Finite Group Databasebeta

← #25080589

Subgroups — #25080589

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#19144918C211yesmaximal, characteristic, complemented
2#19144757C211yesmaximal, characteristic, complemented
3#19144746C211yesmaximal, characteristic
4#19134053C211yesmaximal, characteristic, complemented
5#19134046C211yesmaximal, characteristic, complemented
6#19134039C211yesmaximal, characteristic, complemented
7#19134032C211yesmaximal, characteristic, complemented
8#19134025C211yesmaximal, characteristic, complemented
9#19134018C211yesmaximal, characteristic, complemented
10#19134011C211yesmaximal, characteristic, complemented
11#19134004C211yesmaximal, characteristic, complemented
12#19133358C211yesmaximal, characteristic, complemented
13#19133303C211yesmaximal, characteristic, complemented
14#19133298C211yesmaximal, characteristic, complemented
15C8×#41×C43C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583254—21no—
19#14583254—21no—
20#14583250C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583240—21no—
25#14583223—21no—
26#14583194C2211yescharacteristic
27#14583189C2211yescharacteristic
28#14583184C2211yescharacteristic
29#14583179C2211yescharacteristic
30#14583109C2211yescharacteristic
31#14583104C2211yescharacteristic
32#14583099C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583061—21no—
35#14583044—21no—
36#14583009—21no—
37#14583004—21no—
38#14582999—21no—
39#14582997—21no—
40#14582956C2211yescharacteristic
41#14582956C2211yescharacteristic
42#14582896—21no—
43#14582896—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C8×D4×C43—21no—
60C8×D4×C43—21no—
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#431—21no—
64C43×#431C2211yescharacteristic
65C2×C4×C8×C43—21no—
66C2×C4×C8×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063322C2311yescharacteristic
76#13063317—21no—
77#13063313—21no—
78#13063304—21no—
79#13063304—21no—
80#13063299—21no—
81#13063299—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×D172—21no—
85C4×D172—21no—
86#13063284—21no—
87#13063258—21no—
88#13063258—21no—
89#13063256—21no—
90#13063256—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063250—21no—
96#13063250—21no—
97#13063250—21no—
98#13063250—21no—
99#13063249—21no—
100#13063249—21no—
101#13063248—21no—
102#13063248—21no—
103#13063247—21no—
104#13063247—21no—
105#13063247—21no—
106#13063247—21no—
107#13063246—21no—
108#13063246—21no—
109#13063245—21no—
110#13063245—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113#13063236—21no—
114#13063236—21no—
115C2×#41×C43D411yescharacteristic
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43D411yescharacteristic
119C22×C8×C43D411yescharacteristic
120C4×Q8×C43D411yescharacteristic
121C4×Q8×C43C2311yescharacteristic
122C4×D4×C43—21no—
123C4×D4×C43—21no—
124C4×D4×C43D411yescharacteristic
125C4×D4×C43C2311yescharacteristic
126#117×C43—21no—
127#117×C43D411yescharacteristic
128C2×C42×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C4×C8×C43—21no—
138C4×C8×C43—21no—
139C4×C8×C43—21no—
140C4×C8×C43D411yescharacteristic
141C4×C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—22no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×C22⋊D43—41no—
156#10621898—42no—
157#10621898—42no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×C4×D43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—41no—
168C2×C8×C43—41no—
169C2×C8×C43—42no—
170C2×C8×C43—42no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43#4111yescharacteristic
188C42×C43C2411yescharacteristic
189C22⋊Dic43—41no—
190#10621885—42no—
191#10621884—42no—
192#10621883—42no—
193#10621882—42no—
194(C2×D43)⋊C4—41no—
195(C2×D43)⋊C4—41no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204C4×Dic43—41no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C23×C43—21no—
210C23×C43#12111yescharacteristic
211C22×D43—41no—
212Q8×C43—21no—
213Q8×C43#13512yes—
214D4×C43—24no—
215D4×C43—21no—
216D4×C43#13512yes—
217C2×C4×C43—24no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C22⋊D43—82no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239D172—41no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—81no—
244C4×D43—82no—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—81no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—41no—
255C8×C43—41no—
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×C43C2×#13511yescharacteristic
279C4×C43C2×#13511yescharacteristic
280C4×C43#57511yescharacteristic
281C4×C43#57511yescharacteristic
282Dic43—81no—
283Dic43—81no—
284Dic43—81no—
285#3131—431no—
286#3116—431no—
287#3115—431no—
288C8×#41D4311yescharacteristic, complemented
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#533—431no—
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—861no—
316#482—861no—
317#477—431no—
318#476—431no—
319#475—431no—
320#474—431no—
321#462—431no—
322#461—431no—
323#460—431no—
324#459—431no—
325#452—861no—
326#449—861no—
327C8×Q8C2×D4311yescharacteristic
328C8×Q8C2×D4311yescharacteristic
329#442—861no—
330#441—861no—
331#440—861no—
332#440—861no—
333C8×D4—21no—
334C8×D4—21no—
335C8×D4C2×D4311yescharacteristic
336C8×D4C2×D4311yescharacteristic
337#432—431no—
338#432—431no—
339#431—21no—
340#431C2×D4311yescharacteristic
341#416—861no—
342#416—861no—
343C2×C4×C8—21no—
344C2×C4×C8C2×D4311yescharacteristic
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×#41D17211yescharacteristic
360C2×Q16—861no—
361C2×SD16—861no—
362C2×SD16—861no—
363C2×D8—861no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8C22⋊D4311yescharacteristic
367C22×C8C22⋊D4311yescharacteristic
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8—431no—
371#127—431no—
372#125—861no—
373#124—861no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—861no—
377#121—861no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8D17211yescharacteristic
381C4×Q8C22×D4311yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—861no—
385C4×D4—861no—
386C4×D4D17211yescharacteristic
387C4×D4C22×D4311yescharacteristic
388#117—21no—
389#117—861no—
390#117D17211yescharacteristic
391C2×C42—21no—
392C2×C42C22×D4311yescharacteristic
393#107—861no—
394#107—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
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#102—861no—
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—21no—
423C22⋊C8—21no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—861no—
427#97—861no—
428C4×C8—21no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8C22⋊D4311yescharacteristic
432C4×C8C22⋊D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434C4×C8C22×D4311yescharacteristic
435#41—22no—
436#41—22no—
437#41—1722no—
438#41—1722no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8C2×D17211yescharacteristic
443C2×D4—21no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—1721no—
448C2×D4C2×D17211yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—1721no—
453C22×C4C2×D17211yescharacteristic
454C22×C4#1062189811yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456Q16—1722no—
457SD16—1722no—
458SD16—1722no—
459D8—1722no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—42no—
465C2×C8—42no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8C2×C22⋊D4311yescharacteristic
471C2×C8C2×C22⋊D4311yescharacteristic
472C2×C8C2×C22⋊D4311yescharacteristic
473C2×C8C2×C22⋊D4311yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—1721no—
483C4⋊C4—1721no—
484C4⋊C4C2×D17211yescharacteristic
485C4⋊C4C2×D17211yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—1721no—
496C42C2×D17211yescharacteristic
497C42#1062189811yescharacteristic
498C42C2×C22⋊D4311yescharacteristic
499C42C23×D4311yescharacteristic
500C23—21no—
501C23—1721no—
502C23#1306329911yescharacteristic
503Q8—21no—
504Q8—3441no—
505Q8—1721no—
506Q8—1721no—
507Q8—1721no—
508Q8—1721no—
509Q8#1306334712yes—
510D4—24no—
511D4—21no—
512D4—3441no—
513D4—3442no—
514D4—1721no—
515D4—1721no—
516D4—1721no—
517D4—1721no—
518D4#1306334712yes—
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—3442no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4#1306329911yescharacteristic
536C2×C4#1306329911yescharacteristic
537C2×C4#1306329911yescharacteristic
538C2×C4C22×C22⋊D4311yescharacteristic
539C2×C4C22×D17211yescharacteristic
540C2×C4C2×#1062189811yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—41no—
546C8—41no—
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×#1306329911yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—3441no—
569C4—3441no—
570C4—3441no—
571C4C2×#1306334711yescharacteristic
572C4C2×#1306334711yescharacteristic
573C4#1458369711yescharacteristic
574C4#1458369711yescharacteristic
575C2—41no—
576C2—42no—
577C2—6881no—
578C2#1914408911yescharacteristic
579C2#1914417611yescharacteristic
580C2#1914431511yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC8×#41×C43C2
socleC22×C43C2×#121
prime radical#19144746C2
hypercenterC8×#41D43
hypocenterC43#19278
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. #19144918C2semidirect
2. #19144757C2semidirect
4. #19134053C2semidirect
5. #19134046C2semidirect
6. #19134039C2semidirect
7. #19134032C2semidirect
8. #19134025C2semidirect
9. #19134018C2semidirect
10. #19134011C2semidirect
11. #19134004C2semidirect
12. #19133358C2semidirect
13. #19133303C2semidirect
14. #19133298C2semidirect
15. C8×#41×C43C2semidirect
288. C8×#41D43semidirect
357. C43#19278semidirect

Maximal subgroups

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

subgroupindex
#191449182
#191447572
#191447462
#191340532
#191340462
#191340392
#191340322
#191340252
#191340182
#191340112
#191340042
#191333582
#191333032
#191332982
C8×#41×C432
#1927843