Finite Group Databasebeta

← C89×#19860 #36397708

Subgroups — C89×#19860 #36397708

Order 22784.

632 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3360C211yesmaximal, characteristic, complemented
2C89×#3353C211yesmaximal, characteristic, complemented
3C89×#3335C211yesmaximal, characteristic, complemented
4C89×#3283C211yesmaximal, characteristic
5C89×#1723C211yesmaximal, characteristic, complemented
6C89×#1691C211yesmaximal, characteristic, complemented
7C89×#1683C211yesmaximal, characteristic, complemented
8C89×#1673C211yesmaximal, characteristic, complemented
9C89×#1670C211yesmaximal, characteristic, complemented
10C89×#1650C211yesmaximal, characteristic, complemented
11C89×#1647C211yesmaximal, characteristic, complemented
12C89×#1643C211yesmaximal, characteristic, complemented
13C89×#1635C211yesmaximal, characteristic, complemented
14C89×#1581C211yesmaximal, characteristic, complemented
15C89×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#135×C89—21no—
17#556×C89C2211yescharacteristic
18#554×C89C2211yescharacteristic
19#547×C89C2211yescharacteristic
20#547×C89C2211yescharacteristic
21#500×C89C2211yescharacteristic
22#500×C89C2211yescharacteristic
23#498×C89C2211yescharacteristic
24#494×C89C2211yescharacteristic
25#488×C89—21no—
26#487×C89C2211yescharacteristic
27#487×C89C2211yescharacteristic
28#484×C89—21no—
29#483×C89—21no—
30#482×C89—21no—
31#481×C89—21no—
32#479×C89—21no—
33#476×C89C2211yescharacteristic
34#476×C89C2211yescharacteristic
35#475×C89C2211yescharacteristic
36#475×C89C2211yescharacteristic
37#474×C89C2211yescharacteristic
38#468×C89—21no—
39#467×C89—21no—
40#465×C89—21no—
41#463×C89—21no—
42#461×C89C2211yescharacteristic
43#461×C89C2211yescharacteristic
44#461×C89C2211yescharacteristic
45#452×C89—21no—
46#452×C89—21no—
47C8×Q8×C89C2211yescharacteristic
48C4×SD16×C89—21no—
49C4×SD16×C89C2211yescharacteristic
50C4×D8×C89C2211yescharacteristic
51#436×C89C2211yescharacteristic
52C8×D4×C89C2211yescharacteristic
53C8×D4×C89C2211yescharacteristic
54#428×C89—21no—
55C2×#106×C89—21no—
56#335×C89C2211yescharacteristic
57#335×C89C2211yescharacteristic
58#333×C89C2211yescharacteristic
59#332×C89C2211yescharacteristic
60#332×C89C2211yescharacteristic
61#332×C89C2211yescharacteristic
62Q8⋊C8×C89C2211yescharacteristic
63D4⋊C8×C89C2211yescharacteristic
64D4⋊C8×C89C2211yescharacteristic
65D4⋊C8×C89C2211yescharacteristic
66#322×C89C2211yescharacteristic
67C2×#41×C89—21no—
68C2×#41×C89—21no—
69#135×C89—44no—
70C2×Q16×C89—21no—
71C2×Q16×C89—21no—
72C2×SD16×C89—21no—
73C2×SD16×C89—21no—
74C2×SD16×C89—21no—
75C2×SD16×C89D411yescharacteristic
76C2×D8×C89D411yescharacteristic
77C2×M16×C89—21no—
78C22×C8×C89—21no—
79C22×C8×C89—21no—
80C4⋊Q8×C89C2311yescharacteristic
81C4⋊Q8×C89C2311yescharacteristic
82C4⋊Q8×C89C2311yescharacteristic
83C4⋊Q8×C89C2311yescharacteristic
84#126×C89—41no—
85#125×C89—21no—
86#124×C89—21no—
87#123×C89—41no—
88#123×C89—41no—
89C22⋊Q8×C89—21no—
90C22⋊Q8×C89—21no—
91C22⋊Q8×C89—21no—
92C22⋊Q8×C89—21no—
93C22⋊Q8×C89—41no—
94#121×C89—21no—
95#121×C89—21no—
96C4×Q8×C89—21no—
97C4×Q8×C89C2311yescharacteristic
98C4×D4×C89—21no—
99C4×D4×C89C2311yescharacteristic
100C4×D4×C89C2311yescharacteristic
101C4×D4×C89C2311yescharacteristic
102#117×C89—21no—
103C2×C4⋊C4×C89—21no—
104C2×C4⋊C4×C89—21no—
105C2×C4⋊C4×C89—21no—
106#107×C89—21no—
107#107×C89—21no—
108#107×C89—21no—
109#107×C89—41no—
110#107×C89D411yescharacteristic
111#106×C89—21no—
112#106×C89—21no—
113#106×C89—21no—
114#106×C89—21no—
115#106×C89—21no—
116#106×C89—21no—
117#106×C89D411yescharacteristic
118C4⋊C8×C89—21no—
119C4⋊C8×C89C2311yescharacteristic
120C4⋊C8×C89C2311yescharacteristic
121C4⋊C8×C89C2311yescharacteristic
122C4⋊C8×C89C2311yescharacteristic
123#103×C89—21no—
124#103×C89—21no—
125#103×C89—21no—
126#103×C89—21no—
127#103×C89—21no—
128#103×C89—21no—
129#103×C89—21no—
130#103×C89—41no—
131#103×C89D411yescharacteristic
132#102×C89—21no—
133#102×C89—21no—
134#102×C89—21no—
135#102×C89D411yescharacteristic
136#102×C89D411yescharacteristic
137#102×C89D411yescharacteristic
138C22⋊C8×C89—21no—
139C22⋊C8×C89—21no—
140C22⋊C8×C89—21no—
141C4×C8×C89—21no—
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144C4×C8×C89C2311yescharacteristic
145#41×C89—42no—
146#41×C89—42no—
147#41×C89—81no—
148#41×C89—81no—
149C2×Q8×C89—21no—
150C2×Q8×C89—21no—
151C2×Q8×C89—21no—
152C2×Q8×C89—21no—
153C2×Q8×C89C2×D411yescharacteristic
154C2×D4×C89—41no—
155C2×D4×C89—41no—
156C2×D4×C89C2×D411yescharacteristic
157C2×D4×C89C2×D411yescharacteristic
158C2×D4×C89C2×D411yescharacteristic
159C22×C4×C89—21no—
160C22×C4×C89—21no—
161C22×C4×C89—21no—
162C22×C4×C89—41no—
163C22×C4×C89—41no—
164C22×C4×C89—41no—
165Q16×C89—42no—
166Q16×C89—81no—
167SD16×C89—22no—
168SD16×C89—42no—
169SD16×C89—42no—
170SD16×C89—42no—
171D8×C89—22no—
172M16×C89—42no—
173C2×C8×C89—21no—
174C2×C8×C89—21no—
175C2×C8×C89—21no—
176C2×C8×C89—21no—
177C2×C8×C89—21no—
178C2×C8×C89—42no—
179C2×C8×C89—42no—
180C2×C8×C89C2×D411yescharacteristic
181C2×C8×C89C2×D411yescharacteristic
182C2×C8×C89C2×D411yescharacteristic
183C2×C8×C89C2×D411yescharacteristic
184C4⋊C4×C89—21no—
185C4⋊C4×C89—21no—
186C4⋊C4×C89—21no—
187C4⋊C4×C89—21no—
188C4⋊C4×C89—21no—
189C4⋊C4×C89—21no—
190C4⋊C4×C89—21no—
191C4⋊C4×C89—21no—
192C4⋊C4×C89—21no—
193C4⋊C4×C89—41no—
194C4⋊C4×C89—41no—
195C4⋊C4×C89—41no—
196C4⋊C4×C89—41no—
197C4⋊C4×C89—41no—
198C4⋊C4×C89C2×D411yescharacteristic
199C4⋊C4×C89C2×D411yescharacteristic
200C4⋊C4×C89C2×D411yescharacteristic
201C4⋊C4×C89C2×D411yescharacteristic
202C22⋊C4×C89—21no—
203C22⋊C4×C89—21no—
204C22⋊C4×C89—21no—
205C22⋊C4×C89—41no—
206C22⋊C4×C89—41no—
207C22⋊C4×C89—41no—
208C22⋊C4×C89—41no—
209C22⋊C4×C89—41no—
210C42×C89—21no—
211C42×C89—41no—
212C42×C89C2411yescharacteristic
213C23×C89—21no—
214C23×C89—21no—
215C23×C89—21no—
216Q8×C89—21no—
217Q8×C89—21no—
218Q8×C89—41no—
219Q8×C89—41no—
220Q8×C89—41no—
221Q8×C89—41no—
222Q8×C89—41no—
223Q8×C89—41no—
224Q8×C89—81no—
225D4×C89—21no—
226D4×C89—21no—
227D4×C89—21no—
228D4×C89—21no—
229D4×C89—21no—
230D4×C89—82no—
231D4×C89—82no—
232D4×C89AGL(1,ℤ/8)12yes—
233C2×C4×C89—21no—
234C2×C4×C89—21no—
235C2×C4×C89—21no—
236C2×C4×C89—21no—
237C2×C4×C89—21no—
238C2×C4×C89—41no—
239C2×C4×C89—41no—
240C2×C4×C89—41no—
241C2×C4×C89—41no—
242C2×C4×C89—41no—
243C2×C4×C89—41no—
244C2×C4×C89—41no—
245C2×C4×C89—41no—
246C2×C4×C89—41no—
247C2×C4×C89—41no—
248C2×C4×C89—82no—
249C2×C4×C89—82no—
250C2×C4×C89—161no—
251C2×C4×C89C22×D411yescharacteristic
252C2×C4×C89C22×D411yescharacteristic
253C2×C4×C89H(5,𝔽2)11yescharacteristic
254C8×C89—21no—
255C8×C89—21no—
256C8×C89—21no—
257C8×C89—41no—
258C8×C89—41no—
259C8×C89—41no—
260C8×C89—41no—
261C8×C89—41no—
262C8×C89#13512yescomplemented
263C22×C89—22no—
264C22×C89—41no—
265C22×C89—41no—
266C22×C89—41no—
267C22×C89—41no—
268C22×C89—41no—
269C22×C89—41no—
270C22×C89—41no—
271C22×C89—41no—
272C22×C89D4211yescharacteristic
273C4×C89—21no—
274C4×C89—41no—
275C4×C89—41no—
276C4×C89—41no—
277C4×C89—41no—
278C4×C89—41no—
279C4×C89—81no—
280C4×C89—81no—
281C4×C89—81no—
282C4×C89—81no—
283C4×C89C2×#13511yescharacteristic
284C4×C89C2×AGL(1,ℤ/8)11yescharacteristic
285C4×C89#57711yescharacteristic
286C4×C89#57811yescharacteristic
287#19860C8911yesmaximal, characteristic, direct product factor, Sylow
288C2×C89—42no—
289C2×C89—81no—
290C2×C89—81no—
291C2×C89#326511yescharacteristic
292C2×C89#328311yescharacteristic
293C2×C89#328911yescharacteristic
294#3360C2×C8911yescharacteristic, complemented
295#3353C2×C8911yescharacteristic, complemented
296#3335C2×C8911yescharacteristic, complemented
297#3283C2×C8911yescharacteristic
298#1723C2×C8911yescharacteristic, complemented
299#1691C2×C8911yescharacteristic, complemented
300#1683C2×C8911yescharacteristic, complemented
301#1673C2×C8911yescharacteristic, complemented
302#1670C2×C8911yescharacteristic, complemented
303#1650C2×C8911yescharacteristic, complemented
304#1647C2×C8911yescharacteristic, complemented
305#1643C2×C8911yescharacteristic, complemented
306#1635C2×C8911yescharacteristic, complemented
307#1581C2×C8911yescharacteristic, complemented
308SD16⋊C8C2×C8911yescharacteristic, complemented
309C89#1986011yescharacteristic, direct product factor, Sylow
310C2×#135—21no—
311#556C22×C8911yescharacteristic
312#554C22×C8911yescharacteristic
313#547C22×C8911yescharacteristic
314#547C22×C8911yescharacteristic
315#500C22×C8911yescharacteristic
316#500C22×C8911yescharacteristic
317#498C22×C8911yescharacteristic
318#494C22×C8911yescharacteristic
319#488—21no—
320#487C22×C8911yescharacteristic
321#487C22×C8911yescharacteristic
322#484—21no—
323#483—21no—
324#482—21no—
325#481—21no—
326#479—21no—
327#476C22×C8911yescharacteristic
328#476C22×C8911yescharacteristic
329#475C22×C8911yescharacteristic
330#475C22×C8911yescharacteristic
331#474C22×C8911yescharacteristic
332#468—21no—
333#467—21no—
334#465—21no—
335#463—21no—
336#461C22×C8911yescharacteristic
337#461C22×C8911yescharacteristic
338#461C22×C8911yescharacteristic
339#452—21no—
340#452—21no—
341C8×Q8C22×C8911yescharacteristic
342C4×SD16—21no—
343C4×SD16C22×C8911yescharacteristic
344C4×D8C22×C8911yescharacteristic
345#436C22×C8911yescharacteristic
346C8×D4C22×C8911yescharacteristic
347C8×D4C22×C8911yescharacteristic
348#428—21no—
349C2×#106—21no—
350#335C22×C8911yescharacteristic
351#335C22×C8911yescharacteristic
352#333C22×C8911yescharacteristic
353#332C22×C8911yescharacteristic
354#332C22×C8911yescharacteristic
355#332C22×C8911yescharacteristic
356Q8⋊C8C22×C8911yescharacteristic
357D4⋊C8C22×C8911yescharacteristic
358D4⋊C8C22×C8911yescharacteristic
359D4⋊C8C22×C8911yescharacteristic
360#322C22×C8911yescharacteristic
361C2×#41—21no—
362C2×#41—21no—
363#135—44no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16D4×C8911yescharacteristic
370C2×D8D4×C8911yescharacteristic
371C2×M16—21no—
372C22×C8—21no—
373C22×C8—21no—
374C4⋊Q8C23×C8911yescharacteristic
375C4⋊Q8C23×C8911yescharacteristic
376C4⋊Q8C23×C8911yescharacteristic
377C4⋊Q8C23×C8911yescharacteristic
378#126—41no—
379#125—21no—
380#124—21no—
381#123—41no—
382#123—41no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—41no—
388#121—21no—
389#121—21no—
390C4×Q8—21no—
391C4×Q8C23×C8911yescharacteristic
392C4×D4—21no—
393C4×D4C23×C8911yescharacteristic
394C4×D4C23×C8911yescharacteristic
395C4×D4C23×C8911yescharacteristic
396#117—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400#107—21no—
401#107—21no—
402#107—21no—
403#107—41no—
404#107D4×C8911yescharacteristic
405#106—21no—
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106D4×C8911yescharacteristic
412C4⋊C8—21no—
413C4⋊C8C23×C8911yescharacteristic
414C4⋊C8C23×C8911yescharacteristic
415C4⋊C8C23×C8911yescharacteristic
416C4⋊C8C23×C8911yescharacteristic
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—41no—
425#103D4×C8911yescharacteristic
426#102—21no—
427#102—21no—
428#102—21no—
429#102D4×C8911yescharacteristic
430#102D4×C8911yescharacteristic
431#102D4×C8911yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C4×C8—21no—
436C4×C8C23×C8911yescharacteristic
437C4×C8C23×C8911yescharacteristic
438C4×C8C23×C8911yescharacteristic
439#41—42no—
440#41—42no—
441#41—81no—
442#41—81no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8C2×D4×C8911yescharacteristic
448C2×D4—41no—
449C2×D4—41no—
450C2×D4C2×D4×C8911yescharacteristic
451C2×D4C2×D4×C8911yescharacteristic
452C2×D4C2×D4×C8911yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—42no—
460Q16—81no—
461SD16—22no—
462SD16—42no—
463SD16—42no—
464SD16—42no—
465D8—22no—
466M16—42no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—42no—
473C2×C8—42no—
474C2×C8C2×D4×C8911yescharacteristic
475C2×C8C2×D4×C8911yescharacteristic
476C2×C8C2×D4×C8911yescharacteristic
477C2×C8C2×D4×C8911yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C8911yescharacteristic
493C4⋊C4C2×D4×C8911yescharacteristic
494C4⋊C4C2×D4×C8911yescharacteristic
495C4⋊C4C2×D4×C8911yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—21no—
505C42—41no—
506C42C24×C8911yescharacteristic
507C23—21no—
508C23—21no—
509C23—21no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—81no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—82no—
525D4—82no—
526D4AGL(1,ℤ/8)×C8912yes—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—161no—
545C2×C4C22×D4×C8911yescharacteristic
546C2×C4C22×D4×C8911yescharacteristic
547C2×C4H(5,𝔽2)×C8911yescharacteristic
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8#135×C8912yescomplemented
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22D42×C8911yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C2×#135×C8911yescharacteristic
578C4C2×AGL(1,ℤ/8)×C8911yescharacteristic
579C4#577×C8911yescharacteristic
580C4#578×C8911yescharacteristic
581C2—42no—
582C2—81no—
583C2—81no—
584C2C89×#326511yescharacteristic
585C2C89×#328311yescharacteristic
586C2C89×#328911yescharacteristic
subgroupG/H
center, socleC22×C89D42
commutator, Frattini, cosocleC42C24×C89
prime radicalC89×#3283C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C89 ◁ C42×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#3360C2semidirect
2. C89×#3353C2semidirect
3. C89×#3335C2semidirect
5. C89×#1723C2semidirect
6. C89×#1691C2semidirect
7. C89×#1683C2semidirect
8. C89×#1673C2semidirect
9. C89×#1670C2semidirect
10. C89×#1650C2semidirect
11. C89×#1647C2semidirect
12. C89×#1643C2semidirect
13. C89×#1635C2semidirect
14. C89×#1581C2semidirect
15. C89×SD16⋊C8C2semidirect
262. C8×C89#135semidirect
287. #19860C89direct (N × H)
294. #3360C2×C89semidirect
295. #3353C2×C89semidirect
296. #3335C2×C89semidirect
298. #1723C2×C89semidirect
299. #1691C2×C89semidirect
300. #1683C2×C89semidirect
301. #1673C2×C89semidirect
302. #1670C2×C89semidirect
303. #1650C2×C89semidirect
304. #1647C2×C89semidirect
305. #1643C2×C89semidirect
306. #1635C2×C89semidirect
307. #1581C2×C89semidirect
308. SD16⋊C8C2×C89semidirect
309. C89#19860direct (N × H)
556. C8#135×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#33602
C89×#33532
C89×#33352
C89×#32832
C89×#17232
C89×#16912
C89×#16832
C89×#16732
C89×#16702
C89×#16502
C89×#16472
C89×#16432
C89×#16352
C89×#15812
C89×SD16⋊C82
#1986089