Finite Group Databasebeta

← #36524482

Subgroups — #36524482

Order 22784.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26030299C211yesmaximal, characteristic
2#26029397C211yesmaximal, characteristic, complemented
3#26029276C211yesmaximal, characteristic, complemented
4#26019113C211yesmaximal, characteristic, complemented
5#26019106C211yesmaximal, characteristic, complemented
6#26019085C211yesmaximal, characteristic, complemented
7#26019078C211yesmaximal, characteristic, complemented
8#26019073C211yesmaximal, characteristic, complemented
9#26019061C211yesmaximal, characteristic, complemented
10#26019055C211yesmaximal, characteristic, complemented
11#26019044C211yesmaximal, characteristic, complemented
12#26019043C211yesmaximal, characteristic, complemented
13#26018661C211yesmaximal, characteristic, complemented
14#26018552C211yesmaximal, characteristic, complemented
15C89×#1486C211yesmaximal, characteristic, complemented
16#19152132C2211yescharacteristic
17#19151933C411yescharacteristic
18#19151916C411yescharacteristic
19#19151898C411yescharacteristic
20#19151898C411yescharacteristic
21#19151813C411yescharacteristic
22#19151813C411yescharacteristic
23#19151749C411yescharacteristic
24#19151732C411yescharacteristic
25#19151725C2211yescharacteristic, complemented
26#19151722C2211yescharacteristic, complemented
27C4×#13083562C2211yescharacteristic
28C4×#13083562C2211yescharacteristic
29C4×#13083559C2211yescharacteristic
30C4×#13083559C2211yescharacteristic
31#19151675C2211yescharacteristic, complemented
32#19151674—21no—
33#19151667—21no—
34D4×#10623494—21no—
35D4×#10623494—21no—
36D4×#10623494C2211yescharacteristic
37D4×#10623494C2211yescharacteristic
38D4×#10623494C2211yescharacteristic
39D4×#10623494C2211yescharacteristic
40#19151663C2211yescharacteristic, complemented
41#19151658—21no—
42#19151651C2211yescharacteristic
43#19151651C2211yescharacteristic
44#19151651C2211yescharacteristic
45#19151623—21no—
46C2×C22⋊#10623494—21no—
47C2×C22⋊#10623494—21no—
48#19151350C2211yescharacteristic, complemented
49#19151350C2211yescharacteristic, complemented
50#19151348C2211yescharacteristic, complemented
51#19151348C2211yescharacteristic, complemented
52#19151330C2211yescharacteristic, complemented
53#19151330C2211yescharacteristic, complemented
54#19151327C2211yescharacteristic, complemented
55#19151327C2211yescharacteristic, complemented
56#19151320C2211yescharacteristic, complemented
57#19151320C2211yescharacteristic, complemented
58#19151319C2211yescharacteristic, complemented
59C8×#10623494C2211yescharacteristic, complemented
60C2×C4×D4×C89C2211yescharacteristic
61#431×C89C2211yescharacteristic
62#423×C89C2211yescharacteristic
63D4⋊C8×C89C2211yescharacteristic
64D4⋊C8×C89C2211yescharacteristic
65D4⋊C8×C89C2211yescharacteristic
66D4⋊C8×C89C2211yescharacteristic
67C2×#13083562C2×C411yescharacteristic
68C2×#13083562C2×C411yescharacteristic
69C2×#13083559C2×C411yescharacteristic
70C2×#13083559C2×C411yescharacteristic
71C2×#13083557—21no—
72C22×#10623494—21no—
73C22×#10623494—21no—
74C22×#10623494—21no—
75C22×#10623494—21no—
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⋊#10623494C2×C411yescharacteristic
92C4⋊#10623494C2×C411yescharacteristic
93C4⋊#10623494D411yescharacteristic
94C4⋊#10623494D411yescharacteristic
95C4⋊#10623494C2311yescharacteristic
96C4⋊#10623494C2311yescharacteristic
97#15667941—21no—
98#15667941—21no—
99#15667935C2×C411yescharacteristic
100#15667935C2×C411yescharacteristic
101#15667933C2×C411yescharacteristic
102#15667933C2×C411yescharacteristic
103#15667933C2×C411yescharacteristic
104#15667933C2×C411yescharacteristic
105#15667932C2×C411yescharacteristic
106#15667932C2×C411yescharacteristic
107C22⋊#10623494—21no—
108C22⋊#10623494—21no—
109C22⋊#10623494—21no—
110C22⋊#10623494—21no—
111C22⋊#10623494—21no—
112C22⋊#10623494C2×C411yescharacteristic
113C22⋊#10623494C2×C411yescharacteristic
114C22⋊#10623494D411yescharacteristic
115C22⋊#10623494D411yescharacteristic
116#15667924—21no—
117#15667924—21no—
118#15667922—21no—
119C4×#10623494—21no—
120C4×#10623494C2311yescharacteristic
121C4×#10623494C2311yescharacteristic
122C4×#10623494C2311yescharacteristic
123C4×#10623494C2311yescharacteristic
124C8×Dic89—21no—
125C22×D4×C89C2×C411yescharacteristic
126C23×C4×C89—21no—
127C2×M16×C89—21no—
128C4×D4×C89—21no—
129C4×D4×C89—21no—
130C4×D4×C89C2×C411yescharacteristic
131C4×D4×C89C2×C411yescharacteristic
132C4×D4×C89C2311yescharacteristic
133C4×D4×C89C2311yescharacteristic
134C2×C4⋊C4×C89C2×C411yescharacteristic
135C2×C22⋊C4×C89—21no—
136C2×C42×C89C2311yescharacteristic
137C4⋊C8×C89—21no—
138C4⋊C8×C89—21no—
139C4⋊C8×C89C2311yescharacteristic
140C4⋊C8×C89C2311yescharacteristic
141C22⋊C8×C89—21no—
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144C2×Dic178C22×C411yescharacteristic
145C2×D356C22×C411yescharacteristic
146C2×C22⋊D89—21no—
147C2×C4×D89—21no—
148#13083562—22no—
149#13083562—22no—
150#13083559—22no—
151#13083559—22no—
152#13083557—81no—
153C2×#10623494—21no—
154C2×#10623494—21no—
155C2×#10623494—81no—
156C2×#10623494—81no—
157C2×#10623494—81no—
158C2×#10623494—81no—
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—81no—
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—
180C24×C89—21no—
181C2×D4×C89—22no—
182C2×D4×C89—22no—
183C2×D4×C89—21no—
184C2×D4×C89C22×C411yescharacteristic
185C2×D4×C89C22×C411yescharacteristic
186C22×C4×C89—21no—
187C22×C4×C89—21no—
188C22×C4×C89—21no—
189C22×C4×C89—21no—
190C22×C4×C89—21no—
191C22×C4×C89—81no—
192C22×C4×C89—81no—
193C22×C4×C89C22×C411yescharacteristic
194C22×C4×C89C2×D411yescharacteristic
195C22×C4×C89#4111yescharacteristic
196M16×C89—81no—
197C2×C8×C89—21no—
198C2×C8×C89—21no—
199C2×C8×C89—21no—
200C2×C8×C89—21no—
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—24no—
213C23×C89—21no—
214C23×C89—21no—
215C23×C89—81no—
216C23×C89—81no—
217C23×C89C4×D411yescharacteristic
218C22×D89—21no—
219D4×C89—24no—
220D4×C89—21no—
221D4×C89—21no—
222D4×C89#13112yes—
223D4×C89#13112yes—
224C2×C4×C89—21no—
225C2×C4×C89—21no—
226C2×C4×C89—21no—
227C2×C4×C89—21no—
228C2×C4×C89—21no—
229C2×C4×C89—21no—
230C2×C4×C89—41no—
231C2×C4×C89—41no—
232C2×C4×C89—41no—
233C2×C4×C89—41no—
234C2×C4×C89—41no—
235C2×C4×C89—81no—
236C2×C4×C89—81no—
237C2×C4×C89—81no—
238C2×C4×C89C4×D411yescharacteristic
239C2×C4×C89C4×D411yescharacteristic
240C2×C4×C89C4×D411yescharacteristic
241C2×C4×C89C23×C411yescharacteristic
242C2×C4×C89C22×D411yescharacteristic
243C2×C4×C89C2×#4111yescharacteristic
244C22⋊D89—81no—
245C2×Dic89—21no—
246C2×Dic89—21no—
247C2×Dic89—21no—
248D356—21no—
249D356—21no—
250C4×D89—41no—
251C4×D89—41no—
252Dic178—21no—
253Dic178—21no—
254C8×C89—41no—
255C8×C89—41no—
256C8×C89—41no—
257C8×C89—41no—
258#10623494—21no—
259#10623494—21no—
260#10623494—21no—
261#10623494—21no—
262#10623494—21no—
263#10623494—21no—
264#10623494—21no—
265#10623494—21no—
266#10623494—41no—
267#10623494—41no—
268C22×C89—21no—
269C22×C89—22no—
270C22×C89—22no—
271C22×C89—21no—
272C22×C89—21no—
273C22×C89—41no—
274C22×C89—41no—
275C22×C89—41no—
276C22×C89—41no—
277C22×C89—84no—
278C22×C89C2×C4×D411yescharacteristic
279C2×D89—41no—
280C2×D89—41no—
281C2×D89—41no—
282C4×C89—21no—
283C4×C89—21no—
284C4×C89—21no—
285C4×C89—21no—
286C4×C89—41no—
287C4×C89—41no—
288C4×C89C2×#13111yescharacteristic
289C4×C89C2×#13111yescharacteristic
290C4×C89#57611yescharacteristic
291C4×C89#57711yescharacteristic
292Dic89—41no—
293Dic89—41no—
294Dic89—41no—
295#17918—891nomaximal, Sylow
296C2×C89—41no—
297C2×C89—42no—
298C2×C89—42no—
299C2×C89#292911yescharacteristic
300C2×C89#294611yescharacteristic
301C2×C89#295711yescharacteristic
302D89—81no—
303#3105—891no—
304#2993—891no—
305#2972—891no—
306#1586—891no—
307#1585—891no—
308#1582—891no—
309#1581—891no—
310#1580—891no—
311SD16⋊C8—891no—
312C8×SD16—891no—
313C8×D8—891no—
314#1574—891no—
315#1486D8911yescharacteristic, complemented
316#1482—891no—
317#1454—891no—
318C89#1791811yescharacteristic, complemented, Sylow
319#529—891no—
320C2×C4×D4C2×D8911yescharacteristic
321#484—891no—
322#481—891no—
323#478—891no—
324#478—891no—
325#463—891no—
326#463—891no—
327#450—891no—
328#447—891no—
329#446—891no—
330C8×Q8—891no—
331C4×SD16—891no—
332C4×SD16—891no—
333C4×D8—891no—
334C4×D8—891no—
335#436—891no—
336#436—1781no—
337#435—1781no—
338C8×D4—891no—
339C8×D4—891no—
340C8×D4—891no—
341C8×D4—891no—
342C8×D4—891no—
343C8×D4—1781no—
344C8×D4—1781no—
345#433—1781no—
346#431—891no—
347#431—891no—
348#431—891no—
349#431C2×D8911yescharacteristic
350#424—1781no—
351#423C2×D8911yescharacteristic
352C2×C22⋊C8—1781no—
353C2×C22⋊C8—1781no—
354#335—891no—
355#335—891no—
356#334—891no—
357#334—891no—
358Q8⋊C8—891no—
359Q8⋊C8—891no—
360D4⋊C8—891no—
361D4⋊C8—891no—
362D4⋊C8C2×D8911yescharacteristic
363D4⋊C8C2×D8911yescharacteristic
364D4⋊C8C2×D8911yescharacteristic
365D4⋊C8C2×D8911yescharacteristic
366#322—891no—
367#322—891no—
368#322—891no—
369C82—891no—
370C22×D4C4×D8911yescharacteristic
371C23×C4—21no—
372C2×SD16—891no—
373C2×SD16—891no—
374C2×D8—891no—
375C2×D8—891no—
376C2×M16—21no—
377C2×M16—1781no—
378C22×C8—1781no—
379C22×C8—1781no—
380C22×C8—1781no—
381C22×C8—1781no—
382C22×C8—1781no—
383#126—1781no—
384#125—891no—
385#124—891no—
386#123—1781no—
387C22⋊Q8—891no—
388#121—891no—
389C4×Q8—891no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—891no—
393C4×D4—1781no—
394C4×D4C4×D8911yescharacteristic
395C4×D4C4×D8911yescharacteristic
396C4×D4C22×D8911yescharacteristic
397C4×D4C22×D8911yescharacteristic
398#117—1781no—
399C2×C4⋊C4C4×D8911yescharacteristic
400C2×C22⋊C4—21no—
401C2×C42C22×D8911yescharacteristic
402#107—891no—
403#107—891no—
404#106—891no—
405#106—891no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—891no—
409C4⋊C8—891no—
410C4⋊C8—891no—
411C4⋊C8—891no—
412C4⋊C8—891no—
413C4⋊C8—891no—
414C4⋊C8—1781no—
415C4⋊C8—1781no—
416C4⋊C8C22×D8911yescharacteristic
417C4⋊C8C22×D8911yescharacteristic
418#103—891no—
419#103—891no—
420#102—891no—
421#102—891no—
422#102—891no—
423#102—891no—
424#102—891no—
425#102—891no—
426C22⋊C8—21no—
427C22⋊C8—891no—
428C22⋊C8—891no—
429C22⋊C8—891no—
430C22⋊C8—891no—
431C22⋊C8—1781no—
432C22⋊C8—1781no—
433C22⋊C8—1781no—
434C22⋊C8—1781no—
435C22⋊C8—1781no—
436C22⋊C8—1781no—
437C22⋊C8—1781no—
438#97—1781no—
439C4×C8—891no—
440C4×C8—891no—
441C4×C8—891no—
442C4×C8—891no—
443C4×C8—1781no—
444C4×C8—1781no—
445C4×C8C22×D8911yescharacteristic
446C4×C8C22×D8911yescharacteristic
447C24—21no—
448C2×Q8—891no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—891no—
453C2×D4—1781no—
454C2×D4C2×C4×D8911yescharacteristic
455C2×D4C2×C4×D8911yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—81no—
462C22×C4—81no—
463C22×C4—1781no—
464C22×C4C2×C4×D8911yescharacteristic
465C22×C4D4×D8911yescharacteristic
466C22×C4#1308357311yescharacteristic
467SD16—1782no—
468SD16—1782no—
469D8—1782no—
470D8—1782no—
471M16—81no—
472M16—7121no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—891no—
478C2×C8—891no—
479C2×C8—891no—
480C2×C8—891no—
481C2×C8—891no—
482C2×C8—891no—
483C2×C8—891no—
484C2×C8—891no—
485C2×C8—1781no—
486C2×C8—1781no—
487C2×C8—7121no—
488C2×C8—7121no—
489C2×C8—7121no—
490C2×C8—7121no—
491C2×C8—7121no—
492C4⋊C4—21no—
493C4⋊C4—891no—
494C4⋊C4—891no—
495C4⋊C4—1781no—
496C4⋊C4—1781no—
497C4⋊C4—1781no—
498C4⋊C4—1781no—
499C4⋊C4C2×C4×D8911yescharacteristic
500C4⋊C4C2×C4×D8911yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—1781no—
506C22⋊C4—1781no—
507C22⋊C4—1781no—
508C22⋊C4—1781no—
509C22⋊C4—1781no—
510C42—1781no—
511C42C2×C4×D8911yescharacteristic
512C42D4×D8911yescharacteristic
513C42#1308357311yescharacteristic
514C42C23×D8911yescharacteristic
515C23—24no—
516C23—21no—
517C23—21no—
518C23—81no—
519C23—81no—
520C23—1781no—
521C23#1566797211yescharacteristic
522Q8—1781no—
523Q8—1781no—
524D4—24no—
525D4—21no—
526D4—21no—
527D4—1781no—
528D4—1781no—
529D4—7121no—
530D4#1566802012yes—
531D4#1566802012yes—
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—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—3561no—
547C2×C4—3561no—
548C2×C4—1781no—
549C2×C4—1781no—
550C2×C4—1781no—
551C2×C4#1566797211yescharacteristic
552C2×C4#1566797211yescharacteristic
553C2×C4#1566797211yescharacteristic
554C2×C4C22×C4×D8911yescharacteristic
555C2×C4C2×D4×D8911yescharacteristic
556C2×C4C2×#1308357311yescharacteristic
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—3561no—
562C8—3561no—
563C8—1781no—
564C8—1781no—
565C8—1781no—
566C8—1781no—
567C8—1781no—
568C8—1781no—
569C8—1781no—
570C8—1781no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—22no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—84no—
581C22—3561no—
582C22—3561no—
583C22—3561no—
584C22C2×#1566797211yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—3561no—
592C4—3561no—
593C4—3561no—
594C4C2×#1566802011yescharacteristic
595C4C2×#1566802011yescharacteristic
596C4#1915239911yescharacteristic
597C4#1915240411yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—7121no—
602C2#2602894211yescharacteristic
603C2#2602907811yescharacteristic
604C2#2602916511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#1486C2
socleC22×C89C2×C4×D4
prime radical#19151732C4
cosocleC42×C89C24
hypercenter#1486D89
hypocenterC89#17918
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #26029397C2semidirect
3. #26029276C2semidirect
4. #26019113C2semidirect
5. #26019106C2semidirect
6. #26019085C2semidirect
7. #26019078C2semidirect
8. #26019073C2semidirect
9. #26019061C2semidirect
10. #26019055C2semidirect
11. #26019044C2semidirect
12. #26019043C2semidirect
13. #26018661C2semidirect
14. #26018552C2semidirect
15. C89×#1486C2semidirect
25. #19151725C22semidirect
26. #19151722C22semidirect
31. #19151675C22semidirect
40. #19151663C22semidirect
48. #19151350C22semidirect
49. #19151350C22semidirect
50. #19151348C22semidirect
51. #19151348C22semidirect
52. #19151330C22semidirect
53. #19151330C22semidirect
54. #19151327C22semidirect
55. #19151327C22semidirect
56. #19151320C22semidirect
57. #19151320C22semidirect
58. #19151319C22semidirect
59. C8×#10623494C22semidirect
315. #1486D89semidirect
318. C89#17918semidirect

Maximal subgroups

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

subgroupindex
#260302992
#260293972
#260292762
#260191132
#260191062
#260190852
#260190782
#260190732
#260190612
#260190552
#260190442
#260190432
#260186612
#260185522
C89×#14862
#1791889