Finite Group Databasebeta

← #36525792

Subgroups — #36525792

Order 22784.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26030283C211yesmaximal, characteristic
2#26029318C211yesmaximal, characteristic
3#26019152C211yesmaximal, characteristic, complemented
4#26019142C211yesmaximal, characteristic, complemented
5#26019130C211yesmaximal, characteristic, complemented
6#26019107C211yesmaximal, characteristic, complemented
7#26019095C211yesmaximal, characteristic, complemented
8#26019086C211yesmaximal, characteristic, complemented
9#26019062C211yesmaximal, characteristic, complemented
10C8×#13083561C211yesmaximal, characteristic, complemented
11#26019033C211yesmaximal, characteristic, complemented
12#26018720C211yesmaximal, characteristic
13#26018647C211yesmaximal, characteristic, complemented
14#26018552C211yesmaximal, characteristic, complemented
15C89×#2984C211yesmaximal, characteristic, complemented
16#19152148C2211yescharacteristic
17#19151916C411yescharacteristic
18#19151916C411yescharacteristic
19#19151883C411yescharacteristic
20#19151883C411yescharacteristic
21#19151798C411yescharacteristic
22#19151798C411yescharacteristic
23#19151737C411yescharacteristic
24#19151737C411yescharacteristic
25C4×#13083561C2211yescharacteristic
26C4×#13083561C2211yescharacteristic
27C4×#13083561C2211yescharacteristic
28C4×#13083561C2211yescharacteristic
29#19151677C2211yescharacteristic
30#19151677C2211yescharacteristic
31#19151675—21no—
32C8×D356C2211yescharacteristic
33C8×D356C2211yescharacteristic
34#19151663—21no—
35#19151651C2211yescharacteristic
36#19151651C2211yescharacteristic
37#19151651C2211yescharacteristic
38#19151563—21no—
39#19151563—21no—
40#19151350C2211yescharacteristic
41#19151350C2211yescharacteristic
42#19151348C2211yescharacteristic
43#19151348C2211yescharacteristic
44Q8⋊#10623494C2211yescharacteristic
45Q8⋊#10623494C2211yescharacteristic
46Q8⋊#10623494C2211yescharacteristic
47Q8⋊#10623494C2211yescharacteristic
48#19151325C2211yescharacteristic
49#19151325C2211yescharacteristic
50#19151325C2211yescharacteristic
51#19151325C2211yescharacteristic
52#19151320C2211yescharacteristic
53#19151320C2211yescharacteristic
54#19151319C2211yescharacteristic
55C8×#10623494C2211yescharacteristic
56C2×C4×Q8×C89C2211yescharacteristic
57#446×C89—21no—
58#446×C89—21no—
59#446×C89C2211yescharacteristic
60#446×C89C2211yescharacteristic
61C8×Q8×C89C2211yescharacteristic
62C8×Q8×C89C2211yescharacteristic
63#432×C89—21no—
64#432×C89C2211yescharacteristic
65#431×C89—21no—
66#431×C89C2211yescharacteristic
67C2×#13083574—21no—
68C2×#13083561C2×C411yescharacteristic
69C2×#13083561C2×C411yescharacteristic
70C2×#13083561C2×C411yescharacteristic
71C2×#13083561C2×C411yescharacteristic
72C2×#13083557—21no—
73C2×#13083557—21no—
74C2×C8×D89—21no—
75C2×C8×D89—21no—
76#15668012C2×C411yescharacteristic
77#15668009C2×C411yescharacteristic
78#15668000—21no—
79#15667986—21no—
80#15667986C2×C411yescharacteristic
81#15667986C2×C411yescharacteristic
82C4×D356—21no—
83C4×D356C2311yescharacteristic
84C4×D356C2311yescharacteristic
85#15667943C2×C411yescharacteristic
86#15667943C2×C411yescharacteristic
87#15667943C2×C411yescharacteristic
88#15667943C2×C411yescharacteristic
89C4⋊#10623494—21no—
90C4⋊#10623494C2×C411yescharacteristic
91C4⋊#10623494C2×C411yescharacteristic
92C4⋊#10623494C2311yescharacteristic
93C4⋊#10623494C2311yescharacteristic
94#15667936C2×C411yescharacteristic
95#15667936C2×C411yescharacteristic
96#15667936C2×C411yescharacteristic
97#15667936C2×C411yescharacteristic
98#15667932C2×C411yescharacteristic
99#15667932C2×C411yescharacteristic
100#15667932C2×C411yescharacteristic
101#15667932C2×C411yescharacteristic
102C22⋊#10623494—21no—
103C22⋊#10623494—21no—
104C22⋊#10623494C2×C411yescharacteristic
105C22⋊#10623494C2×C411yescharacteristic
106#15667924—21no—
107#15667924—21no—
108#15667924—21no—
109#15667924—21no—
110C4×#10623494—21no—
111C4×#10623494C2311yescharacteristic
112C4×#10623494C2311yescharacteristic
113C4×#10623494C2311yescharacteristic
114C4×#10623494C2311yescharacteristic
115C22×Q8×C89C2×C411yescharacteristic
116C4×Q8×C89—21no—
117C4×Q8×C89—21no—
118C4×Q8×C89C2×C411yescharacteristic
119C4×Q8×C89C2×C411yescharacteristic
120C4×Q8×C89C2311yescharacteristic
121C4×Q8×C89C2311yescharacteristic
122C2×C4⋊C4×C89—21no—
123C2×C4⋊C4×C89C2×C411yescharacteristic
124C2×C42×C89—21no—
125C2×C42×C89C2311yescharacteristic
126C4⋊C8×C89—21no—
127C4⋊C8×C89—21no—
128C4⋊C8×C89—21no—
129C4⋊C8×C89—21no—
130C4⋊C8×C89D411yescharacteristic
131C4⋊C8×C89D411yescharacteristic
132C4⋊C8×C89C2311yescharacteristic
133C4⋊C8×C89C2311yescharacteristic
134C22⋊C8×C89—21no—
135C22⋊C8×C89D411yescharacteristic
136C22⋊C8×C89D411yescharacteristic
137#97×C89—21no—
138#97×C89—21no—
139#97×C89—21no—
140C4×C8×C89—21no—
141C4×C8×C89—21no—
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144#13083574—81no—
145#13083574—81no—
146C2×Dic178—21no—
147C2×D356—21no—
148C2×D356—21no—
149C2×D356C22×C411yescharacteristic
150C2×D356C22×C411yescharacteristic
151C2×C22⋊D89—21no—
152C2×C22⋊D89—21no—
153C2×C4×D89—21no—
154C2×C4×D89—21no—
155#13083561—22no—
156#13083561—22no—
157#13083561—41no—
158#13083561—41no—
159#13083557—81no—
160#13083557—81no—
161C2×#10623494—21no—
162C2×#10623494—21no—
163C2×#10623494—21no—
164C2×#10623494—21no—
165C2×#10623494C22×C411yescharacteristic
166C2×#10623494C22×C411yescharacteristic
167C2×#10623494C22×C411yescharacteristic
168C2×#10623494C22×C411yescharacteristic
169C8×D89—81no—
170C8×D89—81no—
171C4⋊Dic89—21no—
172C4⋊Dic89C22×C411yescharacteristic
173C4⋊Dic89C22×C411yescharacteristic
174#13083551—21no—
175#13083551—21no—
176#13083551—21no—
177#13083551—21no—
178C2×Q8×C89—21no—
179C2×Q8×C89—22no—
180C2×Q8×C89—41no—
181C2×Q8×C89C22×C411yescharacteristic
182C2×Q8×C89C22×C411yescharacteristic
183C22×C4×C89—21no—
184C22×C4×C89—21no—
185C22×C4×C89C22×C411yescharacteristic
186C22×C4×C89C2×D411yescharacteristic
187C22×C4×C89#4111yescharacteristic
188C2×C8×C89—21no—
189C2×C8×C89—21no—
190C2×C8×C89C2×D411yescharacteristic
191C2×C8×C89C2×D411yescharacteristic
192C2×C8×C89C2×D411yescharacteristic
193C2×C8×C89C2×D411yescharacteristic
194C4⋊C4×C89—21no—
195C4⋊C4×C89—21no—
196C4⋊C4×C89—21no—
197C4⋊C4×C89—21no—
198C4⋊C4×C89—21no—
199C4⋊C4×C89C22×C411yescharacteristic
200C4⋊C4×C89C22×C411yescharacteristic
201C42×C89—21no—
202C42×C89—21no—
203C42×C89—21no—
204C42×C89—21no—
205C42×C89C22×C411yescharacteristic
206C42×C89C2×D411yescharacteristic
207C42×C89#4111yescharacteristic
208C42×C89C2411yescharacteristic
209C23×C89C4×D411yescharacteristic
210C22×D89—21no—
211C22×D89—21no—
212Q8×C89—21no—
213Q8×C89—21no—
214Q8×C89—21no—
215Q8×C89—42no—
216Q8×C89#13112yes—
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—21no—
225C2×C4×C89—41no—
226C2×C4×C89—42no—
227C2×C4×C89—42no—
228C2×C4×C89C4×D411yescharacteristic
229C2×C4×C89C4×D411yescharacteristic
230C2×C4×C89C4×D411yescharacteristic
231C2×C4×C89C23×C411yescharacteristic
232C2×C4×C89C22×D411yescharacteristic
233C2×C4×C89C2×#4111yescharacteristic
234C22⋊D89—81no—
235C22⋊D89—81no—
236C2×Dic89—21no—
237C2×Dic89—21no—
238D356—21no—
239D356—21no—
240D356—21no—
241D356—21no—
242D356—42no—
243D356—81no—
244C4×D89—41no—
245C4×D89—41no—
246C4×D89—41no—
247C4×D89—41no—
248Dic178—81no—
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—21no—
265C22×C89—21no—
266C22×C89C2×C4×D411yescharacteristic
267C2×D89—41no—
268C2×D89—41no—
269C2×D89—41no—
270C2×D89—41no—
271C2×D89—41no—
272C2×D89—41no—
273C4×C89—21no—
274C4×C89—22no—
275C4×C89—21no—
276C4×C89—21no—
277C4×C89—21no—
278C4×C89—41no—
279C4×C89—41no—
280C4×C89—41no—
281C4×C89C2×#13111yescharacteristic
282C4×C89#56811yescharacteristic
283C4×C89#57711yescharacteristic
284C4×C89#57711yescharacteristic
285Dic89—41no—
286Dic89—41no—
287#18030—891nomaximal, Sylow
288C2×C89—41no—
289C2×C89#293311yescharacteristic
290C2×C89#294911yescharacteristic
291C2×C89#295511yescharacteristic
292D89—81no—
293D89—81no—
294#3103—891no—
295#2984D8911yescharacteristic, complemented
296#2979—891no—
297#1592—891no—
298#1590—891no—
299#1588—891no—
300#1585—891no—
301#1583—891no—
302#1582—891no—
303SD16⋊C8—891no—
304C8×SD16—891no—
305#1572—891no—
306#1496—891no—
307#1479—891no—
308#1454—891no—
309C89#1803011yescharacteristic, complemented, Sylow
310#532—891no—
311C2×C4×Q8C2×D8911yescharacteristic
312#481—891no—
313#481—891no—
314#475—891no—
315#475—891no—
316#460—891no—
317#460—891no—
318#448—891no—
319#448—891no—
320#446—21no—
321#446—21no—
322#446C2×D8911yescharacteristic
323#446C2×D8911yescharacteristic
324C8×Q8C2×D8911yescharacteristic
325C8×Q8C2×D8911yescharacteristic
326C4×SD16—891no—
327C4×SD16—891no—
328C4×SD16—891no—
329C4×SD16—891no—
330#436—891no—
331#436—891no—
332#436—1781no—
333C8×D4—891no—
334C8×D4—891no—
335C8×D4—1781no—
336#432—21no—
337#432C2×D8911yescharacteristic
338#431—21no—
339#431—891no—
340#431—891no—
341#431—891no—
342#431C2×D8911yescharacteristic
343#408—1781no—
344#408—1781no—
345#335—891no—
346#335—891no—
347#334—891no—
348#334—891no—
349Q8⋊C8—891no—
350Q8⋊C8—891no—
351Q8⋊C8—891no—
352Q8⋊C8—891no—
353D4⋊C8—891no—
354D4⋊C8—891no—
355D4⋊C8—891no—
356D4⋊C8—891no—
357#322—891no—
358#322—891no—
359#322—891no—
360C82—891no—
361C2×#41—1781no—
362C22×Q8C4×D8911yescharacteristic
363C2×SD16—891no—
364C2×SD16—891no—
365C2×SD16—891no—
366C2×SD16—891no—
367C2×M16—1781no—
368C2×M16—1781no—
369C22×C8—1781no—
370C22×C8—1781no—
371C4⋊Q8—891no—
372#127—891no—
373#124—1781no—
374#121—891no—
375#121—891no—
376#121—1781no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C4×D8911yescharacteristic
380C4×Q8C4×D8911yescharacteristic
381C4×Q8C22×D8911yescharacteristic
382C4×Q8C22×D8911yescharacteristic
383C4×D4—891no—
384C4×D4—891no—
385C4×D4—1781no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4C4×D8911yescharacteristic
388C2×C42—21no—
389C2×C42C22×D8911yescharacteristic
390#106—891no—
391#106—891no—
392#106—891no—
393#106—891no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—891no—
399C4⋊C8—891no—
400C4⋊C8—891no—
401C4⋊C8—891no—
402C4⋊C8—1781no—
403C4⋊C8C22⋊D8911yescharacteristic
404C4⋊C8C22⋊D8911yescharacteristic
405C4⋊C8C22×D8911yescharacteristic
406C4⋊C8C22×D8911yescharacteristic
407#103—891no—
408#103—891no—
409#103—891no—
410#103—891no—
411#102—891no—
412#102—891no—
413#102—891no—
414#102—891no—
415C22⋊C8—21no—
416C22⋊C8—891no—
417C22⋊C8—891no—
418C22⋊C8—1781no—
419C22⋊C8—1781no—
420C22⋊C8—1781no—
421C22⋊C8—1781no—
422C22⋊C8—1781no—
423C22⋊C8—1781no—
424C22⋊C8C22⋊D8911yescharacteristic
425C22⋊C8C22⋊D8911yescharacteristic
426#97—21no—
427#97—21no—
428#97—21no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8—891no—
432C4×C8—891no—
433C4×C8—891no—
434C4×C8—891no—
435C4×C8—1781no—
436C4×C8C22×D8911yescharacteristic
437C4×C8C22×D8911yescharacteristic
438#41—7121no—
439#41—7121no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—41no—
443C2×Q8—1781no—
444C2×Q8C2×C4×D8911yescharacteristic
445C2×Q8C2×C4×D8911yescharacteristic
446C2×D4—891no—
447C2×D4—891no—
448C2×D4—1781no—
449C2×D4—1781no—
450C2×D4—1781no—
451C2×D4—1781no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—1781no—
455C22×C4—1781no—
456C22×C4C2×C4×D8911yescharacteristic
457C22×C4C2×C22⋊D8911yescharacteristic
458C22×C4#1308357411yescharacteristic
459SD16—3561no—
460SD16—3561no—
461SD16—1782no—
462SD16—1782no—
463M16—7121no—
464M16—7121no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—891no—
468C2×C8—891no—
469C2×C8—891no—
470C2×C8—891no—
471C2×C8—1781no—
472C2×C8—1781no—
473C2×C8—1781no—
474C2×C8—1781no—
475C2×C8—7121no—
476C2×C8—7121no—
477C2×C8C2×C22⋊D8911yescharacteristic
478C2×C8C2×C22⋊D8911yescharacteristic
479C2×C8C2×C22⋊D8911yescharacteristic
480C2×C8C2×C22⋊D8911yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—891no—
487C4⋊C4—891no—
488C4⋊C4—1781no—
489C4⋊C4C2×C4×D8911yescharacteristic
490C4⋊C4C2×C4×D8911yescharacteristic
491C22⋊C4—1781no—
492C22⋊C4—1781no—
493C22⋊C4—1781no—
494C22⋊C4—1781no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42C2×C4×D8911yescharacteristic
500C42C2×C22⋊D8911yescharacteristic
501C42#1308357411yescharacteristic
502C42C23×D8911yescharacteristic
503C23—1781no—
504C23—1781no—
505C23C4×C22⋊D8911yescharacteristic
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—42no—
510Q8—7121no—
511Q8#1566802012yes—
512D4—3562no—
513D4—1781no—
514D4—1781no—
515D4—1781no—
516D4—1781no—
517D4—7121no—
518D4—7121no—
519D4—7121no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—3561no—
532C2×C4—3561no—
533C2×C4—3561no—
534C2×C4—3561no—
535C2×C4—1781no—
536C2×C4—1781no—
537C2×C4C4×C22⋊D8911yescharacteristic
538C2×C4C4×C22⋊D8911yescharacteristic
539C2×C4C4×C22⋊D8911yescharacteristic
540C2×C4C22×C4×D8911yescharacteristic
541C2×C4C22×C22⋊D8911yescharacteristic
542C2×C4C2×#1308357411yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—3561no—
550C8—3561no—
551C8—3561no—
552C8—3561no—
553C8—1781no—
554C8—1781no—
555C8—1781no—
556C8—1781no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—3561no—
561C22—3561no—
562C22—3561no—
563C22—3561no—
564C22—3561no—
565C22—3561no—
566C22C2×C4×C22⋊D8911yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—22no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—3561no—
576C4—3561no—
577C4C2×#1566802011yescharacteristic
578C4#1915236411yescharacteristic
579C4#1915240611yescharacteristic
580C4#1915240611yescharacteristic
581C2—41no—
582C2—7121no—
583C2—7121no—
584C2#2602897711yescharacteristic
585C2#2602911111yescharacteristic
586C2#2602915311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#2984C2
socleC22×C89C2×C4×D4
prime radical#19152148C22
cosocleC42×C89C24
hypercenter#2984D89
hypocenterC89#18030
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2984

Complements

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

NH ≅ G/Ntype
3. #26019152C2semidirect
4. #26019142C2semidirect
5. #26019130C2semidirect
6. #26019107C2semidirect
7. #26019095C2semidirect
8. #26019086C2semidirect
9. #26019062C2semidirect
10. C8×#13083561C2semidirect
11. #26019033C2semidirect
13. #26018647C2semidirect
14. #26018552C2semidirect
15. C89×#2984C2semidirect
295. #2984D89semidirect
309. C89#18030semidirect

Maximal subgroups

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

subgroupindex
#260302832
#260293182
#260191522
#260191422
#260191302
#260191072
#260190952
#260190862
#260190622
C8×#130835612
#260190332
#260187202
#260186472
#260185522
C89×#29842
#1803089