Finite Group Databasebeta

← #25196549

Subgroups — #25196549

Order 11008.

612 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145107C211yesmaximal, characteristic, complemented
2C2×#14583014C211yesmaximal, characteristic
3#19135769C212yesmaximal, complemented
4#19135766C212yesmaximal, complemented
5#19135490C212yesmaximal
6#19134717C212yesmaximal, complemented
7#19134649C211yesmaximal, characteristic, complemented
8#19134646C211yesmaximal, characteristic, complemented
9#19134638C211yesmaximal, characteristic, complemented
10#19134476C211yesmaximal, characteristic, complemented
11C43×#1812C211yesmaximal, characteristic, complemented
12C2×#13063345C2211yescharacteristic
13C2×#13063331C2211yescharacteristic
14#14583452C2212yes—
15#14583303—21no—
16#14583300—21no—
17#14583299—21no—
18#14583296—21no—
19#14583014—21no—
20#14583014—21no—
21#14583014—21no—
22#14583014—21no—
23C2×#13063261C2211yescharacteristic
24C2×#13063260C2211yescharacteristic
25#14582937C2211yescharacteristic
26#14582935C2212yes—
27#14582917C2212yes—
28#14582916C2212yes—
29C2×#13063252C2211yescharacteristic
30C2×#13063251C2211yescharacteristic
31#14582872C2212yes—
32#14582855C2212yes—
33C2×C8×Dic43C2211yescharacteristic
34#14582671C2212yes—
35#14582669C2212yes—
36#14582658C2212yes—
37#14582655C2212yes—
38C2×#131×C43C2211yescharacteristic
39C43×#427C2211yescharacteristic
40C43×#427C2211yescharacteristic
41C43×#410C2212yes—
42C43×H(3,ℤ/4)C2212yes—
43C2×#10621898C2311yescharacteristic
44#13063345—21no—
45#13063345—21no—
46#13063345—21no—
47#13063345—21no—
48C2×#10621885Q811yescharacteristic, complemented
49C2×#10621883Q811yescharacteristic, complemented
50C2×#10621884Q811yescharacteristic, complemented
51C2×#10621882Q811yescharacteristic, complemented
52#13063331—21no—
53#13063331—21no—
54#13063331—21no—
55#13063331—21no—
56C2×#10621877C2312yes—
57C2×#10621877C2311yescharacteristic
58C2×#10621872—21no—
59C22×C43⋊C8C2311yescharacteristic
60C2×C8×D43—21no—
61#13063324—22no—
62#13063316—22no—
63#13063302—42no—
64C4×Dic86—42no—
65#13063284C2312yes—
66C2×C4×Dic43C2311yescharacteristic
67#13063261—21no—
68#13063261—21no—
69#13063260—21no—
70#13063260—21no—
71#13063259—21no—
72#13063258—22no—
73#13063257—21no—
74#13063256—22no—
75#13063253—42no—
76#13063252—21no—
77#13063252—21no—
78#13063252—42no—
79#13063251—21no—
80#13063251—21no—
81#13063239—42no—
82#13063236—22no—
83C4×C43⋊C8—22no—
84C8×Dic43D411yescharacteristic
85C8×Dic43D411yescharacteristic
86C8×Dic43D411yescharacteristic
87C8×Dic43D411yescharacteristic
88C2×#41×C43C2311yescharacteristic
89#131×C43—21no—
90#131×C43—21no—
91#131×C43—21no—
92#131×C43—21no—
93C2×M16×C43—21no—
94C2×M16×C43C2311yescharacteristic
95C22×C8×C43—21no—
96C22×C8×C43C2311yescharacteristic
97#117×C43C2312yes—
98#117×C43C2312yes—
99#107×C43—21no—
100#107×C43—21no—
101#106×C43—21no—
102#106×C43—21no—
103#99×C43—42no—
104#41×C43—21no—
105#41×C43—21no—
106#41×C43—21no—
107#41×C43—21no—
108C2×Q8×C43C2×Q811yescharacteristic
109C2×D4×C43—21no—
110C2×D4×C43C2×Q811yescharacteristic
111C22×C4×C43—21no—
112C22×C4×C43C2411yescharacteristic
113C2×C22⋊D43—21no—
114C22×Dic43—21no—
115#10621898—21no—
116#10621898—21no—
117#10621898—21no—
118#10621898—21no—
119C2×D172C2×Q811yescharacteristic
120C2×C4×D43—21no—
121C2×Dic86—42no—
122C2×Dic86C2×Q811yescharacteristic
123M16×C43—21no—
124M16×C43—21no—
125M16×C43—41no—
126M16×C43—41no—
127C2×C8×C43—21no—
128C2×C8×C43—41no—
129C2×C8×C43—41no—
130C2×C8×C43C2×D411yescharacteristic
131C2×C8×C43C2×D411yescharacteristic
132C2×C8×C43#4111yescharacteristic
133C2×C8×C43#4111yescharacteristic
134C2×C8×C43#4111yescharacteristic
135C2×C8×C43#4111yescharacteristic
136C4⋊C4×C43—22no—
137C4⋊C4×C43—22no—
138C22⋊C4×C43—22no—
139C22⋊C4×C43—22no—
140C42×C43—22no—
141C42×C43—22no—
142C22⋊Dic43—22no—
143#10621885—21no—
144#10621885—21no—
145#10621884—21no—
146#10621884—21no—
147#10621883—21no—
148#10621883—21no—
149#10621882—21no—
150#10621882—21no—
151C4⋊Dic43—22no—
152C4⋊Dic43—42no—
153Dic43⋊C4—42no—
154Dic43⋊C4—42no—
155C4×Dic43—21no—
156C4×Dic43—22no—
157C4×Dic43C2×D411yescharacteristic
158C4×Dic43C2×D411yescharacteristic
159#10621877—21no—
160#10621877—22no—
161#10621877—21no—
162#10621877—22no—
163C2×C43⋊C8—22no—
164C2×C43⋊C8—21no—
165C2×C43⋊C8C2×D411yescharacteristic
166C2×C43⋊C8C2×D411yescharacteristic
167C2×C43⋊C8C2×Q811yescharacteristic
168C2×C43⋊C8C2×Q811yescharacteristic
169C2×C43⋊C8#4111yescharacteristic
170C2×C43⋊C8#4111yescharacteristic
171#10621872—41no—
172#10621872—41no—
173C8×D43—41no—
174C8×D43—41no—
175C23×C43—21no—
176C23×C43H(5,𝔽2)11yescharacteristic
177C22×D43—21no—
178Q8×C43—21no—
179Q8×C43—21no—
180D4×C43—21no—
181D4×C43—21no—
182D4×C43—41no—
183D4×C43—41no—
184C2×C4×C43—21no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—42no—
188C2×C4×C43—42no—
189C2×C4×C43C22×D411yescharacteristic
190C2×C4×C43C22×Q811yescharacteristic
191C2×C4×C43C2×#4111yescharacteristic
192C2×C4×C43C2×#4111yescharacteristic
193C2×C4×C43C2×#4111yescharacteristic
194C2×C4×C43H(5,𝔽2)11yescharacteristic
195C22⋊D43—41no—
196C22⋊D43—41no—
197C2×Dic43—21no—
198C2×Dic43—21no—
199C2×Dic43—21no—
200C2×Dic43—42no—
201C2×Dic43—42no—
202D172—21no—
203D172—21no—
204C4×D43—41no—
205C4×D43—41no—
206Dic86—21no—
207Dic86—21no—
208Dic86—84no—
209C8×C43—41no—
210C8×C43#12411yescharacteristic
211C8×C43#12411yescharacteristic
212C8×C43#12411yescharacteristic
213C8×C43#12411yescharacteristic
214C43⋊C8—41no—
215C43⋊C8—42no—
216C43⋊C8C22⋊Q811yescharacteristic
217C43⋊C8C22⋊Q811yescharacteristic
218C43⋊C8C22⋊Q811yescharacteristic
219C43⋊C8C22⋊Q811yescharacteristic
220#29154—431nomaximal, Sylow
221C22×C43—41no—
222C22×C43—41no—
223C22×C43—81no—
224C22×C43#53511yescharacteristic
225C22×C43#55411yescharacteristic
226C22×C43#55511yescharacteristic
227C2×D43—41no—
228C2×D43—81no—
229C4×C43—41no—
230C4×C43—82no—
231C4×C43—82no—
232C4×C43C2×C22⋊Q811yescharacteristic
233C4×C43C2×#12411yescharacteristic
234C4×C43#55411yescharacteristic
235C4×C43#55511yescharacteristic
236Dic43—22no—
237Dic43—41no—
238Dic43—41no—
239Dic43—82no—
240#3160—431no—
241C2×#443—431no—
242#2031—432no—
243#2031—432no—
244#1976—432no—
245#1833—432no—
246#1814—431no—
247#1814—431no—
248#1812—431no—
249#1812D4311yescharacteristic, complemented
250#1772—431no—
251C2×C43—21no—
252C2×C43—21no—
253C2×C43—21no—
254C2×C43—81no—
255C2×C43#256311yescharacteristic
256D43—81no—
257C2×#135—431no—
258C2×#131—431no—
259C2×#131C2×D4311yescharacteristic
260#533—432no—
261#500—861no—
262#499—861no—
263#499—861no—
264#498—861no—
265#443—861no—
266#443—861no—
267#443—861no—
268#443—861no—
269C2×#108—431no—
270C2×#108—431no—
271#427—431no—
272#427—432no—
273#427C2×D4311yescharacteristic
274#427C2×D4311yescharacteristic
275#421—432no—
276#421—432no—
277C2×#104—431no—
278C2×#104—431no—
279#410—432no—
280#410C2×D4312yes—
281#405—432no—
282C2×C4×C8—431no—
283#344—432no—
284#344—432no—
285#339—432no—
286H(3,ℤ/4)—432no—
287H(3,ℤ/4)C2×D4312yes—
288C43#2915411yescharacteristic, complemented, Sylow
289C2×#41—431no—
290C2×#41C22×D4311yescharacteristic
291#135—861no—
292#135—861no—
293#135—861no—
294#135—861no—
295C2×Q16—431no—
296C2×SD16—431no—
297C2×SD16—431no—
298C2×D8—431no—
299#131—21no—
300#131—21no—
301#131—21no—
302#131—21no—
303#131—861no—
304#131—861no—
305#131—861no—
306#131—861no—
307C2×M16—21no—
308C2×M16—431no—
309C2×M16—432no—
310C2×M16—861no—
311C2×M16C22×D4311yescharacteristic
312C22×C8—21no—
313C22×C8—431no—
314C22×C8—861no—
315C22×C8C22×D4311yescharacteristic
316C4⋊Q8—862no—
317#125—862no—
318C22⋊Q8—1722no—
319C4×Q8—1722no—
320#117—432no—
321#117C22×D4312yes—
322#117C22×D4312yes—
323C2×C42—431no—
324#108—861no—
325#108—861no—
326#108—861no—
327#108—861no—
328#107—21no—
329#107—21no—
330#107—862no—
331#107—861no—
332#106—21no—
333#106—21no—
334#106—862no—
335#106—861no—
336#104—861no—
337#104—861no—
338#104—861no—
339#104—861no—
340#104—1722no—
341#104—1722no—
342#99—42no—
343#99—1722no—
344#97—862no—
345C4×C8—431no—
346C4×C8—431no—
347C4×C8—431no—
348C4×C8—431no—
349C4×C8—862no—
350#41—21no—
351#41—21no—
352#41—21no—
353#41—21no—
354#41—861no—
355#41—861no—
356#41—861no—
357#41—861no—
358C2×Q8—431no—
359C2×Q8—1722no—
360C2×Q8Q8×D4311yescharacteristic
361C2×D4—21no—
362C2×D4—431no—
363C2×D4—861no—
364C2×D4Q8×D4311yescharacteristic
365C22×C4—21no—
366C22×C4—861no—
367C22×C4—861no—
368C22×C4C23×D4311yescharacteristic
369Q16—861no—
370Q16—861no—
371SD16—861no—
372SD16—861no—
373SD16—861no—
374SD16—861no—
375D8—861no—
376D8—861no—
377M16—21no—
378M16—21no—
379M16—41no—
380M16—41no—
381M16—861no—
382M16—861no—
383M16—862no—
384M16—862no—
385M16—1721no—
386M16—1721no—
387C2×C8—21no—
388C2×C8—41no—
389C2×C8—41no—
390C2×C8—431no—
391C2×C8—431no—
392C2×C8—431no—
393C2×C8—431no—
394C2×C8—431no—
395C2×C8—431no—
396C2×C8—862no—
397C2×C8—861no—
398C2×C8—1721no—
399C2×C8—1721no—
400C2×C8#1062189811yescharacteristic
401C2×C8#1062189811yescharacteristic
402C2×C8D4×D4311yescharacteristic
403C2×C8D4×D4311yescharacteristic
404C2×C8#1062190011yescharacteristic
405C2×C8#1062190011yescharacteristic
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—862no—
409C4⋊C4—1722no—
410C4⋊C4—1722no—
411C4⋊C4—1722no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—862no—
415C42—22no—
416C42—22no—
417C42—431no—
418C42—431no—
419C42—861no—
420C42—862no—
421C23—21no—
422C23—861no—
423C23#1306337011yescharacteristic
424Q8—21no—
425Q8—21no—
426Q8—861no—
427Q8—861no—
428Q8—3444no—
429D4—21no—
430D4—21no—
431D4—41no—
432D4—41no—
433D4—861no—
434D4—861no—
435D4—1721no—
436D4—1721no—
437C2×C4—21no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—861no—
443C2×C4—861no—
444C2×C4—861no—
445C2×C4—1722no—
446C2×C4—1722no—
447C2×C4—1721no—
448C2×C4—1721no—
449C2×C4C2×D4×D4311yescharacteristic
450C2×C4C2×Q8×D4311yescharacteristic
451C2×C4#41×D4311yescharacteristic
452C2×C4C2×#1062190011yescharacteristic
453C2×C4C2×#1062189811yescharacteristic
454C2×C4#1306337111yescharacteristic
455C8—41no—
456C8—431no—
457C8—431no—
458C8—431no—
459C8—431no—
460C8—1722no—
461C8—1721no—
462C8#1306331111yescharacteristic
463C8#1306331111yescharacteristic
464C8#1306331111yescharacteristic
465C8#1306331111yescharacteristic
466C22—41no—
467C22—41no—
468C22—81no—
469C22—3441no—
470C22—1721no—
471C22#1458346511yescharacteristic
472C22#1458360411yescharacteristic
473C22#1458361311yescharacteristic
474C4—41no—
475C4—82no—
476C4—82no—
477C4—862no—
478C4—3442no—
479C4—1721no—
480C4—1721no—
481C4C22⋊Q8×D4311yescharacteristic
482C4C2×#1306331111yescharacteristic
483C4#1458360711yescharacteristic
484C4#1458361211yescharacteristic
485C2—21no—
486C2—21no—
487C2—21no—
488C2—81no—
489C2—3441no—
490C2#1913976511yescharacteristic
subgroupG/H
centerC4#14583612
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1812C2
socleC2×C43#2563
prime radicalC2×#13063345C22
hypercenter#1812D43
hypocenterC43#29154
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1812

Complements

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

NH ≅ G/Ntype
1. #19145107C2semidirect
3. #19135769C2semidirect
4. #19135766C2semidirect
6. #19134717C2semidirect
7. #19134649C2semidirect
8. #19134646C2semidirect
9. #19134638C2semidirect
10. #19134476C2semidirect
11. C43×#1812C2semidirect
48. C2×#10621885Q8semidirect
49. C2×#10621883Q8semidirect
50. C2×#10621884Q8semidirect
51. C2×#10621882Q8semidirect
249. #1812D43semidirect
288. C43#29154semidirect

Maximal subgroups

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

subgroupindex
#191451072
C2×#145830142
#191357692
#191357662
#191354902
#191347172
#191346492
#191346462
#191346382
#191344762
C43×#18122
#2915443