic, complemented
19C11×#2930C211yesmaximal, characteristic, complemented
20C2×#41×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C2×C11×#131C2211yescharacteristic, complemented
23C22×C11×M16C2211yescharacteristic, complemented
24C11×#525C2211yescharacteristic
25#10623359C2211yescharacteristic
26C2×#67001C2211yescharacteristic, complemented
27#10623322C2211yescharacteristic
28C22×#4318C2211yescharacteristic, complemented
29#10623281—28no—
30C2×#66960C2212yescomplemented
31C2×#66960C2211yescharacteristic, complemented
32C2×M16×D11—28no—
33C2×M16×D11C2211yescharacteristic
34C2×M16×D11C2211yescharacteristic
35C2×M16×D11C2212yes—
36C2×M16×D11C2212yes—
37C2×M16×D11C2212yescomplemented
38C2×M16×D11C2212yescomplemented
39C2×M16×D11C2212yescomplemented
40C2×#66954C2212yescomplemented
41C2×#66954C2211yescharacteristic, complemented
42C22×#4313C2211yescharacteristic
43C22×#4313C2211yescharacteristic
44C22×#4313C2212yescomplemented
45C22×C8×D11C2211yescharacteristic, complemented
46C22×C8×D11C2211yescharacteristic, complemented
47#10623187C412yes—
48D11×#123C412yes—
49#10623158C412yes—
50D11×C22⋊Q8C412yes—
51#10623137C412yes—
52D11×#121C412yes—
53D11×#120C412yes—
54#10623117C412yes—
55#10623078C2214yes—
56C4×D4×D11C2214yes—
57#10623055C2211yescharacteristic
58D11×#117C2211yescharacteristic
59C11×#436C2214yescomplemented
60C11×#435C2214yescomplemented
61C11×#424C2211yescharacteristic, complemented
62C11×#408C2211yescharacteristic, complemented
63C11×#407C2211yescharacteristic, complemented
64C11×#405C2211yescharacteristic, complemented
65#10622847C2211yescharacteristic, complemented
66#10622820C2211yescharacteristic, complemented
67#10622742C2211yescharacteristic, complemented
68#10622741C2214yescomplemented
69#10622740C2214yescomplemented
70#10622740C2214yescomplemented
71#10622739C2211yescharacteristic, complemented
72#10622739C2211yescharacteristic, complemented
73#10622735C2211yescharacteristic, complemented
74#10622732C2211yescharacteristic, complemented
75#10622723C2211yescharacteristic, complemented
76C8×C22⋊D11C2214yescomplemented
77#10622715C2211yescharacteristic, complemented
78#10622714C2211yescharacteristic, complemented
79#10622625C2214yescomplemented
80#10622624C2214yescomplemented
81#10622612C2211yescharacteristic, complemented
82#10622610C2211yescharacteristic, complemented
83#10622452C2214yescomplemented
84#10622450C2214yescomplemented
85#10622449C2214yescomplemented
86#10622447C2214yescomplemented
87#10622342C2214yescomplemented
88#10622341C2214yescomplemented
89#10622341C2214yescomplemented
90#10622340C2214yescomplemented
91#10622339C2214yes—
92#10622339C2214yescomplemented
93(C22⋊D11)⋊C8C2214yescomplemented
94D11×C22⋊C8C2214yescomplemented
95#10622321C2212yescomplemented
96#10622320C2212yescomplemented
97#10622319C2214yescomplemented
98#10622302C2212yescomplemented
99C4×#4313C2212yescomplemented
100C8×D44C2214yescomplemented
101C24×D11C2×C411yescharacteristic
102C2×C11×#41C2311yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C23×Dic11C2×C411yescharacteristic
105#41×D11—24no—
106#41×D11—24no—
107C2×#4343C2×C411yescharacteristic
108C2×Q8×D11C2×C411yescharacteristic
109C2×#4341C2×C412yes—
110C2×#4341C2×C411yescharacteristic
111C2×D4×D11C2×C412yes—
112C2×D4×D11C2×C411yescharacteristic
113C2×D4×D11C2×C414yes—
114C2×#4339C2311yescharacteristic
115C2×#4339C2312yes—
116C22×C4×D11—24no—
117C22×C4×D11—24no—
118C22×C4×D11C2×C412yes—
119C22×C4×D11C2×C412yes—
120C22×C4×D11C2×C411yescharacteristic
121C22×C4×D11C2×C411yescharacteristic
122C22×C4×D11C2311yescharacteristic
123C22×C4×D11C2312yes—
124C22×C4×D11C2312yes—
125C22×C4×D11C2312yes—
126C22×C4×D11C2311yescharacteristic
127C11×#131—24no—
128C2×C11×M16—24no—
129C2×C11×M16C2311yescharacteristic
130C2×C11×M16C2311yescharacteristic
131C2×C11×M16C2312yes—
132C2×C11×M16C2312yes—
133C2×C11×M16C2312yescomplemented
134C22×C8×C11C2311yescharacteristic
135C22×C8×C11C2311yescharacteristic
136C22×C8×C11C2312yescomplemented
137C11×#123C2×C412yes—
138C11×C22⋊Q8C2×C412yes—
139C11×#121C2×C412yes—
140C11×#120C2×C412yes—
141C4×D4×C11C2314yes—
142C11×#117C2311yescharacteristic
143#67006C2×C412yes—
144#67001—24no—
145#66999C2×C412yes—
146#66992C2×C414yes—
147#66991C2×C412yes—
148#66990C2×C414yes—
149#66990C2×C412yes—
150#66988C2×C412yes—
151D4×Dic11C2×C414yes—
152#66983C2×C412yes—
153#66982C2×C412yes—
154C4×C22⋊D11C2314yes—
155C4×C22⋊D11C2314yes—
156#66979C2311yescharacteristic
157#66977C2×C412yes—
158C2×#4318—24no—
159C2×#4318C2311yescharacteristic
160C2×#4318C2311yescharacteristic
161C2×#4318C2312yes—
162C2×#4318C2312yes—
163C2×#4318C2312yescomplemented
164C22×C11⋊C8C2311yescharacteristic
165C22×C11⋊C8C2311yescharacteristic
166C22×C11⋊C8C2312yescomplemented
167#66960—24no—
168#66960—28no—
169M16×D11—24no—
170M16×D11—24no—
171M16×D11—28no—
172M16×D11—28no—
173M16×D11—28no—
174M16×D11—28no—
175M16×D11—28no—
176#66954—24no—
177#66954—28no—
178C2×#4313—24no—
179C2×#4313—28no—
180C2×#4313D418yescomplemented
181C2×#4313C2312yes—
182C2×#4313C2312yes—
183C2×#4313C2312yes—
184C2×#4313C2312yes—
185C2×#4313C2311yescharacteristic
186C2×#4313C2311yescharacteristic
187C2×#4313C2311yescharacteristic
188C2×#4313C2311yescharacteristic
189C2×#4313C2312yescomplemented
190C2×#4313C2312yescomplemented
191C2×C8×D11—24no—
192C2×C8×D11—24no—
193C2×C8×D11C2312yes—
194C2×C8×D11C2312yes—
195C2×C8×D11C2312yes—
196C2×C8×D11C2312yes—
197C2×C8×D11C2312yes—
198C2×C8×D11C2312yes—
199C2×C8×D11C2312yescomplemented
200C2×C8×D11C2312yescomplemented
201#66950C2×C412yes—
202#66949C2×C414yes—
203#66948C2×C412yes—
204#66947C2×C414yes—
205#66946C2×C414yes—
206#66945C2×C412yes—
207C4⋊C4×D11C2×C412yes—
208C4⋊C4×D11C2×C414yes—
209#66939C2×C412yes—
210#66937C2×C414yes—
211#66936C2×C414yes—
212#66935C2×C412yes—
213#66935C2×C414yes—
214(C22⋊D11)⋊C4C2×C414yes—
215(C22⋊D11)⋊C4C2×C414yes—
216C22⋊C4×D11C2×C412yes—
217C22⋊C4×D11C2×C414yes—
218C22⋊C4×D11C2×C414yes—
219#66931C2×C414yes—
220#66930C2×C412yes—
221C4×D44C2314yes—
222#66925C2312yes—
223C42×D11C2312yes—
224C11×C4⋊C8C2314yescomplemented
225C11×C22⋊C8C2314yes—
226C11×C22⋊C8C2314yescomplemented
227C11×#97C2312yescomplemented
228C4×C8×C11C2312yescomplemented
229C22⋊(C11⋊C8)C2314yes—
230C22⋊(C11⋊C8)C2314yescomplemented
231(C2×D11)⋊C8C2314yes—
232(C2×D11)⋊C8C2314yes—
233(C2×D11)⋊C8C2314yescomplemented
234(C2×D11)⋊C8C2314yescomplemented
235#66879C2312yescomplemented
236#66879C2312yescomplemented
237Dic11⋊C8C2314yescomplemented
238Dic11⋊C8C2314yescomplemented
239C8×Dic11C2312yescomplemented
240C8×Dic11C2312yescomplemented
241C4⋊(C11⋊C8)C2314yescomplemented
242#66867C2312yescomplemented
243C4×C11⋊C8C2312yescomplemented
244#60141—111nomaximal, Sylow
245C24×C11C22×C411yescharacteristic
246C23×D11—24no—
247C23×D11—44no—
248C23×D11C22×C411yescharacteristic
249C23×D11C22×C412yes—
250C23×D11C22×C412yes—
251C23×D11C22×C412yes—
252C23×D11C22×C411yescharacteristic
253C11×#41—22no—
254C11×#41—22no—
255C2×Q8×C11C22×C411yescharacteristic
256C2×D4×C11C22×C412yes—
257C2×D4×C11C22×C411yescharacteristic
258C2×D4×C11C22×C414yes—
259C22×C4×C11—22no—
260C22×C4×C11—22no—
261C22×C4×C11C22×C412yes—
262C22×C4×C11C22×C411yescharacteristic
263C22×C4×C11C2412yes—
264C22×C4×C11C2412yes—
265C22×C4×C11C2411yescharacteristic
266C2×C22⋊D11C22×C414yes—
267C2×C22⋊D11C22×C412yes—
268C2×C22⋊D11C22×C412yes—
269C2×C22⋊D11C22×C412yes—
270C2×C22⋊D11C22×C414yes—
271C22×Dic11—24no—
272C22×Dic11C22×C412yes—
273C22×Dic11C22×C412yes—
274C22×Dic11C22×C412yes—
275C22×Dic11C22×C411yescharacteristic
276C22×Dic11C22×C411yescharacteristic
277#4343—24no—
278Q8×D11—24no—
279#4341—28no—
280#4341—24no—
281D4×D11—24no—
282D4×D11—28no—
283D4×D11—48no—
284#4339—24no—
285#4339—24no—
286#4339—22no—
287#4339—22no—
288C2×D44C22×C414yes—
289C2×D44C22×C412yes—
290C2×D44C22×C411yescharacteristic
291C2×C4×D11—24no—
292C2×C4×D11—28no—
293C2×C4×D11—28no—
294C2×C4×D11—24no—
295C2×C4×D11—24no—
296C2×C4×D11—24no—
297C2×C4×D11—24no—
298C2×C4×D11—24no—
299C2×C4×D11—24no—
300C2×C4×D11—24no—
301C2×C4×D11—22no—
302C2×C4×D11—22no—
303C2×C4×D11C22×C412yes—
304C2×C4×D11C22×C412yes—
305C2×C4×D11C22×C412yes—
306C2×C4×D11C22×C412yes—
307C2×C4×D11C22×C412yes—
308C2×C4×D11C22×C412yes—
309C2×C4×D11C22×C412yes—
310C2×C4×D11C22×C414yes—
311C2×C4×D11C22×C411yescharacteristic
312C2×C4×D11C22×C411yescharacteristic
313C2×C4×D11C2×D414yes—
314C2×C4×D11#4114yes—
315C2×C4×D11C2412yes—
316C2×C4×D11C2412yes—
317C2×C4×D11C2411yescharacteristic
318C2×C4×D11C2411yescharacteristic
319C2×Dic22C22×C412yes—
320C2×Dic22C22×C411yescharacteristic
321C11×M16—24no—
322C11×M16—24no—
323C11×M16—24no—
324C11×M16—22no—
325C11×M16—22no—
326C2×C8×C11—24no—
327C2×C8×C11—22no—
328C2×C8×C11C2×D414yescomplemented
329C2×C8×C11C2412yes—
330C2×C8×C11C2412yes—
331C2×C8×C11C2412yes—
332C2×C8×C11C2411yescharacteristic
333C2×C8×C11C2411yescharacteristic
334C11×C4⋊C4C22×C412yes—
335C11×C4⋊C4C22×C414yes—
336C11×C22⋊C4C22×C412yes—
337C11×C22⋊C4C22×C414yes—
338C11×C22⋊C4C22×C414yes—
339C42×C11C2412yes—
340C22⋊Dic11C22×C412yes—
341C22⋊Dic11C22×C414yes—
342C22⋊Dic11C22×C414yes—
343(C2×D11)⋊C4C22×C414yes—
344(C2×D11)⋊C4C22×C414yes—
345(C2×D11)⋊C4C22×C414yes—
346(C2×D11)⋊C4C22×C414yes—
347(C2×D11)⋊C4C22×C414yes—
348C4⋊Dic11C22×C414yes—
349C4⋊Dic11C22×C412yes—
350Dic11⋊C4C22×C414yes—
351Dic11⋊C4C22×C414yes—
352Dic11⋊C4C22×C414yes—
353C4×Dic11C22×C414yes—
354C4×Dic11C2412yes—
355#4318—24no—
356#4318—24no—
357#4318—24no—
358#4318—22no—
359#4318—22no—
360C2×C11⋊C8—24no—
361C2×C11⋊C8—22no—
362C2×C11⋊C8C2×D414yescomplemented
363C2×C11⋊C8C2412yes—
364C2×C11⋊C8C2412yes—
365C2×C11⋊C8C2412yes—
366C2×C11⋊C8C2411yescharacteristic
367C2×C11⋊C8C2411yescharacteristic
368#4313—24no—
369#4313—24no—
370#4313—24no—
371#4313—24no—
372#4313—24no—
373#4313—24no—
374#4313C2×D414yes—
375#4313C2×D414yes—
376#4313C2×D414yescomplemented
377#4313C2×D414yescomplemented
378C8×D11—24no—
379C8×D11—24no—
380C8×D11—24no—
381C8×D11—24no—
382C8×D11—24no—
383C8×D11—24no—
384C8×D11—24no—
385C8×D11—24no—
386C2×#568—111no—
387C23×M16—111no—
388C2×#525—111no—
389D4×M16—114no—
390D4×M16—114no—
391#2933—114no—
392#2933—114no—
393#2930—111no—
394#2930—111no—
395#2930—111no—
396#2930D1111yescharacteristic, complemented
397#2929—111no—
398#2929—111no—
399#2929—111no—
400#2929—111no—
401#2905—111no—
402#2879—111no—
403C2×#407—111no—
404#2873—111no—
405C23×C11—22no—
406C23×C11—42no—
407C23×C11C23×C412yes—
408C23×C11C23×C412yes—
409C23×C11C23×C411yescharacteristic
410C22×D11—22no—
411C22×D11—24no—
412C22×D11—24no—
413C22×D11—24no—
414C22×D11—24no—
415C22×D11—24no—
416C22×D11—24no—
417C22×D11—42no—
418C22×D11—42no—
419C22×D11—42no—
420C22×D11—44no—
421C22×D11—416no—
422C22×D11C4×D414yes—
423C22×D11C23×C412yes—
424C22×D11C23×C411yescharacteristic
425C22×D11C23×C411yescharacteristic
426C22×D11C23×C412yes—
427Q8×C11—22no—
428D4×C11—24no—
429D4×C11—22no—
430D4×C11—44no—
431C2×C4×C11—22no—
432C2×C4×C11—24no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11C23×C414yes—
438C2×C4×C11C23×C412yes—
439C2×C4×C11C23×C412yes—
440C2×C4×C11C23×C411yescharacteristic
441C2×C4×C11C22×D412yes—
442C2×C4×C11C2×#4112yes—
443C2×C4×C11C2511yescharacteristic
444C22⋊D11—24no—
445C22⋊D11—24no—
446C22⋊D11—28no—
447C22⋊D11—24no—
448C22⋊D11—44no—
449C2×Dic11—22no—
450C2×Dic11—24no—
451C2×Dic11—24no—
452C2×Dic11—24no—
453C2×Dic11C4×D414yes—
454C2×Dic11C23×C414yes—
455C2×Dic11C23×C412yes—
456C2×Dic11C23×C412yes—
457C2×Dic11C23×C411yescharacteristic
458C2×Dic11C23×C411yescharacteristic
459D44—24no—
460D44—28no—
461D44—22no—
462C4×D11—24no—
463C4×D11—24no—
464C4×D11—24no—
465C4×D11—24no—
466C4×D11—22no—
467C4×D11—22no—
468C4×D11—22no—
469C4×D11—22no—
470C4×D11—24no—
471C4×D11—24no—
472C4×D11—24no—
473C4×D11—44no—
474C4×D11C4×D414yes—
475C4×D11C4×D414yes—
476C4×D11C22×D412yes—
477C4×D11C22×D412yes—
478C4×D11C2×#4112yes—
479C4×D11C2×#4112yes—
480Dic22—22no—
481Dic22—24no—
482C8×C11—22no—
483C8×C11—22no—
484C8×C11—22no—
485C8×C11C22×D412yes—
486C8×C11C22×D412yes—
487C11⋊C8—22no—
488C11⋊C8—22no—
489C11⋊C8—22no—
490C11⋊C8C22×D412yes—
491C11⋊C8C22×D412yes—
492C22×#41—111no—
493C24×C4—111no—
494#568—228no—
495C2×#131—111no—
496C2×#131—111no—
497C2×#131—112no—
498C2×#131—111no—
499C2×#131—112no—
500C2×#131C2×D1111yescharacteristic, complemented
501C22×M16—111no—
502C22×M16—111no—
503C22×M16—111no—
504C22×M16—112no—
505C22×M16—112no—
506C22×M16—112no—
507C22×M16—112no—
508C22×M16—112no—
509C22×M16—111no—
510C22×M16—111no—
511C22×M16—112no—
512C22×M16—228no—
513C22×M16C2×D1111yescharacteristic, complemented
514C23×C8—111no—
515C23×C8—111no—
516#525—111no—
517#525—111no—
518#525—112no—
519#525—112no—
520#525—112no—
521#525—112no—
522#525—114no—
523#525—111no—
524#525C2×D1111yescharacteristic
525C2×#123—112no—
526C2×C22⋊Q8—112no—
527C2×#121—112no—
528C2×#120—112no—
529C2×C4×D4—114no—
530C2×#117—111no—
531#436—114no—
532#436—114no—
533#436—114no—
534#436C2×D1114yescomplemented
535#435—114no—
536#435—114no—
537#435—114no—
538#435—114no—
539#435—114no—
540#435—114no—
541#435—114no—
542#435C2×D1114yescomplemented
543C8×D4—114no—
544C8×D4—114no—
545C8×D4—114no—
546C8×D4—114no—
547#424—111no—
548#424—111no—
549#424—111no—
550#424—114no—
551#424C2×D1111yescharacteristic, complemented
552#423—114no—
553#408—111no—
554#408—111no—
555#408—111no—
556#408—114no—
557#408C2×D1111yescharacteristic, complemented
558#407—111no—
559#407—111no—
560#407—111no—
561#407—114no—
562#407—114no—
563#407C2×D1111yescharacteristic, complemented
564C2×C22⋊C8—114no—
565#405—111no—
566#405—111no—
567#405—111no—
568#405—112no—
569#405—112no—
570#405C2×D1111yescharacteristic, complemented
571C4×M16—112no—
572C4×M16—112no—
573C22×C11—22no—
574C22×C11—22no—
575C22×C11—22no—
576C22×C11—22no—
577C22×C11—24no—
578C22×C11—22no—
579C22×C11—44no—
580C22×C11C2×C4×D412yes—
581C22×C11C24×C411yescharacteristic
582C2×D11—28no—
583C2×D11—22no—
584C2×D11—22no—
585C2×D11—22no—
586C2×D11—22no—
587C2×D11—22no—
588C2×D11—24no—
589C2×D11—44no—
590C2×D11—48no—
591C2×D11—48no—
592C2×D11—84no—
593C2×D11C2×C4×D412yes—
594C2×D11C2×C4×D412yes—
595C2×D11#56814yescomplemented
596C4×C11—22no—
597C4×C11—22no—
598C4×C11—24no—
599C4×C11C2×C4×D412yes—
600C4×C11C23×D411yescharacteristic
601C4×C11C22×#4111yescharacteristic
602Dic11—22no—
603Dic11—22no—
604Dic11—24no—
605Dic11C2×C4×D412yes—
606Dic11C2×C4×D412yes—
607C25—111no—
608C2×#41—111no—
609C2×#41—112no—
610C2×#41—111no—
611C2×#41—112no—
612C2×#41—111no—
613C2×#41—224no—
614C2×#41—224no—
615C2×#41C22×D1111yescharacteristic
616C22×Q8—111no—
617C22×D4—112no—
618C22×D4—111no—
619C22×D4—114no—
620C23×C4—111no—
621C23×C4—111no—
622C23×C4—112no—
623C23×C4—111no—
624C23×C4—111no—
625C23×C4—112no—
626C23×C4—112no—
627C23×C4—112no—
628C23×C4—111no—
629C23×C4—112no—
630C23×C4—224no—
631C23×C4—224no—
632C23×C4C22×D1111yescharacteristic
633#131—24no—
634#131—228no—
635#131—224no—
636#131—224no—
637#131—228no—
638#131—224no—
639C2×M16—24no—
640C2×M16—112no—
641C2×M16—112no—
642C2×M16—111no—
643C2×M16—112no—
644C2×M16—111no—
645C2×M16—118no—
646C2×M16—111no—
647C2×M16—111no—
648C2×M16—111no—
649C2×M16—111no—
650C2×M16—112no—
651C2×M16—112no—
652C2×M16—112no—
653C2×M16—112no—
654C2×M16—112no—
655C2×M16—112no—
656C2×M16—228no—
657C2×M16—224no—
658C2×M16—224no—
659C2×M16—228no—
660C2×M16—228no—
661C2×M16—228no—
662C2×M16—228no—
663C2×M16—228no—
664C2×M16—224no—
665C2×M16—224no—
666C2×M16C22×D1112yes—
667C2×M16C22×D1112yes—
668C2×M16C22×D1111yescharacteristic
669C2×M16C22×D1111yescharacteristic
670C2×M16C22×D1112yescomplemented
671C22×C8—111no—
672C22×C8—111no—
673C22×C8—112no—
674C22×C8—112no—
675C22×C8—112no—
676C22×C8—112no—
677C22×C8—112no—
678C22×C8—112no—
679C22×C8—112no—
680C22×C8—112no—
681C22×C8—112no—
682C22×C8—224no—
683C22×C8—224no—
684C22×C8C22×D1111yescharacteristic
685C22×C8C22×D1111yescharacteristic
686C22×C8C22×D1112yescomplemented
687#123—112no—
688#123—112no—
689#123—114no—
690#123—114no—
691#123—112no—
692#123C4×D1112yes—
693C22⋊Q8—112no—
694C22⋊Q8—112no—
695C22⋊Q8—114no—
696C22⋊Q8—112no—
697C22⋊Q8—114no—
698C22⋊Q8C4×D1112yes—
699#121—112no—
700#121—114no—
701#121—112no—
702#121—112no—
703#121—114no—
704#121C4×D1112yes—
705#120—112no—
706#120—112no—
707#120—114no—
708#120—114no—
709#120—112no—
710#120C4×D1112yes—
711C4×D4—114no—
712C4×D4—114no—
713C4×D4—114no—
714C4×D4—114no—
715C4×D4—114no—
716C4×D4—114no—
717C4×D4—114no—
718C4×D4C22×D1114yes—
719#117—111no—
720#117—112no—
721#117—112no—
722#117—112no—
723#117C22×D1111yescharacteristic
724C2×C4⋊C4—112no—
725C2×C4⋊C4—114no—
726C2×C22⋊C4—112no—
727C2×C22⋊C4—114no—
728C2×C22⋊C4—114no—
729C2×C42—112no—
730C4⋊C8—114no—
731C4⋊C8—114no—
732C4⋊C8—114no—
733C4⋊C8C22×D1114yescomplemented
734C22⋊C8—114no—
735C22⋊C8—114no—
736C22⋊C8—114no—
737C22⋊C8—114no—
738C22⋊C8—114no—
739C22⋊C8—114no—
740C22⋊C8C22×D1114yes—
741C22⋊C8C22×D1114yescomplemented
742#97—112no—
743#97—112no—
744#97—112no—
745#97C22×D1112yescomplemented
746C4×C8—112no—
747C4×C8—112no—
748C4×C8—112no—
749C4×C8C22×D1112yescomplemented
750C2×C11—22no—
751C2×C11—42no—
752C2×C11—42no—
753C2×C11C22×C4×D411yescharacteristic
754C2×C11C2×#56812yes—
755D11—24no—
756D11—22no—
757D11—22no—
758D11—42no—
759C24—111no—
760C24—111no—
761C24—112no—
762C24—112no—
763C24—112no—
764C24—224no—
765C24—444no—
766C24C2×C4×D1111yescharacteristic
767#41—22no—
768#41—22no—
769#41—224no—
770#41—224no—
771#41—228no—
772#41—224no—
773#41—224no—
774#41—222no—
775#41—222no—
776C2×Q8—112no—
777C2×Q8—111no—
778C2×Q8—224no—
779C2×Q8C2×C4×D1111yescharacteristic
780C2×D4—114no—
781C2×D4—112no—
782C2×D4—112no—
783C2×D4—112no—
784C2×D4—114no—
785C2×D4—114no—
786C2×D4—112no—
787C2×D4—111no—
788C2×D4—224no—
789C2×D4—228no—
790C2×D4—448no—
791C2×D4C2×C4×D1112yes—
792C2×D4C2×C4×D1111yescharacteristic
793C2×D4C2×C4×D1114yes—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—111no—
797C22×C4—111no—
798C22×C4—111no—
799C22×C4—114no—
800C22×C4—114no—
801C22×C4—111no—
802C22×C4—111no—
803C22×C4—112no—
804C22×C4—112no—
805C22×C4—112no—
806C22×C4—111no—
807C22×C4—112no—
808C22×C4—112no—
809C22×C4—112no—
810C22×C4—112no—
811C22×C4—112no—
812C22×C4—112no—
813C22×C4—112no—
814C22×C4—112no—
815C22×C4—112no—
816C22×C4—114no—
817C22×C4—224no—
818C22×C4—224no—
819C22×C4—224no—
820C22×C4—224no—
821C22×C4—228no—
822C22×C4—228no—
823C22×C4—224no—
824C22×C4—224no—
825C22×C4—224no—
826C22×C4—224no—
827C22×C4—224no—
828C22×C4—222no—
829C22×C4—222no—
830C22×C4C2×C4×D1112yes—
831C22×C4C2×C4×D1111yescharacteristic
832C22×C4C23×D1112yes—
833C22×C4C23×D1112yes—
834C22×C4C23×D1111yescharacteristic
835M16—22no—
836M16—22no—
837M16—24no—
838M16—24no—
839M16—24no—
840M16—114no—
841M16—114no—
842M16—114no—
843M16—114no—
844M16—224no—
845M16—224no—
846M16—224no—
847M16—224no—
848M16—224no—
849M16—224no—
850M16—224no—
851M16—224no—
852M16—222no—
853M16—222no—
854M16—224no—
855C2×C8—22no—
856C2×C8—24no—
857C2×C8—114no—
858C2×C8—111no—
859C2×C8—111no—
860C2×C8—112no—
861C2×C8—112no—
862C2×C8—112no—
863C2×C8—224no—
864C2×C8—224no—
865C2×C8—224no—
866C2×C8—224no—
867C2×C8—224no—
868C2×C8—224no—
869C2×C8—222no—
870C2×C8—224no—
871C2×C8—224no—
872C2×C8—224no—
873C2×C8D4×D1114yescomplemented
874C2×C8C23×D1112yes—
875C2×C8C23×D1112yes—
876C2×C8C23×D1112yes—
877C2×C8C23×D1111yescharacteristic
878C2×C8C23×D1111yescharacteristic
879C4⋊C4—114no—
880C4⋊C4—112no—
881C4⋊C4—114no—
882C4⋊C4—114no—
883C4⋊C4—114no—
884C4⋊C4C2×C4×D1112yes—
885C4⋊C4C2×C4×D1114yes—
886C22⋊C4—112no—
887C22⋊C4—114no—
888C22⋊C4—114no—
889C22⋊C4—114no—
890C22⋊C4—114no—
891C22⋊C4—114no—
892C22⋊C4—114no—
893C22⋊C4—114no—
894C22⋊C4C2×C4×D1112yes—
895C22⋊C4C2×C4×D1114yes—
896C22⋊C4C2×C4×D1114yes—
897C42—114no—
898C42—112no—
899C42C23×D1112yes—
900C11#6014111yescharacteristic, complemented, Sylow
901C23—22no—
902C23—42no—
903C23—111no—
904C23—112no—
905C23—111no—
906C23—114no—
907C23—112no—
908C23—224no—
909C23—224no—
910C23—224no—
911C23—224no—
912C23—224no—
913C23—224no—
914C23—222no—
915C23—442no—
916C23—442no—
917C23—442no—
918C23—444no—
919C23—4416no—
920C23C22×C4×D1112yes—
921C23C22×C4×D1112yes—
922C23C22×C4×D1111yescharacteristic
923Q8—22no—
924Q8—224no—
925Q8—222no—
926D4—24no—
927D4—22no—
928D4—44no—
929D4—224no—
930D4—228no—
931D4—224no—
932D4—224no—
933D4—228no—
934D4—224no—
935D4—222no—
936D4—444no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—114no—
944C2×C4—111no—
945C2×C4—111no—
946C2×C4—114no—
947C2×C4—114no—
948C2×C4—112no—
949C2×C4—112no—
950C2×C4—112no—
951C2×C4—112no—
952C2×C4—114no—
953C2×C4—112no—
954C2×C4—112no—
955C2×C4—224no—
956C2×C4—224no—
957C2×C4—224no—
958C2×C4—224no—
959C2×C4—224no—
960C2×C4—224no—
961C2×C4—224no—
962C2×C4—224no—
963C2×C4—224no—
964C2×C4—222no—
965C2×C4—224no—
966C2×C4—222no—
967C2×C4—222no—
968C2×C4—222no—
969C2×C4—222no—
970C2×C4—444no—
971C2×C4C22×C4×D1114yes—
972C2×C4C22×C4×D1112yes—
973C2×C4C22×C4×D1112yes—
974C2×C4C22×C4×D1111yescharacteristic
975C2×C4C2×D4×D1112yes—
976C2×C4#41×D1112yes—
977C2×C4C24×D1111yescharacteristic
978C8—22no—
979C8—22no—
980C8—22no—
981C8—112no—
982C8—112no—
983C8—222no—
984C8—222no—
985C8—222no—
986C8C2×D4×D1112yes—
987C8C2×D4×D1112yes—
988C22—22no—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—24no—
993C22—22no—
994C22—44no—
995C22—112no—
996C22—112no—
997C22—114no—
998C22—228no—
999C22—222no—
1000C22—222no—
1001C22—222no—
1002C22—222no—
1003C22—222no—
1004C22—224no—
1005C22—444no—
1006C22—448no—
1007C22—448no—
1008C22—884no—
1009C22C4×D4×D1112yes—
1010C22C23×C4×D1111yescharacteristic
1011C4—22no—
1012C4—22no—
1013C4—24no—
1014C4—112no—
1015C4—112no—
1016C4—222no—
1017C4—222no—
1018C4—224no—
1019C4C4×D4×D1112yes—
1020C4C22×D4×D1111yescharacteristic
1021C4C2×#41×D1111yescharacteristic
1022C2—22no—
1023C2—42no—
1024C2—42no—
1025C2—224no—
1026C2—222no—
1027C2—222no—
1028C2—442no—
1029C2C2×C4×D4×D1111yescharacteristic
1030C2D11×#56812yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2930C2
prime radicalD11×#525C2
cosocleC2×C4×C11C25
hypercenter#2930D11
hypocenterC11#60141
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2930

Complements

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

NH ≅ G/Ntype
1. C2×#10623281C2semidirect
2. C22×M16×D11C2semidirect
4. #13077352C2semidirect
5. #13077349C2semidirect
6. #13077345C2semidirect
7. #13077339C2semidirect
8. #13077320C2semidirect
9. #13077319C2semidirect
10. #13077315C2semidirect
11. #13077313C2semidirect
12. #13077312C2semidirect
13. #13077309C2semidirect
14. #13077308C2semidirect
15. #13077177C2semidirect
16. #13077058C2semidirect
17. D11×#407C2semidirect
18. #13077032C2semidirect
19. C11×#2930C2semidirect
22. C2×C11×#131C22semidirect
23. C22×C11×M16C22semidirect
26. C2×#67001C22semidirect
28. C22×#4318C22semidirect
30. C2×#66960C22semidirect
31. C2×#66960C22semidirect
37. C2×M16×D11C22semidirect
38. C2×M16×D11C22semidirect
39. C2×M16×D11C22semidirect
40. C2×#66954C22semidirect
41. C2×#66954C22semidirect
44. C22×#4313C22semidirect
45. C22×C8×D11C22semidirect
46. C22×C8×D11C22semidirect
59. C11×#436C22semidirect
60. C11×#435C22semidirect
61. C11×#424C22semidirect
62. C11×#408C22semidirect
63. C11×#407C22semidirect
64. C11×#405C22semidirect
65. #10622847C22semidirect
66. #10622820C22semidirect
67. #10622742C22semidirect
68. #10622741C22semidirect
69. #10622740C22semidirect
70. #10622740C22semidirect
71. #10622739C22semidirect
72. #10622739C22semidirect
73. #10622735C22semidirect
74. #10622732C22semidirect
75. #10622723C22semidirect
76. C8×C22⋊D11C22semidirect
77. #10622715C22semidirect
78. #10622714C22semidirect
79. #10622625C22semidirect
80. #10622624C22semidirect
81. #10622612C22semidirect
82. #10622610C22semidirect
83. #10622452C22semidirect
84. #10622450C22semidirect
85. #10622449C22semidirect
86. #10622447C22semidirect
87. #10622342C22semidirect
88. #10622341C22semidirect
89. #10622341C22semidirect
90. #10622340C22semidirect
92. #10622339C22semidirect
93. (C22⋊D11)⋊C8C22semidirect
94. D11×C22⋊C8C22semidirect
95. #10622321C22semidirect
96. #10622320C22semidirect
97. #10622319C22semidirect
98. #10622302C22semidirect
99. C4×#4313C22semidirect
100. C8×D44C22semidirect
133. C2×C11×M16C23semidirect
136. C22×C8×C11C23semidirect
163. C2×#4318C23semidirect
166. C22×C11⋊C8C23semidirect
180. C2×#4313D4semidirect
189. C2×#4313C23semidirect
190. C2×#4313C23semidirect
199. C2×C8×D11C23semidirect
200. C2×C8×D11C23semidirect
224. C11×C4⋊C8C23semidirect
226. C11×C22⋊C8C23semidirect
227. C11×#97C23semidirect
228. C4×C8×C11C23semidirect
230. C22⋊(C11⋊C8)C23semidirect
233. (C2×D11)⋊C8C23semidirect
234. (C2×D11)⋊C8C23semidirect
235. #66879C23semidirect
236. #66879C23semidirect
237. Dic11⋊C8C23semidirect
238. Dic11⋊C8C23semidirect
239. C8×Dic11C23semidirect
240. C8×Dic11C23semidirect
241. C4⋊(C11⋊C8)C23semidirect
242. #66867C23semidirect
243. C4×C11⋊C8C23semidirect
328. C2×C8×C11C2×D4semidirect
362. C2×C11⋊C8C2×D4semidirect
376. #4313C2×D4semidirect
377. #4313C2×D4semidirect
396. #2930D11semidirect
500. C2×#131C2×D11semidirect
513. C22×M16C2×D11semidirect
534. #436C2×D11semidirect
542. #435C2×D11semidirect
551. #424C2×D11semidirect
557. #408C2×D11semidirect
563. #407C2×D11semidirect
570. #405C2×D11semidirect
595. C2×D11#568semidirect
670. C2×M16C22×D11semidirect
686. C22×C8C22×D11semidirect
733. C4⋊C8C22×D11semidirect
741. C22⋊C8C22×D11semidirect
745. #97C22×D11semidirect
749. C4×C8C22×D11semidirect
873. C2×C8D4×D11semidirect
900. C11#60141semidirect

Maximal subgroups

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

subgroupindex
C2×#106232812
C22×M16×D112
D11×#5252
#130773522
#130773492
#130773452
#130773392
#130773202
#130773192
#130773152
#130773132
#130773122
#130773092
#130773082
#130771772
#130770582
D11×#4072
#130770322
C11×#29302
#6014111