Finite Group Databasebeta

← #25253182

Subgroups — #25253182

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583335C211yesmaximal, characteristic, complemented
2C2×#14583334C211yesmaximal, characteristic, complemented
3#19146282C211yesmaximal, characteristic, complemented
4#19136854C211yesmaximal, characteristic, complemented
5#19136710C211yesmaximal, characteristic, complemented
6#19136706C211yesmaximal, characteristic, complemented
7#19136650C211yesmaximal, characteristic, complemented
8#19136647C211yesmaximal, characteristic, complemented
9#19136535C211yesmaximal, characteristic, complemented
10#19136533C211yesmaximal, characteristic, complemented
11#19136507C211yesmaximal, characteristic, complemented
12#19136506C211yesmaximal, characteristic, complemented
13C4×#13063266C211yesmaximal, characteristic, complemented
14#19136427C211yesmaximal, characteristic, complemented
15C43×#3280C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C22×D344C2211yescharacteristic, complemented
18#14583545—21no—
19#14583335—24no—
20#14583334—24no—
21C2×#13063271C2211yescharacteristic, complemented
22C2×#13063269C2211yescharacteristic, complemented
23C2×#13063269C2211yescharacteristic, complemented
24C2×#13063268C2211yescharacteristic, complemented
25C2×#13063268C2211yescharacteristic, complemented
26C2×#13063266C2211yescharacteristic
27C2×#13063266C2211yescharacteristic
28C2×#13063266C2211yescharacteristic
29C2×#13063266C2211yescharacteristic
30C2×#13063265C2211yescharacteristic, complemented
31C2×#13063265C2211yescharacteristic, complemented
32#14583283C2211yescharacteristic, complemented
33#14583140C2211yescharacteristic, complemented
34#14583135C2211yescharacteristic
35#14583115—21no—
36#14583052—21no—
37#14583046—21no—
38C4×D344C2211yescharacteristic, complemented
39#14582724C2211yescharacteristic, complemented
40C4⋊(C43⋊C16)C2211yescharacteristic, complemented
41#14582703C2211yescharacteristic, complemented
42#14582702C2211yescharacteristic, complemented
43#14582700C2211yescharacteristic, complemented
44#14582700C2211yescharacteristic, complemented
45#14582699C2211yescharacteristic, complemented
46#14582699C2211yescharacteristic, complemented
47C22⋊(C43⋊C16)C2211yescharacteristic, complemented
48C22⋊(C43⋊C16)C2211yescharacteristic, complemented
49C4×C43⋊C16C2211yescharacteristic, complemented
50C2×#135×C43C2211yescharacteristic
51C22×D8×C43C2211yescharacteristic, complemented
52C43×#546—21no—
53C43×#495C2211yescharacteristic, complemented
54C43×#467C2211yescharacteristic, complemented
55C43×#466C2211yescharacteristic
56C43×#463—21no—
57C43×#450—21no—
58C43×#449—21no—
59C4×D8×C43C2211yescharacteristic, complemented
60C8×D4×C43C2211yescharacteristic
61C2×#10621898—21no—
62C22×D172—21no—
63#13063347—22no—
64#13063347—41no—
65C2×Dic172C2311yescharacteristic
66C2×#10621873—21no—
67C2×#10621873—21no—
68C2×D344—22no—
69C2×D344—21no—
70C2×D344—41no—
71C2×D344C2311yescharacteristic
72C2×D344C2311yescharacteristic
73#13063313—21no—
74#13063310—41no—
75#13063304—21no—
76#13063299—21no—
77#13063298—41no—
78#13063293—41no—
79C4×D172—21no—
80C22⋊C4×D43—41no—
81#13063271—41no—
82#13063269—22no—
83#13063269—22no—
84#13063268—22no—
85#13063268—22no—
86#13063266—22no—
87#13063266—22no—
88#13063266—41no—
89#13063266D414yescomplemented
90#13063265—22no—
91#13063265—22no—
92C2×C43⋊C16C2311yescharacteristic
93C2×C43⋊C16C2311yescharacteristic
94C2×C43⋊C16C2311yescharacteristic
95C2×C43⋊C16C2311yescharacteristic
96#13063259C2311yescharacteristic
97#13063250—21no—
98#13063247—21no—
99#13063247—21no—
100C2×#41×C43—21no—
101C22×D4×C43—21no—
102#135×C43—22no—
103#135×C43—41no—
104C2×Q16×C43C2311yescharacteristic
105C2×SD16×C43—21no—
106C2×SD16×C43—21no—
107C2×D8×C43—22no—
108C2×D8×C43—21no—
109C2×D8×C43—41no—
110C2×D8×C43C2311yescharacteristic
111C2×D8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114#124×C43—21no—
115#123×C43—41no—
116C22⋊Q8×C43—21no—
117#121×C43—21no—
118#121×C43—41no—
119#120×C43—41no—
120C4×D4×C43—21no—
121C4×D4×C43D411yescharacteristic
122C2×C22⋊C4×C43—41no—
123#107×C43C2311yescharacteristic
124C4⋊C8×C43D411yescharacteristic
125#103×C43—21no—
126#102×C43—21no—
127#102×C43—21no—
128C22⋊C8×C43D411yescharacteristic
129C22⋊C8×C43D411yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C24×C43—41no—
132C23×D43—41no—
133#41×C43—42no—
134#41×C43—81no—
135C2×Q8×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—41no—
139C2×D4×C43—41no—
140C2×D4×C43—41no—
141C2×D4×C43—42no—
142C2×D4×C43—81no—
143C2×D4×C43D811yescharacteristic
144C22×C4×C43—41no—
145C22×C4×C43—41no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C2×C22⋊D43—41no—
149C2×C22⋊D43—41no—
150#10621898—42no—
151#10621898—81no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—41no—
155C2×D172—42no—
156C2×D172—81no—
157C2×C4×D43—41no—
158C2×C4×D43—41no—
159C2×Dic86—21no—
160Q16×C43—21no—
161Q16×C43—21no—
162SD16×C43—42no—
163SD16×C43—81no—
164D8×C43—21no—
165D8×C43—21no—
166D8×C43—21no—
167D8×C43—42no—
168D8×C43C2×D412yes—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43D811yescharacteristic
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43D811yescharacteristic
186C22⋊C4×C43D811yescharacteristic
187C42×C43C2×D411yescharacteristic
188C22⋊Dic43—41no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—41no—
193C4⋊Dic43—21no—
194Dic43⋊C4—41no—
195Dic172—21no—
196Dic172—21no—
197D344—21no—
198D344—21no—
199D344—21no—
200D344—42no—
201D344C2×D412yes—
202#10621873—42no—
203#10621873—81no—
204C43⋊C16—21no—
205C43⋊C16—21no—
206C43⋊C16—21no—
207C43⋊C16C2×D412yes—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—82no—
211C23×C43—82no—
212C23×C43—161no—
213C23×C43C2×D811yescharacteristic
214C23×C43C2×D811yescharacteristic
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—82no—
218C22×D43—82no—
219C22×D43—161no—
220Q8×C43—41no—
221Q8×C43—41no—
222D4×C43—22no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—82no—
228D4×C43—82no—
229D4×C43—161no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—82no—
237C2×C4×C43—161no—
238C2×C4×C43C2×D811yescharacteristic
239C2×C4×C43C2×D811yescharacteristic
240C2×C4×C43C2×D811yescharacteristic
241C2×C4×C43C2×D811yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C22⋊D43—82no—
244C22⋊D43—161no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247D172—22no—
248D172—41no—
249D172—41no—
250D172—41no—
251D172—82no—
252C4×D43—82no—
253C4×D43—161no—
254Dic86—41no—
255Dic86—41no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43C22×D411yescharacteristic
260C8×C43H(5,𝔽2)11yescharacteristic
261#33839—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—42no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—164no—
275C22×C43C22×D811yescharacteristic
276C2×D43—42no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—164no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43D4211yescharacteristic
290C4×C43#57611yescharacteristic
291Dic43—81no—
292Dic43—81no—
293C2×#509—431no—
294C2×#509—431no—
295#3280—431no—
296#3280D4311yescharacteristic, complemented
297#2249—431no—
298#2220—431no—
299#2220—431no—
300#2210—431no—
301#2210—431no—
302#2189—431no—
303#2189—431no—
304#2184—431no—
305#2184—431no—
306C4×D16—431no—
307#2169—431no—
308C2×C43—41no—
309C2×C43—41no—
310C2×C43—82no—
311C2×C43—161no—
312C2×C43D4×D811yescharacteristic
313C2×C43#341411yescharacteristic
314C2×C43#341511yescharacteristic
315D43—82no—
316D43—161no—
317C2×#135—431no—
318C2×#135C2×D4311yescharacteristic
319C22×D8—431no—
320C22×D8C2×D4311yescharacteristic, complemented
321#546—21no—
322#546—861no—
323#509—864no—
324#509—864no—
325C2×Q32—431no—
326C2×SD32—431no—
327C2×SD32—431no—
328C2×SD32—431no—
329C2×SD32—431no—
330C2×D16—431no—
331C2×D16—431no—
332C2×D16—431no—
333C2×D16—431no—
334C2×M32—431no—
335C2×M32—431no—
336#495—431no—
337#495C2×D4311yescharacteristic, complemented
338#467—431no—
339#467C2×D4311yescharacteristic, complemented
340#466—431no—
341#466C2×D4311yescharacteristic
342#463—21no—
343#463—861no—
344#450—21no—
345#450—861no—
346#449—21no—
347#449—861no—
348C4×D8—431no—
349C4×D8C2×D4311yescharacteristic, complemented
350C8×D4C2×D4311yescharacteristic
351#366—431no—
352C4⋊C16—431no—
353#358—431no—
354#358—431no—
355#357—431no—
356#357—431no—
357#357—431no—
358#357—431no—
359C22⋊C16—431no—
360C22⋊C16—431no—
361C4×C16—431no—
362C43#3383911yescharacteristic, complemented, Sylow
363C2×#41—21no—
364C2×#41—861no—
365C22×D4—21no—
366C22×D4—861no—
367#135—22no—
368#135—41no—
369#135—862no—
370#135—1721no—
371C2×Q16—431no—
372C2×Q16C22×D4311yescharacteristic
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—861no—
376C2×SD16—861no—
377C2×D8—22no—
378C2×D8—21no—
379C2×D8—41no—
380C2×D8—431no—
381C2×D8—431no—
382C2×D8—862no—
383C2×D8—861no—
384C2×D8—1721no—
385C2×D8C22×D4311yescharacteristic
386C2×D8C22×D4311yescharacteristic
387C22×C8C22×D4311yescharacteristic
388C22×C8C22×D4311yescharacteristic
389#124—21no—
390#124—861no—
391#123—41no—
392#123—1721no—
393C22⋊Q8—21no—
394C22⋊Q8—861no—
395#121—21no—
396#121—41no—
397#121—861no—
398#121—1721no—
399#120—41no—
400#120—1721no—
401C4×D4—21no—
402C4×D4—861no—
403C4×D4C22⋊D4311yescharacteristic
404C2×C22⋊C4—41no—
405C2×C22⋊C4—1721no—
406Q32—1721no—
407SD32—862no—
408SD32—862no—
409SD32—862no—
410SD32—862no—
411D16—434no—
412D16—862no—
413D16—862no—
414D16—1721no—
415M32—862no—
416M32—862no—
417C2×C16—431no—
418C2×C16—431no—
419C2×C16—431no—
420C2×C16—431no—
421#107—431no—
422#107C22×D4311yescharacteristic
423C4⋊C8C22⋊D4311yescharacteristic
424#103—21no—
425#103—861no—
426#102—21no—
427#102—21no—
428#102—861no—
429#102—861no—
430C22⋊C8C22⋊D4311yescharacteristic
431C22⋊C8C22⋊D4311yescharacteristic
432C4×C8C22×D4311yescharacteristic
433C24—41no—
434C24—1721no—
435#41—42no—
436#41—81no—
437#41—3441no—
438#41—1722no—
439C2×Q8—21no—
440C2×Q8—861no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—42no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—81no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—3441no—
451C2×D4—1722no—
452C2×D4—1721no—
453C2×D4—1721no—
454C2×D4—1721no—
455C2×D4#1062188211yescharacteristic
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—1721no—
459C22×C4—1721no—
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462Q16—21no—
463Q16—21no—
464Q16—861no—
465Q16—861no—
466SD16—42no—
467SD16—81no—
468SD16—3441no—
469SD16—1722no—
470D8—21no—
471D8—21no—
472D8—21no—
473D8—42no—
474D8—432no—
475D8—861no—
476D8—861no—
477D8—861no—
478D8—1722no—
479D8D4×D4312yes—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8C2×C22⋊D4311yescharacteristic
485C2×C8C2×C22⋊D4311yescharacteristic
486C2×C8C2×C22⋊D4311yescharacteristic
487C2×C8C23×D4311yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—861no—
491C4⋊C4—1721no—
492C4⋊C4#1062188211yescharacteristic
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—1721no—
499C22⋊C4—1721no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C22⋊C4#1062188211yescharacteristic
504C22⋊C4#1062188211yescharacteristic
505C42C2×C22⋊D4311yescharacteristic
506C16—432no—
507C16—861no—
508C16—861no—
509C16—861no—
510C23—41no—
511C23—41no—
512C23—82no—
513C23—82no—
514C23—161no—
515C23—3442no—
516C23—3442no—
517C23—1721no—
518C23—1721no—
519C23—6881no—
520C23C2×#1062188211yescharacteristic
521C23C2×#1062188211yescharacteristic
522Q8—41no—
523Q8—41no—
524Q8—1721no—
525Q8—1721no—
526D4—22no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—82no—
532D4—82no—
533D4—161no—
534D4—862no—
535D4—3442no—
536D4—3442no—
537D4—1721no—
538D4—1721no—
539D4—1721no—
540D4—6881no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4—161no—
549C2×C4—3442no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—6881no—
553C2×C4C2×#1062188211yescharacteristic
554C2×C4C2×#1062188211yescharacteristic
555C2×C4C2×#1062188211yescharacteristic
556C2×C4C2×#1062188211yescharacteristic
557C2×C4C22×C22⋊D4311yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8C2×D4×D4311yescharacteristic
562C8#1306337011yescharacteristic
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—42no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—164no—
576C22—3441no—
577C22—3441no—
578C22—3441no—
579C22—3441no—
580C22—3441no—
581C22—1722no—
582C22—6884no—
583C22C22×#1062188211yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—81no—
589C4—81no—
590C4—3441no—
591C4—3441no—
592C4D4×C22⋊D4311yescharacteristic
593C4#1458370211yescharacteristic
594C2—41no—
595C2—41no—
596C2—82no—
597C2—161no—
598C2—3442no—
599C2—6881no—
600C2D4×#1062188211yescharacteristic
601C2#1914772911yescharacteristic
602C2#1914773411yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3280C2
socleC22×C43C22×D8
hypercenter#3280D43
hypocenterC43#33839
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. C2×#14583335C2semidirect
2. C2×#14583334C2semidirect
3. #19146282C2semidirect
4. #19136854C2semidirect
5. #19136710C2semidirect
6. #19136706C2semidirect
7. #19136650C2semidirect
8. #19136647C2semidirect
9. #19136535C2semidirect
10. #19136533C2semidirect
11. #19136507C2semidirect
12. #19136506C2semidirect
13. C4×#13063266C2semidirect
14. #19136427C2semidirect
15. C43×#3280C2semidirect
17. C22×D344C22semidirect
21. C2×#13063271C22semidirect
22. C2×#13063269C22semidirect
23. C2×#13063269C22semidirect
24. C2×#13063268C22semidirect
25. C2×#13063268C22semidirect
30. C2×#13063265C22semidirect
31. C2×#13063265C22semidirect
32. #14583283C22semidirect
33. #14583140C22semidirect
38. C4×D344C22semidirect
39. #14582724C22semidirect
40. C4⋊(C43⋊C16)C22semidirect
41. #14582703C22semidirect
42. #14582702C22semidirect
43. #14582700C22semidirect
44. #14582700C22semidirect
45. #14582699C22semidirect
46. #14582699C22semidirect
47. C22⋊(C43⋊C16)C22semidirect
48. C22⋊(C43⋊C16)C22semidirect
49. C4×C43⋊C16C22semidirect
51. C22×D8×C43C22semidirect
53. C43×#495C22semidirect
54. C43×#467C22semidirect
59. C4×D8×C43C22semidirect
89. #13063266D4semidirect
296. #3280D43semidirect
320. C22×D8C2×D43semidirect
337. #495C2×D43semidirect
339. #467C2×D43semidirect
349. C4×D8C2×D43semidirect
362. C43#33839semidirect

Maximal subgroups

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

subgroupindex
C2×#145833352
C2×#145833342
#191462822
#191368542
#191367102
#191367062
#191366502
#191366472
#191365352
#191365332
#191365072
#191365062
C4×#130632662
#191364272
C43×#32802
#3383943