Finite Group Databasebeta

← #25080366

Subgroups — #25080366

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145770C211yesmaximal, characteristic, complemented
2#19145309C211yesmaximal, characteristic, complemented
3#19143600C211yesmaximal, characteristic, complemented
4#19134179C211yesmaximal, characteristic, complemented
5#19134133C211yesmaximal, characteristic, complemented
6#19134116C211yesmaximal, characteristic, complemented
7#19134058C211yesmaximal, characteristic, complemented
8#19134048C211yesmaximal, characteristic, complemented
9#19134002C211yesmaximal, characteristic, complemented
10#19133997C211yesmaximal, characteristic, complemented
11#19133941C211yesmaximal, characteristic, complemented
12#19133345C211yesmaximal, characteristic, complemented
13#19133257C211yesmaximal, characteristic, complemented
14#19133253C211yesmaximal, characteristic, complemented
15C43×#3247C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583298—21no—
19#14583271C2211yescharacteristic
20#14583253—21no—
21#14583251C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583237—21no—
24#14583220—21no—
25#14583194C2211yescharacteristic
26#14583189C2211yescharacteristic
27#14583184C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583143—21no—
30#14583143—21no—
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33#14582999—21no—
34#14582999—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#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#478—21no—
59C43×#477C2211yescharacteristic
60C43×#476C2211yescharacteristic
61C43×#466—21no—
62C43×#465—21no—
63C43×#463—21no—
64C43×#460C2211yescharacteristic
65C43×#459C2211yescharacteristic
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621883—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#13063258—21no—
84#13063258—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#13063248—21no—
96#13063248—21no—
97#13063246—21no—
98#13063246—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×#41×C43—21no—
114C2×SD16×C43—21no—
115C2×D8×C43—21no—
116C22×C8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#126×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43—21no—
122#124×C43D411yescharacteristic
123#123×C43—21no—
124C22⋊Q8×C43D411yescharacteristic
125#121×C43—21no—
126#121×C43—21no—
127#121×C43D411yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43C2311yescharacteristic
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#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144#41×C43—82no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C2×Dic86—21no—
159C2×Dic86—21no—
160SD16×C43—81no—
161D8×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×C43C2×D411yescharacteristic
172C4⋊C4×C43C2×D411yescharacteristic
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43C2×D411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43#4111yescharacteristic
184C42×C43C2411yescharacteristic
185C22⋊Dic43—41no—
186#10621883—42no—
187#10621883—42no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—41no—
195#10621877—22no—
196#10621877—41no—
197#10621877—42no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
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—41no—
209C23×C43#12111yescharacteristic
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—81no—
213D4×C43—21no—
214D4×C43—21no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—81no—
220D4×C43—81no—
221D4×C43—82no—
222C2×C4×C43—21no—
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—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—82no—
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×Dic43—41no—
241C2×Dic43—41no—
242Dic86—41no—
243Dic86—41no—
244Dic86—81no—
245C8×C43—41no—
246C8×C43—41no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8#13512yes—
255#19253—431nomaximal, Sylow
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43C2×#12111yescharacteristic
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—81no—
274C4×C43C2×#13511yescharacteristic
275C4×C43#57511yescharacteristic
276C4×C43#57711yescharacteristic
277C4×C43#57811yescharacteristic
278Dic43—81no—
279Dic43—81no—
280#3247D4311yescharacteristic
281#3233—431no—
282#3182—431no—
283#2969—431no—
284#1704—431no—
285#1698—431no—
286#1695—431no—
287#1685—431no—
288#1683—431no—
289#1677—431no—
290#1676—431no—
291#1666—431no—
292#1565—431no—
293#1543—431no—
294#1542—431no—
295C2×C43—41no—
296C2×C43—81no—
297C2×C43—161no—
298C2×C43#303511yescharacteristic
299C2×C43#306311yescharacteristic
300C2×C43#306811yescharacteristic
301#533—431no—
302#532C2×D4311yescharacteristic
303#529C2×D4311yescharacteristic
304#500—431no—
305#499—861no—
306#492—431no—
307#488—861no—
308#487—431no—
309#486—431no—
310#485—861no—
311#482—861no—
312#478—21no—
313#477—431no—
314#477C2×D4311yescharacteristic
315#476—431no—
316#476C2×D4311yescharacteristic
317#475—431no—
318#474—431no—
319#468—861no—
320#468—861no—
321#466—21no—
322#465—21no—
323#463—21no—
324#460C2×D4311yescharacteristic
325#459C2×D4311yescharacteristic
326#446—431no—
327C8×Q8—431no—
328#440—861no—
329#440—861no—
330#436—431no—
331#436—861no—
332#435—861no—
333C8×D4—431no—
334#433—861no—
335#431—431no—
336#431—431no—
337C2×C4⋊C8C2×D4311yescharacteristic
338#405—861no—
339C4×M16—431no—
340#335—431no—
341#335—431no—
342#334—431no—
343#334—431no—
344#333—431no—
345#333—431no—
346#333—431no—
347#333—431no—
348#332—431no—
349#332—431no—
350#331—431no—
351#331—431no—
352C43#1925311yescharacteristic, complemented, Sylow
353C2×#41—21no—
354C2×SD16—21no—
355C2×SD16—861no—
356C2×SD16—861no—
357C2×D8—21no—
358C2×M16—431no—
359C2×M16—431no—
360C2×M16—861no—
361C22×C8—21no—
362C22×C8—861no—
363C4⋊Q8—431no—
364C4⋊Q8—431no—
365C4⋊Q8C22×D4311yescharacteristic
366#127C22×D4311yescharacteristic
367#126—21no—
368#125—861no—
369#125C22⋊D4311yescharacteristic
370#124—21no—
371#124C22⋊D4311yescharacteristic
372#123—21no—
373C22⋊Q8—861no—
374C22⋊Q8—861no—
375C22⋊Q8C22⋊D4311yescharacteristic
376#121—21no—
377#121—21no—
378#121C22⋊D4311yescharacteristic
379C4×Q8—861no—
380C4×Q8—861no—
381C4×Q8C22×D4311yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C22×D4311yescharacteristic
386#117—21no—
387#117—861no—
388C2×C42C22×D4311yescharacteristic
389#107—21no—
390#107—861no—
391#107—861no—
392#107—861no—
393#107—861no—
394#106—21no—
395#106—861no—
396#106—861no—
397C4⋊C8—21no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—21no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418C22⋊C8—861no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422#97—431no—
423#97—431no—
424#97—861no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—861no—
428C4×C8—861no—
429C4×C8—861no—
430#41—82no—
431C2×Q8—21no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×Q8C2×C22⋊D4311yescharacteristic
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4C2×C22⋊D4311yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4D4×D4311yescharacteristic
444C22×C4#1062190011yescharacteristic
445C22×C4C2×C22⋊D4311yescharacteristic
446SD16—81no—
447SD16—1722no—
448SD16—1722no—
449D8—81no—
450M16—862no—
451M16—1722no—
452M16—1721no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—81no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—1722no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—1721no—
476C4⋊C4—1721no—
477C4⋊C4C2×C22⋊D4311yescharacteristic
478C4⋊C4C2×C22⋊D4311yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—1721no—
487C42—21no—
488C42—1721no—
489C42D4×D4311yescharacteristic
490C42#1062190011yescharacteristic
491C42C2×C22⋊D4311yescharacteristic
492C42C23×D4311yescharacteristic
493C23—21no—
494C23—41no—
495C23#1306329711yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8—3441no—
500Q8—1721no—
501Q8—1721no—
502D4—21no—
503D4—21no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—81no—
509D4—81no—
510D4—82no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—82no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4#1306329711yescharacteristic
526C2×C4#1306329711yescharacteristic
527C2×C4#1306329711yescharacteristic
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4C22×C22⋊D4311yescharacteristic
530C2×C4C2×#1062190011yescharacteristic
531C8—41no—
532C8—41no—
533C8—432no—
534C8—861no—
535C8—861no—
536C8—861no—
537C8—1721no—
538C8—1721no—
539C8—1721no—
540C8—1721no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22C2×#1306329711yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—81no—
559C4—3441no—
560C4—3441no—
561C4#135×D4311yescharacteristic
562C4#1458369611yescharacteristic
563C4#1458371011yescharacteristic
564C4#1458371411yescharacteristic
565C2—41no—
566C2—81no—
567C2—161no—
568C2#1914404611yescharacteristic
569C2#1914428811yescharacteristic
570C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3247C2
socleC22×C43C2×#121
hypercenter#3247D43
hypocenterC43#19253
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3247

Complements

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

NH ≅ G/Ntype
1. #19145770C2semidirect
2. #19145309C2semidirect
3. #19143600C2semidirect
4. #19134179C2semidirect
5. #19134133C2semidirect
6. #19134116C2semidirect
7. #19134058C2semidirect
8. #19134048C2semidirect
9. #19134002C2semidirect
10. #19133997C2semidirect
11. #19133941C2semidirect
12. #19133345C2semidirect
13. #19133257C2semidirect
14. #19133253C2semidirect
352. C43#19253semidirect

Maximal subgroups

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

subgroupindex
#191457702
#191453092
#191436002
#191341792
#191341332
#191341162
#191340582
#191340482
#191340022
#191339972
#191339412
#191333452
#191332572
#191332532
C43×#32472
#1925343