Finite Group Databasebeta

← #25087575

Subgroups — #25087575

Order 11008.

578 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147242C211yesmaximal, characteristic, complemented
2#19147215C211yesmaximal, characteristic, complemented
3#19147008C211yesmaximal, characteristic, complemented
4#19134271C211yesmaximal, characteristic, complemented
5#19134096C211yesmaximal, characteristic, complemented
6#19134046C211yesmaximal, characteristic, complemented
7#19133996C211yesmaximal, characteristic, complemented
8#19133992C211yesmaximal, characteristic, complemented
9#19133823C211yesmaximal, characteristic, complemented
10#19133765C211yesmaximal, characteristic, complemented
11#19133740C211yesmaximal, characteristic, complemented
12#19133727C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15C43×#3341C211yesmaximal, characteristic
16#14583619C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583278C2211yescharacteristic
21#14583252—21no—
22#14583250C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583240—21no—
25#14583240—21no—
26#14583220—21no—
27#14583210—21no—
28#14583205—21no—
29#14583191C2211yescharacteristic
30#14583191C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583189C2211yescharacteristic
33#14583179C2211yescharacteristic
34#14583143—21no—
35#14583126—21no—
36#14583112—21no—
37#14583104C2211yescharacteristic
38C8×Dic86C2211yescharacteristic
39#14582990—21no—
40C4×#10621883C2211yescharacteristic
41#14582977C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582942—21no—
44#14582935—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582629C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#555C2211yescharacteristic
57C43×#555C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#482—21no—
60C43×#482—21no—
61C43×#476C2211yescharacteristic
62C43×#476C2211yescharacteristic
63C43×#466—21no—
64C4×D8×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C43×#427—21no—
67C2×#10621885—41no—
68C2×#10621883—21no—
69C2×#10621883D411yescharacteristic
70C2×#10621877—21no—
71C22×C43⋊C8—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063318—41no—
75#13063316—21no—
76#13063312—21no—
77#13063304—21no—
78#13063304—21no—
79#13063302—41no—
80C4×Dic86C2311yescharacteristic
81#13063290—21no—
82D4×Dic43—21no—
83#13063284—21no—
84C2×C4⋊Dic43—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063250—21no—
100#13063250—21no—
101#13063249—41no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248D411yescharacteristic
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×D8×C43D411yescharacteristic
116C22×C8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#124×C43—41no—
120#124×C43—41no—
121#121×C43—21no—
122#121×C43—21no—
123#121×C43—21no—
124#121×C43—21no—
125C4×D4×C43C2311yescharacteristic
126C4×D4×C43C2311yescharacteristic
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129#117×C43—21no—
130#117×C43—21no—
131#117×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43D411yescharacteristic
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×D4×C43—41no—
147C2×D4×C43—41no—
148C2×D4×C43C2×D411yescharacteristic
149C2×D4×C43C2×D411yescharacteristic
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×Dic43—41no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C2×D411yescharacteristic
158D8×C43—41no—
159C2×C8×C43—21no—
160C2×C8×C43—42no—
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43C2×D411yescharacteristic
168C4⋊C4×C43C2×D411yescharacteristic
169C4⋊C4×C43C2×D411yescharacteristic
170C22⋊C4×C43—21no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C42×C43—41no—
178C42×C43—41no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182C22⋊Dic43—41no—
183#10621885—82no—
184#10621883—22no—
185#10621883—42no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—41no—
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197#10621877—42no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—42no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208Q8×C43—81no—
209Q8×C43—81no—
210D4×C43—21no—
211D4×C43—21no—
212D4×C43—21no—
213D4×C43—21no—
214D4×C43—21no—
215D4×C43—21no—
216D4×C43—161no—
217D4×C43—161no—
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—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43H(5,𝔽2)11yescharacteristic
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—161no—
237Dic86—21no—
238Dic86—21no—
239Dic86—41no—
240Dic86—41no—
241Dic86—81no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—41no—
245C43⋊C8—21no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8#13512yes—
251#19864—431nomaximal, Sylow
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43D4211yescharacteristic
262C4×C43—21no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43C2×#13511yescharacteristic
269C4×C43#57511yescharacteristic
270C4×C43#57811yescharacteristic
271C4×C43#57811yescharacteristic
272Dic43—41no—
273Dic43—41no—
274Dic43—81no—
275Dic43—81no—
276#3360—431no—
277#3357—431no—
278#3341D4311yescharacteristic
279#3340—431no—
280#1723—431no—
281#1691—431no—
282#1683—431no—
283#1676—431no—
284#1675—431no—
285#1646—431no—
286#1638—431no—
287#1634—431no—
288#1632—431no—
289#1581—431no—
290SD16⋊C8—431no—
291C2×C43—81no—
292C2×C43—81no—
293C2×C43—81no—
294C2×C43#326911yescharacteristic
295C2×C43#328311yescharacteristic
296C2×C43#328811yescharacteristic
297#556—431no—
298#555C2×D4311yescharacteristic
299#555C2×D4311yescharacteristic
300#554—431no—
301#500—431no—
302#500C2×D4311yescharacteristic
303#498—431no—
304#494—431no—
305#488—861no—
306#487—431no—
307#487—431no—
308#485—861no—
309#485—861no—
310#482—21no—
311#482—21no—
312#482—861no—
313#480—861no—
314#479—861no—
315#477—431no—
316#477—431no—
317#476—431no—
318#476—431no—
319#476C2×D4311yescharacteristic
320#476C2×D4311yescharacteristic
321#474—431no—
322#468—861no—
323#466—21no—
324#465—861no—
325#463—861no—
326#461—431no—
327C8×Q8—431no—
328C4×SD16—431no—
329C4×SD16—861no—
330C4×D8C2×D4311yescharacteristic
331#436—431no—
332C8×D4—431no—
333C8×D4C2×D4311yescharacteristic
334#428—861no—
335#427—21no—
336#427—861no—
337#335—431no—
338#335—431no—
339#333—431no—
340#333—431no—
341#333—431no—
342#332—431no—
343Q8⋊C8—431no—
344D4⋊C8—431no—
345D4⋊C8—431no—
346D4⋊C8—431no—
347#322—431no—
348C43#1986411yescharacteristic, complemented, Sylow
349C2×Q16—1721no—
350C2×SD16—431no—
351C2×SD16—861no—
352C2×D8C22⋊D4311yescharacteristic
353C2×M16—861no—
354C22×C8—21no—
355C22×C8—861no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8C22×D4311yescharacteristic
359C4⋊Q8C22×D4311yescharacteristic
360#126—1721no—
361#125—861no—
362#124—41no—
363#124—41no—
364#124—861no—
365C22⋊Q8—861no—
366C22⋊Q8—861no—
367C22⋊Q8—1721no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372C4×Q8—431no—
373C4×Q8—861no—
374C4×D4—861no—
375C4×D4C22×D4311yescharacteristic
376C4×D4C22×D4311yescharacteristic
377C4×D4C22×D4311yescharacteristic
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—861no—
383C2×C4⋊C4—861no—
384#107—21no—
385#107—21no—
386#107—861no—
387#107—861no—
388#107—861no—
389#107—861no—
390#107—861no—
391#107C22⋊D4311yescharacteristic
392#106—21no—
393#106—21no—
394#106—431no—
395#106—861no—
396#106—861no—
397#106—861no—
398#106—861no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8C22×D4311yescharacteristic
404#103—431no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—1721no—
411#102—21no—
412#102—21no—
413#102—431no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102C22⋊D4311yescharacteristic
418#102C22⋊D4311yescharacteristic
419C22⋊C8—21no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—861no—
425C4×C8C22×D4311yescharacteristic
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—431no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4D4×D4311yescharacteristic
434C2×D4C2×C22⋊D4311yescharacteristic
435C2×D4C2×C22⋊D4311yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—1721no—
440Q16—3442no—
441SD16—862no—
442SD16—1722no—
443D8—41no—
444M16—1722no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—1722no—
454C2×C8C2×C22⋊D4311yescharacteristic
455C2×C8C2×C22⋊D4311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—431no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4—1721no—
469C4⋊C4D4×D4311yescharacteristic
470C4⋊C4C2×C22⋊D4311yescharacteristic
471C4⋊C4C2×C22⋊D4311yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—1721no—
480C22⋊C4—1721no—
481C22⋊C4—1721no—
482C42—41no—
483C42—41no—
484C42—861no—
485C42—1721no—
486C42C23×D4311yescharacteristic
487C23—21no—
488C23—21no—
489C23—21no—
490Q8—81no—
491Q8—81no—
492Q8—861no—
493Q8—861no—
494Q8—3441no—
495Q8—1721no—
496Q8—1721no—
497D4—21no—
498D4—21no—
499D4—21no—
500D4—21no—
501D4—21no—
502D4—21no—
503D4—161no—
504D4—161no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—6881no—
521C2×C4C2×D4×D4311yescharacteristic
522C2×C4C22×C22⋊D4311yescharacteristic
523C2×C4#1306337011yescharacteristic
524C8—21no—
525C8—21no—
526C8—41no—
527C8—432no—
528C8—861no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C8—1721no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22D4×C22⋊D4311yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—81no—
548C4—81no—
549C4—3441no—
550C4—3441no—
551C4—1721no—
552C4—1721no—
553C4#135×D4311yescharacteristic
554C4#1458369711yescharacteristic
555C4#1458371311yescharacteristic
556C4#1458371411yescharacteristic
557C2—81no—
558C2—81no—
559C2—81no—
560C2#1914614611yescharacteristic
561C2#1914631111yescharacteristic
562C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3341C2
socleC22×C43D42
hypercenter#3341D43
hypocenterC43#19864
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3341

Complements

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

NH ≅ G/Ntype
1. #19147242C2semidirect
2. #19147215C2semidirect
3. #19147008C2semidirect
4. #19134271C2semidirect
5. #19134096C2semidirect
6. #19134046C2semidirect
7. #19133996C2semidirect
8. #19133992C2semidirect
9. #19133823C2semidirect
10. #19133765C2semidirect
11. #19133740C2semidirect
12. #19133727C2semidirect
13. #19133425C2semidirect
14. #19133407C2semidirect
348. C43#19864semidirect

Maximal subgroups

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

subgroupindex
#191472422
#191472152
#191470082
#191342712
#191340962
#191340462
#191339962
#191339922
#191338232
#191337652
#191337402
#191337272
#191334252
#191334072
C43×#33412
#1986443