Finite Group Databasebeta

← #25251034

Subgroups — #25251034

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583330C211yesmaximal, characteristic, complemented
2C22×C16×D43C211yesmaximal, characteristic, complemented
3#19144178C211yesmaximal, characteristic, complemented
4#19144174C211yesmaximal, characteristic, complemented
5#19136692C211yesmaximal, characteristic, complemented
6#19136691C211yesmaximal, characteristic, complemented
7#19136688C211yesmaximal, characteristic, complemented
8#19136685C211yesmaximal, characteristic, complemented
9#19136684C211yesmaximal, characteristic, complemented
10#19136680C211yesmaximal, characteristic, complemented
11#19136679C211yesmaximal, characteristic, complemented
12#19136378C211yesmaximal, characteristic, complemented
13#19136301C211yesmaximal, characteristic, complemented
14#19136299C211yesmaximal, characteristic, complemented
15C43×#2217C211yesmaximal, characteristic, complemented
16C2×#13063348C2211yescharacteristic
17C2×#13063344C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583412—21no—
20#14583409—21no—
21#14583330—24no—
22C2×#13063271C2211yescharacteristic, complemented
23C2×#13063270C2211yescharacteristic, complemented
24C2×#13063266C2211yescharacteristic, complemented
25C22×C43⋊C16C2211yescharacteristic
26C2×C16×D43—24no—
27C2×C16×D43C2211yescharacteristic
28C2×C16×D43C2211yescharacteristic
29C2×C16×D43C2211yescharacteristic
30C2×C16×D43C2211yescharacteristic
31#14583141C2211yescharacteristic
32#14583140C2211yescharacteristic
33#14583137C2211yescharacteristic
34#14583136C2211yescharacteristic
35#14583135C2211yescharacteristic
36#14583132C2211yescharacteristic
37#14583131—21no—
38#14583130—21no—
39#14583127—21no—
40#14583126—21no—
41#14582936C2211yescharacteristic
42#14582936C2211yescharacteristic
43#14582894—21no—
44#14582892—21no—
45#14582727C2211yescharacteristic, complemented
46#14582724C2211yescharacteristic, complemented
47#14582724C2211yescharacteristic, complemented
48#14582704C2211yescharacteristic, complemented
49#14582703C2211yescharacteristic, complemented
50#14582702C2211yescharacteristic, complemented
51#14582701C2211yescharacteristic, complemented
52#14582700C2211yescharacteristic, complemented
53#14582699C2211yescharacteristic, complemented
54C2×SD32×C43C2211yescharacteristic, complemented
55C22×C16×C43C2211yescharacteristic
56C43×#467C2211yescharacteristic
57C43×#466C2211yescharacteristic
58C43×#367C2211yescharacteristic, complemented
59C43×#358C2211yescharacteristic, complemented
60C43×#357C2211yescharacteristic, complemented
61C2×#10621902—21no—
62C2×#10621900—21no—
63C22×C4×D43D411yescharacteristic
64#13063348—22no—
65#13063348—22no—
66#13063344—22no—
67#13063344—22no—
68C2×Dic172C2311yescharacteristic
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×D344C2311yescharacteristic
72C22×C43⋊C8D411yescharacteristic
73C2×C8×D43—22no—
74C2×C8×D43—22no—
75C2×C8×D43D411yescharacteristic
76C2×C8×D43D411yescharacteristic
77C2×C8×D43C2311yescharacteristic
78C2×C8×D43C2311yescharacteristic
79#13063310—41no—
80#13063307—41no—
81#13063305—21no—
82#13063304—21no—
83#13063301—21no—
84#13063300—21no—
85#13063299—21no—
86#13063296—21no—
87#13063295—41no—
88#13063293—41no—
89D4×Dic43—41no—
90#13063287—41no—
91(C22⋊D43)⋊C4—41no—
92(C22⋊D43)⋊C4—41no—
93#13063283—21no—
94#13063283—21no—
95#13063271—22no—
96#13063270—22no—
97#13063266—22no—
98C2×C43⋊C16—22no—
99C2×C43⋊C16C2311yescharacteristic
100C2×C43⋊C16C2311yescharacteristic
101C16×D43—22no—
102C16×D43—22no—
103C16×D43—22no—
104C16×D43D414yescomplemented
105#13063259C2311yescharacteristic
106#13063259C2311yescharacteristic
107#13063256—21no—
108#13063256—21no—
109#13063250—21no—
110#13063249—21no—
111#13063248—21no—
112#13063247—21no—
113#13063246—21no—
114#13063245—21no—
115C2×Q16×C43C2311yescharacteristic
116C2×D8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22⋊Q8×C43—21no—
119#121×C43—21no—
120SD32×C43—22no—
121C2×C16×C43—22no—
122C2×C16×C43C2311yescharacteristic
123C2×C16×C43C2311yescharacteristic
124#107×C43C2311yescharacteristic
125#107×C43C2311yescharacteristic
126#103×C43—21no—
127#102×C43—21no—
128C23×D43D811yescharacteristic
129C2×Q8×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—41no—
132C22×C4×C43C2×D411yescharacteristic
133C2×C22⋊D43—41no—
134C2×C22⋊D43—41no—
135C2×C22⋊D43—41no—
136C22×Dic43—41no—
137C22×Dic43D811yescharacteristic
138#10621902—42no—
139#10621902—42no—
140#10621900—42no—
141#10621900—42no—
142C2×D172—21no—
143C2×D172—41no—
144C2×D172—41no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—41no—
148C2×C4×D43D811yescharacteristic
149C2×C4×D43D811yescharacteristic
150C2×C4×D43C2×D411yescharacteristic
151C2×C4×D43C2×D411yescharacteristic
152C2×Dic86—21no—
153Q16×C43—21no—
154Q16×C43—21no—
155D8×C43—21no—
156D8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43C2×D411yescharacteristic
160C2×C8×C43C2411yescharacteristic
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—41no—
164C22⋊C4×C43—41no—
165C22⋊C4×C43—41no—
166C22⋊Dic43—41no—
167C22⋊Dic43—41no—
168#10621884—42no—
169#10621883—42no—
170(C2×D43)⋊C4—41no—
171(C2×D43)⋊C4—41no—
172(C2×D43)⋊C4—41no—
173(C2×D43)⋊C4—41no—
174(C2×D43)⋊C4—41no—
175(C2×D43)⋊C4—41no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—41no—
179Dic43⋊C4—41no—
180Dic43⋊C4—41no—
181C4×Dic43—41no—
182C4×Dic43—41no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8C2×D411yescharacteristic
185C2×C43⋊C8C2×D411yescharacteristic
186Dic172—21no—
187Dic172—21no—
188D344—21no—
189D344—21no—
190C8×D43—22no—
191C8×D43—21no—
192C8×D43—21no—
193C8×D43—22no—
194C8×D43C2×D412yes—
195C8×D43#4112yes—
196C16×C43—21no—
197C16×C43C2×D412yes—
198C43⋊C16—21no—
199C43⋊C16C2×D412yes—
200C23×C43—41no—
201C23×C43C2×D811yescharacteristic
202C22×D43—22no—
203C22×D43—22no—
204C22×D43—22no—
205C22×D43—41no—
206C22×D43C2×D811yescharacteristic
207C22×D43C2×D811yescharacteristic
208Q8×C43—41no—
209Q8×C43—41no—
210D4×C43—41no—
211D4×C43—41no—
212D4×C43—82no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43C2×D811yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C22⋊D43—82no—
221C22⋊D43—82no—
222C22⋊D43—82no—
223C2×Dic43—22no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—82no—
228C2×Dic43C2×D811yescharacteristic
229C2×Dic43C2×D811yescharacteristic
230D172—41no—
231D172—41no—
232D172—82no—
233D172—82no—
234C4×D43—22no—
235C4×D43—21no—
236C4×D43—21no—
237C4×D43—22no—
238C4×D43—82no—
239C4×D43#12112yes—
240C4×D43#13512yes—
241Dic86—41no—
242Dic86—41no—
243C8×C43—21no—
244C8×C43C22×D411yescharacteristic
245C8×C43C2×#4111yescharacteristic
246C43⋊C8—21no—
247C43⋊C8#12112yes—
248#33600—431nomaximal, Sylow
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—81no—
252C22×C43—81no—
253C22×C43—81no—
254C22×C43#50812yescomplemented
255C22×C43C22×D811yescharacteristic
256C2×D43—28no—
257C2×D43—21no—
258C2×D43—21no—
259C2×D43—21no—
260C2×D43—21no—
261C2×D43—81no—
262C2×D43—81no—
263C2×D43—81no—
264C2×D43#46612yes—
265C2×D43#50812yescomplemented
266C4×C43—21no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43C2×#12111yescharacteristic
271C4×C43C2×#13511yescharacteristic
272Dic43—21no—
273Dic43—81no—
274Dic43—81no—
275Dic43—81no—
276Dic43#46612yes—
277C2×#508—431no—
278C23×C16—431no—
279#3050—431no—
280#3050—431no—
281#2217—431no—
282#2217—431no—
283#2217—431no—
284#2217D4311yescharacteristic, complemented
285#2216—431no—
286#2216—431no—
287#2215—431no—
288#2215—431no—
289#2158—431no—
290#2138—431no—
291#2138—431no—
292C2×C43—22no—
293C2×C43—161no—
294C2×C43C2×#46611yescharacteristic
295C2×C43C2×#50811yescharacteristic
296C2×C43C2×#50811yescharacteristic
297D43—22no—
298D43—22no—
299D43—161no—
300C2×#135—431no—
301C2×#135—431no—
302C23×C8—431no—
303#525—861no—
304#525—861no—
305#508—864no—
306C2×Q32—431no—
307C2×SD32—431no—
308C2×SD32C2×D4311yescharacteristic, complemented
309C2×D16—431no—
310C22×C16—431no—
311C22×C16—431no—
312C22×C16—431no—
313C22×C16—431no—
314C22×C16—431no—
315C22×C16—864no—
316C22×C16C2×D4311yescharacteristic
317#467—431no—
318#467—431no—
319#467—431no—
320#467C2×D4311yescharacteristic
321#466—431no—
322#466—431no—
323#466—431no—
324#466C2×D4311yescharacteristic
325#465—861no—
326#465—861no—
327#465—861no—
328#465—861no—
329#427—431no—
330#427—431no—
331#416—861no—
332#416—861no—
333#367—431no—
334#367C2×D4311yescharacteristic, complemented
335#366—431no—
336#366—431no—
337#358—431no—
338#358—431no—
339#358—431no—
340#358C2×D4311yescharacteristic, complemented
341#357—431no—
342#357—431no—
343#357—431no—
344#357C2×D4311yescharacteristic, complemented
345C43#3360011yescharacteristic, complemented, Sylow
346C2×#41—861no—
347C2×#41—861no—
348C23×C4—431no—
349#135—862no—
350#135—862no—
351#135—862no—
352#135—862no—
353C2×Q16—431no—
354C2×Q16C22×D4311yescharacteristic
355C2×SD16—861no—
356C2×SD16—861no—
357C2×D8—431no—
358C2×D8C22×D4311yescharacteristic
359C22×C8—431no—
360C22×C8—431no—
361C22×C8—431no—
362C22×C8—431no—
363C22×C8—431no—
364C22×C8—862no—
365C22×C8—862no—
366C22×C8C22×D4311yescharacteristic
367#123—1721no—
368#123—1721no—
369C22⋊Q8—21no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372C22⋊Q8—861no—
373#121—21no—
374#121—861no—
375#121—861no—
376#121—861no—
377#120—1721no—
378#120—1721no—
379C4×D4—1721no—
380C4×D4—1721no—
381C4×D4—1721no—
382C4×D4—1721no—
383#117—861no—
384#117—861no—
385Q32—862no—
386SD32—22no—
387SD32—862no—
388D16—862no—
389C2×C16—22no—
390C2×C16—431no—
391C2×C16—434no—
392C2×C16—431no—
393C2×C16—862no—
394C2×C16—862no—
395C2×C16—862no—
396C2×C16—862no—
397C2×C16C22×D4311yescharacteristic
398C2×C16C22×D4311yescharacteristic
399#107—431no—
400#107—431no—
401#107C22×D4311yescharacteristic
402#107C22×D4311yescharacteristic
403#106—861no—
404#106—861no—
405#103—21no—
406#103—861no—
407#103—861no—
408#103—861no—
409#102—21no—
410#102—861no—
411#102—861no—
412#102—861no—
413C24—431no—
414#41—1722no—
415#41—1722no—
416#41—1722no—
417#41—1722no—
418C2×Q8—21no—
419C2×Q8—861no—
420C2×D4—21no—
421C2×D4—41no—
422C2×D4—861no—
423C2×D4—1721no—
424C2×D4—1721no—
425C2×D4—1721no—
426C2×D4—1721no—
427C2×D4—1721no—
428C22×C4—431no—
429C22×C4—431no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—1721no—
436C22×C4—1721no—
437C22×C4D4×D4311yescharacteristic
438Q16—21no—
439Q16—21no—
440Q16—861no—
441Q16—861no—
442SD16—1722no—
443SD16—1722no—
444D8—21no—
445D8—21no—
446D8—861no—
447D8—861no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—431no—
451C2×C8—432no—
452C2×C8—432no—
453C2×C8—431no—
454C2×C8—862no—
455C2×C8—862no—
456C2×C8—862no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8D4×D4311yescharacteristic
460C2×C8C23×D4311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4—1721no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—1721no—
472C22⋊C4—1721no—
473C22⋊C4—1721no—
474C22⋊C4—1721no—
475C22⋊C4—1721no—
476C22⋊C4—1721no—
477C22⋊C4—1721no—
478C22⋊C4—1721no—
479C42—1721no—
480C42—1721no—
481C16—21no—
482C16—432no—
483C16—861no—
484C16D4×D4312yes—
485C23—41no—
486C23—431no—
487C23—431no—
488C23—862no—
489C23—862no—
490C23—862no—
491C23—1721no—
492C23D8×D4311yescharacteristic
493Q8—41no—
494Q8—41no—
495Q8—1721no—
496Q8—1721no—
497D4—41no—
498D4—41no—
499D4—82no—
500D4—3442no—
501D4—3442no—
502D4—3442no—
503D4—3442no—
504D4—3442no—
505D4—1721no—
506D4—1721no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—431no—
513C2×C4—432no—
514C2×C4—432no—
515C2×C4—431no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—3442no—
522C2×C4—3442no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4D8×D4311yescharacteristic
527C2×C4C2×D4×D4311yescharacteristic
528C8—21no—
529C8—432no—
530C8—861no—
531C8C2×D4×D4311yescharacteristic
532C8#41×D4311yescharacteristic
533C22—21no—
534C22—21no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—432no—
539C22—432no—
540C22—868no—
541C22—861no—
542C22—861no—
543C22—861no—
544C22—861no—
545C22—3441no—
546C22—3441no—
547C22—3441no—
548C22#1458333012yescomplemented
549C22C2×D8×D4311yescharacteristic
550C4—21no—
551C4—81no—
552C4—81no—
553C4—81no—
554C4—432no—
555C4—861no—
556C4—3441no—
557C4—3441no—
558C4—3441no—
559C4#121×D4311yescharacteristic
560C4#135×D4311yescharacteristic
561C2—22no—
562C2—161no—
563C2—862no—
564C2—862no—
565C2—6881no—
566C2#466×D4311yescharacteristic
567C2#508×D4311yescharacteristic
568C2C2×#1458333011yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2217C2
socleC22×C43C22×D8
hypercenter#2217D43
hypocenterC43#33600
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. C2×#14583330C2semidirect
2. C22×C16×D43C2semidirect
3. #19144178C2semidirect
4. #19144174C2semidirect
5. #19136692C2semidirect
6. #19136691C2semidirect
7. #19136688C2semidirect
8. #19136685C2semidirect
9. #19136684C2semidirect
10. #19136680C2semidirect
11. #19136679C2semidirect
12. #19136378C2semidirect
13. #19136301C2semidirect
14. #19136299C2semidirect
15. C43×#2217C2semidirect
22. C2×#13063271C22semidirect
23. C2×#13063270C22semidirect
24. C2×#13063266C22semidirect
45. #14582727C22semidirect
46. #14582724C22semidirect
47. #14582724C22semidirect
48. #14582704C22semidirect
49. #14582703C22semidirect
50. #14582702C22semidirect
51. #14582701C22semidirect
52. #14582700C22semidirect
53. #14582699C22semidirect
54. C2×SD32×C43C22semidirect
58. C43×#367C22semidirect
59. C43×#358C22semidirect
60. C43×#357C22semidirect
104. C16×D43D4semidirect
254. C22×C43#508semidirect
265. C2×D43#508semidirect
284. #2217D43semidirect
308. C2×SD32C2×D43semidirect
334. #367C2×D43semidirect
340. #358C2×D43semidirect
344. #357C2×D43semidirect
345. C43#33600semidirect
548. C22#14583330semidirect

Maximal subgroups

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

subgroupindex
C2×#145833302
C22×C16×D432
#191441782
#191441742
#191366922
#191366912
#191366882
#191366852
#191366842
#191366802
#191366792
#191363782
#191363012
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