Finite Group Databasebeta

← #25253101

Subgroups — #25253101

Order 11008.

692 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583334C211yesmaximal, characteristic, complemented
2C2×#14583329C211yesmaximal, characteristic, complemented
3#19146282C211yesmaximal, characteristic, complemented
4#19136864C211yesmaximal, characteristic, complemented
5#19136701C211yesmaximal, characteristic, complemented
6#19136693C211yesmaximal, characteristic, complemented
7#19136650C211yesmaximal, characteristic, complemented
8#19136637C211yesmaximal, characteristic, complemented
9#19136535C211yesmaximal, characteristic, complemented
10#19136533C211yesmaximal, characteristic, complemented
11#19136523C211yesmaximal, characteristic, complemented
12#19136518C211yesmaximal, characteristic, complemented
13#19136469C211yesmaximal, characteristic, complemented
14#19136421C211yesmaximal, characteristic, complemented
15C43×#3283C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C22×D344C2211yescharacteristic
18#14583545—21no—
19#14583334—24no—
20#14583329—24no—
21C2×#13063271C2211yescharacteristic, complemented
22C2×#13063271C2211yescharacteristic, complemented
23C2×#13063269C2211yescharacteristic, complemented
24C2×#13063268C2211yescharacteristic
25C2×#13063268C2211yescharacteristic
26C2×#13063268C2211yescharacteristic
27C2×#13063268C2211yescharacteristic
28C2×#13063266C2211yescharacteristic
29C2×#13063266C2211yescharacteristic
30C2×#13063265C2211yescharacteristic
31C22×C43⋊C16C2211yescharacteristic, complemented
32#14583283C2211yescharacteristic
33#14583140C2211yescharacteristic
34#14583135C2211yescharacteristic
35#14583115—21no—
36#14583052—21no—
37#14583046—21no—
38C4×D344C2211yescharacteristic
39#14582726C2211yescharacteristic, complemented
40C4⋊(C43⋊C16)C2211yescharacteristic, complemented
41#14582703C2211yescharacteristic, complemented
42#14582703C2211yescharacteristic, complemented
43#14582702C2211yescharacteristic, complemented
44#14582700C2211yescharacteristic, complemented
45#14582699C2211yescharacteristic
46#14582699C2211yescharacteristic
47C22⋊(C43⋊C16)C2211yescharacteristic
48C22⋊(C43⋊C16)C2211yescharacteristic, complemented
49#14582675C2211yescharacteristic, complemented
50C2×#135×C43C2211yescharacteristic
51C2×#135×C43C2211yescharacteristic, complemented
52C43×#547—21no—
53C43×#494C2211yescharacteristic, complemented
54C43×#467C2211yescharacteristic
55C43×#467C2211yescharacteristic, complemented
56C43×#461—21no—
57C43×#452—21no—
58C43×#452—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—22no—
82#13063271—41no—
83#13063269—22no—
84#13063268—22no—
85#13063268—22no—
86#13063268—22no—
87#13063268—41no—
88#13063266—22no—
89#13063266D414yescomplemented
90#13063265—22no—
91C2×C43⋊C16—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—
101C2×#41×C43—21no—
102#135×C43—22no—
103#135×C43—22no—
104#135×C43—41no—
105#135×C43—41no—
106C2×Q16×C43—21no—
107C2×Q16×C43C2311yescharacteristic
108C2×Q16×C43C2311yescharacteristic
109C2×SD16×C43—21no—
110C2×SD16×C43—21no—
111C2×D8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C4⋊Q8×C43—21no—
115#123×C43—41no—
116#123×C43—41no—
117C22⋊Q8×C43—21no—
118C22⋊Q8×C43—21no—
119#121×C43—41no—
120C4×D4×C43—21no—
121C4×D4×C43D411yescharacteristic
122C2×C4⋊C4×C43—41no—
123#107×C43C2311yescharacteristic
124C4⋊C8×C43D411yescharacteristic
125#103×C43—21no—
126#103×C43—21no—
127#102×C43—21no—
128C22⋊C8×C43D411yescharacteristic
129C22⋊C8×C43D411yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C23×D43—41no—
132#41×C43—42no—
133#41×C43—42no—
134#41×C43—81no—
135#41×C43—81no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—41no—
140C2×D4×C43—41no—
141C2×D4×C43D811yescharacteristic
142C22×C4×C43—41no—
143C22×C4×C43—41no—
144C22×C4×C43—41no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C2×C22⋊D43—41no—
148C2×C22⋊D43—41no—
149#10621898—42no—
150#10621898—81no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—41no—
154C2×D172—42no—
155C2×D172—81no—
156C2×C4×D43—41no—
157C2×C4×D43—41no—
158C2×Dic86—21no—
159Q16×C43—21no—
160Q16×C43—21no—
161Q16×C43—21no—
162Q16×C43—21no—
163Q16×C43—81no—
164SD16×C43—42no—
165SD16×C43—42no—
166D8×C43—21no—
167D8×C43C2×D412yes—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2411yescharacteristic
176C4⋊C4×C43—21no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43D811yescharacteristic
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×C43C2×D811yescharacteristic
210C23×C43C2×D811yescharacteristic
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—82no—
214C22×D43—82no—
215C22×D43—161no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220D4×C43—22no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—82no—
224D4×C43—82no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—82no—
233C2×C4×C43—82no—
234C2×C4×C43—82no—
235C2×C4×C43C2×D811yescharacteristic
236C2×C4×C43C2×D811yescharacteristic
237C2×C4×C43C2×D811yescharacteristic
238C2×C4×C43C2×D811yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C22⋊D43—82no—
241C22⋊D43—161no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244D172—22no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—82no—
249C4×D43—82no—
250C4×D43—161no—
251Dic86—41no—
252Dic86—41no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43C22×D411yescharacteristic
257C8×C43H(5,𝔽2)11yescharacteristic
258#33833—431nomaximal, Sylow
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—42no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43C22×D811yescharacteristic
269C2×D43—42no—
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—164no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43D4211yescharacteristic
284C4×C43#57611yescharacteristic
285Dic43—81no—
286Dic43—81no—
287C2×#509—431no—
288C2×#508—431no—
289#3283D4311yescharacteristic, complemented
290#3280—431no—
291#2251—431no—
292#2219—431no—
293#2217—431no—
294#2210—431no—
295#2208—431no—
296#2189—431no—
297#2189—431no—
298#2187—431no—
299#2186—431no—
300#2177—431no—
301#2168—431no—
302C2×C43—41no—
303C2×C43—41no—
304C2×C43—82no—
305C2×C43D4×D811yescharacteristic
306C2×C43#341411yescharacteristic
307C2×C43#341611yescharacteristic
308D43—82no—
309D43—161no—
310C2×#135—431no—
311C2×#135C2×D4311yescharacteristic
312C2×#135C2×D4311yescharacteristic, complemented
313C22×D8—431no—
314#547—21no—
315#546—861no—
316#509—864no—
317#508—864no—
318C2×Q32—431no—
319C2×Q32—431no—
320C2×SD32—431no—
321C2×SD32—431no—
322C2×SD32—431no—
323C2×SD32—431no—
324C2×SD32—431no—
325C2×D16—431no—
326C2×D16—431no—
327C2×M32—431no—
328C22×C16—431no—
329#495—431no—
330#494C2×D4311yescharacteristic, complemented
331#467—431no—
332#467C2×D4311yescharacteristic
333#467C2×D4311yescharacteristic, complemented
334#466—431no—
335#463—861no—
336#461—21no—
337#452—21no—
338#452—21no—
339#450—861no—
340#449—861no—
341C4×D8—431no—
342C4×D8C2×D4311yescharacteristic, complemented
343C8×D4C2×D4311yescharacteristic
344#367—431no—
345C4⋊C16—431no—
346#358—431no—
347#358—431no—
348#358—431no—
349#357—431no—
350#357—431no—
351#357—431no—
352C22⋊C16—431no—
353C22⋊C16—431no—
354#346—431no—
355C43#3383311yescharacteristic, complemented, Sylow
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—861no—
359C22×D4—861no—
360#135—22no—
361#135—22no—
362#135—41no—
363#135—41no—
364#135—862no—
365#135—1721no—
366C2×Q16—21no—
367C2×Q16—431no—
368C2×Q16C22×D4311yescharacteristic
369C2×Q16C22×D4311yescharacteristic
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×D8—431no—
375C2×D8—431no—
376C2×D8—862no—
377C2×D8—861no—
378C2×D8—1721no—
379C2×D8C22×D4311yescharacteristic
380C22×C8C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382C4⋊Q8—21no—
383#124—861no—
384#123—41no—
385#123—41no—
386#123—1721no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—861no—
390#121—41no—
391#121—861no—
392#121—1721no—
393#120—1721no—
394C4×D4—21no—
395C4×D4—861no—
396C4×D4C22⋊D4311yescharacteristic
397C2×C4⋊C4—41no—
398C2×C22⋊C4—1721no—
399Q32—862no—
400Q32—1721no—
401SD32—862no—
402SD32—862no—
403SD32—862no—
404SD32—862no—
405SD32—1721no—
406D16—434no—
407D16—862no—
408M32—862no—
409C2×C16—431no—
410C2×C16—431no—
411C2×C16—431no—
412C2×C16—431no—
413C2×C16—862no—
414#107—431no—
415#107C22×D4311yescharacteristic
416C4⋊C8C22⋊D4311yescharacteristic
417#103—21no—
418#103—21no—
419#103—861no—
420#102—21no—
421#102—861no—
422#102—861no—
423C22⋊C8C22⋊D4311yescharacteristic
424C22⋊C8C22⋊D4311yescharacteristic
425C4×C8C22×D4311yescharacteristic
426C24—1721no—
427#41—42no—
428#41—42no—
429#41—81no—
430#41—81no—
431#41—3441no—
432#41—1722no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—861no—
436C2×D4—21no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—3441no—
442C2×D4—1722no—
443C2×D4—1721no—
444C2×D4—1721no—
445C2×D4—1721no—
446C2×D4#1062188211yescharacteristic
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—1721no—
451C22×C4—1721no—
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454Q16—21no—
455Q16—21no—
456Q16—21no—
457Q16—21no—
458Q16—81no—
459Q16—861no—
460Q16—861no—
461SD16—42no—
462SD16—42no—
463SD16—3441no—
464SD16—1722no—
465D8—21no—
466D8—432no—
467D8—861no—
468D8—861no—
469D8—861no—
470D8—1722no—
471D8D4×D4312yes—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8C2×C22⋊D4311yescharacteristic
477C2×C8C2×C22⋊D4311yescharacteristic
478C2×C8C2×C22⋊D4311yescharacteristic
479C2×C8C23×D4311yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—861no—
486C4⋊C4—1721no—
487C4⋊C4#1062188211yescharacteristic
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C22⋊C4—1721no—
495C22⋊C4—1721no—
496C22⋊C4#1062188211yescharacteristic
497C22⋊C4#1062188211yescharacteristic
498C42C2×C22⋊D4311yescharacteristic
499C16—432no—
500C16—861no—
501C16—861no—
502C16—861no—
503C23—41no—
504C23—3442no—
505C23—3442no—
506C23—1721no—
507C23—1721no—
508C23—6881no—
509C23C2×#1062188211yescharacteristic
510C23C2×#1062188211yescharacteristic
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—1721no—
516Q8—1721no—
517D4—22no—
518D4—41no—
519D4—41no—
520D4—82no—
521D4—82no—
522D4—862no—
523D4—3442no—
524D4—3442no—
525D4—1721no—
526D4—1721no—
527D4—1721no—
528D4—6881no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—3442no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—6881no—
543C2×C4C2×#1062188211yescharacteristic
544C2×C4C2×#1062188211yescharacteristic
545C2×C4C2×#1062188211yescharacteristic
546C2×C4C2×#1062188211yescharacteristic
547C2×C4C22×C22⋊D4311yescharacteristic
548C8—21no—
549C8—21no—
550C8—21no—
551C8C2×D4×D4311yescharacteristic
552C8#1306337011yescharacteristic
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—42no—
560C22—81no—
561C22—81no—
562C22—3441no—
563C22—3441no—
564C22—3441no—
565C22—3441no—
566C22—3441no—
567C22—1722no—
568C22—6884no—
569C22C22×#1062188211yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—3441no—
578C4—3441no—
579C4D4×C22⋊D4311yescharacteristic
580C4#1458370211yescharacteristic
581C2—41no—
582C2—41no—
583C2—82no—
584C2—3442no—
585C2—6881no—
586C2D4×#1062188211yescharacteristic
587C2#1914772911yescharacteristic
588C2#1914773911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3283C2
socleC22×C43C22×D8
hypercenter#3283D43
hypocenterC43#33833
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. C2×#14583334C2semidirect
2. C2×#14583329C2semidirect
3. #19146282C2semidirect
4. #19136864C2semidirect
5. #19136701C2semidirect
6. #19136693C2semidirect
7. #19136650C2semidirect
8. #19136637C2semidirect
9. #19136535C2semidirect
10. #19136533C2semidirect
11. #19136523C2semidirect
12. #19136518C2semidirect
13. #19136469C2semidirect
14. #19136421C2semidirect
15. C43×#3283C2semidirect
21. C2×#13063271C22semidirect
22. C2×#13063271C22semidirect
23. C2×#13063269C22semidirect
31. C22×C43⋊C16C22semidirect
39. #14582726C22semidirect
40. C4⋊(C43⋊C16)C22semidirect
41. #14582703C22semidirect
42. #14582703C22semidirect
43. #14582702C22semidirect
44. #14582700C22semidirect
48. C22⋊(C43⋊C16)C22semidirect
49. #14582675C22semidirect
51. C2×#135×C43C22semidirect
53. C43×#494C22semidirect
55. C43×#467C22semidirect
59. C4×D8×C43C22semidirect
89. #13063266D4semidirect
289. #3283D43semidirect
312. C2×#135C2×D43semidirect
330. #494C2×D43semidirect
333. #467C2×D43semidirect
342. C4×D8C2×D43semidirect
355. C43#33833semidirect

Maximal subgroups

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

subgroupindex
C2×#145833342
C2×#145833292
#191462822
#191368642
#191367012
#191366932
#191366502
#191366372
#191365352
#191365332
#191365232
#191365182
#191364692
#191364212
C43×#32832
#3383343