Finite Group Databasebeta

← #25080326

Subgroups — #25080326

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145926C211yesmaximal, characteristic
2#19145774C211yesmaximal, characteristic
3#19143599C211yesmaximal, characteristic
4#19134174C211yesmaximal, characteristic, complemented
5#19134146C211yesmaximal, characteristic, complemented
6#19134091C211yesmaximal, characteristic, complemented
7#19134081C211yesmaximal, characteristic, complemented
8#19134043C211yesmaximal, characteristic, complemented
9#19134015C211yesmaximal, characteristic, complemented
10#19133974C211yesmaximal, characteristic, complemented
11#19133962C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133260C211yesmaximal, characteristic, complemented
14#19133252C211yesmaximal, characteristic, complemented
15C43×#3185C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583298—21no—
18#14583256—21no—
19#14583240—21no—
20#14583223—21no—
21#14583206—21no—
22#14583191C2211yescharacteristic
23#14583186C2211yescharacteristic
24#14583181C2211yescharacteristic
25#14583181C2211yescharacteristic
26#14583176C2211yescharacteristic
27#14583176C2211yescharacteristic
28#14583138—21no—
29#14583130—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#14582952C2211yescharacteristic
41#14582952C2211yescharacteristic
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
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
57C43×#533C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#494C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C43×#470—21no—
63C43×#470—21no—
64C43×#441—21no—
65C43×#441—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621884—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#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#13063235—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8—21no—
112C8×Dic43—21no—
113C2×Q16×C43—21no—
114C2×Q16×C43—21no—
115C2×M16×C43D411yescharacteristic
116C2×M16×C43D411yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#125×C43—21no—
122#125×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43—21no—
131#117×C43—21no—
132#117×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#106×C43—21no—
135#106×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—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×C22⋊D43—21no—
152C2×D172C2×D411yescharacteristic
153C2×C4×D43—21no—
154C2×Dic86C2×D411yescharacteristic
155Q16×C43—42no—
156Q16×C43—42no—
157M16×C43—22no—
158M16×C43—41no—
159C2×C8×C43C2×D411yescharacteristic
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
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—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C42×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—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—81no—
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—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
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—81no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234D172—21no—
235D172—21no—
236C4×D43—41no—
237C4×D43—41no—
238Dic86—21no—
239Dic86—21no—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43#13512yes—
244C43⋊C8—41no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250#19251—431nomaximal, Sylow
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43C2×#12111yescharacteristic
255C2×D43—41no—
256C2×D43—41no—
257C2×D43—41no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43—81no—
265C4×C43—81no—
266C4×C43C2×#13511yescharacteristic
267C4×C43#57511yescharacteristic
268C4×C43#57711yescharacteristic
269C4×C43#57811yescharacteristic
270Dic43—41no—
271Dic43—41no—
272Dic43—41no—
273#3248—431no—
274#3233—431no—
275#3185D4311yescharacteristic, complemented
276#2969—431no—
277#1704—431no—
278#1700—431no—
279#1691—431no—
280#1689—431no—
281#1683—431no—
282#1679—431no—
283#1672—431no—
284#1670—431no—
285#1565—431no—
286#1544—431no—
287#1542—431no—
288C2×C43—41no—
289C2×C43#303511yescharacteristic
290C2×C43#306311yescharacteristic
291C2×C43#306911yescharacteristic
292D43—81no—
293#533C2×D4311yescharacteristic
294#533C2×D4311yescharacteristic
295#529—431no—
296#499—861no—
297#498C2×D4311yescharacteristic
298#494C2×D4311yescharacteristic
299#488—861no—
300#487C2×D4311yescharacteristic
301#487C2×D4311yescharacteristic
302#485—861no—
303#482—861no—
304#479—861no—
305#477—431no—
306#476—431no—
307#475—431no—
308#475—431no—
309#474—431no—
310#474—431no—
311#470—21no—
312#470—21no—
313#467—861no—
314#465—861no—
315#464—861no—
316#462—431no—
317#461—431no—
318#446—431no—
319C8×Q8—431no—
320#441—21no—
321#441—21no—
322#436—431no—
323#436—861no—
324#435—861no—
325C8×D4—431no—
326#433—861no—
327#431—431no—
328#431—431no—
329C2×C4⋊C8—431no—
330#405—861no—
331C4×M16C2×D4311yescharacteristic
332#335—431no—
333#335—431no—
334#334—431no—
335#334—431no—
336#333—431no—
337#333—431no—
338#332—431no—
339#332—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344C43#1925111yescharacteristic, complemented, Sylow
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—861no—
348C2×SD16—861no—
349C2×M16—861no—
350C2×M16C22⋊D4311yescharacteristic
351C2×M16C22⋊D4311yescharacteristic
352C22×C8—861no—
353C22×C8—861no—
354C4⋊Q8C22×D4311yescharacteristic
355C4⋊Q8C22×D4311yescharacteristic
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#126—861no—
359#125—21no—
360#125—21no—
361#125—431no—
362#124—431no—
363#123—861no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—431no—
369#121—431no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—431no—
375C4×D4—431no—
376C4×D4—861no—
377#117—21no—
378#117—21no—
379#117—861no—
380C2×C42C22×D4311yescharacteristic
381#107—861no—
382#107—861no—
383#107—861no—
384#106—21no—
385#106—21no—
386#106—861no—
387#106—861no—
388#106—861no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#102—861no—
408#102—861no—
409#102—861no—
410C22⋊C8—861no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414#97—861no—
415#97C22⋊D4311yescharacteristic
416#97C22⋊D4311yescharacteristic
417C4×C8—861no—
418C4×C8—861no—
419C4×C8—861no—
420C4×C8C22×D4311yescharacteristic
421C4×C8C22×D4311yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—431no—
427C2×D4—431no—
428C2×D4—861no—
429C22×C4—861no—
430C22×C4D4×D4311yescharacteristic
431C22×C4#1062190011yescharacteristic
432C22×C4C2×C22⋊D4311yescharacteristic
433Q16—42no—
434Q16—42no—
435Q16—3441no—
436SD16—3441no—
437M16—22no—
438M16—41no—
439M16—1722no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—3441no—
447C2×C8—1722no—
448C2×C8C2×C22⋊D4311yescharacteristic
449C2×C8C2×C22⋊D4311yescharacteristic
450C2×C8C2×C22⋊D4311yescharacteristic
451C2×C8C2×C22⋊D4311yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—431no—
465C4⋊C4—431no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—861no—
473C22⋊C4—861no—
474C22⋊C4—861no—
475C22⋊C4—861no—
476C22⋊C4—861no—
477C42—41no—
478C42—41no—
479C42—861no—
480C42D4×D4311yescharacteristic
481C42#1062190011yescharacteristic
482C42C2×C22⋊D4311yescharacteristic
483C42C23×D4311yescharacteristic
484C23—861no—
485C23#1306329611yescharacteristic
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493Q8—861no—
494Q8—861no—
495D4—861no—
496D4—861no—
497D4—3441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4#1306329611yescharacteristic
513C2×C4#1306329611yescharacteristic
514C2×C4#1306329611yescharacteristic
515C2×C4C2×D4×D4311yescharacteristic
516C2×C4C22×C22⋊D4311yescharacteristic
517C2×C4C2×#1062190011yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—1721no—
522C8—1721no—
523C8—1721no—
524C8—1721no—
525C8—1721no—
526C8—1721no—
527C8#1306334512yes—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—1721no—
532C22—1721no—
533C22—1721no—
534C22C2×#1306329611yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4—1721no—
544C4—1721no—
545C4—1721no—
546C4C2×#1306334511yescharacteristic
547C4#1458369711yescharacteristic
548C4#1458370811yescharacteristic
549C4#1458371511yescharacteristic
550C2—41no—
551C2—3441no—
552C2#1914404411yescharacteristic
553C2#1914428011yescharacteristic
554C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3185C2
socleC22×C43C2×#121
prime radical#13063299D4
hypercenter#3185D43
hypocenterC43#19251
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3185

Complements

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

NH ≅ G/Ntype
4. #19134174C2semidirect
5. #19134146C2semidirect
6. #19134091C2semidirect
7. #19134081C2semidirect
8. #19134043C2semidirect
9. #19134015C2semidirect
10. #19133974C2semidirect
11. #19133962C2semidirect
12. #19133347C2semidirect
13. #19133260C2semidirect
14. #19133252C2semidirect
15. C43×#3185C2semidirect
275. #3185D43semidirect
344. C43#19251semidirect

Maximal subgroups

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

subgroupindex
#191459262
#191457742
#191435992
#191341742
#191341462
#191340912
#191340812
#191340432
#191340152
#191339742
#191339622
#191333472
#191332602
#191332522
C43×#31852
#1925143