Finite Group Databasebeta

← #25080007

Subgroups — #25080007

Order 11008.

596 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145770C211yesmaximal, characteristic, complemented
2#19145567C211yesmaximal, characteristic
3#19145154C211yesmaximal, characteristic, complemented
4#19134101C211yesmaximal, characteristic, complemented
5#19134094C211yesmaximal, characteristic, complemented
6#19134067C211yesmaximal, characteristic, complemented
7#19134060C211yesmaximal, characteristic, complemented
8#19134025C211yesmaximal, characteristic, complemented
9#19134018C211yesmaximal, characteristic, complemented
10#19134011C211yesmaximal, characteristic, complemented
11#19134004C211yesmaximal, characteristic, complemented
12#19133343C211yesmaximal, characteristic, complemented
13#19133306C211yesmaximal, characteristic, complemented
14#19133301C211yesmaximal, characteristic, complemented
15C43×#2966C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583298—21no—
19#14583297C2211yescharacteristic
20#14583281—21no—
21#14583272C2211yescharacteristic
22#14583256—21no—
23#14583253—21no—
24#14583250C2211yescharacteristic
25#14583246C2211yescharacteristic
26#14583237—21no—
27#14583220—21no—
28#14583194C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583184C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583128—21no—
33#14583128—21no—
34#14583109C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583099C2211yescharacteristic
37#14583094C2211yescharacteristic
38#14583059—21no—
39#14583042—21no—
40C4×#10621873—21no—
41C4×#10621873—21no—
42#14582952C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436C2211yescharacteristic
60C43×#435—21no—
61C8×D4×C43—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#432C2211yescharacteristic
65C43×#405—21no—
66C2×C4×C8×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621885—21no—
69C2×#10621873—21no—
70C2×#10621873—21no—
71C2×#10621883—21no—
72C2×#10621884—21no—
73C2×#10621882—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063322C2311yescharacteristic
78#13063317—21no—
79#13063313—21no—
80#13063304—21no—
81#13063304—21no—
82#13063299—21no—
83#13063299—21no—
84C4×Dic86—21no—
85C4×Dic86—21no—
86C4×D172—21no—
87C4×D172—21no—
88#13063284—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#13063249—21no—
102#13063249—21no—
103#13063248—21no—
104#13063248—21no—
105#13063247—21no—
106#13063247—21no—
107#13063246—21no—
108#13063246—21no—
109#13063245—21no—
110#13063245—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8—21no—
115C2×M16×C43—21no—
116C22×C8×C43—21no—
117C22×C8×C43D411yescharacteristic
118C22×C8×C43D411yescharacteristic
119#126×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43D411yescharacteristic
124#121×C43D411yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137#97×C43—21no—
138#97×C43—21no—
139C4×C8×C43—21no—
140C4×C8×C43D411yescharacteristic
141C4×C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×C22⋊D43—41no—
152#10621898—81no—
153#10621898—81no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×C4×D43—41no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161M16×C43—42no—
162C2×C8×C43—22no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—41no—
166C2×C8×C43—42no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
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—
182C42×C43—21no—
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43#4111yescharacteristic
186C42×C43C2411yescharacteristic
187C22⋊Dic43—41no—
188#10621885—81no—
189#10621884—81no—
190#10621883—81no—
191#10621882—81no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200Dic43⋊C4—41no—
201Dic43⋊C4—41no—
202C4×Dic43—41no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207#10621873—42no—
208#10621873—42no—
209C23×C43—21no—
210C23×C43#12111yescharacteristic
211C22×D43—41no—
212Q8×C43—21no—
213Q8×C43—21no—
214D4×C43—21no—
215D4×C43—21no—
216D4×C43—42no—
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#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—82no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237D172—41no—
238D172—41no—
239D172—41no—
240D172—41no—
241D172—81no—
242C4×D43—82no—
243Dic86—41no—
244Dic86—41no—
245Dic86—41no—
246Dic86—41no—
247Dic86—81no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43#13512yes—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258#19224—431nomaximal, Sylow
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43C2×#12111yescharacteristic
266C2×D43—81no—
267C2×D43—81no—
268C2×D43—81no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43C2×#13511yescharacteristic
277C4×C43#57511yescharacteristic
278C4×C43#57711yescharacteristic
279C4×C43#57711yescharacteristic
280Dic43—81no—
281Dic43—81no—
282Dic43—81no—
283#3233—431no—
284#3212—431no—
285#3167—431no—
286#2966D4311yescharacteristic, complemented
287#1692—431no—
288#1691—431no—
289#1686—431no—
290#1685—431no—
291#1680—431no—
292#1679—431no—
293#1678—431no—
294#1677—431no—
295#1564—431no—
296#1554—431no—
297#1553—431no—
298C2×C43—41no—
299C2×C43—81no—
300C2×C43#303511yescharacteristic
301C2×C43#305711yescharacteristic
302C2×C43#306711yescharacteristic
303D43—161no—
304#533—431no—
305#532—431no—
306#529C2×D4311yescharacteristic
307#499—861no—
308#498—431no—
309#495—861no—
310#492—431no—
311#488—861no—
312#488—861no—
313#487—431no—
314#486—431no—
315#485—861no—
316#482—861no—
317#477—431no—
318#476—431no—
319#475—431no—
320#474—431no—
321#465—861no—
322#465—861no—
323#462—431no—
324#461—431no—
325#460—431no—
326#459—431no—
327#452—861no—
328#449—861no—
329#446C2×D4311yescharacteristic
330C8×Q8C2×D4311yescharacteristic
331C4×SD16—861no—
332C4×SD16—861no—
333#436C2×D4311yescharacteristic
334#435—21no—
335C8×D4—21no—
336C8×D4C2×D4311yescharacteristic
337#433—21no—
338#432C2×D4311yescharacteristic
339#431—431no—
340#431—431no—
341#405—21no—
342C2×C4×C8C2×D4311yescharacteristic
343#335—431no—
344#335—431no—
345#334—431no—
346#334—431no—
347#333—431no—
348#333—431no—
349#332—431no—
350#332—431no—
351#332—431no—
352#332—431no—
353#331—431no—
354#331—431no—
355C43#1922411yescharacteristic, complemented, Sylow
356C2×#41—861no—
357C2×Q16—861no—
358C2×SD16—861no—
359C2×SD16—861no—
360C2×SD16—861no—
361C2×SD16—861no—
362C2×D8—861no—
363C2×M16—21no—
364C22×C8—21no—
365C22×C8C22⋊D4311yescharacteristic
366C22×C8C22⋊D4311yescharacteristic
367C4⋊Q8—431no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370#127—431no—
371#126—21no—
372#125—861no—
373#125D17211yescharacteristic
374#124—861no—
375#124D17211yescharacteristic
376#123—21no—
377C22⋊Q8—861no—
378C22⋊Q8—861no—
379C22⋊Q8D17211yescharacteristic
380#121—861no—
381#121—861no—
382#121D17211yescharacteristic
383C4×Q8—861no—
384C4×Q8—861no—
385C4×Q8C22×D4311yescharacteristic
386C4×D4—21no—
387C4×D4—861no—
388C4×D4—861no—
389C4×D4C22×D4311yescharacteristic
390#117—21no—
391#117—861no—
392C2×C42C22×D4311yescharacteristic
393#107—861no—
394#107—861no—
395#106—861no—
396#106—861no—
397#106—861no—
398#106—861no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—21no—
425#97—21no—
426C4×C8—21no—
427C4×C8—861no—
428C4×C8—861no—
429C4×C8C22⋊D4311yescharacteristic
430C4×C8C22⋊D4311yescharacteristic
431C4×C8C22×D4311yescharacteristic
432C4×C8C22×D4311yescharacteristic
433#41—3441no—
434#41—3441no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8C2×D17211yescharacteristic
439C2×D4—21no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—1721no—
444C2×D4C2×D17211yescharacteristic
445C22×C4—21no—
446C22×C4—1721no—
447C22×C4C2×D17211yescharacteristic
448C22×C4#1062189811yescharacteristic
449C22×C4C2×C22⋊D4311yescharacteristic
450Q16—3441no—
451SD16—3441no—
452SD16—3441no—
453SD16—1722no—
454SD16—1722no—
455D8—3441no—
456M16—42no—
457C2×C8—22no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—41no—
461C2×C8—42no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8C2×C22⋊D4311yescharacteristic
467C2×C8C2×C22⋊D4311yescharacteristic
468C2×C8C2×C22⋊D4311yescharacteristic
469C2×C8C2×C22⋊D4311yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—1721no—
481C4⋊C4—1721no—
482C4⋊C4C2×D17211yescharacteristic
483C4⋊C4C2×D17211yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C42—21no—
493C42—1721no—
494C42C2×D17211yescharacteristic
495C42#1062189811yescharacteristic
496C42C2×C22⋊D4311yescharacteristic
497C42C23×D4311yescharacteristic
498C23—21no—
499C23—1721no—
500C23#1306329911yescharacteristic
501Q8—21no—
502Q8—21no—
503Q8—3441no—
504Q8—1721no—
505Q8—1721no—
506Q8—1721no—
507Q8—1721no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—3441no—
512D4—3442no—
513D4—1721no—
514D4—1721no—
515D4—1721no—
516D4—1721no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—3442no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4#1306329911yescharacteristic
532C2×C4#1306329911yescharacteristic
533C2×C4#1306329911yescharacteristic
534C2×C4C22×C22⋊D4311yescharacteristic
535C2×C4C22×D17211yescharacteristic
536C2×C4C2×#1062189811yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—41no—
541C8—41no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C8#1306334512yes—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—3441no—
554C22—3441no—
555C22—3441no—
556C22C2×#1306329911yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—3441no—
565C4—3441no—
566C4—3441no—
567C4C2×#1306334511yescharacteristic
568C4#1458369711yescharacteristic
569C4#1458371111yescharacteristic
570C4#1458371111yescharacteristic
571C2—41no—
572C2—81no—
573C2—6881no—
574C2#1914405011yescharacteristic
575C2#1914423411yescharacteristic
576C2#1914431511yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2966C2
socleC22×C43C2×#121
prime radical#19145567C2
hypercenter#2966D43
hypocenterC43#19224
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #19145770C2semidirect
3. #19145154C2semidirect
4. #19134101C2semidirect
5. #19134094C2semidirect
6. #19134067C2semidirect
7. #19134060C2semidirect
8. #19134025C2semidirect
9. #19134018C2semidirect
10. #19134011C2semidirect
11. #19134004C2semidirect
12. #19133343C2semidirect
13. #19133306C2semidirect
14. #19133301C2semidirect
15. C43×#2966C2semidirect
286. #2966D43semidirect
355. C43#19224semidirect

Maximal subgroups

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

subgroupindex
#191457702
#191455672
#191451542
#191341012
#191340942
#191340672
#191340602
#191340252
#191340182
#191340112
#191340042
#191333432
#191333062
#191333012
C43×#29662
#1922443