Finite Group Databasebeta

← C89×#19856 #36397704

Subgroups — C89×#19856 #36397704

Order 22784.

570 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3398C211yesmaximal, characteristic, complemented
2C89×#3364C211yesmaximal, characteristic, complemented
3C89×#3340C211yesmaximal, characteristic
4C89×#3340C211yesmaximal, characteristic
5C89×#1716C211yesmaximal, characteristic, complemented
6C89×#1692C211yesmaximal, characteristic, complemented
7C89×#1679C211yesmaximal, characteristic, complemented
8C89×#1672C211yesmaximal, characteristic, complemented
9C89×#1669C211yesmaximal, characteristic, complemented
10C89×#1652C211yesmaximal, characteristic, complemented
11C89×#1652C211yesmaximal, characteristic, complemented
12C89×#1646C211yesmaximal, characteristic
13C89×#1636C211yesmaximal, characteristic, complemented
14C89×#1582C211yesmaximal, characteristic, complemented
15C89×SD16⋊C8C211yesmaximal, characteristic, complemented
16#557×C89C2211yescharacteristic
17#556×C89C2211yescharacteristic
18#556×C89C2211yescharacteristic
19#555×C89C2211yescharacteristic
20#498×C89C2211yescharacteristic
21#498×C89C2211yescharacteristic
22#498×C89C2211yescharacteristic
23#497×C89—21no—
24#494×C89C2211yescharacteristic
25#488×C89—21no—
26#487×C89C2211yescharacteristic
27#487×C89C2211yescharacteristic
28#485×C89—21no—
29#485×C89—21no—
30#482×C89—21no—
31#482×C89—21no—
32#479×C89—21no—
33#477×C89C2211yescharacteristic
34#477×C89C2211yescharacteristic
35#474×C89C2211yescharacteristic
36#474×C89C2211yescharacteristic
37#474×C89C2211yescharacteristic
38#465×C89—21no—
39#465×C89—21no—
40#464×C89—21no—
41#464×C89—21no—
42#462×C89—21no—
43#462×C89C2211yescharacteristic
44#462×C89C2211yescharacteristic
45#461×C89C2211yescharacteristic
46#446×C89C2211yescharacteristic
47C8×Q8×C89C2211yescharacteristic
48#441×C89—21no—
49C4×Q16×C89—21no—
50C4×SD16×C89C2211yescharacteristic
51C4×SD16×C89C2211yescharacteristic
52C8×D4×C89C2211yescharacteristic
53C8×D4×C89C2211yescharacteristic
54#427×C89—21no—
55#427×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×Q16×C89—21no—
68C2×Q16×C89—21no—
69C2×Q16×C89—21no—
70C2×Q16×C89—21no—
71C2×SD16×C89—21no—
72C2×SD16×C89D411yescharacteristic
73C2×SD16×C89D411yescharacteristic
74C22×C8×C89—21no—
75C22×C8×C89—21no—
76C4⋊Q8×C89—21no—
77C4⋊Q8×C89C2311yescharacteristic
78C4⋊Q8×C89C2311yescharacteristic
79C4⋊Q8×C89C2311yescharacteristic
80C4⋊Q8×C89C2311yescharacteristic
81#126×C89—41no—
82#126×C89—41no—
83#125×C89—21no—
84#125×C89—41no—
85#124×C89—21no—
86#124×C89—21no—
87#124×C89—41no—
88C22⋊Q8×C89—21no—
89C22⋊Q8×C89—21no—
90#121×C89—21no—
91#121×C89—21no—
92C4×Q8×C89—21no—
93C4×Q8×C89—21no—
94C4×Q8×C89—21no—
95C4×Q8×C89—21no—
96C4×Q8×C89C2311yescharacteristic
97C4×Q8×C89C2311yescharacteristic
98C4×D4×C89C2311yescharacteristic
99C4×D4×C89C2311yescharacteristic
100#117×C89—21no—
101#117×C89—21no—
102#117×C89—21no—
103#117×C89—21no—
104#107×C89—21no—
105#107×C89—21no—
106#107×C89—21no—
107#107×C89—21no—
108#107×C89—21no—
109#106×C89—21no—
110#106×C89—21no—
111#106×C89—21no—
112#106×C89—21no—
113#106×C89—41no—
114#106×C89D411yescharacteristic
115#106×C89D411yescharacteristic
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—21no—
128#103×C89—21no—
129#103×C89—41no—
130#103×C89D411yescharacteristic
131#103×C89D411yescharacteristic
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—
139#97×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×C89—21no—
148C2×Q8×C89C2×D411yescharacteristic
149C2×Q8×C89C2×D411yescharacteristic
150C2×D4×C89—41no—
151C2×D4×C89C2×D411yescharacteristic
152C2×D4×C89C2×D411yescharacteristic
153C22×C4×C89—21no—
154C22×C4×C89—21no—
155Q16×C89—42no—
156Q16×C89—42no—
157Q16×C89—81no—
158Q16×C89—81no—
159SD16×C89—22no—
160SD16×C89—41no—
161SD16×C89—81no—
162C2×C8×C89—21no—
163C2×C8×C89—21no—
164C2×C8×C89—21no—
165C2×C8×C89—21no—
166C2×C8×C89—21no—
167C2×C8×C89—42no—
168C2×C8×C89—42no—
169C2×C8×C89C2×D411yescharacteristic
170C2×C8×C89C2×D411yescharacteristic
171C2×C8×C89C2×D411yescharacteristic
172C2×C8×C89C2×D411yescharacteristic
173C4⋊C4×C89—21no—
174C4⋊C4×C89—21no—
175C4⋊C4×C89—21no—
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—41no—
184C4⋊C4×C89—41no—
185C4⋊C4×C89—41no—
186C4⋊C4×C89—41no—
187C4⋊C4×C89—41no—
188C4⋊C4×C89C2×D411yescharacteristic
189C4⋊C4×C89C2×D411yescharacteristic
190C4⋊C4×C89C2×D411yescharacteristic
191C4⋊C4×C89C2×D411yescharacteristic
192C22⋊C4×C89—21no—
193C22⋊C4×C89—21no—
194C22⋊C4×C89—41no—
195C22⋊C4×C89—41no—
196C22⋊C4×C89—41no—
197C22⋊C4×C89—41no—
198C22⋊C4×C89—41no—
199C22⋊C4×C89—41no—
200C42×C89—21no—
201C42×C89—21no—
202C42×C89—41no—
203C42×C89—41no—
204C42×C89—41no—
205C42×C89—41no—
206C42×C89C2411yescharacteristic
207C23×C89—21no—
208C23×C89—21no—
209Q8×C89—21no—
210Q8×C89—21no—
211Q8×C89—21no—
212Q8×C89—21no—
213Q8×C89—41no—
214Q8×C89—41no—
215Q8×C89—41no—
216Q8×C89—41no—
217Q8×C89—41no—
218Q8×C89—41no—
219Q8×C89—81no—
220D4×C89—21no—
221D4×C89—21no—
222D4×C89—21no—
223D4×C89—21no—
224D4×C89—161no—
225C2×C4×C89—21no—
226C2×C4×C89—21no—
227C2×C4×C89—21no—
228C2×C4×C89—21no—
229C2×C4×C89—21no—
230C2×C4×C89—21no—
231C2×C4×C89—41no—
232C2×C4×C89—41no—
233C2×C4×C89—41no—
234C2×C4×C89—41no—
235C2×C4×C89—41no—
236C2×C4×C89—41no—
237C2×C4×C89—41no—
238C2×C4×C89—41no—
239C2×C4×C89C22×D411yescharacteristic
240C2×C4×C89C22×D411yescharacteristic
241C2×C4×C89H(5,𝔽2)11yescharacteristic
242C8×C89—21no—
243C8×C89—21no—
244C8×C89—21no—
245C8×C89—41no—
246C8×C89—41no—
247C8×C89—41no—
248C8×C89—41no—
249C8×C89—41no—
250C8×C89#13512yes—
251C22×C89—41no—
252C22×C89—41no—
253C22×C89—41no—
254C22×C89—41no—
255C22×C89—41no—
256C22×C89—41no—
257C22×C89D4211yescharacteristic
258C4×C89—21no—
259C4×C89—41no—
260C4×C89—41no—
261C4×C89—41no—
262C4×C89—41no—
263C4×C89—41no—
264C4×C89—41no—
265C4×C89—81no—
266C4×C89—81no—
267C4×C89—81no—
268C4×C89—81no—
269C4×C89C2×#13511yescharacteristic
270C4×C89#57511yescharacteristic
271C4×C89#57711yescharacteristic
272C4×C89#57811yescharacteristic
273#19856C8911yesmaximal, characteristic, direct product factor, Sylow
274C2×C89—81no—
275C2×C89—81no—
276C2×C89#326911yescharacteristic
277C2×C89#328411yescharacteristic
278C2×C89#328911yescharacteristic
279#3398C2×C8911yescharacteristic, complemented
280#3364C2×C8911yescharacteristic, complemented
281#3340C2×C8911yescharacteristic
282#3340C2×C8911yescharacteristic
283#1716C2×C8911yescharacteristic, complemented
284#1692C2×C8911yescharacteristic, complemented
285#1679C2×C8911yescharacteristic, complemented
286#1672C2×C8911yescharacteristic, complemented
287#1669C2×C8911yescharacteristic, complemented
288#1652C2×C8911yescharacteristic, complemented
289#1652C2×C8911yescharacteristic, complemented
290#1646C2×C8911yescharacteristic
291#1636C2×C8911yescharacteristic, complemented
292#1582C2×C8911yescharacteristic, complemented
293SD16⋊C8C2×C8911yescharacteristic, complemented
294C89#1985611yescharacteristic, direct product factor, Sylow
295#557C22×C8911yescharacteristic
296#556C22×C8911yescharacteristic
297#556C22×C8911yescharacteristic
298#555C22×C8911yescharacteristic
299#498C22×C8911yescharacteristic
300#498C22×C8911yescharacteristic
301#498C22×C8911yescharacteristic
302#497—21no—
303#494C22×C8911yescharacteristic
304#488—21no—
305#487C22×C8911yescharacteristic
306#487C22×C8911yescharacteristic
307#485—21no—
308#485—21no—
309#482—21no—
310#482—21no—
311#479—21no—
312#477C22×C8911yescharacteristic
313#477C22×C8911yescharacteristic
314#474C22×C8911yescharacteristic
315#474C22×C8911yescharacteristic
316#474C22×C8911yescharacteristic
317#465—21no—
318#465—21no—
319#464—21no—
320#464—21no—
321#462—21no—
322#462C22×C8911yescharacteristic
323#462C22×C8911yescharacteristic
324#461C22×C8911yescharacteristic
325#446C22×C8911yescharacteristic
326C8×Q8C22×C8911yescharacteristic
327#441—21no—
328C4×Q16—21no—
329C4×SD16C22×C8911yescharacteristic
330C4×SD16C22×C8911yescharacteristic
331C8×D4C22×C8911yescharacteristic
332C8×D4C22×C8911yescharacteristic
333#427—21no—
334#427—21no—
335#335C22×C8911yescharacteristic
336#334C22×C8911yescharacteristic
337#333C22×C8911yescharacteristic
338#332C22×C8911yescharacteristic
339#332C22×C8911yescharacteristic
340#332C22×C8911yescharacteristic
341Q8⋊C8C22×C8911yescharacteristic
342Q8⋊C8C22×C8911yescharacteristic
343D4⋊C8C22×C8911yescharacteristic
344D4⋊C8C22×C8911yescharacteristic
345#322C22×C8911yescharacteristic
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16—21no—
349C2×Q16—21no—
350C2×SD16—21no—
351C2×SD16D4×C8911yescharacteristic
352C2×SD16D4×C8911yescharacteristic
353C22×C8—21no—
354C22×C8—21no—
355C4⋊Q8—21no—
356C4⋊Q8C23×C8911yescharacteristic
357C4⋊Q8C23×C8911yescharacteristic
358C4⋊Q8C23×C8911yescharacteristic
359C4⋊Q8C23×C8911yescharacteristic
360#126—41no—
361#126—41no—
362#125—21no—
363#125—41no—
364#124—21no—
365#124—21no—
366#124—41no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369#121—21no—
370#121—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C23×C8911yescharacteristic
376C4×Q8C23×C8911yescharacteristic
377C4×D4C23×C8911yescharacteristic
378C4×D4C23×C8911yescharacteristic
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106—41no—
393#106D4×C8911yescharacteristic
394#106D4×C8911yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C8911yescharacteristic
398C4⋊C8C23×C8911yescharacteristic
399C4⋊C8C23×C8911yescharacteristic
400C4⋊C8C23×C8911yescharacteristic
401#103—21no—
402#103—21no—
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#102—21no—
412#102—21no—
413#102—21no—
414#102D4×C8911yescharacteristic
415#102D4×C8911yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—21no—
418#97—21no—
419C4×C8—21no—
420C4×C8C23×C8911yescharacteristic
421C4×C8C23×C8911yescharacteristic
422C4×C8C23×C8911yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8C2×D4×C8911yescharacteristic
428C2×Q8C2×D4×C8911yescharacteristic
429C2×D4—41no—
430C2×D4C2×D4×C8911yescharacteristic
431C2×D4C2×D4×C8911yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434Q16—42no—
435Q16—42no—
436Q16—81no—
437Q16—81no—
438SD16—22no—
439SD16—41no—
440SD16—81no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—42no—
448C2×C8C2×D4×C8911yescharacteristic
449C2×C8C2×D4×C8911yescharacteristic
450C2×C8C2×D4×C8911yescharacteristic
451C2×C8C2×D4×C8911yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C8911yescharacteristic
468C4⋊C4C2×D4×C8911yescharacteristic
469C4⋊C4C2×D4×C8911yescharacteristic
470C4⋊C4C2×D4×C8911yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—41no—
482C42—41no—
483C42—41no—
484C42—41no—
485C42C24×C8911yescharacteristic
486C23—21no—
487C23—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499D4—21no—
500D4—21no—
501D4—21no—
502D4—21no—
503D4—161no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4C22×D4×C8911yescharacteristic
519C2×C4C22×D4×C8911yescharacteristic
520C2×C4H(5,𝔽2)×C8911yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8#135×C8912yes—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22D42×C8911yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4C2×#135×C8911yescharacteristic
549C4#575×C8911yescharacteristic
550C4#577×C8911yescharacteristic
551C4#578×C8911yescharacteristic
552C2—81no—
553C2—81no—
554C2C89×#326911yescharacteristic
555C2C89×#328411yescharacteristic
556C2C89×#328911yescharacteristic
subgroupG/H
center, socleC22×C89D42
commutator, Frattini, cosocleC42C24×C89
prime radical#555×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×#3398C2semidirect
2. C89×#3364C2semidirect
5. C89×#1716C2semidirect
6. C89×#1692C2semidirect
7. C89×#1679C2semidirect
8. C89×#1672C2semidirect
9. C89×#1669C2semidirect
10. C89×#1652C2semidirect
11. C89×#1652C2semidirect
13. C89×#1636C2semidirect
14. C89×#1582C2semidirect
15. C89×SD16⋊C8C2semidirect
273. #19856C89direct (N × H)
279. #3398C2×C89semidirect
280. #3364C2×C89semidirect
283. #1716C2×C89semidirect
284. #1692C2×C89semidirect
285. #1679C2×C89semidirect
286. #1672C2×C89semidirect
287. #1669C2×C89semidirect
288. #1652C2×C89semidirect
289. #1652C2×C89semidirect
291. #1636C2×C89semidirect
292. #1582C2×C89semidirect
293. SD16⋊C8C2×C89semidirect
294. C89#19856direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#33982
C89×#33642
C89×#33402
C89×#17162
C89×#16922
C89×#16792
C89×#16722
C89×#16692
C89×#16522
C89×#16462
C89×#16362
C89×#15822
C89×SD16⋊C82
#1985689