Finite Group Databasebeta

← #25084198

Subgroups — #25084198

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145921C211yesmaximal, characteristic
2#19145723C211yesmaximal, characteristic, complemented
3#19143755C211yesmaximal, characteristic, complemented
4#19134165C211yesmaximal, characteristic, complemented
5#19134158C211yesmaximal, characteristic, complemented
6#19134099C211yesmaximal, characteristic, complemented
7#19134092C211yesmaximal, characteristic, complemented
8#19134041C211yesmaximal, characteristic, complemented
9#19134034C211yesmaximal, characteristic, complemented
10#19133975C211yesmaximal, characteristic, complemented
11#19133968C211yesmaximal, characteristic, complemented
12#19133381C211yesmaximal, characteristic, complemented
13#19133291C211yesmaximal, characteristic, complemented
14C2×#14582645C211yesmaximal, characteristic, complemented
15C43×#3218C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583295C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583247C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583217—21no—
22#14583217—21no—
23#14583196—21no—
24#14583194C2211yescharacteristic
25#14583189C2211yescharacteristic
26#14583186—21no—
27#14583186—21no—
28#14583133—21no—
29#14583130—21no—
30#14583111—21no—
31#14583099C2211yescharacteristic
32#14583094C2211yescharacteristic
33#14583030C2211yescharacteristic
34Q8×C43⋊C8C2211yescharacteristic
35#14582977C2211yescharacteristic
36#14582971—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582952C2211yescharacteristic
41#14582926—21no—
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#497—21no—
59C43×#491—21no—
60C43×#462C2211yescharacteristic
61C43×#462C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#461C2211yescharacteristic
64C43×#451—21no—
65C43×#448—21no—
66C43×#432C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884—21no—
69C2×#10621882—21no—
70C2×#10621877—21no—
71C22×C43⋊C8—21no—
72C22×C43⋊C8—21no—
73C22×C43⋊C8—21no—
74#13063325C2311yescharacteristic
75#13063322C2311yescharacteristic
76#13063313—21no—
77#13063299—21no—
78#13063299—21no—
79C4×D172—21no—
80C4×D172—21no—
81#13063258—21no—
82#13063256—21no—
83#13063256—21no—
84#13063256—21no—
85#13063256—21no—
86#13063256—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)D411yescharacteristic
92C4⋊(C43⋊C8)D411yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063249—21no—
98#13063246—21no—
99#13063245—21no—
100#13063245—21no—
101#13063245—21no—
102#13063245—21no—
103#13063245—21no—
104#13063245—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)—21no—
107C22⋊(C43⋊C8)D411yescharacteristic
108C22⋊(C43⋊C8)D411yescharacteristic
109#13063236—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C22×Q8×C43—21no—
114C2×Q16×C43—21no—
115C2×Q16×C43—21no—
116C2×SD16×C43—21no—
117C2×SD16×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#126×C43—21no—
124#125×C43D411yescharacteristic
125#124×C43D411yescharacteristic
126#123×C43—21no—
127C22⋊Q8×C43D411yescharacteristic
128#121×C43D411yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142C22⋊C8×C43—21no—
143#97×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—81no—
148C2×Q8×C43—81no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—41no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C2×C22⋊D43—41no—
158#10621898—82no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×C4×D43—41no—
163C2×Dic86—21no—
164Q16×C43—81no—
165Q16×C43—81no—
166SD16×C43—81no—
167SD16×C43—81no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C42×C43—21no—
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43#4111yescharacteristic
191C42×C43C2411yescharacteristic
192#10621884—81no—
193#10621882—81no—
194(C2×D43)⋊C4—41no—
195(C2×D43)⋊C4—41no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198#10621877—81no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—81no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8—81no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C23×C43—21no—
211C23×C43#12111yescharacteristic
212C22×D43—41no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—82no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—42no—
223C2×C4×C43—22no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—82no—
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—82no—
243C2×Dic43—41no—
244D172—41no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—81no—
249C4×D43—82no—
250Dic86—81no—
251C8×C43—41no—
252C8×C43—41no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—21no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#19589—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43#47112yes—
268C22×C43C2×#12111yescharacteristic
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43#57611yescharacteristic
282C4×C43#57711yescharacteristic
283C4×C43#57711yescharacteristic
284C4×C43#57811yescharacteristic
285Dic43—81no—
286#3247—431no—
287#3227—431no—
288#3218D4311yescharacteristic, complemented
289#2994—431no—
290#1702—431no—
291#1701—431no—
292#1692—431no—
293#1691—431no—
294#1682—431no—
295#1681—431no—
296#1672—431no—
297#1671—431no—
298#1573—431no—
299#1551—431no—
300C2×#332—431no—
301C2×C43—22no—
302C2×C43—81no—
303C2×C43#304611yescharacteristic
304C2×C43#306211yescharacteristic
305C2×C43C2×#47111yescharacteristic
306D43—161no—
307#532—431no—
308C2×C4⋊Q8C2×D4311yescharacteristic
309#529C2×D4311yescharacteristic
310#498—431no—
311#498—431no—
312#497—21no—
313#491—21no—
314#486—431no—
315#486—431no—
316#481—861no—
317#481—861no—
318#478—861no—
319#477—431no—
320#476—431no—
321#476—861no—
322#476—861no—
323#466—861no—
324#465—861no—
325#463—861no—
326#462C2×D4311yescharacteristic
327#462C2×D4311yescharacteristic
328#461C2×D4311yescharacteristic
329#461C2×D4311yescharacteristic
330#460—431no—
331#459—431no—
332#451—21no—
333#448—21no—
334#446—431no—
335C8×Q8—431no—
336#436—431no—
337#435—861no—
338C8×D4—431no—
339C8×D4—861no—
340#433—861no—
341#432C2×D4311yescharacteristic
342#431—431no—
343#424—861no—
344C2×C4⋊C8—431no—
345C2×C4⋊C8—431no—
346#335—431no—
347#335—431no—
348#334—431no—
349#334—431no—
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#331—431no—
357#331—431no—
358C43#1958911yescharacteristic, complemented, Sylow
359C2×#41—861no—
360C22×Q8—21no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—861no—
366C2×D8—861no—
367C2×M16—861no—
368C22×C8—861no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—431no—
375C4⋊Q8C22×D4311yescharacteristic
376C4⋊Q8C22×D4311yescharacteristic
377#127—431no—
378#126—21no—
379#125C22⋊D4311yescharacteristic
380#124—861no—
381#124C22⋊D4311yescharacteristic
382#123—21no—
383C22⋊Q8C22⋊D4311yescharacteristic
384#121—861no—
385#121—861no—
386#121C22⋊D4311yescharacteristic
387C4×Q8C22×D4311yescharacteristic
388C4×D4—21no—
389C4×D4—861no—
390C4×D4—861no—
391C4×D4C22×D4311yescharacteristic
392#117—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C42C22×D4311yescharacteristic
396#107—861no—
397#106—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8C22×D4311yescharacteristic
413C4⋊C8C22×D4311yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426C22⋊C8—21no—
427C22⋊C8—431no—
428C22⋊C8—431no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431#97—21no—
432#97—861no—
433C4×C8—431no—
434C4×C8—431no—
435C4×C8—861no—
436#41—3442no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—81no—
441C2×Q8—81no—
442C2×Q8—861no—
443C2×Q8C2×C22⋊D4311yescharacteristic
444C2×D4—21no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—1721no—
449C2×D4C2×C22⋊D4311yescharacteristic
450C22×C4—21no—
451C22×C4—41no—
452C22×C4—1721no—
453C22×C4D4×D4311yescharacteristic
454C22×C4#1062190011yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456Q16—81no—
457Q16—81no—
458SD16—81no—
459SD16—81no—
460SD16—3441no—
461D8—3441no—
462M16—3441no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—431no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—3441no—
474C2×C8—3441no—
475C2×C8—3441no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4C2×C22⋊D4311yescharacteristic
489C4⋊C4C2×C22⋊D4311yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—1721no—
496C22⋊C4—1721no—
497C42—21no—
498C42D4×D4311yescharacteristic
499C42#1062190011yescharacteristic
500C42C2×C22⋊D4311yescharacteristic
501C42C23×D4311yescharacteristic
502C23—21no—
503C23—1721no—
504C23#1306329711yescharacteristic
505Q8—21no—
506Q8—21no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—82no—
512Q8—3441no—
513D4—21no—
514D4—21no—
515D4—42no—
516D4—3441no—
517D4—3442no—
518D4—1721no—
519D4—1721no—
520D4—1721no—
521D4—1721no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4—3442no—
536C2×C4—1721no—
537C2×C4#1306329711yescharacteristic
538C2×C4#1306329711yescharacteristic
539C2×C4#1306329711yescharacteristic
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C22×C22⋊D4311yescharacteristic
542C2×C4C2×#1062190011yescharacteristic
543C8—41no—
544C8—41no—
545C8—861no—
546C8—861no—
547C8—861no—
548C8—861no—
549C8—1721no—
550C8—1721no—
551C8—1721no—
552C8—1721no—
553C22—21no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—3441no—
559C22—3441no—
560C22—3441no—
561C22#1458316412yes—
562C22C2×#1306329711yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—3441no—
573C4#1458370211yescharacteristic
574C4#1458370811yescharacteristic
575C4#1458371011yescharacteristic
576C4#1458371511yescharacteristic
577C2—22no—
578C2—81no—
579C2—6881no—
580C2#1914414911yescharacteristic
581C2#1914427111yescharacteristic
582C2C2×#1458316411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3218C2
socleC22×C43C2×#121
prime radical#19145921C2
hypercenter#3218D43
hypocenterC43#19589
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3218

Complements

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

NH ≅ G/Ntype
2. #19145723C2semidirect
3. #19143755C2semidirect
4. #19134165C2semidirect
5. #19134158C2semidirect
6. #19134099C2semidirect
7. #19134092C2semidirect
8. #19134041C2semidirect
9. #19134034C2semidirect
10. #19133975C2semidirect
11. #19133968C2semidirect
12. #19133381C2semidirect
13. #19133291C2semidirect
14. C2×#14582645C2semidirect
15. C43×#3218C2semidirect
288. #3218D43semidirect
358. C43#19589semidirect

Maximal subgroups

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

subgroupindex
#191459212
#191457232
#191437552
#191341652
#191341582
#191340992
#191340922
#191340412
#191340342
#191339752
#191339682
#191333812
#191332912
C2×#145826452
C43×#32182
#1958943