Finite Group Databasebeta

← #15638481

Subgroups — #15638481

Order 2816.

2282 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082455C211yesmaximal, characteristic, complemented
2#13080466C214yesmaximal, complemented
3#13080451C214yesmaximal, complemented
4#13080319C214yesmaximal, complemented
5#13080297C214yesmaximal, complemented
6#13079581C212yesmaximal, complemented
7#13079388C211yesmaximal, characteristic, complemented
8#13079381C212yesmaximal, complemented
9#13079369C211yesmaximal, characteristic, complemented
10#13078663C212yesmaximal, complemented
11#13077834C212yesmaximal, complemented
12C2×#10622831C211yesmaximal, characteristic, complemented
13C2×#10622830C211yesmaximal, characteristic, complemented
14#13077640C211yesmaximal, characteristic, complemented
15C2×C11×#546C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C11×#546—22no—
19C11×#546—22no—
20C11×#546C2214yes—
21C11×#546C2214yescomplemented
22C2×C11×#124C2211yescharacteristic, complemented
23C2×C11×#123—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121—21no—
26C2×C11×#121C2211yescharacteristic, complemented
27C2×C11×#120—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic, complemented
30C22×C11×C22⋊C4—21no—
31C2×#67003C2214yescomplemented
32#10623335—21no—
33C22×#4324C2212yescomplemented
34C22×#4323C2212yescomplemented
35#10623322C2212yescomplemented
36C2×#66983C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38#10623096C2212yescomplemented
39#10623087—22no—
40#10623083C2212yescomplemented
41#10623081C2212yescomplemented
42#10623072C2212yescomplemented
43#10623071—22no—
44#10623046—21no—
45#10623025—21no—
46#10623017—21no—
47#10623010C2212yescomplemented
48#10622852C2214yescomplemented
49#10622851C2214yescomplemented
50#10622846C2214yescomplemented
51#10622841C2212yescomplemented
52#10622840C2212yescomplemented
53#10622831C2212yescomplemented
54#10622831C2212yescomplemented
55#10622831C2214yescomplemented
56#10622830C2212yes—
57#10622830C2212yes—
58#10622830C2214yescomplemented
59C2×#66896C2212yescomplemented
60C2×#66896C2212yescomplemented
61C2×C22⋊(C11⋊C8)C2211yescharacteristic
62C2×C22⋊(C11⋊C8)C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2212yescomplemented
64#10622672C2214yescomplemented
65#10622670C2214yescomplemented
66#10622669C2214yescomplemented
67#10622667C2214yescomplemented
68#10622664C2214yescomplemented
69#10622663C2212yescomplemented
70#10622661C2214yescomplemented
71#10622659C2212yescomplemented
72#10622657C2212yescomplemented
73#10622656C2212yescomplemented
74#10622654C2214yescomplemented
75#10622651C2214yescomplemented
76#10622650C2214yescomplemented
77#10622648C2214yescomplemented
78C4×#4324C2214yescomplemented
79#10622629C2214yescomplemented
80C4×#4323C2214yescomplemented
81D4×C11⋊C8C2214yescomplemented
82D4×C11⋊C8C2214yescomplemented
83#10622622C2214yescomplemented
84#10622583C2212yescomplemented
85#10622581C2212yescomplemented
86#10622538C2212yescomplemented
87C25×C11—21no—
88C2×C11×#41—22no—
89C2×C11×#41—44no—
90C2×C11×#41C2314yes—
91C22×Q8×C11C2311yescharacteristic
92C22×D4×C11—21no—
93C22×D4×C11—21no—
94C22×D4×C11—21no—
95C22×D4×C11—21no—
96C22×D4×C11—21no—
97C22×D4×C11—44no—
98C22×D4×C11D411yescharacteristic
99C22×D4×C11C2311yescharacteristic
100C22×D4×C11C2312yes—
101C22×D4×C11C2312yes—
102C22×D4×C11C2311yescharacteristic
103C23×C4×C11—21no—
104C23×C4×C11—21no—
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C22×C22⋊D11—21no—
108C2×#4339C2312yescomplemented
109C22×D44C2311yescharacteristic
110C22×Dic22C2311yescharacteristic
111C11×#124—22no—
112C11×#124C2314yes—
113C11×#123—24no—
114C11×#123—24no—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8C2312yes—
118C11×C22⋊Q8C2312yes—
119C11×#121—22no—
120C11×#121—24no—
121C11×#121—24no—
122C11×#121C2314yes—
123C11×#120—24no—
124C11×#120—24no—
125C4×D4×C11—22no—
126C4×D4×C11D412yes—
127C4×D4×C11D412yes—
128C4×D4×C11C2314yes—
129C4×D4×C11C2312yes—
130C4×D4×C11C2312yes—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4D411yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—24no—
140C2×C11×C22⋊C4—24no—
141C2×C11×C22⋊C4D411yescharacteristic
142C2×C11×C22⋊C4D411yescharacteristic
143C2×C42×C11C2311yescharacteristic
144#67006—22no—
145C2×C22⋊Dic11—21no—
146#67003—48no—
147C2×#4326C2314yescomplemented
148C2×#4325C2314yescomplemented
149#66992—22no—
150#66992—22no—
151#66990—22no—
152#66988—22no—
153C2×#4324—44no—
154C2×#4324C2314yes—
155C2×#4324C2314yes—
156C2×#4323—44no—
157C2×#4323C2314yes—
158C2×#4323C2314yes—
159#66983—21no—
160#66983—21no—
161#66983C2312yes—
162#66983C2312yes—
163#66983C2312yescomplemented
164#66982—22no—
165#66982—22no—
166C4×C22⋊D11—22no—
167C4×C22⋊D11—22no—
168C4×C22⋊D11—22no—
169C2×(C2×D11)⋊C4—21no—
170#66979C2312yescomplemented
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2311yescharacteristic
173#66977—21no—
174#66977—21no—
175#66977C2312yes—
176#66977C2312yes—
177#66977C2312yescomplemented
178C2×Dic11⋊C4—21no—
179C22×C11⋊C8C2312yes—
180C22×C11⋊C8C2312yes—
181C22×C11⋊C8C2314yescomplemented
182#66951—22no—
183#66949—22no—
184#66947—22no—
185#66942—22no—
186#66938—22no—
187#66937—22no—
188#66936—22no—
189(C22⋊D11)⋊C4—22no—
190(C22⋊D11)⋊C4—22no—
191C22⋊C4×D11—22no—
192#66932—22no—
193#66930—22no—
194#66929—22no—
195#66928C2312yescomplemented
196C4×D44C2312yescomplemented
197#66925—22no—
198#66923C2312yescomplemented
199C4×Dic22C2312yescomplemented
200#66899C2314yescomplemented
201#66899C2314yescomplemented
202#66896C2314yes—
203#66896C2314yes—
204#66896C2314yes—
205#66896C2314yes—
206C22⋊(C11⋊C8)C2312yes—
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yes—
209C22⋊(C11⋊C8)C2312yes—
210C22⋊(C11⋊C8)C2314yescomplemented
211#66874C2314yescomplemented
212#66873C2314yescomplemented
213#66872C2314yescomplemented
214#66871C2314yescomplemented
215C4⋊(C11⋊C8)C2314yescomplemented
216C4×C11⋊C8C2314yescomplemented
217#61561—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11—21no—
220C24×C11—22no—
221C24×C11—22no—
222C24×C11—44no—
223C24×C11—44no—
224C24×C11—82no—
225C24×C11C2×D411yescharacteristic
226C24×C11C2×D411yescharacteristic
227C23×D11—21no—
228C11×#41—28no—
229C11×#41—44no—
230C11×#41—48no—
231C2×Q8×C11—21no—
232C2×Q8×C11—42no—
233C2×Q8×C11C2412yes—
234C2×D4×C11—24no—
235C2×D4×C11—24no—
236C2×D4×C11—24no—
237C2×D4×C11—24no—
238C2×D4×C11—24no—
239C2×D4×C11—24no—
240C2×D4×C11—21no—
241C2×D4×C11—22no—
242C2×D4×C11—22no—
243C2×D4×C11—21no—
244C2×D4×C11—42no—
245C2×D4×C11—42no—
246C2×D4×C11—42no—
247C2×D4×C11—44no—
248C2×D4×C11—44no—
249C2×D4×C11—44no—
250C2×D4×C11—44no—
251C2×D4×C11—82no—
252C2×D4×C11C2×D412yes—
253C2×D4×C11C2×D412yes—
254C2×D4×C11C2412yes—
255C2×D4×C11C2412yes—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—24no—
259C22×C4×C11—24no—
260C22×C4×C11—42no—
261C22×C4×C11—42no—
262C22×C4×C11—44no—
263C22×C4×C11—82no—
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D411yescharacteristic
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2×D411yescharacteristic
270C22×C4×C11C2×D412yes—
271C22×C4×C11C2411yescharacteristic
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2412yes—
275C2×C22⋊D11—22no—
276C2×C22⋊D11—22no—
277C2×C22⋊D11—22no—
278C2×C22⋊D11—22no—
279C2×C22⋊D11—44no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283#4339—44no—
284C2×D44—21no—
285C2×D44—42no—
286C2×D44C2412yes—
287C2×C4×D11—22no—
288C2×C4×D11—22no—
289C2×Dic22—21no—
290C2×Dic22—42no—
291C2×Dic22C2412yes—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—21no—
295C11×C4⋊C4C2×D412yes—
296C11×C4⋊C4C2×D412yes—
297C11×C4⋊C4C2412yes—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—24no—
301C11×C22⋊C4—24no—
302C11×C22⋊C4—24no—
303C11×C22⋊C4—24no—
304C11×C22⋊C4C2×D412yes—
305C11×C22⋊C4C2×D412yes—
306C11×C22⋊C4C2×D412yes—
307C11×C22⋊C4C2×D412yes—
308C42×C11C2×D412yes—
309C42×C11C2412yes—
310C22⋊Dic11—22no—
311C22⋊Dic11—22no—
312C22⋊Dic11—22no—
313C22⋊Dic11—22no—
314#4326—44no—
315#4325—44no—
316#4324—28no—
317#4324—44no—
318#4323—28no—
319#4323—44no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326C4⋊Dic11—21no—
327C4⋊Dic11—21no—
328C4⋊Dic11C2412yes—
329C4⋊Dic11C2412yes—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335Dic11⋊C4—22no—
336C4×Dic11—22no—
337C4×Dic11—22no—
338C2×C11⋊C8—42no—
339C2×C11⋊C8—42no—
340C2×C11⋊C8—44no—
341C2×C11⋊C8C2414yes—
342C2×C11⋊C8C2414yes—
343#3505—111no—
344C2×#546D1111yescharacteristic, complemented
345#3297—114no—
346#3296—114no—
347#3282—114no—
348#3280—114no—
349#3211—112no—
350#3189—111no—
351#3188—112no—
352#3187—111no—
353#3105—112no—
354#3002—112no—
355C2×#450—111no—
356C2×#447—111no—
357#2972—111no—
358C23×C11—24no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—44no—
367C23×C11—44no—
368C23×C11—42no—
369C23×C11—42no—
370C23×C11—42no—
371C23×C11—42no—
372C23×C11—44no—
373C23×C11—44no—
374C23×C11—42no—
375C23×C11—82no—
376C23×C11—82no—
377C23×C11—816no—
378C23×C11#13514yescomplemented
379C23×C11C22×D412yes—
380C23×C11C22×D411yescharacteristic
381C23×C11C22×D411yescharacteristic
382C23×C11C22×D411yescharacteristic
383C22×D11—22no—
384C22×D11—42no—
385C22×D11—81no—
386C22×D11—81no—
387Q8×C11—24no—
388Q8×C11—42no—
389D4×C11—24no—
390D4×C11—24no—
391D4×C11—24no—
392D4×C11—22no—
393D4×C11—22no—
394D4×C11—22no—
395D4×C11—44no—
396D4×C11—44no—
397D4×C11—42no—
398D4×C11—48no—
399D4×C11—84no—
400D4×C11H(5,𝔽2)14yes—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—24no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—42no—
413C2×C4×C11—41no—
414C2×C4×C11—48no—
415C2×C4×C11—42no—
416C2×C4×C11—42no—
417C2×C4×C11—84no—
418C2×C4×C11C22×D412yes—
419C2×C4×C11C22×D412yes—
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D412yes—
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C2511yescharacteristic
425C22⋊D11—44no—
426C22⋊D11—44no—
427C22⋊D11—82no—
428C22⋊D11—82no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—42no—
433C2×Dic11—81no—
434C2×Dic11—81no—
435D44—24no—
436D44—81no—
437C4×D11—82no—
438C4×D11—82no—
439Dic22—24no—
440Dic22—81no—
441C11⋊C8—24no—
442C11⋊C8—24no—
443C22×#41C2×D1111yescharacteristic, complemented
444C23×D4C2×D1111yescharacteristic
445C2×#135—114no—
446C22×SD16—112no—
447C22×D8—112no—
448#553—112no—
449#553—222no—
450#552—112no—
451#551—222no—
452#548—112no—
453#546—22no—
454#546—22no—
455#546—112no—
456#546C2×D1114yes—
457#546C2×D1114yescomplemented
458#539—221no—
459#538—221no—
460#534—221no—
461#529—112no—
462C2×#124C2×D1111yescharacteristic, complemented
463#525—112no—
464C2×#123—21no—
465C2×C22⋊Q8—111no—
466C2×C22⋊Q8C2×D1111yescharacteristic
467C2×#121—21no—
468C2×#121—111no—
469C2×#121C2×D1111yescharacteristic, complemented
470C2×#120—21no—
471#518—221no—
472C2×C4×D4C2×D1111yescharacteristic
473C2×C4×D4C2×D1111yescharacteristic, complemented
474C22×C22⋊C4—21no—
475#495—114no—
476#488—114no—
477#484—112no—
478#484—112no—
479#483—112no—
480#482—114no—
481#481—112no—
482#478—114no—
483#467—114no—
484#466—114no—
485#465—114no—
486#465—114no—
487#464—114no—
488#463—114no—
489#463—114no—
490#452—114no—
491#451—112no—
492#451—112no—
493#450—112no—
494#450—112no—
495#450—114no—
496#450—112no—
497#449—114no—
498#449—114no—
499#448—112no—
500#447—112no—
501#447—112no—
502#447—114no—
503C4×SD16—114no—
504C4×D8—114no—
505C8×D4—114no—
506C8×D4—114no—
507#431—112no—
508#416—114no—
509C2×#102—112no—
510C2×#102—112no—
511C2×C22⋊C8—111no—
512C2×C22⋊C8—111no—
513C2×C22⋊C8—112no—
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—21no—
517C22×C11—21no—
518C22×C11—21no—
519C22×C11—21no—
520C22×C11—22no—
521C22×C11—22no—
522C22×C11—24no—
523C22×C11—22no—
524C22×C11—44no—
525C22×C11—48no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11—42no—
530C22×C11—42no—
531C22×C11—82no—
532C22×C11—88no—
533C22×C11—88no—
534C22×C11—84no—
535C22×C11C2×#13512yes—
536C22×C11C2×#13512yes—
537C22×C11C2×#13512yes—
538C22×C11C23×D411yescharacteristic
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—162no—
543C4×C11—22no—
544C4×C11—22no—
545C4×C11—21no—
546C4×C11—21no—
547C4×C11—21no—
548C4×C11—22no—
549C4×C11—42no—
550C4×C11—42no—
551C4×C11C2×H(5,𝔽2)12yes—
552Dic11—42no—
553Dic11—42no—
554Dic11—42no—
555C25—21no—
556C2×#41—22no—
557C2×#41—44no—
558C2×#41—112no—
559C2×#41C22×D1114yes—
560C22×Q8—111no—
561C22×Q8C22×D1111yescharacteristic
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—21no—
567C22×D4—44no—
568C22×D4—111no—
569C22×D4—221no—
570C22×D4C22⋊D1111yescharacteristic
571C22×D4C22×D1111yescharacteristic
572C22×D4C22×D1112yes—
573C22×D4C22×D1112yes—
574C22×D4C22×D1111yescharacteristic
575C23×C4—21no—
576C23×C4—21no—
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579#135—448no—
580C2×Q16—114no—
581C2×SD16—114no—
582C2×SD16—114no—
583C2×SD16—114no—
584C2×SD16—444no—
585C2×D8—114no—
586C2×D8—114no—
587C2×D8—444no—
588C22×C8—112no—
589C22×C8—112no—
590C22×C8—114no—
591#126—222no—
592#126—222no—
593#126—222no—
594#125—112no—
595#125—222no—
596#124—22no—
597#124—112no—
598#124—222no—
599#124C22×D1114yes—
600#123—24no—
601#123—24no—
602#123—222no—
603#123—222no—
604#123—222no—
605#123—222no—
606#123—222no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—112no—
610C22⋊Q8—112no—
611C22⋊Q8—112no—
612C22⋊Q8—221no—
613C22⋊Q8—221no—
614C22⋊Q8—222no—
615C22⋊Q8C22×D1112yes—
616C22⋊Q8C22×D1112yes—
617#121—22no—
618#121—24no—
619#121—24no—
620#121—112no—
621#121—112no—
622#121—112no—
623#121—222no—
624#121—222no—
625#121—221no—
626#121—221no—
627#121—222no—
628#121C22×D1114yes—
629#120—24no—
630#120—24no—
631#120—222no—
632#120—222no—
633C4×Q8—112no—
634C4×D4—22no—
635C4×D4—112no—
636C4×D4—222no—
637C4×D4—222no—
638C4×D4—222no—
639C4×D4—222no—
640C4×D4—222no—
641C4×D4C22⋊D1112yes—
642C4×D4C22⋊D1112yes—
643C4×D4C22×D1114yes—
644C4×D4C22×D1112yes—
645C4×D4C22×D1112yes—
646#117—112no—
647#117—222no—
648#117—222no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—221no—
653C2×C4⋊C4C22⋊D1111yescharacteristic
654C2×C4⋊C4C22×D1111yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—24no—
661C2×C22⋊C4—24no—
662C2×C22⋊C4—221no—
663C2×C22⋊C4—221no—
664C2×C22⋊C4—222no—
665C2×C22⋊C4C22⋊D1111yescharacteristic
666C2×C22⋊C4C22⋊D1111yescharacteristic
667C2×C42C22×D1111yescharacteristic
668#107—114no—
669#106—114no—
670C4⋊C8—114no—
671#103—114no—
672#103—114no—
673#103—114no—
674#102—114no—
675#102—114no—
676#102—114no—
677#102—114no—
678#102—114no—
679C22⋊C8—112no—
680C22⋊C8—112no—
681C22⋊C8—112no—
682C22⋊C8—112no—
683C22⋊C8—114no—
684C4×C8—114no—
685C2×C11—22no—
686C2×C11—22no—
687C2×C11—22no—
688C2×C11—42no—
689C2×C11—44no—
690C2×C11—82no—
691C2×C11#348411yescharacteristic
692C2×C11C22×#13511yescharacteristic
693C2×C11#358511yescharacteristic
694D11—82no—
695C24—21no—
696C24—21no—
697C24—22no—
698C24—22no—
699C24—44no—
700C24—44no—
701C24—82no—
702C24—221no—
703C24C2×C22⋊D1111yescharacteristic
704C24C2×C22⋊D1111yescharacteristic
705#41—28no—
706#41—44no—
707#41—48no—
708#41—444no—
709C2×Q8—21no—
710C2×Q8—42no—
711C2×Q8—112no—
712C2×Q8—221no—
713C2×Q8—442no—
714C2×Q8C23×D1112yes—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—21no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—21no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—82no—
733C2×D4—112no—
734C2×D4—222no—
735C2×D4—222no—
736C2×D4—222no—
737C2×D4—222no—
738C2×D4—221no—
739C2×D4—442no—
740C2×D4—444no—
741C2×D4C2×C22⋊D1112yes—
742C2×D4C2×C22⋊D1112yes—
743C2×D4C23×D1112yes—
744C2×D4C23×D1112yes—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—44no—
752C22×C4—82no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—222no—
757C22×C4—222no—
758C22×C4C2×C22⋊D1111yescharacteristic
759C22×C4C2×C22⋊D1111yescharacteristic
760C22×C4C2×C22⋊D1111yescharacteristic
761C22×C4C2×C22⋊D1111yescharacteristic
762C22×C4C2×C22⋊D1111yescharacteristic
763C22×C4C2×C22⋊D1111yescharacteristic
764C22×C4C2×C22⋊D1112yes—
765C22×C4C23×D1111yescharacteristic
766C22×C4C23×D1111yescharacteristic
767C22×C4C23×D1111yescharacteristic
768C22×C4C23×D1112yes—
769Q16—444no—
770SD16—228no—
771SD16—444no—
772SD16—444no—
773D8—228no—
774D8—444no—
775C2×C8—114no—
776C2×C8—114no—
777C2×C8—442no—
778C2×C8—442no—
779C2×C8—444no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—112no—
784C4⋊C4—112no—
785C4⋊C4—221no—
786C4⋊C4—221no—
787C4⋊C4—222no—
788C4⋊C4—222no—
789C4⋊C4—222no—
790C4⋊C4—222no—
791C4⋊C4—222no—
792C4⋊C4—222no—
793C4⋊C4C2×C22⋊D1112yes—
794C4⋊C4C2×C22⋊D1112yes—
795C4⋊C4C23×D1112yes—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—24no—
802C22⋊C4—222no—
803C22⋊C4—222no—
804C22⋊C4—222no—
805C22⋊C4—222no—
806C22⋊C4—222no—
807C22⋊C4—222no—
808C22⋊C4—222no—
809C22⋊C4—222no—
810C22⋊C4—222no—
811C22⋊C4—222no—
812C22⋊C4C2×C22⋊D1112yes—
813C22⋊C4C2×C22⋊D1112yes—
814C22⋊C4C2×C22⋊D1112yes—
815C22⋊C4C2×C22⋊D1112yes—
816C42—222no—
817C42—222no—
818C42C2×C22⋊D1112yes—
819C42C23×D1112yes—
820C11#6156111yescharacteristic, complemented, Sylow
821C23—24no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—44no—
830C23—44no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—44no—
836C23—44no—
837C23—42no—
838C23—82no—
839C23—82no—
840C23—816no—
841C23—222no—
842C23—442no—
843C23—881no—
844C23—881no—
845C23#6700314yescomplemented
846C23C22×C22⋊D1112yes—
847C23C22×C22⋊D1111yescharacteristic
848C23C22×C22⋊D1111yescharacteristic
849C23C22×C22⋊D1111yescharacteristic
850Q8—24no—
851Q8—42no—
852Q8—224no—
853Q8—881no—
854D4—24no—
855D4—24no—
856D4—24no—
857D4—22no—
858D4—22no—
859D4—22no—
860D4—44no—
861D4—44no—
862D4—42no—
863D4—48no—
864D4—84no—
865D4—224no—
866D4—444no—
867D4—444no—
868D4—881no—
869D4—882no—
870D4—882no—
871D4#6703714yes—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—42no—
884C2×C4—41no—
885C2×C4—48no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—84no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—442no—
893C2×C4—882no—
894C2×C4—882no—
895C2×C4—881no—
896C2×C4—881no—
897C2×C4C22×C22⋊D1112yes—
898C2×C4C22×C22⋊D1112yes—
899C2×C4C22×C22⋊D1111yescharacteristic
900C2×C4C22×C22⋊D1112yes—
901C2×C4C22×C22⋊D1111yescharacteristic
902C2×C4C22×C22⋊D1111yescharacteristic
903C2×C4C24×D1111yescharacteristic
904C8—224no—
905C8—224no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—22no—
913C22—22no—
914C22—24no—
915C22—22no—
916C22—44no—
917C22—48no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—82no—
924C22—88no—
925C22—88no—
926C22—84no—
927C22—442no—
928C22—442no—
929C22—442no—
930C22—1762no—
931C22C2×#6700312yes—
932C22C2×#6700312yes—
933C22C2×#6700312yes—
934C22C23×C22⋊D1111yescharacteristic
935C4—22no—
936C4—22no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—22no—
941C4—42no—
942C4—42no—
943C4—442no—
944C4—442no—
945C4—442no—
946C4C2×#6703712yes—
947C2—22no—
948C2—22no—
949C2—22no—
950C2—42no—
951C2—44no—
952C2—82no—
953C2—882no—
954C2#1308225111yescharacteristic
955C2C22×#6700311yescharacteristic
956C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#546C2
socleC22×C11C23×D4
hypercenterC2×#546D11
hypocenterC11#61561
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. #13082455C2semidirect
2. #13080466C2semidirect
3. #13080451C2semidirect
4. #13080319C2semidirect
5. #13080297C2semidirect
6. #13079581C2semidirect
7. #13079388C2semidirect
8. #13079381C2semidirect
9. #13079369C2semidirect
10. #13078663C2semidirect
11. #13077834C2semidirect
12. C2×#10622831C2semidirect
13. C2×#10622830C2semidirect
14. #13077640C2semidirect
15. C2×C11×#546C2semidirect
16. C22×C11×#41C22semidirect
21. C11×#546C22semidirect
22. C2×C11×#124C22semidirect
26. C2×C11×#121C22semidirect
29. C2×C4×D4×C11C22semidirect
31. C2×#67003C22semidirect
33. C22×#4324C22semidirect
34. C22×#4323C22semidirect
35. #10623322C22semidirect
38. #10623096C22semidirect
40. #10623083C22semidirect
41. #10623081C22semidirect
42. #10623072C22semidirect
47. #10623010C22semidirect
48. #10622852C22semidirect
49. #10622851C22semidirect
50. #10622846C22semidirect
51. #10622841C22semidirect
52. #10622840C22semidirect
53. #10622831C22semidirect
54. #10622831C22semidirect
55. #10622831C22semidirect
58. #10622830C22semidirect
59. C2×#66896C22semidirect
60. C2×#66896C22semidirect
63. C2×C22⋊(C11⋊C8)C22semidirect
64. #10622672C22semidirect
65. #10622670C22semidirect
66. #10622669C22semidirect
67. #10622667C22semidirect
68. #10622664C22semidirect
69. #10622663C22semidirect
70. #10622661C22semidirect
71. #10622659C22semidirect
72. #10622657C22semidirect
73. #10622656C22semidirect
74. #10622654C22semidirect
75. #10622651C22semidirect
76. #10622650C22semidirect
77. #10622648C22semidirect
78. C4×#4324C22semidirect
79. #10622629C22semidirect
80. C4×#4323C22semidirect
81. D4×C11⋊C8C22semidirect
82. D4×C11⋊C8C22semidirect
83. #10622622C22semidirect
84. #10622583C22semidirect
85. #10622581C22semidirect
86. #10622538C22semidirect
108. C2×#4339C23semidirect
147. C2×#4326C23semidirect
148. C2×#4325C23semidirect
163. #66983C23semidirect
170. #66979C23semidirect
177. #66977C23semidirect
181. C22×C11⋊C8C23semidirect
195. #66928C23semidirect
196. C4×D44C23semidirect
198. #66923C23semidirect
199. C4×Dic22C23semidirect
200. #66899C23semidirect
201. #66899C23semidirect
210. C22⋊(C11⋊C8)C23semidirect
211. #66874C23semidirect
212. #66873C23semidirect
213. #66872C23semidirect
214. #66871C23semidirect
215. C4⋊(C11⋊C8)C23semidirect
216. C4×C11⋊C8C23semidirect
344. C2×#546D11semidirect
378. C23×C11#135semidirect
443. C22×#41C2×D11semidirect
457. #546C2×D11semidirect
462. C2×#124C2×D11semidirect
469. C2×#121C2×D11semidirect
473. C2×C4×D4C2×D11semidirect
820. C11#61561semidirect
845. C23#67003semidirect

Maximal subgroups

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

subgroupindex
#130824552
#130804662
#130804512
#130803192
#130802972
#130795812
#130793882
#130793812
#130793692
#130786632
#130778342
C2×#106228312
C2×#106228302
#130776402
C2×C11×#5462
#6156111