Finite Group Databasebeta

← #25087219

Subgroups — #25087219

Order 11008.

600 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#19147300C211yesmaximal, characteristic
2#19146983C211yesmaximal, characteristic, complemented
3#19146528C211yesmaximal, characteristic, complemented
4#19134249C211yesmaximal, characteristic, complemented
5#19134174C211yesmaximal, characteristic, complemented
6#19134034C211yesmaximal, characteristic, complemented
7#19134011C211yesmaximal, characteristic, complemented
8#19133992C211yesmaximal, characteristic, complemented
9#19133800C211yesmaximal, characteristic, complemented
10#19133767C211yesmaximal, characteristic, complemented
11#19133721C211yesmaximal, characteristic, complemented
12#19133667C211yesmaximal, characteristic, complemented
13#19133445C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3360C211yesmaximal, characteristic, complemented
16#14583606C2211yescharacteristic
17#14583570C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583273C2211yescharacteristic
20#14583262—21no—
21#14583251C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583234—21no—
25#14583232—21no—
26#14583223—21no—
27#14583202—21no—
28#14583194C2211yescharacteristic
29#14583191C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583181C2211yescharacteristic
32#14583138—21no—
33#14583130—21no—
34#14583099C2211yescharacteristic
35#14583094C2211yescharacteristic
36#14583092—21no—
37#14583059—21no—
38#14583029C2211yescharacteristic
39#14583008—21no—
40C4×#10621885C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43C2×#13063258—21no—
44#14582893—21no—
45#14582651C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#556C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#488—21no—
59C43×#487C2211yescharacteristic
60C43×#479—21no—
61C43×#476C2211yescharacteristic
62C43×#463—21no—
63C43×#461C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43—21no—
66C4×D8×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621885D411yescharacteristic
69C2×#10621884—21no—
70C2×#10621884—41no—
71C2×#10621882—21no—
72C22×C43⋊C8—21no—
73C22×C43⋊C8—21no—
74#13063325C2311yescharacteristic
75#13063322C2311yescharacteristic
76#13063321—21no—
77#13063316—21no—
78#13063304—21no—
79#13063302—41no—
80#13063299—21no—
81#13063298—41no—
82C4×Dic86C2311yescharacteristic
83D4×Dic43—21no—
84#13063287—21no—
85C2×C4⋊Dic43—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258D411yescharacteristic
91#13063256—21no—
92#13063256—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249D411yescharacteristic
99#13063248—21no—
100#13063248—21no—
101#13063248—41no—
102#13063248D411yescharacteristic
103#13063247—21no—
104#13063247—21no—
105#13063246—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112#13063235—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×SD16×C43—21no—
116C2×D8×C43D411yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#126×C43—41no—
120#125×C43—21no—
121#124×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43—21no—
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131C2×C4⋊C4×C43—21no—
132#107×C43D411yescharacteristic
133#106×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43C2×D411yescharacteristic
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—41no—
152C2×C22⋊D43—41no—
153C2×C22⋊D43—41no—
154C22×Dic43—41no—
155#10621898—42no—
156#10621898—81no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×C4×D43—41no—
161C2×Dic86—21no—
162C2×Dic86C2×D411yescharacteristic
163SD16×C43—42no—
164D8×C43—22no—
165C2×C8×C43—21no—
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C42×C43—21no—
185C42×C43—41no—
186C42×C43C2411yescharacteristic
187C22⋊Dic43—41no—
188#10621885—41no—
189#10621884—81no—
190#10621884—82no—
191#10621882—42no—
192(C2×D43)⋊C4—41no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—41no—
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—21no—
198Dic43⋊C4—41no—
199C4×Dic43—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—42no—
205C2×C43⋊C8—81no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C23×C43—21no—
209C23×C43—21no—
210C22×D43—41no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—81no—
216D4×C43—21no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43#13512yes—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—161no—
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43H(5,𝔽2)11yescharacteristic
234C22⋊D43—82no—
235C22⋊D43—161no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—41no—
239C2×Dic43—161no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—41no—
244D172—81no—
245C4×D43—82no—
246Dic86—21no—
247Dic86—21no—
248Dic86—81no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258#19840—431nomaximal, Sylow
259C22×C43—22no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43D4211yescharacteristic
266C2×D43—81no—
267C2×D43—81no—
268C2×D43—81no—
269C4×C43—21no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43C2×#13511yescharacteristic
277C4×C43#57511yescharacteristic
278C4×C43#57711yescharacteristic
279C4×C43#57811yescharacteristic
280Dic43—41no—
281Dic43—41no—
282Dic43—81no—
283#3366—431no—
284#3360D4311yescharacteristic, complemented
285#3338—431no—
286#3304—431no—
287#1719—431no—
288#1704—431no—
289#1681—431no—
290#1678—431no—
291#1675—431no—
292#1643—431no—
293#1638—431no—
294#1631—431no—
295#1622—431no—
296#1584—431no—
297#1580—431no—
298C2×C43—42no—
299C2×C43—81no—
300C2×C43#326711yescharacteristic
301C2×C43#328511yescharacteristic
302C2×C43#328811yescharacteristic
303D43—161no—
304#556C2×D4311yescharacteristic
305#554—431no—
306#554C2×D4311yescharacteristic
307#550—431no—
308#500—431no—
309#492—431no—
310#490—861no—
311#488—21no—
312#487—431no—
313#487C2×D4311yescharacteristic
314#486—431no—
315#486—431no—
316#484—861no—
317#484—861no—
318#482—861no—
319#479—21no—
320#478—861no—
321#477—431no—
322#477—431no—
323#476—431no—
324#476C2×D4311yescharacteristic
325#475—431no—
326#467—861no—
327#465—861no—
328#463—21no—
329#461C2×D4311yescharacteristic
330#460—431no—
331#459—431no—
332#459—861no—
333#452—861no—
334#446—431no—
335C8×Q8C2×D4311yescharacteristic
336#442—861no—
337C4×Q16—431no—
338C4×SD16—21no—
339C4×D8C2×D4311yescharacteristic
340C8×D4—431no—
341C8×D4—431no—
342C2×#107—861no—
343#416—861no—
344#335—431no—
345#334—431no—
346#333—431no—
347#333—431no—
348#332—431no—
349#331—431no—
350Q8⋊C8—431no—
351Q8⋊C8—431no—
352D4⋊C8—431no—
353D4⋊C8—431no—
354#322—431no—
355C43#1984011yescharacteristic, complemented, Sylow
356C2×#41—861no—
357C2×Q16—431no—
358C2×SD16—21no—
359C2×SD16—861no—
360C2×SD16—1721no—
361C2×D8—861no—
362C2×D8C22⋊D4311yescharacteristic
363C22×C8—861no—
364C22×C8—861no—
365C4⋊Q8—431no—
366C4⋊Q8C22×D4311yescharacteristic
367C4⋊Q8C22×D4311yescharacteristic
368#127—431no—
369#127—861no—
370#126—41no—
371#125—21no—
372#125—861no—
373#124—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—41no—
377C22⋊Q8—861no—
378C22⋊Q8—1721no—
379#121—861no—
380#121—1721no—
381C4×Q8—21no—
382C4×Q8—431no—
383C4×Q8C22×D4311yescharacteristic
384C4×D4—21no—
385C4×D4—861no—
386C4×D4—861no—
387C4×D4C22×D4311yescharacteristic
388C4×D4C22×D4311yescharacteristic
389#117—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—861no—
392#107—431no—
393#107—861no—
394#107—861no—
395#107—861no—
396#107—861no—
397#107C22⋊D4311yescharacteristic
398#106—21no—
399#106—861no—
400#106—861no—
401C4⋊C8—21no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—861no—
406C4⋊C8C22×D4311yescharacteristic
407#103—21no—
408#103—21no—
409#103—21no—
410#103—431no—
411#103—431no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—1721no—
416#102—21no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102C22⋊D4311yescharacteristic
425#102C22⋊D4311yescharacteristic
426C22⋊C8—861no—
427C22⋊C8—861no—
428#97—861no—
429C4×C8—21no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8C22×D4311yescharacteristic
433#41—3441no—
434#41—1722no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—431no—
438C2×Q8—861no—
439C2×Q8D4×D4311yescharacteristic
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—1721no—
444C2×D4—1721no—
445C2×D4C2×C22⋊D4311yescharacteristic
446C2×D4C2×C22⋊D4311yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4—1721no—
451C22×C4—1721no—
452Q16—1721no—
453SD16—42no—
454SD16—3442no—
455SD16—3441no—
456D8—22no—
457D8—1722no—
458C2×C8—21no—
459C2×C8—431no—
460C2×C8—431no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—3441no—
466C2×C8—1722no—
467C2×C8C2×C22⋊D4311yescharacteristic
468C2×C8C2×C22⋊D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—431no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4D4×D4311yescharacteristic
484C4⋊C4C2×C22⋊D4311yescharacteristic
485C4⋊C4C2×C22⋊D4311yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C42—21no—
494C42—41no—
495C42—861no—
496C42C23×D4311yescharacteristic
497C23—21no—
498C23—21no—
499C23—1721no—
500Q8—21no—
501Q8—21no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—861no—
506Q8—861no—
507Q8—3441no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—3441no—
512D4—3442no—
513D4—1721no—
514D4—1721no—
515D4—1721no—
516D4—1721no—
517D4—6881no—
518D4#1306334512yes—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—161no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—3442no—
533C2×C4—1721no—
534C2×C4—6881no—
535C2×C4C2×D4×D4311yescharacteristic
536C2×C4C22×C22⋊D4311yescharacteristic
537C2×C4#1306337011yescharacteristic
538C8—21no—
539C8—21no—
540C8—41no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C8—1721no—
547C22—22no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—3441no—
554C22—3441no—
555C22—3441no—
556C22D4×C22⋊D4311yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—3441no—
565C4—1721no—
566C4—1721no—
567C4C2×#1306334511yescharacteristic
568C4#1458369611yescharacteristic
569C4#1458370611yescharacteristic
570C4#1458371411yescharacteristic
571C2—42no—
572C2—81no—
573C2—6881no—
574C2#1914612011yescharacteristic
575C2#1914633211yescharacteristic
576C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3360C2
socleC22×C43D42
prime radical#19147300C2
hypercenter#3360D43
hypocenterC43#19840
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3360

Complements

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

NH ≅ G/Ntype
2. #19146983C2semidirect
3. #19146528C2semidirect
4. #19134249C2semidirect
5. #19134174C2semidirect
6. #19134034C2semidirect
7. #19134011C2semidirect
8. #19133992C2semidirect
9. #19133800C2semidirect
10. #19133767C2semidirect
11. #19133721C2semidirect
12. #19133667C2semidirect
13. #19133445C2semidirect
14. #19133419C2semidirect
15. C43×#3360C2semidirect
284. #3360D43semidirect
355. C43#19840semidirect

Maximal subgroups

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

subgroupindex
#191473002
#191469832
#191465282
#191342492
#191341742
#191340342
#191340112
#191339922
#191338002
#191337672
#191337212
#191336672
#191334452
#191334192
C43×#33602
#1984043