Finite Group Databasebeta

← #25082004

Subgroups — #25082004

Order 11008.

704 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145536C211yesmaximal, characteristic, complemented
2#19144383C211yesmaximal, characteristic, complemented
3#19143706C211yesmaximal, characteristic, complemented
4#19134009C212yesmaximal, complemented
5#19134002C212yesmaximal, complemented
6#19133941C212yesmaximal, complemented
7#19133934C212yesmaximal, complemented
8#19133367C211yesmaximal, characteristic, complemented
9#19133286C211yesmaximal, characteristic, complemented
10C2×#14582643C211yesmaximal, characteristic, complemented
11C43×#3038C211yesmaximal, characteristic
12#14583456C2211yescharacteristic
13#14583271C2212yes—
14#14583245C2212yes—
15#14583206—21no—
16#14583199—21no—
17#14583194C2211yescharacteristic, complemented
18#14583189C2211yescharacteristic, complemented
19#14583184C2211yescharacteristic, complemented
20#14583179C2211yescharacteristic, complemented
21#14583096—21no—
22#14583096—21no—
23#14583050—22no—
24Q8×C43⋊C8C2212yescomplemented
25D4×C43⋊C8—22no—
26D4×C43⋊C8C2212yescomplemented
27#14582952—21no—
28#14582952C2211yescharacteristic
29#14582935—21no—
30C2×C4⋊(C43⋊C8)—21no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33#14582895—21no—
34#14582649C2212yescomplemented
35#14582649C2212yescomplemented
36#14582647C2212yescomplemented
37#14582644C2212yescomplemented
38#14582643C2212yes—
39#14582643C2212yes—
40C2×AGL(1,ℤ/8)×C43—21no—
41C2×#127×C43C2211yescharacteristic
42C4×#41×C43C2211yescharacteristic
43C43×#460—21no—
44C43×#460C2212yes—
45C43×#459—21no—
46C43×#459C2212yes—
47C43×#423C2211yescharacteristic
48C43×#418—21no—
49C2×#10621883—22no—
50C2×#10621883—22no—
51C22×C43⋊C8—21no—
52C22×C43⋊C8—21no—
53C22×C43⋊C8—22no—
54#13063325C2311yescharacteristic
55#13063325C2311yescharacteristic
56#13063317—21no—
57#13063304—21no—
58#13063304—21no—
59C4×Dic86—21no—
60C4×Dic86—21no—
61#13063284—21no—
62#13063258—21no—
63#13063258—21no—
64#13063256—21no—
65#13063256—21no—
66C4⋊(C43⋊C8)—21no—
67C4⋊(C43⋊C8)—21no—
68C4⋊(C43⋊C8)—22no—
69C4⋊(C43⋊C8)D411yescharacteristic
70C4⋊(C43⋊C8)D411yescharacteristic
71C4⋊(C43⋊C8)C2312yes—
72C4⋊(C43⋊C8)C2311yescharacteristic
73C4⋊(C43⋊C8)C2311yescharacteristic
74#13063249—21no—
75#13063249—21no—
76#13063246—21no—
77#13063246—21no—
78#13063246—22no—
79#13063246—22no—
80C22⋊(C43⋊C8)—22no—
81C22⋊(C43⋊C8)D412yes—
82C4×C43⋊C8—22no—
83C4×C43⋊C8C2312yes—
84C2×#41×C43D411yescharacteristic
85C22×D4×C43—21no—
86C22×D4×C43—21no—
87C22×D4×C43—21no—
88AGL(1,ℤ/8)×C43—44no—
89C2×SD16×C43—22no—
90C2×D8×C43—22no—
91C2×M16×C43—21no—
92#127×C43—21no—
93#127×C43—21no—
94#127×C43—21no—
95#127×C43C2312yes—
96C4×Q8×C43D411yescharacteristic
97C4×Q8×C43C2311yescharacteristic
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43D411yescharacteristic
101C4×D4×C43C2311yescharacteristic
102#117×C43—21no—
103#117×C43D411yescharacteristic
104C2×C42×C43—21no—
105C2×C42×C43C2311yescharacteristic
106C4⋊C8×C43—21no—
107C4⋊C8×C43C2312yes—
108#102×C43—22no—
109#102×C43—22no—
110C24×C43—41no—
111#41×C43—22no—
112#41×C43SD1614yescomplemented
113C2×Q8×C43C2×D411yescharacteristic
114C2×D4×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—81no—
124C2×D4×C43—81no—
125C2×D4×C43—82no—
126C2×D4×C43C2×D411yescharacteristic
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43#4111yescharacteristic
133C2×Dic86—21no—
134C2×Dic86—21no—
135SD16×C43—44no—
136D8×C43—44no—
137M16×C43—42no—
138C2×C8×C43—22no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43C2×D411yescharacteristic
142C4⋊C4×C43C2×D411yescharacteristic
143C22⋊C4×C43—21no—
144C22⋊C4×C43—21no—
145C22⋊C4×C43—21no—
146C42×C43—21no—
147C42×C43—21no—
148C42×C43—21no—
149C42×C43C2×D411yescharacteristic
150C42×C43C2×D411yescharacteristic
151C42×C43#4111yescharacteristic
152C42×C43C2411yescharacteristic
153C22⋊Dic43—41no—
154#10621883—82no—
155#10621883—82no—
156C4⋊Dic43—21no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43—21no—
160Dic43⋊C4—41no—
161Dic43⋊C4—41no—
162C4×Dic43—41no—
163C2×C43⋊C8—22no—
164C2×C43⋊C8—21no—
165C2×C43⋊C8—21no—
166C2×C43⋊C8—42no—
167C2×C43⋊C8—82no—
168C2×C43⋊C8—81no—
169C2×C43⋊C8C2×D412yes—
170C2×C43⋊C8C2×D412yes—
171C23×C43—21no—
172C23×C43—42no—
173C23×C43—82no—
174C23×C43—82no—
175C23×C43—82no—
176C23×C43#12111yescharacteristic
177Q8×C43—21no—
178Q8×C43C2×SD1612yes—
179D4×C43—24no—
180D4×C43—21no—
181D4×C43—42no—
182D4×C43—42no—
183D4×C43—42no—
184D4×C43—42no—
185D4×C43—82no—
186D4×C43—82no—
187D4×C43—82no—
188D4×C43—82no—
189D4×C43C2×SD1612yes—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—24no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—81no—
200C2×C4×C43#12111yescharacteristic
201C2×C4×C43#12111yescharacteristic
202C2×C4×C43#12111yescharacteristic
203C2×C4×C43C2×SD1612yes—
204C2×C4×C43#13512yes—
205C2×C4×C43C22×D411yescharacteristic
206C2×C4×C43C22×D411yescharacteristic
207C2×C4×C43C2×#4111yescharacteristic
208C2×Dic43—41no—
209C2×Dic43—41no—
210Dic86—41no—
211Dic86—41no—
212Dic86—81no—
213C8×C43—42no—
214C43⋊C8—22no—
215C43⋊C8—22no—
216C43⋊C8—41no—
217C43⋊C8—41no—
218C43⋊C8—42no—
219#19409—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—22no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43—82no—
226C22×C43—82no—
227C22×C43—82no—
228C22×C43—164no—
229C22×C43#46512yes—
230C22×C43C2×#12111yescharacteristic
231C4×C43—21no—
232C4×C43—22no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—41no—
236C4×C43—41no—
237C4×C43#46512yes—
238C4×C43C22×SD1611yescharacteristic
239C4×C43C2×#13511yescharacteristic
240C4×C43#57611yescharacteristic
241C4×C43#57711yescharacteristic
242Dic43—81no—
243Dic43—81no—
244#3208—431no—
245#3076—431no—
246#3038D4311yescharacteristic
247#2988—431no—
248#1678—432no—
249#1677—432no—
250#1666—432no—
251#1665—432no—
252#1570—431no—
253#1550—431no—
254C2×#331—431no—
255C2×C43—22no—
256C2×C43—42no—
257C2×C43—162no—
258C2×C43#304511yescharacteristic
259C2×C43C2×#46511yescharacteristic
260C2×C43#306811yescharacteristic
261C2×AGL(1,ℤ/8)—21no—
262#533—431no—
263C2×#127C2×D4311yescharacteristic
264C4×#41C2×D4311yescharacteristic
265#492—432no—
266#486—432no—
267#479—861no—
268#478—861no—
269#477—431no—
270#476—431no—
271#475—431no—
272#474—431no—
273#460—21no—
274#460—861no—
275#460—861no—
276#460C2×D4312yes—
277#459—21no—
278#459C2×D4312yes—
279#450—862no—
280C8×Q8—432no—
281C8×D4—432no—
282C8×D4—862no—
283#431—431no—
284#431—861no—
285#427—861no—
286#423C2×D4311yescharacteristic
287C2×C4⋊C8—431no—
288C2×C4⋊C8—431no—
289C2×C4⋊C8—861no—
290#418—21no—
291#416—861no—
292#334—432no—
293#334—432no—
294#333—432no—
295#332—432no—
296#331—432no—
297#331—432no—
298C43#1940911yescharacteristic, complemented, Sylow
299C2×#41C22⋊D4311yescharacteristic
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303AGL(1,ℤ/8)—44no—
304C2×SD16—22no—
305C2×SD16—862no—
306C2×SD16—862no—
307C2×D8—22no—
308C2×M16—21no—
309C22×C8—862no—
310C22×C8—861no—
311C22×C8—861no—
312C4⋊Q8—431no—
313C4⋊Q8—431no—
314#127—21no—
315#127—21no—
316#127—21no—
317#127C22×D4312yes—
318#125—861no—
319C22⋊Q8—861no—
320C22⋊Q8—861no—
321C4×Q8—861no—
322C4×Q8—861no—
323C4×Q8C22⋊D4311yescharacteristic
324C4×Q8C22×D4311yescharacteristic
325C4×D4—21no—
326C4×D4—21no—
327C4×D4C22⋊D4311yescharacteristic
328C4×D4C22×D4311yescharacteristic
329#117—21no—
330#117—861no—
331#117C22⋊D4311yescharacteristic
332C2×C42—21no—
333C2×C42C22×D4311yescharacteristic
334#107—861no—
335#107—861no—
336#106—861no—
337#106—861no—
338C4⋊C8—21no—
339C4⋊C8—431no—
340C4⋊C8—431no—
341C4⋊C8—432no—
342C4⋊C8—431no—
343C4⋊C8—431no—
344C4⋊C8—862no—
345C4⋊C8—861no—
346C4⋊C8—861no—
347C4⋊C8C22×D4312yes—
348#103—861no—
349#103—861no—
350#102—22no—
351#102—22no—
352#102—862no—
353#102—862no—
354#102—861no—
355#102—861no—
356C22⋊C8—432no—
357C22⋊C8—862no—
358C4×C8—432no—
359C4×C8—862no—
360C24—41no—
361#41—22no—
362#41#1062188314yescomplemented
363C2×Q8—861no—
364C2×Q8—861no—
365C2×Q8C2×C22⋊D4311yescharacteristic
366C2×D4—21no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—42no—
374C2×D4—42no—
375C2×D4—81no—
376C2×D4—81no—
377C2×D4—82no—
378C2×D4C2×C22⋊D4311yescharacteristic
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4D4×D4311yescharacteristic
383C22×C4#1062190011yescharacteristic
384C22×C4C2×C22⋊D4311yescharacteristic
385SD16—44no—
386SD16—3442no—
387SD16—3442no—
388D8—44no—
389M16—42no—
390C2×C8—22no—
391C2×C8—432no—
392C2×C8—432no—
393C2×C8—862no—
394C2×C8—861no—
395C2×C8—861no—
396C2×C8—3442no—
397C2×C8—3441no—
398C2×C8—1722no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—861no—
402C4⋊C4—861no—
403C4⋊C4—861no—
404C4⋊C4—861no—
405C4⋊C4—1721no—
406C4⋊C4—1721no—
407C4⋊C4C2×C22⋊D4311yescharacteristic
408C4⋊C4C2×C22⋊D4311yescharacteristic
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—1721no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42—1721no—
417C42D4×D4311yescharacteristic
418C42#1062190011yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C42C23×D4311yescharacteristic
421C23—21no—
422C23—42no—
423C23—82no—
424C23—82no—
425C23—82no—
426C23#1306329711yescharacteristic
427Q8—21no—
428Q8—3441no—
429Q8—1721no—
430Q8—1721no—
431Q8C2×#1062188312yes—
432D4—24no—
433D4—21no—
434D4—42no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—82no—
439D4—82no—
440D4—82no—
441D4—82no—
442D4C2×#1062188312yes—
443C2×C4—21no—
444C2×C4—24no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—81no—
453C2×C4—1721no—
454C2×C4—1721no—
455C2×C4#1306329711yescharacteristic
456C2×C4#1306329711yescharacteristic
457C2×C4#1306329711yescharacteristic
458C2×C4C2×#1062188312yes—
459C2×C4#1306334512yes—
460C2×C4C2×D4×D4311yescharacteristic
461C2×C4C22×C22⋊D4311yescharacteristic
462C2×C4C2×#1062190011yescharacteristic
463C8—42no—
464C8—862no—
465C8—862no—
466C8—1721no—
467C8—1721no—
468C8—1722no—
469C22—21no—
470C22—21no—
471C22—22no—
472C22—41no—
473C22—41no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—164no—
478C22#1458312612yes—
479C22C2×#1306329711yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—22no—
484C4—41no—
485C4—41no—
486C4—3441no—
487C4—3441no—
488C4#1458312612yes—
489C4C22×#1062188311yescharacteristic
490C4C2×#1306334511yescharacteristic
491C4#1458370311yescharacteristic
492C4#1458370911yescharacteristic
493C2—22no—
494C2—42no—
495C2—162no—
496C2#1914413811yescharacteristic
497C2C2×#1458312611yescharacteristic
498C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3038C2
socleC22×C43C2×#121
hypercenter#3038D43
hypocenterC43#19409
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. #19145536C2semidirect
2. #19144383C2semidirect
3. #19143706C2semidirect
4. #19134009C2semidirect
5. #19134002C2semidirect
6. #19133941C2semidirect
7. #19133934C2semidirect
8. #19133367C2semidirect
9. #19133286C2semidirect
10. C2×#14582643C2semidirect
17. #14583194C22semidirect
18. #14583189C22semidirect
19. #14583184C22semidirect
20. #14583179C22semidirect
24. Q8×C43⋊C8C22semidirect
26. D4×C43⋊C8C22semidirect
34. #14582649C22semidirect
35. #14582649C22semidirect
36. #14582647C22semidirect
37. #14582644C22semidirect
112. #41×C43SD16semidirect
298. C43#19409semidirect
362. #41#10621883semidirect

Maximal subgroups

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

subgroupindex
#191455362
#191443832
#191437062
#191340092
#191340022
#191339412
#191339342
#191333672
#191332862
C2×#145826432
C43×#30382
#1940943