Finite Group Databasebeta

← #25253565

Subgroups — #25253565

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#19146942C211yesmaximal, characteristic, complemented
2#19146281C211yesmaximal, characteristic, complemented
3#19136834C211yesmaximal, characteristic, complemented
4#19136794C211yesmaximal, characteristic, complemented
5#19136782C211yesmaximal, characteristic, complemented
6#19136699C211yesmaximal, characteristic, complemented
7#19136692C211yesmaximal, characteristic, complemented
8#19136651C211yesmaximal, characteristic, complemented
9#19136519C211yesmaximal, characteristic, complemented
10#19136508C211yesmaximal, characteristic, complemented
11#19136469C211yesmaximal, characteristic, complemented
12#19136419C211yesmaximal, characteristic, complemented
13#19136304C211yesmaximal, characteristic, complemented
14#357×D43C211yesmaximal, characteristic, complemented
15C43×#2226C211yesmaximal, characteristic, complemented
16C2×#13063344C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18#14583552—21no—
19#14583544—21no—
20C2×#13063270C2211yescharacteristic, complemented
21C2×D688C2211yescharacteristic
22C2×#13063266C2211yescharacteristic
23C2×#13063264C2211yescharacteristic, complemented
24C2×C16×D43C2211yescharacteristic
25#14583283C2211yescharacteristic
26#14583214—21no—
27#14583214—21no—
28#14583176—21no—
29#14583141C2211yescharacteristic
30#14583136C2211yescharacteristic
31#14583136C2211yescharacteristic
32#14583136C2211yescharacteristic, complemented
33#14583114—21no—
34#14583051—21no—
35#14583045—21no—
36C4×D344C2211yescharacteristic, complemented
37C8×D172C2211yescharacteristic
38#107×D43C2211yescharacteristic
39#107×D43C2211yescharacteristic, complemented
40#14582726C2211yescharacteristic, complemented
41#14582704C2211yescharacteristic, complemented
42#14582702C2211yescharacteristic, complemented
43#14582702C2211yescharacteristic, complemented
44#14582701C2211yescharacteristic
45#14582700C2211yescharacteristic
46#14582699C2211yescharacteristic
47#14582699C2211yescharacteristic
48#14582699C2211yescharacteristic, complemented
49(C2×D43)⋊C16C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic, complemented
51#14582675C2211yescharacteristic, complemented
52C43×#500C2211yescharacteristic, complemented
53C4×D8×C43C2211yescharacteristic
54C43×#367C2211yescharacteristic, complemented
55C43×#367C2211yescharacteristic, complemented
56C43×C4⋊C16C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×#10621902—41no—
60C2×#10621900—21no—
61C2×D4×D43—21no—
62#13063344—22no—
63#13063344—41no—
64C2×Dic172C2311yescharacteristic
65C2×#10621873—21no—
66C2×#10621883—21no—
67C2×D344C2311yescharacteristic
68C2×D344C2311yescharacteristic
69C2×#10621882—21no—
70D8×D43—22no—
71D8×D43—41no—
72C2×C8×D43C2311yescharacteristic
73C2×C8×D43C2311yescharacteristic
74#13063313—21no—
75#13063310—41no—
76#13063310—41no—
77#13063309—41no—
78#13063305—21no—
79#13063301—41no—
80#13063300—21no—
81#13063300—21no—
82#13063300—21no—
83#13063299—41no—
84#13063295—41no—
85C4×D172—21no—
86C4×D172D411yescharacteristic
87C4⋊C4×D43—21no—
88C4⋊C4×D43—21no—
89C2×(C2×D43)⋊C4—41no—
90#13063270—41no—
91D688—41no—
92#13063266—22no—
93#13063264—41no—
94C2×C43⋊C16C2311yescharacteristic
95C2×C43⋊C16C2311yescharacteristic
96C16×D43—41no—
97#13063259C2311yescharacteristic
98#13063258—21no—
99#13063258—21no—
100C4⋊(C43⋊C8)D411yescharacteristic
101#13063248—21no—
102#13063247—21no—
103#13063245—21no—
104#13063245—21no—
105#13063245—21no—
106(C2×D43)⋊C8D411yescharacteristic
107(C2×D43)⋊C8D411yescharacteristic
108C2×D8×C43C2311yescharacteristic
109C4⋊Q8×C43—21no—
110C4×D4×C43—21no—
111C2×C16×C43C2311yescharacteristic
112C2×C16×C43C2311yescharacteristic
113#107×C43—21no—
114#107×C43C2311yescharacteristic
115#107×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#102×C43—21no—
118C4×C8×C43C2311yescharacteristic
119C23×D43—41no—
120C2×Q8×C43—41no—
121C2×D4×C43—21no—
122C22×C4×C43—41no—
123C2×C22⋊D43—41no—
124C2×C22⋊D43—41no—
125C22×Dic43—41no—
126#10621902—84no—
127#10621900—42no—
128#10621900—81no—
129D4×D43—42no—
130D4×D43—81no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—41no—
134C2×D172—41no—
135C2×D172—41no—
136C2×D172D811yescharacteristic
137C2×C4×D43—41no—
138C2×C4×D43—41no—
139C2×C4×D43—41no—
140C2×C4×D43C2×D411yescharacteristic
141C2×C4×D43C2×D411yescharacteristic
142C2×Dic86—21no—
143D8×C43—21no—
144D8×C43#4112yescomplemented
145C2×C8×C43C2×D411yescharacteristic
146C2×C8×C43C2411yescharacteristic
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C42×C43C2×D411yescharacteristic
153#10621883—42no—
154#10621882—42no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4D811yescharacteristic
163(C2×D43)⋊C4D811yescharacteristic
164C4⋊Dic43—21no—
165C4⋊Dic43—41no—
166C4⋊Dic43D811yescharacteristic
167Dic43⋊C4—41no—
168Dic43⋊C4—41no—
169C2×C43⋊C8C2×D411yescharacteristic
170C2×C43⋊C8C2×D411yescharacteristic
171Dic172—21no—
172Dic172—21no—
173D344—21no—
174D344—21no—
175D344—21no—
176D344—21no—
177#10621873—81no—
178C8×D43—21no—
179C8×D43—21no—
180C8×D43—21no—
181C8×D43—21no—
182C16×C43—21no—
183C16×C43—21no—
184C43⋊C16—21no—
185C43⋊C16—21no—
186C23×C43—41no—
187C22×D43—41no—
188C22×D43—41no—
189C22×D43—82no—
190C22×D43—82no—
191C22×D43—161no—
192C22×D43C2×D811yescharacteristic
193C22×D43C2×D811yescharacteristic
194Q8×C43—82no—
195D4×C43—22no—
196D4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—161no—
201C2×C4×C43C2×D811yescharacteristic
202C2×C4×C43C2×D811yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C22⋊D43—82no—
205C22⋊D43—82no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—82no—
209C2×Dic43C2×D811yescharacteristic
210C2×Dic43C2×D811yescharacteristic
211D172—22no—
212D172—41no—
213D172—41no—
214D172—41no—
215D172—41no—
216D172—82no—
217D172—82no—
218D172—161no—
219C4×D43—21no—
220C4×D43—21no—
221C4×D43—21no—
222C4×D43—21no—
223C4×D43—82no—
224C4×D43—82no—
225C4×D43—82no—
226Dic86—41no—
227Dic86—41no—
228C8×C43—21no—
229C8×C43C2×#4111yescharacteristic
230C8×C43H(5,𝔽2)11yescharacteristic
231C43⋊C8—21no—
232C43⋊C8—21no—
233#33873—431nomaximal, Sylow
234C22×C43—42no—
235C22×C43—81no—
236C22×C43—81no—
237C22×C43C22×D811yescharacteristic
238C2×D43—21no—
239C2×D43—21no—
240C2×D43—21no—
241C2×D43—21no—
242C2×D43—21no—
243C2×D43—81no—
244C2×D43—81no—
245C2×D43—81no—
246C2×D43—81no—
247C2×D43—81no—
248C2×D43—81no—
249C2×D43—164no—
250C2×D43#50912yes—
251C4×C43—21no—
252C4×C43—21no—
253C4×C43—81no—
254C4×C43—81no—
255C4×C43—81no—
256C4×C43#54611yescharacteristic
257C4×C43#57711yescharacteristic
258Dic43—21no—
259Dic43—21no—
260Dic43—81no—
261Dic43—81no—
262#3334—431no—
263#3280—431no—
264#2243—431no—
265#2235—431no—
266#2233—431no—
267#2226D4311yescharacteristic, complemented
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—82no—
278C2×C43#329411yescharacteristic
279C2×C43C2×#50911yescharacteristic
280C2×C43#341611yescharacteristic
281D43—22no—
282D43—41no—
283D43—161no—
284D43—161no—
285C2×#135—431no—
286C22×D8—431no—
287#547—861no—
288#546—861no—
289C2×SD32—431no—
290C2×D16—431no—
291C2×D16—431no—
292C2×M32—431no—
293C22×C16—431no—
294#500C2×D4311yescharacteristic, complemented
295#495—431no—
296#480—861no—
297#480—861no—
298#474—861no—
299#467—431no—
300#466—431no—
301#466—431no—
302#466—431no—
303#463—861no—
304#450—861no—
305#449—861no—
306C4×D8—431no—
307C4×D8C2×D4311yescharacteristic
308C8×D4—431no—
309C2×#107—431no—
310C2×#107—431no—
311#367—431no—
312#367C2×D4311yescharacteristic, complemented
313#367C2×D4311yescharacteristic, complemented
314C4⋊C16C2×D4311yescharacteristic, complemented
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#357C2×D4311yescharacteristic
324#357C2×D4311yescharacteristic
325C22⋊C16—431no—
326C22⋊C16—431no—
327#346—431no—
328C43#3387311yescharacteristic, complemented, Sylow
329C2×#41—861no—
330C2×#41—1721no—
331C22×D4—861no—
332#135—862no—
333#135—1721no—
334C2×Q16—431no—
335C2×SD16—861no—
336C2×SD16—861no—
337C2×D8—431no—
338C2×D8—431no—
339C2×D8—861no—
340C2×D8—862no—
341C2×D8—1721no—
342C2×D8C22×D4311yescharacteristic
343C22×C8—431no—
344C22×C8—431no—
345C4⋊Q8—21no—
346#124—861no—
347#123—1721no—
348#123—1721no—
349#123—1721no—
350C22⋊Q8—861no—
351C22⋊Q8—1721no—
352#121—861no—
353#121—861no—
354#121—861no—
355#121—1721no—
356#120—1721no—
357C4×D4—21no—
358C4×D4—431no—
359C4×D4—861no—
360C2×C4⋊C4—861no—
361C2×C4⋊C4—861no—
362C2×C22⋊C4—1721no—
363SD32—1721no—
364D16—862no—
365D16—1721no—
366M32—1721no—
367C2×C16—431no—
368C2×C16—431no—
369C2×C16—1721no—
370C2×C16C22×D4311yescharacteristic
371C2×C16C22×D4311yescharacteristic
372#107—21no—
373#107—431no—
374#107—861no—
375#107—861no—
376#107C22×D4311yescharacteristic
377#107C22×D4311yescharacteristic
378#107C22×D4311yescharacteristic
379C4⋊C8—431no—
380#103—861no—
381#102—21no—
382#102—861no—
383#102—861no—
384#102—861no—
385#102—861no—
386C22⋊C8—431no—
387C22⋊C8—431no—
388C4×C8C22×D4311yescharacteristic
389C24—1721no—
390#41—3441no—
391#41—3444no—
392#41—1722no—
393C2×Q8—41no—
394C2×Q8—861no—
395C2×D4—21no—
396C2×D4—431no—
397C2×D4—861no—
398C2×D4—861no—
399C2×D4—3441no—
400C2×D4—1721no—
401C2×D4—1721no—
402C2×D4—1721no—
403C2×D4—1721no—
404C2×D4—1722no—
405C2×D4—1721no—
406C22×C4—41no—
407C22×C4—431no—
408C22×C4—431no—
409C22×C4—1721no—
410C22×C4—1721no—
411C22×C4—1721no—
412C22×C4—1721no—
413Q16—861no—
414Q16—861no—
415SD16—3441no—
416SD16—1722no—
417D8—21no—
418D8—861no—
419D8—861no—
420D8—861no—
421D8—861no—
422D8—1722no—
423D8#1062190212yescomplemented
424C2×C8—431no—
425C2×C8—431no—
426C2×C8—861no—
427C2×C8—861no—
428C2×C8—861no—
429C2×C8—861no—
430C2×C8D4×D4311yescharacteristic
431C2×C8C23×D4311yescharacteristic
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—41no—
436C4⋊C4—431no—
437C4⋊C4—861no—
438C4⋊C4—1721no—
439C4⋊C4—1721no—
440C4⋊C4—1721no—
441C22⋊C4—41no—
442C22⋊C4—431no—
443C22⋊C4—431no—
444C22⋊C4—1721no—
445C22⋊C4—1721no—
446C22⋊C4—1721no—
447C22⋊C4—1721no—
448C22⋊C4—1721no—
449C22⋊C4—1721no—
450C22⋊C4—1721no—
451C42D4×D4311yescharacteristic
452C16—21no—
453C16—21no—
454C16—861no—
455C16—861no—
456C23—41no—
457C23—431no—
458C23—431no—
459C23—3442no—
460C23—3442no—
461C23—1721no—
462C23—1721no—
463C23—6881no—
464Q8—82no—
465Q8—1721no—
466Q8—1721no—
467D4—22no—
468D4—41no—
469D4—862no—
470D4—3442no—
471D4—3442no—
472D4—3442no—
473D4—3442no—
474D4—1721no—
475D4—1721no—
476D4—1721no—
477D4—1721no—
478D4—6881no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—161no—
483C2×C4—431no—
484C2×C4—431no—
485C2×C4—861no—
486C2×C4—861no—
487C2×C4—861no—
488C2×C4—861no—
489C2×C4—3442no—
490C2×C4—3442no—
491C2×C4—3442no—
492C2×C4—3442no—
493C2×C4—1721no—
494C2×C4—1721no—
495C2×C4D8×D4311yescharacteristic
496C2×C4D8×D4311yescharacteristic
497C2×C4C2×D4×D4311yescharacteristic
498C8—21no—
499C8—861no—
500C8—861no—
501C8C2×#1062190211yescharacteristic
502C8#1306337111yescharacteristic
503C22—42no—
504C22—81no—
505C22—81no—
506C22—432no—
507C22—861no—
508C22—861no—
509C22—861no—
510C22—861no—
511C22—861no—
512C22—3441no—
513C22—3441no—
514C22—3441no—
515C22—3441no—
516C22—3441no—
517C22—3441no—
518C22—6884no—
519C22C2×D8×D4311yescharacteristic
520C4—21no—
521C4—21no—
522C4—81no—
523C4—81no—
524C4—81no—
525C4—861no—
526C4—861no—
527C4—3441no—
528C4—3441no—
529C4#1458354011yescharacteristic
530C4#1458370811yescharacteristic
531C2—82no—
532C2—862no—
533C2—1721no—
534C2—6881no—
535C2—6881no—
536C2#1914640511yescharacteristic
537C2#509×D4311yescharacteristic
538C2#1914773711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2226C2
socleC22×C43C22×D8
hypercenter#2226D43
hypocenterC43#33873
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
1. #19146942C2semidirect
2. #19146281C2semidirect
3. #19136834C2semidirect
4. #19136794C2semidirect
5. #19136782C2semidirect
6. #19136699C2semidirect
7. #19136692C2semidirect
8. #19136651C2semidirect
9. #19136519C2semidirect
10. #19136508C2semidirect
11. #19136469C2semidirect
12. #19136419C2semidirect
13. #19136304C2semidirect
14. #357×D43C2semidirect
15. C43×#2226C2semidirect
20. C2×#13063270C22semidirect
23. C2×#13063264C22semidirect
32. #14583136C22semidirect
36. C4×D344C22semidirect
39. #107×D43C22semidirect
40. #14582726C22semidirect
41. #14582704C22semidirect
42. #14582702C22semidirect
43. #14582702C22semidirect
48. #14582699C22semidirect
50. (C2×D43)⋊C16C22semidirect
51. #14582675C22semidirect
52. C43×#500C22semidirect
54. C43×#367C22semidirect
55. C43×#367C22semidirect
56. C43×C4⋊C16C22semidirect
144. D8×C43#41semidirect
267. #2226D43semidirect
294. #500C2×D43semidirect
312. #367C2×D43semidirect
313. #367C2×D43semidirect
314. C4⋊C16C2×D43semidirect
328. C43#33873semidirect
423. D8#10621902semidirect

Maximal subgroups

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

subgroupindex
#191469422
#191462812
#191368342
#191367942
#191367822
#191366992
#191366922
#191366512
#191365192
#191365082
#191364692
#191364192
#191363042
#357×D432
C43×#22262
#3387343