Finite Group Databasebeta

← #25079403

Subgroups — #25079403

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144599C211yesmaximal, characteristic, complemented
2C2×#14583091C211yesmaximal, characteristic
3M16×D172C211yesmaximal, characteristic, complemented
4#19134153C212yesmaximal, complemented
5#19134125C212yesmaximal, complemented
6#19134029C212yesmaximal, complemented
7#19134001C212yesmaximal, complemented
8#19133347C211yesmaximal, characteristic, complemented
9#19133285C211yesmaximal, characteristic, complemented
10#19133263C211yesmaximal, characteristic, complemented
11C43×#3138C211yesmaximal, characteristic, complemented
12C22×#10621882—21no—
13C2×M16×D43—21no—
14C2×C4×D172C2211yescharacteristic
15#14583227—21no—
16#14583186C2211yescharacteristic, complemented
17#14583186C2211yescharacteristic, complemented
18#14583101C2211yescharacteristic, complemented
19#14583101C2211yescharacteristic, complemented
20#14583091—21no—
21#14583091—21no—
22#14583091C2212yes—
23#14583091C2212yes—
24#14583049—21no—
25C4×#10621884—21no—
26C4×#10621884—21no—
27#14582978C2212yescomplemented
28#14582972—22no—
29C8×D172C2212yescomplemented
30#14582952C2211yescharacteristic
31#14582923C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063246—21no—
34#14582862—21no—
35#14582652C2212yescomplemented
36#14582650C2212yescomplemented
37#14582648C2212yescomplemented
38#14582645C2212yescomplemented
39#14582643C2212yescomplemented
40#14582643C2212yescomplemented
41C43×#533C2211yescharacteristic
42C2×#127×C43C2211yescharacteristic
43C43×#490—22no—
44C43×#486C2212yescomplemented
45C43×#486C2212yescomplemented
46C43×#418—21no—
47C43×#418—21no—
48C4×M16×C43C2211yescharacteristic
49C22×D172D411yescharacteristic
50C22×C4×D43—21no—
51C2×#10621884—21no—
52C2×#10621884—21no—
53C2×#10621882—22no—
54C2×#10621882—22no—
55C2×#10621882—44no—
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#13063256—21no—
70#13063256—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)C2312yes—
74C4⋊(C43⋊C8)C2311yescharacteristic
75C4⋊(C43⋊C8)C2311yescharacteristic
76C4⋊(C43⋊C8)C2312yes—
77#13063249—21no—
78#13063249—21no—
79#13063246—22no—
80#13063246—22no—
81#13063245—21no—
82#13063245—21no—
83C22⋊(C43⋊C8)—21no—
84(C2×D43)⋊C8—22no—
85(C2×D43)⋊C8—22no—
86C4×C43⋊C8—21no—
87C22×D4×C43—21no—
88C22×D4×C43—21no—
89C22×D4×C43—21no—
90C2×M16×C43D411yescharacteristic
91C2×M16×C43D411yescharacteristic
92C4⋊Q8×C43C2311yescharacteristic
93C4⋊Q8×C43C2311yescharacteristic
94#127×C43—21no—
95#127×C43—21no—
96#127×C43—21no—
97#127×C43C2312yes—
98#125×C43—21no—
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43—21no—
101C4×Q8×C43—21no—
102C4×Q8×C43—21no—
103#117×C43—21no—
104C2×C42×C43C2311yescharacteristic
105#102×C43—22no—
106#102×C43—22no—
107#102×C43—22no—
108#102×C43—22no—
109#97×C43D412yes—
110C4×C8×C43C2312yes—
111C24×C43—41no—
112C23×D43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—21no—
115C2×D4×C43—22no—
116C2×D4×C43—22no—
117C2×D4×C43—22no—
118C2×D4×C43—41no—
119C2×D4×C43—41no—
120C2×D4×C43—41no—
121C2×D4×C43—42no—
122C2×D4×C43—42no—
123C2×D4×C43—42no—
124C2×D4×C43—42no—
125C2×D4×C43—82no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43#4111yescharacteristic
129C22×Dic43—21no—
130C2×D172—21no—
131C2×D172—22no—
132C2×D172—41no—
133C2×D172C2×D411yescharacteristic
134C2×D172C2×D411yescharacteristic
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—21no—
139C2×C4×D43—42no—
140C2×C4×D43—42no—
141M16×C43—22no—
142M16×C43—22no—
143C2×C8×C43C2×D412yes—
144C2×C8×C43C2×D412yes—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—41no—
150C4⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C42×C43—41no—
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155C42×C43#4111yescharacteristic
156C42×C43C2411yescharacteristic
157#10621884—42no—
158#10621884—42no—
159#10621882—44no—
160#10621882—44no—
161(C2×D43)⋊C4—21no—
162(C2×D43)⋊C4—21no—
163(C2×D43)⋊C4—21no—
164(C2×D43)⋊C4—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43C2×D411yescharacteristic
167C4⋊Dic43C2×D411yescharacteristic
168#10621877—42no—
169C2×C43⋊C8—21no—
170C2×C43⋊C8—21no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—42no—
174#10621872—44no—
175C8×D43—44no—
176C23×C43—42no—
177C23×C43—82no—
178C23×C43—82no—
179C23×C43—82no—
180C23×C43#12111yescharacteristic
181C22×D43—21no—
182C22×D43—21no—
183C22×D43—42no—
184C22×D43—42no—
185C22×D43—81no—
186Q8×C43—41no—
187Q8×C43—41no—
188Q8×C43—81no—
189D4×C43—42no—
190D4×C43—42no—
191D4×C43—42no—
192D4×C43—42no—
193D4×C43—82no—
194D4×C43—82no—
195D4×C43—82no—
196D4×C43—82no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43#12111yescharacteristic
203C2×C4×C43#12111yescharacteristic
204C2×C4×C43#12111yescharacteristic
205C2×C4×C43#13512yes—
206C2×C4×C43AGL(1,ℤ/8)12yes—
207C2×C4×C43C22×D411yescharacteristic
208C2×C4×C43C22×D411yescharacteristic
209C2×C4×C43C2×#4111yescharacteristic
210C2×Dic43—21no—
211C2×Dic43—21no—
212C2×Dic43—42no—
213D172—21no—
214D172—21no—
215D172—21no—
216D172—42no—
217D172AGL(1,ℤ/8)12yes—
218C4×D43—41no—
219C4×D43—41no—
220C4×D43—41no—
221C4×D43—41no—
222C4×D43—42no—
223C4×D43—42no—
224C8×C43—22no—
225C8×C43—22no—
226C43⋊C8—42no—
227C43⋊C8—42no—
228C43⋊C8—41no—
229C43⋊C8—41no—
230#19166—431nomaximal, Sylow
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—82no—
234C22×C43—82no—
235C22×C43—82no—
236C22×C43—164no—
237C22×C43#46312yes—
238C22×C43C2×#12111yescharacteristic
239C2×D43—22no—
240C2×D43—41no—
241C2×D43—41no—
242C2×D43—41no—
243C2×D43—41no—
244C2×D43—41no—
245C2×D43—84no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—21no—
249C4×C43—81no—
250C4×C43—81no—
251C4×C43#46312yes—
252C4×C43C2×#13511yescharacteristic
253C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
254C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
255C4×C43#57511yescharacteristic
256Dic43—41no—
257Dic43—41no—
258#3138D4311yescharacteristic, complemented
259#3101—431no—
260C2×#459—431no—
261D4×M16—431no—
262#1701—432no—
263#1697—432no—
264#1681—432no—
265#1677—432no—
266#1565—431no—
267#1550—431no—
268#1545—431no—
269C2×C43—22no—
270C2×C43—162no—
271C2×C43C2×#46311yescharacteristic
272C2×C43#305511yescharacteristic
273C2×C43#306811yescharacteristic
274D43—42no—
275D43—81no—
276C22×D8—861no—
277C22×M16—861no—
278#533C2×D4311yescharacteristic
279C2×#127C2×D4311yescharacteristic
280C2×C4×D4—431no—
281#490—22no—
282#486C2×D4312yescomplemented
283#486C2×D4312yescomplemented
284#483—861no—
285#476—431no—
286#476—431no—
287#461—431no—
288#461—431no—
289#459—432no—
290#459—432no—
291#459—861no—
292#459—861no—
293#450—861no—
294C4×SD16—861no—
295C4×SD16—861no—
296#436—432no—
297#435—862no—
298C8×D4—432no—
299#431—431no—
300#423—431no—
301C2×C4⋊C8—431no—
302#418—21no—
303#418—21no—
304C2×#102—861no—
305#407—861no—
306C4×M16C2×D4311yescharacteristic
307#335—432no—
308#334—432no—
309#333—432no—
310#332—432no—
311#331—432no—
312#331—432no—
313C43#1916611yescharacteristic, complemented, Sylow
314C22×D4—21no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4—431no—
318C23×C4—861no—
319C2×SD16—861no—
320C2×SD16—861no—
321C2×D8—862no—
322C2×D8—862no—
323C2×D8—1724no—
324C2×M16—861no—
325C2×M16—862no—
326C2×M16—1724no—
327C2×M16C22⋊D4311yescharacteristic
328C2×M16C22⋊D4311yescharacteristic
329C22×C8—861no—
330C22×C8—862no—
331C4⋊Q8C22×D4311yescharacteristic
332C4⋊Q8C22×D4311yescharacteristic
333#127—21no—
334#127—21no—
335#127—21no—
336#127C22×D4312yes—
337#125—21no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×D4—431no—
343C4×D4—431no—
344C4×D4—431no—
345C4×D4—431no—
346C4×D4—861no—
347C4×D4—861no—
348#117—21no—
349C2×C4⋊C4—431no—
350C2×C22⋊C4—861no—
351C2×C42C22×D4311yescharacteristic
352#106—861no—
353#106—861no—
354C4⋊C8—432no—
355C4⋊C8—431no—
356C4⋊C8—431no—
357C4⋊C8—432no—
358C4⋊C8—861no—
359C4⋊C8—861no—
360#103—861no—
361#103—861no—
362#102—22no—
363#102—22no—
364#102—22no—
365#102—22no—
366#102—861no—
367#102—861no—
368#102—862no—
369#102—862no—
370C22⋊C8—861no—
371C22⋊C8—862no—
372C22⋊C8—862no—
373#97C22⋊D4312yes—
374C4×C8—861no—
375C4×C8C22×D4312yes—
376C24—41no—
377C24—861no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—82no—
391C2×D4—431no—
392C2×D4—431no—
393C2×D4—862no—
394C2×D4—861no—
395C2×D4—1721no—
396C22×C4—861no—
397C22×C4—861no—
398C22×C4—861no—
399C22×C4—861no—
400C22×C4—861no—
401C22×C4—1722no—
402C22×C4—1722no—
403C22×C4D4×D4311yescharacteristic
404C22×C4#1062190011yescharacteristic
405C22×C4C2×C22⋊D4311yescharacteristic
406SD16—1722no—
407SD16—1722no—
408D8—1724no—
409D8—1724no—
410M16—22no—
411M16—22no—
412M16—1724no—
413M16—1722no—
414C2×C8—861no—
415C2×C8—861no—
416C2×C8—862no—
417C2×C8—862no—
418C2×C8—1724no—
419C2×C8—1722no—
420C2×C8C2×C22⋊D4312yes—
421C2×C8C2×C22⋊D4312yes—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—431no—
429C4⋊C4—431no—
430C4⋊C4—861no—
431C22⋊C4—41no—
432C22⋊C4—861no—
433C22⋊C4—861no—
434C22⋊C4—861no—
435C22⋊C4—861no—
436C42—41no—
437C42D4×D4311yescharacteristic
438C42#1062190011yescharacteristic
439C42C2×C22⋊D4311yescharacteristic
440C42C23×D4311yescharacteristic
441C23—42no—
442C23—82no—
443C23—82no—
444C23—82no—
445C23—861no—
446C23—861no—
447C23—3441no—
448C23—1722no—
449C23—1722no—
450C23#1306329611yescharacteristic
451Q8—41no—
452Q8—41no—
453Q8—81no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—82no—
459D4—82no—
460D4—82no—
461D4—82no—
462D4—432no—
463D4—861no—
464D4—861no—
465D4—861no—
466D4—1722no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—861no—
473C2×C4—861no—
474C2×C4—1722no—
475C2×C4—1722no—
476C2×C4—1722no—
477C2×C4—1721no—
478C2×C4—1721no—
479C2×C4—1721no—
480C2×C4—1721no—
481C2×C4#1306329611yescharacteristic
482C2×C4#1306329611yescharacteristic
483C2×C4#1306329611yescharacteristic
484C2×C4#1306334512yes—
485C2×C4#1306335012yes—
486C2×C4C2×D4×D4311yescharacteristic
487C2×C4C22×C22⋊D4311yescharacteristic
488C2×C4C2×#1062190011yescharacteristic
489C8—22no—
490C8—22no—
491C8—1722no—
492C8—1721no—
493C8—1722no—
494C8—1721no—
495C22—21no—
496C22—21no—
497C22—82no—
498C22—82no—
499C22—82no—
500C22—164no—
501C22—862no—
502C22—3444no—
503C22—1721no—
504C22—1721no—
505C22—1721no—
506C22—1721no—
507C22—1721no—
508C22#1458311112yes—
509C22C2×#1306329611yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—81no—
514C4—81no—
515C4—1721no—
516C4—1721no—
517C4#1458311112yes—
518C4C2×#1306334511yescharacteristic
519C4AGL(1,ℤ/8)×D4311yescharacteristic
520C4C2×#1306335011yescharacteristic
521C4#1458369511yescharacteristic
522C2—22no—
523C2—162no—
524C2—3441no—
525C2—1722no—
526C2C2×#1458311111yescharacteristic
527C2#1914420811yescharacteristic
528C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3138C2
socleC22×C43C2×#121
prime radicalC2×#14583091C2
hypercenter#3138D43
hypocenterC43#19166
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
1. #19144599C2semidirect
3. M16×D172C2semidirect
4. #19134153C2semidirect
5. #19134125C2semidirect
6. #19134029C2semidirect
7. #19134001C2semidirect
8. #19133347C2semidirect
9. #19133285C2semidirect
10. #19133263C2semidirect
11. C43×#3138C2semidirect
16. #14583186C22semidirect
17. #14583186C22semidirect
18. #14583101C22semidirect
19. #14583101C22semidirect
27. #14582978C22semidirect
29. C8×D172C22semidirect
35. #14582652C22semidirect
36. #14582650C22semidirect
37. #14582648C22semidirect
38. #14582645C22semidirect
39. #14582643C22semidirect
40. #14582643C22semidirect
44. C43×#486C22semidirect
45. C43×#486C22semidirect
258. #3138D43semidirect
282. #486C2×D43semidirect
283. #486C2×D43semidirect
313. C43#19166semidirect

Maximal subgroups

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

subgroupindex
#191445992
C2×#145830912
M16×D1722
#191341532
#191341252
#191340292
#191340012
#191333472
#191332852
#191332632
C43×#31382
#1916643