Finite Group Databasebeta

← #25082129

Subgroups — #25082129

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145726C211yesmaximal, characteristic, complemented
2#19144754C211yesmaximal, characteristic, complemented
3#19144652C211yesmaximal, characteristic
4#19143702C211yesmaximal, characteristic, complemented
5#19134036C211yesmaximal, characteristic, complemented
6#19134010C211yesmaximal, characteristic, complemented
7#19134002C211yesmaximal, characteristic, complemented
8#19134000C211yesmaximal, characteristic, complemented
9#19133994C211yesmaximal, characteristic, complemented
10#19133976C211yesmaximal, characteristic, complemented
11#19133968C211yesmaximal, characteristic, complemented
12#19133374C211yesmaximal, characteristic, complemented
13#19133287C211yesmaximal, characteristic, complemented
14#19133251C211yesmaximal, characteristic, complemented
15C43×#1681C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583239—21no—
23#14583221—21no—
24#14583221—21no—
25#14583221—21no—
26#14583197—21no—
27#14583197—21no—
28#14583195C2211yescharacteristic
29#14583195C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583106C2211yescharacteristic
33#14583096C2211yescharacteristic
34#14583058—21no—
35#14583041—21no—
36C8×Dic86C2211yescharacteristic
37#14583023C2211yescharacteristic
38#14583003—21no—
39#14583000—21no—
40#14582990—21no—
41D8×Dic43—21no—
42D4×C43⋊C8C2211yescharacteristic
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582955C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582950C2211yescharacteristic
48#14582949—21no—
49C2×Dic43⋊C8—21no—
50C4⋊C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#461C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621900D411yescharacteristic
69C2×#10621885—21no—
70C2×#10621883—21no—
71C22×C43⋊C8—21no—
72C2×C8×D43—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063316—21no—
76#13063312—21no—
77#13063305—21no—
78#13063301—21no—
79#13063296—21no—
80#13063296—21no—
81Q8×Dic43—21no—
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063290D411yescharacteristic
85D4×Dic43—21no—
86D4×Dic43—21no—
87D4×Dic43D411yescharacteristic
88C4×C22⋊D43—21no—
89(C22⋊D43)⋊C4—21no—
90#13063283—21no—
91#13063283D411yescharacteristic
92#13063281—21no—
93C2×C4×Dic43—21no—
94C42×D43C2311yescharacteristic
95#13063259—21no—
96#13063259—21no—
97#13063259—21no—
98#13063259—21no—
99#13063256—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8D411yescharacteristic
110Dic43⋊C8D411yescharacteristic
111#13063250—21no—
112#13063250—21no—
113#13063249—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119C22⋊(C43⋊C8)—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8D411yescharacteristic
123(C2×D43)⋊C8D411yescharacteristic
124#13063235—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43—21no—
130C2×D8×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133#127×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
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—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—41no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—41no—
155#10621900—22no—
156#10621900—22no—
157#10621900—82no—
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43C2×D411yescharacteristic
160C2×C4×D43#4111yescharacteristic
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164SD16×C43—42no—
165D8×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—81no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C2×D411yescharacteristic
175C22⋊C4×C43—21no—
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178C22⋊Dic43—41no—
179C22⋊Dic43—41no—
180#10621885—42no—
181#10621883—42no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—41no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—41no—
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—41no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43#4111yescharacteristic
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—81no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C8×D43—81no—
207C23×C43—21no—
208C23×C43—41no—
209C22×D43#12111yescharacteristic
210Q8×C43—41no—
211Q8×C43—41no—
212D4×C43—21no—
213D4×C43—41no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—81no—
218D4×C43#13512yes—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C22⋊D43—24no—
227C22⋊D43—82no—
228C2×Dic43—24no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—81no—
234C2×Dic43—82no—
235C2×Dic43#12111yescharacteristic
236C2×Dic43#12111yescharacteristic
237C2×Dic43#12111yescharacteristic
238C4×D43—21no—
239C4×D43—21no—
240C4×D43—21no—
241C4×D43—21no—
242C4×D43—41no—
243Dic86—21no—
244Dic86—81no—
245Dic86—81no—
246Dic86#13512yes—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19419—431nomaximal, Sylow
258C22×C43—22no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43C2×#12111yescharacteristic
265C2×D43—21no—
266C2×D43—21no—
267C2×D43—21no—
268C4×C43—21no—
269C4×C43—41no—
270C4×C43—81no—
271C4×C43C2×#13511yescharacteristic
272C4×C43C2×#13511yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57811yescharacteristic
275Dic43—21no—
276Dic43—22no—
277Dic43—21no—
278Dic43—21no—
279Dic43—41no—
280Dic43—81no—
281Dic43—81no—
282#3228—431no—
283#3116—431no—
284#3106—431no—
285#2988—431no—
286#1682—431no—
287#1681D4311yescharacteristic, complemented
288#1678—431no—
289#1677—431no—
290#1676—431no—
291#1675—431no—
292#1672—431no—
293#1671—431no—
294#1572—431no—
295#1551—431no—
296#1542—431no—
297C2×C43—42no—
298C2×C43—161no—
299C2×C43#304611yescharacteristic
300C2×C43#305011yescharacteristic
301C2×C43#306811yescharacteristic
302D43—41no—
303#533—431no—
304#532—431no—
305C4×#41—431no—
306#500—431no—
307#498—431no—
308#486—431no—
309#486C2×D4311yescharacteristic
310#485—861no—
311#482—861no—
312#482—861no—
313#482—861no—
314#478—861no—
315#478—861no—
316#477—431no—
317#477—431no—
318#476—431no—
319#476—431no—
320#462—431no—
321#461C2×D4311yescharacteristic
322#460—431no—
323#459C2×D4311yescharacteristic
324#452—861no—
325#449—861no—
326C8×Q8—431no—
327C8×Q8—431no—
328#441—861no—
329#440—861no—
330C4×SD16—861no—
331C4×D8—861no—
332C8×D4—431no—
333C8×D4—861no—
334C8×D4—861no—
335C8×D4C2×D4311yescharacteristic
336#432—431no—
337#431—431no—
338#431—431no—
339#431—861no—
340C2×C4⋊C8—431no—
341C2×C4⋊C8—861no—
342#335—431no—
343#335C2×D4311yescharacteristic
344#334—431no—
345#334—431no—
346#333—431no—
347#333—431no—
348#333—431no—
349#333—431no—
350#332—431no—
351#332C2×D4311yescharacteristic
352#331—431no—
353#331C2×D4311yescharacteristic
354C43#1941911yescharacteristic, complemented, Sylow
355C2×#41—431no—
356C2×#41—861no—
357C2×Q16—861no—
358C2×SD16—21no—
359C2×SD16—861no—
360C2×D8—21no—
361C22×C8—21no—
362C22×C8—861no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8C22×D4311yescharacteristic
367#127C22×D4311yescharacteristic
368#125—861no—
369#124—861no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372#121—861no—
373#121—861no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—861no—
377C4×Q8—861no—
378C4×D4—431no—
379C4×D4—861no—
380C4×D4—861no—
381C4×D4—861no—
382C4×D4—861no—
383C4×D4C22×D4311yescharacteristic
384#117—431no—
385#117—861no—
386#117—861no—
387C2×C42—431no—
388C2×C42—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—861no—
394#106—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407C4⋊C8C22×D4311yescharacteristic
408#103—21no—
409#103—861no—
410#103—861no—
411#103—861no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420C22⋊C8—21no—
421C22⋊C8—431no—
422C22⋊C8—431no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—861no—
427C4×C8—431no—
428C4×C8—861no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8C22×D4311yescharacteristic
432#41—862no—
433#41—862no—
434#41—3442no—
435C2×Q8—21no—
436C2×Q8—431no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—861no—
443C2×D4—1721no—
444C2×D4D4×D4311yescharacteristic
445C22×C4—21no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—1721no—
452Q16—1722no—
453SD16—42no—
454SD16—1722no—
455D8—42no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—3441no—
466C2×C8—3441no—
467C2×C8D4×D4311yescharacteristic
468C2×C8D4×D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—431no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4D4×D4311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C42—431no—
488C42—431no—
489C42—431no—
490C42—861no—
491C42—861no—
492C42—861no—
493C42—1721no—
494C42C23×D4311yescharacteristic
495C23—21no—
496C23—41no—
497C23—431no—
498Q8—41no—
499Q8—41no—
500Q8—432no—
501Q8—861no—
502Q8—3441no—
503Q8—3441no—
504D4—21no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—81no—
510D4—864no—
511D4—3442no—
512D4#1306334412yes—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—431no—
518C2×C4—431no—
519C2×C4—431no—
520C2×C4—864no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—3442no—
528C2×C4—3441no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4#41×D4311yescharacteristic
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—861no—
541C8—861no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C22—22no—
546C22—41no—
547C22—41no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—861no—
552C22—861no—
553C22—861no—
554C22#121×D4311yescharacteristic
555C4—21no—
556C4—41no—
557C4—81no—
558C4—861no—
559C4—861no—
560C4—861no—
561C4—862no—
562C4—3441no—
563C4—3441no—
564C4—1721no—
565C4#135×D4311yescharacteristic
566C4C2×#1306334411yescharacteristic
567C4#1458370911yescharacteristic
568C4#1458371311yescharacteristic
569C2—42no—
570C2—161no—
571C2—1721no—
572C2#1914414611yescharacteristic
573C2#1914417411yescharacteristic
574C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1681C2
socleC22×C43C2×#121
prime radical#19144652C2
hypercenter#1681D43
hypocenterC43#19419
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1681

Complements

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

NH ≅ G/Ntype
1. #19145726C2semidirect
2. #19144754C2semidirect
4. #19143702C2semidirect
5. #19134036C2semidirect
6. #19134010C2semidirect
7. #19134002C2semidirect
8. #19134000C2semidirect
9. #19133994C2semidirect
10. #19133976C2semidirect
11. #19133968C2semidirect
12. #19133374C2semidirect
13. #19133287C2semidirect
14. #19133251C2semidirect
15. C43×#1681C2semidirect
287. #1681D43semidirect
354. C43#19419semidirect

Maximal subgroups

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

subgroupindex
#191457262
#191447542
#191446522
#191437022
#191340362
#191340102
#191340022
#191340002
#191339942
#191339762
#191339682
#191333742
#191332872
#191332512
C43×#16812
#1941943