Finite Group Databasebeta

← #25086471

Subgroups — #25086471

Order 11008.

626 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147472C211yesmaximal, characteristic, complemented
2#19147374C211yesmaximal, characteristic, complemented
3#19146421C211yesmaximal, characteristic
4#19146420C211yesmaximal, characteristic
5#19134255C211yesmaximal, characteristic, complemented
6#19134136C211yesmaximal, characteristic, complemented
7#19134047C211yesmaximal, characteristic, complemented
8#19134011C211yesmaximal, characteristic, complemented
9#19133970C211yesmaximal, characteristic, complemented
10#19133776C211yesmaximal, characteristic
11#19133732C211yesmaximal, characteristic, complemented
12#19133731C211yesmaximal, characteristic, complemented
13#19133693C211yesmaximal, characteristic, complemented
14#19133433C211yesmaximal, characteristic, complemented
15C43×SD16⋊C8C211yesmaximal, characteristic, complemented
16#14583627C2211yescharacteristic, complemented
17#14583609C2211yescharacteristic
18#14583606C2211yescharacteristic
19D4×D172C2211yescharacteristic
20#14583301—21no—
21#14583297C2211yescharacteristic, complemented
22#14583279C2211yescharacteristic, complemented
23#14583266—21no—
24#14583250C2211yescharacteristic, complemented
25#14583246C2211yescharacteristic
26#14583246C2211yescharacteristic
27#14583246C2211yescharacteristic
28#14583219—21no—
29#14583218—21no—
30#14583209—21no—
31#14583207—21no—
32#14583200—21no—
33#14583195C2211yescharacteristic, complemented
34#14583194C2211yescharacteristic, complemented
35#14583190C2211yescharacteristic
36#14583189C2211yescharacteristic
37#14583180C2211yescharacteristic
38#14583131—21no—
39#14583128—21no—
40#14583104C2211yescharacteristic
41#14583102—21no—
42#14583100C2211yescharacteristic
43#14583099C2211yescharacteristic
44#14583052—21no—
45#14583048—21no—
46#14583029C2211yescharacteristic, complemented
47#14582996—21no—
48C4×#10621873—21no—
49C4×#10621873C2211yescharacteristic
50C8×D172C2211yescharacteristic
51C2×#13063247—21no—
52#102×D43—21no—
53#14582650C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582642C2211yescharacteristic
58#14582631C2211yescharacteristic, complemented
59#14582628C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic, complemented
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic, complemented
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×Dic172—41no—
70C2×#10621873—21no—
71C2×#10621873D411yescharacteristic
72C2×#10621883—21no—
73C2×#10621884—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063323—21no—
79#13063322C2311yescharacteristic
80#13063317—21no—
81#13063317—21no—
82#13063316—21no—
83#13063315—41no—
84#13063304—21no—
85#13063303—41no—
86#13063302—41no—
87#13063301—21no—
88#13063300—21no—
89#13063299—21no—
90#13063295—41no—
91C4×Dic86—21no—
92C4×Dic86C2311yescharacteristic
93#13063290—21no—
94C4×D172—21no—
95C4×D172C2311yescharacteristic
96D4×Dic43—21no—
97C2×C4⋊Dic43—21no—
98C4⋊C4×D43—21no—
99#13063259—21no—
100#13063259—21no—
101#13063258—21no—
102#13063257—21no—
103#13063257—21no—
104#13063257—21no—
105#13063257D411yescharacteristic
106#13063256—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110#13063250—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250D411yescharacteristic
114#13063249—21no—
115#13063248—21no—
116#13063247—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123#13063247—41no—
124#13063247D411yescharacteristic
125#13063246—21no—
126#13063245—21no—
127(C2×D43)⋊C8—21no—
128#13063235—21no—
129C2×SD16×C43D411yescharacteristic
130C22×C8×C43—21no—
131C4×Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#106×C43D411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43D411yescharacteristic
138#102×C43D411yescharacteristic
139C22⋊C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145C2×Q8×C43C2×D411yescharacteristic
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—41no—
149C22×Dic43—41no—
150D4×D43—42no—
151D4×D43—81no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—41no—
156C2×D172—42no—
157C2×D172—81no—
158C2×D172C2×D411yescharacteristic
159C2×C4×D43—21no—
160C2×C4×D43—41no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165SD16×C43—22no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—81no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C42×C43—21no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—41no—
181#10621884—81no—
182#10621883—42no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—41no—
185(C2×D43)⋊C4—41no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—41no—
193C4⋊Dic43C2×D411yescharacteristic
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200Dic43⋊C4—41no—
201Dic43⋊C4—41no—
202C4×Dic43—21no—
203C4×Dic43—41no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206Dic172—82no—
207#10621873—22no—
208#10621873—81no—
209C8×D43—81no—
210C23×C43—21no—
211C22×D43—21no—
212C22×D43—41no—
213C22×D43—82no—
214C22×D43—82no—
215C22×D43—161no—
216Q8×C43—21no—
217Q8×C43—21no—
218D4×C43—21no—
219D4×C43#13512yes—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C22⋊D43—82no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—161no—
236D172—21no—
237D172—41no—
238D172—41no—
239D172—41no—
240D172—41no—
241D172—81no—
242D172—82no—
243D172#13712yes—
244C4×D43—41no—
245C4×D43—41no—
246C4×D43—161no—
247Dic86—21no—
248Dic86—21no—
249Dic86—41no—
250Dic86—41no—
251Dic86—81no—
252Dic86—81no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262#19790—431nomaximal, Sylow
263C22×C43—22no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43D4211yescharacteristic
267C2×D43—22no—
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C2×D43—164no—
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43C2×#13511yescharacteristic
279C4×C43C2×#13711yescharacteristic
280C4×C43#57711yescharacteristic
281C4×C43#57711yescharacteristic
282Dic43—41no—
283Dic43—41no—
284Dic43—41no—
285Dic43—81no—
286Dic43—81no—
287Dic43—81no—
288#3381—431no—
289#3372—431no—
290#3295—431no—
291#3295—431no—
292#1720—431no—
293#1698—431no—
294#1683—431no—
295#1678—431no—
296#1671—431no—
297#1639—431no—
298#1632—431no—
299#1632—431no—
300#1626—431no—
301#1582—431no—
302SD16⋊C8D4311yescharacteristic, complemented
303C2×C43—42no—
304C2×C43#326611yescharacteristic
305C2×C43#328211yescharacteristic
306C2×C43#328811yescharacteristic
307D43—42no—
308D43—161no—
309#557—431no—
310#554—431no—
311#554—431no—
312D42—431no—
313#499—861no—
314#498—431no—
315#494—431no—
316#491—861no—
317#487—431no—
318#486—431no—
319#486—431no—
320#486—431no—
321#481—861no—
322#481—861no—
323#479—861no—
324#479—861no—
325#478—861no—
326#477—431no—
327#477—431no—
328#476—431no—
329#476—431no—
330#474—431no—
331#465—861no—
332#465—861no—
333#461—431no—
334#461—861no—
335#460—431no—
336#460—431no—
337#450—861no—
338#450—861no—
339#446—431no—
340C8×Q8C2×D4311yescharacteristic, complemented
341#440—861no—
342C4×SD16—431no—
343C4×SD16—861no—
344C4×SD16C2×D4311yescharacteristic
345C8×D4—431no—
346C8×D4C2×D4311yescharacteristic
347C2×#102—861no—
348C2×#102—861no—
349#335C2×D4311yescharacteristic, complemented
350#334—431no—
351#333—431no—
352#333—431no—
353#332—431no—
354#331—431no—
355Q8⋊C8—431no—
356Q8⋊C8C2×D4311yescharacteristic, complemented
357D4⋊C8—431no—
358D4⋊C8C2×D4311yescharacteristic
359#322C2×D4311yescharacteristic, complemented
360C43#1979011yescharacteristic, complemented, Sylow
361C22×D4—861no—
362C22×D4—861no—
363C2×Q16—1721no—
364C2×SD16—431no—
365C2×SD16—861no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×SD16D17211yescharacteristic
369C22×C8—21no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8—431no—
374C4⋊Q8—861no—
375#127—431no—
376#125—861no—
377#125—861no—
378#125—861no—
379#125—1721no—
380C22⋊Q8—861no—
381C22⋊Q8—861no—
382C22⋊Q8—1721no—
383C22⋊Q8—1721no—
384#121—861no—
385#121—861no—
386#120—1721no—
387C4×Q8—431no—
388C4×Q8—861no—
389C4×Q8—861no—
390C4×Q8C22×D4311yescharacteristic
391C4×D4—431no—
392C4×D4—861no—
393C4×D4—861no—
394C4×D4C22×D4311yescharacteristic
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397#107—861no—
398#107—861no—
399#107—861no—
400#106—431no—
401#106—861no—
402#106—861no—
403#106—861no—
404#106—861no—
405#106D17211yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412#103—431no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103D17211yescharacteristic
419#102—431no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—1721no—
430#102D17211yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—861no—
433#97—861no—
434C4×C8—21no—
435C4×C8C22×D4311yescharacteristic
436C4×C8C22×D4311yescharacteristic
437C4×C8C22×D4311yescharacteristic
438C24—1721no—
439C2×Q8—431no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8C2×D17211yescharacteristic
444C2×D4—431no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—3441no—
449C2×D4—3441no—
450C2×D4—1721no—
451C2×D4—1722no—
452C2×D4—1721no—
453C2×D4—1722no—
454C2×D4C2×D17211yescharacteristic
455C22×C4—21no—
456C22×C4—861no—
457C22×C4—1721no—
458C22×C4—1721no—
459Q16—3442no—
460SD16—22no—
461SD16—862no—
462SD16—3441no—
463SD16—3441no—
464SD16—1722no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—81no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—3441no—
472C2×C8C2×D17211yescharacteristic
473C2×C8C2×D17211yescharacteristic
474C2×C8D4×D4311yescharacteristic
475C2×C8D4×D4311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—431no—
478C4⋊C4—431no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—1721no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C4⋊C4—1721no—
492C4⋊C4—1721no—
493C4⋊C4C2×D17211yescharacteristic
494C4⋊C4C2×D17211yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—861no—
497C22⋊C4—1721no—
498C22⋊C4—1721no—
499C22⋊C4—1721no—
500C42—21no—
501C42—861no—
502C42—1721no—
503C42C23×D4311yescharacteristic
504C23—21no—
505C23—861no—
506C23—3442no—
507C23—3442no—
508C23—1721no—
509C23—6881no—
510Q8—21no—
511Q8—21no—
512Q8—861no—
513Q8—861no—
514Q8—3441no—
515Q8—3441no—
516Q8—1721no—
517Q8—1721no—
518D4—21no—
519D4—432no—
520D4—861no—
521D4—3441no—
522D4—3442no—
523D4—3442no—
524D4—1721no—
525D4—1721no—
526D4—1721no—
527D4—1721no—
528D4#1306334712yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—6881no—
543C2×C4—6881no—
544C2×C4C2×D4×D4311yescharacteristic
545C2×C4C22×D17211yescharacteristic
546C2×C4#1306337111yescharacteristic
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—1721no—
555C8—1721no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—862no—
560C22—3441no—
561C22—3441no—
562C22—3441no—
563C22—1721no—
564C22—1721no—
565C22—6884no—
566C22D4×D17211yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—3441no—
572C4—3441no—
573C4—3441no—
574C4—1721no—
575C4—1721no—
576C4—1721no—
577C4C2×#1306334711yescharacteristic
578C4#137×D4311yescharacteristic
579C4#1458370911yescharacteristic
580C4#1458371111yescharacteristic
581C2—42no—
582C2—1722no—
583C2—6881no—
584C2#1914610711yescharacteristic
585C2#1914630711yescharacteristic
586C2#1914636211yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×SD16⋊C8C2
socleC22×C43D42
prime radicalD4×D172C22
hypercenterSD16⋊C8D43
hypocenterC43#19790
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
1. #19147472C2semidirect
2. #19147374C2semidirect
5. #19134255C2semidirect
6. #19134136C2semidirect
7. #19134047C2semidirect
8. #19134011C2semidirect
9. #19133970C2semidirect
11. #19133732C2semidirect
12. #19133731C2semidirect
13. #19133693C2semidirect
14. #19133433C2semidirect
15. C43×SD16⋊C8C2semidirect
16. #14583627C22semidirect
21. #14583297C22semidirect
22. #14583279C22semidirect
24. #14583250C22semidirect
33. #14583195C22semidirect
34. #14583194C22semidirect
46. #14583029C22semidirect
53. #14582650C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
56. #14582644C22semidirect
58. #14582631C22semidirect
60. C8×Q8×C43C22semidirect
63. C43×#335C22semidirect
64. C43×Q8⋊C8C22semidirect
66. C43×#322C22semidirect
302. SD16⋊C8D43semidirect
340. C8×Q8C2×D43semidirect
349. #335C2×D43semidirect
356. Q8⋊C8C2×D43semidirect
359. #322C2×D43semidirect
360. C43#19790semidirect

Maximal subgroups

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

subgroupindex
#191474722
#191473742
#191464212
#191464202
#191342552
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