Finite Group Databasebeta

← #25074177

Subgroups — #25074177

Order 11008.

980 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148396C211yesmaximal, characteristic, complemented
2#19145911C211yesmaximal, characteristic, complemented
3#19144055C211yesmaximal, characteristic
4#19133855C212yesmaximal, complemented
5#19133799C212yesmaximal, complemented
6#19133695C212yesmaximal, complemented
7#19133664C212yesmaximal, complemented
8#19133285C211yesmaximal, characteristic, complemented
9#19133051C211yesmaximal, characteristic, complemented
10C2×#14582628C211yesmaximal, characteristic, complemented
11C43×#3167C211yesmaximal, characteristic, complemented
12C2×#13063350—21no—
13#14583610C2212yes—
14#14583609—21no—
15#14583609—22no—
16#14583605—22no—
17Q8×D172—21no—
18#14583564C2212yes—
19#14583527—21no—
20#14583524—22no—
21#14583456C2211yescharacteristic
22C22⋊Q8×D43—22no—
23#14583373—21no—
24C2×C4×D172C2211yescharacteristic
25#14583189—21no—
26#14583181C2212yescomplemented
27#14583126—22no—
28#14583111—22no—
29#14583104—21no—
30#14583101C2212yes—
31#14583096C2212yescomplemented
32#14583091C2212yes—
33#14582923C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35#14582900—21no—
36#14582648C2212yescomplemented
37#14582645C2212yescomplemented
38#14582631C2212yescomplemented
39#14582631C2212yescomplemented
40#14582628C2212yes—
41#14582628C2212yes—
42C43×#533C2211yescharacteristic
43C43×#532C2211yescharacteristic
44C43×#498C2211yescharacteristic, complemented
45C43×#492C2211yescharacteristic, complemented
46C43×#487C2211yescharacteristic, complemented
47C43×#486C2211yescharacteristic, complemented
48C43×#465—22no—
49C4×SD16×C43—22no—
50C2×C4×C8×C43C2211yescharacteristic
51C2×Q8×D43—22no—
52C22×D172D411yescharacteristic
53C22×C4×D43—21no—
54#13063350—44no—
55C2×#10621883—22no—
56C2×#10621884—22no—
57C2×#10621882—22no—
58C2×#10621877—21no—
59C22×C43⋊C8—21no—
60#13063325—22no—
61#13063325D411yescharacteristic
62#13063325D411yescharacteristic
63#13063324—22no—
64#13063317—22no—
65#13063317—21no—
66#13063316—22no—
67#13063305—24no—
68#13063305—22no—
69#13063304—21no—
70#13063304D412yes—
71#13063303—24no—
72#13063303—24no—
73#13063303—24no—
74#13063302—24no—
75#13063301—24no—
76#13063301—22no—
77C4×Dic86—21no—
78C4×Dic86C2312yes—
79C4×D172—22no—
80C4×D172—22no—
81C4×D172—21no—
82C4×D172—21no—
83C4×D172D412yes—
84C4×D172C2312yes—
85#13063287—22no—
86#13063287—22no—
87#13063284—21no—
88C2×C4⋊Dic43D411yescharacteristic
89C4⋊C4×D43—24no—
90C4⋊C4×D43—22no—
91C2×(C2×D43)⋊C4—21no—
92C22⋊C4×D43—24no—
93#13063256—22no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2312yes—
97C4⋊(C43⋊C8)C2312yes—
98#13063249—22no—
99#13063248—22no—
100#13063246—22no—
101#13063246—22no—
102C2×#41×C43—21no—
103C2×SD16×C43—22no—
104C22×C8×C43—21no—
105C4⋊Q8×C43C2311yescharacteristic
106C4⋊Q8×C43C2311yescharacteristic
107C4⋊Q8×C43C2311yescharacteristic
108#127×C43C2311yescharacteristic
109#125×C43—21no—
110#124×C43—21no—
111C22⋊Q8×C43—21no—
112C22⋊Q8×C43D412yes—
113#121×C43—21no—
114#121×C43—21no—
115C4×Q8×C43—21no—
116C4×Q8×C43D412yes—
117C4×D4×C43—21no—
118C4×D4×C43—21no—
119#117×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#106×C43—22no—
122#103×C43—22no—
123#102×C43—22no—
124C4×C8×C43—21no—
125C4×C8×C43C2311yescharacteristic
126C4×C8×C43C2311yescharacteristic
127C23×D43—21no—
128#41×C43—42no—
129#41×C43—42no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43C2×D412yes—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—41no—
137C22×C4×C43—41no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×Dic43—21no—
142Q8×D43—82no—
143Q8×D43—82no—
144C2×D172—21no—
145C2×D172—22no—
146C2×D172SD1614yescomplemented
147C2×D172C2×D412yes—
148C2×C4×D43—22no—
149C2×C4×D43—24no—
150C2×C4×D43—24no—
151C2×C4×D43—22no—
152C2×C4×D43—81no—
153C2×C4×D43—81no—
154C2×Dic86—24no—
155C2×Dic86—21no—
156C2×Dic86C2×D412yes—
157SD16×C43—44no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—42no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43C2×D412yes—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—41no—
171C22⋊C4×C43—41no—
172C42×C43—22no—
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43C2411yescharacteristic
177C22⋊Dic43—22no—
178#10621884—44no—
179#10621883—82no—
180#10621882—44no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—22no—
184(C2×D43)⋊C4—22no—
185C4⋊Dic43—24no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C2×D412yes—
191C4⋊Dic43C2×D412yes—
192Dic43⋊C4—24no—
193Dic43⋊C4—24no—
194Dic43⋊C4—22no—
195Dic43⋊C4—22no—
196C4×Dic43—22no—
197#10621877—42no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—81no—
201C23×C43—41no—
202C23×C43#12011yescharacteristic
203C22×D43—22no—
204C22×D43—24no—
205C22×D43—81no—
206C22×D43—81no—
207Q8×C43—42no—
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—41no—
212D4×C43—42no—
213D4×C43—41no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—82no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—82no—
225C2×C4×C43#12011yescharacteristic
226C2×C4×C43#12011yescharacteristic
227C2×C4×C43#12011yescharacteristic
228C2×C4×C43C2×SD1612yes—
229C2×C4×C43#13712yes—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—81no—
237D172—22no—
238D172—24no—
239D172C2×SD1614yes—
240C4×D43—42no—
241C4×D43—42no—
242C4×D43—82no—
243C4×D43—84no—
244C4×D43—84no—
245Dic86—22no—
246Dic86—22no—
247Dic86—81no—
248Dic86—84no—
249C8×C43—22no—
250C8×C43—41no—
251C43⋊C8—42no—
252C43⋊C8—42no—
253#18664—431nomaximal, Sylow
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—81no—
257C22×C43—81no—
258C22×C43—81no—
259C22×C43#44812yes—
260C22×C43C2×#12011yescharacteristic
261C2×D43—24no—
262C2×D43—42no—
263C2×D43—42no—
264C2×D43—84no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—42no—
269C4×C43—42no—
270C4×C43—81no—
271C4×C43#44812yes—
272C4×C43C22×SD1611yescharacteristic
273C4×C43C2×#13711yescharacteristic
274C4×C43#57611yescharacteristic
275C4×C43#57711yescharacteristic
276Dic43—42no—
277Dic43—42no—
278Dic43—42no—
279#3501—431no—
280#3246—431no—
281#3167D4311yescharacteristic, complemented
282#3036—431no—
283#1651—432no—
284#1643—432no—
285#1627—432no—
286#1622—432no—
287#1550—431no—
288#1493—431no—
289C2×D4⋊C8—431no—
290C2×C43—22no—
291C2×C43—161no—
292C2×C43C2×#44811yescharacteristic
293C2×C43#301211yescharacteristic
294C2×C43#301811yescharacteristic
295D43—44no—
296C2×AGL(1,ℤ/8)—861no—
297#554—432no—
298#554—862no—
299#554—861no—
300#554—862no—
301D4×Q8—432no—
302D4×Q8—861no—
303#544—861no—
304#543—862no—
305#533—431no—
306#533C2×D4311yescharacteristic
307#532C2×D4311yescharacteristic
308C2×C22⋊Q8—862no—
309#518—861no—
310C2×C4×D4—431no—
311#498C2×D4311yescharacteristic, complemented
312#492C2×D4311yescharacteristic, complemented
313#487C2×D4311yescharacteristic, complemented
314#486C2×D4311yescharacteristic, complemented
315#476—861no—
316#475—432no—
317#465—22no—
318#465—862no—
319#463—862no—
320#461—432no—
321#461—861no—
322#460—432no—
323#459—432no—
324C4×SD16—22no—
325#423—431no—
326C2×C4⋊C8—431no—
327#417—861no—
328C2×C4×C8C2×D4311yescharacteristic
329#333—432no—
330#332—432no—
331Q8⋊C8—432no—
332Q8⋊C8—432no—
333D4⋊C8—432no—
334D4⋊C8—432no—
335C43#1866411yescharacteristic, complemented, Sylow
336C2×#41—21no—
337C22×Q8—862no—
338C22×D4—431no—
339C23×C4—861no—
340AGL(1,ℤ/8)—1724no—
341C2×SD16—22no—
342C2×SD16—862no—
343C2×SD16—862no—
344C2×D8—862no—
345C2×M16—861no—
346C22×C8—21no—
347C22×C8—861no—
348C4⋊Q8—431no—
349C4⋊Q8—431no—
350C4⋊Q8—862no—
351C4⋊Q8—862no—
352C4⋊Q8C22×D4311yescharacteristic
353C4⋊Q8C22×D4311yescharacteristic
354C4⋊Q8C22×D4311yescharacteristic
355#127C22×D4311yescharacteristic
356#125—21no—
357#125—862no—
358#125—862no—
359#125—861no—
360#124—21no—
361C22⋊Q8—21no—
362C22⋊Q8—432no—
363C22⋊Q8—864no—
364C22⋊Q8—862no—
365C22⋊Q8—864no—
366C22⋊Q8—864no—
367C22⋊Q8—864no—
368C22⋊Q8—862no—
369C22⋊Q8—864no—
370C22⋊Q8—861no—
371C22⋊Q8—864no—
372C22⋊Q8C22⋊D4312yes—
373#121—21no—
374#121—21no—
375C4×Q8—21no—
376C4×Q8—432no—
377C4×Q8—861no—
378C4×Q8C22⋊D4312yes—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—432no—
382C4×D4—432no—
383C4×D4—862no—
384C4×D4—862no—
385C4×D4—862no—
386C4×D4—862no—
387C4×D4—861no—
388C4×D4—861no—
389#117—21no—
390#117—861no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—862no—
393C2×C4⋊C4—864no—
394C2×C22⋊C4—864no—
395C2×C22⋊C4—861no—
396C2×C42C22×D4311yescharacteristic
397#106—22no—
398#106—862no—
399C4⋊C8—432no—
400C4⋊C8—432no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403#103—22no—
404#103—862no—
405#103—862no—
406#102—22no—
407#102—862no—
408#102—862no—
409C4×C8—21no—
410C4×C8C22×D4311yescharacteristic
411C4×C8C22×D4311yescharacteristic
412C24—861no—
413#41—42no—
414#41—42no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—432no—
418C2×Q8—864no—
419C2×Q8—861no—
420C2×Q8—3442no—
421C2×Q8—3442no—
422C2×Q8C2×C22⋊D4312yes—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—434no—
428C2×D4—432no—
429C2×D4—861no—
430C2×D4—862no—
431C22×C4—41no—
432C22×C4—864no—
433C22×C4—864no—
434C22×C4—861no—
435C22×C4—862no—
436C22×C4—862no—
437C22×C4—3441no—
438C22×C4—3441no—
439C22×C4D4×D4311yescharacteristic
440C22×C4D4×D4311yescharacteristic
441C22×C4C2×C22⋊D4311yescharacteristic
442SD16—44no—
443SD16—3442no—
444SD16—1724no—
445D8—1724no—
446M16—1722no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—42no—
450C2×C8—862no—
451C2×C8—862no—
452C2×C8—3441no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—432no—
461C4⋊C4—432no—
462C4⋊C4—864no—
463C4⋊C4—864no—
464C4⋊C4—864no—
465C4⋊C4—861no—
466C4⋊C4—862no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—862no—
471C4⋊C4C2×C22⋊D4312yes—
472C22⋊C4—22no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—864no—
476C22⋊C4—864no—
477C22⋊C4—862no—
478C22⋊C4—862no—
479C22⋊C4—862no—
480C42—22no—
481C42—862no—
482C42D4×D4311yescharacteristic
483C42D4×D4311yescharacteristic
484C42C2×C22⋊D4311yescharacteristic
485C42C23×D4311yescharacteristic
486C23—41no—
487C23—864no—
488C23—862no—
489C23—3441no—
490C23—3441no—
491C23#1306329311yescharacteristic
492Q8—42no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—862no—
498Q8—862no—
499Q8—3441no—
500Q8—3444no—
501D4—42no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—82no—
507D4—434no—
508D4—862no—
509D4—864no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—82no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—862no—
520C2×C4—3442no—
521C2×C4—3444no—
522C2×C4—3444no—
523C2×C4—3441no—
524C2×C4—1722no—
525C2×C4—1722no—
526C2×C4#1306329311yescharacteristic
527C2×C4#1306329311yescharacteristic
528C2×C4#1306329311yescharacteristic
529C2×C4SD16×D4312yes—
530C2×C4#1306335412yes—
531C2×C4C2×D4×D4311yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C22×C22⋊D4311yescharacteristic
534C8—22no—
535C8—41no—
536C8—1722no—
537C8—1722no—
538C22—21no—
539C22—21no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—864no—
544C22—3444no—
545C22—1722no—
546C22—1722no—
547C22#1458303612yes—
548C22C2×#1306329311yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—42no—
553C4—42no—
554C4—81no—
555C4—1722no—
556C4—1722no—
557C4—1722no—
558C4#1458303612yes—
559C4C2×SD16×D4311yescharacteristic
560C4C2×#1306335411yescharacteristic
561C4#1458370111yescharacteristic
562C4#1458370611yescharacteristic
563C2—22no—
564C2—161no—
565C2—1724no—
566C2C2×#1458303611yescharacteristic
567C2#1914389511yescharacteristic
568C2#1914394311yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3167C2
socleC22×C43C2×#120
prime radical#19144055C2
hypercenter#3167D43
hypocenterC43#18664
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #19148396C2semidirect
2. #19145911C2semidirect
4. #19133855C2semidirect
5. #19133799C2semidirect
6. #19133695C2semidirect
7. #19133664C2semidirect
8. #19133285C2semidirect
9. #19133051C2semidirect
10. C2×#14582628C2semidirect
11. C43×#3167C2semidirect
26. #14583181C22semidirect
31. #14583096C22semidirect
36. #14582648C22semidirect
37. #14582645C22semidirect
38. #14582631C22semidirect
39. #14582631C22semidirect
44. C43×#498C22semidirect
45. C43×#492C22semidirect
46. C43×#487C22semidirect
47. C43×#486C22semidirect
146. C2×D172SD16semidirect
281. #3167D43semidirect
311. #498C2×D43semidirect
312. #492C2×D43semidirect
313. #487C2×D43semidirect
314. #486C2×D43semidirect
335. C43#18664semidirect

Maximal subgroups

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

subgroupindex
#191483962
#191459112
#191440552
#191338552
#191337992
#191336952
#191336642
#191332852
#191330512
C2×#145826282
C43×#31672
#1866443