Finite Group Databasebeta

← #25080083

Subgroups — #25080083

Order 11008.

790 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145510C211yesmaximal, characteristic, complemented
2#19145048C211yesmaximal, characteristic, complemented
3#19143339C211yesmaximal, characteristic, complemented
4#19134072C212yesmaximal, complemented
5#19134062C212yesmaximal, complemented
6#19133948C212yesmaximal, complemented
7#19133938C212yesmaximal, complemented
8#19133345C211yesmaximal, characteristic, complemented
9#19133244C211yesmaximal, characteristic, complemented
10C2×#14582642C211yesmaximal, characteristic, complemented
11C43×#3245C211yesmaximal, characteristic, complemented
12C2×#13063350—21no—
13C2×#13063350—21no—
14C2×#13063332—21no—
15C2×#13063322C2211yescharacteristic
16#14583289—22no—
17#14583275—21no—
18#14583275C2212yes—
19#14583273C2212yes—
20#14583247—21no—
21#14583094C2212yes—
22#14583094C2212yes—
23#14583032—22no—
24#14582977C2212yescomplemented
25#14582971—22no—
26D4×C43⋊C8C2212yescomplemented
27#14582952C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29#14582866—21no—
30C4×#10621877C2211yescharacteristic
31#14582651C2212yescomplemented
32#14582649C2212yescomplemented
33#14582645C2211yescharacteristic, complemented
34#14582645C2211yescharacteristic, complemented
35#14582643C2211yescharacteristic, complemented
36#14582643C2211yescharacteristic, complemented
37#14582642C2212yes—
38#14582642C2212yes—
39C43×#532C2211yescharacteristic
40C43×#532C2211yescharacteristic
41C43×#474—21no—
42C43×#474C2212yescomplemented
43C43×#466—22no—
44C43×#459—21no—
45C43×#459C2212yescomplemented
46C2×C4⋊C8×C43C2211yescharacteristic
47C22×D172—21no—
48C22×D172—21no—
49C22×D172—21no—
50#13063350—44no—
51#13063350—44no—
52C2×#10621884—22no—
53C2×#10621884—22no—
54C2×#10621882—22no—
55C2×#10621882—22no—
56C2×#10621882—22no—
57C2×#10621882—22no—
58#13063332—44no—
59C2×#10621877—22no—
60C2×#10621877D411yescharacteristic
61C2×#10621877D411yescharacteristic
62C22×C43⋊C8—21no—
63C22×C43⋊C8—22no—
64#13063322—21no—
65#13063322—21no—
66#13063322—21no—
67#13063322C2312yes—
68C4⋊(C43⋊C8)—21no—
69C4⋊(C43⋊C8)C2311yescharacteristic
70C4⋊(C43⋊C8)C2311yescharacteristic
71C4⋊(C43⋊C8)C2311yescharacteristic
72C4⋊(C43⋊C8)C2311yescharacteristic
73#13063245—22no—
74#13063245—22no—
75C22⋊(C43⋊C8)—21no—
76C22⋊(C43⋊C8)—22no—
77C22⋊(C43⋊C8)—22no—
78#13063236D412yes—
79C4×C43⋊C8—21no—
80C4×C43⋊C8C2312yes—
81C2×#41×C43—21no—
82C2×#41×C43—21no—
83C2×D8×C43—22no—
84C22×C8×C43—21no—
85C4⋊Q8×C43D411yescharacteristic
86C4⋊Q8×C43C2311yescharacteristic
87#127×C43D411yescharacteristic
88#127×C43C2311yescharacteristic
89#124×C43—21no—
90#124×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94#121×C43D412yes—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43C2312yes—
99C2×C42×C43C2311yescharacteristic
100#107×C43—22no—
101C4⋊C8×C43—21no—
102C4⋊C8×C43C2312yes—
103#102×C43—22no—
104#102×C43—22no—
105C23×D43—41no—
106#41×C43—42no—
107#41×C43—42no—
108#41×C43—42no—
109#41×C43—42no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—22no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—41no—
119C2×D4×C43C2×D412yes—
120C22×C4×C43—22no—
121C22×C4×C43—41no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43#4111yescharacteristic
125C2×D172—22no—
126C2×D172—22no—
127C2×D172—22no—
128C2×D172—41no—
129C2×D172—41no—
130C2×D172—41no—
131C2×D172—42no—
132C2×D172—42no—
133C2×D172—81no—
134C2×D172—81no—
135C2×D172—82no—
136D8×C43—82no—
137C2×C8×C43—22no—
138C2×C8×C43—81no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43C2×D412yes—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—22no—
145C22⋊C4×C43—41no—
146C22⋊C4×C43—41no—
147C42×C43C2×D411yescharacteristic
148C42×C43C2×D411yescharacteristic
149C42×C43#4111yescharacteristic
150C42×C43C2411yescharacteristic
151#10621884—44no—
152#10621884—44no—
153#10621882—44no—
154#10621882—44no—
155#10621882—82no—
156#10621882—82no—
157#10621877—22no—
158#10621877—44no—
159#10621877D814yescomplemented
160C2×C43⋊C8—21no—
161C2×C43⋊C8—21no—
162C2×C43⋊C8—21no—
163C2×C43⋊C8—21no—
164C2×C43⋊C8—42no—
165C2×C43⋊C8—44no—
166C2×C43⋊C8C2×D412yes—
167C2×C43⋊C8C2×D412yes—
168C23×C43—22no—
169C23×C43—41no—
170C23×C43#12111yescharacteristic
171C22×D43—42no—
172C22×D43—82no—
173C22×D43—82no—
174C22×D43—82no—
175Q8×C43—42no—
176Q8×C43—41no—
177Q8×C43—41no—
178D4×C43—22no—
179D4×C43—22no—
180D4×C43—44no—
181D4×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—42no—
186D4×C43—81no—
187D4×C43—81no—
188D4×C43—82no—
189C2×C4×C43—21no—
190C2×C4×C43—21no—
191C2×C4×C43—22no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—41no—
196C2×C4×C43—82no—
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43#12111yescharacteristic
199C2×C4×C43#12111yescharacteristic
200C2×C4×C43C2×D812yes—
201C2×C4×C43AGL(1,ℤ/8)12yes—
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C2×C4×C43C2×#4111yescharacteristic
205D172—42no—
206D172—42no—
207D172—42no—
208D172—42no—
209D172—82no—
210D172—82no—
211D172—82no—
212D172—82no—
213C8×C43—42no—
214C43⋊C8—22no—
215C43⋊C8—41no—
216C43⋊C8—41no—
217C43⋊C8—41no—
218C43⋊C8—41no—
219C43⋊C8C2×D814yes—
220#19230—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—42no—
224C22×C43—42no—
225C22×C43—42no—
226C22×C43—81no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43#45912yes—
230C22×C43C2×#12111yescharacteristic
231C2×D43—82no—
232C2×D43—82no—
233C2×D43—82no—
234C2×D43—164no—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—42no—
239C4×C43—81no—
240C4×C43#45912yes—
241C4×C43C22×D811yescharacteristic
242C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
243C4×C43#57611yescharacteristic
244C4×C43#57711yescharacteristic
245#3245D4311yescharacteristic, complemented
246#3205—431no—
247#3151—431no—
248#2935—431no—
249#1687—432no—
250#1685—432no—
251#1667—432no—
252#1665—432no—
253#1565—431no—
254#1540—431no—
255C2×#331—431no—
256C2×C43—22no—
257C2×C43—82no—
258C2×C43—161no—
259C2×C43C2×#45911yescharacteristic
260C2×C43#306211yescharacteristic
261C2×C43#306811yescharacteristic
262D43—162no—
263C2×AGL(1,ℤ/8)—861no—
264C2×AGL(1,ℤ/8)—861no—
265C2×#131—861no—
266#532C2×D4311yescharacteristic
267#532C2×D4311yescharacteristic
268C2×#127—431no—
269#496—862no—
270#493—432no—
271#493—861no—
272#492—432no—
273#486—861no—
274#474—21no—
275#474C2×D4312yescomplemented
276#466—22no—
277#459—21no—
278#459—432no—
279#459—432no—
280#459C2×D4312yescomplemented
281#447—862no—
282#436—432no—
283#435—862no—
284C8×D4—432no—
285#431—431no—
286C2×C4⋊C8—431no—
287C2×C4⋊C8C2×D4311yescharacteristic
288#408—861no—
289C4×M16—431no—
290#335—432no—
291#334—432no—
292#332—431no—
293#332—431no—
294#331—431no—
295#331—431no—
296#331—432no—
297#331—432no—
298C43#1923011yescharacteristic, complemented, Sylow
299C2×#41—21no—
300C2×#41—21no—
301C22×D4—861no—
302C22×D4—861no—
303C22×D4—861no—
304AGL(1,ℤ/8)—1724no—
305AGL(1,ℤ/8)—1724no—
306C2×SD16—862no—
307C2×SD16—862no—
308C2×D8—22no—
309C2×D8—862no—
310C2×D8—862no—
311C2×D8—862no—
312C2×D8—862no—
313#131—1724no—
314C2×M16—431no—
315C2×M16—431no—
316C2×M16—862no—
317C22×C8—21no—
318C22×C8—862no—
319C22×C8—861no—
320C4⋊Q8C22⋊D4311yescharacteristic
321C4⋊Q8C22×D4311yescharacteristic
322#127—432no—
323#127—861no—
324#127—861no—
325#127—861no—
326#127C22⋊D4311yescharacteristic
327#127C22×D4311yescharacteristic
328#124—21no—
329#124—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121C22⋊D4312yes—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4C22×D4312yes—
338C2×C42C22×D4311yescharacteristic
339#107—22no—
340C4⋊C8—21no—
341C4⋊C8—431no—
342C4⋊C8—431no—
343C4⋊C8—431no—
344C4⋊C8—431no—
345C4⋊C8—861no—
346C4⋊C8C22×D4312yes—
347#102—22no—
348#102—22no—
349#102—862no—
350#102—862no—
351C22⋊C8—862no—
352C22⋊C8—862no—
353C22⋊C8—861no—
354#97—432no—
355C4×C8—432no—
356C4×C8—861no—
357C24—1721no—
358#41—42no—
359#41—42no—
360#41—42no—
361#41—42no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—41no—
371C2×D4—862no—
372C2×D4—862no—
373C2×D4—862no—
374C2×D4—3441no—
375C2×D4—3441no—
376C2×D4—3442no—
377C2×D4—1721no—
378C2×D4—1721no—
379C2×D4—1721no—
380C2×D4—1722no—
381C2×D4—1722no—
382C2×D4C2×C22⋊D4312yes—
383C22×C4—22no—
384C22×C4—41no—
385C22×C4D4×D4311yescharacteristic
386C22×C4#1062190011yescharacteristic
387C22×C4C2×C22⋊D4311yescharacteristic
388SD16—1724no—
389SD16—1724no—
390D8—82no—
391D8—3442no—
392D8—3442no—
393D8—1724no—
394D8—1724no—
395M16—434no—
396M16—862no—
397M16—1724no—
398C2×C8—22no—
399C2×C8—81no—
400C2×C8—432no—
401C2×C8—432no—
402C2×C8—861no—
403C2×C8—861no—
404C2×C8—861no—
405C2×C8—861no—
406C2×C8—1724no—
407C2×C8—1722no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4C2×C22⋊D4312yes—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C42D4×D4311yescharacteristic
417C42#1062190011yescharacteristic
418C42C2×C22⋊D4311yescharacteristic
419C42C23×D4311yescharacteristic
420C23—22no—
421C23—41no—
422C23—3442no—
423C23—3442no—
424C23—3442no—
425C23—1722no—
426C23#1306329711yescharacteristic
427Q8—42no—
428Q8—41no—
429Q8—41no—
430D4—22no—
431D4—22no—
432D4—44no—
433D4—42no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—81no—
439D4—81no—
440D4—82no—
441D4—3442no—
442D4—3442no—
443D4—3442no—
444D4—3442no—
445D4—1722no—
446D4—1722no—
447D4—1722no—
448D4—1722no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—82no—
457C2×C4#1306329711yescharacteristic
458C2×C4#1306329711yescharacteristic
459C2×C4#1306329711yescharacteristic
460C2×C4D8×D4312yes—
461C2×C4#1306334912yes—
462C2×C4C2×D4×D4311yescharacteristic
463C2×C4C22×C22⋊D4311yescharacteristic
464C2×C4C2×#1062190011yescharacteristic
465C8—42no—
466C8—434no—
467C8—862no—
468C8—1721no—
469C8—1721no—
470C8—1721no—
471C8—1721no—
472C22—21no—
473C22—21no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—3442no—
481C22—3442no—
482C22—3442no—
483C22—6884no—
484C22#1458309212yes—
485C22C2×#1306329711yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—42no—
490C4—81no—
491C4#1458309212yes—
492C4C2×D8×D4311yescharacteristic
493C4C2×#1306334911yescharacteristic
494C4#1458370211yescharacteristic
495C4#1458370711yescharacteristic
496C2—22no—
497C2—82no—
498C2—161no—
499C2—6882no—
500C2C2×#1458309211yescharacteristic
501C2#1914427711yescharacteristic
502C2#1914432511yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3245C2
socleC22×C43C2×#121
hypercenter#3245D43
hypocenterC43#19230
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #19145510C2semidirect
2. #19145048C2semidirect
3. #19143339C2semidirect
4. #19134072C2semidirect
5. #19134062C2semidirect
6. #19133948C2semidirect
7. #19133938C2semidirect
8. #19133345C2semidirect
9. #19133244C2semidirect
10. C2×#14582642C2semidirect
11. C43×#3245C2semidirect
24. #14582977C22semidirect
26. D4×C43⋊C8C22semidirect
31. #14582651C22semidirect
32. #14582649C22semidirect
33. #14582645C22semidirect
34. #14582645C22semidirect
35. #14582643C22semidirect
36. #14582643C22semidirect
42. C43×#474C22semidirect
45. C43×#459C22semidirect
159. #10621877D8semidirect
245. #3245D43semidirect
275. #474C2×D43semidirect
280. #459C2×D43semidirect
298. C43#19230semidirect

Maximal subgroups

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

subgroupindex
#191455102
#191450482
#191433392
#191340722
#191340622
#191339482
#191339382
#191333452
#191332442
C2×#145826422
C43×#32452
#1923043