Finite Group Databasebeta

← #25081828

Subgroups — #25081828

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145717C211yesmaximal, characteristic, complemented
2#19144060C211yesmaximal, characteristic
3#461×D43C211yesmaximal, characteristic, complemented
4#19143616C211yesmaximal, characteristic, complemented
5#19134035C211yesmaximal, characteristic, complemented
6#19134034C211yesmaximal, characteristic, complemented
7#19134033C211yesmaximal, characteristic, complemented
8#19134032C211yesmaximal, characteristic, complemented
9#19133983C211yesmaximal, characteristic, complemented
10#19133982C211yesmaximal, characteristic, complemented
11#19133981C211yesmaximal, characteristic, complemented
12#19133368C211yesmaximal, characteristic, complemented
13#19133265C211yesmaximal, characteristic, complemented
14#19133243C211yesmaximal, characteristic, complemented
15C43×#1673C211yesmaximal, characteristic, complemented
16C2×#13063352—21no—
17C2×SD16×D43—21no—
18#14583450C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20C4×D4×D43C2211yescharacteristic
21#14583302C2211yescharacteristic, complemented
22#14583247C2211yescharacteristic, complemented
23#14583246C2211yescharacteristic, complemented
24#14583214—21no—
25#14583214—21no—
26#14583178—21no—
27#14583178—21no—
28#14583117—21no—
29#14583116—21no—
30#14583105C2211yescharacteristic
31#14583104C2211yescharacteristic
32#14583103—21no—
33#14583102—21no—
34#14583101C2211yescharacteristic
35#14583101C2211yescharacteristic
36#14583095C2211yescharacteristic
37#14583094C2211yescharacteristic
38C8×D172C2211yescharacteristic
39D4×C43⋊C8C2211yescharacteristic
40#14582964C2211yescharacteristic
41C8×C22⋊D43—21no—
42(C22⋊D43)⋊C8—21no—
43#14582951C2211yescharacteristic
44#14582950C2211yescharacteristic
45#14582921C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582899—21no—
48#103×D43—21no—
49C2×(C2×D43)⋊C8—21no—
50C22⋊C8×D43—21no—
51#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582645C2211yescharacteristic, complemented
56#14582645C2211yescharacteristic, complemented
57#14582644C2211yescharacteristic, complemented
58#14582642C2211yescharacteristic, complemented
59#14582642C2211yescharacteristic, complemented
60C43×#500C2211yescharacteristic, complemented
61C43×#461C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#332C2211yescharacteristic, complemented
67C2×#10621902—21no—
68C2×Q8×D43—21no—
69C2×D4×D43D411yescharacteristic
70C22×C4×D43—21no—
71#13063352—44no—
72C2×#10621873—21no—
73C2×#10621883—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76SD16×D43—44no—
77C2×D344—21no—
78C2×#10621882—21no—
79C2×#10621872—21no—
80C22×C43⋊C8—21no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83C2×C8×D43—21no—
84#13063325C2311yescharacteristic
85#13063324—21no—
86#13063324—21no—
87#13063323—21no—
88#13063322C2311yescharacteristic
89#13063314—21no—
90#13063300—21no—
91#13063300—21no—
92C4×D172C2311yescharacteristic
93D4×Dic43D411yescharacteristic
94#13063287—21no—
95#13063287—21no—
96#13063287D411yescharacteristic
97C4×C22⋊D43—21no—
98(C22⋊D43)⋊C4—21no—
99C4⋊C4×D43—21no—
100C4⋊C4×D43—21no—
101C4⋊C4×D43D411yescharacteristic
102C22⋊C4×D43—21no—
103C42×D43C2311yescharacteristic
104#13063258—21no—
105#13063258—21no—
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8D411yescharacteristic
112Dic43⋊C8D411yescharacteristic
113#13063250—21no—
114#13063249—21no—
115#13063249—21no—
116#13063248—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063245—21no—
121#13063245—21no—
122#13063245—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8D411yescharacteristic
128(C2×D43)⋊C8D411yescharacteristic
129C4×C43⋊C8C2311yescharacteristic
130C8×Dic43—21no—
131C2×SD16×C43—21no—
132C2×SD16×C43—21no—
133C22×C8×C43—21no—
134C4⋊Q8×C43C2311yescharacteristic
135C4⋊Q8×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137#107×C43—21no—
138#107×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142#103×C43—21no—
143#103×C43—21no—
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C2×C22⋊D43—21no—
152C22×Dic43—21no—
153#10621902—42no—
154#10621902—42no—
155Q8×D43—42no—
156Q8×D43—42no—
157D4×D43—22no—
158D4×D43D814yes—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—41no—
163C2×D172C2×D411yescharacteristic
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—41no—
168C2×C4×D43—41no—
169C2×C4×D43—81no—
170C2×C4×D43—81no—
171C2×C4×D43C2×D411yescharacteristic
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43#4111yescharacteristic
174C2×Dic86—21no—
175C2×Dic86—41no—
176SD16×C43—42no—
177SD16×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×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43C2×D411yescharacteristic
189C22⋊C4×C43—21no—
190C42×C43C2411yescharacteristic
191C22⋊Dic43—21no—
192#10621884—42no—
193#10621884—42no—
194#10621883—42no—
195#10621882—42no—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—41no—
199(C2×D43)⋊C4—41no—
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
215D344—42no—
216#10621873—42no—
217#10621872—42no—
218C8×D43—42no—
219C8×D43—81no—
220C8×D43—81no—
221C23×C43—21no—
222C22×D43—21no—
223C22×D43—24no—
224C22×D43—41no—
225C22×D43—81no—
226C22×D43—81no—
227C22×D43#12111yescharacteristic
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231Q8×C43—41no—
232D4×C43—21no—
233D4×C43C2×D812yes—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—24no—
243C2×Dic43—21no—
244C2×Dic43—41no—
245C2×Dic43—81no—
246C2×Dic43#12111yescharacteristic
247C2×Dic43#12111yescharacteristic
248C2×Dic43#12111yescharacteristic
249D172—21no—
250D172—41no—
251D172—41no—
252D172—41no—
253D172—41no—
254D172—81no—
255D172—82no—
256D172C2×D812yes—
257C4×D43—21no—
258C4×D43—21no—
259C4×D43—41no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—81no—
263C4×D43—81no—
264C4×D43—82no—
265C4×D43—82no—
266C4×D43C2×D812yes—
267C4×D43#13512yes—
268Dic86—41no—
269Dic86—41no—
270Dic86—82no—
271C8×C43—21no—
272C8×C43—21no—
273C8×C43—41no—
274C8×C43—41no—
275C8×C43—41no—
276C43⋊C8—21no—
277C43⋊C8—21no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281#19392—431nomaximal, Sylow
282C22×C43—22no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43C2×#12111yescharacteristic
286C2×D43—21no—
287C2×D43—21no—
288C2×D43—22no—
289C2×D43—41no—
290C2×D43—41no—
291C2×D43—84no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43#46612yes—
296C4×C43—21no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43C22×D811yescharacteristic
301C4×C43C2×#13511yescharacteristic
302C4×C43#57711yescharacteristic
303C4×C43#57711yescharacteristic
304Dic43—21no—
305Dic43—21no—
306Dic43—41no—
307Dic43—81no—
308Dic43#46612yes—
309#3226—431no—
310#3036—431no—
311C2×#461—431no—
312#2972—431no—
313#1681—431no—
314#1681—431no—
315#1681—431no—
316#1681—431no—
317#1673—431no—
318#1673—431no—
319#1673—431no—
320#1673D4311yescharacteristic, complemented
321#1571—431no—
322#1546—431no—
323#1540—431no—
324C2×C43—42no—
325C2×C43#304211yescharacteristic
326C2×C43C2×#46611yescharacteristic
327C2×C43#306911yescharacteristic
328D43—22no—
329D43—42no—
330D43—161no—
331C2×AGL(1,ℤ/8)—861no—
332C22×SD16—861no—
333#532—431no—
334C2×C4⋊Q8—431no—
335C2×C4×D4—431no—
336#500—431no—
337#500C2×D4311yescharacteristic, complemented
338#486—431no—
339#486—431no—
340#480—861no—
341#480—861no—
342#474—861no—
343#474—861no—
344#463—861no—
345#463—861no—
346#461—431no—
347#461—431no—
348#461—431no—
349#461—431no—
350#461—861no—
351#461—861no—
352#461C2×D4311yescharacteristic
353#461C2×D4311yescharacteristic
354#459—431no—
355#459—431no—
356C8×D4—431no—
357C8×D4—431no—
358C8×D4—431no—
359C8×D4—861no—
360C8×D4—861no—
361C8×D4C2×D4311yescharacteristic
362#431—431no—
363#431—431no—
364#423—431no—
365C2×C4⋊C8—431no—
366#417—861no—
367C2×#103—861no—
368C2×C22⋊C8—861no—
369C2×C22⋊C8—861no—
370#335—431no—
371#335—431no—
372#335—431no—
373#335C2×D4311yescharacteristic, complemented
374#332—431no—
375#332—431no—
376#332—431no—
377#332—431no—
378#332C2×D4311yescharacteristic, complemented
379#332C2×D4311yescharacteristic, complemented
380#331—431no—
381#331—431no—
382C43#1939211yescharacteristic, complemented, Sylow
383C2×#41—861no—
384C22×Q8—861no—
385C22×D4—431no—
386C23×C4—861no—
387AGL(1,ℤ/8)—1724no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×SD16—861no—
391C2×SD16—861no—
392C2×SD16—861no—
393C2×SD16—861no—
394C2×SD16—1724no—
395C2×D8—861no—
396C2×D8—861no—
397C2×M16—861no—
398C22×C8—21no—
399C22×C8—861no—
400C22×C8—861no—
401C22×C8—861no—
402C22×C8—861no—
403C4⋊Q8—431no—
404C4⋊Q8—861no—
405C4⋊Q8—861no—
406C4⋊Q8—861no—
407C4⋊Q8C22×D4311yescharacteristic
408C4⋊Q8C22×D4311yescharacteristic
409#127—431no—
410#124—861no—
411#121—861no—
412#121—861no—
413C4×D4—431no—
414C4×D4—431no—
415C4×D4—431no—
416C4×D4—861no—
417C4×D4—861no—
418C4×D4—861no—
419C4×D4—861no—
420C4×D4C22×D4311yescharacteristic
421C2×C4⋊C4—431no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C42—431no—
426#107—21no—
427#107—21no—
428#107—861no—
429#107—861no—
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—431no—
433C4⋊C8—431no—
434C4⋊C8—431no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437C4⋊C8C22×D4311yescharacteristic
438C4⋊C8C22×D4311yescharacteristic
439C4⋊C8C22×D4311yescharacteristic
440#103—21no—
441#103—21no—
442#103—861no—
443#103—861no—
444#103—861no—
445#103—861no—
446#102—861no—
447#102—861no—
448#102—861no—
449#102—861no—
450#102—861no—
451#102—861no—
452C22⋊C8—21no—
453C22⋊C8—431no—
454C22⋊C8—431no—
455C22⋊C8—861no—
456C22⋊C8—861no—
457C22⋊C8—861no—
458C22⋊C8—861no—
459C4×C8—431no—
460C4×C8—861no—
461C4×C8C22×D4311yescharacteristic
462C24—861no—
463#41—1722no—
464#41—1722no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—861no—
468C2×Q8—1721no—
469C2×Q8—1722no—
470C2×Q8—1722no—
471C2×D4—434no—
472C2×D4—431no—
473C2×D4—862no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—1721no—
479C2×D4D4×D4311yescharacteristic
480C22×C4—21no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—3441no—
489C22×C4—3441no—
490C22×C4—1721no—
491C22×C4—1721no—
492SD16—42no—
493SD16—42no—
494SD16—1722no—
495SD16—1722no—
496SD16—1722no—
497SD16—1722no—
498D8—1722no—
499D8—1722no—
500M16—1722no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—81no—
505C2×C8—431no—
506C2×C8—431no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—3441no—
511C2×C8—3441no—
512C2×C8—3441no—
513C2×C8—1722no—
514C2×C8D4×D4311yescharacteristic
515C2×C8D4×D4311yescharacteristic
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—431no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C4⋊C4D4×D4311yescharacteristic
527C22⋊C4—21no—
528C22⋊C4—861no—
529C22⋊C4—861no—
530C22⋊C4—861no—
531C22⋊C4—1721no—
532C22⋊C4—1721no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42C23×D4311yescharacteristic
537C23—21no—
538C23—431no—
539C23—864no—
540C23—861no—
541C23—3441no—
542C23—3441no—
543C23—1721no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—41no—
548Q8—3442no—
549Q8—1721no—
550Q8—1721no—
551D4—21no—
552D4—432no—
553D4—864no—
554D4—861no—
555D4—3441no—
556D4—3442no—
557D4—1721no—
558D4—1721no—
559D4—1721no—
560D4—1721no—
561D4D8×D4312yes—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—431no—
568C2×C4—432no—
569C2×C4—432no—
570C2×C4—431no—
571C2×C4—431no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—3441no—
576C2×C4—3441no—
577C2×C4—3442no—
578C2×C4—3442no—
579C2×C4—3441no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4C2×D4×D4311yescharacteristic
585C2×C4C2×D4×D4311yescharacteristic
586C2×C4#41×D4311yescharacteristic
587C8—21no—
588C8—21no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—861no—
593C8—861no—
594C8—1721no—
595C8—1721no—
596C8—1721no—
597C22—22no—
598C22—41no—
599C22—41no—
600C22—432no—
601C22—861no—
602C22—861no—
603C22—862no—
604C22—3444no—
605C22—3441no—
606C22—3441no—
607C22—3441no—
608C22—1721no—
609C22—1721no—
610C22#121×D4311yescharacteristic
611C4—21no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4—432no—
616C4—861no—
617C4—861no—
618C4—3441no—
619C4—1721no—
620C4C2×D8×D4311yescharacteristic
621C4#135×D4311yescharacteristic
622C4#1458370511yescharacteristic
623C4#1458370811yescharacteristic
624C2—42no—
625C2—862no—
626C2—1722no—
627C2—6881no—
628C2#1914410211yescharacteristic
629C2#466×D4311yescharacteristic
630C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1673C2
socleC22×C43C2×#121
prime radical#19144060C2
hypercenter#1673D43
hypocenterC43#19392
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1673

Complements

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

NH ≅ G/Ntype
1. #19145717C2semidirect
3. #461×D43C2semidirect
4. #19143616C2semidirect
5. #19134035C2semidirect
6. #19134034C2semidirect
7. #19134033C2semidirect
8. #19134032C2semidirect
9. #19133983C2semidirect
10. #19133982C2semidirect
11. #19133981C2semidirect
12. #19133368C2semidirect
13. #19133265C2semidirect
14. #19133243C2semidirect
15. C43×#1673C2semidirect
21. #14583302C22semidirect
22. #14583247C22semidirect
23. #14583246C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582646C22semidirect
55. #14582645C22semidirect
56. #14582645C22semidirect
57. #14582644C22semidirect
58. #14582642C22semidirect
59. #14582642C22semidirect
60. C43×#500C22semidirect
64. C43×#335C22semidirect
65. C43×#332C22semidirect
66. C43×#332C22semidirect
320. #1673D43semidirect
337. #500C2×D43semidirect
373. #335C2×D43semidirect
378. #332C2×D43semidirect
379. #332C2×D43semidirect
382. C43#19392semidirect

Maximal subgroups

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

subgroupindex
#191457172
#191440602
#461×D432
#191436162
#191340352
#191340342
#191340332
#191340322
#191339832
#191339822
#191339812
#191333682
#191332652
#191332432
C43×#16732
#1939243