Finite Group Databasebeta

← C89×#19466 #36397314

Subgroups — C89×#19466 #36397314

Order 22784.

608 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3231C211yesmaximal, characteristic, complemented
2C89×#3101C211yesmaximal, characteristic
3C89×#3077C211yesmaximal, characteristic
4C89×#2974C211yesmaximal, characteristic
5C89×#1703C211yesmaximal, characteristic, complemented
6C89×#1699C211yesmaximal, characteristic, complemented
7C89×#1695C211yesmaximal, characteristic, complemented
8C89×#1691C211yesmaximal, characteristic, complemented
9C89×#1683C211yesmaximal, characteristic, complemented
10C89×#1679C211yesmaximal, characteristic, complemented
11C89×#1675C211yesmaximal, characteristic, complemented
12C89×#1671C211yesmaximal, characteristic, complemented
13C89×#1574C211yesmaximal, characteristic, complemented
14C89×#1559C211yesmaximal, characteristic, complemented
15C89×#1554C211yesmaximal, characteristic, complemented
16#533×C89C2211yescharacteristic
17#533×C89C2211yescharacteristic
18C2×C4×D4×C89C2211yescharacteristic
19#500×C89C2211yescharacteristic, complemented
20#498×C89C2211yescharacteristic, complemented
21#487×C89C2211yescharacteristic, complemented
22#487×C89C2211yescharacteristic, complemented
23#485×C89—21no—
24#485×C89—21no—
25#483×C89—21no—
26#479×C89—21no—
27#479×C89—21no—
28#478×C89—21no—
29#478×C89—21no—
30#476×C89C2211yescharacteristic
31#476×C89C2211yescharacteristic
32#476×C89C2211yescharacteristic
33#476×C89C2211yescharacteristic
34#474×C89C2211yescharacteristic
35#474×C89C2211yescharacteristic
36#461×C89C2211yescharacteristic
37#461×C89C2211yescharacteristic
38#450×C89—21no—
39C4×SD16×C89—21no—
40C4×SD16×C89—21no—
41#436×C89C2211yescharacteristic
42#436×C89C2211yescharacteristic
43#435×C89—21no—
44#435×C89—21no—
45C8×D4×C89C2211yescharacteristic
46C8×D4×C89C2211yescharacteristic
47#432×C89C2211yescharacteristic
48#431×C89C2211yescharacteristic
49#431×C89C2211yescharacteristic
50#428×C89—21no—
51#423×C89C2211yescharacteristic
52#418×C89—21no—
53#407×C89—21no—
54C2×C22⋊C8×C89—21no—
55#335×C89C2211yescharacteristic, complemented
56#335×C89C2211yescharacteristic, complemented
57#334×C89C2211yescharacteristic, complemented
58#334×C89C2211yescharacteristic, complemented
59#333×C89C2211yescharacteristic, complemented
60#333×C89C2211yescharacteristic, complemented
61#333×C89C2211yescharacteristic, complemented
62#333×C89C2211yescharacteristic, complemented
63#332×C89C2211yescharacteristic, complemented
64#332×C89C2211yescharacteristic, complemented
65#332×C89C2211yescharacteristic, complemented
66#332×C89C2211yescharacteristic, complemented
67C22×D4×C89D411yescharacteristic
68C23×C4×C89—21no—
69C2×SD16×C89—21no—
70C2×SD16×C89—21no—
71C2×M16×C89—21no—
72C2×M16×C89—21no—
73C2×M16×C89—21no—
74C22×C8×C89—21no—
75C22×C8×C89—21no—
76C4⋊Q8×C89C2311yescharacteristic
77C4⋊Q8×C89C2311yescharacteristic
78C4⋊Q8×C89C2311yescharacteristic
79C4⋊Q8×C89C2311yescharacteristic
80#125×C89—21no—
81#125×C89—21no—
82C22⋊Q8×C89—21no—
83C22⋊Q8×C89—21no—
84C22⋊Q8×C89—21no—
85C22⋊Q8×C89—21no—
86C4×Q8×C89—21no—
87C4×Q8×C89—21no—
88C4×Q8×C89—21no—
89C4×Q8×C89—21no—
90C4×D4×C89—21no—
91C4×D4×C89—21no—
92C4×D4×C89D411yescharacteristic
93C4×D4×C89D411yescharacteristic
94C4×D4×C89C2311yescharacteristic
95C4×D4×C89C2311yescharacteristic
96#117×C89—21no—
97#117×C89—21no—
98C2×C4⋊C4×C89D411yescharacteristic
99C2×C22⋊C4×C89—21no—
100C2×C42×C89C2311yescharacteristic
101#107×C89—21no—
102#107×C89—21no—
103#107×C89—21no—
104#107×C89—21no—
105#106×C89—21no—
106#106×C89—21no—
107#106×C89—21no—
108#106×C89—21no—
109#106×C89—21no—
110#106×C89—21no—
111C4⋊C8×C89—21no—
112C4⋊C8×C89D411yescharacteristic
113C4⋊C8×C89D411yescharacteristic
114C4⋊C8×C89C2311yescharacteristic
115C4⋊C8×C89C2311yescharacteristic
116C4⋊C8×C89C2311yescharacteristic
117C4⋊C8×C89C2311yescharacteristic
118C4⋊C8×C89C2311yescharacteristic
119C4⋊C8×C89C2311yescharacteristic
120#103×C89—21no—
121#103×C89—21no—
122#103×C89—21no—
123#103×C89—21no—
124#103×C89—21no—
125#103×C89—21no—
126#102×C89—21no—
127#102×C89—21no—
128#102×C89—21no—
129#102×C89—21no—
130#102×C89—21no—
131#102×C89—21no—
132C22⋊C8×C89—21no—
133C22⋊C8×C89—21no—
134C22⋊C8×C89—21no—
135C22⋊C8×C89—21no—
136C22⋊C8×C89—21no—
137C22⋊C8×C89—21no—
138C22⋊C8×C89D411yescharacteristic
139C22⋊C8×C89D411yescharacteristic
140#97×C89—21no—
141C4×C8×C89—21no—
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144C24×C89—21no—
145C2×Q8×C89—21no—
146C2×Q8×C89—21no—
147C2×Q8×C89—21no—
148C2×Q8×C89—21no—
149C2×D4×C89—22no—
150C2×D4×C89—21no—
151C2×D4×C89—41no—
152C2×D4×C89C2×D411yescharacteristic
153C2×D4×C89C2×D411yescharacteristic
154C22×C4×C89—21no—
155C22×C4×C89—21no—
156C22×C4×C89—21no—
157C22×C4×C89—21no—
158C22×C4×C89—21no—
159C22×C4×C89—81no—
160C22×C4×C89—81no—
161C22×C4×C89C2×D411yescharacteristic
162C22×C4×C89C2×D411yescharacteristic
163C22×C4×C89#4111yescharacteristic
164SD16×C89—42no—
165SD16×C89—42no—
166M16×C89—42no—
167M16×C89—81no—
168M16×C89—81no—
169C2×C8×C89—21no—
170C2×C8×C89—21no—
171C2×C8×C89—21no—
172C2×C8×C89—21no—
173C2×C8×C89—21no—
174C2×C8×C89—21no—
175C2×C8×C89—81no—
176C2×C8×C89—81no—
177C2×C8×C89C2×D411yescharacteristic
178C2×C8×C89C2×D411yescharacteristic
179C2×C8×C89C2×D411yescharacteristic
180C2×C8×C89C2×D411yescharacteristic
181C4⋊C4×C89—21no—
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—41no—
191C4⋊C4×C89—41no—
192C4⋊C4×C89—41no—
193C4⋊C4×C89—41no—
194C4⋊C4×C89C2×D411yescharacteristic
195C4⋊C4×C89C2×D411yescharacteristic
196C22⋊C4×C89—21no—
197C22⋊C4×C89—21no—
198C22⋊C4×C89—21no—
199C22⋊C4×C89—21no—
200C22⋊C4×C89—41no—
201C22⋊C4×C89—41no—
202C42×C89—41no—
203C42×C89—41no—
204C42×C89C2×D411yescharacteristic
205C42×C89C2×D411yescharacteristic
206C42×C89#4111yescharacteristic
207C42×C89C2411yescharacteristic
208C23×C89—21no—
209C23×C89—21no—
210C23×C89—42no—
211C23×C89—42no—
212C23×C89—81no—
213C23×C89#12111yescharacteristic
214Q8×C89—41no—
215Q8×C89—41no—
216Q8×C89—41no—
217Q8×C89—41no—
218Q8×C89—81no—
219Q8×C89—81no—
220D4×C89—21no—
221D4×C89—21no—
222D4×C89—21no—
223D4×C89—42no—
224D4×C89#13712yes—
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×C89—41no—
240C2×C4×C89—81no—
241C2×C4×C89—81no—
242C2×C4×C89—81no—
243C2×C4×C89#12111yescharacteristic
244C2×C4×C89#12111yescharacteristic
245C2×C4×C89#12111yescharacteristic
246C2×C4×C89C22×D411yescharacteristic
247C2×C4×C89C22×D411yescharacteristic
248C2×C4×C89C2×#4111yescharacteristic
249C8×C89—21no—
250C8×C89—21no—
251C8×C89—21no—
252C8×C89—21no—
253C8×C89—41no—
254C8×C89—41no—
255C8×C89—41no—
256C8×C89—41no—
257C8×C89—41no—
258C8×C89—41no—
259C22×C89—21no—
260C22×C89—21no—
261C22×C89—22no—
262C22×C89—21no—
263C22×C89—41no—
264C22×C89—41no—
265C22×C89—41no—
266C22×C89—41no—
267C22×C89—41no—
268C22×C89—84no—
269C22×C89C2×#12111yescharacteristic
270C4×C89—21no—
271C4×C89—21no—
272C4×C89—21no—
273C4×C89—21no—
274C4×C89—41no—
275C4×C89—41no—
276C4×C89—81no—
277C4×C89—81no—
278C4×C89—81no—
279C4×C89—81no—
280C4×C89C2×#13711yescharacteristic
281C4×C89#57511yescharacteristic
282C4×C89#57711yescharacteristic
283C4×C89#57711yescharacteristic
284#19466C8911yesmaximal, characteristic, direct product factor, Sylow
285C2×C89—41no—
286C2×C89—42no—
287C2×C89—81no—
288C2×C89#304211yescharacteristic
289C2×C89#305611yescharacteristic
290C2×C89#306711yescharacteristic
291#3231C2×C8911yescharacteristic, complemented
292#3101C2×C8911yescharacteristic
293#3077C2×C8911yescharacteristic
294#2974C2×C8911yescharacteristic
295#1703C2×C8911yescharacteristic, complemented
296#1699C2×C8911yescharacteristic, complemented
297#1695C2×C8911yescharacteristic, complemented
298#1691C2×C8911yescharacteristic, complemented
299#1683C2×C8911yescharacteristic, complemented
300#1679C2×C8911yescharacteristic, complemented
301#1675C2×C8911yescharacteristic, complemented
302#1671C2×C8911yescharacteristic, complemented
303#1574C2×C8911yescharacteristic, complemented
304#1559C2×C8911yescharacteristic, complemented
305#1554C2×C8911yescharacteristic, complemented
306C89#1946611yescharacteristic, direct product factor, Sylow
307#533C22×C8911yescharacteristic
308#533C22×C8911yescharacteristic
309C2×C4×D4C22×C8911yescharacteristic
310#500C22×C8911yescharacteristic, complemented
311#498C22×C8911yescharacteristic, complemented
312#487C22×C8911yescharacteristic, complemented
313#487C22×C8911yescharacteristic, complemented
314#485—21no—
315#485—21no—
316#483—21no—
317#479—21no—
318#479—21no—
319#478—21no—
320#478—21no—
321#476C22×C8911yescharacteristic
322#476C22×C8911yescharacteristic
323#476C22×C8911yescharacteristic
324#476C22×C8911yescharacteristic
325#474C22×C8911yescharacteristic
326#474C22×C8911yescharacteristic
327#461C22×C8911yescharacteristic
328#461C22×C8911yescharacteristic
329#450—21no—
330C4×SD16—21no—
331C4×SD16—21no—
332#436C22×C8911yescharacteristic
333#436C22×C8911yescharacteristic
334#435—21no—
335#435—21no—
336C8×D4C22×C8911yescharacteristic
337C8×D4C22×C8911yescharacteristic
338#432C22×C8911yescharacteristic
339#431C22×C8911yescharacteristic
340#431C22×C8911yescharacteristic
341#428—21no—
342#423C22×C8911yescharacteristic
343#418—21no—
344#407—21no—
345C2×C22⋊C8—21no—
346#335C22×C8911yescharacteristic, complemented
347#335C22×C8911yescharacteristic, complemented
348#334C22×C8911yescharacteristic, complemented
349#334C22×C8911yescharacteristic, complemented
350#333C22×C8911yescharacteristic, complemented
351#333C22×C8911yescharacteristic, complemented
352#333C22×C8911yescharacteristic, complemented
353#333C22×C8911yescharacteristic, complemented
354#332C22×C8911yescharacteristic, complemented
355#332C22×C8911yescharacteristic, complemented
356#332C22×C8911yescharacteristic, complemented
357#332C22×C8911yescharacteristic, complemented
358C22×D4D4×C8911yescharacteristic
359C23×C4—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C22×C8—21no—
366C22×C8—21no—
367C4⋊Q8C23×C8911yescharacteristic
368C4⋊Q8C23×C8911yescharacteristic
369C4⋊Q8C23×C8911yescharacteristic
370C4⋊Q8C23×C8911yescharacteristic
371#125—21no—
372#125—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4D4×C8911yescharacteristic
384C4×D4D4×C8911yescharacteristic
385C4×D4C23×C8911yescharacteristic
386C4×D4C23×C8911yescharacteristic
387#117—21no—
388#117—21no—
389C2×C4⋊C4D4×C8911yescharacteristic
390C2×C22⋊C4—21no—
391C2×C42C23×C8911yescharacteristic
392#107—21no—
393#107—21no—
394#107—21no—
395#107—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402C4⋊C8—21no—
403C4⋊C8D4×C8911yescharacteristic
404C4⋊C8D4×C8911yescharacteristic
405C4⋊C8C23×C8911yescharacteristic
406C4⋊C8C23×C8911yescharacteristic
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#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8D4×C8911yescharacteristic
430C22⋊C8D4×C8911yescharacteristic
431#97—21no—
432C4×C8—21no—
433C4×C8C23×C8911yescharacteristic
434C4×C8C23×C8911yescharacteristic
435C24—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4C2×D4×C8911yescharacteristic
444C2×D4C2×D4×C8911yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—81no—
451C22×C4—81no—
452C22×C4C2×D4×C8911yescharacteristic
453C22×C4C2×D4×C8911yescharacteristic
454C22×C4#41×C8911yescharacteristic
455SD16—42no—
456SD16—42no—
457M16—42no—
458M16—81no—
459M16—81no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—81no—
467C2×C8—81no—
468C2×C8C2×D4×C8911yescharacteristic
469C2×C8C2×D4×C8911yescharacteristic
470C2×C8C2×D4×C8911yescharacteristic
471C2×C8C2×D4×C8911yescharacteristic
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—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4C2×D4×C8911yescharacteristic
486C4⋊C4C2×D4×C8911yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C42—41no—
494C42—41no—
495C42C2×D4×C8911yescharacteristic
496C42C2×D4×C8911yescharacteristic
497C42#41×C8911yescharacteristic
498C42C24×C8911yescharacteristic
499C23—21no—
500C23—21no—
501C23—42no—
502C23—42no—
503C23—81no—
504C23#121×C8911yescharacteristic
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—81no—
510Q8—81no—
511D4—21no—
512D4—21no—
513D4—21no—
514D4—42no—
515D4#137×C8912yes—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4#121×C8911yescharacteristic
535C2×C4#121×C8911yescharacteristic
536C2×C4#121×C8911yescharacteristic
537C2×C4C22×D4×C8911yescharacteristic
538C2×C4C22×D4×C8911yescharacteristic
539C2×C4C2×#41×C8911yescharacteristic
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—22no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—84no—
560C22C2×#121×C8911yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4C2×#137×C8911yescharacteristic
572C4#575×C8911yescharacteristic
573C4#577×C8911yescharacteristic
574C4#577×C8911yescharacteristic
575C2—41no—
576C2—42no—
577C2—81no—
578C2C89×#304211yescharacteristic
579C2C89×#305611yescharacteristic
580C2C89×#306711yescharacteristic
subgroupG/H
center, socleC22×C89C2×#121
commutator, Frattini, cosocleC42C24×C89
prime radicalC22×D4×C89D4
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×#3231C2semidirect
5. C89×#1703C2semidirect
6. C89×#1699C2semidirect
7. C89×#1695C2semidirect
8. C89×#1691C2semidirect
9. C89×#1683C2semidirect
10. C89×#1679C2semidirect
11. C89×#1675C2semidirect
12. C89×#1671C2semidirect
13. C89×#1574C2semidirect
14. C89×#1559C2semidirect
15. C89×#1554C2semidirect
19. #500×C89C22semidirect
20. #498×C89C22semidirect
21. #487×C89C22semidirect
22. #487×C89C22semidirect
55. #335×C89C22semidirect
56. #335×C89C22semidirect
57. #334×C89C22semidirect
58. #334×C89C22semidirect
59. #333×C89C22semidirect
60. #333×C89C22semidirect
61. #333×C89C22semidirect
62. #333×C89C22semidirect
63. #332×C89C22semidirect
64. #332×C89C22semidirect
65. #332×C89C22semidirect
66. #332×C89C22semidirect
284. #19466C89direct (N × H)
291. #3231C2×C89semidirect
295. #1703C2×C89semidirect
296. #1699C2×C89semidirect
297. #1695C2×C89semidirect
298. #1691C2×C89semidirect
299. #1683C2×C89semidirect
300. #1679C2×C89semidirect
301. #1675C2×C89semidirect
302. #1671C2×C89semidirect
303. #1574C2×C89semidirect
304. #1559C2×C89semidirect
305. #1554C2×C89semidirect
306. C89#19466direct (N × H)
310. #500C22×C89semidirect
311. #498C22×C89semidirect
312. #487C22×C89semidirect
313. #487C22×C89semidirect
346. #335C22×C89semidirect
347. #335C22×C89semidirect
348. #334C22×C89semidirect
349. #334C22×C89semidirect
350. #333C22×C89semidirect
351. #333C22×C89semidirect
352. #333C22×C89semidirect
353. #333C22×C89semidirect
354. #332C22×C89semidirect
355. #332C22×C89semidirect
356. #332C22×C89semidirect
357. #332C22×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#32312
C89×#31012
C89×#30772
C89×#29742
C89×#17032
C89×#16992
C89×#16952
C89×#16912
C89×#16832
C89×#16792
C89×#16752
C89×#16712
C89×#15742
C89×#15592
C89×#15542
#1946689