Finite Group Databasebeta

← #36524484

Subgroups — #36524484

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#26030295C211yesmaximal, characteristic
2#26029275C211yesmaximal, characteristic, complemented
3#26019114C211yesmaximal, characteristic, complemented
4#26019107C211yesmaximal, characteristic, complemented
5#26019086C211yesmaximal, characteristic, complemented
6#26019079C211yesmaximal, characteristic, complemented
7#26019074C211yesmaximal, characteristic, complemented
8#26019062C211yesmaximal, characteristic, complemented
9C8×#13083561C211yesmaximal, characteristic, complemented
10C8×#13083559C211yesmaximal, characteristic, complemented
11#26019043C211yesmaximal, characteristic, complemented
12#26018676C211yesmaximal, characteristic, complemented
13#26018660C211yesmaximal, characteristic, complemented
14#26018552C211yesmaximal, characteristic, complemented
15C89×#2993C211yesmaximal, characteristic, complemented
16C2×C4×D356C2211yescharacteristic
17#19151931C411yescharacteristic
18#19151914C411yescharacteristic
19#19151895C411yescharacteristic
20#19151895C411yescharacteristic
21#19151810C411yescharacteristic
22#19151810C411yescharacteristic
23#19151748C411yescharacteristic
24#19151731C411yescharacteristic
25C4×#13083561C2211yescharacteristic
26C4×#13083561C2211yescharacteristic
27C4×#13083559C2211yescharacteristic
28C4×#13083559C2211yescharacteristic
29C8×D356C2211yescharacteristic
30C8×D356C2211yescharacteristic
31C8×D356C2211yescharacteristic
32C8×D356C2211yescharacteristic
33#19151663—21no—
34#19151663—21no—
35#19151651C2211yescharacteristic
36#19151651C2211yescharacteristic
37#19151651C2211yescharacteristic
38C22⋊C8×D89—21no—
39C22⋊C8×D89—21no—
40#19151350C2211yescharacteristic, complemented
41#19151350C2211yescharacteristic, complemented
42#19151348C2211yescharacteristic, complemented
43#19151348C2211yescharacteristic, complemented
44Q8⋊#10623494C2211yescharacteristic, complemented
45Q8⋊#10623494C2211yescharacteristic, complemented
46D4⋊#10623494C2211yescharacteristic, complemented
47D4⋊#10623494C2211yescharacteristic, complemented
48#19151325C2211yescharacteristic
49#19151325C2211yescharacteristic
50#19151325C2211yescharacteristic
51#19151325C2211yescharacteristic
52#19151320C2211yescharacteristic, complemented
53#19151320C2211yescharacteristic, complemented
54#19151319C2211yescharacteristic, complemented
55C8×#10623494C2211yescharacteristic, complemented
56#529×C89C2211yescharacteristic
57#446×C89C2211yescharacteristic, complemented
58C8×Q8×C89C2211yescharacteristic, complemented
59#436×C89—21no—
60#436×C89C2211yescharacteristic, complemented
61#435×C89—21no—
62C8×D4×C89C2211yescharacteristic, complemented
63#433×C89—21no—
64#431×C89C2211yescharacteristic
65#424×C89—21no—
66#423×C89C2211yescharacteristic
67C22×D356C2×C411yescharacteristic
68C22×C4×D89—21no—
69C2×#13083561C2×C411yescharacteristic
70C2×#13083561C2×C411yescharacteristic
71C2×#13083559C2×C411yescharacteristic
72C2×#13083559C2×C411yescharacteristic
73C2×C8×D89—21no—
74C2×C8×D89—21no—
75C2×C8×D89—21no—
76C2×C8×D89—21no—
77C4×D356—21no—
78C4×D356—21no—
79C4×D356C2×C411yescharacteristic
80C4×D356C2×C411yescharacteristic
81C4×D356C2311yescharacteristic
82C4×D356C2311yescharacteristic
83C2×C4⋊Dic89C2×C411yescharacteristic
84C2×#13083551—21no—
85#15667945C2×C411yescharacteristic
86#15667945C2×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#15667933C2×C411yescharacteristic
97#15667933C2×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
115C2×M16×C89—21no—
116C2×M16×C89—21no—
117C22×C8×C89—21no—
118#126×C89—21no—
119#125×C89C2×C411yescharacteristic
120#124×C89C2×C411yescharacteristic
121#123×C89—21no—
122C22⋊Q8×C89C2×C411yescharacteristic
123#121×C89C2×C411yescharacteristic
124C4×Q8×C89C2311yescharacteristic
125C4×D4×C89—21no—
126C4×D4×C89C2311yescharacteristic
127#117×C89—21no—
128C2×C42×C89C2311yescharacteristic
129C4⋊C8×C89—21no—
130C4⋊C8×C89—21no—
131C4⋊C8×C89—21no—
132C4⋊C8×C89D411yescharacteristic
133C4⋊C8×C89D411yescharacteristic
134C4⋊C8×C89C2311yescharacteristic
135C4⋊C8×C89C2311yescharacteristic
136C22⋊C8×C89—21no—
137C22⋊C8×C89—21no—
138C22⋊C8×C89D411yescharacteristic
139C22⋊C8×C89D411yescharacteristic
140#97×C89—21no—
141C4×C8×C89—21no—
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144C23×D89—21no—
145C2×D356—21no—
146C2×D356—22no—
147C2×D356—22no—
148C2×D356C22×C411yescharacteristic
149C2×D356C22×C411yescharacteristic
150C22×Dic89—21no—
151C2×C4×D89—21no—
152C2×C4×D89—21no—
153C2×C4×D89—21no—
154C2×C4×D89—21no—
155C2×C4×D89—81no—
156C2×C4×D89—81no—
157#13083561—22no—
158#13083561—22no—
159#13083559—22no—
160#13083559—22no—
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—
171C8×D89—81no—
172C8×D89—81no—
173C4⋊Dic89—21no—
174C4⋊Dic89C22×C411yescharacteristic
175C4⋊Dic89C22×C411yescharacteristic
176#13083551—21no—
177#13083551—21no—
178#13083551—21no—
179#13083551—21no—
180C2×Q8×C89C22×C411yescharacteristic
181C2×D4×C89—21no—
182C2×D4×C89C22×C411yescharacteristic
183C22×C4×C89—21no—
184C22×C4×C89C22×C411yescharacteristic
185C22×C4×C89C2×D411yescharacteristic
186C22×C4×C89#4111yescharacteristic
187M16×C89—81no—
188M16×C89—81no—
189C2×C8×C89—21no—
190C2×C8×C89—21no—
191C2×C8×C89—81no—
192C2×C8×C89C2×D411yescharacteristic
193C2×C8×C89C2×D411yescharacteristic
194C2×C8×C89C2×D411yescharacteristic
195C2×C8×C89C2×D411yescharacteristic
196C4⋊C4×C89—21no—
197C4⋊C4×C89—21no—
198C4⋊C4×C89—21no—
199C4⋊C4×C89—21no—
200C4⋊C4×C89C22×C411yescharacteristic
201C4⋊C4×C89C22×C411yescharacteristic
202C22⋊C4×C89—21no—
203C22⋊C4×C89—21no—
204C22⋊C4×C89—21no—
205C22⋊C4×C89—21no—
206C22⋊C4×C89—21no—
207C42×C89—21no—
208C42×C89C22×C411yescharacteristic
209C42×C89C2×D411yescharacteristic
210C42×C89#4111yescharacteristic
211C42×C89C2411yescharacteristic
212C23×C89—21no—
213C23×C89C4×D411yescharacteristic
214C22×D89—21no—
215C22×D89—21no—
216C22×D89—24no—
217C22×D89—81no—
218C22×D89—81no—
219Q8×C89—21no—
220Q8×C89—21no—
221D4×C89—21no—
222D4×C89—21no—
223D4×C89—81no—
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—21no—
231C2×C4×C89—41no—
232C2×C4×C89—41no—
233C2×C4×C89—41no—
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—81no—
243D356—24no—
244D356—21no—
245D356—21no—
246D356#13112yes—
247D356#13112yes—
248C4×D89—41no—
249C4×D89—41no—
250C4×D89—41no—
251C4×D89—41no—
252C4×D89—81no—
253C4×D89—81no—
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×C89C2×C4×D411yescharacteristic
275C2×D89—22no—
276C2×D89—22no—
277C2×D89—41no—
278C2×D89—41no—
279C2×D89—41no—
280C2×D89—41no—
281C2×D89—84no—
282C4×C89—21no—
283C4×C89—21no—
284C4×C89—21no—
285C4×C89—21no—
286C4×C89—41no—
287C4×C89—41no—
288C4×C89—41no—
289C4×C89C2×#13111yescharacteristic
290C4×C89C2×#13111yescharacteristic
291C4×C89#57611yescharacteristic
292C4×C89#57711yescharacteristic
293Dic89—41no—
294Dic89—41no—
295#17918—891nomaximal, Sylow
296C2×C89—41no—
297C2×C89—81no—
298C2×C89#292911yescharacteristic
299C2×C89#294611yescharacteristic
300C2×C89#295711yescharacteristic
301D89—42no—
302D89—42no—
303#3105—891no—
304#2993D8911yescharacteristic, complemented
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#1486—891no—
316#1482—891no—
317#1454—891no—
318C89#1791811yescharacteristic, complemented, Sylow
319#529C2×D8911yescharacteristic
320C2×C4×D4—891no—
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#446C2×D8911yescharacteristic, complemented
330C8×Q8C2×D8911yescharacteristic, complemented
331C4×SD16—891no—
332C4×SD16—891no—
333C4×D8—891no—
334C4×D8—891no—
335#436—21no—
336#436C2×D8911yescharacteristic, complemented
337#435—21no—
338C8×D4—891no—
339C8×D4—891no—
340C8×D4—891no—
341C8×D4—891no—
342C8×D4—1781no—
343C8×D4—1781no—
344C8×D4C2×D8911yescharacteristic, complemented
345#433—21no—
346#431—891no—
347#431—891no—
348#431—891no—
349#431C2×D8911yescharacteristic
350#424—21no—
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⋊C8—891no—
363D4⋊C8—891no—
364D4⋊C8—891no—
365D4⋊C8—891no—
366#322—891no—
367#322—891no—
368#322—891no—
369C82—891no—
370C22×D4—891no—
371C23×C4—1781no—
372C2×SD16—891no—
373C2×SD16—891no—
374C2×D8—891no—
375C2×D8—891no—
376C2×M16—21no—
377C2×M16—21no—
378C22×C8—21no—
379C22×C8—1781no—
380C22×C8—1781no—
381C22×C8—1781no—
382C22×C8—1781no—
383#126—21no—
384#125C4×D8911yescharacteristic
385#124C4×D8911yescharacteristic
386#123—21no—
387C22⋊Q8C4×D8911yescharacteristic
388#121C4×D8911yescharacteristic
389C4×Q8C22×D8911yescharacteristic
390C4×D4—21no—
391C4×D4—891no—
392C4×D4—891no—
393C4×D4—891no—
394C4×D4—891no—
395C4×D4—1781no—
396C4×D4—1781no—
397C4×D4C22×D8911yescharacteristic
398#117—21no—
399C2×C4⋊C4—891no—
400C2×C22⋊C4—1781no—
401C2×C42C22×D8911yescharacteristic
402#107—891no—
403#107—891no—
404#106—891no—
405#106—891no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—891no—
410C4⋊C8—891no—
411C4⋊C8—891no—
412C4⋊C8—891no—
413C4⋊C8—1781no—
414C4⋊C8C22⋊D8911yescharacteristic
415C4⋊C8C22⋊D8911yescharacteristic
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—21no—
428C22⋊C8—891no—
429C22⋊C8—891no—
430C22⋊C8—1781no—
431C22⋊C8—1781no—
432C22⋊C8—1781no—
433C22⋊C8—1781no—
434C22⋊C8—1781no—
435C22⋊C8—1781no—
436C22⋊C8C22⋊D8911yescharacteristic
437C22⋊C8C22⋊D8911yescharacteristic
438#97—21no—
439C4×C8—21no—
440C4×C8—891no—
441C4×C8—891no—
442C4×C8—891no—
443C4×C8—891no—
444C4×C8—1781no—
445C4×C8C22×D8911yescharacteristic
446C4×C8C22×D8911yescharacteristic
447C24—1781no—
448C2×Q8C2×C4×D8911yescharacteristic
449C2×D4—21no—
450C2×D4—891no—
451C2×D4—891no—
452C2×D4—1782no—
453C2×D4—1782no—
454C2×D4—1781no—
455C2×D4C2×C4×D8911yescharacteristic
456C22×C4—21no—
457C22×C4—1781no—
458C22×C4—1781no—
459C22×C4—1781no—
460C22×C4—1781no—
461C22×C4—1781no—
462C22×C4—7121no—
463C22×C4—7121no—
464C22×C4C2×C4×D8911yescharacteristic
465C22×C4C2×C22⋊D8911yescharacteristic
466C22×C4#1308357411yescharacteristic
467SD16—1782no—
468SD16—1782no—
469D8—1782no—
470D8—1782no—
471M16—81no—
472M16—81no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—891no—
477C2×C8—891no—
478C2×C8—891no—
479C2×C8—891no—
480C2×C8—1781no—
481C2×C8—1781no—
482C2×C8—1781no—
483C2×C8—1781no—
484C2×C8—7121no—
485C2×C8—7121no—
486C2×C8—7121no—
487C2×C8—7121no—
488C2×C8C2×C22⋊D8911yescharacteristic
489C2×C8C2×C22⋊D8911yescharacteristic
490C2×C8C2×C22⋊D8911yescharacteristic
491C2×C8C2×C22⋊D8911yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—891no—
497C4⋊C4—891no—
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—21no—
506C22⋊C4—1781no—
507C22⋊C4—1781no—
508C22⋊C4—1781no—
509C22⋊C4—1781no—
510C42—21no—
511C42C2×C4×D8911yescharacteristic
512C42C2×C22⋊D8911yescharacteristic
513C42#1308357411yescharacteristic
514C42C23×D8911yescharacteristic
515C23—21no—
516C23—1784no—
517C23—1781no—
518C23—1781no—
519C23—7121no—
520C23—7121no—
521C23C4×C22⋊D8911yescharacteristic
522Q8—21no—
523Q8—21no—
524D4—21no—
525D4—21no—
526D4—81no—
527D4—892no—
528D4—892no—
529D4—1784no—
530D4—1781no—
531D4—1781no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—3561no—
543C2×C4—3561no—
544C2×C4—3561no—
545C2×C4—3561no—
546C2×C4—1781no—
547C2×C4—1781no—
548C2×C4—7121no—
549C2×C4—7121no—
550C2×C4—7121no—
551C2×C4C4×C22⋊D8911yescharacteristic
552C2×C4C4×C22⋊D8911yescharacteristic
553C2×C4C4×C22⋊D8911yescharacteristic
554C2×C4C22×C4×D8911yescharacteristic
555C2×C4C22×C22⋊D8911yescharacteristic
556C2×C4C2×#1308357411yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—3561no—
564C8—3561no—
565C8—3561no—
566C8—3561no—
567C8—1781no—
568C8—1781no—
569C8—1781no—
570C8—1781no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—3561no—
578C22—3561no—
579C22—3561no—
580C22—3561no—
581C22—1782no—
582C22—1782no—
583C22—7124no—
584C22C2×C4×C22⋊D8911yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—3561no—
593C4—3561no—
594C4#131×D8911yescharacteristic
595C4#131×D8911yescharacteristic
596C4#1915240111yescharacteristic
597C4#1915240611yescharacteristic
598C2—41no—
599C2—81no—
600C2—3562no—
601C2—3562no—
602C2#2602894411yescharacteristic
603C2#2602908011yescharacteristic
604C2#2602916711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#2993C2
socleC22×C89C2×C4×D4
prime radical#19151731C4
cosocleC42×C89C24
hypercenter#2993D89
hypocenterC89#17918
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #26029275C2semidirect
3. #26019114C2semidirect
4. #26019107C2semidirect
5. #26019086C2semidirect
6. #26019079C2semidirect
7. #26019074C2semidirect
8. #26019062C2semidirect
9. C8×#13083561C2semidirect
10. C8×#13083559C2semidirect
11. #26019043C2semidirect
12. #26018676C2semidirect
13. #26018660C2semidirect
14. #26018552C2semidirect
15. C89×#2993C2semidirect
40. #19151350C22semidirect
41. #19151350C22semidirect
42. #19151348C22semidirect
43. #19151348C22semidirect
44. Q8⋊#10623494C22semidirect
45. Q8⋊#10623494C22semidirect
46. D4⋊#10623494C22semidirect
47. D4⋊#10623494C22semidirect
52. #19151320C22semidirect
53. #19151320C22semidirect
54. #19151319C22semidirect
55. C8×#10623494C22semidirect
57. #446×C89C22semidirect
58. C8×Q8×C89C22semidirect
60. #436×C89C22semidirect
62. C8×D4×C89C22semidirect
304. #2993D89semidirect
318. C89#17918semidirect
329. #446C2×D89semidirect
330. C8×Q8C2×D89semidirect
336. #436C2×D89semidirect
344. C8×D4C2×D89semidirect

Maximal subgroups

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

subgroupindex
#260302952
#260292752
#260191142
#260191072
#260190862
#260190792
#260190742
#260190622
C8×#130835612
C8×#130835592
#260190432
#260186762
#260186602
#260185522
C89×#29932
#1791889