Finite Group Databasebeta

← #36525824

Subgroups — #36525824

Order 22784.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26029354C211yesmaximal, characteristic
2#26029341C211yesmaximal, characteristic
3#26019161C211yesmaximal, characteristic, complemented
4#26019149C211yesmaximal, characteristic, complemented
5#26019124C211yesmaximal, characteristic, complemented
6#26019124C211yesmaximal, characteristic, complemented
7#26019103C211yesmaximal, characteristic, complemented
8#26019103C211yesmaximal, characteristic, complemented
9#26019071C211yesmaximal, characteristic, complemented
10Q16×#10623494C211yesmaximal, characteristic, complemented
11#26019032C211yesmaximal, characteristic
12#26018725C211yesmaximal, characteristic
13#26018647C211yesmaximal, characteristic
14#26018552C211yesmaximal, characteristic
15C89×#3104C211yesmaximal, characteristic
16#19151729—21no—
17#19151729—21no—
18#19151729—21no—
19#19151729C2211yescharacteristic
20#19151729C2211yescharacteristic
21#19151729C2211yescharacteristic
22#19151729C2211yescharacteristic
23Q8×#10623494—21no—
24Q8×#10623494C2211yescharacteristic
25Q8×#10623494C2211yescharacteristic
26Q8×#10623494C2211yescharacteristic
27Q8×#10623494C2211yescharacteristic
28#19151659—21no—
29#19151659—21no—
30#19151655—21no—
31#19151655C2211yescharacteristic
32#19151651—21no—
33#19151651C2211yescharacteristic
34#19151651C2211yescharacteristic
35#19151651C2211yescharacteristic
36#19151351C2211yescharacteristic
37#19151351C2211yescharacteristic
38#19151349C2211yescharacteristic
39#19151349C2211yescharacteristic
40Q8⋊#10623494C2211yescharacteristic
41Q8⋊#10623494C2211yescharacteristic
42Q8⋊#10623494C2211yescharacteristic
43Q8⋊#10623494C2211yescharacteristic
44Q8⋊#10623494C2211yescharacteristic
45Q8⋊#10623494C2211yescharacteristic
46Q8⋊#10623494C2211yescharacteristic
47Q8⋊#10623494C2211yescharacteristic
48#19151320C2211yescharacteristic
49#19151320C2211yescharacteristic
50#19151319C2211yescharacteristic
51C8×#10623494C2211yescharacteristic
52#533×C89C2211yescharacteristic
53C2×C4×Q8×C89C2211yescharacteristic
54#484×C89C411yescharacteristic
55#484×C89C411yescharacteristic
56#477×C89C411yescharacteristic
57#477×C89C411yescharacteristic
58#462×C89C411yescharacteristic
59#462×C89C411yescharacteristic
60#451×C89C411yescharacteristic
61#451×C89C411yescharacteristic
62C4×Q16×C89C2211yescharacteristic
63C4×Q16×C89C2211yescharacteristic
64C4×Q16×C89C2211yescharacteristic
65C4×Q16×C89C2211yescharacteristic
66#431×C89C2211yescharacteristic
67C4⋊#10623494—21no—
68C4⋊#10623494—21no—
69C4⋊#10623494—21no—
70C4⋊#10623494—21no—
71C4⋊#10623494—21no—
72C4⋊#10623494—21no—
73C4⋊#10623494—21no—
74C4⋊#10623494—21no—
75C4⋊#10623494—21no—
76C4⋊#10623494D411yescharacteristic
77C4⋊#10623494D411yescharacteristic
78C4⋊#10623494C2311yescharacteristic
79C4⋊#10623494C2311yescharacteristic
80C4⋊#10623494C2311yescharacteristic
81C4⋊#10623494C2311yescharacteristic
82C22⋊#10623494—21no—
83C22⋊#10623494—21no—
84C22⋊#10623494—21no—
85C22⋊#10623494D411yescharacteristic
86C22⋊#10623494D411yescharacteristic
87#15667923—21no—
88#15667923—21no—
89#15667923—21no—
90#15667923—21no—
91#15667923—21no—
92C4×#10623494—21no—
93C4×#10623494—21no—
94C4×#10623494—21no—
95C4×#10623494—21no—
96C4×#10623494—21no—
97C4×#10623494C2311yescharacteristic
98C4×#10623494C2311yescharacteristic
99C4×#10623494C2311yescharacteristic
100C4×#10623494C2311yescharacteristic
101C22×Q8×C89C2×C411yescharacteristic
102C2×Q16×C89C2×C411yescharacteristic
103C2×Q16×C89C2×C411yescharacteristic
104C2×Q16×C89C2×C411yescharacteristic
105C2×Q16×C89C2×C411yescharacteristic
106C4⋊Q8×C89C2×C411yescharacteristic
107C4⋊Q8×C89C2×C411yescharacteristic
108#125×C89—21no—
109C22⋊Q8×C89—21no—
110C22⋊Q8×C89C2×C411yescharacteristic
111C22⋊Q8×C89C2×C411yescharacteristic
112C4×Q8×C89—21no—
113C4×Q8×C89—21no—
114C4×Q8×C89—21no—
115C4×Q8×C89C2×C411yescharacteristic
116C4×Q8×C89C2×C411yescharacteristic
117C4×Q8×C89C2311yescharacteristic
118C4×Q8×C89C2311yescharacteristic
119C4×Q8×C89C2311yescharacteristic
120C4×Q8×C89C2311yescharacteristic
121#117×C89—21no—
122C2×C4⋊C4×C89—21no—
123C2×C4⋊C4×C89C2×C411yescharacteristic
124C2×C42×C89—21no—
125C2×C42×C89C2311yescharacteristic
126#107×C89C2×C411yescharacteristic
127#107×C89C2×C411yescharacteristic
128#107×C89C2×C411yescharacteristic
129#107×C89C2×C411yescharacteristic
130C4⋊C8×C89C2×C411yescharacteristic
131C4⋊C8×C89C2×C411yescharacteristic
132#103×C89C2×C411yescharacteristic
133#103×C89C2×C411yescharacteristic
134#103×C89C2×C411yescharacteristic
135#103×C89C2×C411yescharacteristic
136#103×C89C2×C411yescharacteristic
137#103×C89C2×C411yescharacteristic
138#103×C89C2×C411yescharacteristic
139#103×C89C2×C411yescharacteristic
140C22⋊C8×C89C2×C411yescharacteristic
141C22⋊C8×C89C2×C411yescharacteristic
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144C2×#10623494—21no—
145C2×#10623494—21no—
146C2×#10623494—21no—
147C2×#10623494—21no—
148C2×#10623494—21no—
149C2×#10623494—21no—
150C2×#10623494C2×D411yescharacteristic
151C2×#10623494C2×D411yescharacteristic
152C2×#10623494C2×D411yescharacteristic
153C2×#10623494C2×D411yescharacteristic
154C2×Q8×C89—21no—
155C2×Q8×C89—21no—
156C2×Q8×C89—22no—
157C2×Q8×C89—41no—
158C2×Q8×C89C22×C411yescharacteristic
159C2×Q8×C89C22×C411yescharacteristic
160C2×Q8×C89C22×C411yescharacteristic
161C2×Q8×C89C22×C411yescharacteristic
162C22×C4×C89—21no—
163C22×C4×C89—21no—
164C22×C4×C89C22×C411yescharacteristic
165C22×C4×C89C2×D411yescharacteristic
166C22×C4×C89#4111yescharacteristic
167Q16×C89—22no—
168Q16×C89—22no—
169Q16×C89—41no—
170Q16×C89—41no—
171C2×C8×C89C22×C411yescharacteristic
172C2×C8×C89C22×C411yescharacteristic
173C2×C8×C89C22×C411yescharacteristic
174C2×C8×C89C22×C411yescharacteristic
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—21no—
184C4⋊C4×C89—21no—
185C4⋊C4×C89—21no—
186C4⋊C4×C89—21no—
187C4⋊C4×C89C22×C411yescharacteristic
188C4⋊C4×C89C22×C411yescharacteristic
189C4⋊C4×C89C22×C411yescharacteristic
190C4⋊C4×C89C22×C411yescharacteristic
191C22⋊C4×C89—21no—
192C22⋊C4×C89—21no—
193C42×C89—21no—
194C42×C89—21no—
195C42×C89—21no—
196C42×C89—21no—
197C42×C89—21no—
198C42×C89—21no—
199C42×C89C22×C411yescharacteristic
200C42×C89C2×D411yescharacteristic
201C42×C89#4111yescharacteristic
202C42×C89C2411yescharacteristic
203C23×C89C4×D411yescharacteristic
204Q8×C89—21no—
205Q8×C89—21no—
206Q8×C89—21no—
207Q8×C89—21no—
208Q8×C89—21no—
209Q8×C89—21no—
210Q8×C89—21no—
211Q8×C89—42no—
212Q8×C89—42no—
213Q8×C89#13112yes—
214C2×C4×C89—21no—
215C2×C4×C89—21no—
216C2×C4×C89—21no—
217C2×C4×C89—21no—
218C2×C4×C89—21no—
219C2×C4×C89—21no—
220C2×C4×C89—21no—
221C2×C4×C89—21no—
222C2×C4×C89—21no—
223C2×C4×C89—21no—
224C2×C4×C89—21no—
225C2×C4×C89—21no—
226C2×C4×C89—41no—
227C2×C4×C89—42no—
228C2×C4×C89—42no—
229C2×C4×C89C4×D411yescharacteristic
230C2×C4×C89C4×D411yescharacteristic
231C2×C4×C89C4×D411yescharacteristic
232C2×C4×C89C23×C411yescharacteristic
233C2×C4×C89C22×D411yescharacteristic
234C2×C4×C89C2×#4111yescharacteristic
235C8×C89—21no—
236C8×C89—21no—
237C8×C89—21no—
238C8×C89—21no—
239#10623494—21no—
240#10623494—21no—
241#10623494—21no—
242#10623494—21no—
243#10623494—41no—
244#10623494—41no—
245#10623494—41no—
246#10623494—41no—
247#10623494—41no—
248#10623494—41no—
249C22×C89—21no—
250C22×C89—21no—
251C22×C89—21no—
252C22×C89C2×C4×D411yescharacteristic
253C4×C89—21no—
254C4×C89—22no—
255C4×C89—21no—
256C4×C89—21no—
257C4×C89—21no—
258C4×C89—41no—
259C4×C89—41no—
260C4×C89—41no—
261C4×C89—41no—
262C4×C89—41no—
263C4×C89—41no—
264C4×C89—41no—
265C4×C89C2×#13111yescharacteristic
266C4×C89#56811yescharacteristic
267C4×C89#57811yescharacteristic
268C4×C89#57811yescharacteristic
269#18032—891nomaximal, Sylow
270C2×C89—41no—
271C2×C89#293311yescharacteristic
272C2×C89#295011yescharacteristic
273C2×C89#295511yescharacteristic
274#3104D8911yescharacteristic
275#2986—891no—
276#2984—891no—
277#1593—891no—
278#1591—891no—
279#1587—891no—
280#1587—891no—
281#1584—891no—
282#1584—891no—
283#1579—891no—
284C8×Q16—891no—
285#1572—891no—
286#1497—891no—
287#1479—891no—
288#1454—891no—
289C89#1803211yescharacteristic, complemented, Sylow
290#533C2×D8911yescharacteristic
291C2×C4×Q8C2×D8911yescharacteristic
292#484Dic8911yescharacteristic
293#484Dic8911yescharacteristic
294#477Dic8911yescharacteristic
295#477Dic8911yescharacteristic
296#462Dic8911yescharacteristic
297#462Dic8911yescharacteristic
298#451Dic8911yescharacteristic
299#451Dic8911yescharacteristic
300#446—891no—
301#446—891no—
302#446—891no—
303#446—891no—
304#446—1781no—
305#446—1781no—
306#446—1781no—
307C8×Q8—891no—
308C8×Q8—891no—
309C8×Q8—891no—
310C8×Q8—891no—
311C8×Q8—1781no—
312C4×Q16C2×D8911yescharacteristic
313C4×Q16C2×D8911yescharacteristic
314C4×Q16C2×D8911yescharacteristic
315C4×Q16C2×D8911yescharacteristic
316#433—1781no—
317#433—1781no—
318#432—891no—
319#432—1781no—
320#431—891no—
321#431—891no—
322#431—891no—
323#431—1781no—
324#431C2×D8911yescharacteristic
325#335—891no—
326#335—891no—
327#334—891no—
328#334—891no—
329Q8⋊C8—891no—
330Q8⋊C8—891no—
331Q8⋊C8—891no—
332Q8⋊C8—891no—
333Q8⋊C8—891no—
334Q8⋊C8—891no—
335Q8⋊C8—891no—
336Q8⋊C8—891no—
337#322—891no—
338#322—891no—
339#322—891no—
340C82—891no—
341C22×Q8C2×Dic8911yescharacteristic
342C2×Q16C2×Dic8911yescharacteristic
343C2×Q16C2×Dic8911yescharacteristic
344C2×Q16C2×Dic8911yescharacteristic
345C2×Q16C2×Dic8911yescharacteristic
346C4⋊Q8C2×Dic8911yescharacteristic
347C4⋊Q8C2×Dic8911yescharacteristic
348#125—21no—
349C22⋊Q8—21no—
350C22⋊Q8C2×Dic8911yescharacteristic
351C22⋊Q8C2×Dic8911yescharacteristic
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8C2×Dic8911yescharacteristic
356C4×Q8C2×Dic8911yescharacteristic
357C4×Q8C22×D8911yescharacteristic
358C4×Q8C22×D8911yescharacteristic
359C4×Q8C22×D8911yescharacteristic
360C4×Q8C22×D8911yescharacteristic
361#117—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4C2×Dic8911yescharacteristic
364C2×C42—21no—
365C2×C42C22×D8911yescharacteristic
366#107C2×Dic8911yescharacteristic
367#107C2×Dic8911yescharacteristic
368#107C2×Dic8911yescharacteristic
369#107C2×Dic8911yescharacteristic
370C4⋊C8—891no—
371C4⋊C8—891no—
372C4⋊C8—891no—
373C4⋊C8—891no—
374C4⋊C8—891no—
375C4⋊C8—891no—
376C4⋊C8—1781no—
377C4⋊C8—1781no—
378C4⋊C8—1781no—
379C4⋊C8—1781no—
380C4⋊C8—1781no—
381C4⋊C8—1781no—
382C4⋊C8—1781no—
383C4⋊C8—1781no—
384C4⋊C8—1781no—
385C4⋊C8C2×Dic8911yescharacteristic
386C4⋊C8C2×Dic8911yescharacteristic
387#103C2×Dic8911yescharacteristic
388#103C2×Dic8911yescharacteristic
389#103C2×Dic8911yescharacteristic
390#103C2×Dic8911yescharacteristic
391#103C2×Dic8911yescharacteristic
392#103C2×Dic8911yescharacteristic
393#103C2×Dic8911yescharacteristic
394#103C2×Dic8911yescharacteristic
395C22⋊C8—891no—
396C22⋊C8—891no—
397C22⋊C8—1781no—
398C22⋊C8—1781no—
399C22⋊C8—1781no—
400C22⋊C8C2×Dic8911yescharacteristic
401C22⋊C8C2×Dic8911yescharacteristic
402#97—1781no—
403#97—1781no—
404#97—1781no—
405#97—1781no—
406#97—1781no—
407C4×C8—891no—
408C4×C8—891no—
409C4×C8—891no—
410C4×C8—891no—
411C4×C8—1781no—
412C4×C8—1781no—
413C4×C8—1781no—
414C4×C8—1781no—
415C4×C8—1781no—
416C4×C8C22×D8911yescharacteristic
417C4×C8C22×D8911yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—41no—
422C2×Q8C22×Dic8911yescharacteristic
423C2×Q8C22×Dic8911yescharacteristic
424C2×Q8C22×Dic8911yescharacteristic
425C2×Q8C22×Dic8911yescharacteristic
426C22×C4—21no—
427C22×C4—21no—
428C22×C4C22×Dic8911yescharacteristic
429C22×C4D4×D8911yescharacteristic
430C22×C4#1308357311yescharacteristic
431Q16—22no—
432Q16—22no—
433Q16—41no—
434Q16—41no—
435C2×C8—891no—
436C2×C8—891no—
437C2×C8—891no—
438C2×C8—891no—
439C2×C8—1781no—
440C2×C8—1781no—
441C2×C8—1781no—
442C2×C8—1781no—
443C2×C8—1781no—
444C2×C8—1781no—
445C2×C8C22×Dic8911yescharacteristic
446C2×C8C22×Dic8911yescharacteristic
447C2×C8C22×Dic8911yescharacteristic
448C2×C8C22×Dic8911yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
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⋊C4C22×Dic8911yescharacteristic
462C4⋊C4C22×Dic8911yescharacteristic
463C4⋊C4C22×Dic8911yescharacteristic
464C4⋊C4C22×Dic8911yescharacteristic
465C22⋊C4—21no—
466C22⋊C4—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42C22×Dic8911yescharacteristic
474C42D4×D8911yescharacteristic
475C42#1308357311yescharacteristic
476C42C23×D8911yescharacteristic
477C23D4×Dic8911yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—42no—
486Q8—42no—
487Q8#1566801912yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4D4×Dic8911yescharacteristic
504C2×C4D4×Dic8911yescharacteristic
505C2×C4D4×Dic8911yescharacteristic
506C2×C4C23×Dic8911yescharacteristic
507C2×C4C2×D4×D8911yescharacteristic
508C2×C4C2×#1308357311yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—3561no—
514C8—3561no—
515C8—3561no—
516C8—3561no—
517C8—3561no—
518C8—3561no—
519C8—1781no—
520C8—1781no—
521C8—1781no—
522C8—1781no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×D4×Dic8911yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—22no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4C2×#1566801911yescharacteristic
540C4#1915236511yescharacteristic
541C4#1915241111yescharacteristic
542C4#1915241111yescharacteristic
543C2—41no—
544C2#2602897911yescharacteristic
545C2#2602912011yescharacteristic
546C2#2602915511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#3104C2
socleC22×C89C2×C4×D4
prime radicalC23×C89C4×D4
cosocleC42×C89C24
hypercenter#3104D89
hypocenterC89#18032
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
3. #26019161C2semidirect
4. #26019149C2semidirect
5. #26019124C2semidirect
6. #26019124C2semidirect
7. #26019103C2semidirect
8. #26019103C2semidirect
9. #26019071C2semidirect
10. Q16×#10623494C2semidirect
289. C89#18032semidirect

Maximal subgroups

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

subgroupindex
#260293542
#260293412
#260191612
#260191492
#260191242
#260191032
#260190712
Q16×#106234942
#260190322
#260187252
#260186472
#260185522
C89×#31042
#1803289