Finite Group Databasebeta

← #25079610

Subgroups — #25079610

Order 11008.

614 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#19144649C211yesmaximal, characteristic
2#19144377C211yesmaximal, characteristic, complemented
3#19143613C211yesmaximal, characteristic, complemented
4#19134167C211yesmaximal, characteristic, complemented
5#19134125C211yesmaximal, characteristic, complemented
6#19134115C211yesmaximal, characteristic, complemented
7#19134057C211yesmaximal, characteristic, complemented
8#19134050C211yesmaximal, characteristic, complemented
9#19134008C211yesmaximal, characteristic, complemented
10#19133996C211yesmaximal, characteristic, complemented
11#19133940C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133305C211yesmaximal, characteristic, complemented
14#19133290C211yesmaximal, characteristic, complemented
15C43×#3182C211yesmaximal, characteristic, complemented
16C4×#10621898C2211yescharacteristic
17#14583220—21no—
18#14583203—21no—
19#14583196—21no—
20#14583191C2211yescharacteristic
21#14583191C2211yescharacteristic
22#14583186C2211yescharacteristic
23#14583186C2211yescharacteristic
24#14583181C2211yescharacteristic
25#14583176C2211yescharacteristic
26#14583096C2211yescharacteristic
27#14583091C2211yescharacteristic
28#14583042—21no—
29C8×Dic86C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31C4×#10621883—21no—
32C4×#10621882—21no—
33#14582978C2211yescharacteristic
34#14582978C2211yescharacteristic
35#14582975—21no—
36#14582975—21no—
37#14582956C2211yescharacteristic
38#14582954—21no—
39#14582952C2211yescharacteristic
40#14582935—21no—
41C2×C4⋊(C43⋊C8)C2211yescharacteristic
42#14582893—21no—
43#14582851—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×#10621898D411yescharacteristic
68C2×#10621883—21no—
69C2×#10621882—21no—
70C2×#10621872—21no—
71C2×#10621872—21no—
72C22×C43⋊C8—21no—
73C4×Dic86D411yescharacteristic
74C4×Dic86C2311yescharacteristic
75C4×D172D411yescharacteristic
76C4×D172C2311yescharacteristic
77C4×C22⋊D43—21no—
78C4×C22⋊D43—21no—
79#13063284D411yescharacteristic
80#13063282—21no—
81C42×D43—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#13063236—21no—
110C4×C43⋊C8—21no—
111C8×Dic43—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—
157#10621898—22no—
158#10621898—41no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×Dic86C2×D411yescharacteristic
164SD16×C43—42no—
165SD16×C43—42no—
166M16×C43—22no—
167M16×C43—41no—
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C42×C43—41no—
184C42×C43C2×D411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43#4111yescharacteristic
187C42×C43C2411yescharacteristic
188C22⋊Dic43—21no—
189#10621883—42no—
190#10621882—42no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193C4⋊Dic43C2×D411yescharacteristic
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—42no—
207#10621872—42no—
208#10621872—42no—
209C23×C43—41no—
210C23×C43#12111yescharacteristic
211C22×D43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—81no—
215Q8×C43—81no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—81no—
221D4×C43—82no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—82no—
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C22⋊D43—42no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241D172—21no—
242D172—21no—
243C4×D43—42no—
244C4×D43—41no—
245C4×D43—41no—
246C4×D43—81no—
247Dic86—21no—
248Dic86#13712yes—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43#13512yes—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259#19183—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43C2×#12111yescharacteristic
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—41no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43C2×#13511yescharacteristic
278C4×C43C2×#13711yescharacteristic
279C4×C43#57511yescharacteristic
280C4×C43#57511yescharacteristic
281Dic43—22no—
282Dic43—41no—
283Dic43—41no—
284#3182D4311yescharacteristic, complemented
285#3106—431no—
286#3076—431no—
287#2971—431no—
288#1703—431no—
289#1697—431no—
290#1695—431no—
291#1685—431no—
292#1684—431no—
293#1678—431no—
294#1676—431no—
295#1666—431no—
296#1565—431no—
297#1554—431no—
298#1551—431no—
299C2×C43—41no—
300C2×C43—161no—
301C2×C43#303511yescharacteristic
302C2×C43#305611yescharacteristic
303C2×C43#306811yescharacteristic
304D43—81no—
305#533C2×D4311yescharacteristic
306#532C2×D4311yescharacteristic
307C4×#41—431no—
308#500C2×D4311yescharacteristic
309#492C2×D4311yescharacteristic
310#487C2×D4311yescharacteristic
311#486C2×D4311yescharacteristic
312#482—861no—
313#479—861no—
314#478—861no—
315#477—431no—
316#477—431no—
317#476—431no—
318#476—431no—
319#475—431no—
320#474—431no—
321#468—21no—
322#468—21no—
323#460—431no—
324#459—431no—
325#449—861no—
326C8×Q8—431no—
327C8×Q8—431no—
328#440—21no—
329#440—21no—
330C4×SD16—861no—
331C4×D8—861no—
332#436—431no—
333#436—431no—
334#436—861no—
335#436—861no—
336#432—431no—
337#432—861no—
338#431—431no—
339#427—861no—
340C2×C4⋊C8—431no—
341#416—861no—
342C4×M16—861no—
343C4×M16C2×D4311yescharacteristic
344#335—431no—
345#335—431no—
346#334—431no—
347#334—431no—
348#333—431no—
349#333—431no—
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#331—431no—
355#331—431no—
356C43#1918311yescharacteristic, complemented, Sylow
357C2×#41—21no—
358C2×#41—431no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—861no—
362C2×D8—861no—
363C2×M16—861no—
364C2×M16—861no—
365C2×M16C22⋊D4311yescharacteristic
366C2×M16C22⋊D4311yescharacteristic
367C22×C8—861no—
368C4⋊Q8C22×D4311yescharacteristic
369C4⋊Q8C22×D4311yescharacteristic
370C4⋊Q8C22×D4311yescharacteristic
371#127C22×D4311yescharacteristic
372#125—21no—
373#124—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—21no—
377#121—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—431no—
381C4×Q8—431no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—431no—
385C4×D4—431no—
386C4×D4—861no—
387C4×D4—861no—
388#117—21no—
389#117—431no—
390#117—861no—
391C2×C42—861no—
392C2×C42C22×D4311yescharacteristic
393#107—21no—
394#107—21no—
395#107—861no—
396#107—861no—
397#107—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410#103—21no—
411#103—21no—
412#103—861no—
413#103—861no—
414#103—861no—
415#102—21no—
416#102—21no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—861no—
427#97C22⋊D4311yescharacteristic
428#97C22⋊D4311yescharacteristic
429C4×C8—861no—
430C4×C8—861no—
431C4×C8—861no—
432C4×C8C22×D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434#41—82no—
435#41—862no—
436#41—1721no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—431no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4—431no—
446C2×D4—861no—
447C22×C4—41no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4D4×D4311yescharacteristic
452C22×C4#1062190011yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454SD16—42no—
455SD16—42no—
456SD16—1722no—
457D8—1722no—
458M16—22no—
459M16—41no—
460M16—1722no—
461M16—1722no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—1722no—
469C2×C8C2×C22⋊D4311yescharacteristic
470C2×C8C2×C22⋊D4311yescharacteristic
471C2×C8C2×C22⋊D4311yescharacteristic
472C2×C8C2×C22⋊D4311yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—431no—
482C4⋊C4—431no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C42—41no—
492C42—861no—
493C42—861no—
494C42—861no—
495C42D4×D4311yescharacteristic
496C42#1062190011yescharacteristic
497C42C2×C22⋊D4311yescharacteristic
498C42C23×D4311yescharacteristic
499C23—41no—
500C23—861no—
501C23#1306329611yescharacteristic
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—81no—
506Q8—432no—
507Q8—861no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—81no—
513D4—82no—
514D4—861no—
515D4—861no—
516D4—1722no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—3441no—
530C2×C4—1722no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4#1306329611yescharacteristic
534C2×C4#1306329611yescharacteristic
535C2×C4#1306329611yescharacteristic
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4C22×C22⋊D4311yescharacteristic
538C2×C4C2×#1062190011yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C8—1721no—
547C8—1721no—
548C8#1306334512yes—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—1721no—
556C22—1721no—
557C22—1721no—
558C22C2×#1306329611yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—862no—
567C4—1721no—
568C4—1721no—
569C4C2×#1306334511yescharacteristic
570C4#137×D4311yescharacteristic
571C4#1458369711yescharacteristic
572C4#1458369811yescharacteristic
573C2—41no—
574C2—161no—
575C2—3441no—
576C2#1914404411yescharacteristic
577C2#1914421911yescharacteristic
578C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3182C2
socleC22×C43C2×#121
prime radical#19144649C2
hypercenter#3182D43
hypocenterC43#19183
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. #19144377C2semidirect
3. #19143613C2semidirect
4. #19134167C2semidirect
5. #19134125C2semidirect
6. #19134115C2semidirect
7. #19134057C2semidirect
8. #19134050C2semidirect
9. #19134008C2semidirect
10. #19133996C2semidirect
11. #19133940C2semidirect
12. #19133347C2semidirect
13. #19133305C2semidirect
14. #19133290C2semidirect
15. C43×#3182C2semidirect
284. #3182D43semidirect
356. C43#19183semidirect

Maximal subgroups

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

subgroupindex
#191446492
#191443772
#191436132
#191341672
#191341252
#191341152
#191340572
#191340502
#191340082
#191339962
#191339402
#191333472
#191333052
#191332902
C43×#31822
#1918343