Finite Group Databasebeta

← #25087530

Subgroups — #25087530

Order 11008.

596 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147460C211yesmaximal, characteristic, complemented
2#19147215C211yesmaximal, characteristic, complemented
3#19146952C211yesmaximal, characteristic, complemented
4#19134275C211yesmaximal, characteristic, complemented
5#19134092C211yesmaximal, characteristic, complemented
6#19134050C211yesmaximal, characteristic, complemented
7#19133994C211yesmaximal, characteristic, complemented
8#19133992C211yesmaximal, characteristic, complemented
9#19133800C211yesmaximal, characteristic, complemented
10#19133746C211yesmaximal, characteristic, complemented
11#19133740C211yesmaximal, characteristic, complemented
12#19133727C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15C43×#3303C211yesmaximal, characteristic
16#14583606C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583300—21no—
21#14583295C2211yescharacteristic
22#14583278C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583240—21no—
25#14583229—21no—
26#14583215—21no—
27#14583210—21no—
28#14583197—21no—
29#14583197—21no—
30#14583191C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583189C2211yescharacteristic
33#14583189C2211yescharacteristic
34#14583189C2211yescharacteristic
35#14583181C2211yescharacteristic
36#14583143—21no—
37#14583126—21no—
38C8×Dic86C2211yescharacteristic
39C4×#10621883C2211yescharacteristic
40D8×Dic43—21no—
41#14582977C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582942—21no—
44C2×#13063256—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582629C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#555C2211yescharacteristic
57C43×#547C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#485—21no—
60C43×#476C2211yescharacteristic
61C43×#465—21no—
62C43×#461C2211yescharacteristic
63C43×#449—21no—
64C4×D8×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C43×#416—21no—
67C2×#10621885—41no—
68C2×#10621883D411yescharacteristic
69C2×#10621877—21no—
70C22×C43⋊C8—21no—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063316—21no—
74#13063316—21no—
75#13063304—21no—
76#13063304—21no—
77#13063302—41no—
78#13063302—41no—
79C4×Dic86C2311yescharacteristic
80D4×Dic43—21no—
81D4×Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84#13063259—21no—
85#13063259—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256D411yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—41no—
104#13063248D411yescharacteristic
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C2×SD16×C43—21no—
117C2×D8×C43D411yescharacteristic
118C22×C8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#124×C43—41no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127C4×D4×C43C2311yescharacteristic
128C4×D4×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131#117×C43—21no—
132C2×C4⋊C4×C43—21no—
133#107×C43D411yescharacteristic
134#106×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
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×D4×C43—41no—
149C2×D4×C43—41no—
150C2×D4×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—41no—
157C22×Dic43—41no—
158C22×Dic43—41no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86C2×D411yescharacteristic
162SD16×C43—81no—
163D8×C43—22no—
164C2×C8×C43—21no—
165C2×C8×C43—81no—
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×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C42×C43—41no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185C22⋊Dic43—41no—
186#10621885—82no—
187#10621883—22no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—41no—
193C4⋊Dic43—41no—
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—21no—
199#10621877—42no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—42no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—81no—
213D4×C43—21no—
214D4×C43—21no—
215D4×C43—21no—
216D4×C43—21no—
217D4×C43—21no—
218D4×C43—82no—
219D4×C43—161no—
220D4×C43#13712yes—
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—41no—
231C2×C4×C43—41no—
232C2×C4×C43—82no—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—161no—
241C2×Dic43—161no—
242Dic86—21no—
243Dic86—21no—
244Dic86—81no—
245Dic86—81no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8#13512yes—
255#19861—431nomaximal, Sylow
256C22×C43—22no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43D4211yescharacteristic
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—81no—
271C4×C43—81no—
272C4×C43C2×#13511yescharacteristic
273C4×C43C2×#13711yescharacteristic
274C4×C43#57711yescharacteristic
275C4×C43#57811yescharacteristic
276Dic43—41no—
277Dic43—41no—
278Dic43—81no—
279Dic43—81no—
280#3380—431no—
281#3357—431no—
282#3335—431no—
283#3303D4311yescharacteristic
284#1723—431no—
285#1691—431no—
286#1684—431no—
287#1675—431no—
288#1675—431no—
289#1643—431no—
290#1635—431no—
291#1634—431no—
292#1632—431no—
293#1581—431no—
294SD16⋊C8—431no—
295C2×C43—42no—
296C2×C43—81no—
297C2×C43—81no—
298C2×C43#326611yescharacteristic
299C2×C43#328311yescharacteristic
300C2×C43#328811yescharacteristic
301#555C2×D4311yescharacteristic
302#554—431no—
303#554—431no—
304#547C2×D4311yescharacteristic
305#500—431no—
306#500—431no—
307#499—861no—
308#498—431no—
309#494—431no—
310#487—431no—
311#487C2×D4311yescharacteristic
312#485—21no—
313#485—861no—
314#483—861no—
315#481—861no—
316#480—861no—
317#478—861no—
318#478—861no—
319#477—431no—
320#476—431no—
321#476—431no—
322#476—431no—
323#476—431no—
324#476C2×D4311yescharacteristic
325#475—431no—
326#468—861no—
327#465—21no—
328#465—861no—
329#461C2×D4311yescharacteristic
330#449—21no—
331C8×Q8—431no—
332C4×SD16—431no—
333C4×D8—861no—
334C4×D8C2×D4311yescharacteristic
335#436—431no—
336C8×D4—431no—
337C8×D4C2×D4311yescharacteristic
338#428—861no—
339C2×#106—861no—
340#416—21no—
341#335—431no—
342#335—431no—
343#333—431no—
344#333—431no—
345#333—431no—
346#332—431no—
347Q8⋊C8—431no—
348D4⋊C8—431no—
349D4⋊C8—431no—
350D4⋊C8—431no—
351#322—431no—
352C43#1986111yescharacteristic, complemented, Sylow
353C2×#41—21no—
354C2×Q16—1721no—
355C2×SD16—21no—
356C2×SD16—431no—
357C2×D8C22⋊D4311yescharacteristic
358C2×M16—861no—
359C22×C8—21no—
360C22×C8—861no—
361C4⋊Q8—431no—
362C4⋊Q8—431no—
363C4⋊Q8C22×D4311yescharacteristic
364C4⋊Q8C22×D4311yescharacteristic
365#125—861no—
366#125—861no—
367#124—41no—
368#123—41no—
369C22⋊Q8—21no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372C22⋊Q8—1721no—
373C22⋊Q8—1721no—
374#121—21no—
375#121—21no—
376#121—21no—
377C4×Q8—431no—
378C4×D4—861no—
379C4×D4—861no—
380C4×D4C22×D4311yescharacteristic
381C4×D4C22×D4311yescharacteristic
382C4×D4C22×D4311yescharacteristic
383#117—21no—
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388#107—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#107C22⋊D4311yescharacteristic
394#106—21no—
395#106—431no—
396#106—861no—
397#106—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402#106—861no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—861no—
407C4⋊C8C22×D4311yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—431no—
412#103—861no—
413#103—861no—
414#103—1721no—
415#102—21no—
416#102—431no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102C22⋊D4311yescharacteristic
422#102C22⋊D4311yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—861no—
429C4×C8C22×D4311yescharacteristic
430#41—42no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—431no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4D4×D4311yescharacteristic
440C2×D4C2×C22⋊D4311yescharacteristic
441C2×D4C2×C22⋊D4311yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—1721no—
447C22×C4—1721no—
448Q16—3442no—
449SD16—81no—
450SD16—862no—
451D8—22no—
452M16—1722no—
453C2×C8—21no—
454C2×C8—81no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—1722no—
462C2×C8C2×C22⋊D4311yescharacteristic
463C2×C8C2×C22⋊D4311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—431no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—1721no—
476C4⋊C4—1721no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C4⋊C4D4×D4311yescharacteristic
480C4⋊C4C2×C22⋊D4311yescharacteristic
481C4⋊C4C2×C22⋊D4311yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C42—41no—
491C42—861no—
492C42C23×D4311yescharacteristic
493C23—21no—
494C23—21no—
495C23—21no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—861no—
500Q8—861no—
501Q8—3441no—
502Q8—3441no—
503D4—21no—
504D4—21no—
505D4—21no—
506D4—21no—
507D4—21no—
508D4—82no—
509D4—161no—
510D4#1306335512yes—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—82no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—6881no—
528C2×C4—6881no—
529C2×C4C2×D4×D4311yescharacteristic
530C2×C4C22×C22⋊D4311yescharacteristic
531C2×C4#1306337011yescharacteristic
532C8—21no—
533C8—21no—
534C8—41no—
535C8—432no—
536C8—861no—
537C8—1721no—
538C8—1721no—
539C8—1721no—
540C8—1721no—
541C22—22no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22D4×C22⋊D4311yescharacteristic
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—3441no—
558C4—3441no—
559C4—1721no—
560C4—1721no—
561C4#135×D4311yescharacteristic
562C4C2×#1306335511yescharacteristic
563C4#1458371011yescharacteristic
564C4#1458371311yescharacteristic
565C2—42no—
566C2—81no—
567C2—81no—
568C2#1914610111yescharacteristic
569C2#1914631111yescharacteristic
570C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3303C2
socleC22×C43D42
hypercenter#3303D43
hypocenterC43#19861
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3303

Complements

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

NH ≅ G/Ntype
1. #19147460C2semidirect
2. #19147215C2semidirect
3. #19146952C2semidirect
4. #19134275C2semidirect
5. #19134092C2semidirect
6. #19134050C2semidirect
7. #19133994C2semidirect
8. #19133992C2semidirect
9. #19133800C2semidirect
10. #19133746C2semidirect
11. #19133740C2semidirect
12. #19133727C2semidirect
13. #19133425C2semidirect
14. #19133407C2semidirect
352. C43#19861semidirect

Maximal subgroups

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

subgroupindex
#191474602
#191472152
#191469522
#191342752
#191340922
#191340502
#191339942
#191339922
#191338002
#191337462
#191337402
#191337272
#191334252
#191334072
C43×#33032
#1986143