Finite Group Databasebeta

← #25081837

Subgroups — #25081837

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#19145747C211yesmaximal, characteristic, complemented
2#19144393C211yesmaximal, characteristic
3#476×D43C211yesmaximal, characteristic
4#19143616C211yesmaximal, characteristic
5#19134049C211yesmaximal, characteristic, complemented
6#19134048C211yesmaximal, characteristic, complemented
7#19134047C211yesmaximal, characteristic, complemented
8#19134046C211yesmaximal, characteristic, complemented
9#19133993C211yesmaximal, characteristic, complemented
10#19133992C211yesmaximal, characteristic, complemented
11#19133991C211yesmaximal, characteristic, complemented
12#19133368C211yesmaximal, characteristic, complemented
13#19133274C211yesmaximal, characteristic, complemented
14#19133249C211yesmaximal, characteristic, complemented
15C43×#1675C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19#14583302C2211yescharacteristic, complemented
20#14583251C2211yescharacteristic, complemented
21#14583250C2211yescharacteristic, complemented
22#14583236—21no—
23#14583236—21no—
24#14583198—21no—
25#14583197—21no—
26#14583193—21no—
27#14583193—21no—
28#14583190C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583188—21no—
31#14583187—21no—
32#14583186C2211yescharacteristic
33#14583186C2211yescharacteristic
34#14583180C2211yescharacteristic
35#14583179C2211yescharacteristic
36C8×D172C2211yescharacteristic
37D4×C43⋊C8C2211yescharacteristic
38#14582964C2211yescharacteristic
39C8×C22⋊D43—21no—
40(C22⋊D43)⋊C8—21no—
41#14582951C2211yescharacteristic
42#14582950C2211yescharacteristic
43#14582938—21no—
44#106×D43—21no—
45#14582921C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582902—21no—
48#102×D43—21no—
49C2×(C2×D43)⋊C8—21no—
50C22⋊C8×D43—21no—
51#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582648C2211yescharacteristic, complemented
56#14582647C2211yescharacteristic, complemented
57#14582647C2211yescharacteristic, complemented
58#14582646C2211yescharacteristic, complemented
59#14582644C2211yescharacteristic, complemented
60C43×#500C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic
62C43×#476C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#333C2211yescharacteristic, complemented
67C2×Q8×D43—21no—
68C2×D4×D43D411yescharacteristic
69C22×C4×D43—21no—
70C2×#10621872—21no—
71C22×C43⋊C8—21no—
72C2×C8×D43—21no—
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063324—21no—
78#13063324—21no—
79#13063323—21no—
80#13063316—21no—
81#13063305—21no—
82#13063301—21no—
83Q8×Dic43—21no—
84#13063290—21no—
85C4×D172C2311yescharacteristic
86D4×Dic43D411yescharacteristic
87#13063287D411yescharacteristic
88C4×C22⋊D43—21no—
89(C22⋊D43)⋊C4—21no—
90#13063283—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43D411yescharacteristic
94C22⋊C4×D43—21no—
95C42×D43C2311yescharacteristic
96#13063259—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258—21no—
100#13063257—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8D411yescharacteristic
110Dic43⋊C8D411yescharacteristic
111#13063250—21no—
112#13063250—21no—
113#13063248—21no—
114#13063248—21no—
115#13063247—21no—
116#13063247—21no—
117#13063246—21no—
118#13063246—21no—
119#13063245—21no—
120#13063245—21no—
121C22⋊(C43⋊C8)—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8D411yescharacteristic
126(C2×D43)⋊C8D411yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C22×C8×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131C4⋊Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#107×C43—21no—
134#107×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×D4×C43C2×D411yescharacteristic
148C22×C4×C43—21no—
149C2×C22⋊D43—21no—
150C22×Dic43—21no—
151Q8×D43—82no—
152D4×D43—22no—
153D4×D43Q1614yes—
154C2×D172C2×D411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—41no—
159C2×C4×D43—81no—
160C2×C4×D43—81no—
161C2×C4×D43C2×D411yescharacteristic
162C2×C4×D43C2×D411yescharacteristic
163C2×C4×D43#4111yescharacteristic
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—41no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—81no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—41no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—41no—
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—41no—
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43#4111yescharacteristic
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—81no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204#10621872—42no—
205C8×D43—42no—
206C8×D43—81no—
207C8×D43—81no—
208C23×C43—21no—
209C22×D43—21no—
210C22×D43—24no—
211C22×D43—81no—
212C22×D43—81no—
213C22×D43#12111yescharacteristic
214Q8×C43—81no—
215Q8×C43—81no—
216D4×C43—21no—
217D4×C43C2×Q1612yes—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C22⋊D43—24no—
227C2×Dic43—21no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—81no—
231C2×Dic43#12111yescharacteristic
232C2×Dic43#12111yescharacteristic
233C2×Dic43#12111yescharacteristic
234D172—21no—
235D172C2×Q1612yes—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—41no—
239C4×D43—41no—
240C4×D43—41no—
241C4×D43—81no—
242C4×D43—81no—
243C4×D43—82no—
244C4×D43C2×Q1612yes—
245C4×D43#13512yes—
246Dic86—41no—
247Dic86—41no—
248Dic86—82no—
249Dic86—81no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C43⋊C8—21no—
256C43⋊C8—21no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#19393—431nomaximal, Sylow
261C22×C43—22no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43C2×#12111yescharacteristic
265C2×D43—21no—
266C2×D43—21no—
267C2×D43—22no—
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—84no—
271C2×D43#46712yes—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43C22×Q1611yescharacteristic
277C4×C43C2×#13511yescharacteristic
278C4×C43#57711yescharacteristic
279C4×C43#57711yescharacteristic
280Dic43—21no—
281Dic43—21no—
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285Dic43#46712yes—
286#3230—431no—
287#3077—431no—
288C2×#476—431no—
289#2972—431no—
290#1683—431no—
291#1683—431no—
292#1683—431no—
293#1683—431no—
294#1675—431no—
295#1675—431no—
296#1675—431no—
297#1675D4311yescharacteristic, complemented
298#1571—431no—
299#1548—431no—
300#1542—431no—
301C2×C43—42no—
302C2×C43#304211yescharacteristic
303C2×C43C2×#46711yescharacteristic
304C2×C43#306811yescharacteristic
305D43—22no—
306D43—42no—
307#533—431no—
308C2×C4⋊Q8—431no—
309C2×C4×D4—431no—
310#500—431no—
311#500C2×D4311yescharacteristic, complemented
312#487—431no—
313#487—431no—
314#484—861no—
315#484—861no—
316#478—861no—
317#478—861no—
318#477—861no—
319#477—861no—
320#476—431no—
321#476—431no—
322#476—431no—
323#476—431no—
324#476—861no—
325#476—861no—
326#476C2×D4311yescharacteristic
327#476C2×D4311yescharacteristic
328#474—431no—
329#474—431no—
330C8×D4—431no—
331C8×D4—431no—
332C8×D4—431no—
333C8×D4—861no—
334C8×D4—861no—
335C8×D4C2×D4311yescharacteristic
336#431—431no—
337#431—431no—
338#428—861no—
339C2×#106—861no—
340#423—431no—
341C2×C4⋊C8—431no—
342#418—861no—
343C2×#102—861no—
344C2×C22⋊C8—861no—
345C2×C22⋊C8—861no—
346#335—431no—
347#335—431no—
348#335—431no—
349#335C2×D4311yescharacteristic, complemented
350#333—431no—
351#333—431no—
352#333—431no—
353#333—431no—
354#333C2×D4311yescharacteristic, complemented
355#333C2×D4311yescharacteristic, complemented
356#332—431no—
357#332—431no—
358C43#1939311yescharacteristic, complemented, Sylow
359C22×Q8—861no—
360C22×D4—431no—
361C23×C4—861no—
362C2×M16—861no—
363C22×C8—21no—
364C22×C8—861no—
365C22×C8—861no—
366C22×C8—861no—
367C22×C8—861no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8—861no—
371C4⋊Q8—861no—
372C4⋊Q8—861no—
373C4⋊Q8C22×D4311yescharacteristic
374C4⋊Q8C22×D4311yescharacteristic
375#125—861no—
376C22⋊Q8—861no—
377C22⋊Q8—861no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×D4—431no—
381C4×D4—431no—
382C4×D4—431no—
383C4×D4—861no—
384C4×D4—861no—
385C4×D4C22×D4311yescharacteristic
386#117—861no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C42—431no—
392#107—21no—
393#107—21no—
394#107—861no—
395#107—861no—
396#107—861no—
397#107—861no—
398#106—21no—
399#106—21no—
400#106—861no—
401#106—861no—
402#106—861no—
403#106—861no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8C22×D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
413C4⋊C8C22×D4311yescharacteristic
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#102—21no—
419#102—21no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426C22⋊C8—21no—
427C22⋊C8—431no—
428C22⋊C8—431no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C4×C8—431no—
434C4×C8—861no—
435C4×C8C22×D4311yescharacteristic
436C24—861no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—3442no—
442C2×Q8—1721no—
443C2×D4—434no—
444C2×D4—431no—
445C2×D4—862no—
446C2×D4—861no—
447C2×D4D4×D4311yescharacteristic
448C22×C4—21no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—3441no—
457C22×C4—3441no—
458C22×C4—1721no—
459M16—1722no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—81no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—3441no—
470C2×C8—3441no—
471C2×C8—3441no—
472C2×C8—1722no—
473C2×C8D4×D4311yescharacteristic
474C2×C8D4×D4311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—431no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—1721no—
486C4⋊C4—1721no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C4⋊C4D4×D4311yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C22⋊C4—861no—
494C22⋊C4—1721no—
495C42—431no—
496C42—431no—
497C42—431no—
498C42—1721no—
499C42C23×D4311yescharacteristic
500C23—21no—
501C23—431no—
502C23—864no—
503C23—861no—
504C23—3441no—
505C23—3441no—
506Q8—81no—
507Q8—81no—
508Q8—3441no—
509Q8—3442no—
510Q8—1721no—
511Q8—1721no—
512D4—21no—
513D4—432no—
514D4—864no—
515D4—861no—
516D4Q16×D4312yes—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—431no—
523C2×C4—432no—
524C2×C4—432no—
525C2×C4—431no—
526C2×C4—431no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—3441no—
531C2×C4—3441no—
532C2×C4—3442no—
533C2×C4—3441no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4C2×D4×D4311yescharacteristic
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4#41×D4311yescharacteristic
542C8—21no—
543C8—21no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—861no—
548C8—861no—
549C8—1721no—
550C8—1721no—
551C8—1721no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—432no—
556C22—861no—
557C22—861no—
558C22—862no—
559C22—3444no—
560C22—1721no—
561C22—1721no—
562C22#121×D4311yescharacteristic
563C4—21no—
564C4—41no—
565C4—81no—
566C4—81no—
567C4—432no—
568C4—861no—
569C4—861no—
570C4—3441no—
571C4—3441no—
572C4—1721no—
573C4C2×Q16×D4311yescharacteristic
574C4#135×D4311yescharacteristic
575C4#1458370511yescharacteristic
576C4#1458370811yescharacteristic
577C2—42no—
578C2—862no—
579C2—1722no—
580C2#1914410211yescharacteristic
581C2#467×D4311yescharacteristic
582C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1675C2
socleC22×C43C2×#121
prime radicalC2×D4×D43D4
hypercenter#1675D43
hypocenterC43#19393
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1675

Complements

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

NH ≅ G/Ntype
1. #19145747C2semidirect
5. #19134049C2semidirect
6. #19134048C2semidirect
7. #19134047C2semidirect
8. #19134046C2semidirect
9. #19133993C2semidirect
10. #19133992C2semidirect
11. #19133991C2semidirect
12. #19133368C2semidirect
13. #19133274C2semidirect
14. #19133249C2semidirect
15. C43×#1675C2semidirect
19. #14583302C22semidirect
20. #14583251C22semidirect
21. #14583250C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582648C22semidirect
55. #14582648C22semidirect
56. #14582647C22semidirect
57. #14582647C22semidirect
58. #14582646C22semidirect
59. #14582644C22semidirect
60. C43×#500C22semidirect
64. C43×#335C22semidirect
65. C43×#333C22semidirect
66. C43×#333C22semidirect
297. #1675D43semidirect
311. #500C2×D43semidirect
349. #335C2×D43semidirect
354. #333C2×D43semidirect
355. #333C2×D43semidirect
358. C43#19393semidirect

Maximal subgroups

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

subgroupindex
#191457472
#191443932
#476×D432
#191436162
#191340492
#191340482
#191340472
#191340462
#191339932
#191339922
#191339912
#191333682
#191332742
#191332492
C43×#16752
#1939343