Finite Group Databasebeta

← #25087828

Subgroups — #25087828

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#19147600C211yesmaximal, characteristic, complemented
2#19147470C211yesmaximal, characteristic
3#19147276C211yesmaximal, characteristic
4#19134229C211yesmaximal, characteristic, complemented
5#19134084C211yesmaximal, characteristic
6#19134023C211yesmaximal, characteristic, complemented
7#19133979C211yesmaximal, characteristic, complemented
8#19133974C211yesmaximal, characteristic, complemented
9#19133871C211yesmaximal, characteristic, complemented
10#19133865C211yesmaximal, characteristic
11#19133809C211yesmaximal, characteristic
12#19133751C211yesmaximal, characteristic, complemented
13#19133436C211yesmaximal, characteristic
14#19133414C211yesmaximal, characteristic, complemented
15C43×#3356C211yesmaximal, characteristic
16#14583627C2211yescharacteristic
17#14583627C2211yescharacteristic
18#14583298—21no—
19#14583295C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583279C2211yescharacteristic
22#14583277—21no—
23#14583253—21no—
24#14583249C2211yescharacteristic
25#14583249C2211yescharacteristic
26#14583206—21no—
27#14583203—21no—
28#14583199—21no—
29#14583191C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583118—21no—
33#14583109C2211yescharacteristic
34#14583109C2211yescharacteristic
35#14583108—21no—
36#14583108—21no—
37#14583106C2211yescharacteristic
38Q8×C43⋊C8C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41#14582993—21no—
42C4×#10621885—21no—
43C4×#10621883—21no—
44C4×#10621883C2211yescharacteristic
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#556C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#485—21no—
60C43×#483—21no—
61C43×#477C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C43×#470—21no—
64C4×Q16×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic
66C43×#428—21no—
67C2×Dic172—21no—
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621883D411yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063323—21no—
76#13063323—21no—
77#13063317—21no—
78#13063317—21no—
79#13063315—41no—
80#13063315—41no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84#13063290—21no—
85#13063290—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—41no—
92#13063256D411yescharacteristic
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—41no—
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248D411yescharacteristic
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C4×C43⋊C8—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×Q16×C43D411yescharacteristic
116C2×M16×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#126×C43—41no—
120#125×C43—21no—
121#124×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43—21no—
126C4×Q8×C43C2311yescharacteristic
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#107×C43D411yescharacteristic
134#106×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142C22⋊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×C4×C43—41no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86C2×D411yescharacteristic
154Q16×C43—22no—
155M16×C43—42no—
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×C43C2×D411yescharacteristic
169C4⋊C4×C43C2×D411yescharacteristic
170C4⋊C4×C43C2×D411yescharacteristic
171C22⋊C4×C43—21no—
172C22⋊C4×C43—41no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—41no—
178C42×C43C2411yescharacteristic
179#10621885—42no—
180#10621885—81no—
181#10621885—81no—
182#10621883—22no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C2×D411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
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—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204Dic172—42no—
205Dic172—81no—
206C23×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—81no—
214D4×C43—21no—
215D4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—161no—
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—
233Dic86—21no—
234Dic86—41no—
235Dic86—41no—
236Dic86—41no—
237Dic86—41no—
238Dic86#13712yes—
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×C43—41no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43D4211yescharacteristic
253C4×C43—21no—
254C4×C43—41no—
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—22no—
266Dic43—41no—
267Dic43—81no—
268Dic43—81no—
269#3395—431no—
270#3381—431no—
271#3364—431no—
272#3356D4311yescharacteristic
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#557—431no—
290#556C2×D4311yescharacteristic
291#554C2×D4311yescharacteristic
292#499—861no—
293#498—431no—
294#498—431no—
295#498C2×D4311yescharacteristic
296#494—431no—
297#494—861no—
298#488—861no—
299#487—431no—
300#487—431no—
301#485—21no—
302#483—21no—
303#479—861no—
304#479—861no—
305#478—861no—
306#477—431no—
307#477C2×D4311yescharacteristic
308#475C2×D4311yescharacteristic
309#474—431no—
310#474—431no—
311#470—21no—
312#464—861no—
313#462—431no—
314#462—431no—
315#462—431no—
316#462—861no—
317#462—861no—
318C8×Q8—431no—
319C8×Q8—431no—
320C8×Q8—431no—
321C4×Q16—861no—
322C4×Q16—861no—
323C4×Q16C2×D4311yescharacteristic
324C4×SD16—431no—
325C4×SD16—861no—
326#436C2×D4311yescharacteristic
327#428—21no—
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—861no—
341C2×Q16—861no—
342C2×Q16—861no—
343C2×Q16—861no—
344C2×Q16—861no—
345C2×Q16C22⋊D4311yescharacteristic
346C2×SD16—431no—
347C2×M16—21no—
348C4⋊Q8—431no—
349C4⋊Q8—431no—
350C4⋊Q8—861no—
351C4⋊Q8—861no—
352C4⋊Q8C22×D4311yescharacteristic
353C4⋊Q8C22×D4311yescharacteristic
354#126—41no—
355#125—21no—
356#125—861no—
357#125—861no—
358#125—1721no—
359#125—1721no—
360#124—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—41no—
364C4×Q8—21no—
365C4×Q8—431no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8C22×D4311yescharacteristic
371C4×Q8C22×D4311yescharacteristic
372C4×D4—21no—
373C4×D4C22×D4311yescharacteristic
374#117—21no—
375C2×C4⋊C4—21no—
376#107—21no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107C22⋊D4311yescharacteristic
381#106—21no—
382#106—21no—
383#106—21no—
384#106—431no—
385#106—861no—
386#106—861no—
387#106—1721no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—861no—
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—21no—
411C4×C8—431no—
412C4×C8—431no—
413C4×C8—861no—
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×Q8C2×C22⋊D4311yescharacteristic
423C2×Q8C2×C22⋊D4311yescharacteristic
424C2×D4D4×D4311yescharacteristic
425C22×C4—21no—
426C22×C4—41no—
427Q16—22no—
428Q16—3441no—
429Q16—3441no—
430Q16—3441no—
431Q16—1722no—
432Q16—1722no—
433SD16—862no—
434M16—42no—
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—431no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—1721no—
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—41no—
472C42—21no—
473C42—21no—
474C42—41no—
475C42—861no—
476C42—1721no—
477C42—1721no—
478C42C23×D4311yescharacteristic
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—41no—
485Q8—41no—
486Q8—81no—
487Q8—432no—
488Q8—861no—
489Q8—1721no—
490Q8—1721no—
491Q8—1721no—
492Q8—1721no—
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—161no—
505C2×C4—861no—
506C2×C4—861no—
507C2×C4—1721no—
508C2×C4—1721no—
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—41no—
522C22—41no—
523C22—41no—
524C22D4×C22⋊D4311yescharacteristic
525C4—21no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—81no—
532C4—81no—
533C4—862no—
534C4—3441no—
535C4—3441no—
536C4—1721no—
537C4C2×#1306334511yescharacteristic
538C4#137×D4311yescharacteristic
539C4#1458370711yescharacteristic
540C4#1458371511yescharacteristic
541C2—81no—
542C2#1914615911yescharacteristic
543C2#1914632111yescharacteristic
544C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3356C2
socleC22×C43D42
prime radicalC2×D4×C43C2×D4
hypercenter#3356D43
hypocenterC43#19881
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3356

Complements

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

NH ≅ G/Ntype
1. #19147600C2semidirect
4. #19134229C2semidirect
6. #19134023C2semidirect
7. #19133979C2semidirect
8. #19133974C2semidirect
9. #19133871C2semidirect
12. #19133751C2semidirect
14. #19133414C2semidirect
339. C43#19881semidirect

Maximal subgroups

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

subgroupindex
#191476002
#191474702
#191472762
#191342292
#191340842
#191340232
#191339792
#191339742
#191338712
#191338652
#191338092
#191337512
#191334362
#191334142
C43×#33562
#1988143