Finite Group Databasebeta

← #36524838

Subgroups — #36524838

Order 22784.

608 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26030306C211yesmaximal, characteristic
2#26029365C211yesmaximal, characteristic, complemented
3#26019164C211yesmaximal, characteristic, complemented
4#26019154C211yesmaximal, characteristic, complemented
5#26019140C211yesmaximal, characteristic, complemented
6#26019135C211yesmaximal, characteristic, complemented
7#26019116C211yesmaximal, characteristic, complemented
8#26019109C211yesmaximal, characteristic, complemented
9#26019088C211yesmaximal, characteristic, complemented
10#26019081C211yesmaximal, characteristic, complemented
11#26019038C211yesmaximal, characteristic, complemented
12#26018684C211yesmaximal, characteristic, complemented
13#26018651C211yesmaximal, characteristic, complemented
14#26018552C211yesmaximal, characteristic, complemented
15C89×#2981C211yesmaximal, characteristic, complemented
16C4×#13083574C2211yescharacteristic
17#19151919C411yescharacteristic
18#19151919C411yescharacteristic
19#19151890C411yescharacteristic
20#19151885C411yescharacteristic
21#19151795C411yescharacteristic
22#19151790C411yescharacteristic
23#19151741C411yescharacteristic
24#19151741C411yescharacteristic
25#19151728C2211yescharacteristic
26#19151728C2211yescharacteristic
27C4×#13083562C2211yescharacteristic
28C4×#13083562C2211yescharacteristic
29C4×#13083559C2211yescharacteristic
30C4×#13083559C2211yescharacteristic
31#19151677C2211yescharacteristic
32#19151677C2211yescharacteristic
33#19151666—21no—
34#19151666—21no—
35#19151654—21no—
36#19151651C2211yescharacteristic
37#19151651C2211yescharacteristic
38#19151620—21no—
39C2×C4⋊#10623494C2211yescharacteristic
40#19151350C2211yescharacteristic
41#19151350C2211yescharacteristic
42#19151348C2211yescharacteristic
43#19151348C2211yescharacteristic
44#19151328C2211yescharacteristic
45#19151328C2211yescharacteristic
46D4⋊#10623494C2211yescharacteristic
47D4⋊#10623494C2211yescharacteristic
48D4⋊#10623494C2211yescharacteristic
49D4⋊#10623494C2211yescharacteristic
50#19151325C2211yescharacteristic
51#19151325C2211yescharacteristic
52#19151320C2211yescharacteristic
53#19151320C2211yescharacteristic
54#19151319C2211yescharacteristic
55C8×#10623494C2211yescharacteristic
56#532×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#408×C89—21no—
66#408×C89—21no—
67C2×#13083574C2×C411yescharacteristic
68C2×#13083562C2×C411yescharacteristic
69C2×#13083562C2×C411yescharacteristic
70C2×#13083559C2×C411yescharacteristic
71C2×#13083559C2×C411yescharacteristic
72C2×#13083557—21no—
73C2×#13083557—21no—
74C22×#10623494—21no—
75C4×Dic178C2×C411yescharacteristic
76C4×Dic178C2311yescharacteristic
77C4×D356C2×C411yescharacteristic
78C4×D356C2311yescharacteristic
79C4×C22⋊D89—21no—
80C4×C22⋊D89—21no—
81#15667971C2×C411yescharacteristic
82#15667969—21no—
83C42×D89—21no—
84#15667945C2×C411yescharacteristic
85#15667945C2×C411yescharacteristic
86#15667943C2×C411yescharacteristic
87#15667943C2×C411yescharacteristic
88C4⋊#10623494—21no—
89C4⋊#10623494—21no—
90C4⋊#10623494C2×C411yescharacteristic
91C4⋊#10623494C2×C411yescharacteristic
92C4⋊#10623494C2311yescharacteristic
93C4⋊#10623494C2311yescharacteristic
94#15667941—21no—
95#15667941—21no—
96#15667935C2×C411yescharacteristic
97#15667935C2×C411yescharacteristic
98#15667933C2×C411yescharacteristic
99#15667933C2×C411yescharacteristic
100#15667933C2×C411yescharacteristic
101#15667933C2×C411yescharacteristic
102#15667932C2×C411yescharacteristic
103#15667932C2×C411yescharacteristic
104C22⋊#10623494—21no—
105C22⋊#10623494C2×C411yescharacteristic
106C22⋊#10623494C2×C411yescharacteristic
107#15667924—21no—
108#15667924—21no—
109#15667922—21no—
110#15667922—21no—
111C4×#10623494C2311yescharacteristic
112C4×#10623494C2311yescharacteristic
113C4×#10623494C2311yescharacteristic
114C4×#10623494C2311yescharacteristic
115C2×#41×C89—21no—
116C2×M16×C89—21no—
117C2×M16×C89—21no—
118C22×C8×C89—21no—
119C22×C8×C89—21no—
120C4⋊Q8×C89C2×C411yescharacteristic
121#127×C89C2×C411yescharacteristic
122#124×C89—21no—
123#121×C89—21no—
124#121×C89C2×C411yescharacteristic
125#121×C89C2×C411yescharacteristic
126C4×D4×C89—21no—
127C4×D4×C89C2311yescharacteristic
128C4×D4×C89C2311yescharacteristic
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
144#13083574—41no—
145#13083574—41no—
146C2×Dic178C22×C411yescharacteristic
147C2×D356C22×C411yescharacteristic
148C2×C22⋊D89—21no—
149C2×C4×D89—21no—
150C2×C4×D89—21no—
151C2×C4×D89—21no—
152#13083562—41no—
153#13083562—41no—
154#13083559—41no—
155#13083559—41no—
156#13083557—81no—
157#13083557—81no—
158C2×#10623494—21no—
159C2×#10623494—21no—
160C2×#10623494—21no—
161C2×#10623494—21no—
162C2×#10623494—81no—
163C2×#10623494C22×C411yescharacteristic
164C2×#10623494C22×C411yescharacteristic
165C2×#10623494C22×C411yescharacteristic
166C2×#10623494C22×C411yescharacteristic
167C4⋊Dic89C22×C411yescharacteristic
168C4⋊Dic89C22×C411yescharacteristic
169#13083553—21no—
170#13083553—21no—
171C22⋊Dic89—21no—
172#13083551—21no—
173#13083551—21no—
174C4×Dic89—21no—
175C4×Dic89—21no—
176C4×Dic89—21no—
177#41×C89—81no—
178#41×C89—81no—
179C2×Q8×C89—21no—
180C2×D4×C89—21no—
181C2×D4×C89—21no—
182C2×D4×C89—21no—
183C2×D4×C89—21no—
184C2×D4×C89C22×C411yescharacteristic
185C2×D4×C89C22×C411yescharacteristic
186C22×C4×C89—21no—
187C22×C4×C89—21no—
188C22×C4×C89C22×C411yescharacteristic
189C22×C4×C89C2×D411yescharacteristic
190C22×C4×C89#4111yescharacteristic
191M16×C89—81no—
192M16×C89—81no—
193C2×C8×C89—21no—
194C2×C8×C89—21no—
195C2×C8×C89—81no—
196C2×C8×C89—81no—
197C2×C8×C89C2×D411yescharacteristic
198C2×C8×C89C2×D411yescharacteristic
199C2×C8×C89C2×D411yescharacteristic
200C2×C8×C89C2×D411yescharacteristic
201C4⋊C4×C89—21no—
202C4⋊C4×C89C22×C411yescharacteristic
203C4⋊C4×C89C22×C411yescharacteristic
204C22⋊C4×C89—21no—
205C22⋊C4×C89—21no—
206C22⋊C4×C89—21no—
207C22⋊C4×C89—21no—
208C42×C89C22×C411yescharacteristic
209C42×C89C2×D411yescharacteristic
210C42×C89#4111yescharacteristic
211C42×C89C2411yescharacteristic
212C23×C89—21no—
213C23×C89—21no—
214C23×C89C4×D411yescharacteristic
215C22×D89—21no—
216Q8×C89—81no—
217D4×C89—21no—
218D4×C89—21no—
219D4×C89—21no—
220D4×C89—21no—
221D4×C89—81no—
222D4×C89—81no—
223D4×C89—81no—
224D4×C89—81no—
225C2×C4×C89—21no—
226C2×C4×C89—21no—
227C2×C4×C89—21no—
228C2×C4×C89—21no—
229C2×C4×C89—21no—
230C2×C4×C89—21no—
231C2×C4×C89—41no—
232C2×C4×C89—41no—
233C2×C4×C89—41no—
234C2×C4×C89—41no—
235C2×C4×C89—41no—
236C2×C4×C89C4×D411yescharacteristic
237C2×C4×C89C4×D411yescharacteristic
238C2×C4×C89C4×D411yescharacteristic
239C2×C4×C89C23×C411yescharacteristic
240C2×C4×C89C22×D411yescharacteristic
241C2×C4×C89C2×#4111yescharacteristic
242C22⋊D89—42no—
243C2×Dic89—21no—
244C2×Dic89—21no—
245C2×Dic89—21no—
246D356—21no—
247D356—21no—
248C4×D89—42no—
249C4×D89—41no—
250C4×D89—41no—
251C4×D89—81no—
252Dic178—21no—
253Dic178—21no—
254C8×C89—21no—
255C8×C89—21no—
256C8×C89—21no—
257C8×C89—21no—
258C8×C89—41no—
259C8×C89—41no—
260#10623494—21no—
261#10623494—21no—
262#10623494—21no—
263#10623494—21no—
264#10623494—41no—
265#10623494—41no—
266#10623494—41no—
267#10623494—41no—
268C22×C89—21no—
269C22×C89—21no—
270C22×C89—21no—
271C22×C89—41no—
272C22×C89—41no—
273C22×C89—41no—
274C22×C89—41no—
275C22×C89—41no—
276C22×C89—41no—
277C22×C89C2×C4×D411yescharacteristic
278C2×D89—41no—
279C2×D89—41no—
280C2×D89—41no—
281C4×C89—21no—
282C4×C89—21no—
283C4×C89—21no—
284C4×C89—21no—
285C4×C89—41no—
286C4×C89—41no—
287C4×C89#56811yescharacteristic
288C4×C89#56811yescharacteristic
289C4×C89#57611yescharacteristic
290C4×C89#57711yescharacteristic
291Dic89—41no—
292Dic89—41no—
293Dic89—41no—
294#17948—891nomaximal, Sylow
295C2×C89—41no—
296C2×C89—81no—
297C2×C89—81no—
298C2×C89#293011yescharacteristic
299C2×C89#294611yescharacteristic
300C2×C89#295711yescharacteristic
301D89—81no—
302#3106—891no—
303#2989—891no—
304#2981D8911yescharacteristic, complemented
305#1594—891no—
306#1592—891no—
307#1590—891no—
308#1589—891no—
309#1586—891no—
310#1585—891no—
311#1582—891no—
312#1581—891no—
313#1573—891no—
314#1488—891no—
315#1480—891no—
316#1454—891no—
317C89#1794811yescharacteristic, complemented, Sylow
318#532C2×D8911yescharacteristic
319C4×#41—891no—
320#482—891no—
321#482—891no—
322#477—891no—
323#476—891no—
324#460—891no—
325#459—891no—
326#449—891no—
327#449—891no—
328#446—891no—
329#446—891no—
330C4×SD16—891no—
331C4×SD16—891no—
332C4×D8—891no—
333C4×D8—891no—
334#436—891no—
335#436—891no—
336#436C2×D8911yescharacteristic
337#436C2×D8911yescharacteristic
338#435—21no—
339#435—21no—
340#435—1781no—
341#435—1781no—
342C8×D4C2×D8911yescharacteristic
343C8×D4C2×D8911yescharacteristic
344#432—1781no—
345#432C2×D8911yescharacteristic
346#431—891no—
347#431—891no—
348#431C2×D8911yescharacteristic
349#423—1781no—
350C2×C4⋊C8—891no—
351#408—21no—
352#408—21no—
353#335—891no—
354#335—891no—
355#334—891no—
356#334—891no—
357Q8⋊C8—891no—
358Q8⋊C8—891no—
359D4⋊C8—891no—
360D4⋊C8—891no—
361D4⋊C8—891no—
362D4⋊C8—891no—
363D4⋊C8—891no—
364D4⋊C8—891no—
365#322—891no—
366#322—891no—
367#322—891no—
368C82—891no—
369C2×#41—21no—
370C2×#41—891no—
371C2×SD16—891no—
372C2×SD16—891no—
373C2×D8—891no—
374C2×D8—891no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—1781no—
378C2×M16—1781no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—1781no—
382C4⋊Q8C4×D8911yescharacteristic
383#127C4×D8911yescharacteristic
384#124—21no—
385#121—21no—
386#121C4×D8911yescharacteristic
387#121C4×D8911yescharacteristic
388C4×Q8—891no—
389C4×Q8—891no—
390C4×D4—21no—
391C4×D4—891no—
392C4×D4—891no—
393C4×D4—1781no—
394C4×D4—1781no—
395C4×D4C22×D8911yescharacteristic
396C4×D4C22×D8911yescharacteristic
397#117—891no—
398#117—1781no—
399C2×C42—1781no—
400C2×C42C22×D8911yescharacteristic
401#107—891no—
402#107—891no—
403#106—891no—
404#106—891no—
405C4⋊C8—891no—
406C4⋊C8—891no—
407C4⋊C8—891no—
408C4⋊C8—891no—
409C4⋊C8—1781no—
410C4⋊C8—1781no—
411C4⋊C8—1781no—
412C4⋊C8—1781no—
413C4⋊C8C22⋊D8911yescharacteristic
414C4⋊C8C22⋊D8911yescharacteristic
415C4⋊C8C22×D8911yescharacteristic
416C4⋊C8C22×D8911yescharacteristic
417#103—891no—
418#103—891no—
419#102—891no—
420#102—891no—
421#102—891no—
422#102—891no—
423#102—891no—
424#102—891no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—891no—
431C22⋊C8—891no—
432C22⋊C8—1781no—
433C22⋊C8—1781no—
434C22⋊C8—1781no—
435C22⋊C8C22⋊D8911yescharacteristic
436C22⋊C8C22⋊D8911yescharacteristic
437#97—21no—
438#97—1781no—
439#97—1781no—
440C4×C8—891no—
441C4×C8—891no—
442C4×C8—891no—
443C4×C8—891no—
444C4×C8C22×D8911yescharacteristic
445C4×C8C22×D8911yescharacteristic
446#41—81no—
447#41—81no—
448#41—3561no—
449#41—3561no—
450C2×Q8—21no—
451C2×Q8—891no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—891no—
457C2×D4—1781no—
458C2×D4C2×C4×D8911yescharacteristic
459C2×D4C2×C4×D8911yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—1781no—
463C22×C4—1781no—
464C22×C4—1781no—
465C22×C4C2×C4×D8911yescharacteristic
466C22×C4C2×C22⋊D8911yescharacteristic
467C22×C4#1308357411yescharacteristic
468SD16—3561no—
469SD16—3561no—
470D8—3561no—
471D8—3561no—
472M16—81no—
473M16—81no—
474M16—7121no—
475M16—7121no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—81no—
479C2×C8—81no—
480C2×C8—891no—
481C2×C8—891no—
482C2×C8—891no—
483C2×C8—891no—
484C2×C8—1781no—
485C2×C8—1781no—
486C2×C8—1781no—
487C2×C8—1781no—
488C2×C8—7121no—
489C2×C8C2×C22⋊D8911yescharacteristic
490C2×C8C2×C22⋊D8911yescharacteristic
491C2×C8C2×C22⋊D8911yescharacteristic
492C2×C8C2×C22⋊D8911yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—891no—
495C4⋊C4—891no—
496C4⋊C4—1781no—
497C4⋊C4—1781no—
498C4⋊C4C2×C4×D8911yescharacteristic
499C4⋊C4C2×C4×D8911yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—1781no—
505C22⋊C4—1781no—
506C22⋊C4—1781no—
507C42—1781no—
508C42—1781no—
509C42—1781no—
510C42C2×C4×D8911yescharacteristic
511C42C2×C22⋊D8911yescharacteristic
512C42#1308357411yescharacteristic
513C42C23×D8911yescharacteristic
514C23—21no—
515C23—21no—
516C23—1781no—
517C23C4×C22⋊D8911yescharacteristic
518Q8—81no—
519Q8—1781no—
520Q8—1781no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—3562no—
530D4—1781no—
531D4—1781no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—3562no—
544C2×C4—3561no—
545C2×C4—3561no—
546C2×C4—1781no—
547C2×C4—1781no—
548C2×C4—1781no—
549C2×C4—7121no—
550C2×C4C4×C22⋊D8911yescharacteristic
551C2×C4C4×C22⋊D8911yescharacteristic
552C2×C4C4×C22⋊D8911yescharacteristic
553C2×C4C22×C4×D8911yescharacteristic
554C2×C4C22×C22⋊D8911yescharacteristic
555C2×C4C2×#1308357411yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—3561no—
563C8—3561no—
564C8—3561no—
565C8—3561no—
566C8—1781no—
567C8—1781no—
568C8—1781no—
569C8—1781no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—3561no—
580C22—3561no—
581C22—3561no—
582C22C2×C4×C22⋊D8911yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—3561no—
590C4—3561no—
591C4—3561no—
592C4#1915236311yescharacteristic
593C4#1915236311yescharacteristic
594C4#1915240111yescharacteristic
595C4#1915240911yescharacteristic
596C2—41no—
597C2—81no—
598C2—81no—
599C2—7121no—
600C2#2602895311yescharacteristic
601C2#2602908411yescharacteristic
602C2#2602916711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#2981C2
socleC22×C89C2×C4×D4
prime radical#26030306C2
cosocleC42×C89C24
hypercenter#2981D89
hypocenterC89#17948
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. #26029365C2semidirect
3. #26019164C2semidirect
4. #26019154C2semidirect
5. #26019140C2semidirect
6. #26019135C2semidirect
7. #26019116C2semidirect
8. #26019109C2semidirect
9. #26019088C2semidirect
10. #26019081C2semidirect
11. #26019038C2semidirect
12. #26018684C2semidirect
13. #26018651C2semidirect
14. #26018552C2semidirect
15. C89×#2981C2semidirect
304. #2981D89semidirect
317. C89#17948semidirect

Maximal subgroups

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

subgroupindex
#260303062
#260293652
#260191642
#260191542
#260191402
#260191352
#260191162
#260191092
#260190882
#260190812
#260190382
#260186842
#260186512
#260185522
C89×#29812
#1794889