Finite Group Databasebeta

← #25080011

Subgroups — #25080011

Order 11008.

596 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145567C211yesmaximal, characteristic
2#19145155C211yesmaximal, characteristic, complemented
3#19143571C211yesmaximal, characteristic, complemented
4#19134103C211yesmaximal, characteristic, complemented
5#19134096C211yesmaximal, characteristic, complemented
6#19134069C211yesmaximal, characteristic, complemented
7#19134062C211yesmaximal, characteristic, complemented
8#19134023C211yesmaximal, characteristic, complemented
9#19134016C211yesmaximal, characteristic, complemented
10#19134013C211yesmaximal, characteristic, complemented
11#19134006C211yesmaximal, characteristic, complemented
12#19133341C211yesmaximal, characteristic, complemented
13#19133305C211yesmaximal, characteristic, complemented
14#19133298C211yesmaximal, characteristic, complemented
15C43×#3233C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583295C2211yescharacteristic
18#14583281—21no—
19#14583273C2211yescharacteristic
20#14583256—21no—
21#14583249C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583130—21no—
24#14583130—21no—
25#14583109C2211yescharacteristic
26#14583104C2211yescharacteristic
27#14583099C2211yescharacteristic
28#14583094C2211yescharacteristic
29#14583059—21no—
30#14583042—21no—
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33C4×#10621884—21no—
34C4×#10621884—21no—
35#14582977C2211yescharacteristic
36#14582971—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582956C2211yescharacteristic
41#14582952C2211yescharacteristic
42#14582855—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#499—21no—
59C43×#488—21no—
60C43×#485—21no—
61C43×#482—21no—
62C43×#477C2211yescharacteristic
63C43×#476C2211yescharacteristic
64C43×#475C2211yescharacteristic
65C43×#474C2211yescharacteristic
66C43×#431C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×#10621882—21no—
74C2×#10621877—21no—
75C22×C43⋊C8—21no—
76C22×C43⋊C8D411yescharacteristic
77C22×C43⋊C8D411yescharacteristic
78#13063325C2311yescharacteristic
79#13063322C2311yescharacteristic
80#13063313—21no—
81#13063299—21no—
82#13063299—21no—
83C4×D172—21no—
84C4×D172—21no—
85#13063256—21no—
86#13063256—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93#13063249—21no—
94#13063249—21no—
95#13063248—21no—
96#13063248—21no—
97#13063245—21no—
98#13063245—21no—
99#13063245—21no—
100#13063245—21no—
101C22⋊(C43⋊C8)—21no—
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105#13063236—21no—
106#13063236—21no—
107C4×C43⋊C8—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8D411yescharacteristic
110C4×C43⋊C8D411yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C4⋊Q8×C43C2311yescharacteristic
114C4⋊Q8×C43C2311yescharacteristic
115#126×C43—21no—
116#125×C43—21no—
117#125×C43D411yescharacteristic
118#124×C43D411yescharacteristic
119#123×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43D411yescharacteristic
123#121×C43D411yescharacteristic
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43C2311yescharacteristic
129#117×C43—21no—
130#117×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C2×C22⋊D43—41no—
154#10621898—81no—
155#10621898—81no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×C4×D43—41no—
160C2×Dic86—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—41no—
181C42×C43—21no—
182C42×C43—41no—
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43#4111yescharacteristic
186C42×C43C2411yescharacteristic
187#10621885—81no—
188#10621884—42no—
189#10621884—42no—
190#10621884—81no—
191#10621883—81no—
192#10621882—81no—
193(C2×D43)⋊C4—41no—
194(C2×D43)⋊C4—41no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197#10621877—42no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—41no—
204C2×C43⋊C8—42no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C23×C43—21no—
210C23×C43#12111yescharacteristic
211C22×D43—41no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—81no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—42no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C22⋊D43—82no—
239C2×Dic43—41no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—41no—
244D172—81no—
245C4×D43—82no—
246Dic86—41no—
247Dic86—41no—
248C8×C43—41no—
249C8×C43—41no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8#13512yes—
258#19224—431nomaximal, Sylow
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43C2×#12111yescharacteristic
266C2×D43—81no—
267C2×D43—81no—
268C2×D43—81no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43C2×#13511yescharacteristic
279C4×C43#57511yescharacteristic
280C4×C43#57711yescharacteristic
281C4×C43#57711yescharacteristic
282Dic43—81no—
283#3233D4311yescharacteristic, complemented
284#3212—431no—
285#3167—431no—
286#2966—431no—
287#1692—431no—
288#1691—431no—
289#1686—431no—
290#1685—431no—
291#1680—431no—
292#1679—431no—
293#1678—431no—
294#1677—431no—
295#1564—431no—
296#1554—431no—
297#1553—431no—
298C2×C43—41no—
299C2×C43—81no—
300C2×C43#303511yescharacteristic
301C2×C43#305711yescharacteristic
302C2×C43#306711yescharacteristic
303D43—161no—
304#533C2×D4311yescharacteristic
305#532—431no—
306#529C2×D4311yescharacteristic
307#499—21no—
308#498—431no—
309#495—861no—
310#492—431no—
311#488—21no—
312#488—861no—
313#487—431no—
314#486—431no—
315#485—21no—
316#482—21no—
317#477C2×D4311yescharacteristic
318#476C2×D4311yescharacteristic
319#475C2×D4311yescharacteristic
320#474C2×D4311yescharacteristic
321#465—861no—
322#465—861no—
323#462—431no—
324#461—431no—
325#460—431no—
326#459—431no—
327#452—861no—
328#449—861no—
329#446—431no—
330C8×Q8—431no—
331C4×SD16—861no—
332C4×SD16—861no—
333#436—431no—
334#435—861no—
335C8×D4—431no—
336C8×D4—861no—
337#433—861no—
338#432—431no—
339#431—431no—
340#431C2×D4311yescharacteristic
341#405—861no—
342C2×C4×C8—431no—
343#335—431no—
344#335—431no—
345#334—431no—
346#334—431no—
347#333—431no—
348#333—431no—
349#332—431no—
350#332—431no—
351#332—431no—
352#332—431no—
353#331—431no—
354#331—431no—
355C43#1922411yescharacteristic, complemented, Sylow
356C2×#41—861no—
357C2×Q16—861no—
358C2×SD16—861no—
359C2×SD16—861no—
360C2×SD16—861no—
361C2×SD16—861no—
362C2×D8—861no—
363C2×M16—861no—
364C22×C8—431no—
365C22×C8—431no—
366C22×C8—861no—
367C4⋊Q8—431no—
368C4⋊Q8C22×D4311yescharacteristic
369C4⋊Q8C22×D4311yescharacteristic
370#127—431no—
371#126—21no—
372#125—21no—
373#125C22⋊D4311yescharacteristic
374#124—861no—
375#124C22⋊D4311yescharacteristic
376#123—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8C22⋊D4311yescharacteristic
380#121—861no—
381#121—861no—
382#121C22⋊D4311yescharacteristic
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C22×D4311yescharacteristic
386C4×D4—21no—
387C4×D4—861no—
388C4×D4—861no—
389C4×D4C22×D4311yescharacteristic
390#117—21no—
391#117—21no—
392C2×C42C22×D4311yescharacteristic
393#107—21no—
394#107—21no—
395#106—21no—
396#106—21no—
397#106—861no—
398#106—861no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—21no—
408#103—21no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#102—21no—
414#102—21no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419C22⋊C8—21no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—861no—
425#97—861no—
426C4×C8—21no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—861no—
432C4×C8—861no—
433#41—3441no—
434#41—3441no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—861no—
438C2×Q8C2×C22⋊D4311yescharacteristic
439C2×D4—21no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—1721no—
444C2×D4C2×C22⋊D4311yescharacteristic
445C22×C4—21no—
446C22×C4—1721no—
447C22×C4D4×D4311yescharacteristic
448C22×C4#1062190011yescharacteristic
449C22×C4C2×C22⋊D4311yescharacteristic
450Q16—3441no—
451SD16—3441no—
452SD16—3441no—
453SD16—1722no—
454SD16—1722no—
455D8—3441no—
456M16—1722no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—431no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—862no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—1721no—
469C2×C8—1722no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4C2×C22⋊D4311yescharacteristic
483C4⋊C4C2×C22⋊D4311yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C42—21no—
493C42—41no—
494C42D4×D4311yescharacteristic
495C42#1062190011yescharacteristic
496C42C2×C22⋊D4311yescharacteristic
497C42C23×D4311yescharacteristic
498C23—21no—
499C23—1721no—
500C23#1306329711yescharacteristic
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—81no—
506Q8—1721no—
507Q8—1721no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—3441no—
512D4—3442no—
513D4—1721no—
514D4—1721no—
515D4—1721no—
516D4—1721no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—3442no—
530C2×C4—1721no—
531C2×C4#1306329711yescharacteristic
532C2×C4#1306329711yescharacteristic
533C2×C4#1306329711yescharacteristic
534C2×C4C2×D4×D4311yescharacteristic
535C2×C4C22×C22⋊D4311yescharacteristic
536C2×C4C2×#1062190011yescharacteristic
537C8—41no—
538C8—41no—
539C8—432no—
540C8—861no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C8—1721no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—3441no—
554C22—3441no—
555C22—3441no—
556C22C2×#1306329711yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—3441no—
567C4#135×D4311yescharacteristic
568C4#1458369611yescharacteristic
569C4#1458370711yescharacteristic
570C4#1458370711yescharacteristic
571C2—41no—
572C2—81no—
573C2—6881no—
574C2#1914404611yescharacteristic
575C2#1914423611yescharacteristic
576C2#1914431211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3233C2
socleC22×C43C2×#121
prime radical#19145567C2
hypercenter#3233D43
hypocenterC43#19224
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3233

Complements

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

NH ≅ G/Ntype
2. #19145155C2semidirect
3. #19143571C2semidirect
4. #19134103C2semidirect
5. #19134096C2semidirect
6. #19134069C2semidirect
7. #19134062C2semidirect
8. #19134023C2semidirect
9. #19134016C2semidirect
10. #19134013C2semidirect
11. #19134006C2semidirect
12. #19133341C2semidirect
13. #19133305C2semidirect
14. #19133298C2semidirect
15. C43×#3233C2semidirect
283. #3233D43semidirect
355. C43#19224semidirect

Maximal subgroups

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

subgroupindex
#191455672
#191451552
#191435712
#191341032
#191340962
#191340692
#191340622
#191340232
#191340162
#191340132
#191340062
#191333412
#191333052
#191332982
C43×#32332
#1922443