Finite Group Databasebeta

← #25082109

Subgroups — #25082109

Order 11008.

594 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#19145756C211yesmaximal, characteristic, complemented
2#19144757C211yesmaximal, characteristic
3#19144666C211yesmaximal, characteristic
4#19134053C211yesmaximal, characteristic, complemented
5#19134046C211yesmaximal, characteristic, complemented
6#19134025C211yesmaximal, characteristic, complemented
7#19134018C211yesmaximal, characteristic, complemented
8#19133989C211yesmaximal, characteristic, complemented
9#19133984C211yesmaximal, characteristic, complemented
10#19133977C211yesmaximal, characteristic, complemented
11#19133970C211yesmaximal, characteristic, complemented
12#19133375C211yesmaximal, characteristic, complemented
13#19133293C211yesmaximal, characteristic, complemented
14#19133253C211yesmaximal, characteristic, complemented
15C43×#2988C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583456C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583297C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583241—21no—
23#14583241—21no—
24#14583240—21no—
25#14583240—21no—
26#14583207—21no—
27#14583207—21no—
28#14583194C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583184C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583109C2211yescharacteristic
33#14583109C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583061—21no—
37#14583061—21no—
38#14583004—21no—
39#14582999—21no—
40C4×#10621885—21no—
41C4×#10621883—21no—
42#14582956C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C8×D4×C43—21no—
60C8×D4×C43—21no—
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#431—21no—
64C43×#431C2211yescharacteristic
65C2×C4⋊C8×C43—21no—
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063317—21no—
76#13063317—21no—
77#13063304—21no—
78#13063304—21no—
79#13063304—21no—
80#13063304—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×Dic86—21no—
85#13063284—21no—
86#13063284—21no—
87#13063259—21no—
88#13063259—21no—
89#13063258—21no—
90#13063258—21no—
91#13063257—21no—
92#13063257—21no—
93#13063256—21no—
94#13063256—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063250—21no—
100#13063250—21no—
101#13063250—21no—
102#13063250—21no—
103#13063249—21no—
104#13063249—21no—
105#13063248—21no—
106#13063248—21no—
107#13063248—21no—
108#13063248—21no—
109#13063246—21no—
110#13063246—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113#13063236—21no—
114C4×C43⋊C8—21no—
115C2×#41×C43D411yescharacteristic
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43—21no—
119C4×Q8×C43D411yescharacteristic
120C4×Q8×C43C2311yescharacteristic
121C4×D4×C43—21no—
122C4×D4×C43—21no—
123C4×D4×C43D411yescharacteristic
124C4×D4×C43C2311yescharacteristic
125#117×C43—21no—
126#117×C43D411yescharacteristic
127C2×C42×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—21no—
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—22no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—81no—
162C2×C8×C43—81no—
163C2×C8×C43—81no—
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43C2×D411yescharacteristic
171C4⋊C4×C43C2×D411yescharacteristic
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43C2×D411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43#4111yescharacteristic
181C42×C43C2411yescharacteristic
182C22⋊Dic43—41no—
183C22⋊Dic43—41no—
184#10621885—42no—
185#10621885—42no—
186#10621883—42no—
187#10621883—42no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200C4×Dic43—41no—
201C4×Dic43—41no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C23×C43—21no—
207C23×C43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43#13512yes—
210D4×C43—24no—
211D4×C43—21no—
212D4×C43#13512yes—
213C2×C4×C43—24no—
214C2×C4×C43—21no—
215C2×C4×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—81no—
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235Dic86—41no—
236Dic86—41no—
237Dic86—41no—
238Dic86—41no—
239Dic86—41no—
240Dic86—41no—
241Dic86—81no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#19418—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—22no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43C2×#12111yescharacteristic
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—22no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43C2×#13511yescharacteristic
268C4×C43C2×#13511yescharacteristic
269C4×C43#57711yescharacteristic
270C4×C43#57811yescharacteristic
271Dic43—81no—
272Dic43—81no—
273Dic43—81no—
274Dic43—81no—
275#3231—431no—
276#3116—431no—
277#3107—431no—
278#2988D4311yescharacteristic
279#1684—431no—
280#1683—431no—
281#1680—431no—
282#1679—431no—
283#1674—431no—
284#1673—431no—
285#1672—431no—
286#1671—431no—
287#1572—431no—
288#1552—431no—
289#1542—431no—
290C2×C43—41no—
291C2×C43—42no—
292C2×C43#304611yescharacteristic
293C2×C43#305011yescharacteristic
294C2×C43#306911yescharacteristic
295#533—431no—
296#533—431no—
297C4×#41C2×D4311yescharacteristic
298#500—431no—
299#498—431no—
300#487—431no—
301#487—431no—
302#485—861no—
303#485—861no—
304#485—861no—
305#485—861no—
306#479—861no—
307#479—861no—
308#477—431no—
309#476—431no—
310#475—431no—
311#474—431no—
312#462—431no—
313#462—431no—
314#461—431no—
315#461—431no—
316#452—861no—
317#452—861no—
318C8×Q8C2×D4311yescharacteristic
319C8×Q8C2×D4311yescharacteristic
320#441—861no—
321#440—861no—
322C4×Q16—861no—
323C4×SD16—861no—
324C8×D4—21no—
325C8×D4—21no—
326C8×D4C2×D4311yescharacteristic
327C8×D4C2×D4311yescharacteristic
328#432—431no—
329#431—21no—
330#431—431no—
331#431C2×D4311yescharacteristic
332C2×C4⋊C8—21no—
333C2×C4⋊C8C2×D4311yescharacteristic
334#335—431no—
335#335—431no—
336#334—431no—
337#334—431no—
338#333—431no—
339#333—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346C43#1941811yescharacteristic, complemented, Sylow
347C2×#41D17211yescharacteristic
348C2×Q16—861no—
349C2×Q16—861no—
350C2×SD16—861no—
351C2×SD16—861no—
352C22×C8—21no—
353C22×C8—21no—
354C22×C8—21no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8—431no—
359#125—861no—
360#125—861no—
361C22⋊Q8—861no—
362C22⋊Q8—861no—
363C22⋊Q8—861no—
364C22⋊Q8—861no—
365C4×Q8—861no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×Q8—861no—
369C4×Q8D17211yescharacteristic
370C4×Q8C22×D4311yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373C4×D4D17211yescharacteristic
374C4×D4C22×D4311yescharacteristic
375#117—21no—
376#117—861no—
377#117—861no—
378#117D17211yescharacteristic
379C2×C42—21no—
380C2×C42C22×D4311yescharacteristic
381#107—861no—
382#107—861no—
383#107—861no—
384#107—861no—
385#106—861no—
386#106—861no—
387#106—861no—
388#106—861no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8C22⋊D4311yescharacteristic
397C4⋊C8C22⋊D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399C4⋊C8C22×D4311yescharacteristic
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#102—861no—
411#102—861no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416C22⋊C8C22⋊D4311yescharacteristic
417C22⋊C8C22⋊D4311yescharacteristic
418#97—861no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8—861no—
422C4×C8C22×D4311yescharacteristic
423C4×C8C22×D4311yescharacteristic
424#41—22no—
425#41—22no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8C2×D17211yescharacteristic
431C2×D4—21no—
432C2×D4C2×D17211yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4C2×D17211yescharacteristic
437C22×C4#1062189811yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439Q16—1722no—
440Q16—1722no—
441SD16—1722no—
442SD16—1722no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—81no—
447C2×C8—81no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8C2×C22⋊D4311yescharacteristic
453C2×C8C2×C22⋊D4311yescharacteristic
454C2×C8C2×C22⋊D4311yescharacteristic
455C2×C8C2×C22⋊D4311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
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⋊C4—1721no—
470C4⋊C4C2×D17211yescharacteristic
471C4⋊C4C2×D17211yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—1721no—
476C22⋊C4—1721no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—1721no—
481C42—1721no—
482C42C2×D17211yescharacteristic
483C42#1062189811yescharacteristic
484C42C2×C22⋊D4311yescharacteristic
485C42C23×D4311yescharacteristic
486C23—21no—
487C23#1306329911yescharacteristic
488Q8—21no—
489Q8—3441no—
490Q8—1721no—
491Q8—1721no—
492Q8—1721no—
493Q8—1721no—
494Q8—1721no—
495Q8—1721no—
496Q8#1306334712yes—
497D4—24no—
498D4—21no—
499D4#1306334712yes—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—81no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4#1306329911yescharacteristic
517C2×C4#1306329911yescharacteristic
518C2×C4#1306329911yescharacteristic
519C2×C4C22×C22⋊D4311yescharacteristic
520C2×C4C22×D17211yescharacteristic
521C2×C4C2×#1062189811yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—1721no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—22no—
536C22—41no—
537C22—41no—
538C22C2×#1306329911yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—22no—
544C4—41no—
545C4—41no—
546C4—3441no—
547C4—3441no—
548C4—3441no—
549C4—3441no—
550C4C2×#1306334711yescharacteristic
551C4C2×#1306334711yescharacteristic
552C4#1458371011yescharacteristic
553C4#1458371411yescharacteristic
554C2—41no—
555C2—42no—
556C2#1914414511yescharacteristic
557C2#1914417611yescharacteristic
558C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2988C2
socleC22×C43C2×#121
prime radicalC2×#41×C43D4
hypercenter#2988D43
hypocenterC43#19418
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #19145756C2semidirect
4. #19134053C2semidirect
5. #19134046C2semidirect
6. #19134025C2semidirect
7. #19134018C2semidirect
8. #19133989C2semidirect
9. #19133984C2semidirect
10. #19133977C2semidirect
11. #19133970C2semidirect
12. #19133375C2semidirect
13. #19133293C2semidirect
14. #19133253C2semidirect
346. C43#19418semidirect

Maximal subgroups

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

subgroupindex
#191457562
#191447572
#191446662
#191340532
#191340462
#191340252
#191340182
#191339892
#191339842
#191339772
#191339702
#191333752
#191332932
#191332532
C43×#29882
#1941843