Finite Group Databasebeta

← #25079436

Subgroups — #25079436

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144591C211yesmaximal, characteristic
2C2×#14583101C211yesmaximal, characteristic, complemented
3M16×D172C211yesmaximal, characteristic, complemented
4#19134153C212yesmaximal, complemented
5#19134139C212yesmaximal, complemented
6#19134029C212yesmaximal, complemented
7#19134015C212yesmaximal, complemented
8#19133347C211yesmaximal, characteristic, complemented
9#19133280C211yesmaximal, characteristic, complemented
10#19133272C211yesmaximal, characteristic, complemented
11C43×#3141C211yesmaximal, characteristic, complemented
12C22×#10621884—21no—
13C2×M16×D43—21no—
14C2×C4×D172C2211yescharacteristic
15#14583210—21no—
16#14583176C2211yescharacteristic
17#14583176C2211yescharacteristic
18#14583101—21no—
19#14583101—21no—
20#14583101C2212yes—
21#14583101C2212yes—
22#14583091C2211yescharacteristic
23#14583091C2211yescharacteristic
24#14583032—21no—
25C4×#10621882—21no—
26C4×#10621882—21no—
27#14582978C2212yes—
28#14582972—22no—
29C8×D172C2212yes—
30#14582952C2211yescharacteristic
31#14582923C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063249—21no—
34#14582862—21no—
35#14582652C2212yescomplemented
36#14582650C2212yescomplemented
37#14582645C2212yescomplemented
38#14582645C2212yescomplemented
39#14582645C2212yescomplemented
40#14582643C2212yescomplemented
41C43×#532C2211yescharacteristic
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#489—22no—
44C43×#487C2212yescomplemented
45C43×#486C2212yescomplemented
46C43×#417—21no—
47C43×#417—21no—
48C4×M16×C43C2211yescharacteristic
49C22×D172D411yescharacteristic
50C22×C4×D43—21no—
51C2×#10621884—22no—
52C2×#10621884—22no—
53C2×#10621884—44no—
54C2×#10621882—21no—
55C2×#10621882—21no—
56C2×#10621877—21no—
57C2×#10621872—22no—
58M16×D43—44no—
59C22×C43⋊C8—21no—
60C2×C8×D43—22no—
61C4×D172—21no—
62C4×D172—21no—
63C4×D172D411yescharacteristic
64C4×D172D411yescharacteristic
65C4×D172C2311yescharacteristic
66C4×D172C2311yescharacteristic
67C2×C4⋊Dic43D411yescharacteristic
68C2×(C2×D43)⋊C4—21no—
69#13063258—21no—
70#13063258—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)C2311yescharacteristic
74C4⋊(C43⋊C8)C2311yescharacteristic
75C4⋊(C43⋊C8)C2312yes—
76C4⋊(C43⋊C8)C2312yes—
77#13063249—22no—
78#13063249—22no—
79#13063246—21no—
80#13063246—21no—
81#13063245—21no—
82#13063245—21no—
83C22⋊(C43⋊C8)—21no—
84(C2×D43)⋊C8—22no—
85(C2×D43)⋊C8—22no—
86C4×C43⋊C8—21no—
87C2×#41×C43—21no—
88C22×Q8×C43—21no—
89C2×M16×C43D411yescharacteristic
90C2×M16×C43D411yescharacteristic
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43—21no—
93C4⋊Q8×C43—21no—
94C4⋊Q8×C43C2312yes—
95C4⋊Q8×C43C2311yescharacteristic
96#127×C43C2311yescharacteristic
97#124×C43—21no—
98#121×C43—21no—
99#121×C43—21no—
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C42×C43C2311yescharacteristic
105#103×C43—22no—
106#103×C43—22no—
107#102×C43—22no—
108#102×C43—22no—
109#97×C43D412yes—
110C4×C8×C43C2312yes—
111C23×D43—21no—
112#41×C43—42no—
113#41×C43—42no—
114C2×Q8×C43—21no—
115C2×Q8×C43—22no—
116C2×Q8×C43—42no—
117C2×Q8×C43—42no—
118C2×Q8×C43—41no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43#4111yescharacteristic
128C22×Dic43—21no—
129C2×D172—21no—
130C2×D172—22no—
131C2×D172—41no—
132C2×D172C2×D411yescharacteristic
133C2×D172C2×D411yescharacteristic
134C2×C4×D43—21no—
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—42no—
139C2×C4×D43—42no—
140M16×C43—22no—
141M16×C43—22no—
142C2×C8×C43C2×D412yes—
143C2×C8×C43C2×D412yes—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—41no—
149C4⋊C4×C43—41no—
150C22⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C42×C43C2×D411yescharacteristic
153C42×C43C2×D411yescharacteristic
154C42×C43#4111yescharacteristic
155C42×C43C2411yescharacteristic
156#10621884—44no—
157#10621884—44no—
158#10621882—42no—
159#10621882—42no—
160(C2×D43)⋊C4—21no—
161(C2×D43)⋊C4—21no—
162(C2×D43)⋊C4—21no—
163(C2×D43)⋊C4—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43C2×D411yescharacteristic
166C4⋊Dic43C2×D411yescharacteristic
167#10621877—42no—
168C2×C43⋊C8—21no—
169C2×C43⋊C8—21no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—42no—
173#10621872—44no—
174C8×D43—44no—
175C23×C43—41no—
176C23×C43#12111yescharacteristic
177C22×D43—21no—
178C22×D43—21no—
179C22×D43—42no—
180C22×D43—42no—
181C22×D43—81no—
182Q8×C43—41no—
183Q8×C43—42no—
184Q8×C43—41no—
185Q8×C43—42no—
186Q8×C43—82no—
187D4×C43—41no—
188D4×C43—41no—
189D4×C43—41no—
190D4×C43—41no—
191D4×C43—81no—
192D4×C43—82no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—42no—
198C2×C4×C43—82no—
199C2×C4×C43—82no—
200C2×C4×C43#12111yescharacteristic
201C2×C4×C43#12111yescharacteristic
202C2×C4×C43#12111yescharacteristic
203C2×C4×C43#13512yes—
204C2×C4×C43AGL(1,ℤ/8)12yes—
205C2×C4×C43C22×D411yescharacteristic
206C2×C4×C43C22×D411yescharacteristic
207C2×C4×C43C2×#4111yescharacteristic
208C2×Dic43—21no—
209C2×Dic43—21no—
210C2×Dic43—42no—
211D172—21no—
212D172—21no—
213D172—21no—
214D172—42no—
215D172AGL(1,ℤ/8)12yes—
216C4×D43—41no—
217C4×D43—41no—
218C4×D43—41no—
219C4×D43—41no—
220C4×D43—42no—
221C4×D43—42no—
222C8×C43—22no—
223C8×C43—22no—
224C43⋊C8—42no—
225C43⋊C8—42no—
226C43⋊C8—41no—
227C43⋊C8—41no—
228#19169—431nomaximal, Sylow
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—81no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43#46312yes—
235C22×C43C2×#12111yescharacteristic
236C2×D43—22no—
237C2×D43—41no—
238C2×D43—41no—
239C2×D43—41no—
240C2×D43—41no—
241C2×D43—41no—
242C2×D43—84no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—81no—
247C4×C43—82no—
248C4×C43#46312yes—
249C4×C43C2×#13511yescharacteristic
250C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
251C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
252C4×C43#57511yescharacteristic
253Dic43—41no—
254Dic43—41no—
255#3141D4311yescharacteristic, complemented
256#3100—431no—
257C2×#461—431no—
258D4×M16—431no—
259#1701—432no—
260#1699—432no—
261#1681—432no—
262#1679—432no—
263#1565—431no—
264#1549—431no—
265#1547—431no—
266C2×C43—22no—
267C2×C43—161no—
268C2×C43C2×#46311yescharacteristic
269C2×C43#305511yescharacteristic
270C2×C43#306911yescharacteristic
271D43—42no—
272D43—81no—
273C22×SD16—861no—
274C22×M16—861no—
275#532C2×D4311yescharacteristic
276C2×C4⋊Q8C2×D4311yescharacteristic
277C2×C4×D4—431no—
278#489—22no—
279#487C2×D4312yescomplemented
280#486C2×D4312yescomplemented
281#480—861no—
282#474—431no—
283#474—431no—
284#461—432no—
285#461—432no—
286#461—861no—
287#461—861no—
288#459—431no—
289#459—431no—
290#447—861no—
291C4×D8—861no—
292C4×D8—861no—
293#436—432no—
294#435—862no—
295C8×D4—432no—
296#431—431no—
297#423—431no—
298C2×C4⋊C8—431no—
299#417—21no—
300#417—21no—
301C2×#103—861no—
302#407—861no—
303C4×M16C2×D4311yescharacteristic
304#335—432no—
305#334—432no—
306#332—432no—
307#332—432no—
308#332—432no—
309#331—432no—
310C43#1916911yescharacteristic, complemented, Sylow
311C2×#41—21no—
312C22×Q8—21no—
313C22×D4—431no—
314C23×C4—861no—
315C2×SD16—862no—
316C2×SD16—862no—
317C2×SD16—1724no—
318C2×D8—861no—
319C2×D8—861no—
320C2×M16—861no—
321C2×M16—862no—
322C2×M16—1724no—
323C2×M16C22⋊D4311yescharacteristic
324C2×M16C22⋊D4311yescharacteristic
325C22×C8—861no—
326C22×C8—862no—
327C4⋊Q8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8C22×D4312yes—
331C4⋊Q8C22×D4311yescharacteristic
332#127C22×D4311yescharacteristic
333#124—21no—
334#121—21no—
335#121—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—431no—
339C4×D4—431no—
340C4×D4—431no—
341C4×D4—431no—
342C4×D4—861no—
343C4×D4—861no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—431no—
347C2×C22⋊C4—861no—
348C2×C42C22×D4311yescharacteristic
349#107—861no—
350#107—861no—
351C4⋊C8—432no—
352C4⋊C8—432no—
353C4⋊C8—431no—
354C4⋊C8—431no—
355C4⋊C8—861no—
356C4⋊C8—861no—
357#103—22no—
358#103—22no—
359#103—862no—
360#103—862no—
361#102—22no—
362#102—22no—
363#102—861no—
364#102—861no—
365#102—861no—
366#102—861no—
367C22⋊C8—861no—
368C22⋊C8—862no—
369C22⋊C8—862no—
370#97C22⋊D4312yes—
371C4×C8—861no—
372C4×C8C22×D4312yes—
373C24—861no—
374#41—42no—
375#41—42no—
376C2×Q8—22no—
377C2×Q8—21no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×Q8—41no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—41no—
385C2×D4—431no—
386C2×D4—431no—
387C2×D4—862no—
388C2×D4—861no—
389C2×D4—1721no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—861no—
393C22×C4—861no—
394C22×C4—861no—
395C22×C4—861no—
396C22×C4—861no—
397C22×C4—1722no—
398C22×C4—1722no—
399C22×C4D4×D4311yescharacteristic
400C22×C4#1062190011yescharacteristic
401C22×C4C2×C22⋊D4311yescharacteristic
402SD16—1724no—
403SD16—1724no—
404D8—1722no—
405D8—1722no—
406M16—22no—
407M16—22no—
408M16—1724no—
409M16—1722no—
410C2×C8—861no—
411C2×C8—861no—
412C2×C8—862no—
413C2×C8—862no—
414C2×C8—1724no—
415C2×C8—1722no—
416C2×C8C2×C22⋊D4312yes—
417C2×C8C2×C22⋊D4312yes—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—431no—
425C4⋊C4—431no—
426C4⋊C4—861no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—861no—
430C22⋊C4—861no—
431C22⋊C4—861no—
432C22⋊C4—861no—
433C42D4×D4311yescharacteristic
434C42#1062190011yescharacteristic
435C42C2×C22⋊D4311yescharacteristic
436C42C23×D4311yescharacteristic
437C23—41no—
438C23—861no—
439C23—861no—
440C23—3441no—
441C23—1722no—
442C23—1722no—
443C23#1306329611yescharacteristic
444Q8—41no—
445Q8—42no—
446Q8—41no—
447Q8—42no—
448Q8—82no—
449D4—41no—
450D4—41no—
451D4—41no—
452D4—41no—
453D4—81no—
454D4—82no—
455D4—432no—
456D4—861no—
457D4—861no—
458D4—861no—
459D4—1722no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—82no—
466C2×C4—82no—
467C2×C4—861no—
468C2×C4—861no—
469C2×C4—1722no—
470C2×C4—1722no—
471C2×C4—1722no—
472C2×C4—1721no—
473C2×C4—1721no—
474C2×C4—1721no—
475C2×C4—1721no—
476C2×C4#1306329611yescharacteristic
477C2×C4#1306329611yescharacteristic
478C2×C4#1306329611yescharacteristic
479C2×C4#1306334512yes—
480C2×C4#1306335012yes—
481C2×C4C2×D4×D4311yescharacteristic
482C2×C4C22×C22⋊D4311yescharacteristic
483C2×C4C2×#1062190011yescharacteristic
484C8—22no—
485C8—22no—
486C8—1722no—
487C8—1721no—
488C8—1722no—
489C8—1721no—
490C22—21no—
491C22—21no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—862no—
496C22—3444no—
497C22—1721no—
498C22—1721no—
499C22—1721no—
500C22—1721no—
501C22—1721no—
502C22#1458311112yes—
503C22C2×#1306329611yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—82no—
508C4—81no—
509C4—1721no—
510C4—1721no—
511C4#1458311112yes—
512C4C2×#1306334511yescharacteristic
513C4AGL(1,ℤ/8)×D4311yescharacteristic
514C4C2×#1306335011yescharacteristic
515C4#1458369511yescharacteristic
516C2—22no—
517C2—161no—
518C2—3441no—
519C2—1722no—
520C2C2×#1458311111yescharacteristic
521C2#1914420811yescharacteristic
522C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3141C2
socleC22×C43C2×#121
prime radical#19144591C2
hypercenter#3141D43
hypocenterC43#19169
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. C2×#14583101C2semidirect
3. M16×D172C2semidirect
4. #19134153C2semidirect
5. #19134139C2semidirect
6. #19134029C2semidirect
7. #19134015C2semidirect
8. #19133347C2semidirect
9. #19133280C2semidirect
10. #19133272C2semidirect
11. C43×#3141C2semidirect
35. #14582652C22semidirect
36. #14582650C22semidirect
37. #14582645C22semidirect
38. #14582645C22semidirect
39. #14582645C22semidirect
40. #14582643C22semidirect
44. C43×#487C22semidirect
45. C43×#486C22semidirect
255. #3141D43semidirect
279. #487C2×D43semidirect
280. #486C2×D43semidirect
310. C43#19169semidirect

Maximal subgroups

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

subgroupindex
#191445912
C2×#145831012
M16×D1722
#191341532
#191341392
#191340292
#191340152
#191333472
#191332802
#191332722
C43×#31412
#1916943