Finite Group Databasebeta

← #25253085

Subgroups — #25253085

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×#14583338C211yesmaximal, characteristic, complemented
2Q16×C22⋊D43C211yesmaximal, characteristic, complemented
3#19146280C211yesmaximal, characteristic
4#19136865C211yesmaximal, characteristic, complemented
5#19136705C211yesmaximal, characteristic, complemented
6#19136686C211yesmaximal, characteristic, complemented
7#19136655C211yesmaximal, characteristic, complemented
8#19136638C211yesmaximal, characteristic, complemented
9#19136532C211yesmaximal, characteristic, complemented
10#19136529C211yesmaximal, characteristic, complemented
11#19136524C211yesmaximal, characteristic, complemented
12#19136510C211yesmaximal, characteristic, complemented
13#19136460C211yesmaximal, characteristic, complemented
14#19136420C211yesmaximal, characteristic, complemented
15C22×SD32×C43C211yesmaximal, characteristic, complemented
16C2×#13063344C2211yescharacteristic
17C2×Q16×D43C2211yescharacteristic, complemented
18Q8×C22⋊D43—21no—
19#14583543—21no—
20#14583338—24no—
21C2×Dic344C2211yescharacteristic, complemented
22C2×#13063271C2211yescharacteristic, complemented
23C2×#13063271C2211yescharacteristic, complemented
24C2×#13063269C2211yescharacteristic
25C2×#13063269C2211yescharacteristic
26C2×#13063264C2211yescharacteristic, complemented
27#14583282C2211yescharacteristic
28#14583277C2211yescharacteristic, complemented
29#14583140C2211yescharacteristic
30#14583140C2211yescharacteristic
31#14583137C2211yescharacteristic, complemented
32#14583132C2211yescharacteristic
33#14583112—21no—
34#14583107—21no—
35#14583055—21no—
36#14583053—21no—
37#14583050—21no—
38#14583041—21no—
39Q16×Dic43C2211yescharacteristic, complemented
40D8×Dic43C2211yescharacteristic
41C8×C22⋊D43C2211yescharacteristic
42#14582725C2211yescharacteristic, complemented
43Dic43⋊C16C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582704C2211yescharacteristic, complemented
46#14582703C2211yescharacteristic, complemented
47#14582703C2211yescharacteristic, complemented
48#14582700C2211yescharacteristic
49#14582700C2211yescharacteristic
50C22⋊(C43⋊C16)C2211yescharacteristic
51(C2×D43)⋊C16C2211yescharacteristic, complemented
52#14582674C2211yescharacteristic, complemented
53C22×Q16×C43C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C2×SD32×C43—24no—
56C2×SD32×C43C2211yescharacteristic
57C2×SD32×C43C2211yescharacteristic
58C2×SD32×C43C2211yescharacteristic
59C2×SD32×C43C2211yescharacteristic
60C22×C16×C43C2211yescharacteristic
61C2×#10621900—21no—
62C2×Q8×D43—21no—
63#13063344—22no—
64#13063344—41no—
65C2×Dic172C2311yescharacteristic
66C2×Dic172C2311yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69Q16×D43—22no—
70Q16×D43—41no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×C8×D43C2311yescharacteristic
74#13063323—21no—
75#13063323—41no—
76#13063312—21no—
77#13063306—41no—
78#13063304—21no—
79#13063304—21no—
80#13063304—41no—
81#13063301—21no—
82#13063301—41no—
83#13063297—41no—
84#13063296—21no—
85#13063294—41no—
86Q8×Dic43—21no—
87D4×Dic43—21no—
88C4×C22⋊D43—41no—
89C4×C22⋊D43D411yescharacteristic
90C2×C22⋊Dic43—41no—
91Dic344—22no—
92#13063271—22no—
93#13063271—41no—
94#13063269—22no—
95#13063269—41no—
96#13063264—22no—
97C2×C43⋊C16C2311yescharacteristic
98C2×C43⋊C16C2311yescharacteristic
99#13063259C2311yescharacteristic
100#13063259C2311yescharacteristic
101Dic43⋊C8D411yescharacteristic
102#13063250—21no—
103#13063250—21no—
104#13063249—21no—
105#13063249—21no—
106#13063246—21no—
107#13063246—21no—
108C22⋊(C43⋊C8)D411yescharacteristic
109(C2×D43)⋊C8D411yescharacteristic
110C8×Dic43C2311yescharacteristic
111C22×Q8×C43—21no—
112C22×D4×C43—21no—
113C2×Q16×C43—22no—
114C2×Q16×C43—21no—
115C2×Q16×C43—41no—
116C2×Q16×C43C2311yescharacteristic
117C2×Q16×C43C2311yescharacteristic
118C2×D8×C43—22no—
119C2×D8×C43—21no—
120C2×D8×C43—41no—
121C2×D8×C43C2311yescharacteristic
122C2×D8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124SD32×C43—22no—
125SD32×C43—22no—
126SD32×C43—22no—
127SD32×C43D414yescomplemented
128C2×C16×C43—22no—
129C2×C16×C43C2311yescharacteristic
130C2×C16×C43C2311yescharacteristic
131C24×C43—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—21no—
139C2×D4×C43—41no—
140C2×D4×C43—42no—
141C2×D4×C43—81no—
142C22×C4×C43—41no—
143C22×C4×C43C2×D411yescharacteristic
144C2×C22⋊D43—41no—
145C2×C22⋊D43—41no—
146C2×C22⋊D43D811yescharacteristic
147C22×Dic43—41no—
148C22×Dic43—41no—
149Q8×D43—42no—
150Q8×D43—81no—
151#10621900—42no—
152#10621900—81no—
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—
165D8×C43—21no—
166D8×C43—42no—
167D8×C43C2×D412yes—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2411yescharacteristic
172C22⋊Dic43—41no—
173C22⋊Dic43—41no—
174C22⋊Dic43—41no—
175C22⋊Dic43—41no—
176C22⋊Dic43—41no—
177C22⋊Dic43—41no—
178C22⋊Dic43D811yescharacteristic
179#10621885—42no—
180#10621885—81no—
181#10621883—42no—
182#10621883—81no—
183(C2×D43)⋊C4—41no—
184(C2×D43)⋊C4D811yescharacteristic
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—41no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4D811yescharacteristic
194C4×Dic43—41no—
195C4×Dic43C2×D411yescharacteristic
196C2×C43⋊C8C2×D411yescharacteristic
197C2×C43⋊C8C2×D411yescharacteristic
198Dic172—21no—
199Dic172—21no—
200Dic172—21no—
201Dic172—21no—
202C8×D43—21no—
203C8×D43—21no—
204C16×C43—21no—
205C16×C43C2×D412yes—
206C43⋊C16—21no—
207C43⋊C16—21no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—82no—
211C23×C43—82no—
212C23×C43—161no—
213C23×C43C2×D811yescharacteristic
214C22×D43C2×D811yescharacteristic
215Q8×C43—22no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—82no—
220D4×C43—22no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—82no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—82no—
230C2×C4×C43C2×D811yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C22⋊D43—22no—
233C22⋊D43—82no—
234C22⋊D43—161no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—82no—
240C2×Dic43—161no—
241C2×Dic43C2×D811yescharacteristic
242C2×Dic43C2×D811yescharacteristic
243C2×Dic43C2×D811yescharacteristic
244C4×D43—21no—
245C4×D43—21no—
246C4×D43—82no—
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—42no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—164no—
267C22×C43#51012yescomplemented
268C22×C43C22×D811yescharacteristic
269C2×D43—21no—
270C2×D43—21no—
271C2×D43—21no—
272C4×C43—21no—
273C4×C43—42no—
274C4×C43—81no—
275C4×C43D4211yescharacteristic
276C4×C43#57611yescharacteristic
277Dic43—21no—
278Dic43—21no—
279Dic43—21no—
280Dic43—81no—
281Dic43—81no—
282Dic43—81no—
283Dic43—81no—
284C2×#510—431no—
285C22×SD32D4311yescharacteristic, complemented
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#2185—431no—
297#2175—431no—
298#2168—431no—
299C2×C43—22no—
300C2×C43—82no—
301C2×C43—161no—
302C2×C43D4×D811yescharacteristic
303C2×C43C2×#51011yescharacteristic
304C2×C43#341611yescharacteristic
305D43—41no—
306C2×#135—431no—
307C22×Q16—431no—
308C22×Q16C2×D4311yescharacteristic
309C22×D8C2×D4311yescharacteristic
310D4×Q8—861no—
311#546—861no—
312#510—864no—
313C2×Q32—431no—
314C2×Q32—431no—
315C2×Q32—431no—
316C2×SD32—24no—
317C2×SD32—431no—
318C2×SD32—431no—
319C2×SD32C2×D4311yescharacteristic
320C2×SD32C2×D4311yescharacteristic
321C2×SD32C2×D4311yescharacteristic
322C2×SD32C2×D4311yescharacteristic
323C2×M32—431no—
324C22×C16C2×D4311yescharacteristic
325#495—431no—
326#494—431no—
327#467—431no—
328#467—431no—
329#467—431no—
330#466—431no—
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#358—431no—
345#358—431no—
346#357—431no—
347#357—431no—
348C22⋊C16—431no—
349C22⋊C16—431no—
350#346—431no—
351C43#3383211yescharacteristic, complemented, Sylow
352C2×#41—861no—
353C22×Q8—21no—
354C22×Q8—861no—
355C22×D4—21no—
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—22no—
372C2×D8—21no—
373C2×D8—41no—
374C2×D8C22×D4311yescharacteristic
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—861no—
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—22no—
400SD32—22no—
401SD32—862no—
402SD32—1721no—
403SD32C22⋊D4314yescomplemented
404M32—862no—
405C2×C16—22no—
406C2×C16—431no—
407C2×C16—431no—
408C2×C16C22×D4311yescharacteristic
409C2×C16C22×D4311yescharacteristic
410#107—431no—
411#107—431no—
412C4⋊C8—431no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#102—861no—
418#102—861no—
419C22⋊C8—431no—
420C22⋊C8—431no—
421C4×C8—431no—
422C24—41no—
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—21no—
437C2×D4—42no—
438C2×D4—41no—
439C2×D4—81no—
440C2×D4—431no—
441C2×D4—1721no—
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—
459Q16C2×C22⋊D4312yes—
460SD16—3441no—
461SD16—1722no—
462D8—21no—
463D8—21no—
464D8—21no—
465D8—42no—
466D8C2×C22⋊D4312yes—
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—431no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4—1721no—
484C22⋊C4—431no—
485C22⋊C4—431no—
486C22⋊C4—1721no—
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—861no—
497C16—861no—
498C16C2×C22⋊D4312yes—
499C23—41no—
500C23—41no—
501C23—82no—
502C23—82no—
503C23—161no—
504C23—431no—
505C23D8×D4311yescharacteristic
506Q8—22no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—82no—
511Q8—3442no—
512Q8—1721no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516D4—22no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—82no—
521D4—862no—
522D4—3442no—
523D4—6881no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—82no—
529C2×C4—431no—
530C2×C4—431no—
531C2×C4—431no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—3442no—
535C2×C4—3442no—
536C2×C4—1721no—
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—
546C8C22×C22⋊D4311yescharacteristic
547C8#1306337011yescharacteristic
548C22—21no—
549C22—21no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—164no—
557C22—861no—
558C22—861no—
559C22—861no—
560C22#1458333812yescomplemented
561C22C2×D8×D4311yescharacteristic
562C4—21no—
563C4—42no—
564C4—81no—
565C4—861no—
566C4—861no—
567C4—861no—
568C4—3441no—
569C4—3441no—
570C4—3441no—
571C4—3441no—
572C4D4×C22⋊D4311yescharacteristic
573C4#1458370011yescharacteristic
574C2—22no—
575C2—82no—
576C2—161no—
577C2—1721no—
578C2D8×C22⋊D4311yescharacteristic
579C2C2×#1458333811yescharacteristic
580C2#1914773711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC22×SD32×C43C2
socleC22×C43C22×D8
prime radical#19146280C2
hypercenterC22×SD32D43
hypocenterC43#33832
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#14583338C2semidirect
2. Q16×C22⋊D43C2semidirect
4. #19136865C2semidirect
5. #19136705C2semidirect
6. #19136686C2semidirect
7. #19136655C2semidirect
8. #19136638C2semidirect
9. #19136532C2semidirect
10. #19136529C2semidirect
11. #19136524C2semidirect
12. #19136510C2semidirect
13. #19136460C2semidirect
14. #19136420C2semidirect
15. C22×SD32×C43C2semidirect
17. C2×Q16×D43C22semidirect
21. C2×Dic344C22semidirect
22. C2×#13063271C22semidirect
23. C2×#13063271C22semidirect
26. C2×#13063264C22semidirect
28. #14583277C22semidirect
31. #14583137C22semidirect
39. Q16×Dic43C22semidirect
42. #14582725C22semidirect
43. Dic43⋊C16C22semidirect
44. #14582704C22semidirect
45. #14582704C22semidirect
46. #14582703C22semidirect
47. #14582703C22semidirect
51. (C2×D43)⋊C16C22semidirect
52. #14582674C22semidirect
127. SD32×C43D4semidirect
267. C22×C43#510semidirect
285. C22×SD32D43semidirect
351. C43#33832semidirect
403. SD32C22⋊D43semidirect
560. C22#14583338semidirect

Maximal subgroups

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

subgroupindex
C2×#145833382
Q16×C22⋊D432
#191462802
#191368652
#191367052
#191366862
#191366552
#191366382
#191365322
#191365292
#191365242
#191365102
#191364602
#191364202
C22×SD32×C432
#3383243