Finite Group Databasebeta

← #25253568

Subgroups — #25253568

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146943C211yesmaximal, characteristic, complemented
2#19136831C211yesmaximal, characteristic, complemented
3#19136790C211yesmaximal, characteristic, complemented
4#19136778C211yesmaximal, characteristic, complemented
5#19136742C211yesmaximal, characteristic, complemented
6#19136696C211yesmaximal, characteristic, complemented
7#19136693C211yesmaximal, characteristic, complemented
8#19136647C211yesmaximal, characteristic, complemented
9#19136518C211yesmaximal, characteristic, complemented
10#19136507C211yesmaximal, characteristic, complemented
11#19136469C211yesmaximal, characteristic, complemented
12#19136421C211yesmaximal, characteristic, complemented
13#19136307C211yesmaximal, characteristic, complemented
14C2×#14582700C211yesmaximal, characteristic, complemented
15C43×#3280C211yesmaximal, characteristic, complemented
16#14583553—21no—
17C2×#13063268C2211yescharacteristic, complemented
18C2×#13063266C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20C2×#13063265C2211yescharacteristic, complemented
21C22×C43⋊C16C2211yescharacteristic
22#14583304C2211yescharacteristic, complemented
23#14583213—21no—
24#14583213—21no—
25#14583180—21no—
26#14583135C2211yescharacteristic
27#14583135C2211yescharacteristic, complemented
28C4×D344C2211yescharacteristic, complemented
29C2×#13063259C2211yescharacteristic
30C2×#13063259C2211yescharacteristic, complemented
31#14582726C2211yescharacteristic, complemented
32#14582726C2211yescharacteristic, complemented
33#14582726C2211yescharacteristic, complemented
34C4⋊(C43⋊C16)C2211yescharacteristic, complemented
35#14582703C2211yescharacteristic, complemented
36#14582703C2211yescharacteristic, complemented
37#14582703C2211yescharacteristic, complemented
38#14582700C2211yescharacteristic
39#14582700C2211yescharacteristic
40#14582700C2211yescharacteristic
41#14582700C2211yescharacteristic
42#14582700C2211yescharacteristic
43#14582700C2211yescharacteristic
44#14582699C2211yescharacteristic, complemented
45C22⋊(C43⋊C16)C2211yescharacteristic
46C22⋊(C43⋊C16)C2211yescharacteristic, complemented
47#14582675C2211yescharacteristic, complemented
48C2×#135×C43C2211yescharacteristic
49C22×D8×C43C2211yescharacteristic
50C43×#546—21no—
51C43×#495C2211yescharacteristic
52C43×#467C2211yescharacteristic
53C43×#466C2211yescharacteristic
54C43×#463—21no—
55C43×#450—21no—
56C43×#449—21no—
57C4×D8×C43C2211yescharacteristic
58C8×D4×C43C2211yescharacteristic
59C2×#10621900—41no—
60C2×D344C2311yescharacteristic
61#13063325—21no—
62#13063309—41no—
63#13063309—41no—
64#13063305—41no—
65#13063299—21no—
66#13063299—21no—
67C4×D172—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70#13063268—41no—
71#13063266—22no—
72#13063266—41no—
73#13063265—41no—
74C2×C43⋊C16—41no—
75C2×C43⋊C16C2311yescharacteristic
76C2×C43⋊C16C2311yescharacteristic
77C2×C43⋊C16C2311yescharacteristic
78C2×C43⋊C16C2311yescharacteristic
79#13063259—21no—
80#13063259—21no—
81#13063259—21no—
82#13063259C2311yescharacteristic
83#13063259C2311yescharacteristic
84#13063259C2311yescharacteristic
85#13063247—21no—
86#13063247—21no—
87#13063247—21no—
88C2×#41×C43—21no—
89C22×D4×C43—21no—
90#135×C43—22no—
91#135×C43—41no—
92C2×Q16×C43C2311yescharacteristic
93C2×SD16×C43—21no—
94C2×SD16×C43—21no—
95C2×D8×C43—22no—
96C2×D8×C43—21no—
97C2×D8×C43—41no—
98C2×D8×C43C2311yescharacteristic
99C2×D8×C43C2311yescharacteristic
100C22×C8×C43C2311yescharacteristic
101C22×C8×C43C2311yescharacteristic
102#124×C43—21no—
103#123×C43—41no—
104C22⋊Q8×C43—21no—
105#121×C43—21no—
106#121×C43—41no—
107#120×C43—41no—
108C4×D4×C43—21no—
109C4×D4×C43D411yescharacteristic
110C2×C22⋊C4×C43—41no—
111#107×C43C2311yescharacteristic
112C4⋊C8×C43D411yescharacteristic
113#103×C43—21no—
114#102×C43—21no—
115#102×C43—21no—
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119C24×C43—41no—
120#41×C43—42no—
121#41×C43—81no—
122C2×Q8×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—41no—
126C2×D4×C43—41no—
127C2×D4×C43—41no—
128C2×D4×C43—42no—
129C2×D4×C43—81no—
130C2×D4×C43D811yescharacteristic
131C22×C4×C43—41no—
132C22×C4×C43—41no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C2×C22⋊D43—41no—
136C2×C22⋊D43—41no—
137C22×Dic43—41no—
138C22×Dic43—41no—
139#10621900—84no—
140C2×D172—21no—
141C2×C4×D43—41no—
142C2×Dic86—41no—
143Q16×C43—21no—
144Q16×C43—21no—
145SD16×C43—42no—
146SD16×C43—81no—
147D8×C43—21no—
148D8×C43—21no—
149D8×C43—21no—
150D8×C43—42no—
151D8×C43#4112yescomplemented
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43C2×D411yescharacteristic
157C2×C8×C43C2×D411yescharacteristic
158C2×C8×C43C2×D411yescharacteristic
159C2×C8×C43C2411yescharacteristic
160C4⋊C4×C43—21no—
161C4⋊C4×C43—41no—
162C4⋊C4×C43D811yescharacteristic
163C22⋊C4×C43—41no—
164C22⋊C4×C43—41no—
165C22⋊C4×C43—41no—
166C22⋊C4×C43—41no—
167C22⋊C4×C43—41no—
168C22⋊C4×C43D811yescharacteristic
169C22⋊C4×C43D811yescharacteristic
170C42×C43C2×D411yescharacteristic
171(C2×D43)⋊C4—41no—
172(C2×D43)⋊C4—41no—
173(C2×D43)⋊C4—41no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—41no—
178C4⋊Dic43—41no—
179C4⋊Dic43—41no—
180D344—21no—
181D344—21no—
182C43⋊C16—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C43⋊C16—21no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—82no—
189C23×C43—82no—
190C23×C43—161no—
191C23×C43C2×D811yescharacteristic
192C23×C43C2×D811yescharacteristic
193C22×D43—41no—
194Q8×C43—41no—
195Q8×C43—41no—
196D4×C43—22no—
197D4×C43—22no—
198D4×C43—41no—
199D4×C43—41no—
200D4×C43—41no—
201D4×C43—82no—
202D4×C43—82no—
203D4×C43—161no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—82no—
211C2×C4×C43—161no—
212C2×C4×C43C2×D811yescharacteristic
213C2×C4×C43C2×D811yescharacteristic
214C2×C4×C43C2×D811yescharacteristic
215C2×C4×C43C2×D811yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C22⋊D43—82no—
218C22⋊D43—82no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—82no—
223C2×Dic43—82no—
224D172—41no—
225D172—41no—
226C4×D43—82no—
227Dic86—82no—
228C8×C43—21no—
229C8×C43—21no—
230C8×C43—21no—
231C8×C43C2×#4111yescharacteristic
232C8×C43H(5,𝔽2)11yescharacteristic
233#33873—431nomaximal, Sylow
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—21no—
239C22×C43—42no—
240C22×C43—81no—
241C22×C43—81no—
242C22×C43—81no—
243C22×C43—81no—
244C22×C43—81no—
245C22×C43—164no—
246C22×C43#50912yes—
247C22×C43C22×D811yescharacteristic
248C2×D43—81no—
249C2×D43—81no—
250C2×D43—81no—
251C4×C43—21no—
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—81no—
256C4×C43—81no—
257C4×C43#54611yescharacteristic
258C4×C43#57711yescharacteristic
259Dic43—81no—
260Dic43—81no—
261Dic43—81no—
262#3334—431no—
263#3280D4311yescharacteristic, complemented
264#2243—431no—
265#2235—431no—
266#2233—431no—
267#2226—431no—
268#2218—431no—
269#2217—431no—
270#2210—431no—
271#2186—431no—
272#2184—431no—
273#2177—431no—
274#2168—431no—
275#2139—431no—
276C2×#357—431no—
277C2×C43—22no—
278C2×C43—41no—
279C2×C43—82no—
280C2×C43—161no—
281C2×C43#329411yescharacteristic
282C2×C43C2×#50911yescharacteristic
283C2×C43#341611yescharacteristic
284D43—161no—
285C2×#135C2×D4311yescharacteristic
286C22×D8C2×D4311yescharacteristic
287#547—861no—
288#546—21no—
289C2×SD32—431no—
290C2×D16—431no—
291C2×D16—431no—
292C2×M32—431no—
293C22×C16—431no—
294#500—431no—
295#495C2×D4311yescharacteristic
296#480—861no—
297#480—861no—
298#474—861no—
299#467C2×D4311yescharacteristic
300#466—431no—
301#466—431no—
302#466C2×D4311yescharacteristic
303#463—21no—
304#450—21no—
305#449—21no—
306C4×D8—431no—
307C4×D8C2×D4311yescharacteristic
308C8×D4C2×D4311yescharacteristic
309C2×#107—431no—
310C2×#107—431no—
311#367—431no—
312#367—431no—
313#367—431no—
314C4⋊C16—431no—
315#358—431no—
316#358—431no—
317#358—431no—
318#357—431no—
319#357—431no—
320#357—431no—
321#357—431no—
322#357—431no—
323#357—431no—
324#357—431no—
325C22⋊C16—431no—
326C22⋊C16—431no—
327#346—431no—
328C43#3387311yescharacteristic, complemented, Sylow
329C2×#41—21no—
330C2×#41—1721no—
331C22×D4—21no—
332#135—22no—
333#135—41no—
334C2×Q16C22×D4311yescharacteristic
335C2×SD16—21no—
336C2×SD16—21no—
337C2×D8—22no—
338C2×D8—21no—
339C2×D8—41no—
340C2×D8—431no—
341C2×D8C22×D4311yescharacteristic
342C2×D8C22×D4311yescharacteristic
343C22×C8C22×D4311yescharacteristic
344C22×C8C22×D4311yescharacteristic
345C4⋊Q8—861no—
346#124—21no—
347#123—41no—
348#123—1721no—
349#123—1721no—
350C22⋊Q8—21no—
351C22⋊Q8—1721no—
352#121—21no—
353#121—41no—
354#121—861no—
355#121—861no—
356#120—41no—
357C4×D4—21no—
358C4×D4—861no—
359C4×D4C22⋊D4311yescharacteristic
360C2×C4⋊C4—861no—
361C2×C4⋊C4—861no—
362C2×C22⋊C4—41no—
363SD32—1721no—
364D16—862no—
365D16—1721no—
366M32—1721no—
367C2×C16—431no—
368C2×C16—431no—
369C2×C16—431no—
370C2×C16—431no—
371C2×C16—1721no—
372#107—431no—
373#107—431no—
374#107—431no—
375#107—861no—
376#107—861no—
377#107—861no—
378#107C22×D4311yescharacteristic
379C4⋊C8C22⋊D4311yescharacteristic
380#103—21no—
381#102—21no—
382#102—21no—
383#102—861no—
384#102—861no—
385#102—861no—
386C22⋊C8C22⋊D4311yescharacteristic
387C22⋊C8C22⋊D4311yescharacteristic
388C4×C8C22×D4311yescharacteristic
389C24—41no—
390#41—42no—
391#41—81no—
392#41—3444no—
393C2×Q8—21no—
394C2×Q8—1721no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—42no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—81no—
402C2×D4—861no—
403C2×D4—1721no—
404C2×D4—1721no—
405C2×D4#1062188211yescharacteristic
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—1721no—
409C22×C4—1721no—
410C22×C4—1721no—
411C22×C4C2×C22⋊D4311yescharacteristic
412C22×C4C2×C22⋊D4311yescharacteristic
413Q16—21no—
414Q16—21no—
415SD16—42no—
416SD16—81no—
417D8—21no—
418D8—21no—
419D8—21no—
420D8—42no—
421D8—861no—
422D8—861no—
423D8#1062190012yescomplemented
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8C2×C22⋊D4311yescharacteristic
429C2×C8C2×C22⋊D4311yescharacteristic
430C2×C8C2×C22⋊D4311yescharacteristic
431C2×C8C23×D4311yescharacteristic
432C4⋊C4—21no—
433C4⋊C4—41no—
434C4⋊C4—861no—
435C4⋊C4—861no—
436C4⋊C4—861no—
437C4⋊C4—1721no—
438C4⋊C4—1721no—
439C4⋊C4—1721no—
440C4⋊C4#1062188211yescharacteristic
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—1721no—
447C22⋊C4—1721no—
448C22⋊C4—1721no—
449C22⋊C4#1062188211yescharacteristic
450C22⋊C4#1062188211yescharacteristic
451C42C2×C22⋊D4311yescharacteristic
452C16—861no—
453C16—861no—
454C16—861no—
455C16—861no—
456C23—41no—
457C23—41no—
458C23—82no—
459C23—82no—
460C23—161no—
461C23—1721no—
462C23C2×#1062188211yescharacteristic
463C23C2×#1062188211yescharacteristic
464Q8—41no—
465Q8—41no—
466Q8—3442no—
467D4—22no—
468D4—22no—
469D4—41no—
470D4—41no—
471D4—41no—
472D4—82no—
473D4—82no—
474D4—161no—
475D4—3442no—
476D4—3442no—
477D4—1721no—
478D4—1721no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—82no—
486C2×C4—161no—
487C2×C4—3442no—
488C2×C4—3442no—
489C2×C4—3442no—
490C2×C4—1721no—
491C2×C4—1721no—
492C2×C4—1721no—
493C2×C4C2×#1062188211yescharacteristic
494C2×C4C2×#1062188211yescharacteristic
495C2×C4C2×#1062188211yescharacteristic
496C2×C4C2×#1062188211yescharacteristic
497C2×C4C22×C22⋊D4311yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8C2×#1062190011yescharacteristic
502C8#1306337011yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—42no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—164no—
515C22—3441no—
516C22—3441no—
517C22—3441no—
518C22#1458333412yes—
519C22C22×#1062188211yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—3441no—
527C4—3441no—
528C4—3441no—
529C4#1458354311yescharacteristic
530C4#1458371011yescharacteristic
531C2—22no—
532C2—41no—
533C2—82no—
534C2—161no—
535C2—6881no—
536C2#1914640811yescharacteristic
537C2C2×#1458333411yescharacteristic
538C2#1914774211yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3280C2
socleC22×C43C22×D8
hypercenter#3280D43
hypocenterC43#33873
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. #19146943C2semidirect
2. #19136831C2semidirect
3. #19136790C2semidirect
4. #19136778C2semidirect
5. #19136742C2semidirect
6. #19136696C2semidirect
7. #19136693C2semidirect
8. #19136647C2semidirect
9. #19136518C2semidirect
10. #19136507C2semidirect
11. #19136469C2semidirect
12. #19136421C2semidirect
13. #19136307C2semidirect
14. C2×#14582700C2semidirect
15. C43×#3280C2semidirect
17. C2×#13063268C22semidirect
20. C2×#13063265C22semidirect
22. #14583304C22semidirect
27. #14583135C22semidirect
28. C4×D344C22semidirect
30. C2×#13063259C22semidirect
31. #14582726C22semidirect
32. #14582726C22semidirect
33. #14582726C22semidirect
34. C4⋊(C43⋊C16)C22semidirect
35. #14582703C22semidirect
36. #14582703C22semidirect
37. #14582703C22semidirect
44. #14582699C22semidirect
46. C22⋊(C43⋊C16)C22semidirect
47. #14582675C22semidirect
151. D8×C43#41semidirect
263. #3280D43semidirect
328. C43#33873semidirect
423. D8#10621900semidirect

Maximal subgroups

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

subgroupindex
#191469432
#191368312
#191367902
#191367782
#191367422
#191366962
#191366932
#191366472
#191365182
#191365072
#191364692
#191364212
#191363072
C2×#145827002
C43×#32802
#3387343