Finite Group Databasebeta

← #25079605

Subgroups — #25079605

Order 11008.

646 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145314C211yesmaximal, characteristic, complemented
2#19144050C211yesmaximal, characteristic
3#19143615C211yesmaximal, characteristic, complemented
4#19134158C211yesmaximal, characteristic, complemented
5#19134140C211yesmaximal, characteristic, complemented
6#19134106C211yesmaximal, characteristic, complemented
7#19134062C211yesmaximal, characteristic, complemented
8#19134041C211yesmaximal, characteristic, complemented
9#19134023C211yesmaximal, characteristic, complemented
10#19133987C211yesmaximal, characteristic, complemented
11#19133945C211yesmaximal, characteristic, complemented
12#19133348C211yesmaximal, characteristic, complemented
13#19133298C211yesmaximal, characteristic, complemented
14#19133295C211yesmaximal, characteristic, complemented
15C43×#3107C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17#14583449C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583273C2211yescharacteristic
20#14583249C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583147—21no—
23#14583147—21no—
24#14583121—21no—
25#14583114—21no—
26#14583109C2211yescharacteristic
27#14583104C2211yescharacteristic
28#14583099C2211yescharacteristic
29#14583094C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31Q8×C43⋊C8C2211yescharacteristic
32#14582997—21no—
33#14582997—21no—
34#14582977—21no—
35#14582977—21no—
36#14582977C2211yescharacteristic
37#14582977C2211yescharacteristic
38#14582956—21no—
39#14582956C2211yescharacteristic
40C2×C4⋊(C43⋊C8)C2211yescharacteristic
41#14582893—21no—
42C4×#10621877—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#485—21no—
59C43×#475C2211yescharacteristic
60C43×#474C2211yescharacteristic
61C43×#462C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#452—21no—
64C4×Q16×C43—21no—
65C4×SD16×C43—21no—
66C43×#431C2211yescharacteristic
67C2×#10621898—21no—
68#13063345—44no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×#10621882—21no—
75C2×#10621877—21no—
76C2×#10621877—21no—
77C2×#10621877D411yescharacteristic
78C2×#10621877D411yescharacteristic
79C22×C43⋊C8—21no—
80#13063325C2311yescharacteristic
81#13063322C2311yescharacteristic
82#13063313—21no—
83#13063299—21no—
84#13063299—21no—
85C4×D172—21no—
86C4×D172—21no—
87#13063258—21no—
88#13063258—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96#13063249—21no—
97#13063249—21no—
98#13063248—21no—
99#13063248—21no—
100#13063245—21no—
101#13063245—21no—
102#13063245—21no—
103#13063245—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)—21no—
107#13063236—21no—
108#13063236D411yescharacteristic
109#13063236D411yescharacteristic
110C4×C43⋊C8—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C2×#41×C43D411yescharacteristic
115C2×Q16×C43—21no—
116C2×SD16×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#125×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122C4×Q8×C43—21no—
123C4×Q8×C43—21no—
124C4×Q8×C43D411yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43D411yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131#117×C43—21no—
132#117×C43D411yescharacteristic
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43—21no—
145#41×C43—22no—
146#41×C43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C2×C22⋊D43—41no—
159#10621898—42no—
160#10621898—42no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×C4×D43—41no—
165C2×Dic86—21no—
166Q16×C43—42no—
167SD16×C43—42no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—41no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—41no—
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43#4111yescharacteristic
191C42×C43C2411yescharacteristic
192#10621885—42no—
193#10621884—42no—
194#10621884—42no—
195#10621884—42no—
196#10621883—42no—
197#10621882—42no—
198(C2×D43)⋊C4—41no—
199(C2×D43)⋊C4—41no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202#10621877—22no—
203#10621877—41no—
204#10621877—42no—
205#10621877—42no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—42no—
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C23×C43—21no—
216C23×C43#12111yescharacteristic
217C22×D43—41no—
218Q8×C43—21no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43AGL(1,ℤ/8)12yes—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—42no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—42no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—81no—
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C22⋊D43—82no—
248C2×Dic43—41no—
249D172—41no—
250D172—41no—
251D172—41no—
252D172—41no—
253D172—81no—
254C4×D43—82no—
255Dic86—41no—
256Dic86—41no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8#13512yescomplemented
267#19182—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43C2×#12111yescharacteristic
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—22no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43C2×#13511yescharacteristic
288C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
289C4×C43#57511yescharacteristic
290C4×C43#57511yescharacteristic
291Dic43—81no—
292#3182—431no—
293#3107D4311yescharacteristic, complemented
294#3035—431no—
295#2971—431no—
296#1701—431no—
297#1699—431no—
298#1693—431no—
299#1685—431no—
300#1682—431no—
301#1680—431no—
302#1674—431no—
303#1666—431no—
304#1565—431no—
305#1553—431no—
306#1552—431no—
307C2×C43—41no—
308C2×C43—81no—
309C2×C43#303511yescharacteristic
310C2×C43#305511yescharacteristic
311C2×C43#306911yescharacteristic
312D43—161no—
313C2×#135—861no—
314#533C2×D4311yescharacteristic
315#532—431no—
316C4×#41C2×D4311yescharacteristic
317#500—431no—
318#492—431no—
319#487—431no—
320#486—431no—
321#485—21no—
322#475C2×D4311yescharacteristic
323#474C2×D4311yescharacteristic
324#468—861no—
325#468—861no—
326#464—861no—
327#463—861no—
328#462—431no—
329#462C2×D4311yescharacteristic
330#461—431no—
331#461C2×D4311yescharacteristic
332#460—431no—
333#459—431no—
334#452—21no—
335C8×Q8—431no—
336C8×Q8—431no—
337#440—861no—
338#440—861no—
339C4×Q16—21no—
340C4×SD16—21no—
341#436—431no—
342#436—431no—
343#436—861no—
344#436—861no—
345#432—431no—
346#432—861no—
347#431C2×D4311yescharacteristic
348C2×C4⋊C8—431no—
349#416—861no—
350C4×M16—431no—
351C4×M16—861no—
352#335—431no—
353#335—431no—
354#334—431no—
355#334—431no—
356#332—431no—
357#332—431no—
358#332—431no—
359#332—431no—
360#332—431no—
361#332—431no—
362#331—431no—
363#331—431no—
364C43#1918211yescharacteristic, complemented, Sylow
365C2×#41—861no—
366C2×#41C22⋊D4311yescharacteristic
367#135—1724no—
368C2×Q16—21no—
369C2×Q16—861no—
370C2×SD16—21no—
371C2×SD16—861no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×SD16—861no—
375C2×D8—861no—
376C2×M16—431no—
377C2×M16—431no—
378C2×M16—861no—
379C2×M16—861no—
380C22×C8—861no—
381C4⋊Q8—431no—
382C4⋊Q8C22×D4311yescharacteristic
383C4⋊Q8C22×D4311yescharacteristic
384#127—431no—
385#125—21no—
386#124—861no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389#121—861no—
390#121—861no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8C22⋊D4311yescharacteristic
394C4×Q8C22×D4311yescharacteristic
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—861no—
398C4×D4—861no—
399C4×D4C22⋊D4311yescharacteristic
400C4×D4C22×D4311yescharacteristic
401#117—21no—
402#117—21no—
403#117C22⋊D4311yescharacteristic
404C2×C42—21no—
405C2×C42C22×D4311yescharacteristic
406#107—21no—
407#107—861no—
408#107—861no—
409#106—21no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—861no—
415C4⋊C8—861no—
416C4⋊C8—861no—
417C4⋊C8C22×D4311yescharacteristic
418C4⋊C8C22×D4311yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—861no—
423#103—861no—
424#103—861no—
425#103—861no—
426#102—21no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—21no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435#97—431no—
436#97—431no—
437#97—861no—
438C4×C8—21no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—861no—
442C4×C8—861no—
443#41—22no—
444#41—41no—
445#41—1722no—
446#41—1722no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—861no—
450C2×Q8C2×C22⋊D4311yescharacteristic
451C2×D4—21no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—1721no—
456C2×D4C2×C22⋊D4311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—1721no—
461C22×C4D4×D4311yescharacteristic
462C22×C4#1062190011yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464Q16—42no—
465Q16—1722no—
466SD16—42no—
467SD16—1722no—
468SD16—1722no—
469SD16—1722no—
470SD16—1722no—
471D8—1722no—
472M16—862no—
473M16—1722no—
474M16—1721no—
475M16—1722no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—1722no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4C2×C22⋊D4311yescharacteristic
498C4⋊C4C2×C22⋊D4311yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—41no—
503C22⋊C4—1721no—
504C22⋊C4—1721no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—41no—
509C42D4×D4311yescharacteristic
510C42#1062190011yescharacteristic
511C42C2×C22⋊D4311yescharacteristic
512C42C23×D4311yescharacteristic
513C23—21no—
514C23—1721no—
515C23#1306329711yescharacteristic
516Q8—21no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—1721no—
522Q8—1721no—
523Q8#1306335012yes—
524D4—21no—
525D4—21no—
526D4—42no—
527D4—3441no—
528D4—3442no—
529D4—1721no—
530D4—1721no—
531D4—1721no—
532D4—1721no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—81no—
547C2×C4—3442no—
548C2×C4—1721no—
549C2×C4#1306329711yescharacteristic
550C2×C4#1306329711yescharacteristic
551C2×C4#1306329711yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C22×C22⋊D4311yescharacteristic
554C2×C4C2×#1062190011yescharacteristic
555C8—41no—
556C8—41no—
557C8—432no—
558C8—861no—
559C8—861no—
560C8—861no—
561C8—1721no—
562C8—1721no—
563C8—1721no—
564C8—1721no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—3441no—
572C22—3441no—
573C22—3441no—
574C22C2×#1306329711yescharacteristic
575C4—21no—
576C4—22no—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—3441no—
585C4#135×D4311yescharacteristic
586C4C2×#1306335011yescharacteristic
587C4#1458369611yescharacteristic
588C4#1458369711yescharacteristic
589C2—41no—
590C2—81no—
591C2—6881no—
592C2#1914404611yescharacteristic
593C2#1914421611yescharacteristic
594C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3107C2
socleC22×C43C2×#121
prime radical#19144050C2
hypercenter#3107D43
hypocenterC43#19182
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
1. #19145314C2semidirect
3. #19143615C2semidirect
4. #19134158C2semidirect
5. #19134140C2semidirect
6. #19134106C2semidirect
7. #19134062C2semidirect
8. #19134041C2semidirect
9. #19134023C2semidirect
10. #19133987C2semidirect
11. #19133945C2semidirect
12. #19133348C2semidirect
13. #19133298C2semidirect
14. #19133295C2semidirect
15. C43×#3107C2semidirect
266. C43⋊C8#135semidirect
293. #3107D43semidirect
364. C43#19182semidirect

Maximal subgroups

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

subgroupindex
#191453142
#191440502
#191436152
#191341582
#191341402
#191341062
#191340622
#191340412
#191340232
#191339872
#191339452
#191333482
#191332982
#191332952
C43×#31072
#1918243