Finite Group Databasebeta

← #25253088

Subgroups — #25253088

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583340C211yesmaximal, characteristic, complemented
2C2×SD32×D43C211yesmaximal, characteristic, complemented
3Q16×C22⋊D43C211yesmaximal, characteristic, complemented
4#19146283C211yesmaximal, characteristic
5#19136865C211yesmaximal, characteristic, complemented
6#19136706C211yesmaximal, characteristic, complemented
7#19136685C211yesmaximal, characteristic, complemented
8#19136655C211yesmaximal, characteristic, complemented
9#19136639C211yesmaximal, characteristic, complemented
10#19136537C211yesmaximal, characteristic, complemented
11#19136530C211yesmaximal, characteristic, complemented
12#19136522C211yesmaximal, characteristic, complemented
13#19136462C211yesmaximal, characteristic, complemented
14#19136423C211yesmaximal, characteristic, complemented
15C43×#2185C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C2×Q16×D43C2211yescharacteristic
18C2×D8×D43C2211yescharacteristic
19Q8×C22⋊D43—21no—
20#14583546—21no—
21#14583340—24no—
22C2×Dic344C2211yescharacteristic, complemented
23C2×#13063271C2211yescharacteristic, complemented
24C2×#13063271C2211yescharacteristic, complemented
25C2×#13063270C2211yescharacteristic
26C2×#13063269C2211yescharacteristic
27C2×#13063268C2211yescharacteristic
28C2×#13063268C2211yescharacteristic
29SD32×D43—24no—
30C2×#13063265C2211yescharacteristic, complemented
31C2×C16×D43C2211yescharacteristic
32#14583282C2211yescharacteristic
33#14583277C2211yescharacteristic, complemented
34#14583141C2211yescharacteristic
35#14583140C2211yescharacteristic, complemented
36#14583137C2211yescharacteristic
37#14583113—21no—
38#14583107—21no—
39#14583055—21no—
40#14583053—21no—
41#14583051—21no—
42#14583042—21no—
43Q16×Dic43C2211yescharacteristic, complemented
44#14582981C2211yescharacteristic
45C8×C22⋊D43C2211yescharacteristic
46#14582724C2211yescharacteristic, complemented
47Dic43⋊C16C2211yescharacteristic, complemented
48#14582704C2211yescharacteristic, complemented
49#14582702C2211yescharacteristic, complemented
50#14582701C2211yescharacteristic
51#14582700C2211yescharacteristic
52(C2×D43)⋊C16C2211yescharacteristic
53#14582674C2211yescharacteristic, complemented
54C22×Q16×C43C2211yescharacteristic, complemented
55C2×SD32×C43C2211yescharacteristic
56C2×SD32×C43C2211yescharacteristic
57C43×#466C2211yescharacteristic
58C43×#358C2211yescharacteristic, complemented
59C43×#358C2211yescharacteristic, complemented
60C43×C22⋊C16C2211yescharacteristic, complemented
61C2×#10621898—21no—
62C2×Q8×D43—21no—
63C2×D4×D43—21no—
64#13063347—22no—
65#13063347—41no—
66C2×Dic172C2311yescharacteristic
67C2×Dic172C2311yescharacteristic
68C2×#10621885—21no—
69C2×#10621885—21no—
70Q16×D43—22no—
71Q16×D43—41no—
72C2×#10621873—21no—
73C2×#10621883—21no—
74C2×D344C2311yescharacteristic
75C2×#10621882—21no—
76D8×D43—22no—
77D8×D43—41no—
78C2×C8×D43C2311yescharacteristic
79#13063323—21no—
80#13063323—41no—
81#13063312—21no—
82#13063307—41no—
83#13063305—21no—
84#13063304—21no—
85#13063304—41no—
86#13063301—21no—
87#13063301—41no—
88#13063296—41no—
89#13063293—41no—
90Q8×Dic43—21no—
91#13063287—21no—
92C4×C22⋊D43—41no—
93C4×C22⋊D43D411yescharacteristic
94C22⋊C4×D43—41no—
95Dic344—41no—
96#13063271—22no—
97#13063271—22no—
98#13063270—22no—
99#13063269—22no—
100#13063268—22no—
101#13063268D414yescomplemented
102#13063265—22no—
103C2×C43⋊C16C2311yescharacteristic
104C2×C43⋊C16C2311yescharacteristic
105C16×D43—22no—
106#13063259C2311yescharacteristic
107Dic43⋊C8D411yescharacteristic
108#13063250—21no—
109#13063249—21no—
110#13063249—21no—
111#13063248—21no—
112#13063245—21no—
113C22⋊(C43⋊C8)D411yescharacteristic
114(C2×D43)⋊C8D411yescharacteristic
115C8×Dic43C2311yescharacteristic
116C22×Q8×C43—21no—
117C2×Q16×C43—22no—
118C2×Q16×C43—21no—
119C2×Q16×C43—41no—
120C2×Q16×C43C2311yescharacteristic
121C2×Q16×C43C2311yescharacteristic
122C2×D8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124#121×C43—21no—
125SD32×C43—22no—
126SD32×C43—41no—
127C2×C16×C43C2311yescharacteristic
128C2×C16×C43C2311yescharacteristic
129#107×C43C2311yescharacteristic
130#102×C43—21no—
131C23×D43—41no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—42no—
135C2×Q8×C43—41no—
136C2×Q8×C43—81no—
137C2×D4×C43—21no—
138C2×D4×C43—41no—
139C22×C4×C43—41no—
140C22×C4×C43C2×D411yescharacteristic
141C2×C22⋊D43—41no—
142C2×C22⋊D43—41no—
143C2×C22⋊D43D811yescharacteristic
144Q8×D43—42no—
145Q8×D43—81no—
146D4×D43—42no—
147D4×D43—81no—
148#10621898—42no—
149#10621898—81no—
150C2×D172—21no—
151C2×C4×D43—41no—
152C2×C4×D43—41no—
153C2×C4×D43—41no—
154C2×C4×D43C2×D411yescharacteristic
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—41no—
158Q16×C43—21no—
159Q16×C43—21no—
160Q16×C43—21no—
161Q16×C43—42no—
162Q16×C43C2×D412yes—
163D8×C43—21no—
164D8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2411yescharacteristic
169C4⋊C4×C43—21no—
170C22⋊C4×C43—41no—
171C22⋊Dic43—41no—
172C22⋊Dic43—41no—
173C22⋊Dic43—41no—
174C22⋊Dic43D811yescharacteristic
175#10621885—42no—
176#10621885—81no—
177#10621883—81no—
178#10621882—42no—
179(C2×D43)⋊C4—41no—
180(C2×D43)⋊C4—41no—
181(C2×D43)⋊C4—41no—
182(C2×D43)⋊C4D811yescharacteristic
183C4⋊Dic43—21no—
184C4⋊Dic43—41no—
185C4⋊Dic43—41no—
186Dic43⋊C4—41no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190Dic43⋊C4D811yescharacteristic
191C4×Dic43—41no—
192C4×Dic43C2×D411yescharacteristic
193C2×C43⋊C8C2×D411yescharacteristic
194C2×C43⋊C8C2×D411yescharacteristic
195Dic172—21no—
196Dic172—21no—
197Dic172—21no—
198Dic172—21no—
199D344—21no—
200D344C2×D412yes—
201#10621873—42no—
202C8×D43—21no—
203C8×D43—21no—
204C16×C43—21no—
205C16×C43—21no—
206C43⋊C16—21no—
207C43⋊C16C2×D412yes—
208C23×C43—41no—
209C23×C43C2×D811yescharacteristic
210C22×D43—41no—
211C22×D43—82no—
212C22×D43—82no—
213C22×D43—161no—
214C22×D43C2×D811yescharacteristic
215Q8×C43—22no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—82no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—161no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—82no—
229C2×C4×C43C2×D811yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C22⋊D43—22no—
232C22⋊D43—82no—
233C22⋊D43—82no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43C2×D811yescharacteristic
238C2×Dic43C2×D811yescharacteristic
239C2×Dic43C2×D811yescharacteristic
240D172—22no—
241D172—41no—
242C4×D43—21no—
243C4×D43—21no—
244C4×D43—82no—
245C4×D43—82no—
246C4×D43—161no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—41no—
251Dic86—82no—
252C8×C43—21no—
253C8×C43C22×D411yescharacteristic
254C8×C43H(5,𝔽2)11yescharacteristic
255C43⋊C8—21no—
256C43⋊C8—21no—
257#33832—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43C22×D811yescharacteristic
265C2×D43—21no—
266C2×D43—21no—
267C2×D43—42no—
268C2×D43—81no—
269C2×D43—81no—
270C2×D43—164no—
271C2×D43#51012yescomplemented
272C4×C43—21no—
273C4×C43—42no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43D4211yescharacteristic
277C4×C43#57611yescharacteristic
278Dic43—21no—
279Dic43—21no—
280Dic43—21no—
281Dic43—81no—
282Dic43—81no—
283Dic43—81no—
284C2×#510—431no—
285C22×SD32—431no—
286D4×Q16—431no—
287#3280—431no—
288#2251—431no—
289#2220—431no—
290#2216—431no—
291#2211—431no—
292#2208—431no—
293#2189—431no—
294#2188—431no—
295#2187—431no—
296#2185D4311yescharacteristic, complemented
297#2175—431no—
298#2168—431no—
299C2×C43—41no—
300C2×C43—161no—
301C2×C43D4×D811yescharacteristic
302C2×C43C2×#51011yescharacteristic
303C2×C43#341611yescharacteristic
304D43—22no—
305D43—82no—
306C2×#135—431no—
307C22×Q16—431no—
308C22×Q16C2×D4311yescharacteristic, complemented
309C22×D8—431no—
310D4×Q8—861no—
311#546—861no—
312#510—864no—
313C2×Q32—431no—
314C2×Q32—431no—
315C2×Q32—431no—
316C2×SD32—431no—
317C2×SD32—431no—
318C2×SD32—431no—
319C2×SD32—431no—
320C2×SD32—864no—
321C2×SD32C2×D4311yescharacteristic
322C2×SD32C2×D4311yescharacteristic
323C2×M32—431no—
324C22×C16—431no—
325#495—431no—
326#494—431no—
327#467—431no—
328#467—431no—
329#467—431no—
330#466C2×D4311yescharacteristic
331#463—861no—
332#462—861no—
333#451—861no—
334#451—861no—
335#450—861no—
336#449—861no—
337C4×Q16—431no—
338C4×D8—431no—
339C8×D4—431no—
340#366—431no—
341C4⋊C16—431no—
342#358—431no—
343#358—431no—
344#358C2×D4311yescharacteristic, complemented
345#358C2×D4311yescharacteristic, complemented
346#357—431no—
347#357—431no—
348C22⋊C16—431no—
349C22⋊C16C2×D4311yescharacteristic, complemented
350#346—431no—
351C43#3383211yescharacteristic, complemented, Sylow
352C2×#41—861no—
353C22×Q8—21no—
354C22×Q8—861no—
355C22×D4—861no—
356#135—862no—
357#135—1721no—
358C2×Q16—22no—
359C2×Q16—21no—
360C2×Q16—41no—
361C2×Q16—431no—
362C2×Q16—431no—
363C2×Q16—861no—
364C2×Q16—861no—
365C2×Q16—862no—
366C2×Q16—1721no—
367C2×Q16C22×D4311yescharacteristic
368C2×Q16C22×D4311yescharacteristic
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—431no—
372C2×D8—861no—
373C2×D8—862no—
374C2×D8—1721no—
375C2×D8C22×D4311yescharacteristic
376C22×C8—431no—
377C22×C8C22×D4311yescharacteristic
378C4⋊Q8—861no—
379C4⋊Q8—1721no—
380#124—861no—
381#123—1721no—
382C22⋊Q8—861no—
383C22⋊Q8—861no—
384C22⋊Q8—861no—
385C22⋊Q8—1721no—
386C22⋊Q8—1721no—
387#121—21no—
388#121—1721no—
389#120—1721no—
390C4×Q8—861no—
391C4×D4—431no—
392C4×D4—861no—
393C4×D4—1721no—
394C2×C22⋊C4—1721no—
395Q32—862no—
396Q32—862no—
397Q32—1721no—
398SD32—22no—
399SD32—41no—
400SD32—434no—
401SD32—862no—
402SD32—862no—
403SD32—862no—
404M32—862no—
405C2×C16—431no—
406C2×C16—431no—
407C2×C16—862no—
408C2×C16C22×D4311yescharacteristic
409C2×C16C22×D4311yescharacteristic
410#107—431no—
411#107C22×D4311yescharacteristic
412C4⋊C8—431no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#102—21no—
418#102—861no—
419C22⋊C8—431no—
420C22⋊C8—431no—
421C4×C8—431no—
422C24—1721no—
423#41—3441no—
424#41—1722no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—42no—
428C2×Q8—41no—
429C2×Q8—81no—
430C2×Q8—861no—
431C2×Q8—861no—
432C2×Q8—3441no—
433C2×Q8—1721no—
434C2×Q8—1722no—
435C2×D4—21no—
436C2×D4—41no—
437C2×D4—431no—
438C2×D4—861no—
439C2×D4—3441no—
440C2×D4—1721no—
441C2×D4—1722no—
442C2×D4—1721no—
443C22×C4—41no—
444C22×C4—431no—
445C22×C4—1721no—
446C22×C4—1721no—
447C22×C4—1721no—
448C22×C4D4×D4311yescharacteristic
449Q16—21no—
450Q16—21no—
451Q16—21no—
452Q16—42no—
453Q16—861no—
454Q16—861no—
455Q16—861no—
456Q16—861no—
457Q16—3441no—
458Q16—1722no—
459Q16D4×D4312yes—
460SD16—3441no—
461SD16—1722no—
462D8—21no—
463D8—21no—
464D8—432no—
465D8—861no—
466D8—1722no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8D4×D4311yescharacteristic
474C2×C8C23×D4311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—431no—
477C4⋊C4—861no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4—1721no—
484C22⋊C4—41no—
485C22⋊C4—431no—
486C22⋊C4—431no—
487C22⋊C4—1721no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C42—431no—
494C42—1721no—
495C16—21no—
496C16—21no—
497C16—432no—
498C16—861no—
499C23—41no—
500C23—431no—
501C23—3442no—
502C23—3442no—
503C23—1721no—
504C23—6881no—
505C23D8×D4311yescharacteristic
506Q8—22no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—82no—
511Q8—3442no—
512Q8—1721no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516D4—41no—
517D4—41no—
518D4—161no—
519D4—862no—
520D4—862no—
521D4—3442no—
522D4—3442no—
523D4—1721no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4—431no—
531C2×C4—431no—
532C2×C4—431no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—3442no—
536C2×C4—3442no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—6881no—
541C2×C4D8×D4311yescharacteristic
542C2×C4C2×D4×D4311yescharacteristic
543C8—21no—
544C8—861no—
545C8—861no—
546C8C2×D4×D4311yescharacteristic
547C8#1306337011yescharacteristic
548C22—21no—
549C22—21no—
550C22—21no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—432no—
555C22—861no—
556C22—861no—
557C22—3441no—
558C22—3441no—
559C22—1722no—
560C22—6884no—
561C22C2×D8×D4311yescharacteristic
562C4—21no—
563C4—42no—
564C4—81no—
565C4—81no—
566C4—861no—
567C4—861no—
568C4—861no—
569C4—3441no—
570C4—3441no—
571C4—3441no—
572C4#1458353111yescharacteristic
573C4#1458370311yescharacteristic
574C2—41no—
575C2—161no—
576C2—862no—
577C2—3442no—
578C2#1914626511yescharacteristic
579C2#510×D4311yescharacteristic
580C2#1914773711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2185C2
socleC22×C43C22×D8
prime radical#19146283C2
hypercenter#2185D43
hypocenterC43#33832
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2185

Complements

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

NH ≅ G/Ntype
1. C2×#14583340C2semidirect
2. C2×SD32×D43C2semidirect
3. Q16×C22⋊D43C2semidirect
5. #19136865C2semidirect
6. #19136706C2semidirect
7. #19136685C2semidirect
8. #19136655C2semidirect
9. #19136639C2semidirect
10. #19136537C2semidirect
11. #19136530C2semidirect
12. #19136522C2semidirect
13. #19136462C2semidirect
14. #19136423C2semidirect
15. C43×#2185C2semidirect
22. C2×Dic344C22semidirect
23. C2×#13063271C22semidirect
24. C2×#13063271C22semidirect
30. C2×#13063265C22semidirect
33. #14583277C22semidirect
35. #14583140C22semidirect
43. Q16×Dic43C22semidirect
46. #14582724C22semidirect
47. Dic43⋊C16C22semidirect
48. #14582704C22semidirect
49. #14582702C22semidirect
53. #14582674C22semidirect
54. C22×Q16×C43C22semidirect
58. C43×#358C22semidirect
59. C43×#358C22semidirect
60. C43×C22⋊C16C22semidirect
101. #13063268D4semidirect
271. C2×D43#510semidirect
296. #2185D43semidirect
308. C22×Q16C2×D43semidirect
344. #358C2×D43semidirect
345. #358C2×D43semidirect
349. C22⋊C16C2×D43semidirect
351. C43#33832semidirect

Maximal subgroups

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

subgroupindex
C2×#145833402
C2×SD32×D432
Q16×C22⋊D432
#191462832
#191368652
#191367062
#191366852
#191366552
#191366392
#191365372
#191365302
#191365222
#191364622
#191364232
C43×#21852
#3383243