Finite Group Databasebeta

← #25081984

Subgroups — #25081984

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145516C211yesmaximal, characteristic, complemented
2#19144403C211yesmaximal, characteristic, complemented
3#19144043C211yesmaximal, characteristic
4#19143702C211yesmaximal, characteristic, complemented
5#19134026C211yesmaximal, characteristic, complemented
6#19134024C211yesmaximal, characteristic, complemented
7#19134018C211yesmaximal, characteristic, complemented
8#19134016C211yesmaximal, characteristic, complemented
9#19133942C211yesmaximal, characteristic, complemented
10#19133940C211yesmaximal, characteristic, complemented
11#19133934C211yesmaximal, characteristic, complemented
12#19133364C211yesmaximal, characteristic, complemented
13#19133269C211yesmaximal, characteristic, complemented
14#332×D43C211yesmaximal, characteristic, complemented
15C43×#1665C211yesmaximal, characteristic, complemented
16C2×#13063344—21no—
17#14583447C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×#10621900C2211yescharacteristic
20#14583271C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583193—21no—
24#14583187—21no—
25#14583185C2211yescharacteristic
26#14583181C2211yescharacteristic
27#14583179C2211yescharacteristic
28#14583120—21no—
29#14583112—21no—
30#14583110C2211yescharacteristic
31#14583104C2211yescharacteristic
32#14583102—21no—
33#14583102—21no—
34#14583096C2211yescharacteristic
35#14583036—21no—
36#14583036—21no—
37C8×Dic86C2211yescharacteristic
38#14583023C2211yescharacteristic
39D4×C43⋊C8C2211yescharacteristic
40C8×C22⋊D43—21no—
41(C22⋊D43)⋊C8—21no—
42#14582950C2211yescharacteristic
43#14582949—21no—
44#14582940—21no—
45#14582921C2211yescharacteristic
46C2×Dic43⋊C8—21no—
47C4⋊C8×D43C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582897—21no—
50#14582892—21no—
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#492C2211yescharacteristic
61C43×#474C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621900D411yescharacteristic
69C2×Q8×D43—21no—
70#13063344—44no—
71C2×Dic172—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621883—21no—
75C2×#10621883—21no—
76C2×#10621872—21no—
77C22×C43⋊C8—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063324—21no—
83#13063324—21no—
84#13063323—21no—
85#13063312—21no—
86#13063296—21no—
87#13063296—21no—
88C4×Dic86C2311yescharacteristic
89#13063290D411yescharacteristic
90D4×Dic43—21no—
91D4×Dic43—21no—
92D4×Dic43D411yescharacteristic
93C4×C22⋊D43—21no—
94(C22⋊D43)⋊C4—21no—
95#13063283D411yescharacteristic
96#13063281—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—21no—
99C2×C4×Dic43—21no—
100C42×D43C2311yescharacteristic
101#13063258—21no—
102#13063257—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8D411yescharacteristic
113Dic43⋊C8D411yescharacteristic
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063249—21no—
119#13063249—21no—
120#13063248—21no—
121#13063248—21no—
122#13063246—21no—
123#13063246—21no—
124C22⋊(C43⋊C8)—21no—
125(C2×D43)⋊C8D411yescharacteristic
126(C2×D43)⋊C8D411yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C8×Dic43—21no—
130C2×SD16×C43—21no—
131C2×SD16×C43—21no—
132C2×D8×C43—21no—
133C22×C8×C43—21no—
134C4⋊Q8×C43C2311yescharacteristic
135#127×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137#107×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#102×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—41no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—41no—
156Q8×D43—81no—
157Q8×D43—81no—
158#10621900—22no—
159#10621900—42no—
160#10621900—42no—
161#10621900SD1614yescomplemented
162C2×C4×D43—41no—
163C2×C4×D43C2×D411yescharacteristic
164C2×C4×D43C2×D411yescharacteristic
165C2×C4×D43#4111yescharacteristic
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—41no—
169C2×Dic86C2×D411yescharacteristic
170SD16×C43—81no—
171SD16×C43—81no—
172D8×C43—42no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—81no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—21no—
185C22⋊Dic43—41no—
186C22⋊Dic43—41no—
187#10621883—42no—
188#10621883—42no—
189#10621883—81no—
190#10621883—81no—
191(C2×D43)⋊C4—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—21no—
198Dic43⋊C4—21no—
199Dic43⋊C4—41no—
200Dic43⋊C4—41no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43C2×D411yescharacteristic
205C4×Dic43C2×D411yescharacteristic
206C4×Dic43#4111yescharacteristic
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—81no—
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213Dic172—42no—
214#10621872—42no—
215C8×D43—42no—
216C8×D43—81no—
217C23×C43—21no—
218C23×C43—41no—
219C22×D43#12111yescharacteristic
220Q8×C43—41no—
221Q8×C43—41no—
222D4×C43—21no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—81no—
228D4×C43C2×SD1612yes—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C22⋊D43—24no—
237C22⋊D43—82no—
238C2×Dic43—21no—
239C2×Dic43—24no—
240C2×Dic43—21no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—81no—
244C2×Dic43—82no—
245C2×Dic43#12111yescharacteristic
246C2×Dic43#12111yescharacteristic
247C2×Dic43#12111yescharacteristic
248C4×D43—21no—
249C4×D43—21no—
250C4×D43—41no—
251C4×D43—82no—
252C4×D43C2×SD1612yes—
253C4×D43#13512yes—
254Dic86—21no—
255Dic86—41no—
256Dic86—41no—
257Dic86—41no—
258Dic86—41no—
259Dic86—82no—
260Dic86C2×SD1612yes—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—41no—
264C8×C43—41no—
265C8×C43—41no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271#19408—431nomaximal, Sylow
272C22×C43—22no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43C2×#12111yescharacteristic
279C2×D43—21no—
280C2×D43—21no—
281C2×D43#46512yes—
282C4×C43—21no—
283C4×C43—41no—
284C4×C43—81no—
285C4×C43C22×SD1611yescharacteristic
286C4×C43C2×#13511yescharacteristic
287C4×C43#57611yescharacteristic
288C4×C43#57711yescharacteristic
289Dic43—21no—
290Dic43—22no—
291Dic43—21no—
292Dic43—41no—
293Dic43—81no—
294Dic43—81no—
295Dic43#46512yes—
296#3206—431no—
297#3079—431no—
298#3035—431no—
299#2988—431no—
300#1680—431no—
301#1680—431no—
302#1679—431no—
303#1679—431no—
304#1666—431no—
305#1666—431no—
306#1665—431no—
307#1665D4311yescharacteristic, complemented
308#1570—431no—
309#1547—431no—
310C2×#332—431no—
311C2×C43—42no—
312C2×C43—161no—
313C2×C43#304511yescharacteristic
314C2×C43C2×#46511yescharacteristic
315C2×C43#306911yescharacteristic
316D43—22no—
317C2×#135—861no—
318#532—431no—
319C2×C4⋊Q8—431no—
320C4×#41—431no—
321#492—431no—
322#492C2×D4311yescharacteristic
323#487—431no—
324#487—431no—
325#477—861no—
326#476—861no—
327#475—431no—
328#475—431no—
329#474—431no—
330#474C2×D4311yescharacteristic
331#464—861no—
332#463—861no—
333#462—431no—
334#461—431no—
335#461—861no—
336#461—861no—
337#460—431no—
338#459C2×D4311yescharacteristic
339#448—861no—
340#448—861no—
341C8×Q8—431no—
342C8×Q8—431no—
343C8×D4—431no—
344C8×D4—861no—
345C8×D4—861no—
346C8×D4C2×D4311yescharacteristic
347#431—431no—
348#431—861no—
349#428—861no—
350#423—431no—
351C2×C4⋊C8—431no—
352C2×C4⋊C8—431no—
353C2×C4⋊C8—861no—
354#417—861no—
355#416—861no—
356#334—431no—
357#334—431no—
358#334—431no—
359#334C2×D4311yescharacteristic
360#332—431no—
361#332—431no—
362#332—431no—
363#332—431no—
364#332—431no—
365#332C2×D4311yescharacteristic
366#331—431no—
367#331C2×D4311yescharacteristic
368C43#1940811yescharacteristic, complemented, Sylow
369C2×#41—431no—
370C2×#41—861no—
371C22×Q8—861no—
372#135—1724no—
373C2×Q16—861no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—861no—
377C2×SD16—861no—
378C2×SD16—861no—
379C2×SD16—861no—
380C2×D8—21no—
381C2×M16—861no—
382C22×C8—21no—
383C22×C8—861no—
384C22×C8—861no—
385C22×C8—861no—
386C4⋊Q8—431no—
387C4⋊Q8—431no—
388C4⋊Q8—861no—
389C4⋊Q8—861no—
390C4⋊Q8—861no—
391C4⋊Q8C22×D4311yescharacteristic
392#127C22×D4311yescharacteristic
393#124—861no—
394#121—861no—
395#121—861no—
396C4×Q8—431no—
397C4×Q8—431no—
398C4×D4—431no—
399C4×D4—861no—
400C4×D4—861no—
401C4×D4—861no—
402C4×D4—861no—
403C4×D4C22×D4311yescharacteristic
404#117—431no—
405#117—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C42—431no—
409C2×C42—861no—
410#107—21no—
411#107—861no—
412#106—861no—
413#106—861no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—431no—
419C4⋊C8—861no—
420C4⋊C8—861no—
421C4⋊C8—861no—
422C4⋊C8—861no—
423C4⋊C8—861no—
424C4⋊C8C22×D4311yescharacteristic
425C4⋊C8C22×D4311yescharacteristic
426C4⋊C8C22×D4311yescharacteristic
427#103—861no—
428#103—861no—
429#103—861no—
430#103—861no—
431#103—861no—
432#103—861no—
433#103—861no—
434#103—861no—
435#102—21no—
436#102—21no—
437#102—861no—
438#102—861no—
439C22⋊C8—21no—
440C22⋊C8—431no—
441C22⋊C8—431no—
442C22⋊C8—861no—
443C4×C8—431no—
444C4×C8—861no—
445C4×C8—861no—
446C4×C8C22×D4311yescharacteristic
447#41—434no—
448#41—862no—
449#41—1722no—
450#41—1722no—
451C2×Q8—21no—
452C2×Q8—431no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×Q8—3441no—
456C2×Q8—3441no—
457C2×Q8—1721no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—861no—
462C2×D4—1721no—
463C2×D4D4×D4311yescharacteristic
464C22×C4—21no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—1721no—
471C22×C4—1721no—
472Q16—1722no—
473SD16—81no—
474SD16—81no—
475SD16—3441no—
476SD16—3441no—
477SD16—1722no—
478SD16—1722no—
479D8—42no—
480M16—1722no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—81no—
485C2×C8—431no—
486C2×C8—431no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—3441no—
491C2×C8—3441no—
492C2×C8—1722no—
493C2×C8D4×D4311yescharacteristic
494C2×C8D4×D4311yescharacteristic
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—431no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—1721no—
505C4⋊C4—1721no—
506C4⋊C4D4×D4311yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—861no—
509C22⋊C4—861no—
510C22⋊C4—1721no—
511C22⋊C4—1721no—
512C42—431no—
513C42—431no—
514C42—431no—
515C42—861no—
516C42—861no—
517C42—861no—
518C42C23×D4311yescharacteristic
519C23—21no—
520C23—41no—
521C23—431no—
522Q8—41no—
523Q8—41no—
524Q8—432no—
525Q8—861no—
526Q8—3442no—
527Q8—1721no—
528Q8—1721no—
529Q8—1721no—
530Q8—1721no—
531D4—21no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—81no—
537D4—864no—
538D4—3442no—
539D4SD16×D4312yes—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—431no—
545C2×C4—432no—
546C2×C4—432no—
547C2×C4—431no—
548C2×C4—431no—
549C2×C4—864no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—3442no—
555C2×C4—3442no—
556C2×C4—3441no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4C2×D4×D4311yescharacteristic
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4#41×D4311yescharacteristic
563C8—21no—
564C8—21no—
565C8—41no—
566C8—41no—
567C8—41no—
568C8—861no—
569C8—861no—
570C8—1721no—
571C8—1721no—
572C8—1721no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—432no—
580C22—861no—
581C22—861no—
582C22#121×D4311yescharacteristic
583C4—21no—
584C4—41no—
585C4—81no—
586C4—432no—
587C4—861no—
588C4—861no—
589C4—862no—
590C4—3441no—
591C4—3441no—
592C4—1721no—
593C4C2×SD16×D4311yescharacteristic
594C4#135×D4311yescharacteristic
595C4#1458370011yescharacteristic
596C4#1458370911yescharacteristic
597C2—42no—
598C2—161no—
599C2—862no—
600C2#1914412911yescharacteristic
601C2#465×D4311yescharacteristic
602C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1665C2
socleC22×C43C2×#121
prime radical#19144043C2
hypercenter#1665D43
hypocenterC43#19408
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1665

Complements

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

NH ≅ G/Ntype
1. #19145516C2semidirect
2. #19144403C2semidirect
4. #19143702C2semidirect
5. #19134026C2semidirect
6. #19134024C2semidirect
7. #19134018C2semidirect
8. #19134016C2semidirect
9. #19133942C2semidirect
10. #19133940C2semidirect
11. #19133934C2semidirect
12. #19133364C2semidirect
13. #19133269C2semidirect
14. #332×D43C2semidirect
15. C43×#1665C2semidirect
161. #10621900SD16semidirect
307. #1665D43semidirect
368. C43#19408semidirect

Maximal subgroups

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

subgroupindex
#191455162
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