Finite Group Databasebeta

← #25081813

Subgroups — #25081813

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145735C211yesmaximal, characteristic, complemented
2#19144387C211yesmaximal, characteristic
3#461×D43C211yesmaximal, characteristic
4#19143616C211yesmaximal, characteristic
5#19134017C211yesmaximal, characteristic, complemented
6#19134016C211yesmaximal, characteristic, complemented
7#19134015C211yesmaximal, characteristic, complemented
8#19133971C211yesmaximal, characteristic, complemented
9#19133970C211yesmaximal, characteristic, complemented
10#19133969C211yesmaximal, characteristic, complemented
11#19133968C211yesmaximal, characteristic, complemented
12#19133364C211yesmaximal, characteristic, complemented
13#19133265C211yesmaximal, characteristic, complemented
14#19133251C211yesmaximal, characteristic, complemented
15C43×#1679C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17#14583454C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583297C2211yescharacteristic, complemented
21#14583295C2211yescharacteristic, complemented
22#14583249C2211yescharacteristic, complemented
23#14583228—21no—
24#14583228—21no—
25#14583202—21no—
26#14583201—21no—
27#14583190C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583182—21no—
30#14583182—21no—
31#14583176C2211yescharacteristic
32#14583105C2211yescharacteristic
33#14583104C2211yescharacteristic
34#14583103—21no—
35#14583102—21no—
36#14583101C2211yescharacteristic
37C8×D172C2211yescharacteristic
38D4×C43⋊C8C2211yescharacteristic
39#14582964C2211yescharacteristic
40C8×C22⋊D43—21no—
41(C22⋊D43)⋊C8—21no—
42#14582951C2211yescharacteristic
43#14582950C2211yescharacteristic
44#14582940—21no—
45#14582921C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582902—21no—
48#103×D43—21no—
49C2×(C2×D43)⋊C8—21no—
50C22⋊C8×D43—21no—
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582646C2211yescharacteristic, complemented
57#14582645C2211yescharacteristic, complemented
58#14582645C2211yescharacteristic, complemented
59#14582644C2211yescharacteristic, complemented
60C43×#487C2211yescharacteristic, complemented
61C43×#474C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#332C2211yescharacteristic, complemented
67C2×Q8×D43—21no—
68C2×D4×D43D411yescharacteristic
69C22×C4×D43—21no—
70C2×#10621873—21no—
71C2×#10621883—21no—
72C2×#10621884—21no—
73SD16×D43—44no—
74C2×#10621872—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063324—21no—
82#13063324—21no—
83#13063323—21no—
84#13063316—21no—
85#13063305—21no—
86#13063301—21no—
87Q8×Dic43—21no—
88#13063290—21no—
89C4×D172C2311yescharacteristic
90D4×Dic43D411yescharacteristic
91#13063287D411yescharacteristic
92C4×C22⋊D43—21no—
93(C22⋊D43)⋊C4—21no—
94#13063283—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43D411yescharacteristic
98C22⋊C4×D43—21no—
99C42×D43C2311yescharacteristic
100#13063258—21no—
101#13063257—21no—
102#13063257—21no—
103#13063257—21no—
104#13063256—21no—
105#13063256—21no—
106#13063256—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109C4⋊(C43⋊C8)C2311yescharacteristic
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8D411yescharacteristic
113Dic43⋊C8D411yescharacteristic
114#13063250—21no—
115#13063249—21no—
116#13063249—21no—
117#13063249—21no—
118#13063248—21no—
119#13063247—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—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133C4⋊Q8×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#107×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C22×Dic43—21no—
152Q8×D43—42no—
153Q8×D43—42no—
154D4×D43—22no—
155D4×D43SD1614yes—
156C2×D172C2×D411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—41no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×C4×D43C2×D411yescharacteristic
164C2×C4×D43C2×D411yescharacteristic
165C2×C4×D43#4111yescharacteristic
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—41no—
169SD16×C43—42no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—81no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43C2×D411yescharacteristic
181C22⋊C4×C43—21no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—21no—
184#10621884—42no—
185#10621883—42no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—41no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—41no—
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199C4×Dic43—41no—
200C4×Dic43C2×D411yescharacteristic
201C4×Dic43C2×D411yescharacteristic
202C4×Dic43#4111yescharacteristic
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—81no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209#10621873—42no—
210#10621872—42no—
211C8×D43—42no—
212C8×D43—81no—
213C8×D43—81no—
214C23×C43—21no—
215C22×D43—21no—
216C22×D43—24no—
217C22×D43—81no—
218C22×D43—81no—
219C22×D43#12111yescharacteristic
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224D4×C43—21no—
225D4×C43C2×SD1612yes—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C22⋊D43—24no—
235C2×Dic43—21no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—81no—
239C2×Dic43#12111yescharacteristic
240C2×Dic43#12111yescharacteristic
241C2×Dic43#12111yescharacteristic
242D172—21no—
243D172C2×SD1612yes—
244C4×D43—21no—
245C4×D43—21no—
246C4×D43—41no—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—81no—
250C4×D43—81no—
251C4×D43—82no—
252C4×D43C2×SD1612yes—
253C4×D43#13512yes—
254Dic86—41no—
255Dic86—41no—
256Dic86—82no—
257Dic86—81no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#19390—431nomaximal, Sylow
269C22×C43—22no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43C2×#12111yescharacteristic
273C2×D43—21no—
274C2×D43—21no—
275C2×D43—22no—
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—84no—
279C2×D43#46512yes—
280C4×C43—21no—
281C4×C43—41no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43C22×SD1611yescharacteristic
285C4×C43C2×#13511yescharacteristic
286C4×C43#57711yescharacteristic
287C4×C43#57711yescharacteristic
288Dic43—21no—
289Dic43—21no—
290Dic43—41no—
291Dic43—81no—
292Dic43—81no—
293Dic43#46512yes—
294#3229—431no—
295#3077—431no—
296C2×#461—431no—
297#2972—431no—
298#1679—431no—
299#1679—431no—
300#1679—431no—
301#1679D4311yescharacteristic, complemented
302#1671—431no—
303#1671—431no—
304#1671—431no—
305#1671—431no—
306#1570—431no—
307#1546—431no—
308#1542—431no—
309C2×C43—42no—
310C2×C43#304211yescharacteristic
311C2×C43C2×#46511yescharacteristic
312C2×C43#306911yescharacteristic
313D43—22no—
314D43—42no—
315C22×SD16—861no—
316#533—431no—
317C2×C4⋊Q8—431no—
318C2×C4×D4—431no—
319#498—431no—
320#498—431no—
321#487—431no—
322#487C2×D4311yescharacteristic, complemented
323#483—861no—
324#483—861no—
325#478—861no—
326#478—861no—
327#476—431no—
328#476—431no—
329#475—861no—
330#475—861no—
331#474—431no—
332#474C2×D4311yescharacteristic
333#461—431no—
334#461—431no—
335#461—431no—
336#461—861no—
337#461—861no—
338#461C2×D4311yescharacteristic
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—431no—
342C8×D4—861no—
343C8×D4—861no—
344C8×D4C2×D4311yescharacteristic
345#431—431no—
346#431—431no—
347#428—861no—
348#423—431no—
349C2×C4⋊C8—431no—
350#418—861no—
351C2×#103—861no—
352C2×C22⋊C8—861no—
353C2×C22⋊C8—861no—
354#334—431no—
355#334—431no—
356#334—431no—
357#334C2×D4311yescharacteristic, complemented
358#333—431no—
359#333—431no—
360#332—431no—
361#332—431no—
362#332—431no—
363#332—431no—
364#332C2×D4311yescharacteristic, complemented
365#332C2×D4311yescharacteristic, complemented
366C43#1939011yescharacteristic, complemented, Sylow
367C22×Q8—861no—
368C22×D4—431no—
369C23×C4—861no—
370C2×SD16—21no—
371C2×SD16—861no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×SD16—1724no—
375C2×M16—861no—
376C22×C8—21no—
377C22×C8—861no—
378C22×C8—861no—
379C22×C8—861no—
380C22×C8—861no—
381C4⋊Q8—431no—
382C4⋊Q8—431no—
383C4⋊Q8—861no—
384C4⋊Q8—861no—
385C4⋊Q8—861no—
386C4⋊Q8C22×D4311yescharacteristic
387C4⋊Q8C22×D4311yescharacteristic
388#125—861no—
389C22⋊Q8—861no—
390C22⋊Q8—861no—
391C4×Q8—861no—
392C4×Q8—861no—
393C4×D4—431no—
394C4×D4—431no—
395C4×D4—431no—
396C4×D4—861no—
397C4×D4—861no—
398C4×D4C22×D4311yescharacteristic
399#117—861no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C42—431no—
405#107—21no—
406#107—861no—
407#106—861no—
408#106—861no—
409#106—861no—
410#106—861no—
411#106—861no—
412#106—861no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8C22×D4311yescharacteristic
421C4⋊C8C22×D4311yescharacteristic
422C4⋊C8C22×D4311yescharacteristic
423#103—21no—
424#103—21no—
425#103—21no—
426#103—861no—
427#103—861no—
428#103—861no—
429#103—861no—
430#103—861no—
431#102—21no—
432#102—861no—
433#102—861no—
434#102—861no—
435C22⋊C8—21no—
436C22⋊C8—431no—
437C22⋊C8—431no—
438C22⋊C8—861no—
439C22⋊C8—861no—
440C22⋊C8—861no—
441C22⋊C8—861no—
442C4×C8—431no—
443C4×C8—861no—
444C4×C8C22×D4311yescharacteristic
445C24—861no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—1721no—
451C2×Q8—1722no—
452C2×Q8—1722no—
453C2×D4—434no—
454C2×D4—431no—
455C2×D4—862no—
456C2×D4—861no—
457C2×D4D4×D4311yescharacteristic
458C22×C4—21no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—3441no—
467C22×C4—3441no—
468C22×C4—1721no—
469SD16—42no—
470SD16—1722no—
471SD16—1722no—
472SD16—1722no—
473M16—1722no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—81no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—3441no—
484C2×C8—3441no—
485C2×C8—3441no—
486C2×C8—1722no—
487C2×C8D4×D4311yescharacteristic
488C2×C8D4×D4311yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—431no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—1721no—
500C4⋊C4—1721no—
501C4⋊C4—1721no—
502C4⋊C4—1721no—
503C4⋊C4D4×D4311yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C22⋊C4—1721no—
509C42—431no—
510C42—431no—
511C42—431no—
512C42—1721no—
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—431no—
516C23—864no—
517C23—861no—
518C23—3441no—
519C23—3441no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—3441no—
525Q8—3442no—
526Q8—1721no—
527Q8—1721no—
528D4—21no—
529D4—432no—
530D4—864no—
531D4—861no—
532D4SD16×D4312yes—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—431no—
539C2×C4—432no—
540C2×C4—432no—
541C2×C4—431no—
542C2×C4—431no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—3441no—
547C2×C4—3441no—
548C2×C4—3442no—
549C2×C4—3441no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4C2×D4×D4311yescharacteristic
556C2×C4C2×D4×D4311yescharacteristic
557C2×C4#41×D4311yescharacteristic
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—861no—
564C8—861no—
565C8—1721no—
566C8—1721no—
567C8—1721no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—432no—
572C22—861no—
573C22—861no—
574C22—862no—
575C22—3444no—
576C22—1721no—
577C22—1721no—
578C22#121×D4311yescharacteristic
579C4—21no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—432no—
584C4—861no—
585C4—861no—
586C4—3441no—
587C4—3441no—
588C4—1721no—
589C4C2×SD16×D4311yescharacteristic
590C4#135×D4311yescharacteristic
591C4#1458370611yescharacteristic
592C4#1458370911yescharacteristic
593C2—42no—
594C2—862no—
595C2—1722no—
596C2#1914410511yescharacteristic
597C2#465×D4311yescharacteristic
598C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1679C2
socleC22×C43C2×#121
prime radicalC2×D4×D43D4
hypercenter#1679D43
hypocenterC43#19390
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1679

Complements

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

NH ≅ G/Ntype
1. #19145735C2semidirect
5. #19134017C2semidirect
6. #19134016C2semidirect
7. #19134015C2semidirect
8. #19133971C2semidirect
9. #19133970C2semidirect
10. #19133969C2semidirect
11. #19133968C2semidirect
12. #19133364C2semidirect
13. #19133265C2semidirect
14. #19133251C2semidirect
15. C43×#1679C2semidirect
20. #14583297C22semidirect
21. #14583295C22semidirect
22. #14583249C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
56. #14582646C22semidirect
57. #14582645C22semidirect
58. #14582645C22semidirect
59. #14582644C22semidirect
60. C43×#487C22semidirect
64. C43×#334C22semidirect
65. C43×#332C22semidirect
66. C43×#332C22semidirect
301. #1679D43semidirect
322. #487C2×D43semidirect
357. #334C2×D43semidirect
364. #332C2×D43semidirect
365. #332C2×D43semidirect
366. C43#19390semidirect

Maximal subgroups

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

subgroupindex
#191457352
#191443872
#461×D432
#191436162
#191340172
#191340162
#191340152
#191339712
#191339702
#191339692
#191339682
#191333642
#191332652
#191332512
C43×#16792
#1939043