Finite Group Databasebeta

← #25087834

Subgroups — #25087834

Order 11008.

562 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147466C211yesmaximal, characteristic
2#19147280C211yesmaximal, characteristic
3#19147212C211yesmaximal, characteristic
4#19134226C211yesmaximal, characteristic, complemented
5#19134081C211yesmaximal, characteristic
6#19134027C211yesmaximal, characteristic, complemented
7#19133977C211yesmaximal, characteristic, complemented
8#19133975C211yesmaximal, characteristic, complemented
9#19133872C211yesmaximal, characteristic, complemented
10#19133863C211yesmaximal, characteristic
11#19133807C211yesmaximal, characteristic
12#19133753C211yesmaximal, characteristic, complemented
13#19133438C211yesmaximal, characteristic
14#19133414C211yesmaximal, characteristic, complemented
15C43×#3395C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17#14583609C2211yescharacteristic
18#14583298—21no—
19#14583297C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583256—21no—
23#14583251C2211yescharacteristic
24#14583251C2211yescharacteristic
25#14583238—21no—
26#14583228—21no—
27#14583206—21no—
28#14583203—21no—
29#14583196—21no—
30#14583194C2211yescharacteristic
31#14583194C2211yescharacteristic
32#14583184C2211yescharacteristic
33#14583176C2211yescharacteristic
34#14583176C2211yescharacteristic
35#14583154—21no—
36#14583121—21no—
37#14583109C2211yescharacteristic
38Q8×C43⋊C8C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40C4×#10621885—21no—
41C4×#10621884—21no—
42C4×#10621884C2211yescharacteristic
43#14582978C2211yescharacteristic
44#14582940—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#557C2211yescharacteristic
57C43×#557C2211yescharacteristic
58C43×#494—21no—
59C43×#494C2211yescharacteristic
60C43×#462—21no—
61C43×#462—21no—
62C43×#462C2211yescharacteristic
63C43×#462C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×Q16×C43—21no—
66C4×Q16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621884D411yescharacteristic
69C2×#10621872—21no—
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063320—41no—
73#13063317—21no—
74#13063313—21no—
75#13063303—41no—
76#13063301—21no—
77#13063301—21no—
78C4×Dic86—21no—
79C4×D172—21no—
80C4×D172C2311yescharacteristic
81#13063283—21no—
82C4⋊C4×D43—21no—
83#13063258—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063257—21no—
88#13063257—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—41no—
93#13063256D411yescharacteristic
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249D411yescharacteristic
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248—41no—
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110(C2×D43)⋊C8—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×Q16×C43—21no—
116C2×Q16×C43—21no—
117C2×Q16×C43—21no—
118C2×Q16×C43—21no—
119C2×Q16×C43D411yescharacteristic
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43—21no—
122C4⋊Q8×C43C2311yescharacteristic
123C4⋊Q8×C43C2311yescharacteristic
124#125×C43—21no—
125#125×C43—21no—
126#125×C43—41no—
127#125×C43—41no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43—21no—
131C4×Q8×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134C4×Q8×C43C2311yescharacteristic
135#107×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×D172C2×D411yescharacteristic
150C2×C4×D43—21no—
151C2×C4×D43—41no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154Q16×C43—22no—
155Q16×C43—42no—
156Q16×C43—81no—
157Q16×C43—81no—
158Q16×C43—81no—
159C2×C8×C43—21no—
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—41no—
182C42×C43—41no—
183C42×C43C2411yescharacteristic
184#10621885—42no—
185#10621884—22no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—41no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4—41no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—41no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205#10621872—42no—
206C22×D43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43#13712yes—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231D172—21no—
232D172—21no—
233C4×D43—41no—
234C4×D43—41no—
235C4×D43—161no—
236Dic86—41no—
237Dic86—41no—
238Dic86—81no—
239C8×C43—21no—
240C8×C43—41no—
241C8×C43#13512yes—
242C43⋊C8—21no—
243C43⋊C8—21no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248#19881—431nomaximal, Sylow
249C22×C43D4211yescharacteristic
250C2×D43—41no—
251C2×D43—41no—
252C2×D43—41no—
253C4×C43—22no—
254C4×C43—21no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—81no—
261C4×C43—81no—
262C4×C43C2×#13511yescharacteristic
263C4×C43C2×#13711yescharacteristic
264C4×C43#57711yescharacteristic
265C4×C43#57811yescharacteristic
266Dic43—41no—
267Dic43—81no—
268Dic43—81no—
269#3395D4311yescharacteristic, complemented
270#3381—431no—
271#3364—431no—
272#3356—431no—
273#1716—431no—
274#1689—431no—
275#1680—431no—
276#1672—431no—
277#1672—431no—
278#1653—431no—
279#1652—431no—
280#1644—431no—
281#1636—431no—
282#1583—431no—
283#1579—431no—
284C2×C43#327011yescharacteristic
285C2×C43#328411yescharacteristic
286C2×C43#328911yescharacteristic
287D43—81no—
288#557C2×D4311yescharacteristic
289#557C2×D4311yescharacteristic
290#556—431no—
291#554—431no—
292#499—861no—
293#498—431no—
294#498—431no—
295#498—431no—
296#494—21no—
297#494C2×D4311yescharacteristic
298#488—861no—
299#487—431no—
300#487—431no—
301#485—861no—
302#483—861no—
303#479—861no—
304#479—861no—
305#478—861no—
306#477—431no—
307#477—431no—
308#475—431no—
309#474—431no—
310#474—431no—
311#470—861no—
312#464—861no—
313#462—21no—
314#462—21no—
315#462—431no—
316#462C2×D4311yescharacteristic
317#462C2×D4311yescharacteristic
318C8×Q8—431no—
319C8×Q8—431no—
320C8×Q8C2×D4311yescharacteristic
321C4×Q16—21no—
322C4×Q16—861no—
323C4×Q16C2×D4311yescharacteristic
324C4×SD16—431no—
325C4×SD16—861no—
326#436—431no—
327#428—861no—
328#334—431no—
329#334—431no—
330#333—431no—
331#332—431no—
332#332—431no—
333#332—431no—
334Q8⋊C8—431no—
335Q8⋊C8—431no—
336Q8⋊C8—431no—
337D4⋊C8—431no—
338#322—431no—
339C43#1988111yescharacteristic, complemented, Sylow
340C2×Q16—21no—
341C2×Q16—21no—
342C2×Q16—21no—
343C2×Q16—21no—
344C2×Q16—861no—
345C2×Q16C22⋊D4311yescharacteristic
346C2×SD16—431no—
347C2×M16—861no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—431no—
351C4⋊Q8—431no—
352C4⋊Q8C22×D4311yescharacteristic
353C4⋊Q8C22×D4311yescharacteristic
354#126—1721no—
355#125—21no—
356#125—21no—
357#125—41no—
358#125—41no—
359#125—861no—
360#124—861no—
361C22⋊Q8—861no—
362C22⋊Q8—861no—
363C22⋊Q8—1721no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—861no—
369C4×Q8C22×D4311yescharacteristic
370C4×Q8C22×D4311yescharacteristic
371C4×Q8C22×D4311yescharacteristic
372C4×D4—431no—
373C4×D4—861no—
374#117—861no—
375C2×C4⋊C4—861no—
376#107—861no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107C22⋊D4311yescharacteristic
381#106—431no—
382#106—861no—
383#106—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387#106—1721no—
388C4⋊C8—21no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8C22×D4311yescharacteristic
395#103—21no—
396#103—21no—
397#103—431no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—1721no—
405#103C22⋊D4311yescharacteristic
406#103C22⋊D4311yescharacteristic
407#102—431no—
408#102—861no—
409#102—861no—
410C22⋊C8—861no—
411C4×C8—21no—
412C4×C8—431no—
413C4×C8—431no—
414C4×C8—861no—
415C4×C8—861no—
416C4×C8C22×D4311yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8D4×D4311yescharacteristic
422C2×Q8C2×C22⋊D4311yescharacteristic
423C2×Q8C2×C22⋊D4311yescharacteristic
424C2×D4—431no—
425C22×C4—861no—
426C22×C4—1721no—
427Q16—22no—
428Q16—42no—
429Q16—81no—
430Q16—81no—
431Q16—81no—
432Q16—1722no—
433SD16—862no—
434M16—1722no—
435C2×C8—21no—
436C2×C8—431no—
437C2×C8—431no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8C2×C22⋊D4311yescharacteristic
443C2×C8C2×C22⋊D4311yescharacteristic
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—431no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—1721no—
463C4⋊C4—1721no—
464C4⋊C4—1721no—
465C4⋊C4D4×D4311yescharacteristic
466C4⋊C4C2×C22⋊D4311yescharacteristic
467C4⋊C4C2×C22⋊D4311yescharacteristic
468C22⋊C4—861no—
469C22⋊C4—1721no—
470C22⋊C4—1721no—
471C22⋊C4—1721no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—41no—
476C42—41no—
477C42—1721no—
478C42C23×D4311yescharacteristic
479C23—861no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—3441no—
490Q8—1721no—
491Q8—1721no—
492Q8#1306335712yes—
493D4—861no—
494D4—861no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—861no—
504C2×C4—1721no—
505C2×C4—1721no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—6881no—
509C2×C4C2×D4×D4311yescharacteristic
510C2×C4C22×C22⋊D4311yescharacteristic
511C2×C4#1306337011yescharacteristic
512C8—21no—
513C8—41no—
514C8—861no—
515C8—861no—
516C8—1721no—
517C8—1721no—
518C8—1721no—
519C8—1721no—
520C8#1306334512yes—
521C22—1721no—
522C22—1721no—
523C22—1721no—
524C22D4×C22⋊D4311yescharacteristic
525C4—21no—
526C4—22no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—81no—
533C4—81no—
534C4—3441no—
535C4—3441no—
536C4—1721no—
537C4C2×#1306334511yescharacteristic
538C4C2×#1306335711yescharacteristic
539C4#1458371011yescharacteristic
540C4#1458371211yescharacteristic
541C2—3441no—
542C2#1914616511yescharacteristic
543C2#1914632511yescharacteristic
544C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3395C2
socleC22×C43D42
prime radicalC2×D172C2×D4
hypercenter#3395D43
hypocenterC43#19881
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3395

Complements

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

NH ≅ G/Ntype
4. #19134226C2semidirect
6. #19134027C2semidirect
7. #19133977C2semidirect
8. #19133975C2semidirect
9. #19133872C2semidirect
12. #19133753C2semidirect
14. #19133414C2semidirect
15. C43×#3395C2semidirect
269. #3395D43semidirect
339. C43#19881semidirect

Maximal subgroups

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

subgroupindex
#191474662
#191472802
#191472122
#191342262
#191340812
#191340272
#191339772
#191339752
#191338722
#191338632
#191338072
#191337532
#191334382
#191334142
C43×#33952
#1988143