Finite Group Databasebeta

← #25251758

Subgroups — #25251758

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145238C211yesmaximal, characteristic, complemented
2#19143447C211yesmaximal, characteristic, complemented
3#19136787C211yesmaximal, characteristic, complemented
4#19136783C211yesmaximal, characteristic, complemented
5#19136754C211yesmaximal, characteristic, complemented
6#19136750C211yesmaximal, characteristic, complemented
7#19136628C211yesmaximal, characteristic, complemented
8#19136628C211yesmaximal, characteristic, complemented
9#19136507C211yesmaximal, characteristic, complemented
10#19136471C211yesmaximal, characteristic, complemented
11#19136468C211yesmaximal, characteristic, complemented
12D16×Dic43C211yesmaximal, characteristic, complemented
13#19136439C211yesmaximal, characteristic, complemented
14#19136399C211yesmaximal, characteristic, complemented
15C43×#2184C211yesmaximal, characteristic, complemented
16#14583502—21no—
17#14583374—21no—
18C2×#13063266C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20#14583300C2211yescharacteristic, complemented
21#14583274C2211yescharacteristic, complemented
22#14583262—21no—
23#14583150—21no—
24#14583135C2211yescharacteristic
25#14583011—21no—
26#14583011—21no—
27#14583008—21no—
28D8×Dic43C2211yescharacteristic
29D8×Dic43C2211yescharacteristic
30D8×Dic43C2211yescharacteristic
31D8×Dic43C2211yescharacteristic
32D8×Dic43C2211yescharacteristic, complemented
33#14582981C2211yescharacteristic, complemented
34#14582937C2211yescharacteristic
35#14582904—21no—
36#14582854C2211yescharacteristic
37#14582727C2211yescharacteristic, complemented
38#14582726C2211yescharacteristic, complemented
39#14582725C2211yescharacteristic, complemented
40#14582724C2211yescharacteristic, complemented
41Dic43⋊C16C2211yescharacteristic, complemented
42Dic43⋊C16C2211yescharacteristic, complemented
43#14582701C2211yescharacteristic, complemented
44#14582701C2211yescharacteristic, complemented
45#14582700C2211yescharacteristic
46#14582700C2211yescharacteristic
47#14582700C2211yescharacteristic, complemented
48#14582700C2211yescharacteristic, complemented
49C22⋊(C43⋊C16)C2211yescharacteristic
50#14582674C2211yescharacteristic, complemented
51C16×Dic43C2211yescharacteristic, complemented
52C22×D8×C43C2211yescharacteristic
53C2×D16×C43C2211yescharacteristic
54C2×D16×C43C2211yescharacteristic
55C43×#466C2211yescharacteristic
56C43×#357C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×C22⋊C16C2211yescharacteristic
59C2×D344C2311yescharacteristic
60C2×#10621882—21no—
61C2×#10621877D411yescharacteristic
62#13063321—21no—
63#13063316—21no—
64#13063309—41no—
65#13063307—41no—
66#13063299—21no—
67#13063297—41no—
68#13063296—41no—
69D4×Dic43—21no—
70D4×Dic43—21no—
71D4×Dic43—21no—
72D4×Dic43—21no—
73D4×Dic43—21no—
74D4×Dic43—41no—
75D4×Dic43—41no—
76#13063287—21no—
77#13063284—21no—
78#13063284D411yescharacteristic
79C2×C22⋊Dic43—41no—
80C2×C22⋊Dic43—41no—
81#13063266—22no—
82#13063266—22no—
83C2×C43⋊C16C2311yescharacteristic
84C2×C43⋊C16C2311yescharacteristic
85#13063259C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063257—21no—
89#13063256—21no—
90#13063247—21no—
91#13063246—21no—
92#13063246—21no—
93#13063246—21no—
94#13063246—21no—
95#13063246—21no—
96#13063245—21no—
97#13063235D411yescharacteristic
98#13063235D411yescharacteristic
99C8×Dic43C2311yescharacteristic
100C8×Dic43C2311yescharacteristic
101C22×D4×C43—21no—
102C2×D8×C43—22no—
103C2×D8×C43—22no—
104C2×D8×C43—21no—
105C2×D8×C43C2311yescharacteristic
106C2×D8×C43C2311yescharacteristic
107C2×D8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109#121×C43—21no—
110D16×C43—22no—
111D16×C43—22no—
112C2×C16×C43C2311yescharacteristic
113C2×C16×C43C2311yescharacteristic
114#107×C43C2311yescharacteristic
115#102×C43—21no—
116C24×C43—41no—
117C2×D4×C43—24no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—42no—
122C2×D4×C43—41no—
123C2×D4×C43—41no—
124C22×C4×C43C2×D411yescharacteristic
125C2×C22⋊D43—41no—
126C2×C22⋊D43—41no—
127C2×C22⋊D43—41no—
128C22×Dic43—41no—
129C22×Dic43—41no—
130C22×Dic43—41no—
131C22×Dic43—41no—
132C22×Dic43—41no—
133C2×D172—21no—
134C2×C4×D43—41no—
135D8×C43—24no—
136D8×C43—21no—
137D8×C43—21no—
138D8×C43—21no—
139D8×C43—21no—
140D8×C43#4112yes—
141D8×C43#4112yes—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43C2×D411yescharacteristic
145C2×C8×C43C2411yescharacteristic
146C4⋊C4×C43—21no—
147C22⋊C4×C43—41no—
148C22⋊Dic43—41no—
149C22⋊Dic43—41no—
150C22⋊Dic43—41no—
151C22⋊Dic43—41no—
152C22⋊Dic43—41no—
153C22⋊Dic43—41no—
154C22⋊Dic43D811yescharacteristic
155C22⋊Dic43D811yescharacteristic
156#10621882—42no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161C4⋊Dic43—21no—
162C4⋊Dic43—41no—
163C4⋊Dic43D811yescharacteristic
164C4⋊Dic43D811yescharacteristic
165Dic43⋊C4—41no—
166C4×Dic43—41no—
167C4×Dic43C2×D411yescharacteristic
168C4×Dic43C2×D411yescharacteristic
169#10621877—41no—
170C2×C43⋊C8C2×D411yescharacteristic
171C2×C43⋊C8C2×D411yescharacteristic
172D344—21no—
173D344—21no—
174C16×C43—21no—
175C16×C43—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43—44no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—161no—
183C23×C43—161no—
184C23×C43C2×D811yescharacteristic
185C22×D43—41no—
186D4×C43—22no—
187D4×C43—22no—
188D4×C43—44no—
189D4×C43—41no—
190D4×C43—41no—
191D4×C43—41no—
192D4×C43—41no—
193D4×C43—161no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—41no—
197C2×C4×C43C2×D811yescharacteristic
198C2×C4×C43C22×D411yescharacteristic
199C22⋊D43—161no—
200C22⋊D43—161no—
201C22⋊D43—161no—
202C2×Dic43—41no—
203C2×Dic43—41no—
204C2×Dic43—41no—
205C2×Dic43—161no—
206C2×Dic43—161no—
207C2×Dic43—161no—
208C2×Dic43—161no—
209C2×Dic43—161no—
210C2×Dic43C2×D811yescharacteristic
211C2×Dic43C2×D811yescharacteristic
212C2×Dic43C2×D811yescharacteristic
213C2×Dic43C2×D811yescharacteristic
214D172—41no—
215D172—41no—
216C4×D43—161no—
217C8×C43—21no—
218C8×C43C2×#4111yescharacteristic
219C8×C43C2×#4111yescharacteristic
220C43⋊C8—21no—
221C43⋊C8—21no—
222#33682—431nomaximal, Sylow
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—42no—
227C22×C43—42no—
228C22×C43—81no—
229C22×C43—81no—
230C22×C43—81no—
231C22×C43—81no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43—164no—
236C22×C43C22×D811yescharacteristic
237C2×D43—81no—
238C2×D43—81no—
239C2×D43—81no—
240C4×C43—21no—
241C4×C43—81no—
242C4×C43#52511yescharacteristic
243C4×C43#57511yescharacteristic
244Dic43—21no—
245Dic43—21no—
246Dic43—21no—
247Dic43—21no—
248Dic43—81no—
249Dic43—81no—
250Dic43—81no—
251#3176—431no—
252#2948—431no—
253#2234—431no—
254#2234—431no—
255#2228—431no—
256#2228—431no—
257#2206—431no—
258#2206—431no—
259#2184—431no—
260#2184D4311yescharacteristic, complemented
261#2177—431no—
262#2177—431no—
263C4×D16—431no—
264C4×D16—431no—
265#2164—431no—
266C2×C43—41no—
267C2×C43—82no—
268C2×C43—82no—
269C2×C43—161no—
270C2×C43#310011yescharacteristic
271C2×C43#341511yescharacteristic
272C2×C43#341511yescharacteristic
273D43—161no—
274C22×D8C2×D4311yescharacteristic
275#540—861no—
276#518—861no—
277C2×D16—431no—
278C2×D16—431no—
279C2×D16C2×D4311yescharacteristic
280C2×D16C2×D4311yescharacteristic
281#499—431no—
282#493—431no—
283#490—861no—
284#469—861no—
285#466—431no—
286#466C2×D4311yescharacteristic
287#442—861no—
288#442—861no—
289#442—861no—
290C4×D8—431no—
291C4×D8—431no—
292C4×D8—431no—
293C4×D8—431no—
294C4×D8—431no—
295C4×D8—431no—
296#427—431no—
297#418—861no—
298#405—431no—
299#367—431no—
300#367—431no—
301#366—431no—
302#366—431no—
303C4⋊C16—431no—
304C4⋊C16—431no—
305#357—431no—
306#357—431no—
307#357—431no—
308#357—431no—
309#357—431no—
310#357—431no—
311#357C2×D4311yescharacteristic
312#357C2×D4311yescharacteristic
313C22⋊C16—431no—
314C22⋊C16C2×D4311yescharacteristic
315#346—431no—
316C4×C16—431no—
317C43#3368211yescharacteristic, complemented, Sylow
318C22×D4—21no—
319C2×D8—22no—
320C2×D8—22no—
321C2×D8—21no—
322C2×D8—431no—
323C2×D8—861no—
324C2×D8C22×D4311yescharacteristic
325C2×D8C22×D4311yescharacteristic
326C2×D8C22×D4311yescharacteristic
327C2×M16—431no—
328C22×C8C22×D4311yescharacteristic
329#127—861no—
330#125—861no—
331#123—1721no—
332#123—1721no—
333#121—21no—
334#121—861no—
335#121—1721no—
336#121—1721no—
337C4×D4—861no—
338C4×D4—861no—
339C4×D4—861no—
340C4×D4—861no—
341C4×D4—861no—
342C4×D4—861no—
343C4×D4—1721no—
344C4×D4—1721no—
345#117—431no—
346#117—861no—
347C2×C22⋊C4—1721no—
348C2×C22⋊C4—1721no—
349D16—22no—
350D16—22no—
351D16—862no—
352D16—862no—
353C2×C16—431no—
354C2×C16—431no—
355C2×C16C22×D4311yescharacteristic
356C2×C16C22×D4311yescharacteristic
357#107—431no—
358#107—431no—
359#107—431no—
360#107C22×D4311yescharacteristic
361#106—861no—
362#106—861no—
363#102—21no—
364#102—861no—
365#102—861no—
366#102—861no—
367#102—861no—
368#102—861no—
369#102—861no—
370#102—861no—
371#97—431no—
372#97—431no—
373C4×C8—431no—
374C4×C8—431no—
375C24—41no—
376C2×D4—24no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—42no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—861no—
384C2×D4—1721no—
385C2×D4—1721no—
386C2×D4—1721no—
387C22×C4—1721no—
388C22×C4—1721no—
389C22×C4—1721no—
390C22×C4—1721no—
391C22×C4—1721no—
392C22×C4—1721no—
393C22×C4D4×D4311yescharacteristic
394D8—24no—
395D8—21no—
396D8—21no—
397D8—21no—
398D8—21no—
399D8—861no—
400D8—861no—
401D8—1722no—
402D8#1062190012yes—
403D8#1062190012yes—
404M16—1721no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—431no—
408C2×C8—431no—
409C2×C8D4×D4311yescharacteristic
410C2×C8C23×D4311yescharacteristic
411C4⋊C4—21no—
412C4⋊C4—431no—
413C4⋊C4—431no—
414C4⋊C4—861no—
415C4⋊C4—861no—
416C4⋊C4—861no—
417C4⋊C4—1721no—
418C4⋊C4—1721no—
419C22⋊C4—41no—
420C22⋊C4—431no—
421C22⋊C4—431no—
422C22⋊C4—1721no—
423C22⋊C4—1721no—
424C22⋊C4—1721no—
425C22⋊C4—1721no—
426C22⋊C4—1721no—
427C22⋊C4—1721no—
428C22⋊C4—1721no—
429C22⋊C4—1721no—
430C42—431no—
431C42—431no—
432C42—1721no—
433C16—21no—
434C16—21no—
435C16—861no—
436C16—861no—
437C23—44no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—161no—
442C23—161no—
443C23—1721no—
444C23D8×D4311yescharacteristic
445D4—22no—
446D4—22no—
447D4—44no—
448D4—41no—
449D4—41no—
450D4—41no—
451D4—41no—
452D4—161no—
453D4—1721no—
454D4—1721no—
455D4—6881no—
456D4—6881no—
457D4—6881no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—41no—
461C2×C4—431no—
462C2×C4—431no—
463C2×C4—431no—
464C2×C4—431no—
465C2×C4—1721no—
466C2×C4—1721no—
467C2×C4—1721no—
468C2×C4—6881no—
469C2×C4—6881no—
470C2×C4—6881no—
471C2×C4—6881no—
472C2×C4—6881no—
473C2×C4—6881no—
474C2×C4D8×D4311yescharacteristic
475C2×C4C2×D4×D4311yescharacteristic
476C8—21no—
477C8—861no—
478C8—861no—
479C8C2×#1062190011yescharacteristic
480C8C2×#1062190011yescharacteristic
481C22—21no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—164no—
494C22—3441no—
495C22—3441no—
496C22—3441no—
497C22C2×D8×D4311yescharacteristic
498C4—21no—
499C4—81no—
500C4—861no—
501C4—861no—
502C4—861no—
503C4—861no—
504C4—3441no—
505C4—3441no—
506C4—3441no—
507C4#1458340511yescharacteristic
508C4#1458369511yescharacteristic
509C2—41no—
510C2—82no—
511C2—82no—
512C2—161no—
513C2—6881no—
514C2#1914459011yescharacteristic
515C2#1914773211yescharacteristic
516C2#1914773511yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2184C2
socleC22×C43C22×D8
hypercenter#2184D43
hypocenterC43#33682
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2184

Complements

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

NH ≅ G/Ntype
1. #19145238C2semidirect
2. #19143447C2semidirect
3. #19136787C2semidirect
4. #19136783C2semidirect
5. #19136754C2semidirect
6. #19136750C2semidirect
7. #19136628C2semidirect
8. #19136628C2semidirect
9. #19136507C2semidirect
10. #19136471C2semidirect
11. #19136468C2semidirect
12. D16×Dic43C2semidirect
13. #19136439C2semidirect
14. #19136399C2semidirect
15. C43×#2184C2semidirect
20. #14583300C22semidirect
21. #14583274C22semidirect
32. D8×Dic43C22semidirect
33. #14582981C22semidirect
37. #14582727C22semidirect
38. #14582726C22semidirect
39. #14582725C22semidirect
40. #14582724C22semidirect
41. Dic43⋊C16C22semidirect
42. Dic43⋊C16C22semidirect
43. #14582701C22semidirect
44. #14582701C22semidirect
47. #14582700C22semidirect
48. #14582700C22semidirect
50. #14582674C22semidirect
51. C16×Dic43C22semidirect
260. #2184D43semidirect
317. C43#33682semidirect

Maximal subgroups

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

subgroupindex
#191452382
#191434472
#191367872
#191367832
#191367542
#191367502
#191366282
#191365072
#191364712
#191364682
D16×Dic432
#191364392
#191363992
C43×#21842
#3368243