Finite Group Databasebeta

← #25081761

Subgroups — #25081761

Order 11008.

708 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145516C211yesmaximal, characteristic, complemented
2#474×D43C211yesmaximal, characteristic, complemented
3#19144054C211yesmaximal, characteristic
4#19143616C211yesmaximal, characteristic, complemented
5#19134019C211yesmaximal, characteristic, complemented
6#19134018C211yesmaximal, characteristic, complemented
7#19134017C211yesmaximal, characteristic, complemented
8#19134016C211yesmaximal, characteristic, complemented
9#19133935C211yesmaximal, characteristic, complemented
10#19133934C211yesmaximal, characteristic, complemented
11#19133933C211yesmaximal, characteristic, complemented
12#19133364C211yesmaximal, characteristic, complemented
13#19133278C211yesmaximal, characteristic, complemented
14#19133241C211yesmaximal, characteristic, complemented
15C43×#1665C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17#14583447C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583271C2211yescharacteristic, complemented
21#14583250C2211yescharacteristic, complemented
22#14583249C2211yescharacteristic, complemented
23#14583180C2211yescharacteristic
24#14583179C2211yescharacteristic
25#14583178—21no—
26#14583177—21no—
27#14583176C2211yescharacteristic
28#14583113—21no—
29#14583112—21no—
30#14583105C2211yescharacteristic
31#14583104C2211yescharacteristic
32#14583102—21no—
33#14583102—21no—
34#14583091C2211yescharacteristic
35#14583036—21no—
36#14583036—21no—
37C8×D172C2211yescharacteristic
38D4×C43⋊C8C2211yescharacteristic
39#14582964C2211yescharacteristic
40C8×C22⋊D43—21no—
41(C22⋊D43)⋊C8—21no—
42#14582951C2211yescharacteristic
43#14582950C2211yescharacteristic
44#107×D43—21no—
45#14582921C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582897—21no—
48#102×D43—21no—
49C2×(C2×D43)⋊C8—21no—
50C22⋊C8×D43—21no—
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582646C2211yescharacteristic, complemented
56#14582645C2211yescharacteristic, complemented
57#14582644C2211yescharacteristic, complemented
58#14582644C2211yescharacteristic, complemented
59#14582643C2211yescharacteristic, complemented
60C43×#492C2211yescharacteristic, complemented
61C43×#474C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C2×Q8×D43—21no—
69C2×D4×D43D411yescharacteristic
70C22×C4×D43—21no—
71#13063349—44no—
72C2×#10621873—21no—
73C2×#10621883—21no—
74C2×#10621883—21no—
75C2×#10621883—21no—
76C2×#10621882—21no—
77C2×#10621872—21no—
78C22×C43⋊C8—21no—
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82#13063325C2311yescharacteristic
83#13063325C2311yescharacteristic
84#13063324—21no—
85#13063324—21no—
86#13063323—21no—
87#13063312—21no—
88#13063296—21no—
89#13063296—21no—
90C4×D172C2311yescharacteristic
91D4×Dic43—21no—
92D4×Dic43—21no—
93D4×Dic43D411yescharacteristic
94#13063287D411yescharacteristic
95C4×C22⋊D43—21no—
96(C22⋊D43)⋊C4—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43D411yescharacteristic
100C22⋊C4×D43—21no—
101C42×D43C2311yescharacteristic
102#13063259—21no—
103#13063258—21no—
104#13063258—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8D411yescharacteristic
111Dic43⋊C8D411yescharacteristic
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063249—21no—
116#13063249—21no—
117#13063248—21no—
118#13063247—21no—
119#13063246—21no—
120#13063246—21no—
121#13063245—21no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8D411yescharacteristic
127(C2×D43)⋊C8D411yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43—21no—
130C2×SD16×C43—21no—
131C2×SD16×C43—21no—
132C2×D8×C43—21no—
133C22×C8×C43—21no—
134C4⋊Q8×C43C2311yescharacteristic
135#127×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137#107×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#102×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—41no—
154C22×Dic43—21no—
155C22×Dic43—41no—
156Q8×D43—81no—
157Q8×D43—81no—
158#10621900—42no—
159#10621900—42no—
160D4×D43—22no—
161D4×D43SD1614yescomplemented
162C2×D172C2×D411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—41no—
167C2×C4×D43—81no—
168C2×C4×D43—81no—
169C2×C4×D43C2×D411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×C4×D43#4111yescharacteristic
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—41no—
175SD16×C43—81no—
176SD16×C43—81no—
177D8×C43—42no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—81no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C42×C43C2411yescharacteristic
189C22⋊Dic43—21no—
190C22⋊Dic43—41no—
191C22⋊Dic43—41no—
192#10621883—42no—
193#10621883—81no—
194#10621883—81no—
195#10621882—42no—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43C2×D411yescharacteristic
203Dic43⋊C4—21no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206C4×Dic43C2×D411yescharacteristic
207C4×Dic43C2×D411yescharacteristic
208C4×Dic43#4111yescharacteristic
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—81no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215#10621873—42no—
216#10621872—42no—
217C8×D43—42no—
218C8×D43—81no—
219C8×D43—81no—
220C23×C43—21no—
221C23×C43—41no—
222C22×D43—21no—
223C22×D43—24no—
224C22×D43—81no—
225C22×D43—81no—
226C22×D43#12111yescharacteristic
227Q8×C43—41no—
228Q8×C43—41no—
229D4×C43—21no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—81no—
235D4×C43C2×SD1612yes—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C22⋊D43—24no—
244C22⋊D43—82no—
245C2×Dic43—21no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—81no—
249C2×Dic43—82no—
250C2×Dic43#12111yescharacteristic
251C2×Dic43#12111yescharacteristic
252C2×Dic43#12111yescharacteristic
253D172—21no—
254D172C2×SD1612yes—
255C4×D43—21no—
256C4×D43—21no—
257C4×D43—41no—
258C4×D43—41no—
259C4×D43—41no—
260C4×D43—81no—
261C4×D43—81no—
262C4×D43—82no—
263C4×D43C2×SD1612yes—
264C4×D43#13512yes—
265Dic86—41no—
266Dic86—41no—
267Dic86—41no—
268Dic86—41no—
269Dic86—82no—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275C43⋊C8—21no—
276C43⋊C8—21no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280#19385—431nomaximal, Sylow
281C22×C43—22no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43C2×#12111yescharacteristic
288C2×D43—21no—
289C2×D43—21no—
290C2×D43—22no—
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—84no—
294C2×D43#46512yes—
295C4×C43—21no—
296C4×C43—41no—
297C4×C43—81no—
298C4×C43C22×SD1611yescharacteristic
299C4×C43C2×#13511yescharacteristic
300C4×C43#57611yescharacteristic
301C4×C43#57611yescharacteristic
302Dic43—21no—
303Dic43—21no—
304Dic43—41no—
305Dic43—81no—
306Dic43—81no—
307Dic43#46512yes—
308#3206—431no—
309C2×#474—431no—
310#3036—431no—
311#2972—431no—
312#1679—431no—
313#1679—431no—
314#1679—431no—
315#1679—431no—
316#1665—431no—
317#1665—431no—
318#1665—431no—
319#1665D4311yescharacteristic, complemented
320#1570—431no—
321#1549—431no—
322#1540—431no—
323C2×C43—42no—
324C2×C43—161no—
325C2×C43#304111yescharacteristic
326C2×C43C2×#46511yescharacteristic
327C2×C43#306911yescharacteristic
328D43—22no—
329D43—42no—
330C2×AGL(1,ℤ/8)—861no—
331#532—431no—
332C2×C4⋊Q8—431no—
333C2×C4×D4—431no—
334#492—431no—
335#492C2×D4311yescharacteristic, complemented
336#487—431no—
337#487—431no—
338#474—431no—
339#474—431no—
340#474—431no—
341#474—861no—
342#474—861no—
343#474C2×D4311yescharacteristic
344#463—861no—
345#463—861no—
346#461—431no—
347#461—431no—
348#461—861no—
349#461—861no—
350#459—431no—
351#459C2×D4311yescharacteristic
352#448—861no—
353#448—861no—
354C8×D4—431no—
355C8×D4—431no—
356C8×D4—431no—
357C8×D4—861no—
358C8×D4—861no—
359C8×D4C2×D4311yescharacteristic
360#431—431no—
361#431—431no—
362C2×#107—861no—
363#423—431no—
364C2×C4⋊C8—431no—
365#417—861no—
366C2×#102—861no—
367C2×C22⋊C8—861no—
368C2×C22⋊C8—861no—
369#334—431no—
370#334—431no—
371#334—431no—
372#334C2×D4311yescharacteristic, complemented
373#332—431no—
374#332—431no—
375#332—431no—
376#332—431no—
377#332—431no—
378#332C2×D4311yescharacteristic, complemented
379#331—431no—
380#331C2×D4311yescharacteristic, complemented
381C43#1938511yescharacteristic, complemented, Sylow
382C2×#41—861no—
383C22×Q8—861no—
384C22×D4—431no—
385C23×C4—861no—
386AGL(1,ℤ/8)—1724no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—861no—
390C2×SD16—861no—
391C2×SD16—861no—
392C2×SD16—861no—
393C2×D8—21no—
394C2×D8—861no—
395C2×M16—861no—
396C22×C8—21no—
397C22×C8—861no—
398C22×C8—861no—
399C22×C8—861no—
400C22×C8—861no—
401C4⋊Q8—431no—
402C4⋊Q8—431no—
403C4⋊Q8—861no—
404C4⋊Q8—861no—
405C4⋊Q8—861no—
406C4⋊Q8C22×D4311yescharacteristic
407#127C22×D4311yescharacteristic
408#124—861no—
409#121—861no—
410#121—861no—
411C4×D4—431no—
412C4×D4—431no—
413C4×D4—431no—
414C4×D4—861no—
415C4×D4—861no—
416C4×D4—861no—
417C4×D4—861no—
418C4×D4C22×D4311yescharacteristic
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C42—431no—
424#107—21no—
425#107—861no—
426#107—861no—
427#107—861no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—431no—
433C4⋊C8—861no—
434C4⋊C8—861no—
435C4⋊C8C22×D4311yescharacteristic
436C4⋊C8C22×D4311yescharacteristic
437C4⋊C8C22×D4311yescharacteristic
438#103—861no—
439#103—861no—
440#103—861no—
441#103—861no—
442#103—861no—
443#103—861no—
444#102—21no—
445#102—21no—
446#102—861no—
447#102—861no—
448#102—861no—
449#102—861no—
450C22⋊C8—21no—
451C22⋊C8—431no—
452C22⋊C8—431no—
453C22⋊C8—861no—
454C22⋊C8—861no—
455C22⋊C8—861no—
456C22⋊C8—861no—
457C4×C8—431no—
458C4×C8—861no—
459C4×C8C22×D4311yescharacteristic
460C24—861no—
461#41—1722no—
462#41—1722no—
463C2×Q8—21no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—3441no—
467C2×Q8—3441no—
468C2×Q8—1721no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—434no—
473C2×D4—431no—
474C2×D4—862no—
475C2×D4—861no—
476C2×D4—1721no—
477C2×D4D4×D4311yescharacteristic
478C22×C4—21no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—3441no—
487C22×C4—3441no—
488C22×C4—1721no—
489C22×C4—1721no—
490SD16—81no—
491SD16—81no—
492SD16—3441no—
493SD16—3441no—
494SD16—1722no—
495SD16—1722no—
496D8—42no—
497D8—1722no—
498M16—1722no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—81no—
503C2×C8—431no—
504C2×C8—431no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—3441no—
509C2×C8—3441no—
510C2×C8—3441no—
511C2×C8—1722no—
512C2×C8D4×D4311yescharacteristic
513C2×C8D4×D4311yescharacteristic
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—431no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4D4×D4311yescharacteristic
525C22⋊C4—21no—
526C22⋊C4—861no—
527C22⋊C4—861no—
528C22⋊C4—861no—
529C22⋊C4—1721no—
530C22⋊C4—1721no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42C23×D4311yescharacteristic
535C23—21no—
536C23—41no—
537C23—431no—
538C23—864no—
539C23—861no—
540C23—3441no—
541C23—3441no—
542Q8—41no—
543Q8—41no—
544Q8—3442no—
545Q8—1721no—
546Q8—1721no—
547Q8—1721no—
548Q8—1721no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—432no—
556D4—864no—
557D4—861no—
558D4—3442no—
559D4SD16×D4312yes—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—431no—
565C2×C4—432no—
566C2×C4—432no—
567C2×C4—431no—
568C2×C4—431no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—3441no—
573C2×C4—3441no—
574C2×C4—3442no—
575C2×C4—3442no—
576C2×C4—3441no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4C2×D4×D4311yescharacteristic
583C2×C4C2×D4×D4311yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C8—21no—
586C8—21no—
587C8—41no—
588C8—41no—
589C8—41no—
590C8—861no—
591C8—861no—
592C8—1721no—
593C8—1721no—
594C8—1721no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—432no—
602C22—861no—
603C22—861no—
604C22—862no—
605C22—3444no—
606C22—1721no—
607C22—1721no—
608C22#121×D4311yescharacteristic
609C4—21no—
610C4—41no—
611C4—81no—
612C4—432no—
613C4—861no—
614C4—861no—
615C4—3441no—
616C4—3441no—
617C4—1721no—
618C4C2×SD16×D4311yescharacteristic
619C4#135×D4311yescharacteristic
620C4#1458370011yescharacteristic
621C4#1458370311yescharacteristic
622C2—42no—
623C2—161no—
624C2—862no—
625C2—1722no—
626C2#1914409311yescharacteristic
627C2#465×D4311yescharacteristic
628C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1665C2
socleC22×C43C2×#121
prime radical#19144054C2
hypercenter#1665D43
hypocenterC43#19385
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1665

Complements

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

NH ≅ G/Ntype
1. #19145516C2semidirect
2. #474×D43C2semidirect
4. #19143616C2semidirect
5. #19134019C2semidirect
6. #19134018C2semidirect
7. #19134017C2semidirect
8. #19134016C2semidirect
9. #19133935C2semidirect
10. #19133934C2semidirect
11. #19133933C2semidirect
12. #19133364C2semidirect
13. #19133278C2semidirect
14. #19133241C2semidirect
15. C43×#1665C2semidirect
20. #14583271C22semidirect
21. #14583250C22semidirect
22. #14583249C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582646C22semidirect
55. #14582646C22semidirect
56. #14582645C22semidirect
57. #14582644C22semidirect
58. #14582644C22semidirect
59. #14582643C22semidirect
60. C43×#492C22semidirect
64. C43×#334C22semidirect
65. C43×#332C22semidirect
66. C43×#331C22semidirect
161. D4×D43SD16semidirect
319. #1665D43semidirect
335. #492C2×D43semidirect
372. #334C2×D43semidirect
378. #332C2×D43semidirect
380. #331C2×D43semidirect
381. C43#19385semidirect

Maximal subgroups

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

subgroupindex
#191455162
#474×D432
#191440542
#191436162
#191340192
#191340182
#191340172
#191340162
#191339352
#191339342
#191339332
#191333642
#191332782
#191332412
C43×#16652
#1938543