Finite Group Databasebeta

← #36525726

Subgroups — #36525726

Order 22784.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26030252C211yesmaximal, characteristic
2#26029318C211yesmaximal, characteristic, complemented
3#26029287C211yesmaximal, characteristic, complemented
4#26019163C211yesmaximal, characteristic, complemented
5#26019134C211yesmaximal, characteristic, complemented
6#26019119C211yesmaximal, characteristic, complemented
7#26019113C211yesmaximal, characteristic, complemented
8#26019084C211yesmaximal, characteristic, complemented
9#26019078C211yesmaximal, characteristic, complemented
10#26019073C211yesmaximal, characteristic, complemented
11#26019044C211yesmaximal, characteristic, complemented
12#26019030C211yesmaximal, characteristic, complemented
13#26018722C211yesmaximal, characteristic, complemented
14#26018552C211yesmaximal, characteristic, complemented
15C89×#1478C211yesmaximal, characteristic, complemented
16#19152148C2211yescharacteristic
17#19151911C411yescharacteristic
18#19151911C411yescharacteristic
19#19151878C411yescharacteristic
20#19151878C411yescharacteristic
21#19151793C411yescharacteristic
22#19151793C411yescharacteristic
23#19151732C411yescharacteristic
24#19151732C411yescharacteristic
25C4×#13083559C2211yescharacteristic
26C4×#13083559C2211yescharacteristic
27C4×#13083559C2211yescharacteristic
28C4×#13083559C2211yescharacteristic
29#19151677—21no—
30#19151676C2211yescharacteristic
31#19151676C2211yescharacteristic
32#19151675C2211yescharacteristic, complemented
33#19151675C2211yescharacteristic, complemented
34#19151670—21no—
35#19151670—21no—
36C8×D356—21no—
37D4×#10623494C2211yescharacteristic
38D4×#10623494C2211yescharacteristic
39#19151663C2211yescharacteristic, complemented
40#19151663C2211yescharacteristic, complemented
41#19151655C2211yescharacteristic
42#19151651C2211yescharacteristic
43#19151651C2211yescharacteristic
44#19151563—21no—
45#19151563—21no—
46#19151562—21no—
47C2×C22⋊#10623494—21no—
48#19151350C2211yescharacteristic, complemented
49#19151350C2211yescharacteristic, complemented
50#19151348C2211yescharacteristic, complemented
51#19151348C2211yescharacteristic, complemented
52#19151327C2211yescharacteristic, complemented
53#19151327C2211yescharacteristic, 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#431×C89C2211yescharacteristic
63D4⋊C8×C89C2211yescharacteristic
64D4⋊C8×C89C2211yescharacteristic
65D4⋊C8×C89C2211yescharacteristic
66D4⋊C8×C89C2211yescharacteristic
67C2×#13083574—21no—
68C2×#13083559C2×C411yescharacteristic
69C2×#13083559C2×C411yescharacteristic
70C2×#13083559C2×C411yescharacteristic
71C2×#13083559C2×C411yescharacteristic
72C2×#13083558—21no—
73C2×#13083558—21no—
74C2×#13083557—21no—
75C2×#13083557—21no—
76C22×#10623494—21no—
77C22×#10623494—21no—
78C2×C8×D89—21no—
79C2×C8×D89—21no—
80#15668012C2×C411yescharacteristic
81#15668009C2×C411yescharacteristic
82#15668000—21no—
83#15667986—21no—
84#15667986C2×C411yescharacteristic
85#15667986C2×C411yescharacteristic
86C4×D356—21no—
87C4×D356C2311yescharacteristic
88C4×D356C2311yescharacteristic
89#15667945C2×C411yescharacteristic
90#15667945C2×C411yescharacteristic
91#15667945C2×C411yescharacteristic
92#15667945C2×C411yescharacteristic
93C4⋊#10623494C2×C411yescharacteristic
94C4⋊#10623494C2×C411yescharacteristic
95C4⋊#10623494D411yescharacteristic
96C4⋊#10623494D411yescharacteristic
97C4⋊#10623494C2311yescharacteristic
98C4⋊#10623494C2311yescharacteristic
99#15667933C2×C411yescharacteristic
100#15667933C2×C411yescharacteristic
101#15667933C2×C411yescharacteristic
102#15667933C2×C411yescharacteristic
103#15667932C2×C411yescharacteristic
104#15667932C2×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#15667924—21no—
119#15667924—21no—
120#15667923—21no—
121C4×#10623494C2311yescharacteristic
122C4×#10623494C2311yescharacteristic
123C4×#10623494C2311yescharacteristic
124C4×#10623494C2311yescharacteristic
125C22×D4×C89C2×C411yescharacteristic
126C23×C4×C89—21no—
127C4×D4×C89—21no—
128C4×D4×C89—21no—
129C4×D4×C89C2×C411yescharacteristic
130C4×D4×C89C2×C411yescharacteristic
131C4×D4×C89C2311yescharacteristic
132C4×D4×C89C2311yescharacteristic
133C2×C4⋊C4×C89C2×C411yescharacteristic
134C2×C22⋊C4×C89—21no—
135C2×C42×C89C2311yescharacteristic
136C4⋊C8×C89—21no—
137C4⋊C8×C89C2311yescharacteristic
138C4⋊C8×C89C2311yescharacteristic
139C22⋊C8×C89—21no—
140C22⋊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#13083559—22no—
156#13083559—22no—
157#13083559—41no—
158#13083559—41no—
159#13083558—81no—
160#13083558—81no—
161#13083557—81no—
162#13083557—81no—
163C2×#10623494—21no—
164C2×#10623494—21no—
165C2×#10623494—81no—
166C2×#10623494—81no—
167C2×#10623494C22×C411yescharacteristic
168C2×#10623494C22×C411yescharacteristic
169C2×#10623494C22×C411yescharacteristic
170C2×#10623494C22×C411yescharacteristic
171C2×#10623494C2×D411yescharacteristic
172C2×#10623494C2×D411yescharacteristic
173C2×#10623494C2×D411yescharacteristic
174C2×#10623494C2×D411yescharacteristic
175C8×D89—81no—
176C8×D89—81no—
177C4⋊Dic89—21no—
178C4⋊Dic89C22×C411yescharacteristic
179C4⋊Dic89C22×C411yescharacteristic
180#13083551—21no—
181#13083551—21no—
182#13083551—21no—
183#13083551—21no—
184C24×C89—21no—
185C2×D4×C89—22no—
186C2×D4×C89—21no—
187C2×D4×C89—41no—
188C2×D4×C89C22×C411yescharacteristic
189C2×D4×C89C22×C411yescharacteristic
190C22×C4×C89—21no—
191C22×C4×C89—21no—
192C22×C4×C89—21no—
193C22×C4×C89—21no—
194C22×C4×C89—21no—
195C22×C4×C89—81no—
196C22×C4×C89—81no—
197C22×C4×C89C22×C411yescharacteristic
198C22×C4×C89C2×D411yescharacteristic
199C22×C4×C89#4111yescharacteristic
200C2×C8×C89—21no—
201C2×C8×C89—21no—
202C2×C8×C89—21no—
203C2×C8×C89—21no—
204C4⋊C4×C89—21no—
205C4⋊C4×C89C22×C411yescharacteristic
206C4⋊C4×C89C22×C411yescharacteristic
207C22⋊C4×C89—21no—
208C22⋊C4×C89—21no—
209C22⋊C4×C89—21no—
210C22⋊C4×C89—21no—
211C42×C89C22×C411yescharacteristic
212C42×C89C2×D411yescharacteristic
213C42×C89#4111yescharacteristic
214C42×C89C2411yescharacteristic
215C23×C89—21no—
216C23×C89—21no—
217C23×C89—42no—
218C23×C89—42no—
219C23×C89—81no—
220C23×C89C4×D411yescharacteristic
221C22×D89—21no—
222C22×D89—21no—
223D4×C89—21no—
224D4×C89—21no—
225D4×C89—21no—
226D4×C89—42no—
227D4×C89#13112yes—
228C2×C4×C89—21no—
229C2×C4×C89—21no—
230C2×C4×C89—21no—
231C2×C4×C89—21no—
232C2×C4×C89—21no—
233C2×C4×C89—21no—
234C2×C4×C89—41no—
235C2×C4×C89—41no—
236C2×C4×C89—41no—
237C2×C4×C89—41no—
238C2×C4×C89—41no—
239C2×C4×C89—81no—
240C2×C4×C89—81no—
241C2×C4×C89—81no—
242C2×C4×C89C4×D411yescharacteristic
243C2×C4×C89C4×D411yescharacteristic
244C2×C4×C89C4×D411yescharacteristic
245C2×C4×C89C23×C411yescharacteristic
246C2×C4×C89C22×D411yescharacteristic
247C2×C4×C89C2×#4111yescharacteristic
248C22⋊D89—81no—
249C22⋊D89—81no—
250C2×Dic89—21no—
251C2×Dic89—21no—
252D356—21no—
253D356—21no—
254D356—21no—
255D356—21no—
256D356—42no—
257D356—81no—
258C4×D89—41no—
259C4×D89—41no—
260C4×D89—41no—
261C4×D89—41no—
262Dic178—81no—
263C8×C89—41no—
264C8×C89—41no—
265C8×C89—41no—
266C8×C89—41no—
267#10623494—21no—
268#10623494—21no—
269#10623494—21no—
270#10623494—21no—
271#10623494—21no—
272#10623494—21no—
273#10623494—21no—
274#10623494—21no—
275#10623494—41no—
276#10623494—41no—
277C22×C89—21no—
278C22×C89—22no—
279C22×C89—21no—
280C22×C89—21no—
281C22×C89—41no—
282C22×C89—41no—
283C22×C89—41no—
284C22×C89—41no—
285C22×C89—41no—
286C22×C89—84no—
287C22×C89C2×C4×D411yescharacteristic
288C2×D89—41no—
289C2×D89—41no—
290C2×D89—41no—
291C2×D89—41no—
292C2×D89—41no—
293C2×D89—41no—
294C4×C89—21no—
295C4×C89—21no—
296C4×C89—21no—
297C4×C89—21no—
298C4×C89—41no—
299C4×C89—41no—
300C4×C89C2×#13111yescharacteristic
301C4×C89#56811yescharacteristic
302C4×C89#57611yescharacteristic
303C4×C89#57611yescharacteristic
304Dic89—41no—
305Dic89—41no—
306#18026—891nomaximal, Sylow
307C2×C89—41no—
308C2×C89—42no—
309C2×C89—81no—
310C2×C89#293311yescharacteristic
311C2×C89#294811yescharacteristic
312C2×C89#295511yescharacteristic
313D89—81no—
314D89—81no—
315#3100—891no—
316#2979—891no—
317#2974—891no—
318#1594—891no—
319#1589—891no—
320#1586—891no—
321#1586—891no—
322#1581—891no—
323#1581—891no—
324#1580—891no—
325C8×D8—891no—
326#1572—891no—
327#1496—891no—
328#1478D8911yescharacteristic, complemented
329#1454—891no—
330C89#1802611yescharacteristic, complemented, Sylow
331#532—891no—
332C2×C4×D4C2×D8911yescharacteristic
333#480—891no—
334#480—891no—
335#474—891no—
336#474—891no—
337#459—891no—
338#459—891no—
339#447—891no—
340#447—891no—
341C4×D8—891no—
342C4×D8—891no—
343C4×D8—891no—
344C4×D8—891no—
345#436—891no—
346#436—891no—
347#436—891no—
348#436—891no—
349#436—1781no—
350#435—1781no—
351#435—1781no—
352C8×D4—891no—
353C8×D4—891no—
354C8×D4—891no—
355C8×D4—891no—
356C8×D4—1781no—
357#432—891no—
358#431—891no—
359#431—891no—
360#431C2×D8911yescharacteristic
361#431C2×D8911yescharacteristic
362#408—1781no—
363#408—1781no—
364#407—1781no—
365C2×C22⋊C8—1781no—
366#335—891no—
367#335—891no—
368#334—891no—
369#334—891no—
370D4⋊C8—891no—
371D4⋊C8—891no—
372D4⋊C8—891no—
373D4⋊C8—891no—
374D4⋊C8C2×D8911yescharacteristic
375D4⋊C8C2×D8911yescharacteristic
376D4⋊C8C2×D8911yescharacteristic
377D4⋊C8C2×D8911yescharacteristic
378#322—891no—
379#322—891no—
380#322—891no—
381C82—891no—
382C2×#41—1781no—
383C22×D4C4×D8911yescharacteristic
384C23×C4—21no—
385C2×D8—891no—
386C2×D8—891no—
387C2×D8—891no—
388C2×D8—891no—
389C2×M16—1781no—
390C2×M16—1781no—
391C2×M16—1781no—
392C2×M16—1781no—
393C22×C8—1781no—
394C22×C8—1781no—
395C22×C8—1781no—
396C22×C8—1781no—
397C4⋊Q8—891no—
398#127—891no—
399#124—1781no—
400#121—891no—
401#121—891no—
402#121—1781no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—891no—
406C4×D4—891no—
407C4×D4—1781no—
408C4×D4C4×D8911yescharacteristic
409C4×D4C4×D8911yescharacteristic
410C4×D4C22×D8911yescharacteristic
411C4×D4C22×D8911yescharacteristic
412C2×C4⋊C4C4×D8911yescharacteristic
413C2×C22⋊C4—21no—
414C2×C42C22×D8911yescharacteristic
415#107—891no—
416#107—891no—
417#107—891no—
418#107—891no—
419C4⋊C8—21no—
420C4⋊C8—891no—
421C4⋊C8—891no—
422C4⋊C8—891no—
423C4⋊C8—891no—
424C4⋊C8—891no—
425C4⋊C8—891no—
426C4⋊C8C22×D8911yescharacteristic
427C4⋊C8C22×D8911yescharacteristic
428#102—891no—
429#102—891no—
430#102—891no—
431#102—891no—
432#102—891no—
433#102—891no—
434#102—891no—
435#102—891no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—891no—
439C22⋊C8—891no—
440C22⋊C8—891no—
441C22⋊C8—891no—
442C22⋊C8—1781no—
443C22⋊C8—1781no—
444C22⋊C8—1781no—
445C22⋊C8—1781no—
446C22⋊C8—1781no—
447C22⋊C8—1781no—
448C22⋊C8—1781no—
449C22⋊C8—1781no—
450C22⋊C8—1781no—
451#97—1781no—
452C4×C8—21no—
453C4×C8—891no—
454C4×C8—891no—
455C4×C8—891no—
456C4×C8—891no—
457C4×C8C22×D8911yescharacteristic
458C4×C8C22×D8911yescharacteristic
459C24—21no—
460#41—7121no—
461#41—7121no—
462C2×Q8—1781no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—891no—
467C2×D4—891no—
468C2×D4—1781no—
469C2×D4—1781no—
470C2×D4—1781no—
471C2×D4—1781no—
472C2×D4C2×C4×D8911yescharacteristic
473C2×D4C2×C4×D8911yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4—1781no—
482C22×C4—1781no—
483C22×C4C2×C4×D8911yescharacteristic
484C22×C4D4×D8911yescharacteristic
485C22×C4#1308357311yescharacteristic
486D8—3561no—
487D8—3561no—
488D8—1782no—
489D8—1782no—
490M16—7121no—
491M16—7121no—
492M16—7121no—
493M16—7121no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—891no—
499C2×C8—891no—
500C2×C8—891no—
501C2×C8—891no—
502C2×C8—891no—
503C2×C8—891no—
504C2×C8—891no—
505C2×C8—891no—
506C2×C8—1781no—
507C2×C8—1781no—
508C2×C8—7121no—
509C2×C8—7121no—
510C2×C8—7121no—
511C2×C8—7121no—
512C4⋊C4—21no—
513C4⋊C4—891no—
514C4⋊C4—891no—
515C4⋊C4—1781no—
516C4⋊C4C2×C4×D8911yescharacteristic
517C4⋊C4C2×C4×D8911yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—1781no—
523C22⋊C4—1781no—
524C22⋊C4—1781no—
525C22⋊C4—1781no—
526C42C2×C4×D8911yescharacteristic
527C42D4×D8911yescharacteristic
528C42#1308357311yescharacteristic
529C42C23×D8911yescharacteristic
530C23—21no—
531C23—21no—
532C23—42no—
533C23—42no—
534C23—81no—
535C23—1781no—
536C23—1781no—
537C23#1566797211yescharacteristic
538Q8—7121no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—42no—
543D4—3562no—
544D4—1781no—
545D4—1781no—
546D4—1781no—
547D4—1781no—
548D4—7121no—
549D4—7121no—
550D4—7121no—
551D4#1566801812yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—3561no—
567C2×C4—3561no—
568C2×C4—3561no—
569C2×C4—3561no—
570C2×C4—1781no—
571C2×C4—1781no—
572C2×C4#1566797211yescharacteristic
573C2×C4#1566797211yescharacteristic
574C2×C4#1566797211yescharacteristic
575C2×C4C22×C4×D8911yescharacteristic
576C2×C4C2×D4×D8911yescharacteristic
577C2×C4C2×#1308357311yescharacteristic
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—3561no—
583C8—3561no—
584C8—1781no—
585C8—1781no—
586C8—1781no—
587C8—1781no—
588C8—1781no—
589C8—1781no—
590C8—1781no—
591C8—1781no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—84no—
602C22—3561no—
603C22—3561no—
604C22—3561no—
605C22—3561no—
606C22—3561no—
607C22—3561no—
608C22C2×#1566797211yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—41no—
614C4—41no—
615C4—3561no—
616C4—3561no—
617C4C2×#1566801811yescharacteristic
618C4#1915236411yescharacteristic
619C4#1915240211yescharacteristic
620C4#1915240211yescharacteristic
621C2—41no—
622C2—42no—
623C2—81no—
624C2—7121no—
625C2—7121no—
626C2#2602897311yescharacteristic
627C2#2602910011yescharacteristic
628C2#2602915111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#1478C2
socleC22×C89C2×C4×D4
prime radical#26030252C2
cosocleC42×C89C24
hypercenter#1478D89
hypocenterC89#18026
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #26029318C2semidirect
3. #26029287C2semidirect
4. #26019163C2semidirect
5. #26019134C2semidirect
6. #26019119C2semidirect
7. #26019113C2semidirect
8. #26019084C2semidirect
9. #26019078C2semidirect
10. #26019073C2semidirect
11. #26019044C2semidirect
12. #26019030C2semidirect
13. #26018722C2semidirect
14. #26018552C2semidirect
15. C89×#1478C2semidirect
32. #19151675C22semidirect
33. #19151675C22semidirect
39. #19151663C22semidirect
40. #19151663C22semidirect
48. #19151350C22semidirect
49. #19151350C22semidirect
50. #19151348C22semidirect
51. #19151348C22semidirect
52. #19151327C22semidirect
53. #19151327C22semidirect
54. #19151327C22semidirect
55. #19151327C22semidirect
56. #19151320C22semidirect
57. #19151320C22semidirect
58. #19151319C22semidirect
59. C8×#10623494C22semidirect
328. #1478D89semidirect
330. C89#18026semidirect

Maximal subgroups

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

subgroupindex
#260302522
#260293182
#260292872
#260191632
#260191342
#260191192
#260191132
#260190842
#260190782
#260190732
#260190442
#260190302
#260187222
#260185522
C89×#14782
#1802689