Finite Group Databasebeta

← C89×#19808 #36397656

Subgroups — C89×#19808 #36397656

Order 22784.

624 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3381C211yesmaximal, characteristic, complemented
2C89×#3359C211yesmaximal, characteristic, complemented
3C89×#3335C211yesmaximal, characteristic
4C89×#3276C211yesmaximal, characteristic
5C89×#1716C211yesmaximal, characteristic, complemented
6C89×#1691C211yesmaximal, characteristic, complemented
7C89×#1679C211yesmaximal, characteristic, complemented
8C89×#1672C211yesmaximal, characteristic, complemented
9C89×#1670C211yesmaximal, characteristic, complemented
10C89×#1654C211yesmaximal, characteristic
11C89×#1653C211yesmaximal, characteristic, complemented
12C89×#1643C211yesmaximal, characteristic, complemented
13C89×#1637C211yesmaximal, characteristic, complemented
14C89×#1583C211yesmaximal, characteristic, complemented
15C89×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#137×C89—21no—
17#557×C89C2211yescharacteristic
18#554×C89C2211yescharacteristic
19D4×Q8×C89C2211yescharacteristic
20#547×C89C2211yescharacteristic
21#499×C89—21no—
22#498×C89C2211yescharacteristic
23#498×C89C2211yescharacteristic
24#498×C89C2211yescharacteristic
25#494×C89C2211yescharacteristic
26#487×C89—21no—
27#487×C89C2211yescharacteristic
28#487×C89C2211yescharacteristic
29#483×C89—21no—
30#481×C89—21no—
31#479×C89—21no—
32#478×C89—21no—
33#477×C89C2211yescharacteristic
34#476×C89C2211yescharacteristic
35#475×C89—21no—
36#475×C89C2211yescharacteristic
37#475×C89C2211yescharacteristic
38#474×C89C2211yescharacteristic
39#470×C89—21no—
40#465×C89—21no—
41#462×C89C2211yescharacteristic
42#461×C89—21no—
43#461×C89C2211yescharacteristic
44#461×C89C2211yescharacteristic
45#452×C89—21no—
46#451×C89—21no—
47C8×Q8×C89C2211yescharacteristic
48C8×Q8×C89C2211yescharacteristic
49C4×SD16×C89—21no—
50C4×SD16×C89—21no—
51C4×SD16×C89C2211yescharacteristic
52C4×SD16×C89C2211yescharacteristic
53#436×C89C2211yescharacteristic
54C8×D4×C89C2211yescharacteristic
55C2×#106×C89—21no—
56#335×C89C2211yescharacteristic
57#334×C89C2211yescharacteristic
58#333×C89C2211yescharacteristic
59#332×C89C2211yescharacteristic
60#332×C89C2211yescharacteristic
61#332×C89C2211yescharacteristic
62Q8⋊C8×C89C2211yescharacteristic
63Q8⋊C8×C89C2211yescharacteristic
64D4⋊C8×C89C2211yescharacteristic
65D4⋊C8×C89C2211yescharacteristic
66#322×C89C2211yescharacteristic
67C2×#41×C89—21no—
68C22×Q8×C89—21no—
69#137×C89—44no—
70C2×Q16×C89—21no—
71C2×Q16×C89—21no—
72C2×Q16×C89—21no—
73C2×SD16×C89—21no—
74C2×SD16×C89—21no—
75C2×SD16×C89D411yescharacteristic
76C2×SD16×C89D411yescharacteristic
77C2×M16×C89—21no—
78C22×C8×C89—21no—
79C4⋊Q8×C89—21no—
80C4⋊Q8×C89—21no—
81C4⋊Q8×C89C2311yescharacteristic
82C4⋊Q8×C89C2311yescharacteristic
83C4⋊Q8×C89C2311yescharacteristic
84C4⋊Q8×C89C2311yescharacteristic
85#125×C89—21no—
86#125×C89—21no—
87#125×C89—41no—
88#123×C89—41no—
89C22⋊Q8×C89—21no—
90C22⋊Q8×C89—21no—
91C22⋊Q8×C89—21no—
92C22⋊Q8×C89—41no—
93C22⋊Q8×C89—41no—
94#121×C89—21no—
95C4×Q8×C89—21no—
96C4×Q8×C89—21no—
97C4×Q8×C89C2311yescharacteristic
98C4×Q8×C89C2311yescharacteristic
99C4×D4×C89—21no—
100C4×D4×C89—21no—
101C4×D4×C89C2311yescharacteristic
102C4×D4×C89C2311yescharacteristic
103C2×C4⋊C4×C89—21no—
104C2×C4⋊C4×C89—21no—
105#107×C89—21no—
106#107×C89—21no—
107#106×C89—21no—
108#106×C89—21no—
109#106×C89—21no—
110#106×C89—21no—
111#106×C89—21no—
112#106×C89—21no—
113#106×C89—21no—
114#106×C89—41no—
115#106×C89D411yescharacteristic
116#106×C89D411yescharacteristic
117C4⋊C8×C89—21no—
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—21no—
131#103×C89—41no—
132#103×C89D411yescharacteristic
133#103×C89D411yescharacteristic
134#102×C89—21no—
135#102×C89—21no—
136#102×C89D411yescharacteristic
137#102×C89D411yescharacteristic
138C22⋊C8×C89—21no—
139C22⋊C8×C89—21no—
140C4×C8×C89—21no—
141C4×C8×C89—21no—
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144C4×C8×C89C2311yescharacteristic
145#41×C89—42no—
146#41×C89—81no—
147C2×Q8×C89—21no—
148C2×Q8×C89—21no—
149C2×Q8×C89—21no—
150C2×Q8×C89—21no—
151C2×Q8×C89—41no—
152C2×Q8×C89—42no—
153C2×Q8×C89—81no—
154C2×Q8×C89C2×D411yescharacteristic
155C2×Q8×C89C2×D411yescharacteristic
156C2×D4×C89—41no—
157C2×D4×C89C2×D411yescharacteristic
158C2×D4×C89C2×D411yescharacteristic
159C22×C4×C89—21no—
160C22×C4×C89—21no—
161C22×C4×C89—41no—
162C22×C4×C89—41no—
163C22×C4×C89—41no—
164Q16×C89—42no—
165Q16×C89—42no—
166Q16×C89—81no—
167SD16×C89—41no—
168SD16×C89—42no—
169SD16×C89—42no—
170SD16×C89SD1614yescomplemented
171M16×C89—42no—
172C2×C8×C89—21no—
173C2×C8×C89—21no—
174C2×C8×C89—21no—
175C2×C8×C89—21no—
176C2×C8×C89—21no—
177C2×C8×C89—42no—
178C2×C8×C89C2×D411yescharacteristic
179C2×C8×C89C2×D411yescharacteristic
180C2×C8×C89C2×D411yescharacteristic
181C2×C8×C89C2×D411yescharacteristic
182C4⋊C4×C89—21no—
183C4⋊C4×C89—21no—
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—41no—
193C4⋊C4×C89—41no—
194C4⋊C4×C89—41no—
195C4⋊C4×C89—41no—
196C4⋊C4×C89—41no—
197C4⋊C4×C89—41no—
198C4⋊C4×C89—41no—
199C4⋊C4×C89C2×D411yescharacteristic
200C4⋊C4×C89C2×D411yescharacteristic
201C4⋊C4×C89C2×D411yescharacteristic
202C4⋊C4×C89C2×D411yescharacteristic
203C22⋊C4×C89—21no—
204C22⋊C4×C89—21no—
205C22⋊C4×C89—41no—
206C22⋊C4×C89—41no—
207C22⋊C4×C89—41no—
208C42×C89—21no—
209C42×C89—21no—
210C42×C89—41no—
211C42×C89C2411yescharacteristic
212C23×C89—21no—
213C23×C89—21no—
214Q8×C89—21no—
215Q8×C89—21no—
216Q8×C89—21no—
217Q8×C89—41no—
218Q8×C89—41no—
219Q8×C89—41no—
220Q8×C89—41no—
221Q8×C89—41no—
222Q8×C89—41no—
223Q8×C89—82no—
224Q8×C89—81no—
225Q8×C89C2×SD1612yes—
226D4×C89—21no—
227D4×C89—21no—
228D4×C89—21no—
229D4×C89—82no—
230D4×C89C2×SD1612yes—
231C2×C4×C89—21no—
232C2×C4×C89—21no—
233C2×C4×C89—21no—
234C2×C4×C89—21no—
235C2×C4×C89—21no—
236C2×C4×C89—21no—
237C2×C4×C89—41no—
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—82no—
246C2×C4×C89—82no—
247C2×C4×C89—161no—
248C2×C4×C89C22×D411yescharacteristic
249C2×C4×C89C22×D411yescharacteristic
250C2×C4×C89H(5,𝔽2)11yescharacteristic
251C8×C89—21no—
252C8×C89—21no—
253C8×C89—21no—
254C8×C89—41no—
255C8×C89—41no—
256C8×C89—41no—
257C8×C89—41no—
258C8×C89—41no—
259C8×C89C2×SD1612yes—
260C22×C89—22no—
261C22×C89—41no—
262C22×C89—41no—
263C22×C89—41no—
264C22×C89—41no—
265C22×C89—41no—
266C22×C89D4211yescharacteristic
267C4×C89—22no—
268C4×C89—21no—
269C4×C89—41no—
270C4×C89—41no—
271C4×C89—41no—
272C4×C89—41no—
273C4×C89—41no—
274C4×C89—81no—
275C4×C89—81no—
276C4×C89—81no—
277C4×C89—81no—
278C4×C89C22×SD1611yescharacteristic
279C4×C89#57511yescharacteristic
280C4×C89#57711yescharacteristic
281C4×C89#57811yescharacteristic
282#19808C8911yesmaximal, characteristic, direct product factor, Sylow
283C2×C89—42no—
284C2×C89—81no—
285C2×C89#326911yescharacteristic
286C2×C89D4×SD1611yescharacteristic
287C2×C89#328911yescharacteristic
288#3381C2×C8911yescharacteristic, complemented
289#3359C2×C8911yescharacteristic, complemented
290#3335C2×C8911yescharacteristic
291#3276C2×C8911yescharacteristic
292#1716C2×C8911yescharacteristic, complemented
293#1691C2×C8911yescharacteristic, complemented
294#1679C2×C8911yescharacteristic, complemented
295#1672C2×C8911yescharacteristic, complemented
296#1670C2×C8911yescharacteristic, complemented
297#1654C2×C8911yescharacteristic
298#1653C2×C8911yescharacteristic, complemented
299#1643C2×C8911yescharacteristic, complemented
300#1637C2×C8911yescharacteristic, complemented
301#1583C2×C8911yescharacteristic, complemented
302SD16⋊C8C2×C8911yescharacteristic, complemented
303C89#1980811yescharacteristic, direct product factor, Sylow
304C2×#137—21no—
305#557C22×C8911yescharacteristic
306#554C22×C8911yescharacteristic
307D4×Q8C22×C8911yescharacteristic
308#547C22×C8911yescharacteristic
309#499—21no—
310#498C22×C8911yescharacteristic
311#498C22×C8911yescharacteristic
312#498C22×C8911yescharacteristic
313#494C22×C8911yescharacteristic
314#487—21no—
315#487C22×C8911yescharacteristic
316#487C22×C8911yescharacteristic
317#483—21no—
318#481—21no—
319#479—21no—
320#478—21no—
321#477C22×C8911yescharacteristic
322#476C22×C8911yescharacteristic
323#475—21no—
324#475C22×C8911yescharacteristic
325#475C22×C8911yescharacteristic
326#474C22×C8911yescharacteristic
327#470—21no—
328#465—21no—
329#462C22×C8911yescharacteristic
330#461—21no—
331#461C22×C8911yescharacteristic
332#461C22×C8911yescharacteristic
333#452—21no—
334#451—21no—
335C8×Q8C22×C8911yescharacteristic
336C8×Q8C22×C8911yescharacteristic
337C4×SD16—21no—
338C4×SD16—21no—
339C4×SD16C22×C8911yescharacteristic
340C4×SD16C22×C8911yescharacteristic
341#436C22×C8911yescharacteristic
342C8×D4C22×C8911yescharacteristic
343C2×#106—21no—
344#335C22×C8911yescharacteristic
345#334C22×C8911yescharacteristic
346#333C22×C8911yescharacteristic
347#332C22×C8911yescharacteristic
348#332C22×C8911yescharacteristic
349#332C22×C8911yescharacteristic
350Q8⋊C8C22×C8911yescharacteristic
351Q8⋊C8C22×C8911yescharacteristic
352D4⋊C8C22×C8911yescharacteristic
353D4⋊C8C22×C8911yescharacteristic
354#322C22×C8911yescharacteristic
355C2×#41—21no—
356C22×Q8—21no—
357#137—44no—
358C2×Q16—21no—
359C2×Q16—21no—
360C2×Q16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16D4×C8911yescharacteristic
364C2×SD16D4×C8911yescharacteristic
365C2×M16—21no—
366C22×C8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8C23×C8911yescharacteristic
370C4⋊Q8C23×C8911yescharacteristic
371C4⋊Q8C23×C8911yescharacteristic
372C4⋊Q8C23×C8911yescharacteristic
373#125—21no—
374#125—21no—
375#125—41no—
376#123—41no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—41no—
381C22⋊Q8—41no—
382#121—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C23×C8911yescharacteristic
386C4×Q8C23×C8911yescharacteristic
387C4×D4—21no—
388C4×D4—21no—
389C4×D4C23×C8911yescharacteristic
390C4×D4C23×C8911yescharacteristic
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393#107—21no—
394#107—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402#106—41no—
403#106D4×C8911yescharacteristic
404#106D4×C8911yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C8911yescharacteristic
408C4⋊C8C23×C8911yescharacteristic
409C4⋊C8C23×C8911yescharacteristic
410C4⋊C8C23×C8911yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—41no—
420#103D4×C8911yescharacteristic
421#103D4×C8911yescharacteristic
422#102—21no—
423#102—21no—
424#102D4×C8911yescharacteristic
425#102D4×C8911yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428C4×C8—21no—
429C4×C8—21no—
430C4×C8C23×C8911yescharacteristic
431C4×C8C23×C8911yescharacteristic
432C4×C8C23×C8911yescharacteristic
433#41—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—42no—
441C2×Q8—81no—
442C2×Q8C2×D4×C8911yescharacteristic
443C2×Q8C2×D4×C8911yescharacteristic
444C2×D4—41no—
445C2×D4C2×D4×C8911yescharacteristic
446C2×D4C2×D4×C8911yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452Q16—42no—
453Q16—42no—
454Q16—81no—
455SD16—41no—
456SD16—42no—
457SD16—42no—
458SD16SD16×C8914yescomplemented
459M16—42no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—42no—
466C2×C8C2×D4×C8911yescharacteristic
467C2×C8C2×D4×C8911yescharacteristic
468C2×C8C2×D4×C8911yescharacteristic
469C2×C8C2×D4×C8911yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4C2×D4×C8911yescharacteristic
488C4⋊C4C2×D4×C8911yescharacteristic
489C4⋊C4C2×D4×C8911yescharacteristic
490C4⋊C4C2×D4×C8911yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—21no—
497C42—21no—
498C42—41no—
499C42C24×C8911yescharacteristic
500C23—21no—
501C23—21no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—82no—
512Q8—81no—
513Q8C2×SD16×C8912yes—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—82no—
518D4C2×SD16×C8912yes—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—161no—
536C2×C4C22×D4×C8911yescharacteristic
537C2×C4C22×D4×C8911yescharacteristic
538C2×C4H(5,𝔽2)×C8911yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8C2×SD16×C8912yes—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22D42×C8911yescharacteristic
555C4—22no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4C22×SD16×C8911yescharacteristic
567C4#575×C8911yescharacteristic
568C4#577×C8911yescharacteristic
569C4#578×C8911yescharacteristic
570C2—42no—
571C2—81no—
572C2C89×#326911yescharacteristic
573C2D4×SD16×C8911yescharacteristic
574C2C89×#328911yescharacteristic
subgroupG/H
center, socleC22×C89D42
commutator, Frattini, cosocleC42C24×C89
prime radical#547×C89C22
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×#3381C2semidirect
2. C89×#3359C2semidirect
5. C89×#1716C2semidirect
6. C89×#1691C2semidirect
7. C89×#1679C2semidirect
8. C89×#1672C2semidirect
9. C89×#1670C2semidirect
11. C89×#1653C2semidirect
12. C89×#1643C2semidirect
13. C89×#1637C2semidirect
14. C89×#1583C2semidirect
15. C89×SD16⋊C8C2semidirect
170. SD16×C89SD16semidirect
282. #19808C89direct (N × H)
288. #3381C2×C89semidirect
289. #3359C2×C89semidirect
292. #1716C2×C89semidirect
293. #1691C2×C89semidirect
294. #1679C2×C89semidirect
295. #1672C2×C89semidirect
296. #1670C2×C89semidirect
298. #1653C2×C89semidirect
299. #1643C2×C89semidirect
300. #1637C2×C89semidirect
301. #1583C2×C89semidirect
302. SD16⋊C8C2×C89semidirect
303. C89#19808direct (N × H)
458. SD16SD16×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#33812
C89×#33592
C89×#33352
C89×#32762
C89×#17162
C89×#16912
C89×#16792
C89×#16722
C89×#16702
C89×#16542
C89×#16532
C89×#16432
C89×#16372
C89×#15832
C89×SD16⋊C82
#1980889