Finite Group Databasebeta

← #25080072

Subgroups — #25080072

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145926C211yesmaximal, characteristic, complemented
2#19145922C211yesmaximal, characteristic
3#19145155C211yesmaximal, characteristic, complemented
4#19143564C211yesmaximal, characteristic, complemented
5#19134100C211yesmaximal, characteristic, complemented
6#19134093C211yesmaximal, characteristic, complemented
7#19134070C211yesmaximal, characteristic, complemented
8#19134063C211yesmaximal, characteristic, complemented
9#19134052C211yesmaximal, characteristic, complemented
10#19134045C211yesmaximal, characteristic, complemented
11#19134042C211yesmaximal, characteristic, complemented
12#19134035C211yesmaximal, characteristic, complemented
13C2×#14582651C211yesmaximal, characteristic, complemented
14#19133291C211yesmaximal, characteristic, complemented
15C43×#1552C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583273C2211yescharacteristic
20#14583249C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583206—21no—
23#14583200—21no—
24#14583195C2211yescharacteristic
25#14583190C2211yescharacteristic
26#14583181C2211yescharacteristic
27#14583176C2211yescharacteristic
28#14583138—21no—
29#14583135—21no—
30#14583130—21no—
31#14583130—21no—
32#14583130—21no—
33#14583128—21no—
34#14583121—21no—
35#14583115—21no—
36#14583106C2211yescharacteristic
37#14583101C2211yescharacteristic
38#14583100C2211yescharacteristic
39#14583095C2211yescharacteristic
40#14583026C2211yescharacteristic
41#14583023C2211yescharacteristic
42C4×#10621884—21no—
43C4×#10621884—21no—
44#14582976C2211yescharacteristic
45#14582967—21no—
46#14582964C2211yescharacteristic
47(C22⋊D43)⋊C8—21no—
48#14582961—21no—
49C2×C4⋊(C43⋊C8)C2211yescharacteristic
50#14582856—21no—
51C2×C4×C43⋊C8C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582651C2211yescharacteristic
55#14582651C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#533C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621885—21no—
69C2×#10621873—21no—
70C2×#10621884—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×D344—21no—
74C2×#10621872—21no—
75C22×C43⋊C8—21no—
76C22×C43⋊C8D411yescharacteristic
77C22×C43⋊C8D411yescharacteristic
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063319—21no—
82#13063317D411yescharacteristic
83#13063313—21no—
84#13063313D411yescharacteristic
85#13063308—21no—
86#13063304D411yescharacteristic
87#13063299—21no—
88#13063299—21no—
89#13063299D411yescharacteristic
90C4×Dic86C2311yescharacteristic
91C4×D172—21no—
92C4×D172—21no—
93C4×D172C2311yescharacteristic
94C4×C22⋊D43—21no—
95#13063282—21no—
96#13063259—21no—
97#13063258—21no—
98#13063257—21no—
99#13063256—21no—
100#13063256—21no—
101#13063256—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063249—21no—
109#13063249—21no—
110#13063249—21no—
111#13063249—21no—
112#13063248—21no—
113#13063247—21no—
114#13063247—21no—
115#13063247—21no—
116#13063245—21no—
117#13063245—21no—
118#13063245—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063235—21no—
122C4×C43⋊C8D411yescharacteristic
123C4×C43⋊C8D411yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C22×C8×C43—21no—
128C4⋊Q8×C43C2311yescharacteristic
129C4⋊Q8×C43C2311yescharacteristic
130#125×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C4×Q8×C43—21no—
134C4×Q8×C43—21no—
135#117×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C22⋊C8×C43—21no—
143#97×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43#4111yescharacteristic
149C2×C22⋊D43—21no—
150C2×C22⋊D43—41no—
151#10621898—82no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—41no—
158C2×Dic86—21no—
159C2×Dic86C2×D411yescharacteristic
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—81no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—41no—
171C22⋊C4×C43—41no—
172C42×C43—41no—
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43#4111yescharacteristic
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178#10621885—81no—
179#10621884—42no—
180#10621884—42no—
181#10621884—81no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—41no—
187(C2×D43)⋊C4—41no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C2×D411yescharacteristic
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43—21no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—41no—
201C2×C43⋊C8—81no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206D344—81no—
207#10621873—81no—
208#10621872—42no—
209C8×D43—42no—
210C23×C43#12111yescharacteristic
211C22×D43—21no—
212C22×D43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217C2×C4×C43—22no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C22⋊D43—42no—
231C22⋊D43—82no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—41no—
236D172—21no—
237D172—21no—
238D172—41no—
239D172—41no—
240D172—41no—
241D172—41no—
242D172—81no—
243C4×D43—41no—
244C4×D43—41no—
245C4×D43—82no—
246Dic86—21no—
247Dic86—21no—
248Dic86—81no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43—41no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8#13512yes—
259#19229—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43#47112yes—
263C22×C43C2×#12111yescharacteristic
264C2×D43—41no—
265C2×D43—41no—
266C2×D43—41no—
267C2×D43—81no—
268C2×D43—81no—
269C2×D43—81no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43C2×#13511yescharacteristic
277C4×C43#57511yescharacteristic
278C4×C43#57611yescharacteristic
279C4×C43#57811yescharacteristic
280Dic43—41no—
281Dic43—41no—
282Dic43—41no—
283Dic43—81no—
284#3248—431no—
285#3247—431no—
286#3167—431no—
287#2966—431no—
288#1692—431no—
289#1691—431no—
290#1686—431no—
291#1685—431no—
292#1684—431no—
293#1683—431no—
294#1682—431no—
295#1681—431no—
296C2×#335—431no—
297#1552D4311yescharacteristic, complemented
298#1551—431no—
299C2×C43—22no—
300C2×C43#303511yescharacteristic
301C2×C43#306111yescharacteristic
302C2×C43C2×#47111yescharacteristic
303D43—81no—
304D43—161no—
305#533C2×D4311yescharacteristic
306#532—431no—
307#529—431no—
308#498—431no—
309#492—431no—
310#487—431no—
311#486—431no—
312#479—861no—
313#478—861no—
314#477—431no—
315#476—431no—
316#475—431no—
317#474—431no—
318#467—861no—
319#466—861no—
320#465—861no—
321#465—861no—
322#465—861no—
323#465—861no—
324#464—861no—
325#463—861no—
326#462—431no—
327#461—431no—
328#460—431no—
329#459—431no—
330#446—431no—
331C8×Q8—431no—
332C4×SD16—861no—
333C4×SD16—861no—
334#436—431no—
335#435—861no—
336C8×D4—431no—
337C8×D4—861no—
338#433—861no—
339#432C2×D4311yescharacteristic
340C2×C4⋊C8—431no—
341C2×C4⋊C8C2×D4311yescharacteristic
342#405—861no—
343C2×C4×C8—431no—
344#335—431no—
345#335—431no—
346#335—431no—
347#335—431no—
348#333—431no—
349#333—431no—
350#332C2×D4311yescharacteristic
351#332C2×D4311yescharacteristic
352#332C2×D4311yescharacteristic
353#332C2×D4311yescharacteristic
354#331—431no—
355#331—431no—
356C43#1922911yescharacteristic, complemented, Sylow
357C2×#41—861no—
358C2×Q16—861no—
359C2×SD16—861no—
360C2×SD16—861no—
361C2×SD16—861no—
362C2×SD16—861no—
363C2×D8—861no—
364C2×M16—861no—
365C22×C8—21no—
366C22×C8—431no—
367C22×C8—431no—
368C22×C8—861no—
369C22×C8—861no—
370C4⋊Q8—431no—
371C4⋊Q8C22×D4311yescharacteristic
372C4⋊Q8C22×D4311yescharacteristic
373#127—431no—
374#126—861no—
375#125—21no—
376#125—431no—
377#124—431no—
378#124—861no—
379#123—861no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—431no—
383#121—431no—
384#121—861no—
385#121—861no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—431no—
389C4×D4—431no—
390C4×D4—861no—
391C4×D4—861no—
392C4×D4—861no—
393#117—21no—
394#117—861no—
395C2×C42C22×D4311yescharacteristic
396#107—861no—
397#107—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402C4⋊C8—21no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—861no—
406C4⋊C8—861no—
407C4⋊C8—861no—
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424C22⋊C8—21no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427#97—21no—
428#97—861no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—861no—
434#41—3442no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—431no—
438C2×Q8—861no—
439C2×D4—431no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—1721no—
445C22×C4—861no—
446C22×C4—1721no—
447C22×C4#1062189811yescharacteristic
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450Q16—3441no—
451SD16—3441no—
452SD16—3441no—
453SD16—1722no—
454SD16—1722no—
455D8—3441no—
456M16—1722no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—81no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—862no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—3441no—
470C2×C8—1722no—
471C2×C8—1721no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—431no—
479C4⋊C4—431no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C22⋊C4—41no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C22⋊C4—861no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C42—41no—
495C42—861no—
496C42#1062189811yescharacteristic
497C42D4×D4311yescharacteristic
498C42D4×D4311yescharacteristic
499C42C23×D4311yescharacteristic
500C23—861no—
501C23—1721no—
502C23#1306329811yescharacteristic
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—861no—
508Q8—861no—
509Q8—3441no—
510D4—861no—
511D4—861no—
512D4—3441no—
513D4—3442no—
514D4—1722no—
515D4—1721no—
516D4—1721no—
517D4—1721no—
518D4—1721no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—3442no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4#1306329811yescharacteristic
534C2×C4#1306329811yescharacteristic
535C2×C4#1306329811yescharacteristic
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4C2×D4×D4311yescharacteristic
538C2×C4C2×#1062189811yescharacteristic
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—432no—
544C8—861no—
545C8—861no—
546C8—861no—
547C8—1721no—
548C8—1721no—
549C22—21no—
550C22—21no—
551C22—3441no—
552C22—3441no—
553C22—3441no—
554C22—1721no—
555C22—1721no—
556C22—1721no—
557C22#1458316512yes—
558C22C2×#1306329811yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—81no—
564C4—81no—
565C4—3441no—
566C4—1721no—
567C4—1721no—
568C4—1721no—
569C4#135×D4311yescharacteristic
570C4#1458369611yescharacteristic
571C4#1458370311yescharacteristic
572C4#1458371511yescharacteristic
573C2—22no—
574C2—3441no—
575C2—6881no—
576C2#1914404811yescharacteristic
577C2#1914426411yescharacteristic
578C2C2×#1458316511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1552C2
socleC22×C43C2×#121
prime radical#19145922C2
hypercenter#1552D43
hypocenterC43#19229
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1552

Complements

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

NH ≅ G/Ntype
1. #19145926C2semidirect
3. #19145155C2semidirect
4. #19143564C2semidirect
5. #19134100C2semidirect
6. #19134093C2semidirect
7. #19134070C2semidirect
8. #19134063C2semidirect
9. #19134052C2semidirect
10. #19134045C2semidirect
11. #19134042C2semidirect
12. #19134035C2semidirect
13. C2×#14582651C2semidirect
14. #19133291C2semidirect
15. C43×#1552C2semidirect
297. #1552D43semidirect
356. C43#19229semidirect

Maximal subgroups

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

subgroupindex
#191459262
#191459222
#191451552
#191435642
#191341002
#191340932
#191340702
#191340632
#191340522
#191340452
#191340422
#191340352
C2×#145826512
#191332912
C43×#15522
#1922943