Finite Group Databasebeta

← #25080412

Subgroups — #25080412

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#19144687C211yesmaximal, characteristic, complemented
3#19144682C211yesmaximal, characteristic, complemented
4C2×#14582964C211yesmaximal, characteristic, complemented
5#19134007C212yesmaximal, complemented
6#19134003C212yesmaximal, complemented
7#19133993C212yesmaximal, complemented
8#19133949C212yesmaximal, complemented
9#19133356C211yesmaximal, characteristic, complemented
10#19133288C211yesmaximal, characteristic, complemented
11C43×#1551C211yesmaximal, characteristic, complemented
12C22×C8×D43—21no—
13#14583449C2211yescharacteristic
14C2×C4×D172C2211yescharacteristic
15#14583302C2211yescharacteristic, complemented
16#14583275C2211yescharacteristic, complemented
17#14583247C2211yescharacteristic, complemented
18#14583245C2211yescharacteristic, complemented
19#14583218—21no—
20#14583215—21no—
21#14583190C2212yes—
22#14583186C2212yes—
23#14583133—21no—
24#14583133—21no—
25#14583095C2212yes—
26#14583091C2212yes—
27#14583035—21no—
28#14583032—21no—
29#14583012—22no—
30#14583009—22no—
31C4×#10621882—21no—
32C4×#10621882—21no—
33#14582964—21no—
34#14582964—21no—
35#14582964C2212yes—
36#14582964C2212yes—
37#14582956C2211yescharacteristic
38C2×(C2×D43)⋊C8—21no—
39C2×C4×C43⋊C8C2211yescharacteristic
40#14582651C2212yescomplemented
41#14582649C2212yescomplemented
42#14582647C2212yescomplemented
43#14582642C2212yescomplemented
44C43×#532C2211yescharacteristic
45C43×#432C2211yescharacteristic
46C2×C4⋊C8×C43C2211yescharacteristic
47C43×#333C2212yescomplemented
48C43×#331C2212yescomplemented
49C2×#10621898—21no—
50C22×D172D411yescharacteristic
51C22×C4×D43—21no—
52C2×D344—22no—
53C2×#10621882—22no—
54C2×#10621882—21no—
55C2×#10621882—21no—
56C22×C43⋊C8D411yescharacteristic
57C22×C43⋊C8D411yescharacteristic
58C2×C8×D43—22no—
59C2×C8×D43—22no—
60C2×C8×D43—44no—
61#13063325C2311yescharacteristic
62#13063322C2311yescharacteristic
63#13063313—21no—
64#13063299—21no—
65#13063299—21no—
66C4×D172—21no—
67C4×D172—21no—
68C4×D172—21no—
69C4×D172—21no—
70C4×D172D412yes—
71C4×D172C2312yes—
72C2×C4⋊Dic43D411yescharacteristic
73C2×(C2×D43)⋊C4—21no—
74#13063258—21no—
75#13063258—21no—
76#13063257—22no—
77#13063256—22no—
78C4⋊(C43⋊C8)C2312yes—
79#13063247—22no—
80#13063247—22no—
81#13063246—22no—
82#13063246—21no—
83#13063246—21no—
84#13063245—22no—
85#13063245—21no—
86#13063245—21no—
87C22⋊(C43⋊C8)—21no—
88(C2×D43)⋊C8—22no—
89(C2×D43)⋊C8—22no—
90#13063236—21no—
91C4×C43⋊C8D411yescharacteristic
92C4×C43⋊C8D411yescharacteristic
93C4×C43⋊C8C2311yescharacteristic
94C4×C43⋊C8C2311yescharacteristic
95C2×#41×C43—21no—
96C22×C8×C43—21no—
97C4⋊Q8×C43C2311yescharacteristic
98#127×C43C2311yescharacteristic
99#124×C43—21no—
100#121×C43—21no—
101#121×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C2×C42×C43C2311yescharacteristic
105C4⋊C8×C43—21no—
106C4⋊C8×C43C2312yes—
107C4⋊C8×C43C2312yes—
108C22⋊C8×C43—21no—
109#97×C43—21no—
110C23×D43—21no—
111#41×C43—82no—
112C2×Q8×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43#4111yescharacteristic
121C2×C22⋊D43—41no—
122C22×Dic43—21no—
123#10621898—82no—
124C2×D172—21no—
125C2×D172—24no—
126C2×D172—21no—
127C2×D172—21no—
128C2×D172—21no—
129C2×D172C2×D412yes—
130C2×C4×D43—22no—
131C2×C4×D43—22no—
132C2×C4×D43—42no—
133C2×C4×D43—42no—
134C2×C4×D43—41no—
135C2×Dic86—21no—
136C2×C8×C43—22no—
137C2×C8×C43—22no—
138C2×C8×C43—42no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C22⋊C4×C43—41no—
142C22⋊C4×C43—41no—
143C42×C43C2×D411yescharacteristic
144C42×C43C2×D411yescharacteristic
145C42×C43#4111yescharacteristic
146C42×C43C2411yescharacteristic
147#10621882—42no—
148#10621882—44no—
149#10621882—42no—
150(C2×D43)⋊C4—22no—
151(C2×D43)⋊C4—22no—
152(C2×D43)⋊C4—41no—
153(C2×D43)⋊C4—41no—
154C4⋊Dic43—21no—
155C4⋊Dic43—21no—
156C4⋊Dic43—21no—
157C4⋊Dic43C2×D412yes—
158C2×C43⋊C8—22no—
159C2×C43⋊C8—22no—
160C2×C43⋊C8—41no—
161C2×C43⋊C8C2×D411yescharacteristic
162C2×C43⋊C8C2×D411yescharacteristic
163C2×C43⋊C8C2×D411yescharacteristic
164C2×C43⋊C8C2×D411yescharacteristic
165D344—44no—
166C8×D43—44no—
167C8×D43—44no—
168C23×C43—41no—
169C23×C43#12111yescharacteristic
170C22×D43—24no—
171C22×D43—22no—
172C22×D43—42no—
173C22×D43—42no—
174C22×D43—41no—
175Q8×C43—81no—
176D4×C43—42no—
177D4×C43—41no—
178D4×C43—41no—
179D4×C43—81no—
180D4×C43—82no—
181C2×C4×C43—22no—
182C2×C4×C43—22no—
183C2×C4×C43—21no—
184C2×C4×C43—21no—
185C2×C4×C43—41no—
186C2×C4×C43—82no—
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43C22×D411yescharacteristic
191C2×C4×C43C22×D411yescharacteristic
192C2×C4×C43C2×#4111yescharacteristic
193C22⋊D43—82no—
194C2×Dic43—22no—
195C2×Dic43—42no—
196C2×Dic43—41no—
197D172—24no—
198D172—22no—
199D172—42no—
200D172—41no—
201D172—41no—
202D172—81no—
203D172#13514yes—
204C4×D43—44no—
205C4×D43—42no—
206C4×D43—42no—
207C4×D43—82no—
208Dic86—81no—
209C8×C43—42no—
210C8×C43—42no—
211C43⋊C8—21no—
212C43⋊C8—21no—
213C43⋊C8—21no—
214C43⋊C8—42no—
215C43⋊C8AGL(1,ℤ/8)12yes—
216#19258—431nomaximal, Sylow
217C22×C43—21no—
218C22×C43—21no—
219C22×C43—81no—
220C22×C43—81no—
221C22×C43—81no—
222C22×C43#47212yes—
223C22×C43C2×#12111yescharacteristic
224C2×D43—24no—
225C2×D43—48no—
226C2×D43—42no—
227C2×D43—42no—
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—81no—
236C4×C43C2×#13512yes—
237C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
238C4×C43#57511yescharacteristic
239Dic43—42no—
240Dic43—81no—
241#3169—431no—
242#3109—431no—
243#3109—431no—
244C2×C8×D4—431no—
245#1677—432no—
246#1677—432no—
247#1675—432no—
248#1667—432no—
249#1568—431no—
250#1551—431no—
251#1551D4311yescharacteristic, complemented
252C2×C43—22no—
253C2×C43—161no—
254C2×C43#303611yescharacteristic
255C2×C43#305011yescharacteristic
256C2×C43C2×#47211yescharacteristic
257D43—44no—
258D43—161no—
259C23×C8—861no—
260#532—431no—
261#532C2×D4311yescharacteristic
262C2×C4×D4—431no—
263#500—431no—
264#493—431no—
265#486—431no—
266#486—431no—
267#481—861no—
268#481—861no—
269#476—432no—
270#476—432no—
271#466—861no—
272#466—861no—
273#459—432no—
274#459—432no—
275#447—861no—
276#447—861no—
277#442—862no—
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⋊C8C2×D4311yescharacteristic
288C2×C22⋊C8—861no—
289C2×C4×C8—431no—
290#335—432no—
291#334—432no—
292#333—432no—
293#333C2×D4312yescomplemented
294#331—432no—
295#331C2×D4312yescomplemented
296C43#1925811yescharacteristic, complemented, Sylow
297C2×#41—21no—
298C2×#41—861no—
299C22×D4—431no—
300C23×C4—861no—
301C2×D8—862no—
302C2×D8—861no—
303C2×D8—861no—
304C2×D8—862no—
305C22×C8—21no—
306C22×C8—431no—
307C22×C8—431no—
308C22×C8—862no—
309C22×C8—862no—
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—432no—
324C4×D4—432no—
325C4×D4—861no—
326C4×D4—861no—
327C4×D4—861no—
328C4×D4—861no—
329C2×C4⋊C4—431no—
330C2×C22⋊C4—861no—
331C2×C42C22×D4311yescharacteristic
332#107—861no—
333#107—861no—
334#106—862no—
335#106—862no—
336C4⋊C8—21no—
337C4⋊C8—432no—
338C4⋊C8C22×D4312yes—
339C4⋊C8C22×D4312yes—
340#102—861no—
341#102—861no—
342#102—862no—
343#102—862no—
344#102—862no—
345#102—862no—
346#102—861no—
347#102—861no—
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—861no—
359#41—82no—
360#41—3442no—
361C2×Q8—21no—
362C2×Q8—861no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—41no—
367C2×D4—432no—
368C2×D4—864no—
369C2×D4—861no—
370C2×D4—861no—
371C2×D4—861no—
372C2×D4—861no—
373C2×D4—1721no—
374C22×C4—41no—
375C22×C4—861no—
376C22×C4—862no—
377C22×C4—862no—
378C22×C4—1722no—
379C22×C4—1722no—
380C22×C4—1721no—
381C22×C4#1062189811yescharacteristic
382C22×C4D4×D4311yescharacteristic
383C22×C4D4×D4311yescharacteristic
384D8—1724no—
385D8—1722no—
386D8—1722no—
387D8—1724no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—42no—
391C2×C8—431no—
392C2×C8—431no—
393C2×C8—431no—
394C2×C8—431no—
395C2×C8—862no—
396C2×C8—862no—
397C2×C8—1724no—
398C2×C8—1724no—
399C2×C8—1721no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—432no—
403C4⋊C4—861no—
404C4⋊C4—861no—
405C4⋊C4—861no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—862no—
409C22⋊C4—862no—
410C22⋊C4—1721no—
411C22⋊C4—1721no—
412C42#1062189811yescharacteristic
413C42D4×D4311yescharacteristic
414C42D4×D4311yescharacteristic
415C42C23×D4311yescharacteristic
416C23—41no—
417C23—864no—
418C23—862no—
419C23—1722no—
420C23—1721no—
421C23—1722no—
422C23#1306329811yescharacteristic
423Q8—81no—
424Q8—3441no—
425D4—42no—
426D4—41no—
427D4—41no—
428D4—81no—
429D4—82no—
430D4—434no—
431D4—864no—
432D4—862no—
433D4—3441no—
434D4—3442no—
435D4—1722no—
436D4—1721no—
437D4—1721no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—82no—
444C2×C4—862no—
445C2×C4—3442no—
446C2×C4—1724no—
447C2×C4—1721no—
448C2×C4—1722no—
449C2×C4—1722no—
450C2×C4—1722no—
451C2×C4#1306329811yescharacteristic
452C2×C4#1306329811yescharacteristic
453C2×C4#1306329811yescharacteristic
454C2×C4C2×D4×D4311yescharacteristic
455C2×C4C2×D4×D4311yescharacteristic
456C2×C4C2×#1062189811yescharacteristic
457C8—42no—
458C8—42no—
459C8—432no—
460C8—861no—
461C8—861no—
462C8—861no—
463C8—1722no—
464C22—21no—
465C22—21no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—864no—
470C22—3441no—
471C22—3441no—
472C22—3441no—
473C22—1728no—
474C22—1722no—
475C22—1722no—
476C22#1458316812yes—
477C22C2×#1306329811yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—81no—
483C4—3441no—
484C4—1722no—
485C4#135×D4312yes—
486C4AGL(1,ℤ/8)×D4311yescharacteristic
487C4#1458369811yescharacteristic
488C2—22no—
489C2—161no—
490C2—1724no—
491C2—6881no—
492C2#1914405811yescharacteristic
493C2#1914417511yescharacteristic
494C2C2×#1458316811yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1551C2
socleC22×C43C2×#121
hypercenter#1551D43
hypocenterC43#19258
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1551

Complements

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

NH ≅ G/Ntype
1. #19145170C2semidirect
2. #19144687C2semidirect
3. #19144682C2semidirect
4. C2×#14582964C2semidirect
5. #19134007C2semidirect
6. #19134003C2semidirect
7. #19133993C2semidirect
8. #19133949C2semidirect
9. #19133356C2semidirect
10. #19133288C2semidirect
11. C43×#1551C2semidirect
15. #14583302C22semidirect
16. #14583275C22semidirect
17. #14583247C22semidirect
18. #14583245C22semidirect
40. #14582651C22semidirect
41. #14582649C22semidirect
42. #14582647C22semidirect
43. #14582642C22semidirect
47. C43×#333C22semidirect
48. C43×#331C22semidirect
251. #1551D43semidirect
293. #333C2×D43semidirect
295. #331C2×D43semidirect
296. C43#19258semidirect

Maximal subgroups

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

subgroupindex
#191451702
#191446872
#191446822
C2×#145829642
#191340072
#191340032
#191339932
#191339492
#191333562
#191332882
C43×#15512
#1925843