Finite Group Databasebeta

← C89×#19857 #36397705

Subgroups — C89×#19857 #36397705

Order 22784.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3400C211yesmaximal, characteristic, complemented
2C89×#3381C211yesmaximal, characteristic, complemented
3C89×#3361C211yesmaximal, characteristic
4C89×#3338C211yesmaximal, characteristic, complemented
5C89×#1714C211yesmaximal, characteristic, complemented
6C89×#1696C211yesmaximal, characteristic, complemented
7C89×#1678C211yesmaximal, characteristic, complemented
8C89×#1672C211yesmaximal, characteristic, complemented
9C89×#1665C211yesmaximal, characteristic
10C89×#1644C211yesmaximal, characteristic, complemented
11C89×#1636C211yesmaximal, characteristic, complemented
12C89×#1630C211yesmaximal, characteristic, complemented
13C89×#1622C211yesmaximal, characteristic
14C89×#1582C211yesmaximal, characteristic, complemented
15C89×#1579C211yesmaximal, characteristic, complemented
16#559×C89C2211yescharacteristic
17#557×C89C2211yescharacteristic
18#554×C89C2211yescharacteristic
19#554×C89C2211yescharacteristic
20#500×C89C2211yescharacteristic
21#499×C89—21no—
22#498×C89C2211yescharacteristic
23#497×C89—21no—
24#492×C89C2211yescharacteristic
25#492×C89C2211yescharacteristic
26#488×C89—21no—
27#487×C89C2211yescharacteristic
28#486×C89C2211yescharacteristic
29#484×C89—21no—
30#484×C89—21no—
31#479×C89—21no—
32#478×C89—21no—
33#478×C89—21no—
34#477×C89C2211yescharacteristic
35#477×C89C2211yescharacteristic
36#477×C89C2211yescharacteristic
37#477×C89C2211yescharacteristic
38#474×C89C2211yescharacteristic
39#467×C89—21no—
40#464×C89—21no—
41#463×C89—21no—
42#462×C89C2211yescharacteristic
43#461×C89—21no—
44#460×C89C2211yescharacteristic
45#459×C89C2211yescharacteristic
46#446×C89C2211yescharacteristic
47C8×Q8×C89C2211yescharacteristic
48C8×Q8×C89C2211yescharacteristic
49#440×C89—21no—
50C4×Q16×C89C2211yescharacteristic
51C4×SD16×C89—21no—
52C4×SD16×C89C2211yescharacteristic
53C4×D8×C89—21no—
54C8×D4×C89C2211yescharacteristic
55C2×#107×C89—21no—
56#334×C89C2211yescharacteristic
57#334×C89C2211yescharacteristic
58#333×C89C2211yescharacteristic
59#333×C89C2211yescharacteristic
60#332×C89C2211yescharacteristic
61#331×C89C2211yescharacteristic
62Q8⋊C8×C89C2211yescharacteristic
63Q8⋊C8×C89C2211yescharacteristic
64Q8⋊C8×C89C2211yescharacteristic
65D4⋊C8×C89C2211yescharacteristic
66#322×C89C2211yescharacteristic
67C2×Q16×C89—21no—
68C2×Q16×C89D411yescharacteristic
69C2×SD16×C89—21no—
70C2×SD16×C89—21no—
71C2×SD16×C89—21no—
72C2×SD16×C89—41no—
73C2×SD16×C89D411yescharacteristic
74C2×D8×C89—21no—
75C22×C8×C89—21no—
76C4⋊Q8×C89—21no—
77C4⋊Q8×C89C2311yescharacteristic
78C4⋊Q8×C89C2311yescharacteristic
79C4⋊Q8×C89C2311yescharacteristic
80#127×C89C2311yescharacteristic
81#125×C89—21no—
82#125×C89—21no—
83#125×C89—21no—
84#125×C89—41no—
85#124×C89—21no—
86#124×C89—21no—
87#123×C89—41no—
88C22⋊Q8×C89—21no—
89C22⋊Q8×C89—21no—
90C22⋊Q8×C89—41no—
91C22⋊Q8×C89—41no—
92C4×Q8×C89—21no—
93C4×Q8×C89—21no—
94C4×Q8×C89C2311yescharacteristic
95C4×Q8×C89C2311yescharacteristic
96C4×Q8×C89C2311yescharacteristic
97C4×D4×C89—21no—
98C4×D4×C89—21no—
99C4×D4×C89—21no—
100C4×D4×C89—21no—
101C4×D4×C89C2311yescharacteristic
102C2×C4⋊C4×C89—21no—
103C2×C4⋊C4×C89—21no—
104#107×C89—21no—
105#107×C89—21no—
106#107×C89—21no—
107#107×C89—21no—
108#107×C89—21no—
109#107×C89—21no—
110#107×C89—21no—
111#107×C89D411yescharacteristic
112#106×C89—21no—
113#106×C89—21no—
114#106×C89D411yescharacteristic
115C4⋊C8×C89—21no—
116C4⋊C8×C89—21no—
117C4⋊C8×C89—21no—
118C4⋊C8×C89C2311yescharacteristic
119C4⋊C8×C89C2311yescharacteristic
120C4⋊C8×C89C2311yescharacteristic
121C4⋊C8×C89C2311yescharacteristic
122#103×C89—21no—
123#103×C89—21no—
124#103×C89—21no—
125#103×C89—21no—
126#103×C89—21no—
127#103×C89—41no—
128#103×C89D411yescharacteristic
129#103×C89D411yescharacteristic
130#103×C89D411yescharacteristic
131#102×C89—21no—
132#102×C89—21no—
133#102×C89—21no—
134#102×C89—21no—
135#102×C89—21no—
136#102×C89D411yescharacteristic
137C22⋊C8×C89—21no—
138#97×C89—21no—
139C4×C8×C89—21no—
140C4×C8×C89—21no—
141C4×C8×C89C2311yescharacteristic
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144C2×Q8×C89—21no—
145C2×Q8×C89—21no—
146C2×Q8×C89—21no—
147C2×Q8×C89C2×D411yescharacteristic
148C2×Q8×C89C2×D411yescharacteristic
149C2×Q8×C89C2×D411yescharacteristic
150C2×D4×C89—21no—
151C2×D4×C89—21no—
152C2×D4×C89—21no—
153C2×D4×C89C2×D411yescharacteristic
154C22×C4×C89—21no—
155C22×C4×C89—41no—
156C22×C4×C89—41no—
157C22×C4×C89—41no—
158Q16×C89—22no—
159Q16×C89—81no—
160SD16×C89—22no—
161SD16×C89—42no—
162SD16×C89—81no—
163SD16×C89—81no—
164SD16×C89—82no—
165D8×C89—42no—
166C2×C8×C89—21no—
167C2×C8×C89—21no—
168C2×C8×C89—21no—
169C2×C8×C89—21no—
170C2×C8×C89—21no—
171C2×C8×C89—42no—
172C2×C8×C89C2×D411yescharacteristic
173C2×C8×C89C2×D411yescharacteristic
174C2×C8×C89C2×D411yescharacteristic
175C2×C8×C89C2×D411yescharacteristic
176C4⋊C4×C89—21no—
177C4⋊C4×C89—21no—
178C4⋊C4×C89—21no—
179C4⋊C4×C89—21no—
180C4⋊C4×C89—21no—
181C4⋊C4×C89—21no—
182C4⋊C4×C89—21no—
183C4⋊C4×C89—21no—
184C4⋊C4×C89—21no—
185C4⋊C4×C89—41no—
186C4⋊C4×C89—41no—
187C4⋊C4×C89—41no—
188C4⋊C4×C89—41no—
189C4⋊C4×C89—41no—
190C4⋊C4×C89—41no—
191C4⋊C4×C89—41no—
192C4⋊C4×C89C2×D411yescharacteristic
193C4⋊C4×C89C2×D411yescharacteristic
194C4⋊C4×C89C2×D411yescharacteristic
195C4⋊C4×C89C2×D411yescharacteristic
196C22⋊C4×C89—21no—
197C22⋊C4×C89—41no—
198C22⋊C4×C89—41no—
199C22⋊C4×C89—41no—
200C22⋊C4×C89—41no—
201C22⋊C4×C89—41no—
202C42×C89—21no—
203C42×C89—21no—
204C42×C89—21no—
205C42×C89—41no—
206C42×C89C2411yescharacteristic
207C23×C89—21no—
208C23×C89—41no—
209Q8×C89—21no—
210Q8×C89—21no—
211Q8×C89—21no—
212Q8×C89—21no—
213Q8×C89—21no—
214Q8×C89—21no—
215Q8×C89—41no—
216Q8×C89—41no—
217Q8×C89—81no—
218Q8×C89—81no—
219D4×C89—21no—
220D4×C89—41no—
221D4×C89—41no—
222D4×C89—41no—
223D4×C89—41no—
224D4×C89—81no—
225D4×C89#13712yes—
226C2×C4×C89—21no—
227C2×C4×C89—21no—
228C2×C4×C89—21no—
229C2×C4×C89—21no—
230C2×C4×C89—21no—
231C2×C4×C89—21no—
232C2×C4×C89—21no—
233C2×C4×C89—41no—
234C2×C4×C89—41no—
235C2×C4×C89—41no—
236C2×C4×C89—41no—
237C2×C4×C89—41no—
238C2×C4×C89—161no—
239C2×C4×C89—161no—
240C2×C4×C89—161no—
241C2×C4×C89C22×D411yescharacteristic
242C2×C4×C89C22×D411yescharacteristic
243C2×C4×C89H(5,𝔽2)11yescharacteristic
244C8×C89—21no—
245C8×C89—21no—
246C8×C89—21no—
247C8×C89—41no—
248C8×C89—41no—
249C8×C89—41no—
250C8×C89—41no—
251C8×C89—41no—
252C8×C89#13512yes—
253C22×C89—22no—
254C22×C89—41no—
255C22×C89—41no—
256C22×C89—81no—
257C22×C89—81no—
258C22×C89—81no—
259C22×C89D4211yescharacteristic
260C4×C89—21no—
261C4×C89—41no—
262C4×C89—41no—
263C4×C89—41no—
264C4×C89—41no—
265C4×C89—41no—
266C4×C89—41no—
267C4×C89—41no—
268C4×C89—81no—
269C4×C89—81no—
270C4×C89—81no—
271C4×C89C2×#13511yescharacteristic
272C4×C89C2×#13711yescharacteristic
273C4×C89#57711yescharacteristic
274C4×C89#57811yescharacteristic
275#19857C8911yesmaximal, characteristic, direct product factor, Sylow
276C2×C89—42no—
277C2×C89—161no—
278C2×C89#327011yescharacteristic
279C2×C89#328411yescharacteristic
280C2×C89#328811yescharacteristic
281#3400C2×C8911yescharacteristic, complemented
282#3381C2×C8911yescharacteristic, complemented
283#3361C2×C8911yescharacteristic
284#3338C2×C8911yescharacteristic, complemented
285#1714C2×C8911yescharacteristic, complemented
286#1696C2×C8911yescharacteristic, complemented
287#1678C2×C8911yescharacteristic, complemented
288#1672C2×C8911yescharacteristic, complemented
289#1665C2×C8911yescharacteristic
290#1644C2×C8911yescharacteristic, complemented
291#1636C2×C8911yescharacteristic, complemented
292#1630C2×C8911yescharacteristic, complemented
293#1622C2×C8911yescharacteristic
294#1582C2×C8911yescharacteristic, complemented
295#1579C2×C8911yescharacteristic, complemented
296C89#1985711yescharacteristic, direct product factor, Sylow
297#559C22×C8911yescharacteristic
298#557C22×C8911yescharacteristic
299#554C22×C8911yescharacteristic
300#554C22×C8911yescharacteristic
301#500C22×C8911yescharacteristic
302#499—21no—
303#498C22×C8911yescharacteristic
304#497—21no—
305#492C22×C8911yescharacteristic
306#492C22×C8911yescharacteristic
307#488—21no—
308#487C22×C8911yescharacteristic
309#486C22×C8911yescharacteristic
310#484—21no—
311#484—21no—
312#479—21no—
313#478—21no—
314#478—21no—
315#477C22×C8911yescharacteristic
316#477C22×C8911yescharacteristic
317#477C22×C8911yescharacteristic
318#477C22×C8911yescharacteristic
319#474C22×C8911yescharacteristic
320#467—21no—
321#464—21no—
322#463—21no—
323#462C22×C8911yescharacteristic
324#461—21no—
325#460C22×C8911yescharacteristic
326#459C22×C8911yescharacteristic
327#446C22×C8911yescharacteristic
328C8×Q8C22×C8911yescharacteristic
329C8×Q8C22×C8911yescharacteristic
330#440—21no—
331C4×Q16C22×C8911yescharacteristic
332C4×SD16—21no—
333C4×SD16C22×C8911yescharacteristic
334C4×D8—21no—
335C8×D4C22×C8911yescharacteristic
336C2×#107—21no—
337#334C22×C8911yescharacteristic
338#334C22×C8911yescharacteristic
339#333C22×C8911yescharacteristic
340#333C22×C8911yescharacteristic
341#332C22×C8911yescharacteristic
342#331C22×C8911yescharacteristic
343Q8⋊C8C22×C8911yescharacteristic
344Q8⋊C8C22×C8911yescharacteristic
345Q8⋊C8C22×C8911yescharacteristic
346D4⋊C8C22×C8911yescharacteristic
347#322C22×C8911yescharacteristic
348C2×Q16—21no—
349C2×Q16D4×C8911yescharacteristic
350C2×SD16—21no—
351C2×SD16—21no—
352C2×SD16—21no—
353C2×SD16—41no—
354C2×SD16D4×C8911yescharacteristic
355C2×D8—21no—
356C22×C8—21no—
357C4⋊Q8—21no—
358C4⋊Q8C23×C8911yescharacteristic
359C4⋊Q8C23×C8911yescharacteristic
360C4⋊Q8C23×C8911yescharacteristic
361#127C23×C8911yescharacteristic
362#125—21no—
363#125—21no—
364#125—21no—
365#125—41no—
366#124—21no—
367#124—21no—
368#123—41no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—41no—
372C22⋊Q8—41no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C23×C8911yescharacteristic
376C4×Q8C23×C8911yescharacteristic
377C4×Q8C23×C8911yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C23×C8911yescharacteristic
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#107D4×C8911yescharacteristic
393#106—21no—
394#106—21no—
395#106D4×C8911yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C8911yescharacteristic
400C4⋊C8C23×C8911yescharacteristic
401C4⋊C8C23×C8911yescharacteristic
402C4⋊C8C23×C8911yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—41no—
409#103D4×C8911yescharacteristic
410#103D4×C8911yescharacteristic
411#103D4×C8911yescharacteristic
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102D4×C8911yescharacteristic
418C22⋊C8—21no—
419#97—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8C23×C8911yescharacteristic
423C4×C8C23×C8911yescharacteristic
424C4×C8C23×C8911yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C2×D4×C8911yescharacteristic
429C2×Q8C2×D4×C8911yescharacteristic
430C2×Q8C2×D4×C8911yescharacteristic
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4C2×D4×C8911yescharacteristic
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439Q16—22no—
440Q16—81no—
441SD16—22no—
442SD16—42no—
443SD16—81no—
444SD16—81no—
445SD16—82no—
446D8—42no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8C2×D4×C8911yescharacteristic
454C2×C8C2×D4×C8911yescharacteristic
455C2×C8C2×D4×C8911yescharacteristic
456C2×C8C2×D4×C8911yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4C2×D4×C8911yescharacteristic
474C4⋊C4C2×D4×C8911yescharacteristic
475C4⋊C4C2×D4×C8911yescharacteristic
476C4⋊C4C2×D4×C8911yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—41no—
487C42C24×C8911yescharacteristic
488C23—21no—
489C23—41no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—81no—
500D4—21no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—81no—
506D4#137×C8912yes—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—161no—
520C2×C4—161no—
521C2×C4—161no—
522C2×C4C22×D4×C8911yescharacteristic
523C2×C4C22×D4×C8911yescharacteristic
524C2×C4H(5,𝔽2)×C8911yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8#135×C8912yes—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22D42×C8911yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×#135×C8911yescharacteristic
553C4C2×#137×C8911yescharacteristic
554C4#577×C8911yescharacteristic
555C4#578×C8911yescharacteristic
556C2—42no—
557C2—161no—
558C2C89×#327011yescharacteristic
559C2C89×#328411yescharacteristic
560C2C89×#328811yescharacteristic
subgroupG/H
center, socleC22×C89D42
commutator, Frattini, cosocleC42C24×C89
prime radical#459×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×#3400C2semidirect
2. C89×#3381C2semidirect
4. C89×#3338C2semidirect
5. C89×#1714C2semidirect
6. C89×#1696C2semidirect
7. C89×#1678C2semidirect
8. C89×#1672C2semidirect
10. C89×#1644C2semidirect
11. C89×#1636C2semidirect
12. C89×#1630C2semidirect
14. C89×#1582C2semidirect
15. C89×#1579C2semidirect
275. #19857C89direct (N × H)
281. #3400C2×C89semidirect
282. #3381C2×C89semidirect
284. #3338C2×C89semidirect
285. #1714C2×C89semidirect
286. #1696C2×C89semidirect
287. #1678C2×C89semidirect
288. #1672C2×C89semidirect
290. #1644C2×C89semidirect
291. #1636C2×C89semidirect
292. #1630C2×C89semidirect
294. #1582C2×C89semidirect
295. #1579C2×C89semidirect
296. C89#19857direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#34002
C89×#33812
C89×#33612
C89×#33382
C89×#17142
C89×#16962
C89×#16782
C89×#16722
C89×#16652
C89×#16442
C89×#16362
C89×#16302
C89×#16222
C89×#15822
C89×#15792
#1985789