Finite Group Databasebeta

← #25081708

Subgroups — #25081708

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145962C211yesmaximal, characteristic
2#19145825C211yesmaximal, characteristic
3#19143599C211yesmaximal, characteristic
4#19134174C211yesmaximal, characteristic, complemented
5#19134167C211yesmaximal, characteristic, complemented
6#19134146C211yesmaximal, characteristic, complemented
7#19134139C211yesmaximal, characteristic, complemented
8#19134050C211yesmaximal, characteristic, complemented
9#19134043C211yesmaximal, characteristic, complemented
10#19134022C211yesmaximal, characteristic, complemented
11#19134015C211yesmaximal, characteristic, complemented
12#19133362C211yesmaximal, characteristic, complemented
13#19133305C211yesmaximal, characteristic, complemented
14#19133280C211yesmaximal, characteristic, complemented
15C43×#3139C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583305—21no—
18#14583261—21no—
19#14583234—21no—
20#14583217—21no—
21#14583206—21no—
22#14583191C2211yescharacteristic
23#14583186C2211yescharacteristic
24#14583181C2211yescharacteristic
25#14583181C2211yescharacteristic
26#14583176C2211yescharacteristic
27#14583176C2211yescharacteristic
28#14583155—21no—
29#14583147—21no—
30#14583121—21no—
31#14583106C2211yescharacteristic
32#14583101C2211yescharacteristic
33#14583029C2211yescharacteristic
34C8×Dic86C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582975—21no—
37#14582968—21no—
38C8×D172C2211yescharacteristic
39#14582961—21no—
40#14582956C2211yescharacteristic
41#14582952C2211yescharacteristic
42#14582923C2211yescharacteristic
43#14582856—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582645C2211yescharacteristic
55#14582645C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C2×C4⋊Q8×C43C2211yescharacteristic
58C43×#491—21no—
59C43×#491—21no—
60C43×#487C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C43×#487C2211yescharacteristic
63C43×#487C2211yescharacteristic
64C43×#419—21no—
65C43×#419—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621884—21no—
69C2×#10621877—21no—
70C2×#10621872—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#13063249—21no—
98#13063249—21no—
99#13063248—21no—
100#13063248—21no—
101#13063248—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#13063236—21no—
110#13063235—21no—
111C4×C43⋊C8—21no—
112C8×Dic43—21no—
113C22×Q8×C43—21no—
114C2×M16×C43D411yescharacteristic
115C2×M16×C43D411yescharacteristic
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#125×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128#117×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#103×C43—21no—
133#103×C43—21no—
134#103×C43—21no—
135#103×C43—21no—
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#97×C43D411yescharacteristic
141#97×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—42no—
149C2×Q8×C43—42no—
150C2×Q8×C43—41no—
151C22×C4×C43—41no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×C22⋊D43—21no—
156C2×D172C2×D411yescharacteristic
157C2×C4×D43—21no—
158C2×Dic86C2×D411yescharacteristic
159M16×C43—41no—
160M16×C43—41no—
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43—41no—
177C22⋊C4×C43—41no—
178C42×C43—41no—
179C42×C43C2×D411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43#4111yescharacteristic
182C42×C43C2411yescharacteristic
183C22⋊Dic43—21no—
184#10621885—81no—
185#10621884—81no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190C4⋊Dic43C2×D411yescharacteristic
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43—21no—
197#10621877—81no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204#10621872—42no—
205C8×D43—42no—
206C23×C43#12111yescharacteristic
207C22×D43—21no—
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—81no—
215Q8×C43—82no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—82no—
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C22⋊D43—81no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236D172—21no—
237D172—21no—
238C4×D43—41no—
239C4×D43—41no—
240Dic86—21no—
241Dic86—21no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—21no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#19381—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43C2×#12111yescharacteristic
257C2×D43—41no—
258C2×D43—41no—
259C2×D43—41no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—81no—
265C4×C43—81no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43#57511yescharacteristic
269C4×C43#57511yescharacteristic
270C4×C43#57711yescharacteristic
271C4×C43#57811yescharacteristic
272Dic43—41no—
273Dic43—41no—
274Dic43—41no—
275#3252—431no—
276#3239—431no—
277#3139D4311yescharacteristic, complemented
278#2969—431no—
279#1704—431no—
280#1703—431no—
281#1700—431no—
282#1699—431no—
283#1684—431no—
284#1683—431no—
285#1680—431no—
286#1679—431no—
287#1569—431no—
288#1554—431no—
289#1549—431no—
290C2×C43—41no—
291C2×C43#304011yescharacteristic
292C2×C43#306311yescharacteristic
293C2×C43#306911yescharacteristic
294D43—81no—
295#533C2×D4311yescharacteristic
296C2×C4⋊Q8C2×D4311yescharacteristic
297#529—431no—
298#501—861no—
299#491—21no—
300#491—21no—
301#489—861no—
302#487C2×D4311yescharacteristic
303#487C2×D4311yescharacteristic
304#487C2×D4311yescharacteristic
305#487C2×D4311yescharacteristic
306#484—861no—
307#481—861no—
308#479—861no—
309#477—431no—
310#476—431no—
311#475—431no—
312#475—431no—
313#474—431no—
314#474—431no—
315#470—861no—
316#468—861no—
317#464—861no—
318#462—431no—
319#461—431no—
320#446—431no—
321C8×Q8—431no—
322#436—431no—
323#436—861no—
324#435—861no—
325C8×D4—431no—
326#433—861no—
327#432—431no—
328#431—431no—
329#423—431no—
330#419—21no—
331#419—21no—
332#405—861no—
333C4×M16C2×D4311yescharacteristic
334#335—431no—
335#335—431no—
336#334—431no—
337#334—431no—
338#333—431no—
339#333—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346C43#1938111yescharacteristic, complemented, Sylow
347C22×Q8—21no—
348C2×Q16—861no—
349C2×SD16—861no—
350C2×M16—861no—
351C2×M16—861no—
352C2×M16C22⋊D4311yescharacteristic
353C2×M16C22⋊D4311yescharacteristic
354C22×C8—861no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8C22×D4311yescharacteristic
359C4⋊Q8C22×D4311yescharacteristic
360C4⋊Q8C22×D4311yescharacteristic
361C4⋊Q8C22×D4311yescharacteristic
362#126—861no—
363#125—21no—
364#125—431no—
365#124—431no—
366#123—861no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—431no—
370#121—431no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—431no—
374C4×D4—431no—
375C4×D4—861no—
376#117—21no—
377#117—861no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C42C22×D4311yescharacteristic
381#107—861no—
382#107—861no—
383#107—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#102—861no—
410#102—861no—
411#102—861no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416#97—861no—
417#97—861no—
418#97C22⋊D4311yescharacteristic
419#97C22⋊D4311yescharacteristic
420C4×C8—861no—
421C4×C8—861no—
422C4×C8C22×D4311yescharacteristic
423C4×C8C22×D4311yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—41no—
431C2×Q8—431no—
432C2×D4—431no—
433C2×D4—861no—
434C22×C4—41no—
435C22×C4—861no—
436C22×C4D4×D4311yescharacteristic
437C22×C4#1062190011yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439Q16—3441no—
440SD16—3441no—
441M16—41no—
442M16—41no—
443M16—3441no—
444M16—1722no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—1722no—
452C2×C8C2×C22⋊D4311yescharacteristic
453C2×C8C2×C22⋊D4311yescharacteristic
454C2×C8C2×C22⋊D4311yescharacteristic
455C2×C8C2×C22⋊D4311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—431no—
469C4⋊C4—431no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C22⋊C4—41no—
475C22⋊C4—861no—
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C42—41no—
481C42—861no—
482C42D4×D4311yescharacteristic
483C42#1062190011yescharacteristic
484C42C2×C22⋊D4311yescharacteristic
485C42C23×D4311yescharacteristic
486C23—861no—
487C23#1306329611yescharacteristic
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—82no—
496Q8—861no—
497Q8—861no—
498D4—861no—
499D4—861no—
500D4—3441no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—82no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4#1306329611yescharacteristic
517C2×C4#1306329611yescharacteristic
518C2×C4#1306329611yescharacteristic
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C22×C22⋊D4311yescharacteristic
521C2×C4C2×#1062190011yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—1721no—
527C8—1721no—
528C8—1721no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—1721no—
536C22—1721no—
537C22—1721no—
538C22C2×#1306329611yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—1721no—
548C4—1721no—
549C4—1721no—
550C4#1458369711yescharacteristic
551C4#1458369711yescharacteristic
552C4#1458370811yescharacteristic
553C4#1458371511yescharacteristic
554C2—41no—
555C2—3441no—
556C2#1914408511yescharacteristic
557C2#1914428011yescharacteristic
558C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3139C2
socleC22×C43C2×#121
prime radical#13063299D4
hypercenter#3139D43
hypocenterC43#19381
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
4. #19134174C2semidirect
5. #19134167C2semidirect
6. #19134146C2semidirect
7. #19134139C2semidirect
8. #19134050C2semidirect
9. #19134043C2semidirect
10. #19134022C2semidirect
11. #19134015C2semidirect
12. #19133362C2semidirect
13. #19133305C2semidirect
14. #19133280C2semidirect
15. C43×#3139C2semidirect
277. #3139D43semidirect
346. C43#19381semidirect

Maximal subgroups

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

subgroupindex
#191459622
#191458252
#191435992
#191341742
#191341672
#191341462
#191341392
#191340502
#191340432
#191340222
#191340152
#191333622
#191333052
#191332802
C43×#31392
#1938143