Finite Group Databasebeta

← #25253264

Subgroups — #25253264

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063268C211yesmaximal, characteristic, complemented
2C2×SD32×D43C211yesmaximal, characteristic, complemented
3Q16×C22⋊D43C211yesmaximal, characteristic, complemented
4#19146269C211yesmaximal, characteristic
5#19136849C211yesmaximal, characteristic, complemented
6#19136694C211yesmaximal, characteristic, complemented
7#19136689C211yesmaximal, characteristic, complemented
8#19136639C211yesmaximal, characteristic, complemented
9#19136633C211yesmaximal, characteristic, complemented
10#19136526C211yesmaximal, characteristic, complemented
11#19136522C211yesmaximal, characteristic, complemented
12#19136513C211yesmaximal, characteristic, complemented
13#19136444C211yesmaximal, characteristic, complemented
14(C22⋊D43)⋊C16C211yesmaximal, characteristic, complemented
15C43×#2185C211yesmaximal, characteristic, complemented
16C2×Q16×D43C2211yescharacteristic, complemented
17C22×D344C2211yescharacteristic
18C2×D8×D43C2211yescharacteristic
19Q8×C22⋊D43—21no—
20#14583533—21no—
21C2×#13063270C2211yescharacteristic
22C2×#13063270C2211yescharacteristic, complemented
23C2×#13063269C2211yescharacteristic, complemented
24C2×#13063268—24no—
25C2×#13063268C2211yescharacteristic
26C2×#13063268C2211yescharacteristic
27C2×#13063268C2211yescharacteristic, complemented
28C2×#13063268C2211yescharacteristic, complemented
29SD32×D43—24no—
30C22×C43⋊C16C2211yescharacteristic, complemented
31C2×C16×D43C2211yescharacteristic, complemented
32#14583277C2211yescharacteristic, complemented
33#14583274C2211yescharacteristic
34#14583140C2211yescharacteristic, complemented
35#14583137C2211yescharacteristic, complemented
36#14583136C2211yescharacteristic
37#14583107—21no—
38#14583093—21no—
39#14583055—21no—
40#14583053—21no—
41#14583034—21no—
42#14583032—21no—
43Q16×Dic43C2211yescharacteristic, complemented
44#14582981C2211yescharacteristic
45C8×C22⋊D43C2211yescharacteristic
46#14582726C2211yescharacteristic, complemented
47Dic43⋊C16C2211yescharacteristic, complemented
48#14582702C2211yescharacteristic, complemented
49#14582701C2211yescharacteristic
50#14582701C2211yescharacteristic, complemented
51#14582700C2211yescharacteristic, complemented
52(C2×D43)⋊C16C2211yescharacteristic, complemented
53C16×Dic43C2211yescharacteristic, complemented
54C22×Q16×C43C2211yescharacteristic, complemented
55C2×SD32×C43C2211yescharacteristic, complemented
56C2×SD32×C43C2211yescharacteristic, complemented
57C43×#466C2211yescharacteristic
58C43×#358C2211yescharacteristic, complemented
59C43×#358C2211yescharacteristic, complemented
60C43×C22⋊C16C2211yescharacteristic, complemented
61C2×Q8×D43—21no—
62C22×D172—21no—
63C2×D4×D43—21no—
64C2×D4×D43—41no—
65C2×Dic172C2311yescharacteristic
66C2×#10621885—21no—
67C2×#10621885—21no—
68Q16×D43—22no—
69Q16×D43—41no—
70C2×D344—22no—
71C2×D344—21no—
72C2×D344—41no—
73C2×D344C2311yescharacteristic
74C2×D344C2311yescharacteristic
75C2×#10621882—21no—
76C2×#10621882—21no—
77D8×D43—22no—
78D8×D43—41no—
79C2×C8×D43C2311yescharacteristic
80#13063323—21no—
81#13063323—41no—
82#13063321—21no—
83#13063304—21no—
84#13063304—41no—
85#13063301—21no—
86#13063301—41no—
87#13063300—21no—
88#13063298—41no—
89#13063295—41no—
90#13063293—41no—
91Q8×Dic43—21no—
92#13063287—21no—
93C4×C22⋊D43—41no—
94C4×C22⋊D43D411yescharacteristic
95#13063270—22no—
96#13063270—41no—
97#13063269—22no—
98#13063268—22no—
99#13063268—22no—
100#13063268—22no—
101#13063268D414yescomplemented
102C2×C43⋊C16—22no—
103C2×C43⋊C16C2311yescharacteristic
104C2×C43⋊C16C2311yescharacteristic
105C16×D43—22no—
106#13063259C2311yescharacteristic
107Dic43⋊C8D411yescharacteristic
108#13063250—21no—
109#13063249—21no—
110#13063249—21no—
111#13063245—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—
132C23×D43—41no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—42no—
136C2×Q8×C43—41no—
137C2×Q8×C43—81no—
138C2×D4×C43—21no—
139C2×D4×C43—41no—
140C22×C4×C43—41no—
141C22×C4×C43C2×D411yescharacteristic
142C2×C22⋊D43—41no—
143C2×C22⋊D43—41no—
144C2×C22⋊D43—41no—
145C2×C22⋊D43D811yescharacteristic
146Q8×D43—42no—
147Q8×D43—81no—
148D4×D43—42no—
149D4×D43—81no—
150D4×D43—84no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—41no—
154C2×D172—41no—
155C2×D172—42no—
156C2×D172—81no—
157C2×C4×D43—41no—
158C2×C4×D43—41no—
159C2×C4×D43C2×D411yescharacteristic
160C2×Dic86—21no—
161C2×Dic86—41no—
162Q16×C43—21no—
163Q16×C43—21no—
164Q16×C43—21no—
165Q16×C43—42no—
166Q16×C43C2×D412yescomplemented
167D8×C43—21no—
168D8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2411yescharacteristic
173C4⋊C4×C43—21no—
174C22⋊C4×C43—41no—
175C22⋊Dic43—41no—
176C22⋊Dic43D811yescharacteristic
177#10621885—42no—
178#10621885—81no—
179#10621882—42no—
180#10621882—81no—
181(C2×D43)⋊C4—41no—
182(C2×D43)⋊C4—41no—
183(C2×D43)⋊C4—41no—
184(C2×D43)⋊C4D811yescharacteristic
185C4⋊Dic43—21no—
186C4⋊Dic43—41no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191Dic43⋊C4D811yescharacteristic
192C4×Dic43—41no—
193C4×Dic43C2×D411yescharacteristic
194C2×C43⋊C8C2×D411yescharacteristic
195C2×C43⋊C8C2×D411yescharacteristic
196Dic172—21no—
197Dic172—21no—
198D344—21no—
199D344—21no—
200D344—21no—
201D344—42no—
202D344C2×D412yes—
203C8×D43—21no—
204C8×D43—21no—
205C16×C43—21no—
206C16×C43—21no—
207C43⋊C16—21no—
208C43⋊C16C2×D412yescomplemented
209C23×C43—41no—
210C23×C43C2×D811yescharacteristic
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—82no—
214C22×D43—82no—
215C22×D43—82no—
216C22×D43—82no—
217C22×D43—161no—
218C22×D43—161no—
219C22×D43C2×D811yescharacteristic
220Q8×C43—22no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—82no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—82no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—82no—
234C2×C4×C43C2×D811yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C22⋊D43—82no—
237C22⋊D43—82no—
238C22⋊D43—161no—
239C22⋊D43SD3214yescomplemented
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43C2×D811yescharacteristic
243C2×Dic43C2×D811yescharacteristic
244C2×Dic43C2×D811yescharacteristic
245D172—22no—
246D172—41no—
247D172—41no—
248D172—41no—
249D172—82no—
250D172—82no—
251C4×D43—21no—
252C4×D43—21no—
253C4×D43—82no—
254C4×D43—82no—
255Dic86—41no—
256Dic86—41no—
257Dic86—82no—
258C8×C43—21no—
259C8×C43C22×D411yescharacteristic
260C8×C43H(5,𝔽2)11yescharacteristic
261C43⋊C8—21no—
262C43⋊C8—21no—
263D4×SD32—431nomaximal, Sylow
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43C2×SD3212yescomplemented
270C22×C43C22×D811yescharacteristic
271C2×D43—21no—
272C2×D43—21no—
273C2×D43—42no—
274C2×D43—81no—
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—164no—
280C2×D43—164no—
281C2×D43C2×SD3212yescomplemented
282C4×C43—21no—
283C4×C43—42no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43D4211yescharacteristic
287C4×C43#57611yescharacteristic
288Dic43—21no—
289Dic43—21no—
290Dic43—81no—
291Dic43—81no—
292Dic43C2×SD3212yescomplemented
293C22×SD32—431no—
294C22×SD32—431no—
295D4×Q16—431no—
296D4×D8—431no—
297#2248—431no—
298#2217—431no—
299#2217—431no—
300#2208—431no—
301#2207—431no—
302#2187—431no—
303#2187—431no—
304#2185—431no—
305#2185D4311yescharacteristic, complemented
306C4×SD32—431no—
307D4×C16—431no—
308C2×C43—22no—
309C2×C43—161no—
310C2×C43D4×D811yescharacteristic
311C2×C43C22×SD3211yescharacteristic
312C2×C43#341611yescharacteristic
313D43—22no—
314D43—82no—
315D43—161no—
316C22×Q16—431no—
317C22×Q16C2×D4311yescharacteristic, complemented
318C22×D8—431no—
319C22×D8—431no—
320D4×Q8—861no—
321D42—861no—
322C2×SD32—431no—
323C2×SD32—431no—
324C2×SD32—431no—
325C2×SD32—431no—
326C2×SD32—431no—
327C2×SD32—431no—
328C2×SD32—431no—
329C2×SD32—864no—
330C2×SD32—864no—
331C2×SD32C2×D4311yescharacteristic, complemented
332C2×SD32C2×D4311yescharacteristic, complemented
333C22×C16—431no—
334C22×C16—431no—
335#494—431no—
336#493—431no—
337#467—431no—
338#467—431no—
339#466—431no—
340#466C2×D4311yescharacteristic
341#462—861no—
342#459—861no—
343#451—861no—
344#451—861no—
345#447—861no—
346#447—861no—
347C4×Q16—431no—
348C4×D8—431no—
349C8×D4—431no—
350#367—431no—
351C4⋊C16—431no—
352#358—431no—
353#358C2×D4311yescharacteristic, complemented
354#358C2×D4311yescharacteristic, complemented
355#357—431no—
356#357—431no—
357#357—431no—
358C22⋊C16—431no—
359C22⋊C16C2×D4311yescharacteristic, complemented
360C4×C16—431no—
361C43D4×SD3211yescharacteristic, complemented, Sylow
362C22×Q8—21no—
363C22×Q8—861no—
364C22×D4—861no—
365C22×D4—861no—
366C22×D4—1721no—
367C2×Q16—22no—
368C2×Q16—21no—
369C2×Q16—41no—
370C2×Q16—431no—
371C2×Q16—861no—
372C2×Q16—861no—
373C2×Q16—862no—
374C2×Q16—1721no—
375C2×Q16C22×D4311yescharacteristic
376C2×Q16C22×D4311yescharacteristic
377C2×D8—431no—
378C2×D8—431no—
379C2×D8—862no—
380C2×D8—861no—
381C2×D8—861no—
382C2×D8—862no—
383C2×D8—861no—
384C2×D8—1721no—
385C2×D8—1721no—
386C2×D8C22×D4311yescharacteristic
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389C4⋊Q8—861no—
390C4⋊Q8—1721no—
391#127—861no—
392C22⋊Q8—861no—
393C22⋊Q8—861no—
394C22⋊Q8—1721no—
395C22⋊Q8—1721no—
396#121—21no—
397#121—861no—
398#121—1721no—
399#120—1721no—
400#120—1721no—
401C4×Q8—861no—
402C4×D4—431no—
403C4×D4—861no—
404C4×D4—1721no—
405SD32—22no—
406SD32—41no—
407SD32—434no—
408SD32—862no—
409SD32—862no—
410SD32—862no—
411SD32—862no—
412SD32—862no—
413SD32—1721no—
414C2×C16—431no—
415C2×C16—431no—
416C2×C16—862no—
417C2×C16—862no—
418C2×C16C22×D4311yescharacteristic
419C2×C16C22×D4311yescharacteristic
420#107—431no—
421#107C22×D4311yescharacteristic
422C4⋊C8—431no—
423#103—861no—
424#103—861no—
425#103—861no—
426#102—21no—
427#102—861no—
428#102—861no—
429C22⋊C8—431no—
430C22⋊C8—431no—
431C4×C8—431no—
432C24—1721no—
433C24—1721no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—42no—
437C2×Q8—41no—
438C2×Q8—81no—
439C2×Q8—861no—
440C2×Q8—3441no—
441C2×Q8—1721no—
442C2×Q8—1722no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4—431no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—3441no—
449C2×D4—3441no—
450C2×D4—3444no—
451C2×D4—1722no—
452C2×D4—1721no—
453C2×D4—1721no—
454C2×D4—1721no—
455C2×D4—1721no—
456C2×D4—1722no—
457C2×D4—1721no—
458C22×C4—41no—
459C22×C4—431no—
460C22×C4—1721no—
461C22×C4—1721no—
462C22×C4D4×D4311yescharacteristic
463Q16—21no—
464Q16—21no—
465Q16—21no—
466Q16—42no—
467Q16—861no—
468Q16—861no—
469Q16—3441no—
470Q16—1722no—
471Q16D4×D4312yescomplemented
472D8—21no—
473D8—21no—
474D8—432no—
475D8—861no—
476D8—861no—
477D8—861no—
478D8—3441no—
479D8—1722no—
480D8—1722no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8D4×D4311yescharacteristic
488C2×C8C23×D4311yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—431no—
491C4⋊C4—861no—
492C4⋊C4—1721no—
493C4⋊C4—1721no—
494C4⋊C4—1721no—
495C4⋊C4—1721no—
496C4⋊C4—1721no—
497C22⋊C4—41no—
498C22⋊C4—431no—
499C22⋊C4—431no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C42—431no—
505C42—1721no—
506C16—21no—
507C16—21no—
508C16—432no—
509C16—861no—
510C23—41no—
511C23—431no—
512C23—3442no—
513C23—3442no—
514C23—3442no—
515C23—3442no—
516C23—1721no—
517C23—1721no—
518C23—6881no—
519C23—6881no—
520C23D8×D4311yescharacteristic
521Q8—22no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—82no—
526Q8—3442no—
527Q8—1721no—
528Q8—1721no—
529D4—41no—
530D4—41no—
531D4—82no—
532D4—434no—
533D4—862no—
534D4—3442no—
535D4—3442no—
536D4—3442no—
537D4—3442no—
538D4—1721no—
539D4—1721no—
540D4—1721no—
541D4—6881no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4—431no—
549C2×C4—431no—
550C2×C4—431no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—3442no—
554C2×C4—3442no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4D8×D4311yescharacteristic
558C2×C4C2×D4×D4311yescharacteristic
559C8—21no—
560C8—861no—
561C8—861no—
562C8C2×D4×D4311yescharacteristic
563C8#1306337011yescharacteristic
564C22—21no—
565C22—21no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—432no—
570C22—861no—
571C22—861no—
572C22—3441no—
573C22—3441no—
574C22—3441no—
575C22—3441no—
576C22—3441no—
577C22—1722no—
578C22—6884no—
579C22—6884no—
580C22SD32×D4312yescomplemented
581C22C2×D8×D4311yescharacteristic
582C4—21no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—432no—
587C4—861no—
588C4—861no—
589C4—3441no—
590C4—3441no—
591C4#1458353111yescharacteristic
592C4#1458370311yescharacteristic
593C2—22no—
594C2—161no—
595C2—862no—
596C2—3442no—
597C2—6881no—
598C2#1914626511yescharacteristic
599C2C2×SD32×D4311yescharacteristic
600C2#1914774011yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2185C2
socleC22×C43C22×D8
prime radical#19146269C2
hypercenter#2185D43
hypocenterC43D4×SD32
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. C22×#13063268C2semidirect
2. C2×SD32×D43C2semidirect
3. Q16×C22⋊D43C2semidirect
5. #19136849C2semidirect
6. #19136694C2semidirect
7. #19136689C2semidirect
8. #19136639C2semidirect
9. #19136633C2semidirect
10. #19136526C2semidirect
11. #19136522C2semidirect
12. #19136513C2semidirect
13. #19136444C2semidirect
14. (C22⋊D43)⋊C16C2semidirect
15. C43×#2185C2semidirect
16. C2×Q16×D43C22semidirect
22. C2×#13063270C22semidirect
23. C2×#13063269C22semidirect
27. C2×#13063268C22semidirect
28. C2×#13063268C22semidirect
30. C22×C43⋊C16C22semidirect
31. C2×C16×D43C22semidirect
32. #14583277C22semidirect
34. #14583140C22semidirect
35. #14583137C22semidirect
43. Q16×Dic43C22semidirect
46. #14582726C22semidirect
47. Dic43⋊C16C22semidirect
48. #14582702C22semidirect
50. #14582701C22semidirect
51. #14582700C22semidirect
52. (C2×D43)⋊C16C22semidirect
53. C16×Dic43C22semidirect
54. C22×Q16×C43C22semidirect
55. C2×SD32×C43C22semidirect
56. C2×SD32×C43C22semidirect
58. C43×#358C22semidirect
59. C43×#358C22semidirect
60. C43×C22⋊C16C22semidirect
101. #13063268D4semidirect
166. Q16×C43C2×D4semidirect
208. C43⋊C16C2×D4semidirect
239. C22⋊D43SD32semidirect
269. C22×C43C2×SD32semidirect
281. C2×D43C2×SD32semidirect
292. Dic43C2×SD32semidirect
305. #2185D43semidirect
317. C22×Q16C2×D43semidirect
331. C2×SD32C2×D43semidirect
332. C2×SD32C2×D43semidirect
353. #358C2×D43semidirect
354. #358C2×D43semidirect
359. C22⋊C16C2×D43semidirect
361. C43D4×SD32semidirect
471. Q16D4×D43semidirect
580. C22SD32×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632682
C2×SD32×D432
Q16×C22⋊D432
#191462692
#191368492
#191366942
#191366892
#191366392
#191366332
#191365262
#191365222
#191365132
#191364442
(C22⋊D43)⋊C162
C43×#21852
D4×SD3243