Finite Group Databasebeta

← #36525262

Subgroups — #36525262

Order 22784.

566 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26030858C211yesmaximal, characteristic
2#26029403C211yesmaximal, characteristic
3#26029346C211yesmaximal, characteristic, complemented
4#26019132C211yesmaximal, characteristic, complemented
5#26019125C211yesmaximal, characteristic, complemented
6#26019125C211yesmaximal, characteristic, complemented
7#26019111C211yesmaximal, characteristic, complemented
8#26019104C211yesmaximal, characteristic, complemented
9#26019104C211yesmaximal, characteristic, complemented
10#26019097C211yesmaximal, characteristic, complemented
11#26019090C211yesmaximal, characteristic, complemented
12#26019019C211yesmaximal, characteristic, complemented
13#26018713C211yesmaximal, characteristic
14#26018708C211yesmaximal, characteristic, complemented
15C89×#1451C211yesmaximal, characteristic, complemented
16#19152155C2211yescharacteristic
17#19152132C2211yescharacteristic
18#19152007C411yescharacteristic
19#19151992C411yescharacteristic
20#19151967C411yescharacteristic
21#19151958C411yescharacteristic
22#19151856C411yescharacteristic
23#19151856C411yescharacteristic
24#19151844C411yescharacteristic
25#19151844C411yescharacteristic
26#19151728C2211yescharacteristic
27#19151728C2211yescharacteristic
28#19151728C2211yescharacteristic
29#19151727—21no—
30#19151727—21no—
31C8×Dic178C2211yescharacteristic
32C8×Dic178C2211yescharacteristic
33C8×Dic178C2211yescharacteristic
34C4×Dic356C2211yescharacteristic
35C4×Dic356C2211yescharacteristic
36C4×#13083563C2211yescharacteristic
37C4×#13083563C2211yescharacteristic
38#19151677C2211yescharacteristic
39#19151673—21no—
40#19151672—21no—
41C8×D356C2211yescharacteristic
42#19151658—21no—
43#19151656—21no—
44#19151656—21no—
45#19151655C2211yescharacteristic
46#19151623—21no—
47#19151622C2211yescharacteristic
48#19151351C2211yescharacteristic
49#19151351C2211yescharacteristic
50#19151349C2211yescharacteristic
51#19151349C2211yescharacteristic
52#19151330C2211yescharacteristic
53#19151330C2211yescharacteristic
54#19151330C2211yescharacteristic
55#19151330C2211yescharacteristic
56#19151330C2211yescharacteristic
57#19151330C2211yescharacteristic
58#19151327C2211yescharacteristic
59#19151327C2211yescharacteristic
60#431×C89C2211yescharacteristic
61C4×M16×C89C2211yescharacteristic
62C2×C4×C8×C89C2211yescharacteristic
63#322×C89C2211yescharacteristic
64#322×C89C2211yescharacteristic
65#322×C89C2211yescharacteristic
66#322×C89C2211yescharacteristic
67C2×Dic356C2×C411yescharacteristic
68C2×Dic356C2×C411yescharacteristic
69C2×#13083563C2×C411yescharacteristic
70C2×#13083563C2×C411yescharacteristic
71C2×#13083558—21no—
72C2×#13083557—21no—
73C2×C8×D89—21no—
74#15668012C2×C411yescharacteristic
75#15668012C2×C411yescharacteristic
76#15668006—21no—
77#15668004—21no—
78#15668004C2×C411yescharacteristic
79#15668000C2×C411yescharacteristic
80#15667995—21no—
81#15667991—21no—
82#15667991C2×C411yescharacteristic
83#15667991C2×C411yescharacteristic
84#15667991C2×C411yescharacteristic
85#15667986C2×C411yescharacteristic
86C4×Dic178—21no—
87C4×Dic178C2311yescharacteristic
88C4×Dic178C2311yescharacteristic
89C4×Dic178C2311yescharacteristic
90C4×D356C2311yescharacteristic
91C4×C22⋊D89—21no—
92#15667971—21no—
93#15667969—21no—
94#15667946C2×C411yescharacteristic
95#15667946C2×C411yescharacteristic
96#15667944C2×C411yescharacteristic
97#15667944C2×C411yescharacteristic
98C4⋊#10623494—21no—
99C4⋊#10623494C2311yescharacteristic
100C4⋊#10623494C2311yescharacteristic
101C4⋊#10623494C2311yescharacteristic
102C4⋊#10623494C2311yescharacteristic
103#15667941—21no—
104#15667941—21no—
105#15667941—21no—
106#15667941—21no—
107#15667941—21no—
108#15667941—21no—
109#15667937C2×C411yescharacteristic
110#15667937C2×C411yescharacteristic
111#15667937C2×C411yescharacteristic
112#15667937C2×C411yescharacteristic
113#15667937C2×C411yescharacteristic
114#15667937C2×C411yescharacteristic
115#15667934C2×C411yescharacteristic
116#15667934C2×C411yescharacteristic
117C22⋊#10623494—21no—
118#15667924—21no—
119#15667924—21no—
120#15667923—21no—
121#15667922—21no—
122#15667922—21no—
123#15667922—21no—
124C8×Dic89—21no—
125C8×Dic89—21no—
126C8×Dic89—21no—
127C2×M16×C89C2×C411yescharacteristic
128C2×M16×C89C2×C411yescharacteristic
129C22×C8×C89—21no—
130C2×C42×C89C2311yescharacteristic
131C4⋊C8×C89D411yescharacteristic
132C4⋊C8×C89D411yescharacteristic
133C22⋊C8×C89D411yescharacteristic
134C22⋊C8×C89D411yescharacteristic
135#97×C89C2×C411yescharacteristic
136#97×C89C2×C411yescharacteristic
137C4×C8×C89—21no—
138C4×C8×C89C2311yescharacteristic
139C4×C8×C89C2311yescharacteristic
140C4×C8×C89C2311yescharacteristic
141C4×C8×C89C2311yescharacteristic
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144C2×Dic178—21no—
145C2×Dic178C22×C411yescharacteristic
146C2×Dic178C22×C411yescharacteristic
147C2×Dic178C22×C411yescharacteristic
148C2×D356C22×C411yescharacteristic
149C2×C22⋊D89—21no—
150C2×C4×D89—21no—
151Dic356—41no—
152Dic356—41no—
153#13083563—41no—
154#13083563—41no—
155#13083558—81no—
156#13083557—81no—
157C2×#10623494—21no—
158C2×#10623494—21no—
159C2×#10623494—21no—
160C2×#10623494—21no—
161C8×D89—81no—
162C4⋊Dic89—21no—
163C4⋊Dic89—21no—
164C4⋊Dic89—21no—
165C4⋊Dic89C22×C411yescharacteristic
166C4⋊Dic89C22×C411yescharacteristic
167C4⋊Dic89C22×C411yescharacteristic
168C4⋊Dic89C22×C411yescharacteristic
169#13083553—21no—
170#13083553—21no—
171#13083553—21no—
172#13083553—21no—
173#13083553—21no—
174#13083553—21no—
175#13083553—21no—
176#13083553—21no—
177C22⋊Dic89—21no—
178C22⋊Dic89—21no—
179C22⋊Dic89—21no—
180#13083551—21no—
181#13083551—21no—
182#13083551—21no—
183#13083551—21no—
184C4×Dic89—21no—
185C4×Dic89—21no—
186C4×Dic89—21no—
187C22×C4×C89C22×C411yescharacteristic
188C22×C4×C89C2×D411yescharacteristic
189C22×C4×C89#4111yescharacteristic
190M16×C89—41no—
191M16×C89—41no—
192C2×C8×C89—21no—
193C2×C8×C89—21no—
194C2×C8×C89—42no—
195C2×C8×C89C22×C411yescharacteristic
196C2×C8×C89C22×C411yescharacteristic
197C2×C8×C89C22×C411yescharacteristic
198C2×C8×C89C22×C411yescharacteristic
199C2×C8×C89C2×D411yescharacteristic
200C2×C8×C89C2×D411yescharacteristic
201C2×C8×C89C2×D411yescharacteristic
202C2×C8×C89C2×D411yescharacteristic
203C42×C89C22×C411yescharacteristic
204C42×C89C2×D411yescharacteristic
205C42×C89#4111yescharacteristic
206C42×C89C2411yescharacteristic
207C23×C89C4×D411yescharacteristic
208C22×D89—21no—
209C2×C4×C89—21no—
210C2×C4×C89—21no—
211C2×C4×C89—21no—
212C2×C4×C89—21no—
213C2×C4×C89—41no—
214C2×C4×C89C4×D411yescharacteristic
215C2×C4×C89C4×D411yescharacteristic
216C2×C4×C89C4×D411yescharacteristic
217C2×C4×C89C23×C411yescharacteristic
218C2×C4×C89C22×D411yescharacteristic
219C2×C4×C89C2×#4111yescharacteristic
220C22⋊D89—81no—
221C2×Dic89—21no—
222C2×Dic89—21no—
223C2×Dic89—21no—
224C2×Dic89—21no—
225C2×Dic89—21no—
226C2×Dic89—21no—
227C2×Dic89—21no—
228D356—21no—
229D356—21no—
230C4×D89—41no—
231C4×D89—41no—
232Dic178—21no—
233Dic178—21no—
234Dic178—21no—
235Dic178—21no—
236Dic178—21no—
237Dic178—21no—
238Dic178—81no—
239C8×C89—22no—
240C8×C89—21no—
241C8×C89—21no—
242C8×C89—21no—
243C8×C89—21no—
244C8×C89—21no—
245C8×C89—21no—
246C8×C89—21no—
247C8×C89—21no—
248C8×C89—41no—
249#10623494—41no—
250#10623494—41no—
251#10623494—41no—
252#10623494—41no—
253C22×C89—21no—
254C22×C89—21no—
255C22×C89—21no—
256C22×C89C2×C4×D411yescharacteristic
257C2×D89—41no—
258C2×D89—41no—
259C2×D89—41no—
260C4×C89—21no—
261C4×C89—21no—
262C4×C89—21no—
263C4×C89—21no—
264C4×C89#56811yescharacteristic
265C4×C89#56811yescharacteristic
266C4×C89#57711yescharacteristic
267C4×C89#57811yescharacteristic
268Dic89—41no—
269Dic89—41no—
270Dic89—41no—
271Dic89—41no—
272Dic89—41no—
273Dic89—41no—
274Dic89—41no—
275#17988—891nomaximal, Sylow
276C2×C89—41no—
277C2×C89#293211yescharacteristic
278C2×C89#294711yescharacteristic
279C2×C89#295611yescharacteristic
280D89—81no—
281#3172—891no—
282#2993—891no—
283#2985—891no—
284#1588—891no—
285#1587—891no—
286#1587—891no—
287#1585—891no—
288#1584—891no—
289#1584—891no—
290#1583—891no—
291#1582—891no—
292#1569—891no—
293#1494—891no—
294#1493—891no—
295#1451D8911yescharacteristic, complemented
296C89#1798811yescharacteristic, complemented, Sylow
297#533—891no—
298#529—891no—
299#501—891no—
300#497—891no—
301#491—891no—
302#489—891no—
303#470—891no—
304#470—891no—
305#468—891no—
306#468—891no—
307#446—891no—
308#446—891no—
309#446—891no—
310#446—1781no—
311#446—1781no—
312C8×Q8—891no—
313C8×Q8—891no—
314C8×Q8—891no—
315C4×Q16—891no—
316C4×Q16—891no—
317C4×SD16—891no—
318C4×SD16—891no—
319#436—891no—
320#436—1781no—
321#435—1781no—
322C8×D4—891no—
323#433—1781no—
324#433—1781no—
325#433—1781no—
326#432—891no—
327#431C2×D8911yescharacteristic
328#424—1781no—
329#423—891no—
330C4×M16C2×D8911yescharacteristic
331C2×C4×C8C2×D8911yescharacteristic
332#335—891no—
333#335—891no—
334#334—891no—
335#334—891no—
336Q8⋊C8—891no—
337Q8⋊C8—891no—
338Q8⋊C8—891no—
339Q8⋊C8—891no—
340Q8⋊C8—891no—
341Q8⋊C8—891no—
342D4⋊C8—891no—
343D4⋊C8—891no—
344#322C2×D8911yescharacteristic
345#322C2×D8911yescharacteristic
346#322C2×D8911yescharacteristic
347#322C2×D8911yescharacteristic
348C2×Q16—891no—
349C2×Q16—891no—
350C2×SD16—891no—
351C2×SD16—891no—
352C2×M16—1781no—
353C2×M16—1781no—
354C2×M16C4×D8911yescharacteristic
355C2×M16C4×D8911yescharacteristic
356C22×C8—21no—
357C22×C8—1781no—
358C4⋊Q8—891no—
359C4⋊Q8—891no—
360#126—1781no—
361#125—891no—
362#125—1781no—
363#124—891no—
364#123—1781no—
365C22⋊Q8—891no—
366C22⋊Q8—891no—
367C22⋊Q8—891no—
368C22⋊Q8—1781no—
369#121—891no—
370C4×Q8—891no—
371C4×Q8—891no—
372C4×Q8—891no—
373C4×Q8—1781no—
374C4×D4—891no—
375C4×D4—1781no—
376#117—1781no—
377#117—1781no—
378C2×C42C22×D8911yescharacteristic
379#107—891no—
380#107—891no—
381#106—891no—
382#106—891no—
383C4⋊C8—891no—
384C4⋊C8—891no—
385C4⋊C8—891no—
386C4⋊C8—891no—
387C4⋊C8—1781no—
388C4⋊C8—1781no—
389C4⋊C8—1781no—
390C4⋊C8—1781no—
391C4⋊C8—1781no—
392C4⋊C8—1781no—
393C4⋊C8—1781no—
394C4⋊C8D35611yescharacteristic
395C4⋊C8D35611yescharacteristic
396#103—891no—
397#103—891no—
398#103—891no—
399#103—891no—
400#103—891no—
401#103—891no—
402#102—891no—
403#102—891no—
404C22⋊C8—1781no—
405C22⋊C8—1781no—
406C22⋊C8—1781no—
407C22⋊C8D35611yescharacteristic
408C22⋊C8D35611yescharacteristic
409#97—1781no—
410#97—1781no—
411#97—1781no—
412#97—1781no—
413#97C4×D8911yescharacteristic
414#97C4×D8911yescharacteristic
415C4×C8—21no—
416C4×C8—1781no—
417C4×C8—1781no—
418C4×C8—1781no—
419C4×C8C22×D8911yescharacteristic
420C4×C8C22×D8911yescharacteristic
421C4×C8C22×D8911yescharacteristic
422C4×C8C22×D8911yescharacteristic
423C4×C8C22×D8911yescharacteristic
424C4×C8C22×D8911yescharacteristic
425C2×Q8—891no—
426C2×Q8—891no—
427C2×Q8—891no—
428C2×Q8—1781no—
429C2×D4—891no—
430C2×D4—1781no—
431C22×C4—1781no—
432C22×C4C2×C4×D8911yescharacteristic
433C22×C4C2×D35611yescharacteristic
434C22×C4#1308357411yescharacteristic
435Q16—3561no—
436Q16—3561no—
437SD16—3561no—
438SD16—3561no—
439M16—41no—
440M16—41no—
441M16—7121no—
442M16—7121no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—42no—
446C2×C8—1781no—
447C2×C8—1781no—
448C2×C8—1781no—
449C2×C8—1781no—
450C2×C8—7121no—
451C2×C8C2×C4×D8911yescharacteristic
452C2×C8C2×C4×D8911yescharacteristic
453C2×C8C2×C4×D8911yescharacteristic
454C2×C8C2×C4×D8911yescharacteristic
455C2×C8C2×D35611yescharacteristic
456C2×C8C2×D35611yescharacteristic
457C2×C8C2×D35611yescharacteristic
458C2×C8C2×D35611yescharacteristic
459C4⋊C4—891no—
460C4⋊C4—891no—
461C4⋊C4—891no—
462C4⋊C4—891no—
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⋊C4—1781no—
472C4⋊C4—1781no—
473C4⋊C4—1781no—
474C22⋊C4—1781no—
475C22⋊C4—1781no—
476C22⋊C4—1781no—
477C22⋊C4—1781no—
478C22⋊C4—1781no—
479C22⋊C4—1781no—
480C22⋊C4—1781no—
481C42—1781no—
482C42—1781no—
483C42—1781no—
484C42C2×C4×D8911yescharacteristic
485C42C2×D35611yescharacteristic
486C42#1308357411yescharacteristic
487C42C23×D8911yescharacteristic
488C23—1781no—
489C23C4×D35611yescharacteristic
490Q8—1781no—
491Q8—1781no—
492Q8—1781no—
493Q8—1781no—
494Q8—1781no—
495Q8—1781no—
496Q8—7121no—
497D4—1781no—
498D4—1781no—
499D4—7121no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—3561no—
506C2×C4—3561no—
507C2×C4—1781no—
508C2×C4—1781no—
509C2×C4—1781no—
510C2×C4—1781no—
511C2×C4—1781no—
512C2×C4—1781no—
513C2×C4—1781no—
514C2×C4C4×D35611yescharacteristic
515C2×C4C4×D35611yescharacteristic
516C2×C4C4×D35611yescharacteristic
517C2×C4C22×C4×D8911yescharacteristic
518C2×C4C22×D35611yescharacteristic
519C2×C4C2×#1308357411yescharacteristic
520C8—22no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—3561no—
531C8—3561no—
532C8—3561no—
533C8—3561no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—3561no—
538C22—3561no—
539C22—3561no—
540C22C2×C4×D35611yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—3561no—
546C4—3561no—
547C4—3561no—
548C4—3561no—
549C4—3561no—
550C4—3561no—
551C4—3561no—
552C4#1915236411yescharacteristic
553C4#1915236411yescharacteristic
554C4#1915241011yescharacteristic
555C4#1915241511yescharacteristic
556C2—41no—
557C2—7121no—
558C2#2602897111yescharacteristic
559C2#2602909711yescharacteristic
560C2#2602916311yescharacteristic
subgroupG/H
centerC2×C4C22×D356
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#1451C2
socleC22×C89C2×C4×D4
prime radical#15667986C2×C4
cosocleC42×C89C24
hypercenter#1451D89
hypocenterC89#17988
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1451

Complements

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

NH ≅ G/Ntype
3. #26029346C2semidirect
4. #26019132C2semidirect
5. #26019125C2semidirect
6. #26019125C2semidirect
7. #26019111C2semidirect
8. #26019104C2semidirect
9. #26019104C2semidirect
10. #26019097C2semidirect
11. #26019090C2semidirect
12. #26019019C2semidirect
14. #26018708C2semidirect
15. C89×#1451C2semidirect
295. #1451D89semidirect
296. C89#17988semidirect

Maximal subgroups

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

subgroupindex
#260308582
#260294032
#260293462
#260191322
#260191252
#260191112
#260191042
#260190972
#260190902
#260190192
#260187132
#260187082
C89×#14512
#1798889