Finite Group Databasebeta

← #36524518

Subgroups — #36524518

Order 22784.

638 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#26030312C211yesmaximal, characteristic
2#26029327C211yesmaximal, characteristic, complemented
3#26019130C211yesmaximal, characteristic, complemented
4#26019116C211yesmaximal, characteristic, complemented
5#26019095C211yesmaximal, characteristic, complemented
6#26019081C211yesmaximal, characteristic, complemented
7#26019074C211yesmaximal, characteristic, complemented
8#26019062C211yesmaximal, characteristic, complemented
9C8×#13083561C211yesmaximal, characteristic, complemented
10C8×#13083559C211yesmaximal, characteristic, complemented
11#26019035C211yesmaximal, characteristic, complemented
12#26018686C211yesmaximal, characteristic, complemented
13#26018650C211yesmaximal, characteristic, complemented
14#26018552C211yesmaximal, characteristic, complemented
15C89×#2988C211yesmaximal, characteristic, complemented
16#19152148C2211yescharacteristic
17#19151922C411yescharacteristic
18#19151922C411yescharacteristic
19#19151893C411yescharacteristic
20#19151888C411yescharacteristic
21#19151798C411yescharacteristic
22#19151793C411yescharacteristic
23#19151743C411yescharacteristic
24#19151743C411yescharacteristic
25C4×#13083561C2211yescharacteristic
26C4×#13083561C2211yescharacteristic
27C4×#13083559C2211yescharacteristic
28C4×#13083559C2211yescharacteristic
29#19151677C2211yescharacteristic
30#19151677C2211yescharacteristic
31#19151668—21no—
32#19151668—21no—
33C8×D356C2211yescharacteristic
34C8×D356C2211yescharacteristic
35#19151655C2211yescharacteristic
36#19151651C2211yescharacteristic
37#19151651C2211yescharacteristic
38#19151563—21no—
39#19151563—21no—
40#19151350C2211yescharacteristic
41#19151350C2211yescharacteristic
42#19151348C2211yescharacteristic
43#19151348C2211yescharacteristic
44Q8⋊#10623494C2211yescharacteristic
45Q8⋊#10623494C2211yescharacteristic
46D4⋊#10623494C2211yescharacteristic
47D4⋊#10623494C2211yescharacteristic
48#19151325C2211yescharacteristic
49#19151325C2211yescharacteristic
50#19151325C2211yescharacteristic
51#19151325C2211yescharacteristic
52#19151320C2211yescharacteristic
53#19151320C2211yescharacteristic
54#19151319C2211yescharacteristic
55C8×#10623494C2211yescharacteristic
56C4×#41×C89C2211yescharacteristic
57C8×Q8×C89C2211yescharacteristic
58C8×Q8×C89C2211yescharacteristic
59C8×D4×C89—21no—
60C8×D4×C89—21no—
61C8×D4×C89C2211yescharacteristic
62C8×D4×C89C2211yescharacteristic
63#431×C89—21no—
64#431×C89C2211yescharacteristic
65C2×C4⋊C8×C89—21no—
66C2×C4⋊C8×C89C2211yescharacteristic
67C2×#13083574—21no—
68C2×#13083561C2×C411yescharacteristic
69C2×#13083561C2×C411yescharacteristic
70C2×#13083559C2×C411yescharacteristic
71C2×#13083559C2×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#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—
110#15667923—21no—
111C4×#10623494C2311yescharacteristic
112C4×#10623494C2311yescharacteristic
113C4×#10623494C2311yescharacteristic
114C4×#10623494C2311yescharacteristic
115C2×#41×C89C2×C411yescharacteristic
116C22×C8×C89—21no—
117C22×C8×C89—21no—
118C22×C8×C89—21no—
119C4×Q8×C89C2×C411yescharacteristic
120C4×Q8×C89C2311yescharacteristic
121C4×D4×C89—21no—
122C4×D4×C89—21no—
123C4×D4×C89C2×C411yescharacteristic
124C4×D4×C89C2311yescharacteristic
125#117×C89—21no—
126#117×C89C2×C411yescharacteristic
127C2×C42×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
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#13083559—22no—
158#13083559—22no—
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—
178#41×C89—22no—
179#41×C89—22no—
180C2×Q8×C89C22×C411yescharacteristic
181C2×D4×C89—21no—
182C2×D4×C89C22×C411yescharacteristic
183C22×C4×C89—21no—
184C22×C4×C89—21no—
185C22×C4×C89—21no—
186C22×C4×C89C22×C411yescharacteristic
187C22×C4×C89C2×D411yescharacteristic
188C22×C4×C89#4111yescharacteristic
189C2×C8×C89—21no—
190C2×C8×C89—21no—
191C2×C8×C89—81no—
192C2×C8×C89—81no—
193C2×C8×C89—81no—
194C2×C8×C89C2×D411yescharacteristic
195C2×C8×C89C2×D411yescharacteristic
196C2×C8×C89C2×D411yescharacteristic
197C2×C8×C89C2×D411yescharacteristic
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—
205C42×C89—21no—
206C42×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—
216Q8×C89—21no—
217Q8×C89#13112yes—
218D4×C89—24no—
219D4×C89—21no—
220D4×C89#13112yes—
221C2×C4×C89—24no—
222C2×C4×C89—21no—
223C2×C4×C89—21no—
224C2×C4×C89—21no—
225C2×C4×C89—21no—
226C2×C4×C89—21no—
227C2×C4×C89—21no—
228C2×C4×C89—21no—
229C2×C4×C89—41no—
230C2×C4×C89—41no—
231C2×C4×C89—41no—
232C2×C4×C89—81no—
233C2×C4×C89C4×D411yescharacteristic
234C2×C4×C89C4×D411yescharacteristic
235C2×C4×C89C4×D411yescharacteristic
236C2×C4×C89C23×C411yescharacteristic
237C2×C4×C89C22×D411yescharacteristic
238C2×C4×C89C2×#4111yescharacteristic
239C22⋊D89—81no—
240C22⋊D89—81no—
241C2×Dic89—21no—
242C2×Dic89—21no—
243D356—21no—
244D356—21no—
245D356—21no—
246D356—21no—
247D356—81no—
248D356—81no—
249C4×D89—41no—
250C4×D89—41no—
251C4×D89—41no—
252C4×D89—41no—
253Dic178—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—22no—
270C22×C89—21no—
271C22×C89—21no—
272C22×C89—41no—
273C22×C89—41no—
274C22×C89C2×C4×D411yescharacteristic
275C2×D89—41no—
276C2×D89—41no—
277C2×D89—41no—
278C2×D89—41no—
279C2×D89—41no—
280C2×D89—41no—
281C4×C89—21no—
282C4×C89—22no—
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—
294#17920—891nomaximal, Sylow
295C2×C89—41no—
296C2×C89—42no—
297C2×C89#292911yescharacteristic
298C2×C89#294611yescharacteristic
299C2×C89#295711yescharacteristic
300D89—81no—
301D89—81no—
302#3106—891no—
303#2988D8911yescharacteristic, complemented
304#2981—891no—
305#1588—891no—
306#1586—891no—
307#1583—891no—
308#1581—891no—
309#1580—891no—
310SD16⋊C8—891no—
311C8×SD16—891no—
312C8×D8—891no—
313#1573—891no—
314#1488—891no—
315#1480—891no—
316#1454—891no—
317C89#1792011yescharacteristic, complemented, Sylow
318#532—891no—
319C4×#41C2×D8911yescharacteristic
320#482—891no—
321#482—891no—
322#477—891no—
323#476—891no—
324#460—891no—
325#459—891no—
326#449—891no—
327#449—891no—
328C8×Q8C2×D8911yescharacteristic
329C8×Q8C2×D8911yescharacteristic
330C4×SD16—891no—
331C4×SD16—891no—
332C4×D8—891no—
333C4×D8—891no—
334#436—891no—
335#436—891no—
336#435—1781no—
337#435—1781no—
338C8×D4—21no—
339C8×D4—21no—
340C8×D4—891no—
341C8×D4—891no—
342C8×D4C2×D8911yescharacteristic
343C8×D4C2×D8911yescharacteristic
344#432—891no—
345#431—21no—
346#431—891no—
347#431—891no—
348#431C2×D8911yescharacteristic
349C2×C4⋊C8—21no—
350C2×C4⋊C8C2×D8911yescharacteristic
351#408—1781no—
352#408—1781no—
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—1781no—
370C2×#41C4×D8911yescharacteristic
371C2×SD16—891no—
372C2×SD16—891no—
373C2×D8—891no—
374C2×D8—891no—
375C2×M16—1781no—
376C2×M16—1781no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—1781no—
381C22×C8—1781no—
382C4⋊Q8—891no—
383#127—891no—
384#124—1781no—
385#121—891no—
386#121—891no—
387#121—1781no—
388C4×Q8C4×D8911yescharacteristic
389C4×Q8C22×D8911yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—891no—
393C4×D4—891no—
394C4×D4—1781no—
395C4×D4C4×D8911yescharacteristic
396C4×D4C22×D8911yescharacteristic
397#117—21no—
398#117C4×D8911yescharacteristic
399C2×C42—21no—
400C2×C42C22×D8911yescharacteristic
401#107—891no—
402#107—891no—
403#106—891no—
404#106—891no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—891no—
409C4⋊C8—891no—
410C4⋊C8—891no—
411C4⋊C8—891no—
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—891no—
428C22⋊C8—891no—
429C22⋊C8—1781no—
430C22⋊C8—1781no—
431C22⋊C8—1781no—
432C22⋊C8—1781no—
433C22⋊C8—1781no—
434C22⋊C8—1781no—
435C22⋊C8C22⋊D8911yescharacteristic
436C22⋊C8C22⋊D8911yescharacteristic
437#97—1781no—
438C4×C8—21no—
439C4×C8—21no—
440C4×C8—891no—
441C4×C8—891no—
442C4×C8—891no—
443C4×C8—891no—
444C4×C8C22×D8911yescharacteristic
445C4×C8C22×D8911yescharacteristic
446#41—22no—
447#41—22no—
448#41—7121no—
449#41—7121no—
450C2×Q8—1781no—
451C2×Q8C2×C4×D8911yescharacteristic
452C2×D4—21no—
453C2×D4—891no—
454C2×D4—891no—
455C2×D4—1781no—
456C2×D4—1781no—
457C2×D4—1781no—
458C2×D4—1781no—
459C2×D4C2×C4×D8911yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—1781no—
464C22×C4—1781no—
465C22×C4C2×C4×D8911yescharacteristic
466C22×C4C2×C22⋊D8911yescharacteristic
467C22×C4#1308357411yescharacteristic
468SD16—1782no—
469SD16—1782no—
470D8—1782no—
471D8—1782no—
472M16—7121no—
473M16—7121no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—81no—
479C2×C8—891no—
480C2×C8—891no—
481C2×C8—891no—
482C2×C8—891no—
483C2×C8—1781no—
484C2×C8—1781no—
485C2×C8—1781no—
486C2×C8—1781no—
487C2×C8—7121no—
488C2×C8—7121no—
489C2×C8C2×C22⋊D8911yescharacteristic
490C2×C8C2×C22⋊D8911yescharacteristic
491C2×C8C2×C22⋊D8911yescharacteristic
492C2×C8C2×C22⋊D8911yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—891no—
496C4⋊C4—891no—
497C4⋊C4—1781no—
498C4⋊C4C2×C4×D8911yescharacteristic
499C4⋊C4C2×C4×D8911yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—1781no—
504C22⋊C4—1781no—
505C22⋊C4—1781no—
506C22⋊C4—1781no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42C2×C4×D8911yescharacteristic
511C42C2×C22⋊D8911yescharacteristic
512C42#1308357411yescharacteristic
513C42C23×D8911yescharacteristic
514C23—21no—
515C23—1781no—
516C23—1781no—
517C23C4×C22⋊D8911yescharacteristic
518Q8—21no—
519Q8—7121no—
520Q8#1566801812yes—
521D4—24no—
522D4—21no—
523D4—1781no—
524D4—1781no—
525D4—1781no—
526D4—1781no—
527D4—7121no—
528D4—7121no—
529D4—7121no—
530D4—7121no—
531D4#1566801812yes—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—3561no—
545C2×C4—3561no—
546C2×C4—3561no—
547C2×C4—3561no—
548C2×C4—1781no—
549C2×C4—1781no—
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—22no—
574C22—41no—
575C22—41no—
576C22—3561no—
577C22—3561no—
578C22—3561no—
579C22—3561no—
580C22—3561no—
581C22—3561no—
582C22C2×C4×C22⋊D8911yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—3561no—
591C4—3561no—
592C4C2×#1566801811yescharacteristic
593C4C2×#1566801811yescharacteristic
594C4#1915240111yescharacteristic
595C4#1915240611yescharacteristic
596C2—41no—
597C2—42no—
598C2—7121no—
599C2—7121no—
600C2#2602894611yescharacteristic
601C2#2602908011yescharacteristic
602C2#2602916711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#2988C2
socleC22×C89C2×C4×D4
prime radical#26030312C2
cosocleC42×C89C24
hypercenter#2988D89
hypocenterC89#17920
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2988

Complements

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

NH ≅ G/Ntype
2. #26029327C2semidirect
3. #26019130C2semidirect
4. #26019116C2semidirect
5. #26019095C2semidirect
6. #26019081C2semidirect
7. #26019074C2semidirect
8. #26019062C2semidirect
9. C8×#13083561C2semidirect
10. C8×#13083559C2semidirect
11. #26019035C2semidirect
12. #26018686C2semidirect
13. #26018650C2semidirect
14. #26018552C2semidirect
15. C89×#2988C2semidirect
303. #2988D89semidirect
317. C89#17920semidirect

Maximal subgroups

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

subgroupindex
#260303122
#260293272
#260191302
#260191162
#260190952
#260190812
#260190742
#260190622
C8×#130835612
C8×#130835592
#260190352
#260186862
#260186502
#260185522
C89×#29882
#1792089