Finite Group Databasebeta

← #25081725

Subgroups — #25081725

Order 11008.

594 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145813C211yesmaximal, characteristic, complemented
2#19144988C211yesmaximal, characteristic, complemented
3#19143600C211yesmaximal, characteristic, complemented
4#19134175C211yesmaximal, characteristic, complemented
5#19134168C211yesmaximal, characteristic, complemented
6#19134133C211yesmaximal, characteristic, complemented
7#19134126C211yesmaximal, characteristic, complemented
8#19134051C211yesmaximal, characteristic, complemented
9#19134044C211yesmaximal, characteristic, complemented
10#19134009C211yesmaximal, characteristic, complemented
11#19134002C211yesmaximal, characteristic, complemented
12#19133360C211yesmaximal, characteristic, complemented
13#19133300C211yesmaximal, characteristic, complemented
14#19133277C211yesmaximal, characteristic, complemented
15C43×#3251C211yesmaximal, characteristic
16C2×#13063325C2211yescharacteristic
17#14583309—21no—
18#14583258—21no—
19#14583258—21no—
20#14583258—21no—
21#14583249C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583245C2211yescharacteristic
25#14583227—21no—
26#14583210—21no—
27#14583194C2211yescharacteristic
28#14583194C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33#14582977—21no—
34#14582977C2211yescharacteristic
35#14582971—21no—
36D4×C43⋊C8C2211yescharacteristic
37#14582960—21no—
38#14582956C2211yescharacteristic
39#14582952C2211yescharacteristic
40#14582900—21no—
41#14582900—21no—
42#14582855—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#478—21no—
59C43×#475C2211yescharacteristic
60C43×#474C2211yescharacteristic
61C43×#469—21no—
62C43×#468—21no—
63C43×#463—21no—
64C43×#460C2211yescharacteristic
65C43×#459C2211yescharacteristic
66C43×#423C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621877—21no—
69C2×#10621877D411yescharacteristic
70C2×#10621877D411yescharacteristic
71C22×C43⋊C8—21no—
72#13063325—21no—
73#13063325—21no—
74#13063325—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79#13063258—21no—
80#13063258—21no—
81#13063256—21no—
82#13063256—21no—
83C4⋊(C43⋊C8)—21no—
84C4⋊(C43⋊C8)—21no—
85C4⋊(C43⋊C8)C2311yescharacteristic
86C4⋊(C43⋊C8)C2311yescharacteristic
87C4⋊(C43⋊C8)C2311yescharacteristic
88C4⋊(C43⋊C8)C2311yescharacteristic
89#13063249—21no—
90#13063249—21no—
91#13063249—21no—
92#13063249—21no—
93#13063249—21no—
94#13063249—21no—
95#13063246—21no—
96#13063246—21no—
97#13063246—21no—
98#13063246—21no—
99#13063246—21no—
100#13063246—21no—
101C22⋊(C43⋊C8)—21no—
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105#13063236—21no—
106#13063236—21no—
107#13063236D411yescharacteristic
108#13063236D411yescharacteristic
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43—21no—
114C2×SD16×C43—21no—
115C2×D8×C43—21no—
116C2×M16×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#126×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43—21no—
122#124×C43D411yescharacteristic
123#123×C43—21no—
124C22⋊Q8×C43D411yescharacteristic
125#121×C43—21no—
126#121×C43—21no—
127#121×C43D411yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43C2311yescharacteristic
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144#41×C43—42no—
145#41×C43—42no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43C2×D411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—41no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4111yescharacteristic
159C22×Dic43—41no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—41no—
163C2×Dic86—82no—
164SD16×C43—81no—
165D8×C43—81no—
166M16×C43—81no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C42×C43—21no—
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43#4111yescharacteristic
188C42×C43C2411yescharacteristic
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—41no—
194C4⋊Dic43—41no—
195#10621877—41no—
196#10621877—41no—
197#10621877—42no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—42no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43—41no—
209C23×C43#12111yescharacteristic
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214D4×C43—21no—
215D4×C43—21no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—81no—
221D4×C43—81no—
222D4×C43—82no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—82no—
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—82no—
244Dic86—82no—
245Dic86—81no—
246Dic86—81no—
247C8×C43—41no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19382—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43C2×#12111yescharacteristic
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—81no—
276C4×C43#57511yescharacteristic
277C4×C43#57511yescharacteristic
278C4×C43#57711yescharacteristic
279C4×C43#57811yescharacteristic
280Dic43—81no—
281Dic43—81no—
282#3251D4311yescharacteristic
283#3238—431no—
284#3141—431no—
285#2969—431no—
286#1704—431no—
287#1703—431no—
288#1698—431no—
289#1697—431no—
290#1684—431no—
291#1683—431no—
292#1678—431no—
293#1677—431no—
294#1569—431no—
295#1553—431no—
296#1548—431no—
297C2×C43—41no—
298C2×C43—81no—
299C2×C43—161no—
300C2×C43#304011yescharacteristic
301C2×C43#306311yescharacteristic
302C2×C43#306811yescharacteristic
303#532C2×D4311yescharacteristic
304C2×C4⋊Q8—431no—
305#529C2×D4311yescharacteristic
306#501—861no—
307#489—861no—
308#489—861no—
309#489—861no—
310#487—431no—
311#487—431no—
312#486—431no—
313#486—431no—
314#483—861no—
315#480—861no—
316#478—21no—
317#477—431no—
318#477—431no—
319#476—431no—
320#476—431no—
321#475C2×D4311yescharacteristic
322#474C2×D4311yescharacteristic
323#469—21no—
324#468—21no—
325#463—21no—
326#460C2×D4311yescharacteristic
327#459C2×D4311yescharacteristic
328#446—431no—
329C8×Q8—431no—
330#436—431no—
331#436—861no—
332#435—861no—
333C8×D4—431no—
334#433—861no—
335#432—431no—
336#431—431no—
337#423C2×D4311yescharacteristic
338#417—861no—
339#417—861no—
340#405—861no—
341C4×M16—431no—
342#335—431no—
343#335—431no—
344#334—431no—
345#334—431no—
346#333—431no—
347#333—431no—
348#333—431no—
349#333—431no—
350#332—431no—
351#332—431no—
352#331—431no—
353#331—431no—
354C43#1938211yescharacteristic, complemented, Sylow
355C2×#41—21no—
356C22×Q8—861no—
357C2×SD16—21no—
358C2×D8—21no—
359C2×M16—21no—
360C2×M16—431no—
361C2×M16—431no—
362C2×M16—861no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8—861no—
367C4⋊Q8—861no—
368C4⋊Q8—861no—
369C4⋊Q8C22×D4311yescharacteristic
370#127C22×D4311yescharacteristic
371#126—21no—
372#125C22⋊D4311yescharacteristic
373#124—21no—
374#124C22⋊D4311yescharacteristic
375#123—21no—
376C22⋊Q8C22⋊D4311yescharacteristic
377#121—21no—
378#121—21no—
379#121C22⋊D4311yescharacteristic
380C4×Q8C22×D4311yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4C22×D4311yescharacteristic
385#117—21no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C42C22×D4311yescharacteristic
389#107—21no—
390#107—861no—
391#107—861no—
392#106—21no—
393#106—861no—
394#106—861no—
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404#103—21no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—431no—
425#97—431no—
426#97—861no—
427#97—861no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—861no—
431C4×C8—861no—
432#41—42no—
433#41—42no—
434C2×Q8—21no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—3442no—
438C2×Q8—1721no—
439C2×Q8C2×C22⋊D4311yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4C2×C22⋊D4311yescharacteristic
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—1721no—
449C22×C4D4×D4311yescharacteristic
450C22×C4#1062190011yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452SD16—81no—
453D8—81no—
454M16—81no—
455M16—1721no—
456M16—1721no—
457M16—1722no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—1722no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C4⋊C4C2×C22⋊D4311yescharacteristic
482C4⋊C4C2×C22⋊D4311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42D4×D4311yescharacteristic
492C42#1062190011yescharacteristic
493C42C2×C22⋊D4311yescharacteristic
494C42C23×D4311yescharacteristic
495C23—21no—
496C23—41no—
497C23#1306329711yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—41no—
501Q8—41no—
502Q8—3441no—
503Q8—3441no—
504Q8—3442no—
505D4—21no—
506D4—21no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—81no—
512D4—81no—
513D4—82no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4—3442no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4#1306329711yescharacteristic
530C2×C4#1306329711yescharacteristic
531C2×C4#1306329711yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C22×C22⋊D4311yescharacteristic
534C2×C4C2×#1062190011yescharacteristic
535C8—41no—
536C8—41no—
537C8—861no—
538C8—861no—
539C8—861no—
540C8—861no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22C2×#1306329711yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—3441no—
564C4—3441no—
565C4#1458369511yescharacteristic
566C4#1458369511yescharacteristic
567C4#1458371011yescharacteristic
568C4#1458371411yescharacteristic
569C2—41no—
570C2—81no—
571C2—161no—
572C2#1914408711yescharacteristic
573C2#1914428811yescharacteristic
574C2#1914432511yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3251C2
socleC22×C43C2×#121
hypercenter#3251D43
hypocenterC43#19382
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3251

Complements

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

NH ≅ G/Ntype
1. #19145813C2semidirect
2. #19144988C2semidirect
3. #19143600C2semidirect
4. #19134175C2semidirect
5. #19134168C2semidirect
6. #19134133C2semidirect
7. #19134126C2semidirect
8. #19134051C2semidirect
9. #19134044C2semidirect
10. #19134009C2semidirect
11. #19134002C2semidirect
12. #19133360C2semidirect
13. #19133300C2semidirect
14. #19133277C2semidirect
354. C43#19382semidirect

Maximal subgroups

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

subgroupindex
#191458132
#191449882
#191436002
#191341752
#191341682
#191341332
#191341262
#191340512
#191340442
#191340092
#191340022
#191333602
#191333002
#191332772
C43×#32512
#1938243