Finite Group Databasebeta

← #25087599

Subgroups — #25087599

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147460C211yesmaximal, characteristic
2#19147242C211yesmaximal, characteristic
3#19147211C211yesmaximal, characteristic, complemented
4#19146988C211yesmaximal, characteristic, complemented
5#19134272C211yesmaximal, characteristic, complemented
6#19134118C211yesmaximal, characteristic, complemented
7#19134054C211yesmaximal, characteristic, complemented
8#19134000C211yesmaximal, characteristic, complemented
9#19133970C211yesmaximal, characteristic, complemented
10#19133804C211yesmaximal, characteristic, complemented
11#19133769C211yesmaximal, characteristic, complemented
12#19133731C211yesmaximal, characteristic, complemented
13#19133731C211yesmaximal, characteristic, complemented
14#19133415C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic
16#14583619C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583606C2211yescharacteristic
19#14583606C2211yescharacteristic
20#14583304C2211yescharacteristic
21#14583304C2211yescharacteristic
22#14583300—21no—
23#14583297C2211yescharacteristic
24#14583279C2211yescharacteristic
25#14583252—21no—
26#14583250C2211yescharacteristic
27#14583250C2211yescharacteristic
28#14583241—21no—
29#14583235—21no—
30#14583235—21no—
31#14583230—21no—
32#14583205—21no—
33#14583197—21no—
34#14583197—21no—
35#14583195C2211yescharacteristic
36#14583195C2211yescharacteristic
37#14583195C2211yescharacteristic
38#14583189C2211yescharacteristic
39#14583189C2211yescharacteristic
40#14583189C2211yescharacteristic
41#14583185C2211yescharacteristic
42#14583157—21no—
43#14583140—21no—
44#14583112—21no—
45#14583104C2211yescharacteristic
46C8×Dic86C2211yescharacteristic
47C8×Dic86C2211yescharacteristic
48C4×Dic172C2211yescharacteristic
49#14582990—21no—
50D8×Dic43—21no—
51#14582941—21no—
52C2×#13063259—21no—
53#14582650C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582631C2211yescharacteristic
59#14582631C2211yescharacteristic
60C4×D8×C43C2211yescharacteristic
61C43×#436C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Dic172—41no—
68C2×Dic172D411yescharacteristic
69C2×#10621883—21no—
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063318—41no—
75#13063316—21no—
76#13063316—21no—
77#13063316—21no—
78#13063312—21no—
79#13063304—21no—
80#13063304—21no—
81#13063304—21no—
82#13063304—21no—
83#13063302—41no—
84#13063302—41no—
85#13063302—41no—
86C4×Dic86C2311yescharacteristic
87C4×Dic86C2311yescharacteristic
88#13063290—21no—
89D4×Dic43—21no—
90D4×Dic43—21no—
91D4×Dic43—21no—
92#13063284—21no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96#13063259—21no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063259D411yescharacteristic
104#13063257—21no—
105#13063257—21no—
106#13063257—21no—
107#13063256—21no—
108#13063256—21no—
109#13063256—21no—
110C4⋊(C43⋊C8)C2311yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063250—21no—
119#13063250—21no—
120#13063250—41no—
121#13063250D411yescharacteristic
122#13063250D411yescharacteristic
123#13063248—21no—
124#13063246—21no—
125#13063246—21no—
126#13063246—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×D8×C43D411yescharacteristic
130C2×M16×C43—21no—
131C22×C8×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#102×C43D411yescharacteristic
138#102×C43D411yescharacteristic
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×D4×C43C2×D411yescharacteristic
145C2×D4×C43C2×D411yescharacteristic
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×Dic43—41no—
149C22×Dic43—41no—
150C22×Dic43—41no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86C2×D411yescharacteristic
156C2×Dic86C2×D411yescharacteristic
157D8×C43—22no—
158M16×C43—42no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—42no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43C2×D411yescharacteristic
168C4⋊C4×C43C2×D411yescharacteristic
169C22⋊C4×C43—21no—
170C22⋊C4×C43—21no—
171C42×C43C2411yescharacteristic
172C22⋊Dic43—41no—
173C22⋊Dic43—41no—
174C22⋊Dic43—41no—
175C22⋊Dic43—41no—
176C22⋊Dic43—41no—
177#10621883—42no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—41no—
187C4⋊Dic43—41no—
188C4⋊Dic43—41no—
189C4⋊Dic43C2×D411yescharacteristic
190C4⋊Dic43C2×D411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—41no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202Dic172—22no—
203Dic172—82no—
204C23×C43—21no—
205C23×C43—21no—
206D4×C43—21no—
207D4×C43—21no—
208D4×C43—21no—
209D4×C43#13712yes—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43H(5,𝔽2)11yescharacteristic
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—161no—
228C2×Dic43—161no—
229C2×Dic43—161no—
230Dic86—21no—
231Dic86—21no—
232Dic86—21no—
233Dic86—21no—
234Dic86—41no—
235Dic86—41no—
236Dic86—81no—
237Dic86—81no—
238Dic86—81no—
239C8×C43—21no—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43#13512yes—
246C43⋊C8—41no—
247C43⋊C8—41no—
248#19865—431nomaximal, Sylow
249C22×C43—22no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43D4211yescharacteristic
256C4×C43—21no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43C2×#13511yescharacteristic
260C4×C43C2×#13711yescharacteristic
261C4×C43#57811yescharacteristic
262C4×C43#57811yescharacteristic
263Dic43—41no—
264Dic43—41no—
265Dic43—41no—
266Dic43—41no—
267Dic43—81no—
268Dic43—81no—
269Dic43—81no—
270Dic43—81no—
271#3380—431no—
272#3360—431no—
273#3356—431no—
274#3338—431no—
275#1723—431no—
276#1695—431no—
277#1684—431no—
278#1676—431no—
279#1671—431no—
280#1643—431no—
281#1638—431no—
282#1632—431no—
283#1632—431no—
284#1581D4311yescharacteristic
285#1579—431no—
286C2×C43—42no—
287C2×C43—81no—
288C2×C43#327011yescharacteristic
289C2×C43#328311yescharacteristic
290C2×C43#328811yescharacteristic
291#556—431no—
292#554—431no—
293#554—431no—
294#554—431no—
295#500—431no—
296#500—431no—
297#499—861no—
298#498—431no—
299#494—431no—
300#488—861no—
301#487—431no—
302#487—431no—
303#485—861no—
304#484—861no—
305#484—861no—
306#483—861no—
307#479—861no—
308#478—861no—
309#478—861no—
310#477—431no—
311#477—431no—
312#477—431no—
313#476—431no—
314#476—431no—
315#476—431no—
316#475—431no—
317#470—861no—
318#467—861no—
319#463—861no—
320#461—431no—
321C8×Q8—431no—
322C8×Q8—431no—
323C4×Q16—431no—
324C4×SD16—861no—
325C4×D8—861no—
326C4×D8C2×D4311yescharacteristic
327#436C2×D4311yescharacteristic
328C8×D4C2×D4311yescharacteristic
329#428—861no—
330C2×#107—861no—
331#335C2×D4311yescharacteristic
332#334—431no—
333#333—431no—
334#333—431no—
335#333—431no—
336#332—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339D4⋊C8C2×D4311yescharacteristic
340D4⋊C8C2×D4311yescharacteristic
341#322C2×D4311yescharacteristic
342C43#1986511yescharacteristic, complemented, Sylow
343C2×Q16—431no—
344C2×Q16—1721no—
345C2×SD16—861no—
346C2×D8D17211yescharacteristic
347C2×M16—21no—
348C22×C8—21no—
349C4⋊Q8—431no—
350C4⋊Q8—431no—
351C4⋊Q8—431no—
352C4⋊Q8—431no—
353#126—1721no—
354#125—861no—
355#125—861no—
356#125—861no—
357#124—861no—
358C22⋊Q8—861no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361C22⋊Q8—861no—
362C22⋊Q8—1721no—
363C22⋊Q8—1721no—
364C22⋊Q8—1721no—
365C4×Q8—431no—
366C4×Q8—431no—
367C4×Q8—861no—
368C4×D4—861no—
369C4×D4—861no—
370C4×D4—861no—
371C4×D4C22×D4311yescharacteristic
372C4×D4C22×D4311yescharacteristic
373#117—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377#107—431no—
378#107—861no—
379#107—861no—
380#107—861no—
381#107—861no—
382#107—861no—
383#107—861no—
384#107—861no—
385#107D17211yescharacteristic
386#106—861no—
387#106—861no—
388#106—861no—
389#106—861no—
390#106—861no—
391#106—861no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398#103—431no—
399#103—431no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—1721no—
408#102—861no—
409#102—861no—
410#102—861no—
411#102D17211yescharacteristic
412#102D17211yescharacteristic
413C22⋊C8—21no—
414C22⋊C8—21no—
415C4×C8—861no—
416C4×C8—861no—
417C4×C8C22×D4311yescharacteristic
418C4×C8C22×D4311yescharacteristic
419C4×C8C22×D4311yescharacteristic
420C2×Q8—431no—
421C2×Q8—431no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×D4C2×D17211yescharacteristic
427C2×D4C2×D17211yescharacteristic
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—1721no—
431C22×C4—1721no—
432C22×C4—1721no—
433Q16—862no—
434Q16—3442no—
435SD16—1722no—
436D8—22no—
437M16—42no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—42no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8C2×D17211yescharacteristic
445C2×C8C2×D17211yescharacteristic
446C2×C8D4×D4311yescharacteristic
447C2×C8D4×D4311yescharacteristic
448C4⋊C4—431no—
449C4⋊C4—431no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—1721no—
461C4⋊C4—1721no—
462C4⋊C4—1721no—
463C4⋊C4—1721no—
464C4⋊C4—1721no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4C2×D17211yescharacteristic
468C4⋊C4C2×D17211yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—1721no—
472C22⋊C4—1721no—
473C22⋊C4—1721no—
474C22⋊C4—1721no—
475C22⋊C4—1721no—
476C42—861no—
477C42—861no—
478C42—1721no—
479C42C23×D4311yescharacteristic
480C23—21no—
481C23—21no—
482Q8—861no—
483Q8—861no—
484Q8—861no—
485Q8—861no—
486Q8—3441no—
487Q8—3441no—
488Q8—3441no—
489Q8—1721no—
490Q8—1721no—
491D4—21no—
492D4—21no—
493D4—21no—
494D4#1306335812yes—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—1721no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1721no—
509C2×C4—6881no—
510C2×C4—6881no—
511C2×C4—6881no—
512C2×C4C2×D4×D4311yescharacteristic
513C2×C4C22×D17211yescharacteristic
514C2×C4#1306337111yescharacteristic
515C8—21no—
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—1721no—
522C8—1721no—
523C8#1306334412yes—
524C22—22no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22D4×D17211yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—3441no—
535C4—3441no—
536C4—3441no—
537C4—3441no—
538C4—1721no—
539C4—1721no—
540C4—1721no—
541C4—1721no—
542C4C2×#1306334411yescharacteristic
543C4C2×#1306335811yescharacteristic
544C4#1458371311yescharacteristic
545C4#1458371611yescharacteristic
546C2—42no—
547C2—81no—
548C2#1914617011yescharacteristic
549C2#1914631611yescharacteristic
550C2#1914636211yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1581C2
socleC22×C43D42
prime radicalC2×D8×C43D4
hypercenter#1581D43
hypocenterC43#19865
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1581

Complements

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

NH ≅ G/Ntype
3. #19147211C2semidirect
4. #19146988C2semidirect
5. #19134272C2semidirect
6. #19134118C2semidirect
7. #19134054C2semidirect
8. #19134000C2semidirect
9. #19133970C2semidirect
10. #19133804C2semidirect
11. #19133769C2semidirect
12. #19133731C2semidirect
13. #19133731C2semidirect
14. #19133415C2semidirect
342. C43#19865semidirect

Maximal subgroups

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

subgroupindex
#191474602
#191472422
#191472112
#191469882
#191342722
#191341182
#191340542
#191340002
#191339702
#191338042
#191337692
#191337312
#191334152
C43×#15812
#1986543