Finite Group Databasebeta

← C89×#19481 #36397329

Subgroups — C89×#19481 #36397329

Order 22784.

610 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×#3210C211yesmaximal, characteristic, complemented
2C89×#3115C211yesmaximal, characteristic
3C89×#3076C211yesmaximal, characteristic, complemented
4C89×#2990C211yesmaximal, characteristic, complemented
5C89×#1704C211yesmaximal, characteristic, complemented
6C89×#1698C211yesmaximal, characteristic, complemented
7C89×#1690C211yesmaximal, characteristic, complemented
8C89×#1686C211yesmaximal, characteristic, complemented
9C89×#1683C211yesmaximal, characteristic, complemented
10C89×#1677C211yesmaximal, characteristic, complemented
11C89×#1669C211yesmaximal, characteristic, complemented
12C89×#1665C211yesmaximal, characteristic, complemented
13C89×#1573C211yesmaximal, characteristic, complemented
14C89×#1559C211yesmaximal, characteristic, complemented
15C89×#1547C211yesmaximal, characteristic, complemented
16#533×C89C2211yescharacteristic
17#532×C89C2211yescharacteristic
18C4×#41×C89C2211yescharacteristic
19#494×C89C2211yescharacteristic
20#492×C89C2211yescharacteristic
21#487×C89C2211yescharacteristic
22#486×C89C2211yescharacteristic
23#482×C89—21no—
24#479×C89—21no—
25#478×C89—21no—
26#477×C89C2211yescharacteristic
27#476×C89C2211yescharacteristic
28#475×C89C2211yescharacteristic
29#475×C89C2211yescharacteristic
30#474×C89C2211yescharacteristic
31#474×C89C2211yescharacteristic
32#464×C89—21no—
33#464×C89—21no—
34#460×C89C2211yescharacteristic
35#459×C89C2211yescharacteristic
36#452×C89—21no—
37#452×C89—21no—
38#449×C89—21no—
39#446×C89C2211yescharacteristic
40#446×C89C2211yescharacteristic
41#442×C89—21no—
42#440×C89—21no—
43#435×C89—21no—
44#435×C89—21no—
45C8×D4×C89C2211yescharacteristic
46C8×D4×C89C2211yescharacteristic
47#432×C89—21no—
48#432×C89C2211yescharacteristic
49#431×C89C2211yescharacteristic
50#427×C89—21no—
51#423×C89C2211yescharacteristic
52C2×C4⋊C8×C89—21no—
53C2×C4⋊C8×C89C2211yescharacteristic
54#416×C89—21no—
55#335×C89C2211yescharacteristic
56#335×C89C2211yescharacteristic
57#334×C89C2211yescharacteristic
58#334×C89C2211yescharacteristic
59#333×C89C2211yescharacteristic
60#333×C89C2211yescharacteristic
61#332×C89C2211yescharacteristic
62#332×C89C2211yescharacteristic
63#332×C89C2211yescharacteristic
64#332×C89C2211yescharacteristic
65#331×C89C2211yescharacteristic
66#331×C89C2211yescharacteristic
67C2×#41×C89—21no—
68C2×#41×C89D411yescharacteristic
69C2×Q16×C89—21no—
70C2×Q16×C89—21no—
71C2×SD16×C89—21no—
72C2×SD16×C89—21no—
73C2×SD16×C89—21no—
74C2×D8×C89—21no—
75C2×M16×C89—21no—
76C22×C8×C89—21no—
77C22×C8×C89—21no—
78C22×C8×C89—21no—
79C4⋊Q8×C89C2311yescharacteristic
80C4⋊Q8×C89C2311yescharacteristic
81C4⋊Q8×C89C2311yescharacteristic
82#127×C89C2311yescharacteristic
83#125×C89—21no—
84#124×C89—21no—
85C22⋊Q8×C89—21no—
86C22⋊Q8×C89—21no—
87#121×C89—21no—
88#121×C89—21no—
89C4×Q8×C89—21no—
90C4×Q8×C89—21no—
91C4×Q8×C89D411yescharacteristic
92C4×Q8×C89C2311yescharacteristic
93C4×D4×C89—21no—
94C4×D4×C89—21no—
95C4×D4×C89—21no—
96C4×D4×C89—21no—
97C4×D4×C89D411yescharacteristic
98C4×D4×C89C2311yescharacteristic
99#117×C89—21no—
100#117×C89—21no—
101#117×C89D411yescharacteristic
102C2×C42×C89—21no—
103C2×C42×C89C2311yescharacteristic
104#107×C89—21no—
105#107×C89—21no—
106#107×C89—21no—
107#106×C89—21no—
108#106×C89—21no—
109#106×C89—21no—
110C4⋊C8×C89—21no—
111C4⋊C8×C89—21no—
112C4⋊C8×C89—21no—
113C4⋊C8×C89—21no—
114C4⋊C8×C89D411yescharacteristic
115C4⋊C8×C89D411yescharacteristic
116C4⋊C8×C89C2311yescharacteristic
117C4⋊C8×C89C2311yescharacteristic
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#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—
134C22⋊C8×C89—21no—
135C22⋊C8×C89—21no—
136C22⋊C8×C89—21no—
137C22⋊C8×C89D411yescharacteristic
138C22⋊C8×C89D411yescharacteristic
139#97×C89—21no—
140#97×C89—21no—
141#97×C89—21no—
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144#41×C89—22no—
145#41×C89—41no—
146#41×C89—81no—
147#41×C89—81no—
148C2×Q8×C89—21no—
149C2×Q8×C89—21no—
150C2×Q8×C89—21no—
151C2×Q8×C89C2×D411yescharacteristic
152C2×D4×C89—21no—
153C2×D4×C89—21no—
154C2×D4×C89—21no—
155C2×D4×C89—21no—
156C2×D4×C89—41no—
157C2×D4×C89C2×D411yescharacteristic
158C22×C4×C89—21no—
159C22×C4×C89—21no—
160C22×C4×C89—21no—
161C22×C4×C89—41no—
162C22×C4×C89C2×D411yescharacteristic
163C22×C4×C89C2×D411yescharacteristic
164C22×C4×C89#4111yescharacteristic
165Q16×C89—81no—
166Q16×C89—81no—
167SD16×C89—42no—
168SD16×C89—81no—
169SD16×C89—81no—
170D8×C89—42no—
171M16×C89—81no—
172C2×C8×C89—21no—
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—81no—
180C2×C8×C89—81no—
181C2×C8×C89C2×D411yescharacteristic
182C2×C8×C89C2×D411yescharacteristic
183C2×C8×C89C2×D411yescharacteristic
184C2×C8×C89C2×D411yescharacteristic
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×C89C2×D411yescharacteristic
196C4⋊C4×C89C2×D411yescharacteristic
197C22⋊C4×C89—21no—
198C22⋊C4×C89—21no—
199C22⋊C4×C89—21no—
200C22⋊C4×C89—41no—
201C22⋊C4×C89—41no—
202C22⋊C4×C89—41no—
203C42×C89—21no—
204C42×C89—21no—
205C42×C89—21no—
206C42×C89—41no—
207C42×C89C2×D411yescharacteristic
208C42×C89C2×D411yescharacteristic
209C42×C89#4111yescharacteristic
210C42×C89C2411yescharacteristic
211C23×C89—21no—
212C23×C89—41no—
213C23×C89#12111yescharacteristic
214Q8×C89—21no—
215Q8×C89—21no—
216Q8×C89—41no—
217Q8×C89—41no—
218Q8×C89—41no—
219Q8×C89—41no—
220Q8×C89—81no—
221D4×C89—21no—
222D4×C89—42no—
223D4×C89—41no—
224D4×C89—41no—
225D4×C89—41no—
226D4×C89—41no—
227D4×C89—81no—
228D4×C89—82no—
229D4×C89#13712yes—
230C2×C4×C89—21no—
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—42no—
239C2×C4×C89—42no—
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#12111yescharacteristic
247C2×C4×C89#12111yescharacteristic
248C2×C4×C89#12111yescharacteristic
249C2×C4×C89C22×D411yescharacteristic
250C2×C4×C89C22×D411yescharacteristic
251C2×C4×C89C2×#4111yescharacteristic
252C8×C89—21no—
253C8×C89—21no—
254C8×C89—21no—
255C8×C89—21no—
256C8×C89—41no—
257C8×C89—41no—
258C8×C89—41no—
259C8×C89—41no—
260C8×C89—41no—
261C8×C89—41no—
262C22×C89—21no—
263C22×C89—21no—
264C22×C89—22no—
265C22×C89—21no—
266C22×C89—41no—
267C22×C89—41no—
268C22×C89—81no—
269C22×C89—81no—
270C22×C89—81no—
271C22×C89C2×#12111yescharacteristic
272C4×C89—21no—
273C4×C89—21no—
274C4×C89—21no—
275C4×C89—21no—
276C4×C89—41no—
277C4×C89—41no—
278C4×C89—41no—
279C4×C89—81no—
280C4×C89—81no—
281C4×C89—81no—
282C4×C89C2×#13711yescharacteristic
283C4×C89#57511yescharacteristic
284C4×C89#57611yescharacteristic
285C4×C89#57711yescharacteristic
286#19481C8911yesmaximal, characteristic, direct product factor, Sylow
287C2×C89—41no—
288C2×C89—42no—
289C2×C89—161no—
290C2×C89#304511yescharacteristic
291C2×C89#305611yescharacteristic
292C2×C89#306711yescharacteristic
293#3210C2×C8911yescharacteristic, complemented
294#3115C2×C8911yescharacteristic
295#3076C2×C8911yescharacteristic, complemented
296#2990C2×C8911yescharacteristic, complemented
297#1704C2×C8911yescharacteristic, complemented
298#1698C2×C8911yescharacteristic, complemented
299#1690C2×C8911yescharacteristic, complemented
300#1686C2×C8911yescharacteristic, complemented
301#1683C2×C8911yescharacteristic, complemented
302#1677C2×C8911yescharacteristic, complemented
303#1669C2×C8911yescharacteristic, complemented
304#1665C2×C8911yescharacteristic, complemented
305#1573C2×C8911yescharacteristic, complemented
306#1559C2×C8911yescharacteristic, complemented
307#1547C2×C8911yescharacteristic, complemented
308C89#1948111yescharacteristic, direct product factor, Sylow
309#533C22×C8911yescharacteristic
310#532C22×C8911yescharacteristic
311C4×#41C22×C8911yescharacteristic
312#494C22×C8911yescharacteristic
313#492C22×C8911yescharacteristic
314#487C22×C8911yescharacteristic
315#486C22×C8911yescharacteristic
316#482—21no—
317#479—21no—
318#478—21no—
319#477C22×C8911yescharacteristic
320#476C22×C8911yescharacteristic
321#475C22×C8911yescharacteristic
322#475C22×C8911yescharacteristic
323#474C22×C8911yescharacteristic
324#474C22×C8911yescharacteristic
325#464—21no—
326#464—21no—
327#460C22×C8911yescharacteristic
328#459C22×C8911yescharacteristic
329#452—21no—
330#452—21no—
331#449—21no—
332#446C22×C8911yescharacteristic
333#446C22×C8911yescharacteristic
334#442—21no—
335#440—21no—
336#435—21no—
337#435—21no—
338C8×D4C22×C8911yescharacteristic
339C8×D4C22×C8911yescharacteristic
340#432—21no—
341#432C22×C8911yescharacteristic
342#431C22×C8911yescharacteristic
343#427—21no—
344#423C22×C8911yescharacteristic
345C2×C4⋊C8—21no—
346C2×C4⋊C8C22×C8911yescharacteristic
347#416—21no—
348#335C22×C8911yescharacteristic
349#335C22×C8911yescharacteristic
350#334C22×C8911yescharacteristic
351#334C22×C8911yescharacteristic
352#333C22×C8911yescharacteristic
353#333C22×C8911yescharacteristic
354#332C22×C8911yescharacteristic
355#332C22×C8911yescharacteristic
356#332C22×C8911yescharacteristic
357#332C22×C8911yescharacteristic
358#331C22×C8911yescharacteristic
359#331C22×C8911yescharacteristic
360C2×#41—21no—
361C2×#41D4×C8911yescharacteristic
362C2×Q16—21no—
363C2×Q16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×D8—21no—
368C2×M16—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C4⋊Q8C23×C8911yescharacteristic
373C4⋊Q8C23×C8911yescharacteristic
374C4⋊Q8C23×C8911yescharacteristic
375#127C23×C8911yescharacteristic
376#125—21no—
377#124—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380#121—21no—
381#121—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8D4×C8911yescharacteristic
385C4×Q8C23×C8911yescharacteristic
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4D4×C8911yescharacteristic
391C4×D4C23×C8911yescharacteristic
392#117—21no—
393#117—21no—
394#117D4×C8911yescharacteristic
395C2×C42—21no—
396C2×C42C23×C8911yescharacteristic
397#107—21no—
398#107—21no—
399#107—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8D4×C8911yescharacteristic
408C4⋊C8D4×C8911yescharacteristic
409C4⋊C8C23×C8911yescharacteristic
410C4⋊C8C23×C8911yescharacteristic
411C4⋊C8C23×C8911yescharacteristic
412C4⋊C8C23×C8911yescharacteristic
413C4⋊C8C23×C8911yescharacteristic
414C4⋊C8C23×C8911yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8D4×C8911yescharacteristic
431C22⋊C8D4×C8911yescharacteristic
432#97—21no—
433#97—21no—
434#97—21no—
435C4×C8C23×C8911yescharacteristic
436C4×C8C23×C8911yescharacteristic
437#41—22no—
438#41—41no—
439#41—81no—
440#41—81no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8C2×D4×C8911yescharacteristic
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—41no—
450C2×D4C2×D4×C8911yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—41no—
455C22×C4C2×D4×C8911yescharacteristic
456C22×C4C2×D4×C8911yescharacteristic
457C22×C4#41×C8911yescharacteristic
458Q16—81no—
459Q16—81no—
460SD16—42no—
461SD16—81no—
462SD16—81no—
463D8—42no—
464M16—81no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—81no—
473C2×C8—81no—
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—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C8911yescharacteristic
489C4⋊C4C2×D4×C8911yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—41no—
500C42C2×D4×C8911yescharacteristic
501C42C2×D4×C8911yescharacteristic
502C42#41×C8911yescharacteristic
503C42C24×C8911yescharacteristic
504C23—21no—
505C23—41no—
506C23#121×C8911yescharacteristic
507Q8—21no—
508Q8—21no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—81no—
514D4—21no—
515D4—42no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—81no—
521D4—82no—
522D4#137×C8912yes—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4#121×C8911yescharacteristic
540C2×C4#121×C8911yescharacteristic
541C2×C4#121×C8911yescharacteristic
542C2×C4C22×D4×C8911yescharacteristic
543C2×C4C22×D4×C8911yescharacteristic
544C2×C4C2×#41×C8911yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C2×#121×C8911yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×#137×C8911yescharacteristic
576C4#575×C8911yescharacteristic
577C4#576×C8911yescharacteristic
578C4#577×C8911yescharacteristic
579C2—41no—
580C2—42no—
581C2—161no—
582C2C89×#304511yescharacteristic
583C2C89×#305611yescharacteristic
584C2C89×#306711yescharacteristic
subgroupG/H
center, socleC22×C89C2×#121
commutator, Frattini, cosocleC42C24×C89
prime radicalC89×#3115C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#3210C2semidirect
3. C89×#3076C2semidirect
4. C89×#2990C2semidirect
5. C89×#1704C2semidirect
6. C89×#1698C2semidirect
7. C89×#1690C2semidirect
8. C89×#1686C2semidirect
9. C89×#1683C2semidirect
10. C89×#1677C2semidirect
11. C89×#1669C2semidirect
12. C89×#1665C2semidirect
13. C89×#1573C2semidirect
14. C89×#1559C2semidirect
15. C89×#1547C2semidirect
286. #19481C89direct (N × H)
293. #3210C2×C89semidirect
295. #3076C2×C89semidirect
296. #2990C2×C89semidirect
297. #1704C2×C89semidirect
298. #1698C2×C89semidirect
299. #1690C2×C89semidirect
300. #1686C2×C89semidirect
301. #1683C2×C89semidirect
302. #1677C2×C89semidirect
303. #1669C2×C89semidirect
304. #1665C2×C89semidirect
305. #1573C2×C89semidirect
306. #1559C2×C89semidirect
307. #1547C2×C89semidirect
308. C89#19481direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#32102
C89×#31152
C89×#30762
C89×#29902
C89×#17042
C89×#16982
C89×#16902
C89×#16862
C89×#16832
C89×#16772
C89×#16692
C89×#16652
C89×#15732
C89×#15592
C89×#15472
#1948189