Finite Group Databasebeta

← #25080356

Subgroups — #25080356

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#19145915C211yesmaximal, characteristic
2#19145774C211yesmaximal, characteristic, complemented
3#19143599C211yesmaximal, characteristic, complemented
4#19134174C211yesmaximal, characteristic, complemented
5#19134132C211yesmaximal, characteristic, complemented
6#19134115C211yesmaximal, characteristic, complemented
7#19134057C211yesmaximal, characteristic, complemented
8#19134043C211yesmaximal, characteristic, complemented
9#19134001C211yesmaximal, characteristic, complemented
10#19133996C211yesmaximal, characteristic, complemented
11#19133940C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133257C211yesmaximal, characteristic, complemented
14#19133252C211yesmaximal, characteristic, complemented
15C43×#3182C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583298—21no—
18#14583256—21no—
19#14583240—21no—
20#14583223—21no—
21#14583199—21no—
22#14583191C2211yescharacteristic
23#14583191C2211yescharacteristic
24#14583186C2211yescharacteristic
25#14583186C2211yescharacteristic
26#14583181C2211yescharacteristic
27#14583176C2211yescharacteristic
28#14583133—21no—
29#14583126—21no—
30#14583114—21no—
31#14583096C2211yescharacteristic
32#14583091C2211yescharacteristic
33#14583029C2211yescharacteristic
34C8×Dic86C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582975—21no—
37#14582968—21no—
38C8×D172C2211yescharacteristic
39#14582961—21no—
40#14582952C2211yescharacteristic
41#14582952C2211yescharacteristic
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43#14582856—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582648C2211yescharacteristic
51#14582648C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#532C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#468—21no—
63C43×#468—21no—
64C43×#440—21no—
65C43×#440—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621882—21no—
69C2×#10621872—21no—
70C22×C43⋊C8—21no—
71C2×C8×D43—21no—
72#13063319—21no—
73#13063317D411yescharacteristic
74#13063313D411yescharacteristic
75#13063308—21no—
76#13063304D411yescharacteristic
77#13063299D411yescharacteristic
78C4×Dic86C2311yescharacteristic
79C4×D172C2311yescharacteristic
80C4×C22⋊D43—21no—
81#13063282—21no—
82#13063258—21no—
83#13063258—21no—
84#13063258—21no—
85#13063256—21no—
86#13063256—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95Dic43⋊C8—21no—
96Dic43⋊C8—21no—
97#13063248—21no—
98#13063248—21no—
99#13063248—21no—
100#13063246—21no—
101#13063246—21no—
102#13063245—21no—
103#13063245—21no—
104#13063245—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)—21no—
107(C2×D43)⋊C8—21no—
108(C2×D43)⋊C8—21no—
109#13063235—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8—21no—
112C8×Dic43—21no—
113C2×#41×C43—21no—
114C2×SD16×C43—21no—
115C2×SD16×C43—21no—
116C2×M16×C43D411yescharacteristic
117C2×M16×C43D411yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43C2311yescharacteristic
122#125×C43—21no—
123#124×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132#117×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—21no—
135#107×C43—21no—
136#103×C43—21no—
137#103×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#97×C43D411yescharacteristic
141#97×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—82no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C22×C4×C43—41no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C2×C22⋊D43—21no—
157C2×D172C2×D411yescharacteristic
158C2×C4×D43—21no—
159C2×Dic86C2×D411yescharacteristic
160SD16×C43—42no—
161SD16×C43—42no—
162M16×C43—22no—
163M16×C43—41no—
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C42×C43—41no—
180C42×C43C2×D411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43#4111yescharacteristic
183C42×C43C2411yescharacteristic
184C22⋊Dic43—21no—
185#10621883—81no—
186#10621882—81no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191C4⋊Dic43C2×D411yescharacteristic
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197C4×Dic43—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—81no—
205#10621872—42no—
206C8×D43—42no—
207C23×C43—41no—
208C23×C43#12111yescharacteristic
209C22×D43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—81no—
213Q8×C43—81no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—81no—
219D4×C43—82no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—82no—
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—81no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239D172—21no—
240D172—21no—
241C4×D43—41no—
242C4×D43—41no—
243Dic86—21no—
244Dic86—21no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43#13512yes—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#19253—431nomaximal, Sylow
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43C2×#12111yescharacteristic
263C2×D43—41no—
264C2×D43—41no—
265C2×D43—41no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—81no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43C2×#13511yescharacteristic
274C4×C43#57511yescharacteristic
275C4×C43#57711yescharacteristic
276C4×C43#57811yescharacteristic
277Dic43—41no—
278Dic43—41no—
279Dic43—41no—
280#3247—431no—
281#3233—431no—
282#3182D4311yescharacteristic, complemented
283#2969—431no—
284#1704—431no—
285#1698—431no—
286#1695—431no—
287#1685—431no—
288#1683—431no—
289#1677—431no—
290#1676—431no—
291#1666—431no—
292#1565—431no—
293#1543—431no—
294#1542—431no—
295C2×C43—41no—
296C2×C43—161no—
297C2×C43#303511yescharacteristic
298C2×C43#306311yescharacteristic
299C2×C43#306811yescharacteristic
300D43—81no—
301#533C2×D4311yescharacteristic
302#532C2×D4311yescharacteristic
303#529—431no—
304#500C2×D4311yescharacteristic
305#499—861no—
306#492C2×D4311yescharacteristic
307#488—861no—
308#487C2×D4311yescharacteristic
309#486C2×D4311yescharacteristic
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#474—431no—
319#468—21no—
320#468—21no—
321#466—861no—
322#465—861no—
323#463—861no—
324#460—431no—
325#459—431no—
326#446—431no—
327C8×Q8—431no—
328#440—21no—
329#440—21no—
330#436—431no—
331#436—861no—
332#435—861no—
333C8×D4—431no—
334#433—861no—
335#431—431no—
336#431—431no—
337C2×C4⋊C8—431no—
338#405—861no—
339C4×M16C2×D4311yescharacteristic
340#335—431no—
341#335—431no—
342#334—431no—
343#334—431no—
344#333—431no—
345#333—431no—
346#333—431no—
347#333—431no—
348#332—431no—
349#332—431no—
350#331—431no—
351#331—431no—
352C43#1925311yescharacteristic, complemented, Sylow
353C2×#41—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—861no—
357C2×D8—861no—
358C2×M16—861no—
359C2×M16C22⋊D4311yescharacteristic
360C2×M16C22⋊D4311yescharacteristic
361C22×C8—861no—
362C22×C8—861no—
363C4⋊Q8C22×D4311yescharacteristic
364C4⋊Q8C22×D4311yescharacteristic
365C4⋊Q8C22×D4311yescharacteristic
366#127C22×D4311yescharacteristic
367#126—861no—
368#125—21no—
369#125—431no—
370#124—21no—
371#124—431no—
372#123—861no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—431no—
376#121—21no—
377#121—21no—
378#121—431no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8—431no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—431no—
385C4×D4—861no—
386#117—21no—
387#117—861no—
388C2×C42C22×D4311yescharacteristic
389#107—21no—
390#107—21no—
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—431no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406#103—21no—
407#103—21no—
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—861no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422#97—861no—
423#97C22⋊D4311yescharacteristic
424#97C22⋊D4311yescharacteristic
425C4×C8—861no—
426C4×C8—861no—
427C4×C8—861no—
428C4×C8C22×D4311yescharacteristic
429C4×C8C22×D4311yescharacteristic
430#41—82no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—431no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—41no—
439C2×D4—431no—
440C2×D4—861no—
441C22×C4—41no—
442C22×C4—861no—
443C22×C4D4×D4311yescharacteristic
444C22×C4#1062190011yescharacteristic
445C22×C4C2×C22⋊D4311yescharacteristic
446SD16—42no—
447SD16—42no—
448SD16—3441no—
449D8—3441no—
450M16—22no—
451M16—41no—
452M16—1722no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—3441no—
460C2×C8—1722no—
461C2×C8C2×C22⋊D4311yescharacteristic
462C2×C8C2×C22⋊D4311yescharacteristic
463C2×C8C2×C22⋊D4311yescharacteristic
464C2×C8C2×C22⋊D4311yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—431no—
474C4⋊C4—431no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C22⋊C4—861no—
486C22⋊C4—861no—
487C42—41no—
488C42—861no—
489C42D4×D4311yescharacteristic
490C42#1062190011yescharacteristic
491C42C2×C22⋊D4311yescharacteristic
492C42C23×D4311yescharacteristic
493C23—41no—
494C23—861no—
495C23#1306329611yescharacteristic
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—81no—
500Q8—861no—
501Q8—861no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—81no—
507D4—82no—
508D4—861no—
509D4—861no—
510D4—3441no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—82no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4#1306329611yescharacteristic
526C2×C4#1306329611yescharacteristic
527C2×C4#1306329611yescharacteristic
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4C22×C22⋊D4311yescharacteristic
530C2×C4C2×#1062190011yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—1721no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C8—1721no—
539C8—1721no—
540C8#1306334512yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—1721no—
548C22—1721no—
549C22—1721no—
550C22C2×#1306329611yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4—1721no—
559C4—1721no—
560C4—1721no—
561C4C2×#1306334511yescharacteristic
562C4#1458369711yescharacteristic
563C4#1458370811yescharacteristic
564C4#1458371511yescharacteristic
565C2—41no—
566C2—161no—
567C2—3441no—
568C2#1914404411yescharacteristic
569C2#1914428011yescharacteristic
570C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3182C2
socleC22×C43C2×#121
prime radical#19145915C2
hypercenter#3182D43
hypocenterC43#19253
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3182

Complements

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

NH ≅ G/Ntype
2. #19145774C2semidirect
3. #19143599C2semidirect
4. #19134174C2semidirect
5. #19134132C2semidirect
6. #19134115C2semidirect
7. #19134057C2semidirect
8. #19134043C2semidirect
9. #19134001C2semidirect
10. #19133996C2semidirect
11. #19133940C2semidirect
12. #19133347C2semidirect
13. #19133257C2semidirect
14. #19133252C2semidirect
15. C43×#3182C2semidirect
282. #3182D43semidirect
352. C43#19253semidirect

Maximal subgroups

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

subgroupindex
#191459152
#191457742
#191435992
#191341742
#191341322
#191341152
#191340572
#191340432
#191340012
#191339962
#191339402
#191333472
#191332572
#191332522
C43×#31822
#1925343