Finite Group Databasebeta

← #25138095

Subgroups — #25138095

Order 11008.

690 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144416C211yesmaximal, characteristic, complemented
2C2×#14583197C211yesmaximal, characteristic, complemented
3#19143399C211yesmaximal, characteristic
4#19143259C211yesmaximal, characteristic, complemented
5#19136044C211yesmaximal, characteristic, complemented
6#19136037C211yesmaximal, characteristic, complemented
7#19135888C211yesmaximal, characteristic
8#19135887C211yesmaximal, characteristic
9#19135586C211yesmaximal, characteristic, complemented
10#19135380C211yesmaximal, characteristic, complemented
11#19135372C211yesmaximal, characteristic, complemented
12#19135369C211yesmaximal, characteristic, complemented
13#19135260C211yesmaximal, characteristic, complemented
14#19134585C211yesmaximal, characteristic, complemented
15C43×#1931C211yesmaximal, characteristic, complemented
16C2×#13063351C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18#14583367C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20#14583209—21no—
21#14583205—21no—
22#14583202—21no—
23#14583198—21no—
24#14583197—21no—
25#14583197—21no—
26#14583197—21no—
27#14583197—21no—
28#14583008—21no—
29#14582996—21no—
30#14582990—21no—
31#14582979—21no—
32#14582961—21no—
33#14582958—21no—
34#14582954—21no—
35#14582950—21no—
36C2×#13063261C2211yescharacteristic
37C2×#13063260C2211yescharacteristic
38#14582942C2211yescharacteristic
39#14582942C2211yescharacteristic
40C2×#13063259C2211yescharacteristic
41C2×#13063256C2211yescharacteristic
42#14582922C2211yescharacteristic
43#14582922C2211yescharacteristic
44C2×Dic43⋊C8C2211yescharacteristic
45#14582901C2211yescharacteristic
46#14582901C2211yescharacteristic
47#14582898C2211yescharacteristic
48C2×#13063246C2211yescharacteristic
49C2×#13063242C2211yescharacteristic
50#14582867C2211yescharacteristic
51#14582865C2211yescharacteristic
52#14582855C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582663C2211yescharacteristic
60C43×#428C2211yescharacteristic
61C43×#418C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#100×C43C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C23×Dic43—21no—
69#13063351—22no—
70#13063351—22no—
71C2×#10621883—21no—
72C2×#10621882—21no—
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063316—21no—
78#13063316—21no—
79#13063316—21no—
80#13063316—21no—
81#13063290D411yescharacteristic
82#13063290D411yescharacteristic
83D4×Dic43—21no—
84D4×Dic43—21no—
85D4×Dic43—21no—
86D4×Dic43—21no—
87#13063287D411yescharacteristic
88#13063287D411yescharacteristic
89(C22⋊D43)⋊C4—21no—
90(C22⋊D43)⋊C4—21no—
91#13063282—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×C22⋊Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98C42×D43—21no—
99#13063261—22no—
100#13063260—22no—
101#13063259—21no—
102#13063259—21no—
103#13063258—21no—
104#13063258—21no—
105#13063256—21no—
106#13063256—21no—
107#13063256—21no—
108#13063256—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8D411yescharacteristic
114Dic43⋊C8D411yescharacteristic
115Dic43⋊C8D411yescharacteristic
116Dic43⋊C8D411yescharacteristic
117#13063250—21no—
118#13063250—21no—
119#13063248—21no—
120#13063247—21no—
121#13063247—21no—
122#13063246—21no—
123#13063246—21no—
124#13063245—21no—
125#13063242—22no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8—21no—
128(C2×D43)⋊C8—21no—
129(C2×D43)⋊C8—21no—
130#13063236—21no—
131#13063235—21no—
132C4×C43⋊C8—21no—
133C8×Dic43—21no—
134C22×D4×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C2×M16×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139#117×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141#107×C43—21no—
142#106×C43—21no—
143#102×C43—21no—
144#102×C43—21no—
145#102×C43—21no—
146#102×C43—21no—
147#100×C43—22no—
148#97×C43—21no—
149C4×C8×C43—21no—
150C24×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43#4112yes—
157C22×C4×C43—21no—
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—41no—
163C22×Dic43—41no—
164C22×Dic43—82no—
165C22×Dic43#4111yescharacteristic
166C22×Dic43#4111yescharacteristic
167#10621898—21no—
168#10621898—21no—
169#10621898—21no—
170#10621898—21no—
171C2×D172C2×D411yescharacteristic
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×Dic86C2×D411yescharacteristic
176M16×C43—21no—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43—21no—
180M16×C43—21no—
181M16×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C22⋊C4×C43—21no—
194C42×C43—21no—
195C22⋊Dic43—41no—
196C22⋊Dic43—41no—
197#10621883—24no—
198#10621882—24no—
199(C2×D43)⋊C4—21no—
200(C2×D43)⋊C4—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—41no—
206C4⋊Dic43—41no—
207Dic43⋊C4—21no—
208Dic43⋊C4—21no—
209Dic43⋊C4—41no—
210Dic43⋊C4—41no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43C2×D411yescharacteristic
214C4×Dic43C2×D411yescharacteristic
215C4×Dic43C2×D411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877#4112yes—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8C2×D411yescharacteristic
229C2×C43⋊C8C2×D411yescharacteristic
230C23×C43—22no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—81no—
234C23×C43—81no—
235C23×C43C2×#4111yescharacteristic
236C22×D43—21no—
237D4×C43—22no—
238D4×C43—22no—
239D4×C43—41no—
240D4×C43—41no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—81no—
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C2×C4×C432−1+411yescharacteristic
251C22⋊D43—41no—
252C22⋊D43—41no—
253C2×Dic43—21no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—82no—
259C2×Dic43—82no—
260C2×Dic43—81no—
261C2×Dic43—81no—
262C2×Dic43#12111yescharacteristic
263C2×Dic43#12111yescharacteristic
264C2×Dic43#12111yescharacteristic
265C2×Dic43#12111yescharacteristic
266D172—21no—
267D172—21no—
268C4×D43—42no—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—81no—
272Dic86—21no—
273Dic86—21no—
274C8×C43—21no—
275C8×C43—21no—
276C8×C43—41no—
277C8×C43—41no—
278C8×C43—41no—
279C43⋊C8—22no—
280C43⋊C8—21no—
281C43⋊C8—21no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#24724—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—42no—
288C22×C43—82no—
289C22×C43—82no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43C2×#12111yescharacteristic
293C22×C43#55211yescharacteristic
294C22×C43#55611yescharacteristic
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43#52511yescharacteristic
302C4×C43#53611yescharacteristic
303C4×C43#54711yescharacteristic
304C4×C43#54811yescharacteristic
305Dic43—21no—
306Dic43—21no—
307Dic43—21no—
308Dic43—21no—
309Dic43—41no—
310Dic43—81no—
311Dic43—81no—
312#3080—431no—
313C2×#478—431no—
314C4×AGL(1,ℤ/8)—431no—
315#2925—431no—
316#2079—431no—
317#2078—431no—
318#2051—431no—
319#2051—431no—
320#1998—431no—
321#1952—431no—
322#1951—431no—
323#1950—431no—
324#1931—431no—
325#1931D4311yescharacteristic, complemented
326#1800—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43—82no—
330C2×C43#241511yescharacteristic
331C2×C43#306711yescharacteristic
332C2×C43#306811yescharacteristic
333D43—81no—
334C2×AGL(1,ℤ/8)—431no—
335C2×#125—431no—
336C4×#41—431no—
337C2×C4×D4—431no—
338#479—861no—
339#479—861no—
340#478—861no—
341#478—861no—
342#478—861no—
343#478—861no—
344#478—861no—
345#478—861no—
346#442—861no—
347#440—861no—
348C4×SD16—861no—
349C4×D8—861no—
350#433—861no—
351#433—861no—
352#432—861no—
353#431—861no—
354C2×#108—431no—
355C2×#108—431no—
356#428—431no—
357#428—431no—
358#428C2×D4311yescharacteristic
359C2×#107—431no—
360C2×#106—431no—
361#423—431no—
362#423—431no—
363C2×C4⋊C8—431no—
364#418C2×D4311yescharacteristic
365#417—431no—
366#417—431no—
367#417—431no—
368C2×#102—431no—
369C2×#102C2×D4311yescharacteristic
370C2×#100—431no—
371C2×#100C2×D4311yescharacteristic
372#408—431no—
373#408—431no—
374#405—431no—
375#405C2×D4311yescharacteristic
376C4×M16—431no—
377#343—431no—
378#343—431no—
379#343—431no—
380#343—431no—
381#343—431no—
382#343C2×D4311yescharacteristic
383#341—431no—
384#341C2×D4311yescharacteristic
385C43#2472411yescharacteristic, complemented, Sylow
386C2×#41—431no—
387C22×D4C22×D4311yescharacteristic
388C23×C4—861no—
389AGL(1,ℤ/8)—862no—
390AGL(1,ℤ/8)—862no—
391C2×SD16—861no—
392C2×D8—861no—
393C2×M16—431no—
394C2×M16—431no—
395C2×M16—431no—
396C2×M16C22×D4311yescharacteristic
397C2×M16C22×D4311yescharacteristic
398C2×M16C22×D4311yescharacteristic
399C22×C8—431no—
400C22×C8C22×D4311yescharacteristic
401#125—861no—
402#125—861no—
403#125—861no—
404#125—861no—
405C4×Q8—431no—
406C4×Q8—431no—
407C4×D4—431no—
408C4×D4—431no—
409C4×D4—861no—
410C4×D4—861no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4—861no—
414C4×D4—861no—
415#117—861no—
416#117C22×D4311yescharacteristic
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—861no—
423C2×C42—431no—
424C2×C42—861no—
425#108—862no—
426#108—862no—
427#107—21no—
428#107—861no—
429#107—861no—
430#107—861no—
431#107—861no—
432#106—21no—
433#106—861no—
434#106—861no—
435#106—861no—
436#106—861no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—861no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445#103—861no—
446#103—861no—
447#103—861no—
448#102—21no—
449#102—21no—
450#102—21no—
451#102—21no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#100—22no—
458#100—862no—
459C22⋊C8—861no—
460C22⋊C8—861no—
461C22⋊C8—861no—
462C22⋊C8—861no—
463#97—21no—
464#97—861no—
465#97—861no—
466C4×C8—21no—
467C4×C8—861no—
468C4×C8—861no—
469C24—21no—
470#41—861no—
471#41—861no—
472#41—861no—
473#41—861no—
474C2×Q8—431no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—431no—
481C2×D4—861no—
482C2×D4#1062189812yes—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—3442no—
492C22×C4—1721no—
493C22×C4—1721no—
494C22×C4C23×D4311yescharacteristic
495SD16—864no—
496D8—864no—
497M16—21no—
498M16—21no—
499M16—21no—
500M16—21no—
501M16—21no—
502M16—21no—
503M16—432no—
504M16—861no—
505M16—861no—
506M16—861no—
507M16—861no—
508M16—861no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—431no—
515C2×C8—431no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8D4×D4311yescharacteristic
522C2×C8D4×D4311yescharacteristic
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—1721no—
532C4⋊C4—1721no—
533C4⋊C4—1721no—
534C4⋊C4—1721no—
535C4⋊C4D4×D4311yescharacteristic
536C4⋊C4D4×D4311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C22⋊C4—1721no—
541C22⋊C4—1721no—
542C42—21no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—861no—
548C42—861no—
549C23—22no—
550C23—41no—
551C23—41no—
552C23—81no—
553C23—81no—
554C23—861no—
555C23#41×D4311yescharacteristic
556Q8—861no—
557Q8—861no—
558D4—22no—
559D4—22no—
560D4—41no—
561D4—41no—
562D4—861no—
563D4—861no—
564D4—1721no—
565D4—1721no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—81no—
570C2×C4—431no—
571C2×C4—431no—
572C2×C4—431no—
573C2×C4—431no—
574C2×C4—861no—
575C2×C4—3441no—
576C2×C4—3442no—
577C2×C4—3442no—
578C2×C4—3441no—
579C2×C4—3441no—
580C2×C4—1722no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4C2×D4×D4311yescharacteristic
588C2×C4C2×D4×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4C2×#1062189811yescharacteristic
591C2×C4#1306337211yescharacteristic
592C2×C4#1306337211yescharacteristic
593C8—21no—
594C8—21no—
595C8—41no—
596C8—41no—
597C8—41no—
598C8—862no—
599C8—861no—
600C8—861no—
601C8—1721no—
602C8—1721no—
603C22—21no—
604C22—21no—
605C22—42no—
606C22—82no—
607C22—82no—
608C22—81no—
609C22—81no—
610C22—1721no—
611C22—1721no—
612C22—1721no—
613C22#121×D4311yescharacteristic
614C22#1458358211yescharacteristic
615C22#1458361611yescharacteristic
616C4—41no—
617C4—41no—
618C4—81no—
619C4—861no—
620C4—861no—
621C4—861no—
622C4—861no—
623C4—3441no—
624C4—3441no—
625C4—1721no—
626C4#1458340811yescharacteristic
627C4#1458346911yescharacteristic
628C4#1458354711yescharacteristic
629C4#1458355811yescharacteristic
630C2—21no—
631C2—21no—
632C2—82no—
633C2—3441no—
634C2#1913802111yescharacteristic
635C2#1914431311yescharacteristic
636C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1931C2
socleC22×C43C2×#121
prime radicalC2×#13063351C22
hypercenter#1931D43
hypocenterC43#24724
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1931

Complements

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

NH ≅ G/Ntype
1. #19144416C2semidirect
2. C2×#14583197C2semidirect
4. #19143259C2semidirect
5. #19136044C2semidirect
6. #19136037C2semidirect
9. #19135586C2semidirect
10. #19135380C2semidirect
11. #19135372C2semidirect
12. #19135369C2semidirect
13. #19135260C2semidirect
14. #19134585C2semidirect
15. C43×#1931C2semidirect
325. #1931D43semidirect
385. C43#24724semidirect

Maximal subgroups

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

subgroupindex
#191444162
C2×#145831972
#191433992
#191432592
#191360442
#191360372
#191358882
#191358872
#191355862
#191353802
#191353722
#191353692
#191352602
#191345852
C43×#19312
#2472443