Finite Group Databasebeta

← #25086555

Subgroups — #25086555

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147335C211yesmaximal, characteristic, complemented
2#19146514C211yesmaximal, characteristic
3#19146460C211yesmaximal, characteristic
4#19134239C211yesmaximal, characteristic, complemented
5#19134147C211yesmaximal, characteristic, complemented
6#19134048C211yesmaximal, characteristic, complemented
7#19134025C211yesmaximal, characteristic, complemented
8#19133967C211yesmaximal, characteristic, complemented
9#19133850C211yesmaximal, characteristic, complemented
10#19133844C211yesmaximal, characteristic, complemented
11#19133816C211yesmaximal, characteristic, complemented
12#19133744C211yesmaximal, characteristic
13#19133432C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic, complemented
15Q8×SD16×C43C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17#14583553C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583261—21no—
20#14583251C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583243—21no—
25#14583227—21no—
26#14583186C2211yescharacteristic
27#14583184C2211yescharacteristic
28#14583181—21no—
29#14583179C2211yescharacteristic
30#14583139—21no—
31#14583130—21no—
32#14583121—21no—
33#14583109C2211yescharacteristic
34#14583109C2211yescharacteristic
35#14583101C2211yescharacteristic
36#14583058—21no—
37#14583038—21no—
38#14583030C2211yescharacteristic
39#14583004—21no—
40C4×#10621884C2211yescharacteristic
41C8×D172C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582892—21no—
44C2×#13063249—21no—
45#14582651C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#498—21no—
59C43×#498C2211yescharacteristic
60C43×#476—21no—
61C43×#476C2211yescharacteristic
62C43×#475—21no—
63C43×#475C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621884—21no—
71C2×#10621884D411yescharacteristic
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063320—41no—
77#13063313—21no—
78#13063309—41no—
79#13063305—21no—
80#13063301—21no—
81#13063299—21no—
82C4×Dic86—21no—
83C4×D172C2311yescharacteristic
84#13063283—21no—
85C2×C4⋊Dic43—21no—
86#13063258—21no—
87#13063258—41no—
88#13063256—21no—
89#13063256—21no—
90#13063256D411yescharacteristic
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063250—21no—
96#13063250—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—41no—
102#13063249D411yescharacteristic
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248—21no—
107#13063246—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111(C2×D43)⋊C8—21no—
112#13063236—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×Q8×C43—21no—
116C2×SD16×C43D411yescharacteristic
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—41no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131#106×C43—21no—
132#106×C43—21no—
133#106×C43—21no—
134#106×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43D411yescharacteristic
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—41no—
148C2×Q8×C43—42no—
149C2×Q8×C43—81no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C2×C22⋊D43—41no—
156C22×Dic43—41no—
157#10621900—42no—
158#10621900—81no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163SD16×C43—22no—
164C2×C8×C43—21no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
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—41no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—41no—
184C42×C43C2411yescharacteristic
185#10621885—42no—
186#10621885—81no—
187#10621884—22no—
188#10621884—81no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—41no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—41no—
198C4⋊Dic43C2×D411yescharacteristic
199Dic43⋊C4—41no—
200C4×Dic43—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—81no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C8×D43—81no—
209C23×C43—21no—
210C22×D43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—82no—
217Q8×C43—81no—
218Q8×C43—161no—
219Q8×C43#13512yes—
220D4×C43—21no—
221D4×C43#13712yes—
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—82no—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43H(5,𝔽2)11yescharacteristic
235C22⋊D43—82no—
236C2×Dic43—21no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—82no—
240D172—21no—
241D172—21no—
242C4×D43—41no—
243C4×D43—41no—
244Dic86—41no—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—41no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19796—431nomaximal, Sylow
258C22×C43—22no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43D4211yescharacteristic
262C2×D43—41no—
263C2×D43—41no—
264C2×D43—41no—
265C4×C43—22no—
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43C2×#13511yescharacteristic
274C4×C43C2×#13711yescharacteristic
275C4×C43#57711yescharacteristic
276C4×C43#57711yescharacteristic
277Dic43—41no—
278Dic43—81no—
279Dic43—81no—
280Q8×SD16D4311yescharacteristic, complemented
281#3369—431no—
282#3302—431no—
283#3298—431no—
284#1718—431no—
285#1700—431no—
286#1683—431no—
287#1680—431no—
288#1671—431no—
289#1650—431no—
290#1649—431no—
291#1645—431no—
292#1635—431no—
293#1582—431no—
294SD16⋊C8—431no—
295C2×C43—42no—
296C2×C43#326611yescharacteristic
297C2×C43#328211yescharacteristic
298C2×C43#328911yescharacteristic
299D43—81no—
300Q82C2×D4311yescharacteristic
301#556—431no—
302D4×Q8C2×D4311yescharacteristic
303#547—431no—
304#500—431no—
305#498—21no—
306#498C2×D4311yescharacteristic
307#489—861no—
308#487—431no—
309#487—431no—
310#487—431no—
311#487—431no—
312#485—861no—
313#483—861no—
314#476—21no—
315#476—431no—
316#476C2×D4311yescharacteristic
317#475—21no—
318#475—431no—
319#475—861no—
320#475C2×D4311yescharacteristic
321#474—431no—
322#467—861no—
323#465—861no—
324#464—861no—
325#462—431no—
326#462—431no—
327#461—431no—
328#452—861no—
329#448—861no—
330#446—431no—
331C8×Q8C2×D4311yescharacteristic
332#441—861no—
333C4×SD16—21no—
334C4×SD16—431no—
335C4×SD16C2×D4311yescharacteristic
336C8×D4—431no—
337C8×D4—431no—
338#416—861no—
339C2×#103—861no—
340#335—431no—
341#334—431no—
342#333—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346Q8⋊C8—431no—
347Q8⋊C8—431no—
348D4⋊C8—431no—
349D4⋊C8—431no—
350#322—431no—
351C43#1979611yescharacteristic, complemented, Sylow
352C2×#41—861no—
353C22×Q8—21no—
354C2×Q16—861no—
355C2×Q16—861no—
356C2×SD16—431no—
357C2×SD16—861no—
358C2×SD16C22⋊D4311yescharacteristic
359C22×C8—861no—
360C22×C8—861no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—41no—
365C4⋊Q8—431no—
366C4⋊Q8—431no—
367C4⋊Q8C22×D4311yescharacteristic
368C4⋊Q8C22×D4311yescharacteristic
369#126—1721no—
370#124—861no—
371#123—1721no—
372C22⋊Q8—21no—
373C22⋊Q8—41no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—861no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—861no—
380C4×Q8C22×D4311yescharacteristic
381C4×Q8C22×D4311yescharacteristic
382C4×D4—21no—
383C4×D4—431no—
384C4×D4C22×D4311yescharacteristic
385#117—861no—
386C2×C4⋊C4—861no—
387#107—861no—
388#107—1721no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106—431no—
394#106—861no—
395#106—861no—
396#106C22⋊D4311yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403#103—21no—
404#103—431no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—1721no—
416#103C22⋊D4311yescharacteristic
417#102—21no—
418#102—431no—
419#102—861no—
420#102—861no—
421#102C22⋊D4311yescharacteristic
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—861no—
425C4×C8—21no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8C22×D4311yescharacteristic
429#41—3441no—
430#41—1722no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—42no—
436C2×Q8—81no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8D4×D4311yescharacteristic
440C2×Q8C2×C22⋊D4311yescharacteristic
441C2×D4—431no—
442C2×D4—1721no—
443C2×D4C2×C22⋊D4311yescharacteristic
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—861no—
447C22×C4—1721no—
448Q16—3441no—
449Q16—1722no—
450SD16—22no—
451SD16—862no—
452SD16—3441no—
453C2×C8—21no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—3441no—
461C2×C8—3441no—
462C2×C8C2×C22⋊D4311yescharacteristic
463C2×C8C2×C22⋊D4311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—431no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4D4×D4311yescharacteristic
481C4⋊C4C2×C22⋊D4311yescharacteristic
482C4⋊C4C2×C22⋊D4311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—861no—
486C22⋊C4—1721no—
487C22⋊C4—1721no—
488C22⋊C4—1721no—
489C42—21no—
490C42—21no—
491C42—41no—
492C42—1721no—
493C42C23×D4311yescharacteristic
494C23—21no—
495C23—861no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—82no—
502Q8—81no—
503Q8—161no—
504Q8—1721no—
505Q8—1721no—
506Q8—1721no—
507Q8—1721no—
508Q8#1306334612yes—
509D4—21no—
510D4—861no—
511D4—861no—
512D4—3442no—
513D4#1306335612yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—82no—
524C2×C4—861no—
525C2×C4—3442no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4C2×D4×D4311yescharacteristic
531C2×C4C22×C22⋊D4311yescharacteristic
532C2×C4#1306337011yescharacteristic
533C8—21no—
534C8—21no—
535C8—41no—
536C8—861no—
537C8—861no—
538C8—1721no—
539C8—1721no—
540C8—1721no—
541C8—1721no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—1721no—
546C22—1721no—
547C22—1721no—
548C22D4×C22⋊D4311yescharacteristic
549C4—22no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—3441no—
558C4—3441no—
559C4—1721no—
560C4C2×#1306334611yescharacteristic
561C4C2×#1306335611yescharacteristic
562C4#1458370511yescharacteristic
563C4#1458370711yescharacteristic
564C2—42no—
565C2—3441no—
566C2#1914610611yescharacteristic
567C2#1914630211yescharacteristic
568C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingQ8×SD16×C43C2
socleC22×C43D42
prime radical#14583553C22
hypercenterQ8×SD16D43
hypocenterC43#19796
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ Q8×SD16

Complements

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

NH ≅ G/Ntype
1. #19147335C2semidirect
4. #19134239C2semidirect
5. #19134147C2semidirect
6. #19134048C2semidirect
7. #19134025C2semidirect
8. #19133967C2semidirect
9. #19133850C2semidirect
10. #19133844C2semidirect
11. #19133816C2semidirect
13. #19133432C2semidirect
14. #19133405C2semidirect
15. Q8×SD16×C43C2semidirect
280. Q8×SD16D43semidirect
351. C43#19796semidirect

Maximal subgroups

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

subgroupindex
#191473352
#191465142
#191464602
#191342392
#191341472
#191340482
#191340252
#191339672
#191338502
#191338442
#191338162
#191337442
#191334322
#191334052
Q8×SD16×C432
#1979643