Finite Group Databasebeta

← #25080359

Subgroups — #25080359

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145917C211yesmaximal, characteristic
2#19145772C211yesmaximal, characteristic, complemented
3#19145311C211yesmaximal, characteristic, complemented
4#19143602C211yesmaximal, characteristic, complemented
5#19134176C211yesmaximal, characteristic, complemented
6#19134134C211yesmaximal, characteristic, complemented
7#19134118C211yesmaximal, characteristic, complemented
8#19134044C211yesmaximal, characteristic, complemented
9#19134002C211yesmaximal, characteristic, complemented
10#19134000C211yesmaximal, characteristic, complemented
11#19133940C211yesmaximal, characteristic, complemented
12#19133346C211yesmaximal, characteristic, complemented
13#19133254C211yesmaximal, characteristic, complemented
14#19133251C211yesmaximal, characteristic, complemented
15C43×#1685C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18#14583431C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583300—21no—
21#14583252—21no—
22#14583249C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583242—21no—
25#14583221—21no—
26#14583197—21no—
27#14583195C2211yescharacteristic
28#14583195C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583181C2211yescharacteristic
32#14583142—21no—
33#14583142—21no—
34#14583132—21no—
35#14583127—21no—
36#14583112—21no—
37#14583096C2211yescharacteristic
38#14583026C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40#14583000—21no—
41#14583000—21no—
42#14582975—21no—
43#14582967—21no—
44D4×C43⋊C8C2211yescharacteristic
45#14582957—21no—
46#14582951C2211yescharacteristic
47#14582951C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582857—21no—
50C4×#10621872C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582650C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#492C2211yescharacteristic
61C43×#474C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621883—21no—
69C2×#10621872D411yescharacteristic
70C2×#10621872D411yescharacteristic
71C22×C43⋊C8—21no—
72C2×C8×D43—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063318—21no—
76#13063316—21no—
77#13063316D411yescharacteristic
78#13063312—21no—
79#13063312D411yescharacteristic
80#13063307—21no—
81#13063305—21no—
82#13063305D411yescharacteristic
83#13063301—21no—
84#13063296—21no—
85#13063296—21no—
86#13063296D411yescharacteristic
87Q8×Dic43—21no—
88C4×Dic86C2311yescharacteristic
89#13063290—21no—
90D4×Dic43—21no—
91D4×Dic43—21no—
92C4×C22⋊D43—21no—
93#13063284—21no—
94#13063283—21no—
95C42×D43C2311yescharacteristic
96#13063259—21no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063250—21no—
110#13063250—21no—
111#13063249—21no—
112#13063249—21no—
113#13063248—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119C22⋊(C43⋊C8)—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122#13063235—21no—
123#13063235D411yescharacteristic
124#13063235D411yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43—21no—
130C2×SD16×C43—21no—
131C2×D8×C43—21no—
132C2×M16×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—41no—
153#10621900—82no—
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43C2×D411yescharacteristic
156C2×C4×D43#4111yescharacteristic
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86C2×D411yescharacteristic
160SD16×C43—42no—
161SD16×C43—42no—
162D8×C43—81no—
163M16×C43—42no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43C2×D411yescharacteristic
172C22⋊C4×C43—21no—
173C42×C43C2411yescharacteristic
174C22⋊Dic43—21no—
175C22⋊Dic43—21no—
176C22⋊Dic43—21no—
177C22⋊Dic43—41no—
178C22⋊Dic43—41no—
179#10621883—81no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—41no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
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—41no—
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43#4111yescharacteristic
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—42no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204#10621872—22no—
205#10621872—41no—
206C8×D43—81no—
207C23×C43—21no—
208C23×C43—41no—
209C22×D43#12111yescharacteristic
210Q8×C43—41no—
211Q8×C43—41no—
212D4×C43—21no—
213D4×C43—21no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—81no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C22⋊D43—81no—
227C22⋊D43—82no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—82no—
233C2×Dic43#12111yescharacteristic
234C2×Dic43#12111yescharacteristic
235C2×Dic43#12111yescharacteristic
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—21no—
240C4×D43—41no—
241Dic86—21no—
242Dic86—21no—
243Dic86—81no—
244Dic86—81no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43#13512yes—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#19253—431nomaximal, Sylow
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43C2×#12111yescharacteristic
263C2×D43—21no—
264C2×D43—21no—
265C2×D43—21no—
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—81no—
269C4×C43C2×#13511yescharacteristic
270C4×C43#57511yescharacteristic
271C4×C43#57711yescharacteristic
272C4×C43#57811yescharacteristic
273Dic43—21no—
274Dic43—21no—
275Dic43—21no—
276Dic43—41no—
277Dic43—41no—
278Dic43—81no—
279Dic43—81no—
280#3247—431no—
281#3233—431no—
282#3182—431no—
283#2969—431no—
284#1704—431no—
285#1698—431no—
286#1695—431no—
287#1685D4311yescharacteristic, complemented
288#1683—431no—
289#1677—431no—
290#1676—431no—
291#1666—431no—
292#1565—431no—
293#1543—431no—
294#1542—431no—
295C2×C43—81no—
296C2×C43—161no—
297C2×C43#303511yescharacteristic
298C2×C43#306311yescharacteristic
299C2×C43#306811yescharacteristic
300D43—41no—
301#533—431no—
302#532—431no—
303#529—431no—
304#500—431no—
305#499—861no—
306#492C2×D4311yescharacteristic
307#488—861no—
308#487—431no—
309#486—431no—
310#485—861no—
311#482—861no—
312#478—861no—
313#477—431no—
314#477—431no—
315#476—431no—
316#476—431no—
317#475—431no—
318#474C2×D4311yescharacteristic
319#468—861no—
320#468—861no—
321#466—861no—
322#465—861no—
323#463—861no—
324#460—431no—
325#459C2×D4311yescharacteristic
326#446—431no—
327C8×Q8—431no—
328#440—861no—
329#440—861no—
330#436—861no—
331#436C2×D4311yescharacteristic
332#435—861no—
333C8×D4—431no—
334#433—861no—
335#431—431no—
336#431—431no—
337C2×C4⋊C8—431no—
338#405—861no—
339C4×M16—431no—
340#335—431no—
341#335C2×D4311yescharacteristic
342#334—431no—
343#334—431no—
344#333—431no—
345#333—431no—
346#333—431no—
347#333—431no—
348#332—431no—
349#332C2×D4311yescharacteristic
350#331—431no—
351#331C2×D4311yescharacteristic
352C43#1925311yescharacteristic, complemented, Sylow
353C2×#41—861no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—861no—
357C2×D8—21no—
358C2×M16—21no—
359C2×M16—431no—
360C2×M16—431no—
361C22×C8—861no—
362C22×C8—861no—
363C4⋊Q8—431no—
364C4⋊Q8—431no—
365C4⋊Q8C22×D4311yescharacteristic
366#127C22×D4311yescharacteristic
367#126—861no—
368#125—431no—
369#125—861no—
370#124—431no—
371#124—861no—
372#123—861no—
373C22⋊Q8—431no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—431no—
377#121—861no—
378#121—861no—
379C4×Q8—431no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×D4—861no—
383C4×D4—861no—
384C4×D4—861no—
385C4×D4C22×D4311yescharacteristic
386#117—861no—
387#117—861no—
388C2×C42—431no—
389#107—21no—
390#107—861no—
391#107—861no—
392#107—861no—
393#107—861no—
394#106—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#102—21no—
412#102—21no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418C22⋊C8—21no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422#97—431no—
423#97—431no—
424#97—861no—
425C4×C8—431no—
426C4×C8—861no—
427C4×C8—861no—
428C4×C8—861no—
429C4×C8C22×D4311yescharacteristic
430#41—3442no—
431C2×Q8—21no—
432C2×Q8—431no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—861no—
439C2×D4—1721no—
440C2×D4D4×D4311yescharacteristic
441C22×C4—21no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—1721no—
446SD16—42no—
447SD16—42no—
448SD16—3441no—
449D8—81no—
450M16—42no—
451M16—862no—
452M16—1721no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—3441no—
462C2×C8—1722no—
463C2×C8D4×D4311yescharacteristic
464C2×C8D4×D4311yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—431no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—1721no—
477C4⋊C4—1721no—
478C4⋊C4D4×D4311yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C42—431no—
488C42—431no—
489C42—431no—
490C42—861no—
491C42—1721no—
492C42C23×D4311yescharacteristic
493C23—21no—
494C23—41no—
495C23—431no—
496Q8—41no—
497Q8—41no—
498Q8—861no—
499Q8—861no—
500Q8—3441no—
501Q8—3441no—
502D4—21no—
503D4—21no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—81no—
509D4—3442no—
510D4—3441no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—431no—
516C2×C4—431no—
517C2×C4—431no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—3442no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4C2×D4×D4311yescharacteristic
530C2×C4#41×D4311yescharacteristic
531C8—21no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—861no—
536C8—861no—
537C8—1721no—
538C8—1721no—
539C8—1721no—
540C8#1306334412yes—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—861no—
548C22—861no—
549C22—861no—
550C22#121×D4311yescharacteristic
551C4—21no—
552C4—41no—
553C4—81no—
554C4—861no—
555C4—861no—
556C4—861no—
557C4—3441no—
558C4—3441no—
559C4—1721no—
560C4—1721no—
561C4C2×#1306334411yescharacteristic
562C4#1458369511yescharacteristic
563C4#1458370911yescharacteristic
564C4#1458371511yescharacteristic
565C2—81no—
566C2—161no—
567C2—1721no—
568C2#1914404311yescharacteristic
569C2#1914428111yescharacteristic
570C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1685C2
socleC22×C43C2×#121
prime radical#19145917C2
hypercenter#1685D43
hypocenterC43#19253
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1685

Complements

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

NH ≅ G/Ntype
2. #19145772C2semidirect
3. #19145311C2semidirect
4. #19143602C2semidirect
5. #19134176C2semidirect
6. #19134134C2semidirect
7. #19134118C2semidirect
8. #19134044C2semidirect
9. #19134002C2semidirect
10. #19134000C2semidirect
11. #19133940C2semidirect
12. #19133346C2semidirect
13. #19133254C2semidirect
14. #19133251C2semidirect
15. C43×#1685C2semidirect
287. #1685D43semidirect
352. C43#19253semidirect

Maximal subgroups

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

subgroupindex
#191459172
#191457722
#191453112
#191436022
#191341762
#191341342
#191341182
#191340442
#191340022
#191340002
#191339402
#191333462
#191332542
#191332512
C43×#16852
#1925343