Finite Group Databasebeta

← #25079060

Subgroups — #25079060

Order 11008.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145155C211yesmaximal, characteristic, complemented
2#19144655C211yesmaximal, characteristic
3#41×C43⋊C8C211yesmaximal, characteristic, complemented
4#19134051C211yesmaximal, characteristic, complemented
5#19134044C211yesmaximal, characteristic, complemented
6#19134041C211yesmaximal, characteristic, complemented
7#19134034C211yesmaximal, characteristic, complemented
8#19133975C211yesmaximal, characteristic, complemented
9#19133968C211yesmaximal, characteristic, complemented
10#19133945C211yesmaximal, characteristic, complemented
11#19133938C211yesmaximal, characteristic, complemented
12#19133341C211yesmaximal, characteristic, complemented
13#19133260C211yesmaximal, characteristic, complemented
14#19133255C211yesmaximal, characteristic, complemented
15C43×#3107C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583295C2211yescharacteristic
18#14583273C2211yescharacteristic
19#14583249C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583223—21no—
22#14583194C2211yescharacteristic
23#14583189C2211yescharacteristic
24#14583130—21no—
25#14583130—21no—
26#14583099C2211yescharacteristic
27#14583094C2211yescharacteristic
28#14583044—21no—
29Q8×C43⋊C8C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31C4×#10621884—21no—
32C4×#10621884—21no—
33C4×#10621884—21no—
34C4×#10621882—21no—
35D4×C43⋊C8—21no—
36D4×C43⋊C8—21no—
37D4×C43⋊C8C2211yescharacteristic
38D4×C43⋊C8C2211yescharacteristic
39#14582952—21no—
40#14582952C2211yescharacteristic
41#14582952C2211yescharacteristic
42C2×C4×C43⋊C8—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#485—21no—
59C43×#475C2211yescharacteristic
60C43×#474C2211yescharacteristic
61C43×#462C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#452—21no—
64C4×Q16×C43—21no—
65C4×SD16×C43—21no—
66C43×#431C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884—21no—
69C2×#10621884—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C22×C43⋊C8—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8D411yescharacteristic
75C22×C43⋊C8D411yescharacteristic
76#13063325C2311yescharacteristic
77#13063322C2311yescharacteristic
78#13063313—21no—
79#13063299—21no—
80#13063299—21no—
81C4×D172—21no—
82C4×D172—21no—
83#13063258—21no—
84#13063256—21no—
85#13063256—21no—
86#13063256—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93#13063249—21no—
94#13063249—21no—
95#13063249—21no—
96#13063246—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—
105C4×C43⋊C8—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—
143C4×C8×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—82no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×C4×D43—41no—
163C2×Dic86—21no—
164Q16×C43—42no—
165SD16×C43—42no—
166C2×C8×C43—21no—
167C2×C8×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—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—41no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—41no—
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43#4111yescharacteristic
189C42×C43C2411yescharacteristic
190#10621884—42no—
191#10621884—42no—
192#10621884—42no—
193#10621882—42no—
194(C2×D43)⋊C4—41no—
195(C2×D43)⋊C4—41no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—41no—
204C2×C43⋊C8—42no—
205C2×C43⋊C8—42no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C23×C43—21no—
211C23×C43#12111yescharacteristic
212C22×D43—41no—
213Q8×C43—21no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43#13512yes—
219D4×C43—24no—
220D4×C43—21no—
221D4×C43#13512yes—
222C2×C4×C43—24no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—42no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—82no—
243C2×Dic43—41no—
244D172—41no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—81no—
249C4×D43—82no—
250Dic86—81no—
251C8×C43—41no—
252C8×C43—41no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8#13512yes—
261#19127—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—22no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43C2×#12111yescharacteristic
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—22no—
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43#47112yes—
281C4×C43C2×#13511yescharacteristic
282C4×C43C2×#13511yescharacteristic
283C4×C43C2×#13511yescharacteristic
284C4×C43#57511yescharacteristic
285Dic43—81no—
286#3167—431no—
287#3107D4311yescharacteristic, complemented
288#3106—431no—
289C8×#41—431no—
290#1684—431no—
291#1683—431no—
292#1682—431no—
293#1681—431no—
294#1672—431no—
295#1671—431no—
296#1666—431no—
297#1665—431no—
298#1564—431no—
299#1544—431no—
300#1543—431no—
301C2×C43—41no—
302C2×C43—42no—
303C2×C43#303511yescharacteristic
304C2×C43#305011yescharacteristic
305C2×C43C2×#47111yescharacteristic
306D43—161no—
307#533C2×D4311yescharacteristic
308#532—431no—
309C4×#41C2×D4311yescharacteristic
310#498—431no—
311#492—431no—
312#487—431no—
313#486—431no—
314#485—21no—
315#482—861no—
316#477—431no—
317#476—431no—
318#475C2×D4311yescharacteristic
319#474C2×D4311yescharacteristic
320#465—861no—
321#465—861no—
322#462C2×D4311yescharacteristic
323#461C2×D4311yescharacteristic
324#460—431no—
325#459—431no—
326#452—21no—
327#449—861no—
328C8×Q8—431no—
329C8×Q8—431no—
330C4×Q16—21no—
331C4×SD16—21no—
332C4×SD16—861no—
333C4×SD16—861no—
334C4×SD16—861no—
335C4×D8—861no—
336C8×D4—431no—
337C8×D4—431no—
338C8×D4—861no—
339C8×D4—861no—
340#431—431no—
341#431—431no—
342#431—861no—
343#431C2×D4311yescharacteristic
344C2×C4×C8—431no—
345C2×C4×C8—861no—
346#335—431no—
347#335—431no—
348#334—431no—
349#334—431no—
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#331—431no—
357#331—431no—
358C43#1912711yescharacteristic, complemented, Sylow
359C2×#41—861no—
360C2×#41C22⋊D4311yescharacteristic
361C2×Q16—21no—
362C2×SD16—21no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×D8—861no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8C22×D4311yescharacteristic
373C4⋊Q8C22×D4311yescharacteristic
374#127—431no—
375#125—21no—
376#124—861no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379#121—861no—
380#121—861no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8C22⋊D4311yescharacteristic
384C4×Q8C22×D4311yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—861no—
388C4×D4—861no—
389C4×D4C22⋊D4311yescharacteristic
390C4×D4C22×D4311yescharacteristic
391#117—21no—
392#117—21no—
393#117C22⋊D4311yescharacteristic
394C2×C42—21no—
395C2×C42C22×D4311yescharacteristic
396#107—21no—
397#107—861no—
398#106—21no—
399#106—861no—
400#106—861no—
401#106—861no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—861no—
407C4⋊C8—861no—
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—861no—
414#103—861no—
415#103—861no—
416#102—21no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422C22⋊C8—21no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427C4×C8—21no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—861no—
433C4×C8—861no—
434C4×C8—861no—
435C4×C8—861no—
436#41—22no—
437#41—22no—
438#41—3442no—
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—
459SD16—1722no—
460SD16—1722no—
461D8—1722no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—862no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—1722no—
474C2×C8—1721no—
475C2×C8—1722no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4C2×C22⋊D4311yescharacteristic
487C4⋊C4C2×C22⋊D4311yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—41no—
498C42D4×D4311yescharacteristic
499C42#1062190011yescharacteristic
500C42C2×C22⋊D4311yescharacteristic
501C42C23×D4311yescharacteristic
502C23—21no—
503C23—1721no—
504C23#1306329711yescharacteristic
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—3441no—
511Q8#1306334512yes—
512D4—24no—
513D4—21no—
514D4—3441no—
515D4—3442no—
516D4—1721no—
517D4—1721no—
518D4—1721no—
519D4—1721no—
520D4#1306334512yes—
521C2×C4—24no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—3442no—
536C2×C4—1721no—
537C2×C4#1306329711yescharacteristic
538C2×C4#1306329711yescharacteristic
539C2×C4#1306329711yescharacteristic
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C22×C22⋊D4311yescharacteristic
542C2×C4C2×#1062190011yescharacteristic
543C8—41no—
544C8—41no—
545C8—432no—
546C8—861no—
547C8—861no—
548C8—861no—
549C8—1721no—
550C8—1721no—
551C8—1721no—
552C8—1721no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—3441no—
560C22—3441no—
561C22—3441no—
562C22C2×#1306329711yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—3441no—
572C4#1458316412yes—
573C4#135×D4311yescharacteristic
574C4C2×#1306334511yescharacteristic
575C4C2×#1306334511yescharacteristic
576C4#1458369611yescharacteristic
577C2—41no—
578C2—42no—
579C2—6881no—
580C2#1914404611yescharacteristic
581C2#1914417311yescharacteristic
582C2C2×#1458316411yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3107C2
socleC22×C43C2×#121
prime radical#19144655C2
hypercenter#3107D43
hypocenterC43#19127
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
1. #19145155C2semidirect
3. #41×C43⋊C8C2semidirect
4. #19134051C2semidirect
5. #19134044C2semidirect
6. #19134041C2semidirect
7. #19134034C2semidirect
8. #19133975C2semidirect
9. #19133968C2semidirect
10. #19133945C2semidirect
11. #19133938C2semidirect
12. #19133341C2semidirect
13. #19133260C2semidirect
14. #19133255C2semidirect
15. C43×#3107C2semidirect
287. #3107D43semidirect
358. C43#19127semidirect

Maximal subgroups

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

subgroupindex
#191451552
#191446552
#41×C43⋊C82
#191340512
#191340442
#191340412
#191340342
#191339752
#191339682
#191339452
#191339382
#191333412
#191332602
#191332552
C43×#31072
#1912743