Finite Group Databasebeta

← #36525762

Subgroups — #36525762

Order 22784.

616 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26030260C211yesmaximal, characteristic
2#26029353C211yesmaximal, characteristic, complemented
3#26019154C211yesmaximal, characteristic, complemented
4#26019140C211yesmaximal, characteristic, complemented
5#26019128C211yesmaximal, characteristic, complemented
6#26019109C211yesmaximal, characteristic, complemented
7#26019093C211yesmaximal, characteristic, complemented
8#26019088C211yesmaximal, characteristic, complemented
9#26019064C211yesmaximal, characteristic, complemented
10C8×#13083562C211yesmaximal, characteristic, complemented
11#26019033C211yesmaximal, characteristic, complemented
12#26018724C211yesmaximal, characteristic, complemented
13#26018643C211yesmaximal, characteristic
14#26018552C211yesmaximal, characteristic, complemented
15C89×#2974C211yesmaximal, characteristic
16#19152155C2211yescharacteristic
17#19151928C411yescharacteristic
18#19151928C411yescharacteristic
19#19151888C411yescharacteristic
20#19151888C411yescharacteristic
21#19151803C411yescharacteristic
22#19151803C411yescharacteristic
23#19151749C411yescharacteristic
24#19151749C411yescharacteristic
25#19151728C2211yescharacteristic, complemented
26#19151728C2211yescharacteristic, complemented
27#19151725—21no—
28C8×Dic178C2211yescharacteristic, complemented
29C8×Dic178C2211yescharacteristic, complemented
30#19151722—21no—
31C4×#13083562C2211yescharacteristic
32C4×#13083562C2211yescharacteristic
33C4×#13083562C2211yescharacteristic
34C4×#13083562C2211yescharacteristic
35#19151656—21no—
36#19151656—21no—
37#19151651C2211yescharacteristic
38#19151651C2211yescharacteristic
39#19151651C2211yescharacteristic
40#19151350C2211yescharacteristic, complemented
41#19151350C2211yescharacteristic, complemented
42#19151348C2211yescharacteristic, complemented
43#19151348C2211yescharacteristic, complemented
44#19151328C2211yescharacteristic, complemented
45#19151328C2211yescharacteristic, complemented
46#19151328C2211yescharacteristic, complemented
47#19151328C2211yescharacteristic, complemented
48D4⋊#10623494C2211yescharacteristic
49D4⋊#10623494C2211yescharacteristic
50D4⋊#10623494C2211yescharacteristic
51D4⋊#10623494C2211yescharacteristic
52#19151320C2211yescharacteristic, complemented
53#19151320C2211yescharacteristic, complemented
54#19151319C2211yescharacteristic, complemented
55C8×#10623494C2211yescharacteristic, complemented
56C2×C4×D4×C89C2211yescharacteristic
57#436×C89C2211yescharacteristic
58#436×C89C2211yescharacteristic
59#435×C89—21no—
60#435×C89—21no—
61C8×D4×C89C2211yescharacteristic
62C8×D4×C89C2211yescharacteristic
63#432×C89C2211yescharacteristic
64#431×C89C2211yescharacteristic
65#407×C89—21no—
66C2×C22⋊C8×C89—21no—
67C2×#13083562C2×C411yescharacteristic
68C2×#13083562C2×C411yescharacteristic
69C2×#13083562C2×C411yescharacteristic
70C2×#13083562C2×C411yescharacteristic
71#15668012C2×C411yescharacteristic
72#15668012C2×C411yescharacteristic
73#15668004—21no—
74#15667991—21no—
75#15667991C2×C411yescharacteristic
76#15667991C2×C411yescharacteristic
77C4×Dic178—21no—
78C4×Dic178C2311yescharacteristic
79C4×Dic178C2311yescharacteristic
80#15667971—21no—
81#15667943C2×C411yescharacteristic
82#15667943C2×C411yescharacteristic
83#15667943C2×C411yescharacteristic
84#15667943C2×C411yescharacteristic
85C4⋊#10623494—21no—
86C4⋊#10623494C2×C411yescharacteristic
87C4⋊#10623494C2×C411yescharacteristic
88C4⋊#10623494C2311yescharacteristic
89C4⋊#10623494C2311yescharacteristic
90#15667941—21no—
91#15667941—21no—
92#15667941—21no—
93#15667941—21no—
94#15667935C2×C411yescharacteristic
95#15667935C2×C411yescharacteristic
96#15667935C2×C411yescharacteristic
97#15667935C2×C411yescharacteristic
98#15667933C2×C411yescharacteristic
99#15667933C2×C411yescharacteristic
100#15667933C2×C411yescharacteristic
101#15667933C2×C411yescharacteristic
102C22⋊#10623494—21no—
103C22⋊#10623494—21no—
104C22⋊#10623494C2×C411yescharacteristic
105C22⋊#10623494C2×C411yescharacteristic
106#15667922—21no—
107#15667922—21no—
108C4×#10623494—21no—
109C4×#10623494C2311yescharacteristic
110C4×#10623494C2311yescharacteristic
111C4×#10623494C2311yescharacteristic
112C4×#10623494C2311yescharacteristic
113C8×Dic89—21no—
114C8×Dic89—21no—
115C22×D4×C89C2×C411yescharacteristic
116C23×C4×C89—21no—
117C2×M16×C89—21no—
118C2×M16×C89—21no—
119C22×C8×C89—21no—
120C22×C8×C89—21no—
121C4×D4×C89—21no—
122C4×D4×C89—21no—
123C4×D4×C89C2×C411yescharacteristic
124C4×D4×C89C2×C411yescharacteristic
125C4×D4×C89C2311yescharacteristic
126C4×D4×C89C2311yescharacteristic
127C2×C4⋊C4×C89C2×C411yescharacteristic
128C2×C22⋊C4×C89—21no—
129C2×C42×C89C2311yescharacteristic
130C4⋊C8×C89D411yescharacteristic
131C4⋊C8×C89D411yescharacteristic
132C4⋊C8×C89C2311yescharacteristic
133C4⋊C8×C89C2311yescharacteristic
134C22⋊C8×C89—21no—
135C22⋊C8×C89—21no—
136C22⋊C8×C89—21no—
137C22⋊C8×C89—21no—
138C22⋊C8×C89—21no—
139C22⋊C8×C89D411yescharacteristic
140C22⋊C8×C89D411yescharacteristic
141#97×C89—21no—
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144C2×Dic178—21no—
145C2×Dic178C22×C411yescharacteristic
146C2×Dic178C22×C411yescharacteristic
147#13083562—22no—
148#13083562—22no—
149#13083562—41no—
150#13083562—41no—
151C2×#10623494—21no—
152C2×#10623494—21no—
153C2×#10623494—21no—
154C2×#10623494—21no—
155C2×#10623494C22×C411yescharacteristic
156C2×#10623494C22×C411yescharacteristic
157C2×#10623494C22×C411yescharacteristic
158C2×#10623494C22×C411yescharacteristic
159C4⋊Dic89—21no—
160C4⋊Dic89—21no—
161C4⋊Dic89—21no—
162C4⋊Dic89C22×C411yescharacteristic
163C4⋊Dic89C22×C411yescharacteristic
164#13083553—21no—
165#13083553—21no—
166#13083553—21no—
167#13083553—21no—
168C22⋊Dic89—21no—
169C22⋊Dic89—21no—
170C4×Dic89—21no—
171C4×Dic89—21no—
172C24×C89—21no—
173C2×D4×C89—22no—
174C2×D4×C89—21no—
175C2×D4×C89—41no—
176C2×D4×C89C22×C411yescharacteristic
177C2×D4×C89C22×C411yescharacteristic
178C22×C4×C89—21no—
179C22×C4×C89—21no—
180C22×C4×C89—21no—
181C22×C4×C89—21no—
182C22×C4×C89—21no—
183C22×C4×C89—81no—
184C22×C4×C89—81no—
185C22×C4×C89C22×C411yescharacteristic
186C22×C4×C89C2×D411yescharacteristic
187C22×C4×C89#4111yescharacteristic
188M16×C89—81no—
189M16×C89—81no—
190C2×C8×C89—21no—
191C2×C8×C89—21no—
192C2×C8×C89—81no—
193C2×C8×C89—81no—
194C2×C8×C89C2×D411yescharacteristic
195C2×C8×C89C2×D411yescharacteristic
196C2×C8×C89C2×D411yescharacteristic
197C2×C8×C89C2×D411yescharacteristic
198C4⋊C4×C89—21no—
199C4⋊C4×C89C22×C411yescharacteristic
200C4⋊C4×C89C22×C411yescharacteristic
201C22⋊C4×C89—21no—
202C22⋊C4×C89—21no—
203C22⋊C4×C89—21no—
204C22⋊C4×C89—21no—
205C42×C89C22×C411yescharacteristic
206C42×C89C2×D411yescharacteristic
207C42×C89#4111yescharacteristic
208C42×C89C2411yescharacteristic
209C23×C89—21no—
210C23×C89—21no—
211C23×C89—42no—
212C23×C89—42no—
213C23×C89—81no—
214C23×C89C4×D411yescharacteristic
215D4×C89—21no—
216D4×C89—21no—
217D4×C89—21no—
218D4×C89—42no—
219D4×C89#13112yes—
220C2×C4×C89—21no—
221C2×C4×C89—21no—
222C2×C4×C89—21no—
223C2×C4×C89—21no—
224C2×C4×C89—21no—
225C2×C4×C89—21no—
226C2×C4×C89—41no—
227C2×C4×C89—41no—
228C2×C4×C89—41no—
229C2×C4×C89—41no—
230C2×C4×C89—41no—
231C2×C4×C89—81no—
232C2×C4×C89—81no—
233C2×C4×C89—81no—
234C2×C4×C89C4×D411yescharacteristic
235C2×C4×C89C4×D411yescharacteristic
236C2×C4×C89C4×D411yescharacteristic
237C2×C4×C89C23×C411yescharacteristic
238C2×C4×C89C22×D411yescharacteristic
239C2×C4×C89C2×#4111yescharacteristic
240C2×Dic89—21no—
241C2×Dic89—21no—
242C2×Dic89—21no—
243C2×Dic89—21no—
244Dic178—21no—
245Dic178—21no—
246Dic178—21no—
247Dic178—21no—
248Dic178—42no—
249C8×C89—21no—
250C8×C89—21no—
251C8×C89—21no—
252C8×C89—21no—
253C8×C89—41no—
254C8×C89—41no—
255#10623494—21no—
256#10623494—21no—
257#10623494—21no—
258#10623494—21no—
259#10623494—41no—
260#10623494—41no—
261#10623494—41no—
262#10623494—41no—
263C22×C89—21no—
264C22×C89—22no—
265C22×C89—21no—
266C22×C89—21no—
267C22×C89—41no—
268C22×C89—41no—
269C22×C89—41no—
270C22×C89—41no—
271C22×C89—41no—
272C22×C89—84no—
273C22×C89C2×C4×D411yescharacteristic
274C4×C89—21no—
275C4×C89—21no—
276C4×C89—21no—
277C4×C89—21no—
278C4×C89—41no—
279C4×C89—41no—
280C4×C89C2×#13111yescharacteristic
281C4×C89#56811yescharacteristic
282C4×C89#57711yescharacteristic
283C4×C89#57711yescharacteristic
284Dic89—41no—
285Dic89—41no—
286Dic89—41no—
287Dic89—41no—
288#18028—891nomaximal, Sylow
289C2×C89—41no—
290C2×C89—42no—
291C2×C89—81no—
292C2×C89#293311yescharacteristic
293C2×C89#294911yescharacteristic
294C2×C89#295511yescharacteristic
295#3101—891no—
296#2986—891no—
297#2974D8911yescharacteristic
298#1592—891no—
299#1590—891no—
300#1588—891no—
301#1585—891no—
302#1583—891no—
303#1582—891no—
304SD16⋊C8—891no—
305C8×SD16—891no—
306#1572—891no—
307#1497—891no—
308#1478—891no—
309#1454—891no—
310C89#1802811yescharacteristic, complemented, Sylow
311#533—891no—
312C2×C4×D4C2×D8911yescharacteristic
313#483—891no—
314#483—891no—
315#476—891no—
316#476—891no—
317#461—891no—
318#461—891no—
319#450—891no—
320#450—891no—
321#446—891no—
322#446—891no—
323#446—1781no—
324C8×Q8—891no—
325C8×Q8—891no—
326C8×Q8—1781no—
327C4×SD16—891no—
328C4×SD16—891no—
329C4×SD16—891no—
330C4×SD16—891no—
331#436C2×D8911yescharacteristic
332#436C2×D8911yescharacteristic
333#435—21no—
334#435—21no—
335C8×D4C2×D8911yescharacteristic
336C8×D4C2×D8911yescharacteristic
337#433—1781no—
338#433—1781no—
339#432C2×D8911yescharacteristic
340#431—891no—
341#431—891no—
342#431—891no—
343#431C2×D8911yescharacteristic
344#407—21no—
345C2×C22⋊C8—21no—
346#335—891no—
347#335—891no—
348#334—891no—
349#334—891no—
350Q8⋊C8—891no—
351Q8⋊C8—891no—
352Q8⋊C8—891no—
353Q8⋊C8—891no—
354D4⋊C8—891no—
355D4⋊C8—891no—
356D4⋊C8—891no—
357D4⋊C8—891no—
358#322—891no—
359#322—891no—
360#322—891no—
361C82—891no—
362C22×D4C4×D8911yescharacteristic
363C23×C4—21no—
364C2×SD16—891no—
365C2×SD16—891no—
366C2×SD16—891no—
367C2×SD16—891no—
368C2×M16—21no—
369C2×M16—21no—
370C22×C8—21no—
371C22×C8—21no—
372C4⋊Q8—891no—
373C4⋊Q8—891no—
374#125—1781no—
375C22⋊Q8—891no—
376C22⋊Q8—891no—
377C22⋊Q8—1781no—
378C4×Q8—891no—
379C4×Q8—891no—
380C4×Q8—1781no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C4×D8911yescharacteristic
384C4×D4C4×D8911yescharacteristic
385C4×D4C22×D8911yescharacteristic
386C4×D4C22×D8911yescharacteristic
387#117—1781no—
388C2×C4⋊C4C4×D8911yescharacteristic
389C2×C22⋊C4—21no—
390C2×C42C22×D8911yescharacteristic
391#106—891no—
392#106—891no—
393#106—891no—
394#106—891no—
395C4⋊C8—891no—
396C4⋊C8—891no—
397C4⋊C8—891no—
398C4⋊C8—891no—
399C4⋊C8—1781no—
400C4⋊C8—1781no—
401C4⋊C8—1781no—
402C4⋊C8—1781no—
403C4⋊C8—1781no—
404C4⋊C8C22⋊D8911yescharacteristic
405C4⋊C8C22⋊D8911yescharacteristic
406C4⋊C8C22×D8911yescharacteristic
407C4⋊C8C22×D8911yescharacteristic
408#103—891no—
409#103—891no—
410#103—891no—
411#103—891no—
412#102—891no—
413#102—891no—
414#102—891no—
415#102—891no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—891no—
422C22⋊C8—891no—
423C22⋊C8—1781no—
424C22⋊C8—1781no—
425C22⋊C8C22⋊D8911yescharacteristic
426C22⋊C8C22⋊D8911yescharacteristic
427#97—21no—
428#97—1781no—
429#97—1781no—
430C4×C8—891no—
431C4×C8—891no—
432C4×C8—891no—
433C4×C8—891no—
434C4×C8—1781no—
435C4×C8—1781no—
436C4×C8—1781no—
437C4×C8C22×D8911yescharacteristic
438C4×C8C22×D8911yescharacteristic
439C24—21no—
440C2×Q8—891no—
441C2×Q8—891no—
442C2×Q8—1781no—
443C2×D4—22no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4C2×C4×D8911yescharacteristic
447C2×D4C2×C4×D8911yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4C2×C4×D8911yescharacteristic
456C22×C4C2×C22⋊D8911yescharacteristic
457C22×C4#1308357411yescharacteristic
458SD16—3561no—
459SD16—3561no—
460SD16—1782no—
461SD16—1782no—
462M16—81no—
463M16—81no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—81no—
467C2×C8—81no—
468C2×C8—891no—
469C2×C8—891no—
470C2×C8—891no—
471C2×C8—891no—
472C2×C8—1781no—
473C2×C8—1781no—
474C2×C8—1781no—
475C2×C8—1781no—
476C2×C8C2×C22⋊D8911yescharacteristic
477C2×C8C2×C22⋊D8911yescharacteristic
478C2×C8C2×C22⋊D8911yescharacteristic
479C2×C8C2×C22⋊D8911yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—891no—
482C4⋊C4—891no—
483C4⋊C4—1781no—
484C4⋊C4—1781no—
485C4⋊C4—1781no—
486C4⋊C4—1781no—
487C4⋊C4—1781no—
488C4⋊C4—1781no—
489C4⋊C4—1781no—
490C4⋊C4C2×C4×D8911yescharacteristic
491C4⋊C4C2×C4×D8911yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—1781no—
497C22⋊C4—1781no—
498C42—1781no—
499C42—1781no—
500C42C2×C4×D8911yescharacteristic
501C42C2×C22⋊D8911yescharacteristic
502C42#1308357411yescharacteristic
503C42C23×D8911yescharacteristic
504C23—21no—
505C23—21no—
506C23—42no—
507C23—42no—
508C23—81no—
509C23C4×C22⋊D8911yescharacteristic
510Q8—3562no—
511Q8—1781no—
512Q8—1781no—
513Q8—1781no—
514Q8—1781no—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—42no—
519D4#1566802012yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—1781no—
535C2×C4—1781no—
536C2×C4—1781no—
537C2×C4—1781no—
538C2×C4C4×C22⋊D8911yescharacteristic
539C2×C4C4×C22⋊D8911yescharacteristic
540C2×C4C4×C22⋊D8911yescharacteristic
541C2×C4C22×C4×D8911yescharacteristic
542C2×C4C22×C22⋊D8911yescharacteristic
543C2×C4C2×#1308357411yescharacteristic
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—3561no—
551C8—3561no—
552C8—3561no—
553C8—3561no—
554C8—1781no—
555C8—1781no—
556C8—1781no—
557C8—1781no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—84no—
568C22C2×C4×C22⋊D8911yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—3561no—
576C4—3561no—
577C4—3561no—
578C4—3561no—
579C4C2×#1566802011yescharacteristic
580C4#1915236411yescharacteristic
581C4#1915240911yescharacteristic
582C4#1915240911yescharacteristic
583C2—41no—
584C2—42no—
585C2—81no—
586C2#2602897711yescharacteristic
587C2#2602910911yescharacteristic
588C2#2602915311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#2974C2
socleC22×C89C2×C4×D4
prime radicalC22×D4×C89C2×C4
cosocleC42×C89C24
hypercenter#2974D89
hypocenterC89#18028
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #26029353C2semidirect
3. #26019154C2semidirect
4. #26019140C2semidirect
5. #26019128C2semidirect
6. #26019109C2semidirect
7. #26019093C2semidirect
8. #26019088C2semidirect
9. #26019064C2semidirect
10. C8×#13083562C2semidirect
11. #26019033C2semidirect
12. #26018724C2semidirect
14. #26018552C2semidirect
25. #19151728C22semidirect
26. #19151728C22semidirect
28. C8×Dic178C22semidirect
29. C8×Dic178C22semidirect
40. #19151350C22semidirect
41. #19151350C22semidirect
42. #19151348C22semidirect
43. #19151348C22semidirect
44. #19151328C22semidirect
45. #19151328C22semidirect
46. #19151328C22semidirect
47. #19151328C22semidirect
52. #19151320C22semidirect
53. #19151320C22semidirect
54. #19151319C22semidirect
55. C8×#10623494C22semidirect
310. C89#18028semidirect

Maximal subgroups

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

subgroupindex
#260302602
#260293532
#260191542
#260191402
#260191282
#260191092
#260190932
#260190882
#260190642
C8×#130835622
#260190332
#260187242
#260186432
#260185522
C89×#29742
#1802889