Finite Group Databasebeta

← #25079780

Subgroups — #25079780

Order 11008.

660 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145907C211yesmaximal, characteristic, complemented
2#19145902C211yesmaximal, characteristic
3#19143308C211yesmaximal, characteristic, complemented
4#19134139C212yesmaximal, complemented
5#19134125C212yesmaximal, complemented
6#19134043C212yesmaximal, complemented
7#19134029C212yesmaximal, complemented
8C2×#14582652C211yesmaximal, characteristic, complemented
9#19133285C211yesmaximal, characteristic, complemented
10#19133272C211yesmaximal, characteristic, complemented
11C43×#3131C211yesmaximal, characteristic, complemented
12C2×#13063331—21no—
13#14583449C2211yescharacteristic
14#14583186C2212yes—
15#14583184—21no—
16#14583179—21no—
17#14583176C2212yes—
18#14583133—22no—
19#14583130—22no—
20#14583101C2212yes—
21#14583099—21no—
22#14583094—21no—
23#14583091C2212yes—
24#14582978—21no—
25#14582978C2212yes—
26C8×D172—21no—
27C8×D172C2212yes—
28#14582923C2211yescharacteristic
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31#14582865—21no—
32#14582652C2212yes—
33#14582652C2212yes—
34#14582648C2212yes—
35#14582645C2212yes—
36#14582645C2212yes—
37#14582643C2212yes—
38C43×#533C2211yescharacteristic
39C43×#532C2211yescharacteristic
40C43×#488—21no—
41C43×#488—21no—
42C43×#487C2211yescharacteristic
43C43×#487C2211yescharacteristic
44C43×#486C2211yescharacteristic
45C43×#486C2211yescharacteristic
46C43×#416—21no—
47C43×#416—21no—
48C2×C4×C8×C43C2211yescharacteristic
49C2×#10621898—21no—
50C2×#10621884—22no—
51C2×#10621882—22no—
52#13063331—44no—
53C2×#10621877—21no—
54C2×#10621872—22no—
55C22×C43⋊C8—21no—
56C22×C43⋊C8—21no—
57C2×C8×D43—22no—
58#13063325D411yescharacteristic
59#13063322D411yescharacteristic
60#13063313—21no—
61#13063299—21no—
62#13063299D412yes—
63C4×D172—21no—
64C4×D172C2312yes—
65#13063258—22no—
66#13063256—22no—
67C4⋊(C43⋊C8)—21no—
68C4⋊(C43⋊C8)—21no—
69C4⋊(C43⋊C8)—21no—
70C4⋊(C43⋊C8)C2312yes—
71C4⋊(C43⋊C8)C2312yes—
72C4⋊(C43⋊C8)C2312yes—
73#13063249—22no—
74#13063246—22no—
75#13063245—22no—
76#13063245—22no—
77(C2×D43)⋊C8—22no—
78(C2×D43)⋊C8—22no—
79C2×#41×C43—21no—
80C22×C8×C43D411yescharacteristic
81C22×C8×C43D411yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85#127×C43C2311yescharacteristic
86#125×C43—21no—
87#124×C43—21no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—21no—
90#121×C43—21no—
91#121×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96#117×C43—21no—
97C2×C42×C43C2311yescharacteristic
98#103×C43—21no—
99#103×C43—21no—
100#103×C43—21no—
101#103×C43—21no—
102#102×C43—21no—
103#102×C43—21no—
104#102×C43—21no—
105#102×C43—21no—
106C4×C8×C43D411yescharacteristic
107C4×C8×C43D411yescharacteristic
108C4×C8×C43C2311yescharacteristic
109C4×C8×C43C2311yescharacteristic
110#41×C43—42no—
111#41×C43—42no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43#4111yescharacteristic
123C2×C22⋊D43—22no—
124#10621898—42no—
125#10621898—42no—
126C2×D172—21no—
127C2×D172—21no—
128C2×D172C2×D412yes—
129C2×C4×D43—22no—
130C2×Dic86—21no—
131C2×C8×C43—22no—
132C2×C8×C43—22no—
133C2×C8×C43C2×D411yescharacteristic
134C2×C8×C43C2×D411yescharacteristic
135C2×C8×C43C2×D411yescharacteristic
136C2×C8×C43C2×D411yescharacteristic
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C22⋊C4×C43—41no—
147C22⋊C4×C43—41no—
148C42×C43—41no—
149C42×C43C2×D411yescharacteristic
150C42×C43C2×D411yescharacteristic
151C42×C43#4111yescharacteristic
152C42×C43C2411yescharacteristic
153#10621884—82no—
154#10621882—82no—
155(C2×D43)⋊C4—22no—
156(C2×D43)⋊C4—22no—
157C4⋊Dic43—21no—
158C4⋊Dic43C2×D412yes—
159#10621877—42no—
160C2×C43⋊C8—22no—
161C2×C43⋊C8—22no—
162C2×C43⋊C8—22no—
163C2×C43⋊C8—81no—
164C2×C43⋊C8—81no—
165#10621872—44no—
166C8×D43—44no—
167C23×C43—41no—
168C23×C43#12111yescharacteristic
169C22×D43—22no—
170Q8×C43—41no—
171Q8×C43—41no—
172Q8×C43—41no—
173Q8×C43—41no—
174Q8×C43—81no—
175D4×C43—41no—
176D4×C43—41no—
177D4×C43—41no—
178D4×C43—41no—
179D4×C43—81no—
180D4×C43—82no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—82no—
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#13512yes—
192C2×C4×C43AGL(1,ℤ/8)12yes—
193C2×C4×C43C22×D411yescharacteristic
194C2×C4×C43C22×D411yescharacteristic
195C2×C4×C43C2×#4111yescharacteristic
196C22⋊D43—44no—
197C2×Dic43—22no—
198D172—22no—
199D172—22no—
200D172—42no—
201D172—42no—
202C4×D43—42no—
203C4×D43—42no—
204Dic86—42no—
205C8×C43—21no—
206C8×C43—21no—
207C8×C43—21no—
208C8×C43—21no—
209C43⋊C8—42no—
210C43⋊C8—42no—
211C43⋊C8—42no—
212#19201—431nomaximal, Sylow
213C22×C43—21no—
214C22×C43—21no—
215C22×C43—81no—
216C22×C43—81no—
217C22×C43—81no—
218C22×C43#46312yes—
219C22×C43C2×#12111yescharacteristic
220C2×D43—42no—
221C2×D43—42no—
222C2×D43—42no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—81no—
227C4×C43—81no—
228C4×C43—81no—
229C4×C43#46312yes—
230C4×C43C2×#13511yescharacteristic
231C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
232C4×C43#57611yescharacteristic
233C4×C43#57811yescharacteristic
234Dic43—42no—
235#3246—431no—
236#3245—431no—
237#3131D4311yescharacteristic, complemented
238#2931—431no—
239#1699—432no—
240#1697—432no—
241#1683—432no—
242#1681—432no—
243C2×#335—431no—
244#1550—431no—
245#1547—431no—
246C2×C43—22no—
247C2×C43—161no—
248C2×C43C2×#46311yescharacteristic
249C2×C43#306111yescharacteristic
250C2×C43#306711yescharacteristic
251D43—82no—
252C2×#131—861no—
253#533C2×D4311yescharacteristic
254#532—431no—
255#532C2×D4311yescharacteristic
256#488—21no—
257#488—21no—
258#487C2×D4311yescharacteristic
259#487C2×D4311yescharacteristic
260#486C2×D4311yescharacteristic
261#486C2×D4311yescharacteristic
262#476—432no—
263#475—861no—
264#474—432no—
265#474—861no—
266#466—862no—
267#465—862no—
268#461—432no—
269#460—861no—
270#459—432no—
271#459—861no—
272#436—432no—
273#436—861no—
274C8×D4—432no—
275C8×D4—861no—
276#423—431no—
277C2×C4⋊C8—431no—
278C2×C4⋊C8—431no—
279#416—21no—
280#416—21no—
281#408—861no—
282C2×C4×C8C2×D4311yescharacteristic
283#335—432no—
284#335—432no—
285#333—432no—
286#332—432no—
287#332—432no—
288#331—432no—
289C43#1920111yescharacteristic, complemented, Sylow
290C2×#41—21no—
291C2×#41—861no—
292C2×SD16—862no—
293C2×D8—862no—
294#131—1724no—
295C2×M16—861no—
296C2×M16—862no—
297C22×C8—861no—
298C22×C8—861no—
299C22×C8—862no—
300C22×C8C22⋊D4311yescharacteristic
301C22×C8C22⋊D4311yescharacteristic
302C4⋊Q8—431no—
303C4⋊Q8C22×D4311yescharacteristic
304C4⋊Q8C22×D4311yescharacteristic
305C4⋊Q8C22×D4311yescharacteristic
306#127—431no—
307#127C22×D4311yescharacteristic
308#125—21no—
309#124—21no—
310#124—861no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313#121—21no—
314#121—21no—
315#121—432no—
316#121—861no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—432no—
322C4×D4—861no—
323#117—21no—
324C2×C42C22×D4311yescharacteristic
325#107—862no—
326#106—862no—
327C4⋊C8—432no—
328C4⋊C8—432no—
329C4⋊C8—432no—
330C4⋊C8—861no—
331C4⋊C8—861no—
332C4⋊C8—861no—
333#103—21no—
334#103—21no—
335#103—21no—
336#103—21no—
337#103—862no—
338#102—21no—
339#102—21no—
340#102—21no—
341#102—21no—
342#102—862no—
343#102—862no—
344#102—862no—
345C22⋊C8—862no—
346C22⋊C8—862no—
347C4×C8C22⋊D4311yescharacteristic
348C4×C8C22⋊D4311yescharacteristic
349C4×C8C22×D4311yescharacteristic
350C4×C8C22×D4311yescharacteristic
351#41—42no—
352#41—42no—
353#41—1722no—
354#41—1722no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—861no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—41no—
363C2×D4—432no—
364C2×D4—862no—
365C2×D4—861no—
366C2×D4—861no—
367C22×C4—41no—
368C22×C4—862no—
369C22×C4D4×D4311yescharacteristic
370C22×C4#1062190011yescharacteristic
371C22×C4C2×C22⋊D4311yescharacteristic
372SD16—3442no—
373D8—3442no—
374M16—1724no—
375M16—1722no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—862no—
379C2×C8—862no—
380C2×C8—862no—
381C2×C8—3441no—
382C2×C8—3441no—
383C2×C8—1724no—
384C2×C8C2×C22⋊D4311yescharacteristic
385C2×C8C2×C22⋊D4311yescharacteristic
386C2×C8C2×C22⋊D4311yescharacteristic
387C2×C8C2×C22⋊D4311yescharacteristic
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—432no—
397C4⋊C4—861no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—862no—
402C22⋊C4—862no—
403C42—41no—
404C42D4×D4311yescharacteristic
405C42#1062190011yescharacteristic
406C42C2×C22⋊D4311yescharacteristic
407C42C23×D4311yescharacteristic
408C23—41no—
409C23—862no—
410C23#1306329611yescharacteristic
411Q8—41no—
412Q8—41no—
413Q8—41no—
414Q8—41no—
415Q8—81no—
416Q8—1722no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—41no—
421D4—81no—
422D4—82no—
423D4—862no—
424D4—862no—
425D4—1722no—
426D4—1724no—
427D4—1722no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—82no—
435C2×C4—862no—
436C2×C4—1722no—
437C2×C4—1722no—
438C2×C4#1306329611yescharacteristic
439C2×C4#1306329611yescharacteristic
440C2×C4#1306329611yescharacteristic
441C2×C4#1306334512yes—
442C2×C4#1306335012yes—
443C2×C4C2×D4×D4311yescharacteristic
444C2×C4C22×C22⋊D4311yescharacteristic
445C2×C4C2×#1062190011yescharacteristic
446C8—21no—
447C8—21no—
448C8—21no—
449C8—21no—
450C8—1722no—
451C8—1722no—
452C8—1722no—
453C22—21no—
454C22—21no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—1722no—
459C22—1722no—
460C22—1722no—
461C22#1458311112yes—
462C22C2×#1306329611yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—1722no—
470C4#1458311112yes—
471C4C2×#1306334511yescharacteristic
472C4C2×#1306335011yescharacteristic
473C4#1458370111yescharacteristic
474C4#1458371311yescharacteristic
475C2—22no—
476C2—161no—
477C2—3442no—
478C2C2×#1458311111yescharacteristic
479C2#1914426111yescharacteristic
480C2#1914431111yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3131C2
socleC22×C43C2×#121
prime radical#19145902C2
hypercenter#3131D43
hypocenterC43#19201
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #19145907C2semidirect
3. #19143308C2semidirect
4. #19134139C2semidirect
5. #19134125C2semidirect
6. #19134043C2semidirect
7. #19134029C2semidirect
8. C2×#14582652C2semidirect
9. #19133285C2semidirect
10. #19133272C2semidirect
11. C43×#3131C2semidirect
237. #3131D43semidirect
289. C43#19201semidirect

Maximal subgroups

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

subgroupindex
#191459072
#191459022
#191433082
#191341392
#191341252
#191340432
#191340292
C2×#145826522
#191332852
#191332722
C43×#31312
#1920143