Finite Group Databasebeta

← #25093912

Subgroups — #25093912

Order 11008.

570 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#19147507C211yesmaximal, characteristic, complemented
2#19147503C211yesmaximal, characteristic, complemented
3#19147223C211yesmaximal, characteristic
4#19147222C211yesmaximal, characteristic
5#19134213C211yesmaximal, characteristic, complemented
6#19134124C211yesmaximal, characteristic, complemented
7#19134123C211yesmaximal, characteristic, complemented
8#19134119C211yesmaximal, characteristic, complemented
9#19134118C211yesmaximal, characteristic, complemented
10#19133742C211yesmaximal, characteristic
11#19133737C211yesmaximal, characteristic, complemented
12#19133732C211yesmaximal, characteristic, complemented
13#19133731C211yesmaximal, characteristic, complemented
14#19133487C211yesmaximal, characteristic, complemented
15C43×#1590C211yesmaximal, characteristic, complemented
16Q8×Dic86C2211yescharacteristic
17#14583614C2211yescharacteristic
18#14583609C2211yescharacteristic
19#14583606C2211yescharacteristic
20#14583308—21no—
21#14583306—21no—
22#14583304C2211yescharacteristic
23#14583304C2211yescharacteristic
24#14583304C2211yescharacteristic
25#14583304C2211yescharacteristic
26#14583279C2211yescharacteristic
27#14583279C2211yescharacteristic
28#14583241—21no—
29#14583239—21no—
30#14583213—21no—
31#14583211—21no—
32#14583208—21no—
33#14583207—21no—
34#14583195C2211yescharacteristic
35#14583195C2211yescharacteristic
36#14583194C2211yescharacteristic
37#14583194C2211yescharacteristic
38#14583190C2211yescharacteristic
39#14583190C2211yescharacteristic
40#14583189C2211yescharacteristic
41#14583189C2211yescharacteristic
42#14583180—21no—
43#14583177—21no—
44#14583145—21no—
45#14583142—21no—
46#14583029C2211yescharacteristic
47#14583001—21no—
48#14583000—21no—
49C4×#10621873C2211yescharacteristic
50#14582978C2211yescharacteristic
51#14582941—21no—
52#14582938—21no—
53#14582650C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582631C2211yescharacteristic
59#14582628C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×Dic172—41no—
68C2×Dic172—41no—
69C2×#10621873D411yescharacteristic
70C2×#10621872—21no—
71#13063325—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063324—21no—
77#13063324—41no—
78#13063317—21no—
79#13063316—21no—
80#13063311—41no—
81#13063304—21no—
82#13063303—41no—
83#13063302—41no—
84#13063301—21no—
85#13063299—21no—
86#13063296—21no—
87Q8×Dic43—21no—
88C4×Dic86—21no—
89C4×Dic86C2311yescharacteristic
90C4×D172—21no—
91C4×D172C2311yescharacteristic
92D4×Dic43—21no—
93#13063284—21no—
94#13063283—21no—
95C2×C4⋊Dic43—21no—
96C4⋊C4×D43—21no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063259—21no—
104#13063259—21no—
105#13063259—21no—
106#13063259—21no—
107#13063258—21no—
108#13063258—21no—
109#13063257—21no—
110#13063257—21no—
111#13063257D411yescharacteristic
112#13063256—21no—
113#13063256—21no—
114C4⋊(C43⋊C8)C2311yescharacteristic
115C4⋊(C43⋊C8)C2311yescharacteristic
116Dic43⋊C8—21no—
117#13063250—21no—
118#13063250—21no—
119#13063250D411yescharacteristic
120#13063249—21no—
121#13063249—21no—
122#13063247—21no—
123#13063247—21no—
124#13063247D411yescharacteristic
125#13063246—21no—
126#13063246—21no—
127(C2×D43)⋊C8—21no—
128#13063235—21no—
129C2×SD16×C43D411yescharacteristic
130C2×M16×C43—21no—
131C4×Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#106×C43D411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43D411yescharacteristic
138#102×C43D411yescharacteristic
139C22⋊C8×C43—21no—
140#97×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×D4×C43C2×D411yescharacteristic
146C22×C4×C43—21no—
147C2×C22⋊D43—41no—
148C22×Dic43—41no—
149C2×D172C2×D411yescharacteristic
150C2×C4×D43—21no—
151C2×C4×D43—41no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—41no—
157C2×Dic86C2×D411yescharacteristic
158SD16×C43—22no—
159M16×C43—42no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43C2×D411yescharacteristic
169C4⋊C4×C43C2×D411yescharacteristic
170C22⋊C4×C43—21no—
171C42×C43—21no—
172C42×C43C2411yescharacteristic
173C22⋊Dic43—41no—
174C22⋊Dic43—41no—
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—41no—
177(C2×D43)⋊C4—41no—
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⋊Dic43C2×D411yescharacteristic
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C4×Dic43—41no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200Dic172—82no—
201Dic172—82no—
202#10621873—22no—
203#10621872—42no—
204C23×C43—21no—
205C22×D43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208D4×C43—21no—
209D4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43H(5,𝔽2)11yescharacteristic
218C22⋊D43—161no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—161no—
227D172—21no—
228D172—21no—
229C4×D43—41no—
230C4×D43—41no—
231C4×D43—161no—
232Dic86—21no—
233Dic86—21no—
234Dic86—81no—
235Dic86—81no—
236Dic86—81no—
237Dic86—81no—
238Dic86—161no—
239C8×C43—22no—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43#13712yes—
245C8×C43#13712yes—
246C43⋊C8—41no—
247C43⋊C8—41no—
248#20324—431nomaximal, Sylow
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43D4211yescharacteristic
253C2×D43—41no—
254C2×D43—41no—
255C2×D43—41no—
256C4×C43—21no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43C2×#13711yescharacteristic
261C4×C43C2×#13711yescharacteristic
262C4×C43#57811yescharacteristic
263C4×C43#57811yescharacteristic
264Dic43—41no—
265Dic43—41no—
266Dic43—41no—
267Dic43—81no—
268Dic43—81no—
269Dic43—81no—
270Dic43—81no—
271#3385—431no—
272#3385—431no—
273#3357—431no—
274#3357—431no—
275#1713—431no—
276#1696—431no—
277#1696—431no—
278#1695—431no—
279#1695—431no—
280#1634—431no—
281#1633—431no—
282#1632—431no—
283#1632—431no—
284#1590—431no—
285#1590D4311yescharacteristic, complemented
286C2×C43—81no—
287C2×C43#327611yescharacteristic
288C2×C43#327611yescharacteristic
289C2×C43#329211yescharacteristic
290D43—81no—
291Q82—431no—
292#555—431no—
293#554—431no—
294#554—431no—
295#501—861no—
296#501—861no—
297#500—431no—
298#500—431no—
299#500—431no—
300#500—431no—
301#494—431no—
302#494—431no—
303#485—861no—
304#485—861no—
305#480—861no—
306#480—861no—
307#479—861no—
308#479—861no—
309#477—431no—
310#477—431no—
311#477—431no—
312#477—431no—
313#476—431no—
314#476—431no—
315#476—431no—
316#476—431no—
317#474—861no—
318#474—861no—
319#468—861no—
320#468—861no—
321#446—431no—
322#446C2×D4311yescharacteristic
323#440—861no—
324#440—861no—
325C4×SD16—431no—
326C4×SD16C2×D4311yescharacteristic
327#436—431no—
328#436C2×D4311yescharacteristic
329#428—861no—
330#428—861no—
331#334—431no—
332#334C2×D4311yescharacteristic
333#333—431no—
334#333—431no—
335#333—431no—
336#333—431no—
337Q8⋊C8—431no—
338Q8⋊C8C2×D4311yescharacteristic
339D4⋊C8—431no—
340D4⋊C8C2×D4311yescharacteristic
341C82C2×D4311yescharacteristic
342C43#2032411yescharacteristic, complemented, Sylow
343C2×Q16—1721no—
344C2×Q16—1721no—
345C2×SD16—431no—
346C2×SD16D17211yescharacteristic
347C2×M16—21no—
348C2×M16—861no—
349C4⋊Q8—431no—
350C4⋊Q8—431no—
351C4⋊Q8—431no—
352C4⋊Q8—431no—
353C4⋊Q8—861no—
354C4⋊Q8—861no—
355C4⋊Q8—1721no—
356#125—861no—
357#125—861no—
358#124—1721no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361C22⋊Q8—1721no—
362C22⋊Q8—1721no—
363#121—861no—
364#121—861no—
365C4×Q8—431no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×Q8C22×D4311yescharacteristic
369C4×D4—431no—
370C4×D4—861no—
371C4×D4—861no—
372C4×D4C22×D4311yescharacteristic
373#117—861no—
374#117—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107—861no—
381#107—861no—
382#107—861no—
383#107—861no—
384#107—861no—
385#107—861no—
386#107—861no—
387#107—861no—
388#107—861no—
389#106—431no—
390#106—861no—
391#106—861no—
392#106—861no—
393#106—861no—
394#106D17211yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—861no—
399C4⋊C8C22×D4311yescharacteristic
400C4⋊C8C22×D4311yescharacteristic
401#103—431no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103D17211yescharacteristic
407#102—431no—
408#102—861no—
409#102—861no—
410#102—861no—
411#102—861no—
412#102D17211yescharacteristic
413C22⋊C8—21no—
414C22⋊C8—861no—
415#97—21no—
416#97—861no—
417C4×C8C22×D4311yescharacteristic
418C4×C8C22×D4311yescharacteristic
419C4×C8C22×D4311yescharacteristic
420C2×Q8—431no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—1721no—
426C2×Q8C2×D17211yescharacteristic
427C2×D4—431no—
428C2×D4—1721no—
429C2×D4C2×D17211yescharacteristic
430C22×C4—21no—
431C22×C4—861no—
432C22×C4—1721no—
433C22×C4—1721no—
434Q16—3442no—
435Q16—3442no—
436SD16—22no—
437SD16—862no—
438M16—42no—
439M16—1722no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8C2×D17211yescharacteristic
446C2×C8C2×D17211yescharacteristic
447C2×C8D4×D4311yescharacteristic
448C2×C8D4×D4311yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—431no—
451C4⋊C4—431no—
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—861no—
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—861no—
471C22⋊C4—1721no—
472C22⋊C4—1721no—
473C22⋊C4—1721no—
474C22⋊C4—1721no—
475C42—21no—
476C42—861no—
477C42—1721no—
478C42—1721no—
479C42C23×D4311yescharacteristic
480C23—21no—
481C23—861no—
482Q8—21no—
483Q8—21no—
484Q8—861no—
485Q8—861no—
486Q8—3441no—
487Q8—3441no—
488Q8—3441no—
489Q8—3441no—
490Q8—6881no—
491D4—21no—
492D4—21no—
493D4—861no—
494D4—861no—
495D4—6881no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4—1721no—
505C2×C4—1721no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4—6881no—
511C2×C4—6881no—
512C2×C4C2×D4×D4311yescharacteristic
513C2×C4C22×D17211yescharacteristic
514C2×C4#1306337111yescharacteristic
515C8—22no—
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—1721no—
521C8—1721no—
522C8#1306335412yes—
523C8#1306335812yes—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—1721no—
528C22—1721no—
529C22—1721no—
530C22D4×D17211yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—3441no—
536C4—3441no—
537C4—3441no—
538C4—3441no—
539C4—1721no—
540C4—1721no—
541C4—1721no—
542C4C2×#1306335411yescharacteristic
543C4C2×#1306335811yescharacteristic
544C4#1458371311yescharacteristic
545C4#1458371611yescharacteristic
546C2—81no—
547C2—3441no—
548C2#1914624211yescharacteristic
549C2#1914624311yescharacteristic
550C2#1914639511yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1590C2
socleC22×C43D42
prime radical#14583614C22
hypercenter#1590D43
hypocenterC43#20324
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1590

Complements

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

NH ≅ G/Ntype
1. #19147507C2semidirect
2. #19147503C2semidirect
5. #19134213C2semidirect
6. #19134124C2semidirect
7. #19134123C2semidirect
8. #19134119C2semidirect
9. #19134118C2semidirect
11. #19133737C2semidirect
12. #19133732C2semidirect
13. #19133731C2semidirect
14. #19133487C2semidirect
15. C43×#1590C2semidirect
285. #1590D43semidirect
342. C43#20324semidirect

Maximal subgroups

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

subgroupindex
#191475072
#191475032
#191472232
#191472222
#191342132
#191341242
#191341232
#191341192
#191341182
#191337422
#191337372
#191337322
#191337312
#191334872
C43×#15902
#2032443