Finite Group Databasebeta

← #25087830

Subgroups — #25087830

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#19147598C211yesmaximal, characteristic, complemented
2#19147468C211yesmaximal, characteristic
3#19147204C211yesmaximal, characteristic
4#19134230C211yesmaximal, characteristic, complemented
5#19134082C211yesmaximal, characteristic
6#19134022C211yesmaximal, characteristic, complemented
7#19133977C211yesmaximal, characteristic, complemented
8#19133975C211yesmaximal, characteristic, complemented
9#19133870C211yesmaximal, characteristic, complemented
10#19133865C211yesmaximal, characteristic
11#19133808C211yesmaximal, characteristic
12#19133753C211yesmaximal, characteristic, complemented
13#19133439C211yesmaximal, characteristic
14#19133412C211yesmaximal, characteristic, complemented
15C43×#3364C211yesmaximal, characteristic
16#14583628C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583299—21no—
19#14583297C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583278—21no—
23#14583278C2211yescharacteristic
24#14583251C2211yescharacteristic
25#14583240—21no—
26#14583227—21no—
27#14583204—21no—
28#14583201—21no—
29#14583194C2211yescharacteristic
30#14583194C2211yescharacteristic
31#14583181C2211yescharacteristic
32#14583179C2211yescharacteristic
33#14583155—21no—
34#14583109—21no—
35#14583109C2211yescharacteristic
36#14583106—21no—
37#14583106C2211yescharacteristic
38Q8×C43⋊C8C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40C4×#10621885—21no—
41C4×#10621885C2211yescharacteristic
42SD16×Dic43—21no—
43#14582977C2211yescharacteristic
44#14582942—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#557C2211yescharacteristic
57C43×#556C2211yescharacteristic
58C43×#488—21no—
59C43×#487C2211yescharacteristic
60C43×#479—21no—
61C43×#474C2211yescharacteristic
62C43×#464—21no—
63C43×#462C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×Q16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621885D411yescharacteristic
72C2×#10621877—21no—
73#13063325—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063316—21no—
77#13063316—21no—
78#13063316—41no—
79#13063304—21no—
80#13063302—41no—
81Q8×Dic43—21no—
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84D4×Dic43—21no—
85C2×C4⋊Dic43—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258D411yescharacteristic
90#13063257—21no—
91#13063257—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—41no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249D411yescharacteristic
105#13063248—21no—
106#13063248—21no—
107#13063248—41no—
108#13063248D411yescharacteristic
109#13063246—21no—
110C22⋊(C43⋊C8)—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×Q16×C43—21no—
116C2×SD16×C43D411yescharacteristic
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120#126×C43—41no—
121#125×C43—21no—
122#125×C43—41no—
123#124×C43—21no—
124C22⋊Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2311yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131#117×C43—21no—
132#107×C43—21no—
133#106×C43D411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43D411yescharacteristic
140#102×C43—21no—
141#102×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×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×Dic43—41no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86C2×D411yescharacteristic
154Q16×C43—42no—
155SD16×C43—22no—
156C2×C8×C43—21no—
157C2×C8×C43C2×D411yescharacteristic
158C2×C8×C43C2×D411yescharacteristic
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—41no—
166C4⋊C4×C43—41no—
167C4⋊C4×C43—41no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43C2×D411yescharacteristic
170C4⋊C4×C43C2×D411yescharacteristic
171C4⋊C4×C43C2×D411yescharacteristic
172C22⋊C4×C43—21no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—41no—
178C42×C43—41no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—41no—
181#10621885—22no—
182#10621885—42no—
183#10621885—81no—
184#10621885—81no—
185#10621885—81no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—41no—
191C4⋊Dic43—41no—
192C4⋊Dic43—41no—
193C4⋊Dic43C2×D411yescharacteristic
194Dic43⋊C4—21no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
198C4×Dic43—41no—
199#10621877—42no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C23×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43#13712yes—
215D4×C43—21no—
216D4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43H(5,𝔽2)11yescharacteristic
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—161no—
234Dic86—21no—
235Dic86—21no—
236Dic86—41no—
237Dic86—41no—
238Dic86—81no—
239C8×C43—21no—
240C8×C43—21no—
241C8×C43—41no—
242C43⋊C8—21no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8#13512yes—
248#19881—431nomaximal, Sylow
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43D4211yescharacteristic
253C4×C43—22no—
254C4×C43—21no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—81no—
260C4×C43—81no—
261C4×C43C2×#13511yescharacteristic
262C4×C43C2×#13711yescharacteristic
263C4×C43#57711yescharacteristic
264C4×C43#57811yescharacteristic
265Dic43—41no—
266Dic43—41no—
267Dic43—81no—
268Dic43—81no—
269#3395—431no—
270#3381—431no—
271#3364D4311yescharacteristic
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—81no—
285C2×C43#327011yescharacteristic
286C2×C43#328411yescharacteristic
287C2×C43#328911yescharacteristic
288#557—431no—
289#557C2×D4311yescharacteristic
290#556C2×D4311yescharacteristic
291#554—431no—
292#499—861no—
293#498—431no—
294#498—431no—
295#498—431no—
296#494—431no—
297#494—861no—
298#488—21no—
299#487—431no—
300#487C2×D4311yescharacteristic
301#485—861no—
302#483—861no—
303#479—21no—
304#479—861no—
305#478—861no—
306#477—431no—
307#477—431no—
308#475—431no—
309#474—431no—
310#474C2×D4311yescharacteristic
311#470—861no—
312#464—21no—
313#462—431no—
314#462—431no—
315#462—861no—
316#462—861no—
317#462C2×D4311yescharacteristic
318C8×Q8—431no—
319C8×Q8—431no—
320C8×Q8C2×D4311yescharacteristic
321C4×Q16—21no—
322C4×Q16—431no—
323C4×Q16—861no—
324C4×SD16—861no—
325C4×SD16C2×D4311yescharacteristic
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—431no—
342C2×Q16—861no—
343C2×Q16—861no—
344C2×Q16—861no—
345C2×Q16—861no—
346C2×SD16C22⋊D4311yescharacteristic
347C2×M16—861no—
348C4⋊Q8—21no—
349C4⋊Q8—431no—
350C4⋊Q8—431no—
351C4⋊Q8—861no—
352C4⋊Q8C22×D4311yescharacteristic
353C4⋊Q8C22×D4311yescharacteristic
354#126—41no—
355#125—21no—
356#125—41no—
357#125—861no—
358#125—861no—
359#125—1721no—
360#124—21no—
361C22⋊Q8—21no—
362C22⋊Q8—861no—
363C22⋊Q8—1721no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—431no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8C22×D4311yescharacteristic
371C4×Q8C22×D4311yescharacteristic
372C4×D4—861no—
373C4×D4C22×D4311yescharacteristic
374#117—21no—
375C2×C4⋊C4—861no—
376#107—21no—
377#107—431no—
378#107—861no—
379#107—861no—
380#107—861no—
381#106—861no—
382#106—861no—
383#106—861no—
384#106—861no—
385#106—861no—
386#106—1721no—
387#106C22⋊D4311yescharacteristic
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—21no—
398#103—431no—
399#103—431no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—1721no—
406#103C22⋊D4311yescharacteristic
407#102—21no—
408#102—861no—
409#102C22⋊D4311yescharacteristic
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—431no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8D4×D4311yescharacteristic
423C2×Q8C2×C22⋊D4311yescharacteristic
424C2×D4C2×C22⋊D4311yescharacteristic
425C22×C4—21no—
426C22×C4—1721no—
427Q16—42no—
428Q16—862no—
429Q16—3441no—
430Q16—3441no—
431Q16—3441no—
432Q16—1722no—
433SD16—22no—
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—41no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—431no—
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⋊C4D4×D4311yescharacteristic
466C4⋊C4C2×C22⋊D4311yescharacteristic
467C4⋊C4C2×C22⋊D4311yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—1721no—
472C42—21no—
473C42—21no—
474C42—41no—
475C42—41no—
476C42—861no—
477C42—1721no—
478C42C23×D4311yescharacteristic
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—41no—
484Q8—41no—
485Q8—41no—
486Q8—41no—
487Q8—861no—
488Q8—861no—
489Q8—3441no—
490Q8—1721no—
491Q8—1721no—
492Q8#1306335512yes—
493D4—21no—
494D4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—861no—
505C2×C4—861no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—6881no—
509C2×C4C2×D4×D4311yescharacteristic
510C2×C4C22×C22⋊D4311yescharacteristic
511C2×C4#1306337011yescharacteristic
512C8—21no—
513C8—21no—
514C8—41no—
515C8—432no—
516C8—861no—
517C8—1721no—
518C8—1721no—
519C8—1721no—
520C8—1721no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22D4×C22⋊D4311yescharacteristic
525C4—21no—
526C4—22no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—81no—
532C4—81no—
533C4—3441no—
534C4—3441no—
535C4—1721no—
536C4—1721no—
537C4#135×D4311yescharacteristic
538C4C2×#1306335511yescharacteristic
539C4#1458370611yescharacteristic
540C4#1458371411yescharacteristic
541C2—81no—
542C2#1914616111yescharacteristic
543C2#1914631911yescharacteristic
544C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3364C2
socleC22×C43D42
prime radicalC2×D4×C43C2×D4
hypercenter#3364D43
hypocenterC43#19881
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3364

Complements

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

NH ≅ G/Ntype
1. #19147598C2semidirect
4. #19134230C2semidirect
6. #19134022C2semidirect
7. #19133977C2semidirect
8. #19133975C2semidirect
9. #19133870C2semidirect
12. #19133753C2semidirect
14. #19133412C2semidirect
339. C43#19881semidirect

Maximal subgroups

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

subgroupindex
#191475982
#191474682
#191472042
#191342302
#191340822
#191340222
#191339772
#191339752
#191338702
#191338652
#191338082
#191337532
#191334392
#191334122
C43×#33642
#1988143