Finite Group Databasebeta

← #25082054

Subgroups — #25082054

Order 11008.

628 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
1#19145551C211yesmaximal, characteristic, complemented
2#19144666C211yesmaximal, characteristic, complemented
3#19143706C211yesmaximal, characteristic, complemented
4#19134037C211yesmaximal, characteristic, complemented
5#19134030C211yesmaximal, characteristic, complemented
6#19134023C211yesmaximal, characteristic, complemented
7#19134016C211yesmaximal, characteristic, complemented
8#19133963C211yesmaximal, characteristic, complemented
9#19133958C211yesmaximal, characteristic, complemented
10#19133941C211yesmaximal, characteristic, complemented
11#19133934C211yesmaximal, characteristic, complemented
12#19133376C211yesmaximal, characteristic, complemented
13#19133296C211yesmaximal, characteristic, complemented
14#19133244C211yesmaximal, characteristic, complemented
15C43×#3115C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583278C2211yescharacteristic
18#14583271C2211yescharacteristic
19#14583249C2211yescharacteristic
20#14583245C2211yescharacteristic
21#14583240—21no—
22#14583184C2211yescharacteristic
23#14583179C2211yescharacteristic
24#14583118—21no—
25#14583118—21no—
26#14583109C2211yescharacteristic
27#14583104C2211yescharacteristic
28#14583061—21no—
29#14583061—21no—
30#14583061—21no—
31Q8×C43⋊C8C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33C4×#10621885—21no—
34C4×#10621883—21no—
35D4×C43⋊C8—21no—
36D4×C43⋊C8—21no—
37D4×C43⋊C8C2211yescharacteristic
38D4×C43⋊C8C2211yescharacteristic
39#14582952—21no—
40#14582952C2211yescharacteristic
41#14582952C2211yescharacteristic
42C2×C4⋊(C43⋊C8)—21no—
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#482—21no—
59C43×#475C2211yescharacteristic
60C43×#474C2211yescharacteristic
61C43×#460C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C43×#442—21no—
65C43×#440—21no—
66C43×#432C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063317—21no—
79#13063304—21no—
80#13063304—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83#13063284—21no—
84#13063258—21no—
85#13063256—21no—
86C4⋊(C43⋊C8)—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)D411yescharacteristic
90C4⋊(C43⋊C8)D411yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—21no—
96#13063249—21no—
97#13063249—21no—
98#13063248—21no—
99#13063248—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)D411yescharacteristic
107C22⋊(C43⋊C8)D411yescharacteristic
108C4×C43⋊C8—21no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43—21no—
114C2×#41×C43D411yescharacteristic
115C2×SD16×C43—21no—
116C2×D8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#124×C43—21no—
120#121×C43—21no—
121#121×C43—21no—
122C4×Q8×C43D411yescharacteristic
123C4×Q8×C43C2311yescharacteristic
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43D411yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131#117×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143#97×C43—21no—
144#41×C43—22no—
145#41×C43—22no—
146#41×C43—81no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—41no—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43#4111yescharacteristic
163C2×Dic86—21no—
164C2×Dic86—21no—
165SD16×C43—42no—
166D8×C43—42no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43#4111yescharacteristic
186C42×C43C2411yescharacteristic
187C22⋊Dic43—41no—
188#10621885—42no—
189#10621885—81no—
190#10621885—81no—
191#10621883—42no—
192#10621883—81no—
193#10621883—81no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200C4×Dic43—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—81no—
206C2×C43⋊C8—81no—
207C2×C43⋊C8—81no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C23×C43—21no—
213C23×C43—41no—
214C23×C43#12111yescharacteristic
215Q8×C43—21no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43#13512yes—
219D4×C43—24no—
220D4×C43—21no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—81no—
226D4×C43—82no—
227D4×C43#13512yes—
228C2×C4×C43—24no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—81no—
241C2×C4×C43—82no—
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43#12111yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×Dic43—41no—
249C2×Dic43—41no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254C8×C43—41no—
255C8×C43—41no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#19413—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—22no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43C2×#12111yescharacteristic
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—22no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—81no—
283C4×C43C2×#13511yescharacteristic
284C4×C43C2×#13511yescharacteristic
285C4×C43#57611yescharacteristic
286C4×C43#57711yescharacteristic
287Dic43—81no—
288Dic43—81no—
289#3210—431no—
290#3115D4311yescharacteristic
291#3107—431no—
292#2988—431no—
293#1682—431no—
294#1681—431no—
295#1680—431no—
296#1679—431no—
297#1670—431no—
298#1669—431no—
299#1666—431no—
300#1665—431no—
301#1572—431no—
302#1552—431no—
303#1540—431no—
304C2×C43—41no—
305C2×C43—42no—
306C2×C43—161no—
307C2×C43#304511yescharacteristic
308C2×C43#305011yescharacteristic
309C2×C43#306911yescharacteristic
310#533—431no—
311#532C2×D4311yescharacteristic
312C4×#41C2×D4311yescharacteristic
313#494—431no—
314#492—431no—
315#487—431no—
316#486—431no—
317#485—861no—
318#482—21no—
319#475—431no—
320#475C2×D4311yescharacteristic
321#474—431no—
322#474C2×D4311yescharacteristic
323#464—861no—
324#464—861no—
325#462—431no—
326#461—431no—
327#460C2×D4311yescharacteristic
328#459C2×D4311yescharacteristic
329#452—861no—
330#452—861no—
331#452—861no—
332#449—21no—
333C8×Q8—431no—
334C8×Q8—431no—
335#442—21no—
336#440—21no—
337C4×Q16—861no—
338C4×SD16—861no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—861no—
342C8×D4—861no—
343#432C2×D4311yescharacteristic
344#431—431no—
345#431—431no—
346#431—861no—
347C2×C4⋊C8—431no—
348C2×C4⋊C8—861no—
349#335—431no—
350#335—431no—
351#334—431no—
352#334—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#332—431no—
358#332—431no—
359#331—431no—
360#331—431no—
361C43#1941311yescharacteristic, complemented, Sylow
362C2×#41—21no—
363C2×#41C22⋊D4311yescharacteristic
364C2×Q16—861no—
365C2×Q16—861no—
366C2×Q16—861no—
367C2×SD16—21no—
368C2×SD16—861no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—21no—
372C22×C8—861no—
373C22×C8—861no—
374C22×C8—861no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377C4⋊Q8C22×D4311yescharacteristic
378#127C22×D4311yescharacteristic
379#125—861no—
380#124—21no—
381C22⋊Q8—861no—
382C22⋊Q8—861no—
383#121—21no—
384#121—21no—
385C4×Q8—861no—
386C4×Q8—861no—
387C4×Q8C22⋊D4311yescharacteristic
388C4×Q8C22×D4311yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4C22⋊D4311yescharacteristic
394C4×D4C22×D4311yescharacteristic
395#117—21no—
396#117—861no—
397#117C22⋊D4311yescharacteristic
398C2×C42—21no—
399C2×C42C22×D4311yescharacteristic
400#107—21no—
401#107—861no—
402#106—21no—
403#106—861no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8C22×D4311yescharacteristic
414C4⋊C8C22×D4311yescharacteristic
415#103—21no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—861no—
425#102—861no—
426#102—861no—
427C22⋊C8—21no—
428C22⋊C8—431no—
429C22⋊C8—431no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—21no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—861no—
437C4×C8—861no—
438C4×C8—861no—
439#41—22no—
440#41—22no—
441#41—81no—
442#41—81no—
443C2×Q8—21no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8C2×C22⋊D4311yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4C2×C22⋊D4311yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4D4×D4311yescharacteristic
458C22×C4#1062190011yescharacteristic
459C22×C4C2×C22⋊D4311yescharacteristic
460Q16—3441no—
461Q16—3441no—
462Q16—1722no—
463SD16—42no—
464SD16—3441no—
465SD16—3441no—
466SD16—1722no—
467D8—42no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—431no—
473C2×C8—431no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—3441no—
479C2×C8—3441no—
480C2×C8—3441no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C4⋊C4C2×C22⋊D4311yescharacteristic
492C4⋊C4C2×C22⋊D4311yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—1721no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—1721no—
503C42D4×D4311yescharacteristic
504C42#1062190011yescharacteristic
505C42C2×C22⋊D4311yescharacteristic
506C42C23×D4311yescharacteristic
507C23—21no—
508C23—41no—
509C23#1306329711yescharacteristic
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516Q8—1721no—
517Q8#1306334512yes—
518D4—24no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4#1306334512yes—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—81no—
540C2×C4—82no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4#1306329711yescharacteristic
544C2×C4#1306329711yescharacteristic
545C2×C4#1306329711yescharacteristic
546C2×C4C2×D4×D4311yescharacteristic
547C2×C4C22×C22⋊D4311yescharacteristic
548C2×C4C2×#1062190011yescharacteristic
549C8—41no—
550C8—41no—
551C8—861no—
552C8—861no—
553C8—861no—
554C8—861no—
555C8—1721no—
556C8—1721no—
557C8—1721no—
558C8—1721no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C2×#1306329711yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—3441no—
578C4—3441no—
579C4C2×#1306334511yescharacteristic
580C4C2×#1306334511yescharacteristic
581C4#1458370311yescharacteristic
582C4#1458370911yescharacteristic
583C2—41no—
584C2—42no—
585C2—161no—
586C2#1914413811yescharacteristic
587C2#1914417311yescharacteristic
588C2#1914433411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3115C2
socleC22×C43C2×#121
hypercenter#3115D43
hypocenterC43#19413
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3115

Complements

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

NH ≅ G/Ntype
1. #19145551C2semidirect
2. #19144666C2semidirect
3. #19143706C2semidirect
4. #19134037C2semidirect
5. #19134030C2semidirect
6. #19134023C2semidirect
7. #19134016C2semidirect
8. #19133963C2semidirect
9. #19133958C2semidirect
10. #19133941C2semidirect
11. #19133934C2semidirect
12. #19133376C2semidirect
13. #19133296C2semidirect
14. #19133244C2semidirect
361. C43#19413semidirect

Maximal subgroups

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

subgroupindex
#191455512
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