Finite Group Databasebeta

← #25080410

Subgroups — #25080410

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145170C211yesmaximal, characteristic, complemented
2#19144686C211yesmaximal, characteristic, complemented
3C2×D4×C43⋊C8C211yesmaximal, characteristic, complemented
4#19134006C212yesmaximal, complemented
5#19134002C212yesmaximal, complemented
6#19133992C212yesmaximal, complemented
7#19133948C212yesmaximal, complemented
8#19133356C211yesmaximal, characteristic, complemented
9#19133291C211yesmaximal, characteristic, complemented
10#19133290C211yesmaximal, characteristic, complemented
11C43×#3109C211yesmaximal, characteristic, complemented
12C23×C43⋊C8—21no—
13#14583449C2211yescharacteristic
14#14583302C2211yescharacteristic, complemented
15#14583275C2211yescharacteristic, complemented
16#14583247C2211yescharacteristic, complemented
17#14583245C2211yescharacteristic, complemented
18#14583217—21no—
19#14583189C2212yes—
20#14583133—21no—
21#14583133—21no—
22#14583094C2212yes—
23#14583033—21no—
24#14583009—22no—
25C4×#10621882—21no—
26C4×#10621882—21no—
27D4×C43⋊C8—21no—
28D4×C43⋊C8—21no—
29D4×C43⋊C8C2212yes—
30D4×C43⋊C8C2212yes—
31#14582956C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)—21no—
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582651C2212yescomplemented
36#14582649C2212yescomplemented
37#14582648C2212yescomplemented
38#14582647C2212yescomplemented
39#14582643C2212yescomplemented
40#14582642C2212yescomplemented
41C43×#532C2211yescharacteristic
42C2×C4×D4×C43C2211yescharacteristic
43C43×#481—21no—
44C43×#476C2212yes—
45C43×#459C2212yes—
46C43×#447—21no—
47C43×#442—22no—
48C43×#432C2211yescharacteristic
49C2×#10621898—21no—
50C2×#10621882—22no—
51C2×#10621882—21no—
52C2×#10621882—21no—
53C22×C43⋊C8—21no—
54C22×C43⋊C8—22no—
55C22×C43⋊C8—22no—
56C22×C43⋊C8—44no—
57C22×C43⋊C8D411yescharacteristic
58C22×C43⋊C8D411yescharacteristic
59#13063325C2311yescharacteristic
60#13063322C2311yescharacteristic
61#13063313—21no—
62#13063299—21no—
63#13063299—21no—
64C4×D172—21no—
65C4×D172—21no—
66#13063258—21no—
67#13063258—21no—
68#13063256—22no—
69C4⋊(C43⋊C8)—21no—
70C4⋊(C43⋊C8)C2312yes—
71C4⋊(C43⋊C8)C2312yes—
72#13063246—22no—
73#13063246—21no—
74#13063246—21no—
75#13063245—22no—
76#13063245—21no—
77#13063245—21no—
78C22⋊(C43⋊C8)—21no—
79C22⋊(C43⋊C8)—22no—
80C22⋊(C43⋊C8)—22no—
81#13063236—21no—
82C4×C43⋊C8D411yescharacteristic
83C4×C43⋊C8D411yescharacteristic
84C4×C43⋊C8C2311yescharacteristic
85C4×C43⋊C8C2311yescharacteristic
86C2×#41×C43—21no—
87C22×D4×C43D411yescharacteristic
88C23×C4×C43—21no—
89C2×D8×C43—22no—
90C4⋊Q8×C43C2311yescharacteristic
91#127×C43C2311yescharacteristic
92#124×C43—21no—
93#121×C43—21no—
94#121×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43D412yes—
100C4×D4×C43C2312yes—
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C22⋊C4×C43—21no—
103C2×C42×C43C2311yescharacteristic
104#106×C43—22no—
105C4⋊C8×C43C2312yes—
106#102×C43—22no—
107#102×C43—22no—
108C22⋊C8×C43—21no—
109#97×C43—21no—
110C24×C43—21no—
111#41×C43—82no—
112C2×Q8×C43—21no—
113C2×D4×C43—24no—
114C2×D4×C43—21no—
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—22no—
122C22×C4×C43—21no—
123C22×C4×C43—42no—
124C22×C4×C43—42no—
125C22×C4×C43—41no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43#4111yescharacteristic
129C2×C22⋊D43—41no—
130#10621898—82no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—21no—
134C2×C4×D43—41no—
135C2×Dic86—21no—
136D8×C43—44no—
137C2×C8×C43—22no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43C2×D412yes—
142C22⋊C4×C43—22no—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43#4111yescharacteristic
149C42×C43C2411yescharacteristic
150#10621882—42no—
151#10621882—44no—
152#10621882—42no—
153(C2×D43)⋊C4—41no—
154(C2×D43)⋊C4—41no—
155C4⋊Dic43—21no—
156C4⋊Dic43—21no—
157C2×C43⋊C8—22no—
158C2×C43⋊C8—22no—
159C2×C43⋊C8—22no—
160C2×C43⋊C8—41no—
161C2×C43⋊C8—44no—
162C2×C43⋊C8—42no—
163C2×C43⋊C8—44no—
164C2×C43⋊C8C2×D411yescharacteristic
165C2×C43⋊C8C2×D411yescharacteristic
166C2×C43⋊C8C2×D411yescharacteristic
167C2×C43⋊C8C2×D411yescharacteristic
168C23×C43—24no—
169C23×C43—22no—
170C23×C43—42no—
171C23×C43—42no—
172C23×C43—41no—
173C23×C43#12111yescharacteristic
174C22×D43—41no—
175Q8×C43—81no—
176D4×C43—24no—
177D4×C43—22no—
178D4×C43—42no—
179D4×C43—41no—
180D4×C43—41no—
181D4×C43—81no—
182D4×C43—82no—
183D4×C43#13514yes—
184C2×C4×C43—22no—
185C2×C4×C43—22no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—22no—
189C2×C4×C43—44no—
190C2×C4×C43—42no—
191C2×C4×C43—42no—
192C2×C4×C43—42no—
193C2×C4×C43—41no—
194C2×C4×C43—82no—
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43#12111yescharacteristic
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43C22×D411yescharacteristic
199C2×C4×C43C22×D411yescharacteristic
200C2×C4×C43C2×#4111yescharacteristic
201C22⋊D43—82no—
202C2×Dic43—41no—
203D172—42no—
204D172—41no—
205D172—41no—
206D172—81no—
207C4×D43—82no—
208Dic86—81no—
209C8×C43—42no—
210C43⋊C8—21no—
211C43⋊C8—21no—
212C43⋊C8—21no—
213C43⋊C8—42no—
214C43⋊C8—42no—
215C43⋊C8AGL(1,ℤ/8)12yes—
216#19258—431nomaximal, Sylow
217C22×C43—21no—
218C22×C43—21no—
219C22×C43—24no—
220C22×C43—48no—
221C22×C43—42no—
222C22×C43—42no—
223C22×C43—81no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43#47212yes—
227C22×C43C2×#12111yescharacteristic
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—42no—
236C4×C43—81no—
237C4×C43C2×#13512yes—
238C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
239C4×C43#57511yescharacteristic
240Dic43—81no—
241#3169—431no—
242#3109—431no—
243#3109D4311yescharacteristic, complemented
244C2×C8×D4—431no—
245#1677—432no—
246#1677—432no—
247#1675—432no—
248#1667—432no—
249#1568—431no—
250#1551—431no—
251#1551—431no—
252C2×C43—22no—
253C2×C43—44no—
254C2×C43—161no—
255C2×C43#303611yescharacteristic
256C2×C43#305011yescharacteristic
257C2×C43C2×#47211yescharacteristic
258D43—161no—
259C23×C8—861no—
260#532—431no—
261#532C2×D4311yescharacteristic
262C2×C4×D4C2×D4311yescharacteristic
263#500—431no—
264#493—431no—
265#486—431no—
266#486—431no—
267#481—21no—
268#481—861no—
269#476—432no—
270#476C2×D4312yes—
271#466—861no—
272#466—861no—
273#459—432no—
274#459C2×D4312yes—
275#447—21no—
276#447—861no—
277#442—22no—
278#442—862no—
279C4×D8—861no—
280C4×D8—861no—
281C8×D4—432no—
282C8×D4—432no—
283C8×D4—861no—
284C8×D4—861no—
285#432—431no—
286#432C2×D4311yescharacteristic
287C2×C4⋊C8—431no—
288C2×C22⋊C8—861no—
289C2×C4×C8—431no—
290#335—432no—
291#334—432no—
292#333—432no—
293#333—432no—
294#331—432no—
295#331—432no—
296C43#1925811yescharacteristic, complemented, Sylow
297C2×#41—21no—
298C2×#41—861no—
299C22×D4C22⋊D4311yescharacteristic
300C23×C4—21no—
301C2×D8—22no—
302C2×D8—861no—
303C2×D8—861no—
304C2×D8—862no—
305C22×C8—431no—
306C22×C8—431no—
307C22×C8—862no—
308C22×C8—862no—
309C22×C8—861no—
310C22×C8—1724no—
311C4⋊Q8—431no—
312C4⋊Q8C22×D4311yescharacteristic
313#127—431no—
314#127C22×D4311yescharacteristic
315#124—21no—
316#124—861no—
317#121—21no—
318#121—21no—
319#121—861no—
320#121—861no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—861no—
326C4×D4—861no—
327C4×D4C22⋊D4312yes—
328C4×D4C22×D4312yes—
329C2×C4⋊C4C22⋊D4311yescharacteristic
330C2×C22⋊C4—21no—
331C2×C42C22×D4311yescharacteristic
332#107—861no—
333#107—861no—
334#106—22no—
335#106—862no—
336C4⋊C8—432no—
337C4⋊C8—432no—
338C4⋊C8—861no—
339C4⋊C8C22×D4312yes—
340#102—22no—
341#102—22no—
342#102—861no—
343#102—861no—
344#102—861no—
345#102—861no—
346#102—862no—
347#102—862no—
348C22⋊C8—21no—
349C22⋊C8—862no—
350C22⋊C8—862no—
351C22⋊C8—861no—
352#97—21no—
353#97—861no—
354C4×C8—431no—
355C4×C8—431no—
356C4×C8—431no—
357C4×C8—431no—
358C24—21no—
359#41—82no—
360#41—3442no—
361C2×Q8—21no—
362C2×Q8—861no—
363C2×D4—24no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4—861no—
370C2×D4—861no—
371C2×D4—861no—
372C2×D4—1721no—
373C2×D4C2×C22⋊D4312yes—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—41no—
380C22×C4—1721no—
381C22×C4D4×D4311yescharacteristic
382C22×C4#1062190011yescharacteristic
383C22×C4C2×C22⋊D4311yescharacteristic
384D8—44no—
385D8—1722no—
386D8—1722no—
387D8—1724no—
388C2×C8—22no—
389C2×C8—431no—
390C2×C8—431no—
391C2×C8—431no—
392C2×C8—431no—
393C2×C8—862no—
394C2×C8—862no—
395C2×C8—862no—
396C2×C8—1724no—
397C2×C8—1721no—
398C2×C8—1724no—
399C2×C8—1722no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—861no—
404C4⋊C4—861no—
405C4⋊C4C2×C22⋊D4312yes—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—1721no—
411C22⋊C4—1721no—
412C42D4×D4311yescharacteristic
413C42#1062190011yescharacteristic
414C42C2×C22⋊D4311yescharacteristic
415C42C23×D4311yescharacteristic
416C23—24no—
417C23—22no—
418C23—42no—
419C23—42no—
420C23—41no—
421C23—1721no—
422C23#1306329711yescharacteristic
423Q8—81no—
424Q8—3441no—
425D4—24no—
426D4—22no—
427D4—42no—
428D4—41no—
429D4—41no—
430D4—81no—
431D4—82no—
432D4—3441no—
433D4—3442no—
434D4—1722no—
435D4—1721no—
436D4—1721no—
437D4#1306334514yes—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—22no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—82no—
449C2×C4—3442no—
450C2×C4—1721no—
451C2×C4#1306329711yescharacteristic
452C2×C4#1306329711yescharacteristic
453C2×C4#1306329711yescharacteristic
454C2×C4C2×D4×D4311yescharacteristic
455C2×C4C22×C22⋊D4311yescharacteristic
456C2×C4C2×#1062190011yescharacteristic
457C8—42no—
458C8—432no—
459C8—861no—
460C8—861no—
461C8—861no—
462C8—1722no—
463C8—1722no—
464C22—21no—
465C22—21no—
466C22—24no—
467C22—48no—
468C22—42no—
469C22—42no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—3441no—
474C22—3441no—
475C22—3441no—
476C22#1458316712yes—
477C22C2×#1306329711yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—3441no—
485C4C2×#1306334512yes—
486C4AGL(1,ℤ/8)×D4311yescharacteristic
487C4#1458369511yescharacteristic
488C2—22no—
489C2—44no—
490C2—161no—
491C2—6881no—
492C2#1914405611yescharacteristic
493C2#1914417311yescharacteristic
494C2C2×#1458316711yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3109C2
socleC22×C43C2×#121
hypercenter#3109D43
hypocenterC43#19258
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3109

Complements

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

NH ≅ G/Ntype
1. #19145170C2semidirect
2. #19144686C2semidirect
3. C2×D4×C43⋊C8C2semidirect
4. #19134006C2semidirect
5. #19134002C2semidirect
6. #19133992C2semidirect
7. #19133948C2semidirect
8. #19133356C2semidirect
9. #19133291C2semidirect
10. #19133290C2semidirect
11. C43×#3109C2semidirect
14. #14583302C22semidirect
15. #14583275C22semidirect
16. #14583247C22semidirect
17. #14583245C22semidirect
35. #14582651C22semidirect
36. #14582649C22semidirect
37. #14582648C22semidirect
38. #14582647C22semidirect
39. #14582643C22semidirect
40. #14582642C22semidirect
243. #3109D43semidirect
296. C43#19258semidirect

Maximal subgroups

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

subgroupindex
#191451702
#191446862
C2×D4×C43⋊C82
#191340062
#191340022
#191339922
#191339482
#191333562
#191332912
#191332902
C43×#31092
#1925843