Finite Group Databasebeta

← #25080582

Subgroups — #25080582

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#19144914C211yesmaximal, characteristic, complemented
2#19144759C211yesmaximal, characteristic, complemented
3#19144743C211yesmaximal, characteristic
4C8×#10621900C211yesmaximal, characteristic, complemented
5#19134056C211yesmaximal, characteristic, complemented
6#19134048C211yesmaximal, characteristic, complemented
7#19134038C211yesmaximal, characteristic, complemented
8#19134030C211yesmaximal, characteristic, complemented
9#19134026C211yesmaximal, characteristic, complemented
10#19134018C211yesmaximal, characteristic, complemented
11#19134008C211yesmaximal, characteristic, complemented
12#19133355C211yesmaximal, characteristic, complemented
13#19133304C211yesmaximal, characteristic, complemented
14#19133297C211yesmaximal, characteristic, complemented
15C43×#1677C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583252—21no—
20#14583252—21no—
21#14583251C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583243—21no—
25#14583222—21no—
26#14583191C2211yescharacteristic
27#14583185C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583110C2211yescharacteristic
30#14583104C2211yescharacteristic
31#14583096C2211yescharacteristic
32#14583062—21no—
33#14583041—21no—
34C8×Dic86C2211yescharacteristic
35#14583023C2211yescharacteristic
36#14583011—21no—
37#14583005—21no—
38#14582996—21no—
39#14582996—21no—
40D4×C43⋊C8C2211yescharacteristic
41C8×C22⋊D43—21no—
42(C22⋊D43)⋊C8—21no—
43#14582955C2211yescharacteristic
44#14582955C2211yescharacteristic
45#14582951C2211yescharacteristic
46#14582949—21no—
47#14582892—21no—
48#14582892—21no—
49C2×C8×Dic43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582650C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#476C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621900D411yescharacteristic
69C2×Dic172—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C22×C43⋊C8—21no—
73C2×C8×D43D411yescharacteristic
74C2×C8×D43D411yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063316—21no—
78#13063312—21no—
79#13063305—21no—
80#13063301—21no—
81#13063296—21no—
82#13063296—21no—
83Q8×Dic43—21no—
84C4×Dic86C2311yescharacteristic
85#13063290—21no—
86#13063290D411yescharacteristic
87D4×Dic43—21no—
88D4×Dic43—21no—
89D4×Dic43D411yescharacteristic
90C4×C22⋊D43—21no—
91(C22⋊D43)⋊C4—21no—
92#13063283—21no—
93#13063283D411yescharacteristic
94#13063281—21no—
95C2×C4×Dic43—21no—
96C42×D43C2311yescharacteristic
97#13063258—21no—
98#13063258—21no—
99#13063257—21no—
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250—21no—
106#13063250—21no—
107#13063250—21no—
108#13063250—21no—
109#13063248—21no—
110#13063248—21no—
111#13063248—21no—
112#13063248—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063235—21no—
122#13063235—21no—
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×D8×C43—21no—
130C22×C8×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132#127×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#106×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—41no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—41no—
155#10621900—22no—
156#10621900—22no—
157#10621900—42no—
158#10621900—42no—
159C2×C4×D43C2×D411yescharacteristic
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165D8×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—42no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C2×D411yescharacteristic
175C22⋊C4×C43—21no—
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178C22⋊Dic43—41no—
179C22⋊Dic43—41no—
180#10621883—42no—
181#10621883—42no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—41no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—41no—
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—41no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43#4111yescharacteristic
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—42no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206Dic172—42no—
207C8×D43—41no—
208C8×D43—41no—
209C23×C43—21no—
210C23×C43—41no—
211C22×D43#12111yescharacteristic
212Q8×C43—81no—
213D4×C43—21no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—81no—
219D4×C43#13512yes—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C22⋊D43—24no—
228C22⋊D43—82no—
229C2×Dic43—24no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—42no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—82no—
236C2×Dic43#12111yescharacteristic
237C2×Dic43#12111yescharacteristic
238C2×Dic43#12111yescharacteristic
239C4×D43—21no—
240C4×D43—21no—
241C4×D43—21no—
242C4×D43—21no—
243C4×D43—41no—
244Dic86—21no—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86#13512yes—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C43⋊C8—21no—
256C43⋊C8—21no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#19278—431nomaximal, Sylow
261C22×C43—22no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43C2×#12111yescharacteristic
268C2×D43—21no—
269C2×D43—21no—
270C2×D43—21no—
271C4×C43—21no—
272C4×C43—41no—
273C4×C43—81no—
274C4×C43C2×#13511yescharacteristic
275C4×C43C2×#13511yescharacteristic
276C4×C43#57511yescharacteristic
277C4×C43#57511yescharacteristic
278Dic43—21no—
279Dic43—22no—
280Dic43—21no—
281Dic43—21no—
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285#3131—431no—
286#3116—431no—
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#1677D4311yescharacteristic, complemented
297#1568—431no—
298#1554—431no—
299#1553—431no—
300C2×C43—42no—
301C2×C43—161no—
302C2×C43#304011yescharacteristic
303C2×C43#305011yescharacteristic
304C2×C43#306711yescharacteristic
305D43—41no—
306#533—431no—
307#532—431no—
308C4×#41—431no—
309#488—861no—
310#488—861no—
311#487—431no—
312#487—431no—
313#486—431no—
314#486C2×D4311yescharacteristic
315#485—861no—
316#482—861no—
317#477—431no—
318#476C2×D4311yescharacteristic
319#475—431no—
320#474—431no—
321#462—431no—
322#461—431no—
323#460—431no—
324#459C2×D4311yescharacteristic
325#452—861no—
326#449—861no—
327C8×Q8—431no—
328C8×Q8—431no—
329#442—861no—
330#441—861no—
331#440—861no—
332#440—861no—
333C8×D4—431no—
334C8×D4—861no—
335C8×D4—861no—
336C8×D4C2×D4311yescharacteristic
337#432—431no—
338#432—431no—
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#334C2×D4311yescharacteristic
349#333—431no—
350#333C2×D4311yescharacteristic
351#332—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#331—431no—
356#331C2×D4311yescharacteristic
357C43#1927811yescharacteristic, complemented, Sylow
358C2×#41—431no—
359C2×#41—861no—
360C2×Q16—861no—
361C2×SD16—861no—
362C2×SD16—861no—
363C2×D8—21no—
364C22×C8—21no—
365C22×C8—431no—
366C22×C8—431no—
367C22×C8—861no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8C22×D4311yescharacteristic
371#127C22×D4311yescharacteristic
372#125—861no—
373#124—861no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—861no—
377#121—861no—
378C4×Q8—431no—
379C4×Q8—431no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×D4—431no—
383C4×D4—861no—
384C4×D4—861no—
385C4×D4—861no—
386C4×D4—861no—
387C4×D4C22×D4311yescharacteristic
388#117—431no—
389#117—861no—
390#117—861no—
391C2×C42—431no—
392C2×C42—861no—
393#107—861no—
394#107—861no—
395#106—21no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
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—21no—
414#102—21no—
415#102—21no—
416#102—21no—
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—861no—
427#97—861no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—861no—
432C4×C8—861no—
433C4×C8—861no—
434C4×C8C22×D4311yescharacteristic
435#41—862no—
436#41—862no—
437#41—1722no—
438#41—1722no—
439C2×Q8—21no—
440C2×Q8—431no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—861no—
447C2×D4—1721no—
448C2×D4D4×D4311yescharacteristic
449C22×C4—21no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—1721no—
456Q16—1722no—
457SD16—1722no—
458SD16—1722no—
459D8—42no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—42no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—1721no—
470C2×C8—1721no—
471C2×C8—1722no—
472C2×C8D4×D4311yescharacteristic
473C2×C8D4×D4311yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—431no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—1721no—
484C4⋊C4—1721no—
485C4⋊C4D4×D4311yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C42—431no—
493C42—431no—
494C42—431no—
495C42—861no—
496C42—861no—
497C42—861no—
498C42—1721no—
499C42C23×D4311yescharacteristic
500C23—21no—
501C23—41no—
502C23—431no—
503Q8—81no—
504Q8—432no—
505Q8—861no—
506Q8—1721no—
507Q8—1721no—
508Q8—1721no—
509Q8—1721no—
510D4—21no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—864no—
517D4—3442no—
518D4#1306334612yes—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—431no—
524C2×C4—431no—
525C2×C4—431no—
526C2×C4—864no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—3442no—
534C2×C4—1721no—
535C2×C4—1722no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4C2×D4×D4311yescharacteristic
539C2×C4C2×D4×D4311yescharacteristic
540C2×C4#41×D4311yescharacteristic
541C8—21no—
542C8—21no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—861no—
547C8—861no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C22—22no—
552C22—41no—
553C22—41no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—861no—
558C22—861no—
559C22—861no—
560C22#121×D4311yescharacteristic
561C4—21no—
562C4—41no—
563C4—81no—
564C4—861no—
565C4—861no—
566C4—861no—
567C4—862no—
568C4—3441no—
569C4—3441no—
570C4—1721no—
571C4#135×D4311yescharacteristic
572C4C2×#1306334611yescharacteristic
573C4#1458369511yescharacteristic
574C4#1458369611yescharacteristic
575C2—42no—
576C2—161no—
577C2—1721no—
578C2#1914408411yescharacteristic
579C2#1914417111yescharacteristic
580C2#1914431311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1677C2
socleC22×C43C2×#121
prime radical#19144743C2
hypercenter#1677D43
hypocenterC43#19278
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1677

Complements

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

NH ≅ G/Ntype
1. #19144914C2semidirect
2. #19144759C2semidirect
4. C8×#10621900C2semidirect
5. #19134056C2semidirect
6. #19134048C2semidirect
7. #19134038C2semidirect
8. #19134030C2semidirect
9. #19134026C2semidirect
10. #19134018C2semidirect
11. #19134008C2semidirect
12. #19133355C2semidirect
13. #19133304C2semidirect
14. #19133297C2semidirect
15. C43×#1677C2semidirect
296. #1677D43semidirect
357. C43#19278semidirect

Maximal subgroups

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

subgroupindex
#191449142
#191447592
#191447432
C8×#106219002
#191340562
#191340482
#191340382
#191340302
#191340262
#191340182
#191340082
#191333552
#191333042
#191332972
C43×#16772
#1927843