Finite Group Databasebeta

← #25079049

Subgroups — #25079049

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#19145152C211yesmaximal, characteristic, complemented
2#19144668C211yesmaximal, characteristic, complemented
3#19144652C211yesmaximal, characteristic
4C8×#10621900C211yesmaximal, characteristic, complemented
5#19134052C211yesmaximal, characteristic, complemented
6#19134044C211yesmaximal, characteristic, complemented
7#19134038C211yesmaximal, characteristic, complemented
8#19134030C211yesmaximal, characteristic, complemented
9#19133978C211yesmaximal, characteristic, complemented
10#19133970C211yesmaximal, characteristic, complemented
11#19133940C211yesmaximal, characteristic, complemented
12#19133340C211yesmaximal, characteristic, complemented
13#19133258C211yesmaximal, characteristic, complemented
14#19133254C211yesmaximal, characteristic, complemented
15C43×#1665C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583297C2211yescharacteristic
20#14583249C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583242—21no—
23#14583221—21no—
24#14583195C2211yescharacteristic
25#14583189C2211yescharacteristic
26#14583181C2211yescharacteristic
27#14583125—21no—
28#14583125—21no—
29#14583110C2211yescharacteristic
30#14583104C2211yescharacteristic
31#14583096C2211yescharacteristic
32#14583062—21no—
33#14583041—21no—
34C8×Dic86C2211yescharacteristic
35#14583023C2211yescharacteristic
36#14582993—21no—
37#14582990—21no—
38#14582990—21no—
39SD16×Dic43—21no—
40SD16×Dic43—21no—
41D8×Dic43—21no—
42D4×C43⋊C8C2211yescharacteristic
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582951C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582951C2211yescharacteristic
48#14582949—21no—
49C2×C8×Dic43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582650C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#492C2211yescharacteristic
61C43×#474C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#332C2211yescharacteristic
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#13063259—21no—
98#13063257—21no—
99#13063257—21no—
100#13063256—21no—
101#13063256—21no—
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063250—21no—
109#13063249—21no—
110#13063249—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—
121C4×C43⋊C8C2311yescharacteristic
122C8×Dic43—21no—
123C8×Dic43—21no—
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×SD16×C43—21no—
130C2×SD16×C43—21no—
131C2×D8×C43—21no—
132C22×C8×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134#127×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#107×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
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—82no—
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43C2×D411yescharacteristic
160C2×C4×D43#4111yescharacteristic
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164SD16×C43—42no—
165SD16×C43—42no—
166D8×C43—42no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—42no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C42×C43C2411yescharacteristic
178C22⋊Dic43—21no—
179C22⋊Dic43—41no—
180C22⋊Dic43—41no—
181#10621883—42no—
182#10621883—42no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—41no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—41no—
190C4⋊Dic43C2×D411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—41no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—41no—
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—42no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207Dic172—42no—
208C8×D43—22no—
209C8×D43—41no—
210C23×C43—21no—
211C23×C43—41no—
212C22×D43#12111yescharacteristic
213Q8×C43—41no—
214Q8×C43—41no—
215D4×C43—21no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—81no—
221D4×C43#13512yes—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C22⋊D43—24no—
230C22⋊D43—82no—
231C2×Dic43—24no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—42no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—82no—
238C2×Dic43#12111yescharacteristic
239C2×Dic43#12111yescharacteristic
240C2×Dic43#12111yescharacteristic
241C4×D43—21no—
242C4×D43—21no—
243C4×D43—21no—
244C4×D43—21no—
245C4×D43—22no—
246Dic86—21no—
247Dic86—41no—
248Dic86—41no—
249Dic86—81no—
250Dic86#13512yes—
251C8×C43—21no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C8×C43#13512yes—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#19127—431nomaximal, Sylow
262C22×C43—22no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43C2×#12111yescharacteristic
269C2×D43—21no—
270C2×D43—21no—
271C2×D43—21no—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—81no—
275C4×C43C2×#13511yescharacteristic
276C4×C43C2×#13511yescharacteristic
277C4×C43C2×#13511yescharacteristic
278C4×C43#57511yescharacteristic
279Dic43—21no—
280Dic43—22no—
281Dic43—21no—
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285Dic43#47112yes—
286#3167—431no—
287#3107—431no—
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#1665D4311yescharacteristic, complemented
298#1564—431no—
299#1544—431no—
300#1543—431no—
301C2×C43—42no—
302C2×C43—161no—
303C2×C43#303511yescharacteristic
304C2×C43#305011yescharacteristic
305C2×C43C2×#47111yescharacteristic
306D43—41no—
307#533—431no—
308#532—431no—
309C4×#41—431no—
310#498—431no—
311#492C2×D4311yescharacteristic
312#487—431no—
313#486—431no—
314#485—861no—
315#482—861no—
316#477—431no—
317#476—431no—
318#475—431no—
319#474C2×D4311yescharacteristic
320#465—861no—
321#465—861no—
322#462—431no—
323#461—431no—
324#460—431no—
325#459C2×D4311yescharacteristic
326#452—861no—
327#449—861no—
328C8×Q8—431no—
329C8×Q8—431no—
330C4×Q16—861no—
331C4×SD16—861no—
332C4×SD16—861no—
333C4×SD16—861no—
334C4×SD16—861no—
335C4×D8—861no—
336C8×D4—431no—
337C8×D4—861no—
338C8×D4—861no—
339C8×D4C2×D4311yescharacteristic
340#431—431no—
341#431—431no—
342#431—431no—
343#431—861no—
344C2×C4×C8—431no—
345C2×C4×C8—861no—
346#335—431no—
347#335—431no—
348#334—431no—
349#334C2×D4311yescharacteristic
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332C2×D4311yescharacteristic
356#331—431no—
357#331C2×D4311yescharacteristic
358C43#1912711yescharacteristic, complemented, Sylow
359C2×#41—431no—
360C2×#41—861no—
361C2×Q16—861no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×D8—21no—
367C22×C8—21no—
368C22×C8—431no—
369C22×C8—431no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8C22×D4311yescharacteristic
374#127C22×D4311yescharacteristic
375#125—861no—
376#124—861no—
377C22⋊Q8—861no—
378C22⋊Q8—861no—
379#121—861no—
380#121—861no—
381C4×Q8—431no—
382C4×Q8—431no—
383C4×Q8—861no—
384C4×Q8—861no—
385C4×D4—431no—
386C4×D4—861no—
387C4×D4—861no—
388C4×D4—861no—
389C4×D4—861no—
390C4×D4C22×D4311yescharacteristic
391#117—431no—
392#117—861no—
393#117—861no—
394C2×C42—431no—
395C2×C42—861no—
396#107—21no—
397#107—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—861no—
406C4⋊C8—861no—
407C4⋊C8C22×D4311yescharacteristic
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#102—21no—
417#102—21no—
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—431no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—861no—
431C4×C8—861no—
432C4×C8—861no—
433C4×C8—861no—
434C4×C8—861no—
435C4×C8C22×D4311yescharacteristic
436#41—862no—
437#41—862no—
438#41—3442no—
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—42no—
458SD16—42no—
459SD16—1722no—
460SD16—1722no—
461D8—42no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—42no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—862no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—1721no—
473C2×C8—1722no—
474C2×C8D4×D4311yescharacteristic
475C2×C8D4×D4311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—431no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—1721no—
486C4⋊C4—1721no—
487C4⋊C4D4×D4311yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C42—431no—
495C42—431no—
496C42—431no—
497C42—861no—
498C42—861no—
499C42—861no—
500C42—1721no—
501C42C23×D4311yescharacteristic
502C23—21no—
503C23—41no—
504C23—431no—
505Q8—41no—
506Q8—41no—
507Q8—432no—
508Q8—861no—
509Q8—3441no—
510Q8—1721no—
511Q8—1721no—
512D4—21no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—81no—
518D4—864no—
519D4—3442no—
520D4#1306334612yes—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—431no—
526C2×C4—431no—
527C2×C4—431no—
528C2×C4—862no—
529C2×C4—864no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—3442no—
537C2×C4—1722no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C2×D4×D4311yescharacteristic
542C2×C4#41×D4311yescharacteristic
543C8—21no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—861no—
548C8—861no—
549C8—1721no—
550C8—1721no—
551C8—1721no—
552C8#1306334412yes—
553C22—22no—
554C22—41no—
555C22—41no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—861no—
560C22—861no—
561C22—861no—
562C22#121×D4311yescharacteristic
563C4—21no—
564C4—41no—
565C4—81no—
566C4—432no—
567C4—861no—
568C4—861no—
569C4—862no—
570C4—3441no—
571C4—3441no—
572C4—1721no—
573C4#135×D4311yescharacteristic
574C4C2×#1306334411yescharacteristic
575C4C2×#1306334611yescharacteristic
576C4#1458369511yescharacteristic
577C2—42no—
578C2—161no—
579C2—1721no—
580C2#1914404311yescharacteristic
581C2#1914417111yescharacteristic
582C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1665C2
socleC22×C43C2×#121
prime radical#19144652C2
hypercenter#1665D43
hypocenterC43#19127
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1665

Complements

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

NH ≅ G/Ntype
1. #19145152C2semidirect
2. #19144668C2semidirect
4. C8×#10621900C2semidirect
5. #19134052C2semidirect
6. #19134044C2semidirect
7. #19134038C2semidirect
8. #19134030C2semidirect
9. #19133978C2semidirect
10. #19133970C2semidirect
11. #19133940C2semidirect
12. #19133340C2semidirect
13. #19133258C2semidirect
14. #19133254C2semidirect
15. C43×#1665C2semidirect
297. #1665D43semidirect
358. C43#19127semidirect

Maximal subgroups

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

subgroupindex
#191451522
#191446682
#191446522
C8×#106219002
#191340522
#191340442
#191340382
#191340302
#191339782
#191339702
#191339402
#191333402
#191332582
#191332542
C43×#16652
#1912743