Finite Group Databasebeta

← #25079041

Subgroups — #25079041

Order 11008.

618 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145177C211yesmaximal, characteristic, complemented
2#19144383C211yesmaximal, characteristic
3#41×C43⋊C8C211yesmaximal, characteristic
4#19134055C211yesmaximal, characteristic, complemented
5#19134051C211yesmaximal, characteristic, complemented
6#19134048C211yesmaximal, characteristic, complemented
7#19134044C211yesmaximal, characteristic, complemented
8#19133997C211yesmaximal, characteristic, complemented
9#19133992C211yesmaximal, characteristic, complemented
10#19133963C211yesmaximal, characteristic, complemented
11#19133958C211yesmaximal, characteristic, complemented
12C2×#14582651C211yesmaximal, characteristic, complemented
13#19133253C211yesmaximal, characteristic, complemented
14#19133252C211yesmaximal, characteristic, complemented
15C43×#3076C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583278C2211yescharacteristic
19#14583251C2211yescharacteristic
20#14583249C2211yescharacteristic
21#14583206—21no—
22#14583199—21no—
23#14583194C2211yescharacteristic
24#14583189C2211yescharacteristic
25#14583184C2211yescharacteristic
26#14583179C2211yescharacteristic
27#14583138—21no—
28#14583138—21no—
29Q8×C43⋊C8C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31C4×#10621885—21no—
32C4×#10621885—21no—
33D4×C43⋊C8—21no—
34D4×C43⋊C8—21no—
35D4×C43⋊C8C2211yescharacteristic
36D4×C43⋊C8C2211yescharacteristic
37#14582952—21no—
38#14582952C2211yescharacteristic
39#14582935—21no—
40C2×C4⋊(C43⋊C8)C2211yescharacteristic
41#14582895—21no—
42C2×C4×C43⋊C8—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582651C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#479—21no—
59C43×#478—21no—
60C43×#477C2211yescharacteristic
61C43×#476C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C43×#474C2211yescharacteristic
64C43×#427—21no—
65C2×C4⋊C8×C43C2211yescharacteristic
66C43×#416—21no—
67C2×#10621885—21no—
68C2×#10621885—21no—
69C22×C43⋊C8—21no—
70C22×C43⋊C8—21no—
71C22×C43⋊C8—21no—
72C22×C43⋊C8D411yescharacteristic
73C22×C43⋊C8D411yescharacteristic
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063317—21no—
77#13063304—21no—
78#13063304—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81#13063284—21no—
82#13063258—21no—
83#13063258—21no—
84#13063258—21no—
85#13063258—21no—
86#13063256—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—21no—
96#13063249—21no—
97#13063249—21no—
98#13063249—21no—
99#13063248—21no—
100#13063248—21no—
101#13063246—21no—
102#13063246—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106C4×C43⋊C8—21no—
107C4×C43⋊C8—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8D411yescharacteristic
110C4×C43⋊C8D411yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43D411yescharacteristic
114C22×C8×C43—21no—
115C4⋊Q8×C43C2311yescharacteristic
116C4⋊Q8×C43C2311yescharacteristic
117#125×C43—21no—
118C22⋊Q8×C43—21no—
119C22⋊Q8×C43—21no—
120C4×Q8×C43—21no—
121C4×Q8×C43—21no—
122C4×Q8×C43D411yescharacteristic
123C4×Q8×C43C2311yescharacteristic
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43D411yescharacteristic
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129#117×C43—21no—
130#117×C43D411yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#107×C43—21no—
134#107×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144#41×C43—22no—
145#41×C43Q1614yescomplemented
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—42no—
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—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43C2×D411yescharacteristic
171C4⋊C4×C43C2×D411yescharacteristic
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—41no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—41no—
180C42×C43C2×D411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43#4111yescharacteristic
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185#10621885—42no—
186#10621885—42no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193C4×Dic43—41no—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—41no—
200C2×C43⋊C8—42no—
201C2×C43⋊C8—42no—
202C2×C43⋊C8—42no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43#12111yescharacteristic
209Q8×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—81no—
213Q8×C43C2×Q1612yes—
214D4×C43—24no—
215D4×C43—21no—
216D4×C43C2×Q1612yes—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—24no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—42no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43C2×Q1612yes—
233C2×C4×C43#13512yes—
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×Dic43—41no—
238C2×Dic43—41no—
239Dic86—41no—
240Dic86—41no—
241Dic86—81no—
242C8×C43—41no—
243C8×C43—41no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8#13512yes—
252#19126—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—22no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43#46712yes—
259C22×C43C2×#12111yescharacteristic
260C4×C43—21no—
261C4×C43—22no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43#46712yes—
269C4×C43C22×Q1611yescharacteristic
270C4×C43C2×#13511yescharacteristic
271C4×C43C2×#13511yescharacteristic
272C4×C43#57511yescharacteristic
273Dic43—81no—
274Dic43—81no—
275#3170—431no—
276#3076—431no—
277#3076D4311yescharacteristic
278C8×#41—431no—
279#1684—431no—
280#1684—431no—
281#1683—431no—
282#1683—431no—
283#1676—431no—
284#1675—431no—
285#1670—431no—
286#1669—431no—
287C2×#335—431no—
288#1542—431no—
289#1542—431no—
290C2×C43—22no—
291C2×C43—42no—
292C2×C43#303511yescharacteristic
293C2×C43C2×#46711yescharacteristic
294C2×C43#306711yescharacteristic
295#533—431no—
296#533C2×D4311yescharacteristic
297C4×#41C2×D4311yescharacteristic
298#500—431no—
299#494—431no—
300#487—431no—
301#487—431no—
302#479—21no—
303#479—861no—
304#478—21no—
305#478—861no—
306#477—431no—
307#477C2×D4311yescharacteristic
308#476—431no—
309#476C2×D4311yescharacteristic
310#475—431no—
311#475C2×D4311yescharacteristic
312#474—431no—
313#474C2×D4311yescharacteristic
314#467—861no—
315#467—861no—
316C8×Q8—431no—
317C8×Q8—431no—
318C4×Q16—861no—
319C4×Q16—861no—
320C8×D4—431no—
321C8×D4—431no—
322C8×D4—861no—
323C8×D4—861no—
324#431—431no—
325#431—861no—
326#427—21no—
327#427—861no—
328C2×C4⋊C8—431no—
329C2×C4⋊C8C2×D4311yescharacteristic
330#416—21no—
331#416—861no—
332C2×C4×C8—431no—
333C2×C4×C8—861no—
334#335—431no—
335#335—431no—
336#335—431no—
337#335—431no—
338#333—431no—
339#333—431no—
340#333—431no—
341#333—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346C43#1912611yescharacteristic, complemented, Sylow
347C2×#41C22⋊D4311yescharacteristic
348C2×Q16—861no—
349C2×Q16—861no—
350C22×C8—21no—
351C22×C8—431no—
352C22×C8—431no—
353C22×C8—861no—
354C22×C8—861no—
355C22×C8—861no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8C22×D4311yescharacteristic
359C4⋊Q8C22×D4311yescharacteristic
360#125—21no—
361#125—861no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—861no—
365C22⋊Q8—861no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8C22⋊D4311yescharacteristic
371C4×Q8C22×D4311yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4C22⋊D4311yescharacteristic
375C4×D4C22×D4311yescharacteristic
376#117—21no—
377#117—21no—
378#117—861no—
379#117C22⋊D4311yescharacteristic
380C2×C42—21no—
381C2×C42C22×D4311yescharacteristic
382#107—21no—
383#107—21no—
384#107—861no—
385#107—861no—
386#107—861no—
387#107—861no—
388#106—21no—
389#106—21no—
390#106—861no—
391#106—861no—
392C4⋊C8—21no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402#103—21no—
403#103—21no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#102—21no—
411#102—21no—
412#102—861no—
413#102—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8—861no—
424#41—22no—
425#41#1062188514yescomplemented
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8C2×C22⋊D4311yescharacteristic
431C2×D4—21no—
432C2×D4C2×C22⋊D4311yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4D4×D4311yescharacteristic
437C22×C4#1062190011yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439Q16—1722no—
440Q16—1722no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—42no—
444C2×C8—431no—
445C2×C8—431no—
446C2×C8—431no—
447C2×C8—431no—
448C2×C8—862no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—1722no—
454C2×C8—1721no—
455C2×C8—1722no—
456C2×C8—1722no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4C2×C22⋊D4311yescharacteristic
472C4⋊C4C2×C22⋊D4311yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—41no—
477C22⋊C4—1721no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—41no—
482C42—1721no—
483C42D4×D4311yescharacteristic
484C42#1062190011yescharacteristic
485C42C2×C22⋊D4311yescharacteristic
486C42C23×D4311yescharacteristic
487C23—21no—
488C23#1306329711yescharacteristic
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493Q8—3441no—
494Q8—1721no—
495Q8—1721no—
496Q8C2×#1062188512yes—
497D4—24no—
498D4—21no—
499D4C2×#1062188512yes—
500C2×C4—21no—
501C2×C4—24no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4#1306329711yescharacteristic
515C2×C4#1306329711yescharacteristic
516C2×C4#1306329711yescharacteristic
517C2×C4C2×#1062188512yes—
518C2×C4#1306334512yes—
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C22×C22⋊D4311yescharacteristic
521C2×C4C2×#1062190011yescharacteristic
522C8—41no—
523C8—41no—
524C8—432no—
525C8—861no—
526C8—861no—
527C8—861no—
528C8—1721no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C22—21no—
533C22—21no—
534C22—22no—
535C22—41no—
536C22—41no—
537C22#1458313812yes—
538C22C2×#1306329711yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—22no—
543C4—41no—
544C4—41no—
545C4—81no—
546C4—81no—
547C4—3441no—
548C4—3441no—
549C4#1458313812yes—
550C4C22×#1062188511yescharacteristic
551C4#135×D4311yescharacteristic
552C4C2×#1306334511yescharacteristic
553C4#1458369611yescharacteristic
554C2—22no—
555C2—42no—
556C2#1914404611yescharacteristic
557C2C2×#1458313811yescharacteristic
558C2#1914431211yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3076C2
socleC22×C43C2×#121
prime radicalC2×#41×C43D4
hypercenter#3076D43
hypocenterC43#19126
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #19145177C2semidirect
4. #19134055C2semidirect
5. #19134051C2semidirect
6. #19134048C2semidirect
7. #19134044C2semidirect
8. #19133997C2semidirect
9. #19133992C2semidirect
10. #19133963C2semidirect
11. #19133958C2semidirect
12. C2×#14582651C2semidirect
13. #19133253C2semidirect
14. #19133252C2semidirect
145. #41×C43Q16semidirect
346. C43#19126semidirect
425. #41#10621885semidirect

Maximal subgroups

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

subgroupindex
#191451772
#191443832
#41×C43⋊C82
#191340552
#191340512
#191340482
#191340442
#191339972
#191339922
#191339632
#191339582
C2×#145826512
#191332532
#191332522
C43×#30762
#1912643