Finite Group Databasebeta

← #36524652

Subgroups — #36524652

Order 22784.

604 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26030270C211yesmaximal, characteristic
2#26029221C211yesmaximal, characteristic, complemented
3#26029219C211yesmaximal, characteristic, complemented
4#26019146C211yesmaximal, characteristic, complemented
5#26019145C211yesmaximal, characteristic, complemented
6#26019139C211yesmaximal, characteristic, complemented
7#26019134C211yesmaximal, characteristic, complemented
8#26019105C211yesmaximal, characteristic, complemented
9#26019098C211yesmaximal, characteristic, complemented
10#26019091C211yesmaximal, characteristic, complemented
11#26019084C211yesmaximal, characteristic, complemented
12#26019033C211yesmaximal, characteristic, complemented
13#26018661C211yesmaximal, characteristic, complemented
14#26018536C211yesmaximal, characteristic, complemented
15C89×#1488C211yesmaximal, characteristic, complemented
16#19152132C2211yescharacteristic
17#19151939C411yescharacteristic
18#19151922C411yescharacteristic
19#19151905C411yescharacteristic
20#19151898C411yescharacteristic
21#19151820C411yescharacteristic
22#19151813C411yescharacteristic
23#19151760C411yescharacteristic
24#19151743C411yescharacteristic
25#19151729C2211yescharacteristic
26#19151729C2211yescharacteristic
27#19151725C2211yescharacteristic
28#19151722C2211yescharacteristic
29C4×#13083564C2211yescharacteristic
30C4×#13083561C2211yescharacteristic
31C4×#13083562C2211yescharacteristic
32C4×#13083559C2211yescharacteristic
33#19151676C2211yescharacteristic
34#19151676C2211yescharacteristic
35#19151675C2211yescharacteristic
36#19151670—21no—
37#19151670—21no—
38#19151666—21no—
39#19151663C2211yescharacteristic
40#19151661—21no—
41#19151660—21no—
42#19151651—21no—
43#19151651C2211yescharacteristic
44#19151651C2211yescharacteristic
45#19151555—21no—
46C4×#13083558—21no—
47C2×C4×#10623494C2211yescharacteristic
48#19151350C2211yescharacteristic
49#19151350C2211yescharacteristic
50#19151348C2211yescharacteristic
51#19151348C2211yescharacteristic
52#19151330C2211yescharacteristic
53#19151330C2211yescharacteristic
54#19151327C2211yescharacteristic
55#19151327C2211yescharacteristic
56#19151320C2211yescharacteristic
57#19151320C2211yescharacteristic
58C8×#10623494C2211yescharacteristic
59C8×#10623494C2211yescharacteristic
60C4×#41×C89C2211yescharacteristic
61#432×C89C2211yescharacteristic
62#431×C89C2211yescharacteristic
63Q8⋊C8×C89C2211yescharacteristic
64Q8⋊C8×C89C2211yescharacteristic
65D4⋊C8×C89C2211yescharacteristic
66D4⋊C8×C89C2211yescharacteristic
67C2×#13083564C2×C411yescharacteristic
68C2×#13083562C2×C411yescharacteristic
69C2×#13083561C2×C411yescharacteristic
70C2×#13083559C2×C411yescharacteristic
71C2×#13083558—21no—
72C2×#13083558—21no—
73C2×#13083557—21no—
74C22×#10623494D411yescharacteristic
75C22×#10623494D411yescharacteristic
76C2×C8×D89—21no—
77#15668006—21no—
78#15668004C2×C411yescharacteristic
79#15668000C2×C411yescharacteristic
80#15667995—21no—
81#15667991C2×C411yescharacteristic
82#15667986C2×C411yescharacteristic
83C4×Dic178C2311yescharacteristic
84C4×D356C2311yescharacteristic
85C4×C22⋊D89—21no—
86#15667969—21no—
87#15667945C2×C411yescharacteristic
88#15667945C2×C411yescharacteristic
89#15667943C2×C411yescharacteristic
90#15667943C2×C411yescharacteristic
91C4⋊#10623494—21no—
92C4⋊#10623494—21no—
93C4⋊#10623494C2×C411yescharacteristic
94C4⋊#10623494C2×C411yescharacteristic
95C4⋊#10623494C2311yescharacteristic
96C4⋊#10623494C2311yescharacteristic
97#15667941—21no—
98#15667941—21no—
99#15667936C2×C411yescharacteristic
100#15667936C2×C411yescharacteristic
101#15667935C2×C411yescharacteristic
102#15667935C2×C411yescharacteristic
103#15667933C2×C411yescharacteristic
104#15667933C2×C411yescharacteristic
105#15667932C2×C411yescharacteristic
106#15667932C2×C411yescharacteristic
107C22⋊#10623494—21no—
108C22⋊#10623494—21no—
109C22⋊#10623494—21no—
110C22⋊#10623494C2×C411yescharacteristic
111C22⋊#10623494C2×C411yescharacteristic
112#15667924—21no—
113#15667924—21no—
114#15667923—21no—
115#15667923—21no—
116#15667922—21no—
117C4×#10623494—21no—
118C4×#10623494D411yescharacteristic
119C4×#10623494D411yescharacteristic
120C4×#10623494C2311yescharacteristic
121C4×#10623494C2311yescharacteristic
122C4×#10623494C2311yescharacteristic
123C4×#10623494C2311yescharacteristic
124C8×Dic89—21no—
125C2×#41×C89C2×C411yescharacteristic
126C4×Q8×C89C2×C411yescharacteristic
127C4×Q8×C89C2311yescharacteristic
128C4×D4×C89—21no—
129C4×D4×C89—21no—
130C4×D4×C89C2×C411yescharacteristic
131C4×D4×C89C2311yescharacteristic
132#117×C89—21no—
133#117×C89C2×C411yescharacteristic
134C2×C42×C89—21no—
135C2×C42×C89C2311yescharacteristic
136C4⋊C8×C89—21no—
137C4⋊C8×C89C2311yescharacteristic
138C4⋊C8×C89C2311yescharacteristic
139C22⋊C8×C89—21no—
140C22⋊C8×C89—21no—
141#97×C89—21no—
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144C2×Dic178C22×C411yescharacteristic
145C2×D356C22×C411yescharacteristic
146C2×C22⋊D89—21no—
147C2×C4×D89—21no—
148#13083564—41no—
149#13083562—41no—
150#13083561—41no—
151#13083559—41no—
152#13083558—42no—
153#13083558—42no—
154#13083557—42no—
155C2×#10623494—22no—
156C2×#10623494—22no—
157C2×#10623494—21no—
158C2×#10623494—21no—
159C2×#10623494C22×C411yescharacteristic
160C2×#10623494C22×C411yescharacteristic
161C2×#10623494C22×C411yescharacteristic
162C2×#10623494C22×C411yescharacteristic
163C2×#10623494C2×D411yescharacteristic
164C2×#10623494C2×D411yescharacteristic
165C2×#10623494C2×D411yescharacteristic
166C2×#10623494C2×D411yescharacteristic
167C8×D89—42no—
168C4⋊Dic89C22×C411yescharacteristic
169C4⋊Dic89C22×C411yescharacteristic
170#13083553—21no—
171#13083553—21no—
172#13083553—21no—
173#13083553—21no—
174C22⋊Dic89—21no—
175#13083551—21no—
176#13083551—21no—
177#13083551—21no—
178#13083551—21no—
179C4×Dic89—21no—
180#41×C89—41no—
181#41×C89—41no—
182C2×Q8×C89C22×C411yescharacteristic
183C2×D4×C89—21no—
184C2×D4×C89C22×C411yescharacteristic
185C22×C4×C89—21no—
186C22×C4×C89—21no—
187C22×C4×C89—21no—
188C22×C4×C89C22×C411yescharacteristic
189C22×C4×C89C2×D411yescharacteristic
190C22×C4×C89#4111yescharacteristic
191C2×C8×C89—21no—
192C2×C8×C89—21no—
193C2×C8×C89—21no—
194C2×C8×C89—21no—
195C4⋊C4×C89—21no—
196C4⋊C4×C89—21no—
197C4⋊C4×C89C22×C411yescharacteristic
198C4⋊C4×C89C22×C411yescharacteristic
199C22⋊C4×C89—21no—
200C22⋊C4×C89—21no—
201C22⋊C4×C89—21no—
202C42×C89—21no—
203C42×C89—21no—
204C42×C89—21no—
205C42×C89C22×C411yescharacteristic
206C42×C89C2×D411yescharacteristic
207C42×C89#4111yescharacteristic
208C42×C89C2411yescharacteristic
209C23×C89—21no—
210C23×C89C4×D411yescharacteristic
211C22×D89—21no—
212Q8×C89—21no—
213Q8×C89—21no—
214D4×C89—21no—
215D4×C89—21no—
216D4×C89—42no—
217C2×C4×C89—21no—
218C2×C4×C89—21no—
219C2×C4×C89—21no—
220C2×C4×C89—21no—
221C2×C4×C89—21no—
222C2×C4×C89—21no—
223C2×C4×C89—21no—
224C2×C4×C89—41no—
225C2×C4×C89—42no—
226C2×C4×C89—42no—
227C2×C4×C89—41no—
228C2×C4×C89—41no—
229C2×C4×C89C4×D411yescharacteristic
230C2×C4×C89C4×D411yescharacteristic
231C2×C4×C89C4×D411yescharacteristic
232C2×C4×C89C23×C411yescharacteristic
233C2×C4×C89C22×D411yescharacteristic
234C2×C4×C89C2×#4111yescharacteristic
235C22⋊D89—42no—
236C2×Dic89—21no—
237C2×Dic89—21no—
238C2×Dic89—21no—
239D356—21no—
240D356—21no—
241C4×D89—41no—
242C4×D89—41no—
243Dic178—21no—
244Dic178—21no—
245C8×C89—41no—
246C8×C89—41no—
247C8×C89—41no—
248C8×C89—41no—
249#10623494—21no—
250#10623494—21no—
251#10623494—21no—
252#10623494—21no—
253#10623494—21no—
254#10623494—21no—
255#10623494—41no—
256#10623494—41no—
257#10623494#13512yes—
258#10623494#13512yes—
259C22×C89—21no—
260C22×C89—21no—
261C22×C89—21no—
262C22×C89—41no—
263C22×C89—41no—
264C22×C89—41no—
265C22×C89C2×C4×D411yescharacteristic
266C2×D89—41no—
267C2×D89—41no—
268C2×D89—41no—
269C4×C89—21no—
270C4×C89—21no—
271C4×C89—21no—
272C4×C89—21no—
273C4×C89—41no—
274C4×C89—41no—
275C4×C89—41no—
276C4×C89#56811yescharacteristic
277C4×C89#56811yescharacteristic
278C4×C89C2×#13511yescharacteristic
279C4×C89C2×#13511yescharacteristic
280Dic89—41no—
281Dic89—41no—
282Dic89—41no—
283#17932—891nomaximal, Sylow
284C2×C89—41no—
285C2×C89—81no—
286C2×C89#293011yescharacteristic
287C2×C89C4×#13511yescharacteristic
288C2×C89#295511yescharacteristic
289D89—81no—
290#3102—891no—
291#2966—891no—
292#2965—891no—
293#1591—891no—
294#1590—891no—
295#1590—891no—
296#1589—891no—
297#1584—891no—
298#1583—891no—
299#1582—891no—
300#1581—891no—
301#1572—891no—
302#1488D8911yescharacteristic, complemented
303#1482—891no—
304#1450—891no—
305C89#1793211yescharacteristic, complemented, Sylow
306#529—891no—
307C4×#41C2×D8911yescharacteristic
308#485—891no—
309#482—891no—
310#479—891no—
311#478—891no—
312#464—891no—
313#463—891no—
314#452—891no—
315#449—891no—
316#446—891no—
317#446—891no—
318#446—891no—
319C8×Q8—891no—
320C4×Q16—891no—
321C4×SD16—891no—
322C4×SD16—891no—
323C4×D8—891no—
324#436—891no—
325#436—891no—
326#436—891no—
327#435—1781no—
328#435—1781no—
329#435—1781no—
330C8×D4—891no—
331C8×D4—1781no—
332#433—1781no—
333#432C2×D8911yescharacteristic
334#431—891no—
335#431—891no—
336#431—1781no—
337#431C2×D8911yescharacteristic
338#405—1781no—
339C4×M16—1781no—
340C2×C4×C8—891no—
341#335—891no—
342#335—891no—
343#334—891no—
344#334—891no—
345Q8⋊C8—891no—
346Q8⋊C8—891no—
347Q8⋊C8C2×D8911yescharacteristic
348Q8⋊C8C2×D8911yescharacteristic
349D4⋊C8—891no—
350D4⋊C8—891no—
351D4⋊C8C2×D8911yescharacteristic
352D4⋊C8C2×D8911yescharacteristic
353#322—891no—
354#322—891no—
355C82—891no—
356C82—891no—
357C2×#41C4×D8911yescharacteristic
358C2×Q16—891no—
359C2×SD16—891no—
360C2×SD16—891no—
361C2×D8—891no—
362C2×M16—1781no—
363C2×M16—1781no—
364C2×M16—1781no—
365C22×C8—891no—
366C22×C8—891no—
367C22×C8—1781no—
368#126—1781no—
369#125—891no—
370#124—891no—
371#123—1781no—
372C22⋊Q8—891no—
373#121—891no—
374C4×Q8—891no—
375C4×Q8C4×D8911yescharacteristic
376C4×Q8C22×D8911yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—891no—
380C4×D4—1781no—
381C4×D4C4×D8911yescharacteristic
382C4×D4C22×D8911yescharacteristic
383#117—21no—
384#117—1781no—
385#117C4×D8911yescharacteristic
386C2×C42—21no—
387C2×C42C22×D8911yescharacteristic
388#107—891no—
389#107—891no—
390#106—891no—
391#106—891no—
392C4⋊C8—21no—
393C4⋊C8—891no—
394C4⋊C8—891no—
395C4⋊C8—891no—
396C4⋊C8—891no—
397C4⋊C8—1781no—
398C4⋊C8—1781no—
399C4⋊C8—1781no—
400C4⋊C8—1781no—
401C4⋊C8C22×D8911yescharacteristic
402C4⋊C8C22×D8911yescharacteristic
403#103—891no—
404#103—891no—
405#103—891no—
406#103—891no—
407#102—891no—
408#102—891no—
409#102—891no—
410#102—891no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—891no—
414C22⋊C8—891no—
415C22⋊C8—1781no—
416C22⋊C8—1781no—
417C22⋊C8—1781no—
418C22⋊C8—1781no—
419C22⋊C8—1781no—
420#97—21no—
421#97—1781no—
422#97—1781no—
423#97—1781no—
424C4×C8—891no—
425C4×C8—891no—
426C4×C8—891no—
427C4×C8—891no—
428C4×C8—891no—
429C4×C8—891no—
430C4×C8—1781no—
431C4×C8—1781no—
432C4×C8C22×D8911yescharacteristic
433C4×C8C22×D8911yescharacteristic
434#41—41no—
435#41—41no—
436C2×Q8—891no—
437C2×Q8C2×C4×D8911yescharacteristic
438C2×D4—21no—
439C2×D4—891no—
440C2×D4—1781no—
441C2×D4C2×C4×D8911yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—1781no—
446C22×C4C2×C4×D8911yescharacteristic
447C22×C4D4×D8911yescharacteristic
448C22×C4#1308357311yescharacteristic
449Q16—3561no—
450SD16—3561no—
451SD16—3561no—
452D8—3561no—
453M16—3562no—
454M16—3562no—
455M16—3562no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—891no—
461C2×C8—891no—
462C2×C8—891no—
463C2×C8—891no—
464C2×C8—891no—
465C2×C8—891no—
466C2×C8—891no—
467C2×C8—891no—
468C2×C8—3562no—
469C2×C8—1782no—
470C2×C8—1782no—
471C2×C8—1781no—
472C2×C8—1781no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—891no—
476C4⋊C4—891no—
477C4⋊C4—1781no—
478C4⋊C4—1781no—
479C4⋊C4—1781no—
480C4⋊C4—1781no—
481C4⋊C4C2×C4×D8911yescharacteristic
482C4⋊C4C2×C4×D8911yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—1781no—
487C22⋊C4—1781no—
488C22⋊C4—1781no—
489C22⋊C4—1781no—
490C22⋊C4—1781no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—1781no—
495C42C2×C4×D8911yescharacteristic
496C42D4×D8911yescharacteristic
497C42#1308357311yescharacteristic
498C42C23×D8911yescharacteristic
499C23—21no—
500C23—1781no—
501C23#1566797211yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—1781no—
505Q8—1781no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—3562no—
510D4—1781no—
511D4—1781no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—3561no—
525C2×C4—3561no—
526C2×C4—1781no—
527C2×C4—1781no—
528C2×C4—1781no—
529C2×C4#1566797211yescharacteristic
530C2×C4#1566797211yescharacteristic
531C2×C4#1566797211yescharacteristic
532C2×C4C22×C4×D8911yescharacteristic
533C2×C4C2×D4×D8911yescharacteristic
534C2×C4C2×#1308357311yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—892no—
540C8—892no—
541C8—3561no—
542C8—3561no—
543C8—1781no—
544C8—1781no—
545C8—1781no—
546C8—1781no—
547C8—1781no—
548C8—1781no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—3561no—
556C22—3561no—
557C22—3561no—
558C22C2×#1566797211yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—3561no—
567C4—3561no—
568C4—3561no—
569C4#1915236411yescharacteristic
570C4#1915236411yescharacteristic
571C4#135×D8911yescharacteristic
572C4#135×D8911yescharacteristic
573C2—41no—
574C2—81no—
575C2—7121no—
576C2#2602895111yescharacteristic
577C2#2602902011yescharacteristic
578C2#2602915111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#1488C2
socleC22×C89C2×C4×D4
prime radical#19151743C4
cosocleC42×C89C24
hypercenter#1488D89
hypocenterC89#17932
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #26029221C2semidirect
3. #26029219C2semidirect
4. #26019146C2semidirect
5. #26019145C2semidirect
6. #26019139C2semidirect
7. #26019134C2semidirect
8. #26019105C2semidirect
9. #26019098C2semidirect
10. #26019091C2semidirect
11. #26019084C2semidirect
12. #26019033C2semidirect
13. #26018661C2semidirect
14. #26018536C2semidirect
15. C89×#1488C2semidirect
302. #1488D89semidirect
305. C89#17932semidirect

Maximal subgroups

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

subgroupindex
#260302702
#260292212
#260292192
#260191462
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