Finite Group Databasebeta

← C89×#19781 #36397629

Subgroups — C89×#19781 #36397629

Order 22784.

616 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3380C211yesmaximal, characteristic, complemented
2C89×#3358C211yesmaximal, characteristic
3C89×#3333C211yesmaximal, characteristic, complemented
4C89×#3299C211yesmaximal, characteristic, complemented
5C89×#1719C211yesmaximal, characteristic, complemented
6C89×#1703C211yesmaximal, characteristic, complemented
7C89×#1682C211yesmaximal, characteristic, complemented
8C89×#1677C211yesmaximal, characteristic, complemented
9C89×#1676C211yesmaximal, characteristic, complemented
10C89×#1644C211yesmaximal, characteristic, complemented
11C89×#1637C211yesmaximal, characteristic, complemented
12C89×#1631C211yesmaximal, characteristic, complemented
13C89×#1622C211yesmaximal, characteristic, complemented
14C89×#1581C211yesmaximal, characteristic, complemented
15C89×#1579C211yesmaximal, characteristic, complemented
16#554×C89C2211yescharacteristic
17#554×C89C2211yescharacteristic
18#550×C89C2211yescharacteristic
19D4×Q8×C89C2211yescharacteristic
20#500×C89C2211yescharacteristic
21#499×C89—21no—
22#492×C89C2211yescharacteristic
23#487×C89C2211yescharacteristic
24#487×C89C2211yescharacteristic
25#486×C89—21no—
26#486×C89C2211yescharacteristic
27#486×C89C2211yescharacteristic
28#484×C89—21no—
29#480×C89—21no—
30#478×C89—21no—
31#478×C89—21no—
32#477×C89C2211yescharacteristic
33#477×C89C2211yescharacteristic
34#476×C89C2211yescharacteristic
35#476×C89C2211yescharacteristic
36#474×C89—21no—
37#474×C89C2211yescharacteristic
38#468×C89—21no—
39#467×C89—21no—
40#462×C89C2211yescharacteristic
41#460×C89C2211yescharacteristic
42#459×C89—21no—
43#459×C89C2211yescharacteristic
44#452×C89—21no—
45#451×C89—21no—
46C8×Q8×C89C2211yescharacteristic
47C8×Q8×C89C2211yescharacteristic
48C4×Q16×C89C2211yescharacteristic
49C4×D8×C89—21no—
50C4×D8×C89—21no—
51C4×D8×C89C2211yescharacteristic
52#436×C89C2211yescharacteristic
53C8×D4×C89C2211yescharacteristic
54#417×C89—21no—
55C2×#103×C89—21no—
56#335×C89C2211yescharacteristic
57#334×C89C2211yescharacteristic
58#333×C89C2211yescharacteristic
59#333×C89C2211yescharacteristic
60#332×C89C2211yescharacteristic
61#331×C89C2211yescharacteristic
62Q8⋊C8×C89C2211yescharacteristic
63Q8⋊C8×C89C2211yescharacteristic
64D4⋊C8×C89C2211yescharacteristic
65D4⋊C8×C89C2211yescharacteristic
66#322×C89C2211yescharacteristic
67C2×#41×C89—21no—
68C22×Q8×C89—21no—
69C2×Q16×C89—21no—
70C2×Q16×C89D411yescharacteristic
71C2×SD16×C89—21no—
72C2×SD16×C89—41no—
73C2×D8×C89—21no—
74C2×D8×C89D411yescharacteristic
75C2×M16×C89—21no—
76C22×C8×C89—21no—
77C4⋊Q8×C89—21no—
78C4⋊Q8×C89C2311yescharacteristic
79C4⋊Q8×C89C2311yescharacteristic
80C4⋊Q8×C89C2311yescharacteristic
81#127×C89—21no—
82#127×C89C2311yescharacteristic
83#125×C89—21no—
84#125×C89—21no—
85C22⋊Q8×C89—21no—
86C22⋊Q8×C89—21no—
87C22⋊Q8×C89—21no—
88C22⋊Q8×C89—41no—
89C22⋊Q8×C89—41no—
90C22⋊Q8×C89—41no—
91#121×C89—21no—
92#121×C89—41no—
93C4×Q8×C89C2311yescharacteristic
94C4×Q8×C89C2311yescharacteristic
95C4×D4×C89—21no—
96C4×D4×C89—21no—
97C4×D4×C89—21no—
98C4×D4×C89—21no—
99C4×D4×C89C2311yescharacteristic
100C4×D4×C89C2311yescharacteristic
101C2×C4⋊C4×C89—21no—
102C2×C4⋊C4×C89—21no—
103#107×C89—21no—
104#107×C89—21no—
105#107×C89—21no—
106#107×C89—21no—
107#107×C89—21no—
108#107×C89D411yescharacteristic
109#107×C89D411yescharacteristic
110#106×C89—21no—
111#106×C89—21no—
112C4⋊C8×C89—21no—
113C4⋊C8×C89—21no—
114C4⋊C8×C89C2311yescharacteristic
115C4⋊C8×C89C2311yescharacteristic
116C4⋊C8×C89C2311yescharacteristic
117C4⋊C8×C89C2311yescharacteristic
118#103×C89—21no—
119#103×C89—21no—
120#103×C89—21no—
121#103×C89—21no—
122#103×C89—21no—
123#103×C89—41no—
124#103×C89D411yescharacteristic
125#103×C89D411yescharacteristic
126#102×C89—21no—
127#102×C89—21no—
128#102×C89—21no—
129#102×C89—21no—
130#102×C89—21no—
131#102×C89—21no—
132#102×C89—21no—
133#102×C89—21no—
134#102×C89—21no—
135#102×C89D411yescharacteristic
136#102×C89D411yescharacteristic
137C22⋊C8×C89—21no—
138C22⋊C8×C89—21no—
139C4×C8×C89—21no—
140C4×C8×C89—21no—
141C4×C8×C89C2311yescharacteristic
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144#41×C89—42no—
145#41×C89—81no—
146C2×Q8×C89—21no—
147C2×Q8×C89—21no—
148C2×Q8×C89—21no—
149C2×Q8×C89—41no—
150C2×Q8×C89—42no—
151C2×Q8×C89—81no—
152C2×Q8×C89C2×D411yescharacteristic
153C2×Q8×C89C2×D411yescharacteristic
154C2×D4×C89—21no—
155C2×D4×C89—21no—
156C2×D4×C89—21no—
157C2×D4×C89—41no—
158C2×D4×C89—41no—
159C2×D4×C89C2×D411yescharacteristic
160C2×D4×C89C2×D411yescharacteristic
161C22×C4×C89—21no—
162C22×C4×C89—21no—
163C22×C4×C89—41no—
164C22×C4×C89—41no—
165C22×C4×C89—41no—
166C22×C4×C89—41no—
167Q16×C89—22no—
168Q16×C89—81no—
169SD16×C89—81no—
170SD16×C89—82no—
171D8×C89—22no—
172D8×C89—42no—
173M16×C89—81no—
174C2×C8×C89—21no—
175C2×C8×C89—21no—
176C2×C8×C89—21no—
177C2×C8×C89—21no—
178C2×C8×C89—21no—
179C2×C8×C89—81no—
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—41no—
193C4⋊C4×C89—41no—
194C4⋊C4×C89—41no—
195C4⋊C4×C89—41no—
196C4⋊C4×C89—41no—
197C4⋊C4×C89C2×D411yescharacteristic
198C4⋊C4×C89C2×D411yescharacteristic
199C4⋊C4×C89C2×D411yescharacteristic
200C4⋊C4×C89C2×D411yescharacteristic
201C22⋊C4×C89—21no—
202C22⋊C4×C89—21no—
203C22⋊C4×C89—41no—
204C22⋊C4×C89—41no—
205C22⋊C4×C89—41no—
206C22⋊C4×C89—41no—
207C42×C89—21no—
208C42×C89—21no—
209C42×C89C2411yescharacteristic
210C23×C89—21no—
211C23×C89—21no—
212C23×C89—41no—
213Q8×C89—21no—
214Q8×C89—21no—
215Q8×C89—21no—
216Q8×C89—41no—
217Q8×C89—41no—
218Q8×C89—82no—
219Q8×C89—81no—
220Q8×C89—81no—
221Q8×C89#13512yes—
222D4×C89—21no—
223D4×C89—21no—
224D4×C89—21no—
225D4×C89—41no—
226D4×C89—41no—
227D4×C89—41no—
228D4×C89—41no—
229D4×C89—82no—
230D4×C89—81no—
231D4×C89—161no—
232D4×C89#13712yes—
233C2×C4×C89—21no—
234C2×C4×C89—21no—
235C2×C4×C89—21no—
236C2×C4×C89—21no—
237C2×C4×C89—21no—
238C2×C4×C89—21no—
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—82no—
247C2×C4×C89—82no—
248C2×C4×C89—161no—
249C2×C4×C89—161no—
250C2×C4×C89C22×D411yescharacteristic
251C2×C4×C89C22×D411yescharacteristic
252C2×C4×C89H(5,𝔽2)11yescharacteristic
253C8×C89—21no—
254C8×C89—21no—
255C8×C89—21no—
256C8×C89—21no—
257C8×C89—41no—
258C8×C89—41no—
259C8×C89—41no—
260C8×C89—41no—
261C8×C89—41no—
262C22×C89—22no—
263C22×C89—41no—
264C22×C89—41no—
265C22×C89—41no—
266C22×C89—41no—
267C22×C89—41no—
268C22×C89—81no—
269C22×C89—81no—
270C22×C89—81no—
271C22×C89D4211yescharacteristic
272C4×C89—22no—
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×C89C2×#13511yescharacteristic
283C4×C89C2×#13711yescharacteristic
284C4×C89#57611yescharacteristic
285C4×C89#57811yescharacteristic
286#19781C8911yesmaximal, characteristic, direct product factor, Sylow
287C2×C89—42no—
288C2×C89—81no—
289C2×C89—161no—
290C2×C89#327011yescharacteristic
291C2×C89#328011yescharacteristic
292C2×C89#328811yescharacteristic
293#3380C2×C8911yescharacteristic, complemented
294#3358C2×C8911yescharacteristic
295#3333C2×C8911yescharacteristic, complemented
296#3299C2×C8911yescharacteristic, complemented
297#1719C2×C8911yescharacteristic, complemented
298#1703C2×C8911yescharacteristic, complemented
299#1682C2×C8911yescharacteristic, complemented
300#1677C2×C8911yescharacteristic, complemented
301#1676C2×C8911yescharacteristic, complemented
302#1644C2×C8911yescharacteristic, complemented
303#1637C2×C8911yescharacteristic, complemented
304#1631C2×C8911yescharacteristic, complemented
305#1622C2×C8911yescharacteristic, complemented
306#1581C2×C8911yescharacteristic, complemented
307#1579C2×C8911yescharacteristic, complemented
308C89#1978111yescharacteristic, direct product factor, Sylow
309#554C22×C8911yescharacteristic
310#554C22×C8911yescharacteristic
311#550C22×C8911yescharacteristic
312D4×Q8C22×C8911yescharacteristic
313#500C22×C8911yescharacteristic
314#499—21no—
315#492C22×C8911yescharacteristic
316#487C22×C8911yescharacteristic
317#487C22×C8911yescharacteristic
318#486—21no—
319#486C22×C8911yescharacteristic
320#486C22×C8911yescharacteristic
321#484—21no—
322#480—21no—
323#478—21no—
324#478—21no—
325#477C22×C8911yescharacteristic
326#477C22×C8911yescharacteristic
327#476C22×C8911yescharacteristic
328#476C22×C8911yescharacteristic
329#474—21no—
330#474C22×C8911yescharacteristic
331#468—21no—
332#467—21no—
333#462C22×C8911yescharacteristic
334#460C22×C8911yescharacteristic
335#459—21no—
336#459C22×C8911yescharacteristic
337#452—21no—
338#451—21no—
339C8×Q8C22×C8911yescharacteristic
340C8×Q8C22×C8911yescharacteristic
341C4×Q16C22×C8911yescharacteristic
342C4×D8—21no—
343C4×D8—21no—
344C4×D8C22×C8911yescharacteristic
345#436C22×C8911yescharacteristic
346C8×D4C22×C8911yescharacteristic
347#417—21no—
348C2×#103—21no—
349#335C22×C8911yescharacteristic
350#334C22×C8911yescharacteristic
351#333C22×C8911yescharacteristic
352#333C22×C8911yescharacteristic
353#332C22×C8911yescharacteristic
354#331C22×C8911yescharacteristic
355Q8⋊C8C22×C8911yescharacteristic
356Q8⋊C8C22×C8911yescharacteristic
357D4⋊C8C22×C8911yescharacteristic
358D4⋊C8C22×C8911yescharacteristic
359#322C22×C8911yescharacteristic
360C2×#41—21no—
361C22×Q8—21no—
362C2×Q16—21no—
363C2×Q16D4×C8911yescharacteristic
364C2×SD16—21no—
365C2×SD16—41no—
366C2×D8—21no—
367C2×D8D4×C8911yescharacteristic
368C2×M16—21no—
369C22×C8—21no—
370C4⋊Q8—21no—
371C4⋊Q8C23×C8911yescharacteristic
372C4⋊Q8C23×C8911yescharacteristic
373C4⋊Q8C23×C8911yescharacteristic
374#127—21no—
375#127C23×C8911yescharacteristic
376#125—21no—
377#125—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—41no—
382C22⋊Q8—41no—
383C22⋊Q8—41no—
384#121—21no—
385#121—41no—
386C4×Q8C23×C8911yescharacteristic
387C4×Q8C23×C8911yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C23×C8911yescharacteristic
393C4×D4C23×C8911yescharacteristic
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396#107—21no—
397#107—21no—
398#107—21no—
399#107—21no—
400#107—21no—
401#107D4×C8911yescharacteristic
402#107D4×C8911yescharacteristic
403#106—21no—
404#106—21no—
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—41no—
417#103D4×C8911yescharacteristic
418#103D4×C8911yescharacteristic
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102D4×C8911yescharacteristic
429#102D4×C8911yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—21no—
432C4×C8—21no—
433C4×C8—21no—
434C4×C8C23×C8911yescharacteristic
435C4×C8C23×C8911yescharacteristic
436C4×C8C23×C8911yescharacteristic
437#41—42no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—41no—
443C2×Q8—42no—
444C2×Q8—81no—
445C2×Q8C2×D4×C8911yescharacteristic
446C2×Q8C2×D4×C8911yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4C2×D4×C8911yescharacteristic
453C2×D4C2×D4×C8911yescharacteristic
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460Q16—22no—
461Q16—81no—
462SD16—81no—
463SD16—82no—
464D8—22no—
465D8—42no—
466M16—81no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—81no—
473C2×C8C2×D4×C8911yescharacteristic
474C2×C8C2×D4×C8911yescharacteristic
475C2×C8C2×D4×C8911yescharacteristic
476C2×C8C2×D4×C8911yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4C2×D4×C8911yescharacteristic
491C4⋊C4C2×D4×C8911yescharacteristic
492C4⋊C4C2×D4×C8911yescharacteristic
493C4⋊C4C2×D4×C8911yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C42—21no—
501C42—21no—
502C42C24×C8911yescharacteristic
503C23—21no—
504C23—21no—
505C23—41no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—41no—
510Q8—41no—
511Q8—82no—
512Q8—81no—
513Q8—81no—
514Q8#135×C8912yes—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—82no—
523D4—81no—
524D4—161no—
525D4#137×C8912yes—
526C2×C4—21no—
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—82no—
540C2×C4—82no—
541C2×C4—161no—
542C2×C4—161no—
543C2×C4C22×D4×C8911yescharacteristic
544C2×C4C22×D4×C8911yescharacteristic
545C2×C4H(5,𝔽2)×C8911yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C22—22no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22D42×C8911yescharacteristic
565C4—22no—
566C4—21no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×#135×C8911yescharacteristic
576C4C2×#137×C8911yescharacteristic
577C4#576×C8911yescharacteristic
578C4#578×C8911yescharacteristic
579C2—42no—
580C2—81no—
581C2—161no—
582C2C89×#327011yescharacteristic
583C2C89×#328011yescharacteristic
584C2C89×#328811yescharacteristic
subgroupG/H
center, socleC22×C89D42
commutator, Frattini, cosocleC42C24×C89
prime radicalC89×#3358C2
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×#3380C2semidirect
3. C89×#3333C2semidirect
4. C89×#3299C2semidirect
5. C89×#1719C2semidirect
6. C89×#1703C2semidirect
7. C89×#1682C2semidirect
8. C89×#1677C2semidirect
9. C89×#1676C2semidirect
10. C89×#1644C2semidirect
11. C89×#1637C2semidirect
12. C89×#1631C2semidirect
13. C89×#1622C2semidirect
14. C89×#1581C2semidirect
15. C89×#1579C2semidirect
286. #19781C89direct (N × H)
293. #3380C2×C89semidirect
295. #3333C2×C89semidirect
296. #3299C2×C89semidirect
297. #1719C2×C89semidirect
298. #1703C2×C89semidirect
299. #1682C2×C89semidirect
300. #1677C2×C89semidirect
301. #1676C2×C89semidirect
302. #1644C2×C89semidirect
303. #1637C2×C89semidirect
304. #1631C2×C89semidirect
305. #1622C2×C89semidirect
306. #1581C2×C89semidirect
307. #1579C2×C89semidirect
308. C89#19781direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#33802
C89×#33582
C89×#33332
C89×#32992
C89×#17192
C89×#17032
C89×#16822
C89×#16772
C89×#16762
C89×#16442
C89×#16372
C89×#16312
C89×#16222
C89×#15812
C89×#15792
#1978189