Finite Group Databasebeta

← #25079054

Subgroups — #25079054

Order 11008.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145150C211yesmaximal, characteristic, complemented
2#19144667C211yesmaximal, characteristic, complemented
3#19144649C211yesmaximal, characteristic
4#19143551C211yesmaximal, characteristic, complemented
5#19134056C211yesmaximal, characteristic, complemented
6#19134049C211yesmaximal, characteristic, complemented
7#19134038C211yesmaximal, characteristic, complemented
8#19134031C211yesmaximal, characteristic, complemented
9#19133980C211yesmaximal, characteristic, complemented
10#19133973C211yesmaximal, characteristic, complemented
11#19133942C211yesmaximal, characteristic, complemented
12#19133935C211yesmaximal, characteristic, complemented
13#19133341C211yesmaximal, characteristic, complemented
14#19133259C211yesmaximal, characteristic, complemented
15C43×#1543C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583271C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583241—21no—
23#14583220—21no—
24#14583191C2211yescharacteristic
25#14583186C2211yescharacteristic
26#14583185C2211yescharacteristic
27#14583180C2211yescharacteristic
28#14583126—21no—
29#14583126—21no—
30#14583110C2211yescharacteristic
31#14583105C2211yescharacteristic
32#14583096C2211yescharacteristic
33#14583091C2211yescharacteristic
34#14583063—21no—
35#14583042—21no—
36#14583023C2211yescharacteristic
37#14583023C2211yescharacteristic
38C4×Dic172—21no—
39C4×#10621873—21no—
40C4×#10621883—21no—
41C4×#10621883—21no—
42C4×#10621883—21no—
43C4×#10621882—21no—
44#14582964C2211yescharacteristic
45#14582964C2211yescharacteristic
46(C22⋊D43)⋊C8—21no—
47(C22⋊D43)⋊C8—21no—
48#14582952C2211yescharacteristic
49#14582950—21no—
50C2×C4×C43⋊C8C2211yescharacteristic
51C4×C8×D43—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×Dic172—21no—
69C2×#10621873—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621882—21no—
74C22×C43⋊C8D411yescharacteristic
75C22×C43⋊C8D411yescharacteristic
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063317—21no—
81#13063304—21no—
82#13063304—21no—
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×Dic86D411yescharacteristic
86C4×Dic86C2311yescharacteristic
87C4×D172D411yescharacteristic
88C4×D172C2311yescharacteristic
89C4×C22⋊D43—21no—
90C4×C22⋊D43—21no—
91#13063284—21no—
92#13063284D411yescharacteristic
93#13063282—21no—
94C42×D43—21no—
95#13063259—21no—
96#13063258—21no—
97#13063257—21no—
98#13063256—21no—
99#13063256—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#13063250—21no—
108#13063248—21no—
109#13063248—21no—
110#13063248—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—
120C4×C43⋊C8—21no—
121C4×C43⋊C8D411yescharacteristic
122C4×C43⋊C8D411yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C2×#41×C43—21no—
128C4⋊Q8×C43C2311yescharacteristic
129#127×C43C2311yescharacteristic
130#124×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133C4×D4×C43—21no—
134C4×D4×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142C4×C8×C43—21no—
143C4×C8×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—22no—
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—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C22⋊C4×C43—41no—
171C22⋊C4×C43—41no—
172C42×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43#4111yescharacteristic
175C42×C43C2411yescharacteristic
176C22⋊Dic43—21no—
177C22⋊Dic43—41no—
178#10621883—42no—
179#10621883—42no—
180#10621883—42no—
181#10621882—42no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43C2×D411yescharacteristic
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—41no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—41no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206Dic172—42no—
207#10621873—42no—
208C8×D43—42no—
209C8×D43—42no—
210C23×C43—41no—
211C23×C43#12111yescharacteristic
212C22×D43—21no—
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—22no—
225C2×C4×C43—41no—
226C2×C4×C43—82no—
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—24no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239D172—21no—
240D172#13512yes—
241C4×D43—24no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—42no—
245Dic86—21no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86#13512yes—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C43⋊C8—21no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8#13512yes—
261#19127—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43C2×#12111yescharacteristic
269C2×D43—22no—
270C2×D43—41no—
271C2×D43—41no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—81no—
276C4×C43#47112yes—
277C4×C43C2×#13511yescharacteristic
278C4×C43C2×#13511yescharacteristic
279C4×C43C2×#13511yescharacteristic
280C4×C43#57511yescharacteristic
281Dic43—22no—
282Dic43—41no—
283Dic43—41no—
284Dic43—81no—
285Dic43—81no—
286#3167—431no—
287#3107—431no—
288#3106—431no—
289C8×#41—431no—
290#1684—431no—
291#1683—431no—
292#1682—431no—
293#1681—431no—
294#1672—431no—
295#1671—431no—
296#1666—431no—
297#1665—431no—
298#1564—431no—
299#1544—431no—
300#1543D4311yescharacteristic, complemented
301C2×C43—41no—
302C2×C43—161no—
303C2×C43#303511yescharacteristic
304C2×C43#305011yescharacteristic
305C2×C43C2×#47111yescharacteristic
306D43—42no—
307#533—431no—
308#532C2×D4311yescharacteristic
309C4×#41—431no—
310#498—431no—
311#492—431no—
312#487—431no—
313#486—431no—
314#485—861no—
315#482—861no—
316#477—431no—
317#476—431no—
318#475—431no—
319#474—431no—
320#465—861no—
321#465—861no—
322#462—431no—
323#461—431no—
324#460—431no—
325#459—431no—
326#452—861no—
327#449—861no—
328C8×Q8—431no—
329C8×Q8—431no—
330C4×Q16—861no—
331C4×SD16—861no—
332C4×SD16—861no—
333C4×SD16—861no—
334C4×SD16—861no—
335C4×D8—861no—
336C8×D4—431no—
337C8×D4—431no—
338C8×D4—861no—
339C8×D4—861no—
340#431—431no—
341#431—861no—
342#431C2×D4311yescharacteristic
343#431C2×D4311yescharacteristic
344C2×C4×C8—431no—
345C2×C4×C8—861no—
346#335—431no—
347#335—431no—
348#334—431no—
349#334—431no—
350#333C2×D4311yescharacteristic
351#333C2×D4311yescharacteristic
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#331C2×D4311yescharacteristic
357#331C2×D4311yescharacteristic
358C43#1912711yescharacteristic, complemented, Sylow
359C2×#41—21no—
360C2×#41—431no—
361C2×Q16—861no—
362C2×SD16—861no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×D8—861no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8C22×D4311yescharacteristic
374#127C22×D4311yescharacteristic
375#125—861no—
376#124—21no—
377C22⋊Q8—861no—
378C22⋊Q8—861no—
379#121—21no—
380#121—21no—
381C4×Q8—431no—
382C4×Q8—431no—
383C4×Q8—861no—
384C4×Q8—861no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—431no—
388C4×D4—431no—
389C4×D4—861no—
390C4×D4—861no—
391#117—431no—
392#117—861no—
393#117—861no—
394C2×C42—861no—
395C2×C42C22×D4311yescharacteristic
396#107—861no—
397#107—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
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#103—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427C4×C8—21no—
428C4×C8—21no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—861no—
434C4×C8—861no—
435C4×C8—861no—
436#41—82no—
437#41—862no—
438#41—862no—
439C2×Q8—21no—
440C2×Q8—431no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—431no—
448C2×D4—861no—
449C22×C4—41no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4#1062189811yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456Q16—1722no—
457SD16—1722no—
458SD16—1722no—
459SD16—1722no—
460SD16—1722no—
461D8—1722no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—431no—
470C2×C8—862no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—1722no—
474C2×C8—1722no—
475C2×C8—1721no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—431no—
479C4⋊C4—431no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—1721no—
487C4⋊C4—1721no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—861no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C22⋊C4—1721no—
494C42—861no—
495C42—861no—
496C42—861no—
497C42—1721no—
498C42#1062189811yescharacteristic
499C42D4×D4311yescharacteristic
500C42D4×D4311yescharacteristic
501C42C23×D4311yescharacteristic
502C23—41no—
503C23—861no—
504C23#1306329811yescharacteristic
505Q8—81no—
506Q8—432no—
507Q8—861no—
508Q8—1721no—
509Q8—1721no—
510Q8—1721no—
511Q8—1721no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—81no—
517D4—82no—
518D4—432no—
519D4—864no—
520D4—861no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—864no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1722no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4#1306329811yescharacteristic
538C2×C4#1306329811yescharacteristic
539C2×C4#1306329811yescharacteristic
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C2×D4×D4311yescharacteristic
542C2×C4C2×#1062189811yescharacteristic
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—432no—
548C8—861no—
549C8—861no—
550C8—861no—
551C8—1721no—
552C8—1721no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—862no—
560C22—1721no—
561C22—1721no—
562C22C2×#1306329811yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—81no—
567C4—862no—
568C4—3441no—
569C4—3441no—
570C4—1721no—
571C4—1721no—
572C4#1458316112yes—
573C4#135×D4311yescharacteristic
574C4#135×D4311yescharacteristic
575C4#135×D4311yescharacteristic
576C4#1458369611yescharacteristic
577C2—41no—
578C2—161no—
579C2—1722no—
580C2#1914404811yescharacteristic
581C2#1914417511yescharacteristic
582C2C2×#1458316111yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1543C2
socleC22×C43C2×#121
prime radical#19144649C2
hypercenter#1543D43
hypocenterC43#19127
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1543

Complements

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

NH ≅ G/Ntype
1. #19145150C2semidirect
2. #19144667C2semidirect
4. #19143551C2semidirect
5. #19134056C2semidirect
6. #19134049C2semidirect
7. #19134038C2semidirect
8. #19134031C2semidirect
9. #19133980C2semidirect
10. #19133973C2semidirect
11. #19133942C2semidirect
12. #19133935C2semidirect
13. #19133341C2semidirect
14. #19133259C2semidirect
15. C43×#1543C2semidirect
300. #1543D43semidirect
358. C43#19127semidirect

Maximal subgroups

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

subgroupindex
#191451502
#191446672
#191446492
#191435512
#191340562
#191340492
#191340382
#191340312
#191339802
#191339732
#191339422
#191339352
#191333412
#191332592
C43×#15432
#1912743