Finite Group Databasebeta

← #25080070

Subgroups — #25080070

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145921C211yesmaximal, characteristic
2#19145155C211yesmaximal, characteristic, complemented
3#19143571C211yesmaximal, characteristic, complemented
4#19134099C211yesmaximal, characteristic, complemented
5#19134092C211yesmaximal, characteristic, complemented
6#19134069C211yesmaximal, characteristic, complemented
7#19134062C211yesmaximal, characteristic, complemented
8#19134051C211yesmaximal, characteristic, complemented
9#19134044C211yesmaximal, characteristic, complemented
10#19134041C211yesmaximal, characteristic, complemented
11#19134034C211yesmaximal, characteristic, complemented
12C2×#14582651C211yesmaximal, characteristic, complemented
13#19133295C211yesmaximal, characteristic, complemented
14#19133288C211yesmaximal, characteristic, complemented
15C43×#3248C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583295C2211yescharacteristic
18#14583273C2211yescharacteristic
19#14583249C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583196—21no—
22#14583194C2211yescharacteristic
23#14583189C2211yescharacteristic
24#14583133—21no—
25#14583130—21no—
26#14583130—21no—
27#14583130—21no—
28#14583111—21no—
29#14583099C2211yescharacteristic
30#14583094C2211yescharacteristic
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33C4×#10621884—21no—
34C4×#10621884—21no—
35#14582977C2211yescharacteristic
36#14582971—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582956C2211yescharacteristic
41C2×C4⋊(C43⋊C8)C2211yescharacteristic
42#14582855—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582651C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
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×#10621898—21no—
68C2×#10621884—21no—
69C2×#10621884—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C2×#10621877—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8D411yescharacteristic
76C22×C43⋊C8D411yescharacteristic
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063313—21no—
80#13063299—21no—
81#13063299—21no—
82C4×D172—21no—
83C4×D172—21no—
84#13063258—21no—
85#13063256—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#13063246—21no—
99#13063245—21no—
100#13063245—21no—
101#13063245—21no—
102#13063245—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106#13063236—21no—
107#13063236—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8D411yescharacteristic
110C4×C43⋊C8D411yescharacteristic
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×C22⋊D43—41no—
154#10621898—82no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×C4×D43—41no—
159C2×Dic86—21no—
160Q16×C43—81no—
161SD16×C43—81no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—81no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C42×C43—21no—
184C42×C43—41no—
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43#4111yescharacteristic
188C42×C43C2411yescharacteristic
189#10621884—42no—
190#10621884—42no—
191#10621884—81no—
192#10621882—81no—
193(C2×D43)⋊C4—41no—
194(C2×D43)⋊C4—41no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197#10621877—42no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—41no—
204C2×C43⋊C8—42no—
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—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—42no—
222C2×C4×C43—22no—
223C2×C4×C43—21no—
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—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C22⋊D43—82no—
241C2×Dic43—41no—
242D172—41no—
243D172—41no—
244D172—41no—
245D172—41no—
246D172—81no—
247C4×D43—82no—
248Dic86—81no—
249C8×C43—41no—
250C8×C43—41no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8#13512yes—
259#19229—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43#47112yes—
266C22×C43C2×#12111yescharacteristic
267C2×D43—81no—
268C2×D43—81no—
269C2×D43—81no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43C2×#13511yescharacteristic
280C4×C43#57511yescharacteristic
281C4×C43#57611yescharacteristic
282C4×C43#57811yescharacteristic
283Dic43—81no—
284#3248D4311yescharacteristic, complemented
285#3247—431no—
286#3167—431no—
287#2966—431no—
288#1692—431no—
289#1691—431no—
290#1686—431no—
291#1685—431no—
292#1684—431no—
293#1683—431no—
294#1682—431no—
295#1681—431no—
296C2×#335—431no—
297#1552—431no—
298#1551—431no—
299C2×C43—22no—
300C2×C43—81no—
301C2×C43#303511yescharacteristic
302C2×C43#306111yescharacteristic
303C2×C43C2×#47111yescharacteristic
304D43—161no—
305#533C2×D4311yescharacteristic
306#532—431no—
307#529C2×D4311yescharacteristic
308#498—431no—
309#492—431no—
310#487—431no—
311#486—431no—
312#479—21no—
313#478—861no—
314#477—431no—
315#476—431no—
316#475C2×D4311yescharacteristic
317#474C2×D4311yescharacteristic
318#467—21no—
319#466—861no—
320#465—21no—
321#465—861no—
322#465—861no—
323#465—861no—
324#464—21no—
325#463—861no—
326#462C2×D4311yescharacteristic
327#461C2×D4311yescharacteristic
328#460—431no—
329#459—431no—
330#446—431no—
331C8×Q8—431no—
332C4×SD16—861no—
333C4×SD16—861no—
334#436—431no—
335#435—861no—
336C8×D4—431no—
337C8×D4—861no—
338#433—861no—
339#432—431no—
340C2×C4⋊C8—431no—
341C2×C4⋊C8C2×D4311yescharacteristic
342#405—861no—
343C2×C4×C8—431no—
344#335—431no—
345#335—431no—
346#335—431no—
347#335—431no—
348#333—431no—
349#333—431no—
350#332—431no—
351#332—431no—
352#332—431no—
353#332—431no—
354#331—431no—
355#331—431no—
356C43#1922911yescharacteristic, complemented, Sylow
357C2×#41—861no—
358C2×Q16—21no—
359C2×SD16—21no—
360C2×SD16—861no—
361C2×SD16—861no—
362C2×SD16—861no—
363C2×D8—861no—
364C2×M16—861no—
365C22×C8—21no—
366C22×C8—431no—
367C22×C8—431no—
368C22×C8—861no—
369C22×C8—861no—
370C4⋊Q8—431no—
371C4⋊Q8C22×D4311yescharacteristic
372C4⋊Q8C22×D4311yescharacteristic
373#127—431no—
374#126—21no—
375#125—21no—
376#125C22⋊D4311yescharacteristic
377#124—861no—
378#124C22⋊D4311yescharacteristic
379#123—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8C22⋊D4311yescharacteristic
383#121—861no—
384#121—861no—
385#121C22⋊D4311yescharacteristic
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8C22×D4311yescharacteristic
389C4×D4—21no—
390C4×D4—861no—
391C4×D4—861no—
392C4×D4C22×D4311yescharacteristic
393#117—21no—
394#117—21no—
395C2×C42C22×D4311yescharacteristic
396#107—21no—
397#107—861no—
398#106—21no—
399#106—861no—
400#106—861no—
401#106—861no—
402C4⋊C8—21no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—861no—
416#103—861no—
417#103—861no—
418#102—21no—
419#102—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427#97—861no—
428#97—861no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—861no—
434#41—3442no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—861no—
438C2×Q8C2×C22⋊D4311yescharacteristic
439C2×D4—21no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—1721no—
444C2×D4C2×C22⋊D4311yescharacteristic
445C22×C4—21no—
446C22×C4—1721no—
447C22×C4D4×D4311yescharacteristic
448C22×C4#1062190011yescharacteristic
449C22×C4C2×C22⋊D4311yescharacteristic
450Q16—81no—
451SD16—81no—
452SD16—3441no—
453SD16—1722no—
454SD16—1722no—
455D8—3441no—
456M16—1722no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—862no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—3441no—
470C2×C8—1721no—
471C2×C8—1722no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4C2×C22⋊D4311yescharacteristic
485C4⋊C4C2×C22⋊D4311yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C42—21no—
495C42—41no—
496C42D4×D4311yescharacteristic
497C42#1062190011yescharacteristic
498C42C2×C22⋊D4311yescharacteristic
499C42C23×D4311yescharacteristic
500C23—21no—
501C23—1721no—
502C23#1306329711yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—3441no—
510D4—21no—
511D4—21no—
512D4—42no—
513D4—3441no—
514D4—3442no—
515D4—1721no—
516D4—1721no—
517D4—1721no—
518D4—1721no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—3442no—
532C2×C4—1721no—
533C2×C4#1306329711yescharacteristic
534C2×C4#1306329711yescharacteristic
535C2×C4#1306329711yescharacteristic
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4C22×C22⋊D4311yescharacteristic
538C2×C4C2×#1062190011yescharacteristic
539C8—41no—
540C8—41no—
541C8—432no—
542C8—861no—
543C8—861no—
544C8—861no—
545C8—1721no—
546C8—1721no—
547C8—1721no—
548C8—1721no—
549C22—21no—
550C22—21no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—3441no—
555C22—3441no—
556C22—3441no—
557C22#1458316412yes—
558C22C2×#1306329711yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—3441no—
569C4#135×D4311yescharacteristic
570C4#1458369611yescharacteristic
571C4#1458370211yescharacteristic
572C4#1458371411yescharacteristic
573C2—22no—
574C2—81no—
575C2—6881no—
576C2#1914404611yescharacteristic
577C2#1914426211yescharacteristic
578C2C2×#1458316411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3248C2
socleC22×C43C2×#121
prime radical#19145921C2
hypercenter#3248D43
hypocenterC43#19229
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. #19145155C2semidirect
3. #19143571C2semidirect
4. #19134099C2semidirect
5. #19134092C2semidirect
6. #19134069C2semidirect
7. #19134062C2semidirect
8. #19134051C2semidirect
9. #19134044C2semidirect
10. #19134041C2semidirect
11. #19134034C2semidirect
12. C2×#14582651C2semidirect
13. #19133295C2semidirect
14. #19133288C2semidirect
15. C43×#3248C2semidirect
284. #3248D43semidirect
356. C43#19229semidirect

Maximal subgroups

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

subgroupindex
#191459212
#191451552
#191435712
#191340992
#191340922
#191340692
#191340622
#191340512
#191340442
#191340412
#191340342
C2×#145826512
#191332952
#191332882
C43×#32482
#1922943