Finite Group Databasebeta

← #25080593

Subgroups — #25080593

Order 11008.

630 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144920C211yesmaximal, characteristic, complemented
2#19144746C211yesmaximal, characteristic
3#41×C43⋊C8C211yesmaximal, characteristic, complemented
4#19134055C211yesmaximal, characteristic, complemented
5#19134048C211yesmaximal, characteristic, complemented
6#19134041C211yesmaximal, characteristic, complemented
7#19134034C211yesmaximal, characteristic, complemented
8#19134027C211yesmaximal, characteristic, complemented
9#19134020C211yesmaximal, characteristic, complemented
10#19134013C211yesmaximal, characteristic, complemented
11#19134006C211yesmaximal, characteristic, complemented
12#19133356C211yesmaximal, characteristic, complemented
13#19133305C211yesmaximal, characteristic, complemented
14#19133301C211yesmaximal, characteristic, complemented
15C43×#3116C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583256—21no—
18#14583256—21no—
19#14583251C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583223—21no—
24#14583184C2211yescharacteristic
25#14583179C2211yescharacteristic
26#14583099C2211yescharacteristic
27#14583094C2211yescharacteristic
28#14583044—21no—
29Q8×C43⋊C8C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31#14583009—21no—
32#14582997—21no—
33D4×C43⋊C8—21no—
34D4×C43⋊C8—21no—
35D4×C43⋊C8C2211yescharacteristic
36D4×C43⋊C8C2211yescharacteristic
37#14582956C2211yescharacteristic
38#14582952—21no—
39#14582952C2211yescharacteristic
40#14582893—21no—
41#14582893—21no—
42C2×C4×C43⋊C8—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#485—21no—
59C43×#477C2211yescharacteristic
60C43×#476C2211yescharacteristic
61C43×#462C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#452—21no—
64C43×#441—21no—
65C43×#440—21no—
66C43×#432C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884—21no—
69C2×#10621882—21no—
70C22×C43⋊C8—21no—
71C22×C43⋊C8—21no—
72C22×C43⋊C8D411yescharacteristic
73C22×C43⋊C8D411yescharacteristic
74#13063325C2311yescharacteristic
75#13063322C2311yescharacteristic
76#13063313—21no—
77#13063299—21no—
78#13063299—21no—
79C4×D172—21no—
80C4×D172—21no—
81#13063258—21no—
82#13063256—21no—
83C4⋊(C43⋊C8)—21no—
84C4⋊(C43⋊C8)—21no—
85C4⋊(C43⋊C8)C2311yescharacteristic
86C4⋊(C43⋊C8)C2311yescharacteristic
87C4⋊(C43⋊C8)C2311yescharacteristic
88C4⋊(C43⋊C8)C2311yescharacteristic
89#13063249—21no—
90#13063248—21no—
91#13063248—21no—
92#13063248—21no—
93#13063248—21no—
94#13063246—21no—
95#13063245—21no—
96#13063245—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—
106C4×C43⋊C8—21no—
107C4×C43⋊C8—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8D411yescharacteristic
110C4×C43⋊C8D411yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43D411yescharacteristic
114C2×Q16×C43—21no—
115C2×SD16×C43—21no—
116C4⋊Q8×C43C2311yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118#125×C43—21no—
119C22⋊Q8×C43—21no—
120C22⋊Q8×C43—21no—
121C4×Q8×C43—21no—
122C4×Q8×C43—21no—
123C4×Q8×C43D411yescharacteristic
124C4×Q8×C43C2311yescharacteristic
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43D411yescharacteristic
128C4×D4×C43C2311yescharacteristic
129#117×C43—21no—
130#117×C43—21no—
131#117×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143#97×C43—21no—
144#41×C43—22no—
145#41×C43—22no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C2×C22⋊D43—41no—
158#10621898—42no—
159#10621898—42no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×C4×D43—41no—
164C2×Dic86—21no—
165Q16×C43—42no—
166SD16×C43—42no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—41no—
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43#4111yescharacteristic
190C42×C43C2411yescharacteristic
191#10621884—42no—
192#10621882—42no—
193(C2×D43)⋊C4—41no—
194(C2×D43)⋊C4—41no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—41no—
202C2×C43⋊C8—41no—
203C2×C43⋊C8—42no—
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—41no—
214Q8×C43—41no—
215Q8×C43—81no—
216Q8×C43#13512yes—
217D4×C43—24no—
218D4×C43—21no—
219D4×C43#13512yes—
220C2×C4×C43—24no—
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—21no—
228C2×C4×C43—41no—
229C2×C4×C43—42no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C22⋊D43—82no—
241C2×Dic43—41no—
242D172—41no—
243D172—41no—
244D172—41no—
245D172—41no—
246D172—81no—
247C4×D43—82no—
248Dic86—41no—
249Dic86—41no—
250C8×C43—41no—
251C8×C43—41no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#19278—431nomaximal, Sylow
261C22×C43—21no—
262C22×C43—22no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43C2×#12111yescharacteristic
268C2×D43—81no—
269C2×D43—81no—
270C2×D43—81no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—22no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43C2×#13511yescharacteristic
281C4×C43C2×#13511yescharacteristic
282C4×C43#57511yescharacteristic
283C4×C43#57511yescharacteristic
284Dic43—81no—
285#3131—431no—
286#3116D4311yescharacteristic, complemented
287#3115—431no—
288C8×#41—431no—
289#1684—431no—
290#1683—431no—
291#1682—431no—
292#1681—431no—
293#1680—431no—
294#1679—431no—
295#1678—431no—
296#1677—431no—
297#1568—431no—
298#1554—431no—
299#1553—431no—
300C2×C43—41no—
301C2×C43—42no—
302C2×C43#304011yescharacteristic
303C2×C43#305011yescharacteristic
304C2×C43#306711yescharacteristic
305D43—161no—
306#533C2×D4311yescharacteristic
307#532—431no—
308C4×#41C2×D4311yescharacteristic
309#488—861no—
310#488—861no—
311#487—431no—
312#487—431no—
313#486—431no—
314#486—431no—
315#485—21no—
316#482—861no—
317#477C2×D4311yescharacteristic
318#476C2×D4311yescharacteristic
319#475—431no—
320#474—431no—
321#462C2×D4311yescharacteristic
322#461C2×D4311yescharacteristic
323#460—431no—
324#459—431no—
325#452—21no—
326#449—861no—
327C8×Q8—431no—
328C8×Q8—431no—
329#442—861no—
330#441—21no—
331#440—21no—
332#440—861no—
333C8×D4—431no—
334C8×D4—431no—
335C8×D4—861no—
336C8×D4—861no—
337#432—431no—
338#432C2×D4311yescharacteristic
339#431—431no—
340#431—861no—
341#416—861no—
342#416—861no—
343C2×C4×C8—431no—
344C2×C4×C8—861no—
345#335—431no—
346#335—431no—
347#334—431no—
348#334—431no—
349#333—431no—
350#333—431no—
351#332—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#331—431no—
356#331—431no—
357C43#1927811yescharacteristic, complemented, Sylow
358C2×#41—861no—
359C2×#41C22⋊D4311yescharacteristic
360C2×Q16—21no—
361C2×SD16—21no—
362C2×SD16—861no—
363C2×D8—861no—
364C22×C8—431no—
365C22×C8—431no—
366C22×C8—861no—
367C22×C8—861no—
368C4⋊Q8—431no—
369C4⋊Q8C22×D4311yescharacteristic
370C4⋊Q8C22×D4311yescharacteristic
371#127—431no—
372#125—21no—
373#124—861no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—861no—
377#121—861no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8C22⋊D4311yescharacteristic
381C4×Q8C22×D4311yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—861no—
385C4×D4—861no—
386C4×D4C22⋊D4311yescharacteristic
387C4×D4C22×D4311yescharacteristic
388#117—21no—
389#117—21no—
390#117C22⋊D4311yescharacteristic
391C2×C42—21no—
392C2×C42C22×D4311yescharacteristic
393#107—21no—
394#107—861no—
395#106—21no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#102—21no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421C22⋊C8—21no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—21no—
427#97—861no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—861no—
433C4×C8—861no—
434C4×C8—861no—
435#41—22no—
436#41—22no—
437#41—1722no—
438#41—1722no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—861no—
442C2×Q8C2×C22⋊D4311yescharacteristic
443C2×D4—21no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—1721no—
448C2×D4C2×C22⋊D4311yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—1721no—
453C22×C4D4×D4311yescharacteristic
454C22×C4#1062190011yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456Q16—42no—
457SD16—42no—
458SD16—1722no—
459D8—1722no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—1721no—
471C2×C8—1721no—
472C2×C8—1722no—
473C2×C8—1722no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4C2×C22⋊D4311yescharacteristic
485C4⋊C4C2×C22⋊D4311yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42D4×D4311yescharacteristic
497C42#1062190011yescharacteristic
498C42C2×C22⋊D4311yescharacteristic
499C42C23×D4311yescharacteristic
500C23—21no—
501C23—1721no—
502C23#1306329711yescharacteristic
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507Q8—1721no—
508Q8—1721no—
509Q8#1306334512yes—
510D4—24no—
511D4—21no—
512D4—3441no—
513D4—3442no—
514D4—1721no—
515D4—1721no—
516D4—1721no—
517D4—1721no—
518D4#1306334512yes—
519C2×C4—24no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—3442no—
534C2×C4—1721no—
535C2×C4#1306329711yescharacteristic
536C2×C4#1306329711yescharacteristic
537C2×C4#1306329711yescharacteristic
538C2×C4C2×D4×D4311yescharacteristic
539C2×C4C22×C22⋊D4311yescharacteristic
540C2×C4C2×#1062190011yescharacteristic
541C8—41no—
542C8—41no—
543C8—861no—
544C8—861no—
545C8—861no—
546C8—861no—
547C8—1721no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—3441no—
558C22—3441no—
559C22—3441no—
560C22C2×#1306329711yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—81no—
570C4—3441no—
571C4C2×#1306334511yescharacteristic
572C4C2×#1306334511yescharacteristic
573C4#1458369811yescharacteristic
574C4#1458369811yescharacteristic
575C2—41no—
576C2—42no—
577C2—6881no—
578C2#1914409111yescharacteristic
579C2#1914417311yescharacteristic
580C2#1914431211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3116C2
socleC22×C43C2×#121
prime radical#19144746C2
hypercenter#3116D43
hypocenterC43#19278
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3116

Complements

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

NH ≅ G/Ntype
1. #19144920C2semidirect
3. #41×C43⋊C8C2semidirect
4. #19134055C2semidirect
5. #19134048C2semidirect
6. #19134041C2semidirect
7. #19134034C2semidirect
8. #19134027C2semidirect
9. #19134020C2semidirect
10. #19134013C2semidirect
11. #19134006C2semidirect
12. #19133356C2semidirect
13. #19133305C2semidirect
14. #19133301C2semidirect
15. C43×#3116C2semidirect
286. #3116D43semidirect
357. C43#19278semidirect

Maximal subgroups

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

subgroupindex
#191449202
#191447462
#41×C43⋊C82
#191340552
#191340482
#191340412
#191340342
#191340272
#191340202
#191340132
#191340062
#191333562
#191333052
#191333012
C43×#31162
#1927843