Finite Group Databasebeta

← #25080336

Subgroups — #25080336

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145770C211yesmaximal, characteristic
2#19145336C211yesmaximal, characteristic, complemented
3#19143600C211yesmaximal, characteristic
4#19134175C211yesmaximal, characteristic, complemented
5#19134151C211yesmaximal, characteristic, complemented
6#19134092C211yesmaximal, characteristic, complemented
7#19134082C211yesmaximal, characteristic, complemented
8#19134044C211yesmaximal, characteristic, complemented
9#19134020C211yesmaximal, characteristic, complemented
10#19133975C211yesmaximal, characteristic, complemented
11#19133963C211yesmaximal, characteristic, complemented
12#19133345C211yesmaximal, characteristic, complemented
13#19133260C211yesmaximal, characteristic, complemented
14#19133253C211yesmaximal, characteristic, complemented
15C43×#3248C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583298—21no—
18#14583295C2211yescharacteristic
19#14583278C2211yescharacteristic
20#14583253—21no—
21#14583251C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583237—21no—
24#14583220—21no—
25#14583194C2211yescharacteristic
26#14583189C2211yescharacteristic
27#14583184C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583155—21no—
30#14583155—21no—
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33#14583004—21no—
34#14583004—21no—
35#14582977—21no—
36#14582977C2211yescharacteristic
37#14582971—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582952C2211yescharacteristic
41#14582952C2211yescharacteristic
42#14582855—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#479—21no—
59C43×#475C2211yescharacteristic
60C43×#474C2211yescharacteristic
61C43×#467—21no—
62C43×#465—21no—
63C43×#464—21no—
64C43×#462C2211yescharacteristic
65C43×#461C2211yescharacteristic
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621877—21no—
70C2×#10621877D411yescharacteristic
71C2×#10621877D411yescharacteristic
72C22×C43⋊C8—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063317—21no—
76#13063304—21no—
77#13063304—21no—
78C4×Dic86—21no—
79C4×Dic86—21no—
80#13063284—21no—
81#13063258—21no—
82#13063258—21no—
83#13063256—21no—
84#13063256—21no—
85#13063256—21no—
86#13063256—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93#13063249—21no—
94#13063249—21no—
95#13063249—21no—
96#13063249—21no—
97#13063248—21no—
98#13063248—21no—
99#13063246—21no—
100#13063246—21no—
101C22⋊(C43⋊C8)—21no—
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105#13063236—21no—
106#13063236D411yescharacteristic
107#13063236D411yescharacteristic
108C4×C43⋊C8—21no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×Q16×C43—21no—
114C2×SD16×C43—21no—
115C22×C8×C43—21no—
116C4⋊Q8×C43C2311yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118#126×C43—21no—
119#125×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43D411yescharacteristic
126#121×C43D411yescharacteristic
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×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#103×C43—21no—
143#102×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C2×Dic86—21no—
154C2×Dic86—21no—
155Q16×C43—81no—
156SD16×C43—81no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—81no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
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—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
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—
194#10621877—22no—
195#10621877—41no—
196#10621877—42no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—42no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C23×C43—21no—
207C23×C43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214D4×C43—21no—
215D4×C43—21no—
216D4×C43—81no—
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—21no—
224C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×Dic43—41no—
236C2×Dic43—41no—
237Dic86—41no—
238Dic86—41no—
239Dic86—81no—
240C8×C43—41no—
241C8×C43—41no—
242C43⋊C8—21no—
243C43⋊C8—21no—
244C43⋊C8—21no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8#13512yes—
250#19251—431nomaximal, Sylow
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43C2×#12111yescharacteristic
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—81no—
266C4×C43—81no—
267C4×C43C2×#13511yescharacteristic
268C4×C43#57511yescharacteristic
269C4×C43#57711yescharacteristic
270C4×C43#57811yescharacteristic
271Dic43—81no—
272Dic43—81no—
273#3248D4311yescharacteristic
274#3233—431no—
275#3185—431no—
276#2969—431no—
277#1704—431no—
278#1700—431no—
279#1691—431no—
280#1689—431no—
281#1683—431no—
282#1679—431no—
283#1672—431no—
284#1670—431no—
285#1565—431no—
286#1544—431no—
287#1542—431no—
288C2×C43—41no—
289C2×C43—81no—
290C2×C43#303511yescharacteristic
291C2×C43#306311yescharacteristic
292C2×C43#306911yescharacteristic
293#533—431no—
294#533C2×D4311yescharacteristic
295#529C2×D4311yescharacteristic
296#499—861no—
297#498—431no—
298#494—431no—
299#488—861no—
300#487—431no—
301#487—431no—
302#485—861no—
303#482—861no—
304#479—21no—
305#477—431no—
306#476—431no—
307#475—431no—
308#475C2×D4311yescharacteristic
309#474—431no—
310#474C2×D4311yescharacteristic
311#470—861no—
312#470—861no—
313#467—21no—
314#465—21no—
315#464—21no—
316#462C2×D4311yescharacteristic
317#461C2×D4311yescharacteristic
318#446—431no—
319C8×Q8—431no—
320#441—861no—
321#441—861no—
322#436—431no—
323#436—861no—
324#435—861no—
325C8×D4—431no—
326#433—861no—
327#431—431no—
328#431—431no—
329C2×C4⋊C8C2×D4311yescharacteristic
330#405—861no—
331C4×M16—431no—
332#335—431no—
333#335—431no—
334#334—431no—
335#334—431no—
336#333—431no—
337#333—431no—
338#332—431no—
339#332—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344C43#1925111yescharacteristic, complemented, Sylow
345C2×Q16—21no—
346C2×Q16—861no—
347C2×Q16—861no—
348C2×SD16—21no—
349C2×M16—431no—
350C2×M16—431no—
351C2×M16—861no—
352C22×C8—21no—
353C22×C8—861no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#126—21no—
359#125—21no—
360#125—861no—
361#125C22⋊D4311yescharacteristic
362#124C22⋊D4311yescharacteristic
363#123—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—861no—
367C22⋊Q8—861no—
368C22⋊Q8C22⋊D4311yescharacteristic
369#121C22⋊D4311yescharacteristic
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—861no—
373C4×Q8—861no—
374C4×Q8C22×D4311yescharacteristic
375C4×D4—21no—
376C4×D4C22×D4311yescharacteristic
377#117—21no—
378#117—21no—
379#117—861no—
380C2×C42C22×D4311yescharacteristic
381#107—21no—
382#107—861no—
383#107—861no—
384#106—21no—
385#106—861no—
386#106—861no—
387#106—861no—
388#106—861no—
389C4⋊C8—21no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#102—21no—
408#102—861no—
409#102—861no—
410C22⋊C8—861no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414#97—431no—
415#97—431no—
416#97—861no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8—861no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8C2×C22⋊D4311yescharacteristic
427C2×D4—21no—
428C2×D4C2×C22⋊D4311yescharacteristic
429C22×C4—21no—
430C22×C4D4×D4311yescharacteristic
431C22×C4#1062190011yescharacteristic
432C22×C4C2×C22⋊D4311yescharacteristic
433Q16—81no—
434Q16—1722no—
435Q16—1722no—
436SD16—81no—
437M16—862no—
438M16—1722no—
439M16—1721no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—81no—
443C2×C8—431no—
444C2×C8—431no—
445C2×C8—431no—
446C2×C8—431no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—1722no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4C2×C22⋊D4311yescharacteristic
469C4⋊C4C2×C22⋊D4311yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—1721no—
477C42—21no—
478C42—41no—
479C42—1721no—
480C42D4×D4311yescharacteristic
481C42#1062190011yescharacteristic
482C42C2×C22⋊D4311yescharacteristic
483C42C23×D4311yescharacteristic
484C23—21no—
485C23#1306329711yescharacteristic
486Q8—21no—
487Q8—21no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—3441no—
493Q8—1721no—
494Q8—1721no—
495D4—21no—
496D4—21no—
497D4—81no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4#1306329711yescharacteristic
513C2×C4#1306329711yescharacteristic
514C2×C4#1306329711yescharacteristic
515C2×C4C2×D4×D4311yescharacteristic
516C2×C4C22×C22⋊D4311yescharacteristic
517C2×C4C2×#1062190011yescharacteristic
518C8—41no—
519C8—41no—
520C8—432no—
521C8—861no—
522C8—861no—
523C8—861no—
524C8—1721no—
525C8—1721no—
526C8—1721no—
527C8—1721no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22C2×#1306329711yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—3441no—
545C4—3441no—
546C4#135×D4311yescharacteristic
547C4#1458369611yescharacteristic
548C4#1458371011yescharacteristic
549C4#1458371411yescharacteristic
550C2—41no—
551C2—81no—
552C2#1914404611yescharacteristic
553C2#1914428811yescharacteristic
554C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3248C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#3248D43
hypocenterC43#19251
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3248

Complements

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

NH ≅ G/Ntype
2. #19145336C2semidirect
4. #19134175C2semidirect
5. #19134151C2semidirect
6. #19134092C2semidirect
7. #19134082C2semidirect
8. #19134044C2semidirect
9. #19134020C2semidirect
10. #19133975C2semidirect
11. #19133963C2semidirect
12. #19133345C2semidirect
13. #19133260C2semidirect
14. #19133253C2semidirect
344. C43#19251semidirect

Maximal subgroups

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

subgroupindex
#191457702
#191453362
#191436002
#191341752
#191341512
#191340922
#191340822
#191340442
#191340202
#191339752
#191339632
#191333452
#191332602
#191332532
C43×#32482
#1925143