Finite Group Databasebeta

← #25079052

Subgroups — #25079052

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#19145150C211yesmaximal, characteristic, complemented
2#19144666C211yesmaximal, characteristic, complemented
3#41×C43⋊C8C211yesmaximal, characteristic, complemented
4#19134055C211yesmaximal, characteristic, complemented
5#19134048C211yesmaximal, characteristic, complemented
6#19134037C211yesmaximal, characteristic, complemented
7#19134030C211yesmaximal, characteristic, complemented
8#19133979C211yesmaximal, characteristic, complemented
9#19133972C211yesmaximal, characteristic, complemented
10#19133941C211yesmaximal, characteristic, complemented
11#19133934C211yesmaximal, characteristic, complemented
12#19133341C211yesmaximal, characteristic, complemented
13#19133259C211yesmaximal, characteristic, complemented
14#19133257C211yesmaximal, characteristic, complemented
15C43×#3106C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583295C2211yescharacteristic
18#14583271C2211yescharacteristic
19#14583251C2211yescharacteristic
20#14583245C2211yescharacteristic
21#14583240—21no—
22#14583184C2211yescharacteristic
23#14583179C2211yescharacteristic
24#14583126—21no—
25#14583126—21no—
26#14583109C2211yescharacteristic
27#14583104C2211yescharacteristic
28#14583061—21no—
29Q8×C43⋊C8C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31C4×#10621885—21no—
32C4×#10621883—21no—
33C4×#10621883—21no—
34C4×#10621883—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#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#482—21no—
59C43×#477C2211yescharacteristic
60C43×#476C2211yescharacteristic
61C43×#460C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C4×SD16×C43—21no—
65C4×D8×C43—21no—
66C43×#431C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C22×C43⋊C8—21no—
72C22×C43⋊C8—21no—
73C22×C43⋊C8D411yescharacteristic
74C22×C43⋊C8D411yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063317—21no—
78#13063304—21no—
79#13063304—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82#13063284—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#13063248—21no—
95#13063248—21no—
96#13063248—21no—
97#13063248—21no—
98#13063246—21no—
99#13063246—21no—
100#13063246—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×C43—21no—
114C2×#41×C43D411yescharacteristic
115C2×SD16×C43—21no—
116C2×D8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#124×C43—21no—
120#121×C43—21no—
121#121×C43—21no—
122C4×Q8×C43D411yescharacteristic
123C4×Q8×C43C2311yescharacteristic
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43D411yescharacteristic
129C4×D4×C43C2311yescharacteristic
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#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144#41×C43—22no—
145#41×C43—22no—
146#41×C43—82no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86—21no—
164SD16×C43—42no—
165D8×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×C43C2×D411yescharacteristic
173C4⋊C4×C43C2×D411yescharacteristic
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43C2×D411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C42×C43#4111yescharacteristic
185C42×C43C2411yescharacteristic
186C22⋊Dic43—41no—
187#10621885—42no—
188#10621883—42no—
189#10621883—42no—
190#10621883—42no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—41no—
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—41no—
212C23×C43#12111yescharacteristic
213Q8×C43—21no—
214Q8×C43—81no—
215Q8×C43#13512yes—
216D4×C43—24no—
217D4×C43—21no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—81no—
223D4×C43—82no—
224D4×C43#13512yes—
225C2×C4×C43—24no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—42no—
237C2×C4×C43—41no—
238C2×C4×C43—82no—
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×Dic43—41no—
246C2×Dic43—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—41no—
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×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43C2×#12111yescharacteristic
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—22no—
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43#47112yes—
280C4×C43C2×#13511yescharacteristic
281C4×C43C2×#13511yescharacteristic
282C4×C43C2×#13511yescharacteristic
283C4×C43#57511yescharacteristic
284Dic43—81no—
285Dic43—81no—
286#3167—431no—
287#3107—431no—
288#3106D4311yescharacteristic
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—161no—
304C2×C43#303511yescharacteristic
305C2×C43#305011yescharacteristic
306C2×C43C2×#47111yescharacteristic
307#533—431no—
308#532C2×D4311yescharacteristic
309C4×#41C2×D4311yescharacteristic
310#498—431no—
311#492—431no—
312#487—431no—
313#486—431no—
314#485—861no—
315#482—21no—
316#477C2×D4311yescharacteristic
317#476C2×D4311yescharacteristic
318#475—431no—
319#474—431no—
320#465—861no—
321#465—861no—
322#462—431no—
323#461—431no—
324#460C2×D4311yescharacteristic
325#459C2×D4311yescharacteristic
326#452—861no—
327#449—21no—
328C8×Q8—431no—
329C8×Q8—431no—
330C4×Q16—861no—
331C4×SD16—21no—
332C4×SD16—861no—
333C4×SD16—861no—
334C4×SD16—861no—
335C4×D8—21no—
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—21no—
360C2×#41C22⋊D4311yescharacteristic
361C2×Q16—861no—
362C2×SD16—21no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×D8—21no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8C22×D4311yescharacteristic
374#127C22×D4311yescharacteristic
375#125—861no—
376#124—21no—
377C22⋊Q8—861no—
378C22⋊Q8—861no—
379#121—21no—
380#121—21no—
381C4×Q8—861no—
382C4×Q8—861no—
383C4×Q8C22⋊D4311yescharacteristic
384C4×Q8C22×D4311yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4C22⋊D4311yescharacteristic
390C4×D4C22×D4311yescharacteristic
391#117—21no—
392#117—861no—
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—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#102—21no—
417#102—21no—
418#102—21no—
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—82no—
439C2×Q8—21no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8C2×C22⋊D4311yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4C2×C22⋊D4311yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4D4×D4311yescharacteristic
454C22×C4#1062190011yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456Q16—1722no—
457SD16—42no—
458SD16—1722no—
459SD16—1722no—
460SD16—1722no—
461D8—42no—
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—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—1721no—
485C4⋊C4—1721no—
486C4⋊C4C2×C22⋊D4311yescharacteristic
487C4⋊C4C2×C22⋊D4311yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—1721no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—1721no—
498C42D4×D4311yescharacteristic
499C42#1062190011yescharacteristic
500C42C2×C22⋊D4311yescharacteristic
501C42C23×D4311yescharacteristic
502C23—21no—
503C23—41no—
504C23#1306329711yescharacteristic
505Q8—21no—
506Q8—81no—
507Q8—1721no—
508Q8—1721no—
509Q8—1721no—
510Q8—1721no—
511Q8#1306334512yes—
512D4—24no—
513D4—21no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—41no—
518D4—81no—
519D4—82no—
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—82no—
535C2×C4—1721no—
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—81no—
560C22—81no—
561C22—81no—
562C22C2×#1306329711yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—3441no—
571C4—3441no—
572C4#1458316012yes—
573C4#135×D4311yescharacteristic
574C4C2×#1306334511yescharacteristic
575C4C2×#1306334511yescharacteristic
576C4#1458369611yescharacteristic
577C2—41no—
578C2—42no—
579C2—161no—
580C2#1914404611yescharacteristic
581C2#1914417311yescharacteristic
582C2C2×#1458316011yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3106C2
socleC22×C43C2×#121
hypercenter#3106D43
hypocenterC43#19127
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #19145150C2semidirect
2. #19144666C2semidirect
3. #41×C43⋊C8C2semidirect
4. #19134055C2semidirect
5. #19134048C2semidirect
6. #19134037C2semidirect
7. #19134030C2semidirect
8. #19133979C2semidirect
9. #19133972C2semidirect
10. #19133941C2semidirect
11. #19133934C2semidirect
12. #19133341C2semidirect
13. #19133259C2semidirect
14. #19133257C2semidirect
358. C43#19127semidirect

Maximal subgroups

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

subgroupindex
#191451502
#191446662
#41×C43⋊C82
#191340552
#191340482
#191340372
#191340302
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