Finite Group Databasebeta

← #25079622

Subgroups — #25079622

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#19145309C211yesmaximal, characteristic, complemented
2#19144649C211yesmaximal, characteristic
3#19144385C211yesmaximal, characteristic, complemented
4#19143612C211yesmaximal, characteristic, complemented
5#19134173C211yesmaximal, characteristic, complemented
6#19134127C211yesmaximal, characteristic, complemented
7#19134117C211yesmaximal, characteristic, complemented
8#19134059C211yesmaximal, characteristic, complemented
9#19134056C211yesmaximal, characteristic, complemented
10#19134010C211yesmaximal, characteristic, complemented
11#19133998C211yesmaximal, characteristic, complemented
12#19133942C211yesmaximal, characteristic, complemented
13#19133345C211yesmaximal, characteristic, complemented
14#19133306C211yesmaximal, characteristic, complemented
15C43×#1551C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583271C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583220—21no—
23#14583207—21no—
24#14583200—21no—
25#14583195C2211yescharacteristic
26#14583191C2211yescharacteristic
27#14583190C2211yescharacteristic
28#14583186C2211yescharacteristic
29#14583185C2211yescharacteristic
30#14583180C2211yescharacteristic
31#14583143—21no—
32#14583143—21no—
33#14583096C2211yescharacteristic
34#14583091C2211yescharacteristic
35#14583042—21no—
36#14583023C2211yescharacteristic
37#14583023C2211yescharacteristic
38#14582999—21no—
39#14582999—21no—
40C4×#10621883—21no—
41C4×#10621882—21no—
42#14582976C2211yescharacteristic
43#14582976C2211yescharacteristic
44#14582974—21no—
45#14582974—21no—
46#14582954—21no—
47#14582952C2211yescharacteristic
48#14582937—21no—
49#14582896—21no—
50C4×#10621877C2211yescharacteristic
51#14582851—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582646C2211yescharacteristic
59#14582646C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621882—21no—
72C2×#10621877D411yescharacteristic
73C2×#10621877D411yescharacteristic
74C2×#10621872—21no—
75C2×#10621872—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063317—21no—
79#13063304—21no—
80#13063304—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86D411yescharacteristic
84C4×Dic86C2311yescharacteristic
85C4×D172D411yescharacteristic
86C4×D172C2311yescharacteristic
87C4×C22⋊D43—21no—
88C4×C22⋊D43—21no—
89#13063284—21no—
90#13063284D411yescharacteristic
91#13063282—21no—
92C42×D43—21no—
93#13063259—21no—
94#13063259—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063257—21no—
99#13063257—21no—
100#13063256—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250—21no—
106#13063250—21no—
107#13063248—21no—
108#13063248—21no—
109#13063248—21no—
110#13063247—21no—
111#13063247—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063245—21no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120#13063236D411yescharacteristic
121#13063236D411yescharacteristic
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C2×#41×C43—21no—
128C22×C8×C43—21no—
129C4⋊Q8×C43C2311yescharacteristic
130#127×C43C2311yescharacteristic
131#124×C43—21no—
132#121×C43—21no—
133#121×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C22⋊C8×C43—21no—
143#97×C43—21no—
144#41×C43—82no—
145C2×Q8×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—41no—
150C22×C4×C43—41no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C2×C22⋊D43—21no—
155#10621898—22no—
156#10621898—41no—
157C2×D172C2×D411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—42no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C22⋊C4×C43—41no—
172C22⋊C4×C43—41no—
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43#4111yescharacteristic
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178C22⋊Dic43—41no—
179#10621883—42no—
180#10621883—42no—
181#10621883—42no—
182#10621882—42no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C2×D411yescharacteristic
190C4⋊Dic43C2×D411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—41no—
199#10621877—22no—
200#10621877—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207#10621872—42no—
208#10621872—42no—
209C23×C43—41no—
210C23×C43#12111yescharacteristic
211C22×D43—21no—
212Q8×C43—81no—
213D4×C43—41no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—81no—
218D4×C43—82no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
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—42no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238D172—21no—
239D172—21no—
240C4×D43—42no—
241C4×D43—41no—
242C4×D43—41no—
243C4×D43—81no—
244Dic86—21no—
245Dic86—41no—
246Dic86—41no—
247Dic86—81no—
248Dic86#13712yes—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43—41no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8#13512yes—
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×C43C2×#13511yescharacteristic
276C4×C43C2×#13711yescharacteristic
277C4×C43#57511yescharacteristic
278C4×C43#57511yescharacteristic
279Dic43—22no—
280Dic43—41no—
281Dic43—41no—
282Dic43—81no—
283Dic43—81no—
284#3182—431no—
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#1551D4311yescharacteristic, complemented
299C2×C43—41no—
300C2×C43—161no—
301C2×C43#303511yescharacteristic
302C2×C43#305611yescharacteristic
303C2×C43#306811yescharacteristic
304D43—81no—
305#533—431no—
306#532C2×D4311yescharacteristic
307C4×#41—431no—
308#500—431no—
309#492—431no—
310#487—431no—
311#486—431no—
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—861no—
322#468—861no—
323#460—431no—
324#459—431no—
325#449—861no—
326C8×Q8—431no—
327C8×Q8—431no—
328#440—861no—
329#440—861no—
330C4×SD16—861no—
331C4×D8—861no—
332#436—431no—
333#436—431no—
334#436—861no—
335#436—861no—
336#432—861no—
337#432C2×D4311yescharacteristic
338#431—431no—
339#427—861no—
340C2×C4⋊C8C2×D4311yescharacteristic
341#416—861no—
342C4×M16—431no—
343C4×M16—861no—
344#335—431no—
345#335—431no—
346#334—431no—
347#334—431no—
348#333—431no—
349#333—431no—
350#333C2×D4311yescharacteristic
351#333C2×D4311yescharacteristic
352#332—431no—
353#332—431no—
354#331C2×D4311yescharacteristic
355#331C2×D4311yescharacteristic
356C43#1918311yescharacteristic, complemented, Sylow
357C2×#41—21no—
358C2×#41—431no—
359C2×SD16—861no—
360C2×SD16—861no—
361C2×SD16—861no—
362C2×D8—861no—
363C2×M16—431no—
364C2×M16—431no—
365C2×M16—861no—
366C2×M16—861no—
367C22×C8—21no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8C22×D4311yescharacteristic
371#127C22×D4311yescharacteristic
372#125—861no—
373#124—21no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—21no—
377#121—21no—
378C4×Q8—431no—
379C4×Q8—431no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—431no—
385C4×D4—431no—
386C4×D4—861no—
387C4×D4—861no—
388#117—431no—
389#117—861no—
390#117—861no—
391C2×C42—861no—
392C2×C42C22×D4311yescharacteristic
393#107—861no—
394#107—861no—
395#107—861no—
396#107—861no—
397#107—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401C4⋊C8—21no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406C4⋊C8C22×D4311yescharacteristic
407C4⋊C8C22×D4311yescharacteristic
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422C22⋊C8—21no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—21no—
427#97—431no—
428#97—431no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—861no—
432C4×C8—861no—
433C4×C8—861no—
434#41—82no—
435#41—862no—
436#41—1721no—
437C2×Q8—21no—
438C2×Q8—431no—
439C2×Q8—861no—
440C2×Q8—861no—
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×C4#1062189811yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4D4×D4311yescharacteristic
454SD16—1722no—
455SD16—1722no—
456SD16—1722no—
457D8—1722no—
458M16—862no—
459M16—1722no—
460M16—1722no—
461M16—1721no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—42no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—861no—
472C2×C8—861no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—431no—
476C4⋊C4—431no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—1721no—
484C4⋊C4—1721no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—1721no—
491C42—861no—
492C42—861no—
493C42—861no—
494C42—1721no—
495C42#1062189811yescharacteristic
496C42D4×D4311yescharacteristic
497C42D4×D4311yescharacteristic
498C42C23×D4311yescharacteristic
499C23—41no—
500C23—861no—
501C23#1306329811yescharacteristic
502Q8—81no—
503Q8—432no—
504Q8—861no—
505Q8—3441no—
506Q8—1721no—
507Q8—1721no—
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—82no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—3441no—
528C2×C4—1722no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4#1306329811yescharacteristic
534C2×C4#1306329811yescharacteristic
535C2×C4#1306329811yescharacteristic
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4C2×D4×D4311yescharacteristic
538C2×C4C2×#1062189811yescharacteristic
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—432no—
544C8—861no—
545C8—861no—
546C8—861no—
547C8—1721no—
548C8—1721no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—1721no—
556C22—1721no—
557C22—1721no—
558C22C2×#1306329811yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—81no—
564C4—862no—
565C4—3441no—
566C4—3441no—
567C4—1721no—
568C4—1721no—
569C4#135×D4311yescharacteristic
570C4#137×D4311yescharacteristic
571C4#1458369511yescharacteristic
572C4#1458369611yescharacteristic
573C2—41no—
574C2—161no—
575C2—3441no—
576C2#1914404811yescharacteristic
577C2#1914422811yescharacteristic
578C2#1914432211yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1551C2
socleC22×C43C2×#121
prime radical#19144649C2
hypercenter#1551D43
hypocenterC43#19183
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1551

Complements

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

NH ≅ G/Ntype
1. #19145309C2semidirect
3. #19144385C2semidirect
4. #19143612C2semidirect
5. #19134173C2semidirect
6. #19134127C2semidirect
7. #19134117C2semidirect
8. #19134059C2semidirect
9. #19134056C2semidirect
10. #19134010C2semidirect
11. #19133998C2semidirect
12. #19133942C2semidirect
13. #19133345C2semidirect
14. #19133306C2semidirect
15. C43×#1551C2semidirect
298. #1551D43semidirect
356. C43#19183semidirect

Maximal subgroups

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

subgroupindex
#191453092
#191446492
#191443852
#191436122
#191341732
#191341272
#191341172
#191340592
#191340562
#191340102
#191339982
#191339422
#191333452
#191333062
C43×#15512
#1918343