Finite Group Databasebeta

← #25086615

Subgroups — #25086615

Order 11008.

598 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#19147335C211yesmaximal, characteristic, complemented
2#19147010C211yesmaximal, characteristic, complemented
3#19146545C211yesmaximal, characteristic
4#19134257C211yesmaximal, characteristic, complemented
5#19134133C211yesmaximal, characteristic, complemented
6#19134048C211yesmaximal, characteristic, complemented
7#19134001C211yesmaximal, characteristic, complemented
8#19133977C211yesmaximal, characteristic, complemented
9#19133788C211yesmaximal, characteristic, complemented
10#19133739C211yesmaximal, characteristic, complemented
11#19133735C211yesmaximal, characteristic, complemented
12#19133704C211yesmaximal, characteristic, complemented
13#19133432C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic, complemented
15C43×#3362C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17#14583614C2211yescharacteristic
18#14583297C2211yescharacteristic
19#14583278C2211yescharacteristic
20#14583261—21no—
21#14583251C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583238—21no—
25#14583222—21no—
26#14583220—21no—
27#14583194C2211yescharacteristic
28#14583194C2211yescharacteristic
29#14583186C2211yescharacteristic
30#14583181—21no—
31#14583179C2211yescharacteristic
32#14583133—21no—
33#14583125—21no—
34#14583121—21no—
35#14583109C2211yescharacteristic
36#14583091C2211yescharacteristic
37#14583044—21no—
38#14583030C2211yescharacteristic
39#14583004—21no—
40C4×#10621884C2211yescharacteristic
41C8×D172C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582934—21no—
44#14582895—21no—
45#14582651C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582644C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57C43×#550C2211yescharacteristic
58C43×#486—21no—
59C43×#486C2211yescharacteristic
60C43×#476—21no—
61C43×#476C2211yescharacteristic
62C43×#460—21no—
63C43×#460C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—41no—
69C2×#10621884D411yescharacteristic
70C2×#10621882—21no—
71C22×C43⋊C8—21no—
72C2×C8×D43—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063320—41no—
76#13063313—21no—
77#13063311—41no—
78#13063301—21no—
79#13063299—21no—
80#13063296—21no—
81C4×Dic86—21no—
82C4×D172C2311yescharacteristic
83#13063284—21no—
84#13063283—21no—
85#13063283—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063257—21no—
90#13063257—21no—
91#13063256—21no—
92#13063256D411yescharacteristic
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063249—21no—
98#13063249—21no—
99#13063249D411yescharacteristic
100#13063248—21no—
101#13063248—21no—
102#13063248—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—41no—
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111(C2×D43)⋊C8—21no—
112#13063236—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×SD16×C43—21no—
117C2×SD16×C43D411yescharacteristic
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—41no—
121C4⋊Q8×C43C2311yescharacteristic
122#127×C43—21no—
123#127×C43C2311yescharacteristic
124#121×C43—21no—
125#121×C43—41no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2311yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#106×C43—21no—
133#106×C43D411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43D411yescharacteristic
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—41no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—41no—
158C2×C22⋊D43—41no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163SD16×C43—41no—
164SD16×C43—42no—
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—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—41no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—41no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184#10621885—42no—
185#10621885—82no—
186#10621884—22no—
187#10621882—81no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—41no—
198C4×Dic43—41no—
199C4×Dic43—41no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C8×D43—42no—
208C23×C43—21no—
209C23×C43—41no—
210C22×D43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—81no—
215Q8×C43—161no—
216Q8×C43#13512yes—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—82no—
224D4×C43—81no—
225D4×C43—161no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—82no—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C22⋊D43—161no—
239C2×Dic43—21no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242D172—21no—
243D172—21no—
244C4×D43—41no—
245C4×D43—41no—
246Dic86—41no—
247Dic86—41no—
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#19800—431nomaximal, Sylow
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43D4211yescharacteristic
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—41no—
269C4×C43—22no—
270C4×C43—21no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—81no—
276C4×C43C2×#13511yescharacteristic
277C4×C43#57511yescharacteristic
278C4×C43#57711yescharacteristic
279C4×C43#57811yescharacteristic
280Dic43—41no—
281Dic43—81no—
282Dic43—81no—
283#3369—431no—
284#3362D4311yescharacteristic, complemented
285#3340—431no—
286#3305—431no—
287#1720—431no—
288#1698—431no—
289#1683—431no—
290#1677—431no—
291#1672—431no—
292#1641—431no—
293#1634—431no—
294#1633—431no—
295#1628—431no—
296#1582—431no—
297SD16⋊C8—431no—
298C2×C43—81no—
299C2×C43—161no—
300C2×C43#326911yescharacteristic
301C2×C43#328211yescharacteristic
302C2×C43#328811yescharacteristic
303D43—81no—
304Q82C2×D4311yescharacteristic
305#556—431no—
306#555—431no—
307#550C2×D4311yescharacteristic
308#498—431no—
309#494—431no—
310#489—861no—
311#487—431no—
312#486—21no—
313#486—431no—
314#486—431no—
315#486C2×D4311yescharacteristic
316#485—861no—
317#482—861no—
318#482—861no—
319#477—431no—
320#477—431no—
321#476—21no—
322#476—431no—
323#476C2×D4311yescharacteristic
324#475—861no—
325#474—431no—
326#466—861no—
327#465—861no—
328#464—861no—
329#462—431no—
330#460—21no—
331#460C2×D4311yescharacteristic
332#459—431no—
333#449—861no—
334#446—431no—
335C8×Q8C2×D4311yescharacteristic
336#441—861no—
337C4×SD16—21no—
338C4×SD16—431no—
339C4×SD16C2×D4311yescharacteristic
340C8×D4—431no—
341C8×D4—431no—
342#427—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#1980011yescharacteristic, complemented, Sylow
356C2×#41—21no—
357C2×Q16—861no—
358C2×Q16—1721no—
359C2×SD16—21no—
360C2×SD16—431no—
361C2×SD16C22⋊D4311yescharacteristic
362C2×D8—861no—
363C22×C8—861no—
364C22×C8—861no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—41no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8C22×D4311yescharacteristic
371#127—21no—
372#127C22×D4311yescharacteristic
373#126—1721no—
374#124—861no—
375#124—1721no—
376C22⋊Q8—861no—
377#121—21no—
378#121—41no—
379#121—861no—
380#121—861no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8—861no—
384C4×Q8C22×D4311yescharacteristic
385C4×Q8C22×D4311yescharacteristic
386C4×D4—21no—
387C4×D4—431no—
388C4×D4C22×D4311yescharacteristic
389#117—861no—
390#117—861no—
391#117—861no—
392#107—861no—
393#107—861no—
394#107—861no—
395#106—21no—
396#106—431no—
397#106—861no—
398#106—861no—
399#106—861no—
400#106C22⋊D4311yescharacteristic
401C4⋊C8—21no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—861no—
406C4⋊C8C22×D4311yescharacteristic
407#103—431no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103C22⋊D4311yescharacteristic
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—431no—
419#102—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—1721no—
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—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8D4×D4311yescharacteristic
440C2×Q8C2×C22⋊D4311yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—431no—
447C2×D4—1721no—
448C2×D4C2×C22⋊D4311yescharacteristic
449C22×C4—21no—
450C22×C4—41no—
451C22×C4—861no—
452Q16—3442no—
453Q16—1722no—
454SD16—41no—
455SD16—42no—
456SD16—862no—
457D8—3441no—
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—41no—
474C4⋊C4—41no—
475C4⋊C4—431no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—1721no—
481C4⋊C4D4×D4311yescharacteristic
482C4⋊C4C2×C22⋊D4311yescharacteristic
483C4⋊C4C2×C22⋊D4311yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—861no—
487C22⋊C4—1721no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C42—21no—
492C42—21no—
493C42—41no—
494C42—1721no—
495C42—1721no—
496C42C23×D4311yescharacteristic
497C23—21no—
498C23—41no—
499C23—861no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—81no—
504Q8—161no—
505Q8—3441no—
506Q8—1721no—
507Q8—1721no—
508Q8#1306334612yes—
509D4—21no—
510D4—21no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—82no—
516D4—81no—
517D4—161no—
518D4—861no—
519D4—861no—
520D4—6881no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4—861no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
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—41no—
548C22—41no—
549C22—41no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—1721no—
554C22—1721no—
555C22—1721no—
556C22D4×C22⋊D4311yescharacteristic
557C4—22no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—81no—
564C4—3441no—
565C4—3441no—
566C4—1721no—
567C4C2×#1306334611yescharacteristic
568C4#1458369711yescharacteristic
569C4#1458370511yescharacteristic
570C4#1458371411yescharacteristic
571C2—81no—
572C2—161no—
573C2—3441no—
574C2#1914615111yescharacteristic
575C2#1914630211yescharacteristic
576C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3362C2
socleC22×C43D42
prime radical#19146545C2
hypercenter#3362D43
hypocenterC43#19800
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3362

Complements

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

NH ≅ G/Ntype
1. #19147335C2semidirect
2. #19147010C2semidirect
4. #19134257C2semidirect
5. #19134133C2semidirect
6. #19134048C2semidirect
7. #19134001C2semidirect
8. #19133977C2semidirect
9. #19133788C2semidirect
10. #19133739C2semidirect
11. #19133735C2semidirect
12. #19133704C2semidirect
13. #19133432C2semidirect
14. #19133405C2semidirect
15. C43×#3362C2semidirect
284. #3362D43semidirect
355. C43#19800semidirect

Maximal subgroups

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

subgroupindex
#191473352
#191470102
#191465452
#191342572
#191341332
#191340482
#191340012
#191339772
#191337882
#191337392
#191337352
#191337042
#191334322
#191334052
C43×#33622
#1980043