Finite Group Databasebeta

← #25079631

Subgroups — #25079631

Order 11008.

668 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145333C211yesmaximal, characteristic, complemented
2#19144655C211yesmaximal, characteristic, complemented
3#19144050C211yesmaximal, characteristic, complemented
4#19134156C211yesmaximal, characteristic, complemented
5#19134128C211yesmaximal, characteristic, complemented
6#19134094C211yesmaximal, characteristic, complemented
7#19134074C211yesmaximal, characteristic, complemented
8#19134039C211yesmaximal, characteristic, complemented
9#19134011C211yesmaximal, characteristic, complemented
10#19133977C211yesmaximal, characteristic, complemented
11#19133955C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133301C211yesmaximal, characteristic, complemented
14#19133291C211yesmaximal, characteristic, complemented
15C43×#2971C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17#14583449C2211yescharacteristic
18#14583449C2211yescharacteristic
19#14583297C2211yescharacteristic
20#14583276C2211yescharacteristic
21#14583246C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583223—21no—
24#14583194C2211yescharacteristic
25#14583189C2211yescharacteristic
26#14583152—21no—
27#14583152—21no—
28#14583121—21no—
29#14583114—21no—
30#14583109C2211yescharacteristic
31#14583104C2211yescharacteristic
32#14583099C2211yescharacteristic
33#14583099C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583094C2211yescharacteristic
36#14583044—21no—
37#14583012—21no—
38#14583012—21no—
39C4×#10621884—21no—
40C4×#10621882—21no—
41#14582952C2211yescharacteristic
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43#14582893—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582644C2211yescharacteristic
51#14582644C2211yescharacteristic
52#14582642C2211yescharacteristic
53#14582642C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436—21no—
61C43×#436C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#432—21no—
64C43×#432C2211yescharacteristic
65C4×M16×C43—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898—21no—
69#13063345—44no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×D344—21no—
75C2×D344—21no—
76C2×#10621882—21no—
77C2×#10621882—21no—
78C22×C43⋊C8—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063322C2311yescharacteristic
82#13063322C2311yescharacteristic
83#13063313—21no—
84#13063313—21no—
85#13063299—21no—
86#13063299—21no—
87#13063299—21no—
88#13063299—21no—
89C4×D172—21no—
90C4×D172—21no—
91C4×D172—21no—
92C4×D172—21no—
93#13063258—21no—
94#13063257—21no—
95#13063257—21no—
96#13063256—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102#13063249—21no—
103#13063248—21no—
104#13063248—21no—
105#13063247—21no—
106#13063247—21no—
107#13063247—21no—
108#13063247—21no—
109#13063246—21no—
110#13063245—21no—
111#13063245—21no—
112#13063245—21no—
113#13063245—21no—
114C22⋊(C43⋊C8)—21no—
115C4×C43⋊C8—21no—
116C2×#41×C43D411yescharacteristic
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43D411yescharacteristic
120C2×M16×C43D411yescharacteristic
121C4×Q8×C43D411yescharacteristic
122C4×Q8×C43C2311yescharacteristic
123C4×D4×C43—21no—
124C4×D4×C43—21no—
125C4×D4×C43D411yescharacteristic
126C4×D4×C43C2311yescharacteristic
127#117×C43—21no—
128#117×C43D411yescharacteristic
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43—21no—
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43—21no—
139#97×C43D411yescharacteristic
140#97×C43D411yescharacteristic
141C4×C8×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—22no—
146#41×C43—41no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C2×C22⋊D43—41no—
157C2×C22⋊D43—41no—
158#10621898—42no—
159#10621898—42no—
160#10621898—82no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×C4×D43—41no—
168C2×C4×D43—41no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171M16×C43—22no—
172M16×C43—41no—
173M16×C43—42no—
174M16×C43—42no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43#4111yescharacteristic
194C42×C43C2411yescharacteristic
195#10621885—42no—
196#10621884—42no—
197#10621884—42no—
198#10621883—42no—
199#10621882—42no—
200#10621882—42no—
201(C2×D43)⋊C4—41no—
202(C2×D43)⋊C4—41no—
203(C2×D43)⋊C4—41no—
204(C2×D43)⋊C4—41no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—42no—
214D344—42no—
215D344—42no—
216C23×C43—21no—
217C23×C43#12111yescharacteristic
218C22×D43—41no—
219C22×D43—41no—
220Q8×C43—21no—
221Q8×C43AGL(1,ℤ/8)12yes—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—42no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—42no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—81no—
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C22⋊D43—82no—
244C22⋊D43—82no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247D172—41no—
248D172—41no—
249D172—41no—
250D172—41no—
251D172—41no—
252D172—41no—
253D172—41no—
254D172—41no—
255D172—81no—
256D172—81no—
257C4×D43—82no—
258C4×D43—82no—
259Dic86—41no—
260Dic86—41no—
261Dic86—81no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43#13512yescomplemented
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#19184—431nomaximal, Sylow
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43C2×#12111yescharacteristic
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—22no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43C2×#13511yescharacteristic
294C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C43#57511yescharacteristic
296C4×C43#57511yescharacteristic
297Dic43—81no—
298Dic43—81no—
299#3184—431no—
300#3106—431no—
301#3035—431no—
302#2971D4311yescharacteristic, complemented
303#1701—431no—
304#1697—431no—
305#1691—431no—
306#1687—431no—
307#1682—431no—
308#1678—431no—
309#1672—431no—
310#1668—431no—
311#1565—431no—
312#1553—431no—
313#1551—431no—
314C2×C43—41no—
315C2×C43—81no—
316C2×C43#303511yescharacteristic
317C2×C43#305511yescharacteristic
318C2×C43#306811yescharacteristic
319D43—161no—
320D43—161no—
321C2×#135—861no—
322#532—431no—
323#532—431no—
324C4×#41C2×D4311yescharacteristic
325#498—431no—
326#493—431no—
327#486—431no—
328#486—431no—
329#482—861no—
330#477—431no—
331#476—431no—
332#469—861no—
333#469—861no—
334#464—861no—
335#463—861no—
336#462—431no—
337#461—431no—
338#460—431no—
339#460—431no—
340#459—431no—
341#459—431no—
342#449—861no—
343C8×Q8C2×D4311yescharacteristic
344C8×Q8C2×D4311yescharacteristic
345#442—861no—
346#442—861no—
347C4×SD16—861no—
348C4×D8—861no—
349#436—21no—
350#436—21no—
351#436C2×D4311yescharacteristic
352#436C2×D4311yescharacteristic
353#432—21no—
354#432C2×D4311yescharacteristic
355#431—431no—
356C2×C4⋊C8—431no—
357#416—861no—
358C4×M16—21no—
359C4×M16C2×D4311yescharacteristic
360#335—431no—
361#335—431no—
362#334—431no—
363#334—431no—
364#333—431no—
365#333—431no—
366#332—431no—
367#332—431no—
368#331—431no—
369#331—431no—
370#331—431no—
371#331—431no—
372C43#1918411yescharacteristic, complemented, Sylow
373C2×#41—861no—
374C2×#41—861no—
375C2×#41D17211yescharacteristic
376#135—1724no—
377C2×Q16—861no—
378C2×SD16—861no—
379C2×SD16—861no—
380C2×SD16—861no—
381C2×D8—861no—
382C2×D8—861no—
383C2×D8—861no—
384C2×D8—861no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16C22⋊D4311yescharacteristic
388C2×M16C22⋊D4311yescharacteristic
389C22×C8—861no—
390C4⋊Q8—431no—
391C4⋊Q8—431no—
392#127—431no—
393#127—431no—
394#124—861no—
395#124—861no—
396#121—861no—
397#121—861no—
398#121—861no—
399#121—861no—
400C4×Q8D17211yescharacteristic
401C4×Q8C22×D4311yescharacteristic
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—861no—
405C4×D4—861no—
406C4×D4—861no—
407C4×D4—861no—
408C4×D4D17211yescharacteristic
409C4×D4C22×D4311yescharacteristic
410#117—21no—
411#117D17211yescharacteristic
412C2×C42—21no—
413C2×C42C22×D4311yescharacteristic
414#107—861no—
415#106—861no—
416#106—861no—
417#106—861no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8—861no—
425C4⋊C8C22×D4311yescharacteristic
426C4⋊C8C22×D4311yescharacteristic
427#103—861no—
428#103—861no—
429#103—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—861no—
443#97—21no—
444#97C22⋊D4311yescharacteristic
445#97C22⋊D4311yescharacteristic
446C4×C8—21no—
447C4×C8—21no—
448C4×C8—861no—
449C4×C8C22×D4311yescharacteristic
450C4×C8C22×D4311yescharacteristic
451#41—22no—
452#41—41no—
453#41—3442no—
454#41—1722no—
455#41—1722no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8C2×D17211yescharacteristic
459C2×D4—21no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—1721no—
467C2×D4—1721no—
468C2×D4C2×D17211yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—1721no—
473C22×C4—1721no—
474C22×C4C2×D17211yescharacteristic
475C22×C4#1062189811yescharacteristic
476C22×C4C2×C22⋊D4311yescharacteristic
477Q16—1722no—
478SD16—1722no—
479SD16—1722no—
480SD16—1722no—
481D8—1722no—
482D8—1722no—
483D8—1722no—
484D8—1722no—
485M16—22no—
486M16—41no—
487M16—42no—
488M16—42no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—1722no—
496C2×C8C2×C22⋊D4311yescharacteristic
497C2×C8C2×C22⋊D4311yescharacteristic
498C2×C8C2×C22⋊D4311yescharacteristic
499C2×C8C2×C22⋊D4311yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4C2×D17211yescharacteristic
507C4⋊C4C2×D17211yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—1721no—
512C22⋊C4—1721no—
513C22⋊C4—1721no—
514C22⋊C4—1721no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42C2×D17211yescharacteristic
519C42#1062189811yescharacteristic
520C42C2×C22⋊D4311yescharacteristic
521C42C23×D4311yescharacteristic
522C23—21no—
523C23—1721no—
524C23—1721no—
525C23#1306329911yescharacteristic
526Q8—21no—
527Q8—3441no—
528Q8—1721no—
529Q8—1721no—
530Q8#1306335312yes—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—3441no—
535D4—3441no—
536D4—3442no—
537D4—3442no—
538D4—1721no—
539D4—1721no—
540D4—1721no—
541D4—1721no—
542D4—1721no—
543D4—1721no—
544D4—1721no—
545D4—1721no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—81no—
558C2×C4—3442no—
559C2×C4—3442no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4#1306329911yescharacteristic
563C2×C4#1306329911yescharacteristic
564C2×C4#1306329911yescharacteristic
565C2×C4C22×C22⋊D4311yescharacteristic
566C2×C4C22×D17211yescharacteristic
567C2×C4C2×#1062189811yescharacteristic
568C8—21no—
569C8—21no—
570C8—21no—
571C8—41no—
572C8—41no—
573C8—1721no—
574C8—1721no—
575C8—1721no—
576C8—1721no—
577C8#1306334512yescomplemented
578C22—21no—
579C22—21no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—3441no—
585C22—3441no—
586C22—3441no—
587C22—3441no—
588C22—3441no—
589C22—3441no—
590C22C2×#1306329911yescharacteristic
591C4—21no—
592C4—22no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—41no—
597C4—41no—
598C4—3441no—
599C4—3441no—
600C4C2×#1306334511yescharacteristic
601C4C2×#1306335311yescharacteristic
602C4#1458369711yescharacteristic
603C4#1458369911yescharacteristic
604C2—41no—
605C2—81no—
606C2—6881no—
607C2—6881no—
608C2#1914405011yescharacteristic
609C2#1914421411yescharacteristic
610C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2971C2
socleC22×C43C2×#121
hypercenter#2971D43
hypocenterC43#19184
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2971

Complements

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

NH ≅ G/Ntype
1. #19145333C2semidirect
2. #19144655C2semidirect
3. #19144050C2semidirect
4. #19134156C2semidirect
5. #19134128C2semidirect
6. #19134094C2semidirect
7. #19134074C2semidirect
8. #19134039C2semidirect
9. #19134011C2semidirect
10. #19133977C2semidirect
11. #19133955C2semidirect
12. #19133347C2semidirect
13. #19133301C2semidirect
14. #19133291C2semidirect
15. C43×#2971C2semidirect
267. C8×C43#135semidirect
302. #2971D43semidirect
372. C43#19184semidirect
577. C8#13063345semidirect

Maximal subgroups

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

subgroupindex
#191453332
#191446552
#191440502
#191341562
#191341282
#191340942
#191340742
#191340392
#191340112
#191339772
#191339552
#191333472
#191333012
#191332912
C43×#29712
#1918443