Finite Group Databasebeta

← #36524642

Subgroups — #36524642

Order 22784.

590 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26030289C211yesmaximal, characteristic
2#26029181C211yesmaximal, characteristic
3#446×D89C211yesmaximal, characteristic
4#26019149C211yesmaximal, characteristic, complemented
5#26019148C211yesmaximal, characteristic, complemented
6#26019146C211yesmaximal, characteristic, complemented
7#26019146C211yesmaximal, characteristic, complemented
8#26019104C211yesmaximal, characteristic, complemented
9#26019102C211yesmaximal, characteristic, complemented
10#26019100C211yesmaximal, characteristic, complemented
11#26019025C211yesmaximal, characteristic
12#26018679C211yesmaximal, characteristic
13#26018653C211yesmaximal, characteristic
14#26018537C211yesmaximal, characteristic
15C89×#1584C211yesmaximal, characteristic, complemented
16#19152152C2211yescharacteristic
17C4×Q8×D89C2211yescharacteristic
18#19151935C411yescharacteristic
19#19151932C411yescharacteristic
20#19151892C411yescharacteristic
21#19151891C411yescharacteristic
22#19151807C411yescharacteristic
23#19151806C411yescharacteristic
24#19151755C411yescharacteristic
25#19151752C411yescharacteristic
26#19151729C2211yescharacteristic
27#19151729C2211yescharacteristic
28#19151728C2211yescharacteristic
29#19151727—21no—
30#19151727—21no—
31#19151726—21no—
32#19151725C2211yescharacteristic
33#19151725C2211yescharacteristic
34C8×Dic178—21no—
35C8×Dic178C2211yescharacteristic
36C4×Dic356C2211yescharacteristic
37C4×#13083564C2211yescharacteristic
38C4×#13083564C2211yescharacteristic
39#19151649C2211yescharacteristic
40#19151649C2211yescharacteristic
41#19151623—21no—
42#19151620C2211yescharacteristic
43C4⋊C8×D89—21no—
44C4⋊C8×D89C2211yescharacteristic
45#19151552—21no—
46#97×D89—21no—
47C4×C8×D89C2211yescharacteristic
48#19151351C2211yescharacteristic
49#19151350C2211yescharacteristic
50#19151350C2211yescharacteristic
51#19151330C2211yescharacteristic
52#19151330C2211yescharacteristic
53Q8⋊#10623494C2211yescharacteristic
54Q8⋊#10623494C2211yescharacteristic
55#19151328C2211yescharacteristic
56#19151328C2211yescharacteristic
57#19151319C2211yescharacteristic
58C8×#10623494C2211yescharacteristic
59C8×#10623494C2211yescharacteristic
60#446×C89C2211yescharacteristic
61C8×Q8×C89C2211yescharacteristic
62C4×Q16×C89C2211yescharacteristic
63#335×C89C2211yescharacteristic
64Q8⋊C8×C89C2211yescharacteristic
65Q8⋊C8×C89C2211yescharacteristic
66#322×C89C2211yescharacteristic
67C2×Q8×D89C2×C411yescharacteristic
68C2×Dic356C2×C411yescharacteristic
69C2×#13083564C2×C411yescharacteristic
70C2×#13083564C2×C411yescharacteristic
71C2×#13083557—21no—
72C2×C8×D89—21no—
73C2×C8×D89D411yescharacteristic
74C2×C8×D89D411yescharacteristic
75#15668011C2×C411yescharacteristic
76#15668010C2×C411yescharacteristic
77#15668002—21no—
78#15667992C2×C411yescharacteristic
79#15667990—21no—
80#15667988C2×C411yescharacteristic
81Q8×Dic89C2×C411yescharacteristic
82C4×Dic178—21no—
83C4×Dic178—21no—
84C4×Dic178C2311yescharacteristic
85C4×Dic178C2311yescharacteristic
86#15667977—21no—
87#15667977C2×C411yescharacteristic
88#15667969—21no—
89C4⋊C4×D89—21no—
90C4⋊C4×D89C2×C411yescharacteristic
91C42×D89—21no—
92C42×D89C2311yescharacteristic
93#15667946C2×C411yescharacteristic
94#15667945C2×C411yescharacteristic
95#15667945C2×C411yescharacteristic
96C4⋊#10623494—21no—
97C4⋊#10623494—21no—
98C4⋊#10623494C2311yescharacteristic
99C4⋊#10623494C2311yescharacteristic
100#15667941—21no—
101#15667941—21no—
102#15667941—21no—
103#15667941—21no—
104#15667941—21no—
105#15667941—21no—
106#15667941—21no—
107#15667941C2×C411yescharacteristic
108#15667941C2×C411yescharacteristic
109#15667937C2×C411yescharacteristic
110#15667937C2×C411yescharacteristic
111#15667936C2×C411yescharacteristic
112#15667936C2×C411yescharacteristic
113#15667935C2×C411yescharacteristic
114#15667935C2×C411yescharacteristic
115#15667924—21no—
116#15667924C2×C411yescharacteristic
117#15667924C2×C411yescharacteristic
118#15667923—21no—
119#15667923—21no—
120#15667922—21no—
121#15667922—21no—
122#15667922—21no—
123C4×#10623494C2311yescharacteristic
124C4×#10623494C2311yescharacteristic
125C4×#10623494C2311yescharacteristic
126C8×Dic89—21no—
127C8×Dic89D411yescharacteristic
128C8×Dic89D411yescharacteristic
129C2×Q16×C89C2×C411yescharacteristic
130C4×Q8×C89C2311yescharacteristic
131C4×Q8×C89C2311yescharacteristic
132#107×C89C2×C411yescharacteristic
133C4⋊C8×C89—21no—
134C4⋊C8×C89—21no—
135C4⋊C8×C89C2311yescharacteristic
136C4⋊C8×C89C2311yescharacteristic
137#103×C89C2×C411yescharacteristic
138#103×C89C2×C411yescharacteristic
139#97×C89—21no—
140C4×C8×C89—21no—
141C4×C8×C89C2311yescharacteristic
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144C2×Dic178—21no—
145C2×Dic178—21no—
146C2×Dic178C22×C411yescharacteristic
147C2×Dic178C22×C411yescharacteristic
148Q8×D89—41no—
149Q8×D89—41no—
150C2×C4×D89—21no—
151C2×C4×D89—21no—
152C2×C4×D89C22×C411yescharacteristic
153C2×C4×D89C2×D411yescharacteristic
154C2×C4×D89#4111yescharacteristic
155Dic356—41no—
156#13083564—41no—
157#13083564—41no—
158#13083557—42no—
159C2×#10623494—21no—
160C2×#10623494—21no—
161C2×#10623494—21no—
162C2×#10623494C22×C411yescharacteristic
163C2×#10623494C22×C411yescharacteristic
164C2×#10623494C2×D411yescharacteristic
165C2×#10623494C2×D411yescharacteristic
166C8×D89—22no—
167C8×D89—42no—
168C8×D89Q1614yescomplemented
169C4⋊Dic89—21no—
170C4⋊Dic89—21no—
171C4⋊Dic89C22×C411yescharacteristic
172C4⋊Dic89C22×C411yescharacteristic
173#13083553—21no—
174#13083553—21no—
175#13083553—21no—
176#13083553—21no—
177#13083553—21no—
178#13083553—21no—
179#13083553—21no—
180#13083553—21no—
181#13083551—21no—
182#13083551—21no—
183C4×Dic89—21no—
184C4×Dic89—21no—
185C4×Dic89—21no—
186C4×Dic89—21no—
187C4×Dic89C22×C411yescharacteristic
188C4×Dic89C2×D411yescharacteristic
189C4×Dic89#4111yescharacteristic
190C2×Q8×C89C22×C411yescharacteristic
191C2×Q8×C89C22×C411yescharacteristic
192Q16×C89—41no—
193C2×C8×C89—21no—
194C2×C8×C89—21no—
195C2×C8×C89—21no—
196C2×C8×C89C22×C411yescharacteristic
197C2×C8×C89C22×C411yescharacteristic
198C2×C8×C89C2×D411yescharacteristic
199C2×C8×C89C2×D411yescharacteristic
200C4⋊C4×C89—21no—
201C4⋊C4×C89—21no—
202C4⋊C4×C89C22×C411yescharacteristic
203C4⋊C4×C89C22×C411yescharacteristic
204C42×C89—21no—
205C42×C89—21no—
206C42×C89C2411yescharacteristic
207C22×D89C4×D411yescharacteristic
208Q8×C89—21no—
209Q8×C89—21no—
210Q8×C89—21no—
211Q8×C89—21no—
212C2×C4×C89—21no—
213C2×C4×C89—21no—
214C2×C4×C89—21no—
215C2×C4×C89—21no—
216C2×C4×C89C23×C411yescharacteristic
217C2×C4×C89C22×D411yescharacteristic
218C2×C4×C89C2×#4111yescharacteristic
219C2×Dic89—21no—
220C2×Dic89—21no—
221C2×Dic89—21no—
222C2×Dic89—21no—
223C2×Dic89C4×D411yescharacteristic
224C2×Dic89C4×D411yescharacteristic
225C2×Dic89C4×D411yescharacteristic
226C4×D89—21no—
227C4×D89—21no—
228C4×D89—41no—
229C4×D89—42no—
230C4×D89—42no—
231C4×D89C2×Q1612yes—
232C4×D89#13512yes—
233Dic178—21no—
234Dic178—21no—
235Dic178—21no—
236Dic178—21no—
237Dic178—42no—
238Dic178—42no—
239C8×C89—21no—
240C8×C89—21no—
241C8×C89—21no—
242C8×C89—41no—
243C8×C89—41no—
244C8×C89—41no—
245C8×C89C2×Q1612yes—
246#10623494—21no—
247#10623494—21no—
248#10623494—21no—
249#10623494—41no—
250#10623494—41no—
251#10623494—41no—
252#10623494C2×Q1612yes—
253C22×C89C2×C4×D411yescharacteristic
254C2×D89—21no—
255C2×D89—21no—
256C2×D89C4×Q1612yes—
257C4×C89—21no—
258C4×C89—41no—
259C4×C89—41no—
260C4×C89—41no—
261C4×C89—41no—
262C4×C89#56811yescharacteristic
263C4×C89#56811yescharacteristic
264C4×C89C22×Q1611yescharacteristic
265C4×C89C2×#13511yescharacteristic
266Dic89—21no—
267Dic89—21no—
268Dic89—41no—
269Dic89—41no—
270Dic89—41no—
271Dic89—41no—
272Dic89C4×Q1612yes—
273#17931—891nomaximal, Sylow
274C2×C89#293011yescharacteristic
275C2×C89C2×C4×Q1611yescharacteristic
276C2×C89#295511yescharacteristic
277D89—22no—
278#3104—891no—
279#2960—891no—
280C2×#446—891no—
281#1591—891no—
282#1591—891no—
283#1591—891no—
284#1591—891no—
285#1584—891no—
286#1584—891no—
287#1584—891no—
288#1584D8911yescharacteristic, complemented
289#1571—891no—
290#1487—891no—
291#1481—891no—
292#1450—891no—
293C89#1793111yescharacteristic, complemented, Sylow
294#533—891no—
295C2×C4×Q8—891no—
296#484—891no—
297#484—891no—
298#477—891no—
299#477—891no—
300#462—891no—
301#462—891no—
302#451—891no—
303#451—891no—
304#446—891no—
305#446—891no—
306#446—891no—
307#446—891no—
308#446—891no—
309#446—1781no—
310#446—1781no—
311#446—1781no—
312#446C2×D8911yescharacteristic
313C8×Q8—891no—
314C8×Q8—1781no—
315C8×Q8C2×D8911yescharacteristic
316C4×Q16—891no—
317C4×Q16—891no—
318C4×Q16—891no—
319C4×Q16C2×D8911yescharacteristic
320#431—891no—
321#431—891no—
322#424—1781no—
323#423—891no—
324C2×C4⋊C8—891no—
325C2×C4⋊C8—1781no—
326#405—1781no—
327C2×#97—1781no—
328C2×C4×C8—891no—
329#335—891no—
330#335—891no—
331#335—891no—
332#335C2×D8911yescharacteristic
333Q8⋊C8—891no—
334Q8⋊C8—891no—
335Q8⋊C8—891no—
336Q8⋊C8—891no—
337Q8⋊C8—891no—
338Q8⋊C8—891no—
339Q8⋊C8C2×D8911yescharacteristic
340Q8⋊C8C2×D8911yescharacteristic
341#322—891no—
342#322C2×D8911yescharacteristic
343C82—891no—
344C82—891no—
345C22×Q8—891no—
346C2×Q16—891no—
347C2×Q16—891no—
348C2×Q16—891no—
349C2×Q16C4×D8911yescharacteristic
350C2×M16—1781no—
351C22×C8—891no—
352C22×C8—891no—
353C22×C8—1781no—
354C4⋊Q8—891no—
355C4⋊Q8—891no—
356#125—1781no—
357C22⋊Q8—891no—
358C22⋊Q8—891no—
359C22⋊Q8—1781no—
360C4×Q8—891no—
361C4×Q8—891no—
362C4×Q8—891no—
363C4×Q8—891no—
364C4×Q8—1781no—
365C4×Q8—1781no—
366C4×Q8—1781no—
367C4×Q8C22×D8911yescharacteristic
368C4×Q8C22×D8911yescharacteristic
369#117—1781no—
370C2×C4⋊C4—891no—
371C2×C4⋊C4—1781no—
372C2×C42—891no—
373C2×C42—1781no—
374#107—891no—
375#107—891no—
376#107—891no—
377#107C4×D8911yescharacteristic
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—891no—
381C4⋊C8—891no—
382C4⋊C8—891no—
383C4⋊C8—891no—
384C4⋊C8—1781no—
385C4⋊C8—1781no—
386C4⋊C8—1781no—
387C4⋊C8—1781no—
388C4⋊C8—1781no—
389C4⋊C8—1781no—
390C4⋊C8—1781no—
391C4⋊C8—1781no—
392C4⋊C8—1781no—
393C4⋊C8C22×D8911yescharacteristic
394C4⋊C8C22×D8911yescharacteristic
395#103—891no—
396#103—891no—
397#103—891no—
398#103—891no—
399#103—891no—
400#103—891no—
401#103C4×D8911yescharacteristic
402#103C4×D8911yescharacteristic
403C22⋊C8—891no—
404C22⋊C8—891no—
405C22⋊C8—1781no—
406#97—21no—
407#97—1781no—
408#97—1781no—
409#97—1781no—
410#97—1781no—
411#97—1781no—
412C4×C8—21no—
413C4×C8—891no—
414C4×C8—891no—
415C4×C8—891no—
416C4×C8—891no—
417C4×C8—891no—
418C4×C8—1781no—
419C4×C8C22×D8911yescharacteristic
420C4×C8C22×D8911yescharacteristic
421C4×C8C22×D8911yescharacteristic
422C2×Q8—891no—
423C2×Q8—891no—
424C2×Q8—3561no—
425C2×Q8—3561no—
426C2×Q8—1781no—
427C2×Q8—1781no—
428C2×Q8C2×C4×D8911yescharacteristic
429C2×Q8C2×C4×D8911yescharacteristic
430C22×C4—891no—
431C22×C4—891no—
432C22×C4—891no—
433C22×C4—1781no—
434C22×C4—1781no—
435Q16—41no—
436Q16—3561no—
437Q16—3561no—
438Q16—3561no—
439M16—3562no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—891no—
444C2×C8—894no—
445C2×C8—891no—
446C2×C8—891no—
447C2×C8—891no—
448C2×C8—3562no—
449C2×C8—1782no—
450C2×C8—1781no—
451C2×C8—1781no—
452C2×C8—1781no—
453C2×C8C2×C4×D8911yescharacteristic
454C2×C8C2×C4×D8911yescharacteristic
455C2×C8D4×D8911yescharacteristic
456C2×C8D4×D8911yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—891no—
460C4⋊C4—891no—
461C4⋊C4—1781no—
462C4⋊C4—1781no—
463C4⋊C4—1781no—
464C4⋊C4—1781no—
465C4⋊C4—1781no—
466C4⋊C4—1781no—
467C4⋊C4—1781no—
468C4⋊C4—1781no—
469C4⋊C4—1781no—
470C4⋊C4—1781no—
471C4⋊C4C2×C4×D8911yescharacteristic
472C4⋊C4C2×C4×D8911yescharacteristic
473C22⋊C4—1781no—
474C22⋊C4—1781no—
475C42—21no—
476C42—21no—
477C42—891no—
478C42—891no—
479C42—891no—
480C42—1781no—
481C42—1781no—
482C42—1781no—
483C42—1781no—
484C42C23×D8911yescharacteristic
485C23—891no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—3562no—
491Q8—3562no—
492Q8—1781no—
493Q8—1781no—
494Q8—1781no—
495Q8—1781no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—891no—
501C2×C4—892no—
502C2×C4—892no—
503C2×C4—891no—
504C2×C4—891no—
505C2×C4—3561no—
506C2×C4—3562no—
507C2×C4—3562no—
508C2×C4—1781no—
509C2×C4—1781no—
510C2×C4—1781no—
511C2×C4—1781no—
512C2×C4—1781no—
513C2×C4—1781no—
514C2×C4C22×C4×D8911yescharacteristic
515C2×C4C2×D4×D8911yescharacteristic
516C2×C4#41×D8911yescharacteristic
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—892no—
524C8—3561no—
525C8—3561no—
526C8—3561no—
527C8—1781no—
528C8—1781no—
529C8—1781no—
530C8Q16×D8912yes—
531C22—892no—
532C22—1781no—
533C22—1781no—
534C22C4×D4×D8911yescharacteristic
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—892no—
541C4—3561no—
542C4—3561no—
543C4—3561no—
544C4—3561no—
545C4—1781no—
546C4—1781no—
547C4#1915236311yescharacteristic
548C4#1915236411yescharacteristic
549C4C2×Q16×D8911yescharacteristic
550C4#135×D8911yescharacteristic
551C2—1782no—
552C2#2602895011yescharacteristic
553C2C4×Q16×D8911yescharacteristic
554C2#2602915211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#1584C2
socleC22×C89C2×C4×D4
prime radicalC22×D89C4×D4
cosocleC42×C89C24
hypercenter#1584D89
hypocenterC89#17931
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #26019149C2semidirect
5. #26019148C2semidirect
6. #26019146C2semidirect
7. #26019146C2semidirect
8. #26019104C2semidirect
9. #26019102C2semidirect
10. #26019100C2semidirect
15. C89×#1584C2semidirect
168. C8×D89Q16semidirect
288. #1584D89semidirect
293. C89#17931semidirect

Maximal subgroups

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

subgroupindex
#260302892
#260291812
#446×D892
#260191492
#260191482
#260191462
#260191042
#260191022
#260191002
#260190252
#260186792
#260186532
#260185372
C89×#15842
#1793189