Finite Group Databasebeta

← #25079175

Subgroups — #25079175

Order 11008.

684 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144599C211yesmaximal, characteristic, complemented
2#19144591C211yesmaximal, characteristic
3C2×#14582978C211yesmaximal, characteristic, complemented
4#19134167C212yesmaximal, complemented
5#19134153C212yesmaximal, complemented
6#19134139C212yesmaximal, complemented
7#19134125C212yesmaximal, complemented
8#19133343C211yesmaximal, characteristic, complemented
9#19133252C211yesmaximal, characteristic, complemented
10#19133244C211yesmaximal, characteristic, complemented
11C43×#3131C211yesmaximal, characteristic, complemented
12C22×#10621872—21no—
13C2×C4×D172C2211yescharacteristic
14#14583227—21no—
15#14583210—21no—
16#14583186C2212yes—
17#14583176C2212yes—
18#14583101C2212yes—
19#14583091C2212yes—
20#14583049—21no—
21#14583032—21no—
22C4×#10621884—22no—
23C4×#10621882—22no—
24#14582978—21no—
25#14582978—21no—
26#14582978C2212yes—
27#14582978C2212yes—
28#14582952C2211yescharacteristic
29#14582952C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×(C2×D43)⋊C8—21no—
32#14582652C2212yescomplemented
33#14582650C2212yescomplemented
34#14582648C2212yescomplemented
35#14582645C2212yescomplemented
36#14582645C2212yescomplemented
37#14582643C2212yescomplemented
38C43×#533C2211yescharacteristic
39C43×#532C2211yescharacteristic
40C43×#488—21no—
41C43×#488—21no—
42C43×#487C2211yescharacteristic, complemented
43C43×#487C2211yescharacteristic, complemented
44C43×#486C2211yescharacteristic, complemented
45C43×#486C2211yescharacteristic, complemented
46C43×#416—21no—
47C43×#416—21no—
48C2×C4×C8×C43C2211yescharacteristic
49C22×D172D411yescharacteristic
50C22×C4×D43—21no—
51C2×#10621884—22no—
52C2×#10621882—22no—
53C2×#10621872—22no—
54C2×#10621872—22no—
55C2×#10621872—44no—
56C22×C43⋊C8—21no—
57C4×D172—21no—
58C4×D172—21no—
59C4×D172D412yes—
60C4×D172C2312yes—
61C2×C4⋊Dic43D411yescharacteristic
62C2×(C2×D43)⋊C4—21no—
63#13063258—22no—
64#13063256—22no—
65C4⋊(C43⋊C8)—21no—
66C4⋊(C43⋊C8)C2312yes—
67C4⋊(C43⋊C8)C2312yes—
68C4⋊(C43⋊C8)C2312yes—
69#13063249—22no—
70#13063246—22no—
71#13063245—22no—
72#13063245—22no—
73C22⋊(C43⋊C8)—21no—
74C22⋊(C43⋊C8)—21no—
75(C2×D43)⋊C8—22no—
76(C2×D43)⋊C8—22no—
77C4×C43⋊C8—21no—
78C4×C43⋊C8—21no—
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
110C23×D43—21no—
111#41×C43—42no—
112#41×C43—42no—
113C2×Q8×C43—21no—
114C2×Q8×C43—21no—
115C2×Q8×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43#4111yescharacteristic
124C22×Dic43—21no—
125C2×D172—21no—
126C2×D172—42no—
127C2×D172C2×D412yes—
128C2×C4×D43—22no—
129C2×C4×D43—22no—
130C2×C4×D43—42no—
131C2×C4×D43—42no—
132C2×C8×C43—22no—
133C2×C8×C43—22no—
134C2×C8×C43C2×D411yescharacteristic
135C2×C8×C43C2×D411yescharacteristic
136C2×C8×C43C2×D411yescharacteristic
137C2×C8×C43C2×D411yescharacteristic
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—41no—
145C4⋊C4×C43—41no—
146C22⋊C4×C43—41no—
147C22⋊C4×C43—41no—
148C22⋊C4×C43—41no—
149C42×C43—41no—
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43#4111yescharacteristic
153C42×C43C2411yescharacteristic
154#10621884—44no—
155#10621882—44no—
156(C2×D43)⋊C4—22no—
157(C2×D43)⋊C4—22no—
158C4⋊Dic43—21no—
159C4⋊Dic43C2×D412yes—
160C2×C43⋊C8—22no—
161C2×C43⋊C8—22no—
162C2×C43⋊C8—22no—
163C2×C43⋊C8—42no—
164#10621872—44no—
165#10621872—44no—
166C23×C43—41no—
167C23×C43#12111yescharacteristic
168C22×D43—22no—
169C22×D43—42no—
170C22×D43—42no—
171C22×D43—42no—
172Q8×C43—41no—
173Q8×C43—41no—
174Q8×C43—42no—
175Q8×C43—81no—
176D4×C43—41no—
177D4×C43—41no—
178D4×C43—42no—
179D4×C43—81no—
180D4×C43—82no—
181C2×C4×C43—22no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—82no—
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#13512yes—
191C2×C4×C43AGL(1,ℤ/8)12yes—
192C2×C4×C43C22×D411yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×C4×C43C2×#4111yescharacteristic
195C2×Dic43—22no—
196C2×Dic43—42no—
197D172—22no—
198D172—22no—
199D172—42no—
200C4×D43—42no—
201C4×D43—42no—
202C4×D43—44no—
203C8×C43—21no—
204C8×C43—21no—
205C8×C43—21no—
206C8×C43—21no—
207C43⋊C8—42no—
208C43⋊C8—42no—
209C43⋊C8—42no—
210#19142—431nomaximal, Sylow
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—81no—
214C22×C43—81no—
215C22×C43—81no—
216C22×C43#46312yes—
217C22×C43C2×#12111yescharacteristic
218C2×D43—42no—
219C2×D43—42no—
220C2×D43—42no—
221C2×D43—84no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—81no—
226C4×C43—81no—
227C4×C43—81no—
228C4×C43#46312yes—
229C4×C43C2×#13511yescharacteristic
230C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
231C4×C43#57512yes—
232Dic43—42no—
233#3131D4311yescharacteristic, complemented
234#3101—431no—
235#3100—431no—
236C2×#436—431no—
237#1703—432no—
238#1701—432no—
239#1699—432no—
240#1697—432no—
241#1564—431no—
242#1542—431no—
243#1540—431no—
244C2×C43—22no—
245C2×C43—161no—
246C2×C43C2×#46311yescharacteristic
247C2×C43#305411yescharacteristic
248C2×C43#306711yescharacteristic
249D43—82no—
250C22×M16—861no—
251#533C2×D4311yescharacteristic
252#532C2×D4311yescharacteristic
253C2×C4×D4—431no—
254#488—21no—
255#488—21no—
256#487C2×D4311yescharacteristic, complemented
257#487C2×D4311yescharacteristic, complemented
258#486C2×D4311yescharacteristic, complemented
259#486C2×D4311yescharacteristic, complemented
260#483—861no—
261#480—861no—
262#476—432no—
263#474—432no—
264#461—432no—
265#459—432no—
266#450—861no—
267#447—861no—
268C4×SD16—862no—
269C4×D8—862no—
270#436—432no—
271#436—432no—
272#436—861no—
273#436—861no—
274#431—431no—
275#431—431no—
276C2×C4⋊C8—431no—
277#416—21no—
278#416—21no—
279C2×C22⋊C8—861no—
280C2×C4×C8C2×D4311yescharacteristic
281#335—432no—
282#334—432no—
283#333—432no—
284#332—432no—
285#332—432no—
286#331—432no—
287C43#1914211yescharacteristic, complemented, Sylow
288C2×#41—21no—
289C22×D4—431no—
290C23×C4—861no—
291C2×SD16—862no—
292C2×D8—862no—
293C2×M16—862no—
294C2×M16—862no—
295C2×M16—1724no—
296C22×C8—861no—
297C22×C8C22⋊D4311yescharacteristic
298C22×C8C22⋊D4311yescharacteristic
299C4⋊Q8C22×D4311yescharacteristic
300C4⋊Q8C22×D4311yescharacteristic
301C4⋊Q8C22×D4311yescharacteristic
302#127C22×D4311yescharacteristic
303#125—21no—
304#124—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307#121—21no—
308#121—21no—
309C4×Q8—21no—
310C4×Q8—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—432no—
314C4×D4—432no—
315C4×D4—861no—
316C4×D4—861no—
317#117—21no—
318C2×C4⋊C4—431no—
319C2×C22⋊C4—861no—
320C2×C42C22×D4311yescharacteristic
321#107—862no—
322#106—862no—
323C4⋊C8—432no—
324C4⋊C8—432no—
325C4⋊C8—432no—
326C4⋊C8—861no—
327#103—21no—
328#103—21no—
329#103—21no—
330#103—21no—
331#103—862no—
332#102—21no—
333#102—21no—
334#102—21no—
335#102—21no—
336#102—862no—
337#102—862no—
338#102—862no—
339C22⋊C8—861no—
340C22⋊C8—861no—
341C22⋊C8—862no—
342C22⋊C8—862no—
343C4×C8—861no—
344C4×C8—861no—
345C4×C8C22⋊D4311yescharacteristic
346C4×C8C22⋊D4311yescharacteristic
347C4×C8C22×D4311yescharacteristic
348C4×C8C22×D4311yescharacteristic
349C24—861no—
350#41—42no—
351#41—42no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—41no—
359C2×D4—432no—
360C2×D4—861no—
361C2×D4—1722no—
362C22×C4—41no—
363C22×C4—861no—
364C22×C4—862no—
365C22×C4—862no—
366C22×C4—1722no—
367C22×C4—1722no—
368C22×C4D4×D4311yescharacteristic
369C22×C4#1062190011yescharacteristic
370C22×C4C2×C22⋊D4311yescharacteristic
371SD16—1724no—
372D8—1724no—
373M16—1724no—
374M16—1724no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—862no—
378C2×C8—862no—
379C2×C8—862no—
380C2×C8—1722no—
381C2×C8C2×C22⋊D4311yescharacteristic
382C2×C8C2×C22⋊D4311yescharacteristic
383C2×C8C2×C22⋊D4311yescharacteristic
384C2×C8C2×C22⋊D4311yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—432no—
394C4⋊C4—861no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—862no—
399C22⋊C4—862no—
400C42—41no—
401C42D4×D4311yescharacteristic
402C42#1062190011yescharacteristic
403C42C2×C22⋊D4311yescharacteristic
404C42C23×D4311yescharacteristic
405C23—41no—
406C23—862no—
407C23—1722no—
408C23—1722no—
409C23—1722no—
410C23#1306329611yescharacteristic
411Q8—41no—
412Q8—41no—
413Q8—42no—
414Q8—81no—
415D4—41no—
416D4—41no—
417D4—42no—
418D4—81no—
419D4—82no—
420D4—862no—
421D4—862no—
422D4—1722no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—82no—
429C2×C4—862no—
430C2×C4—1722no—
431C2×C4—1724no—
432C2×C4—1722no—
433C2×C4—1722no—
434C2×C4#1306329611yescharacteristic
435C2×C4#1306329611yescharacteristic
436C2×C4#1306329611yescharacteristic
437C2×C4#1306334512yes—
438C2×C4#1306335012yes—
439C2×C4C2×D4×D4311yescharacteristic
440C2×C4C22×C22⋊D4311yescharacteristic
441C2×C4C2×#1062190011yescharacteristic
442C8—21no—
443C8—21no—
444C8—21no—
445C8—21no—
446C8—1722no—
447C8—1722no—
448C8—1722no—
449C22—21no—
450C22—21no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—3444no—
455C22—1722no—
456C22—1722no—
457C22—1722no—
458C22#1458311112yes—
459C22C2×#1306329611yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4—1722no—
467C4#1458311112yes—
468C4C2×#1306334511yescharacteristic
469C4C2×#1306335011yescharacteristic
470C4#1458369612yes—
471C2—22no—
472C2—161no—
473C2—3442no—
474C2C2×#1458311111yescharacteristic
475C2#1914420011yescharacteristic
476C2#1914431111yescharacteristic
subgroupG/H
centerC2×C4#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3131C2
socleC22×C43C2×#121
prime radical#19144591C2
hypercenter#3131D43
hypocenterC43#19142
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #19144599C2semidirect
3. C2×#14582978C2semidirect
4. #19134167C2semidirect
5. #19134153C2semidirect
6. #19134139C2semidirect
7. #19134125C2semidirect
8. #19133343C2semidirect
9. #19133252C2semidirect
10. #19133244C2semidirect
11. C43×#3131C2semidirect
32. #14582652C22semidirect
33. #14582650C22semidirect
34. #14582648C22semidirect
35. #14582645C22semidirect
36. #14582645C22semidirect
37. #14582643C22semidirect
42. C43×#487C22semidirect
43. C43×#487C22semidirect
44. C43×#486C22semidirect
45. C43×#486C22semidirect
233. #3131D43semidirect
256. #487C2×D43semidirect
257. #487C2×D43semidirect
258. #486C2×D43semidirect
259. #486C2×D43semidirect
287. C43#19142semidirect

Maximal subgroups

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

subgroupindex
#191445992
#191445912
C2×#145829782
#191341672
#191341532
#191341392
#191341252
#191333432
#191332522
#191332442
C43×#31312
#1914243