Finite Group Databasebeta

← #25251710

Subgroups — #25251710

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145237C211yesmaximal, characteristic, complemented
2#19143442C211yesmaximal, characteristic, complemented
3#19136806C211yesmaximal, characteristic, complemented
4#19136788C211yesmaximal, characteristic, complemented
5#19136729C211yesmaximal, characteristic, complemented
6#19136651C211yesmaximal, characteristic, complemented
7#19136650C211yesmaximal, characteristic, complemented
8#19136525C211yesmaximal, characteristic, complemented
9#19136508C211yesmaximal, characteristic
10#19136470C211yesmaximal, characteristic, complemented
11#19136456C211yesmaximal, characteristic, complemented
12#19136446C211yesmaximal, characteristic, complemented
13#19136439C211yesmaximal, characteristic, complemented
14#19136401C211yesmaximal, characteristic, complemented
15C43×#2226C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17#14583523—21no—
18#14583371—21no—
19C2×#13063270C2211yescharacteristic
20C2×#13063269C2211yescharacteristic
21C2×D688C2211yescharacteristic
22C2×#13063266C2211yescharacteristic
23#14583283C2211yescharacteristic, complemented
24#14583261—21no—
25#14583146—21no—
26#14583141C2211yescharacteristic
27#14583136C2211yescharacteristic
28#14583009—21no—
29#14583008—21no—
30#14582998—21no—
31#14582993C2211yescharacteristic, complemented
32C4×D344C2211yescharacteristic
33D8×Dic43C2211yescharacteristic
34#14582981C2211yescharacteristic
35#14582981C2211yescharacteristic, complemented
36#14582936C2211yescharacteristic
37#14582902—21no—
38#14582853C2211yescharacteristic
39#14582724C2211yescharacteristic, complemented
40#14582724C2211yescharacteristic, complemented
41C4⋊(C43⋊C16)C2211yescharacteristic, complemented
42#14582704C2211yescharacteristic, complemented
43#14582702C2211yescharacteristic, complemented
44#14582701C2211yescharacteristic, complemented
45#14582699C2211yescharacteristic
46#14582699C2211yescharacteristic
47#14582699C2211yescharacteristic, complemented
48(C2×D43)⋊C16C2211yescharacteristic
49(C2×D43)⋊C16C2211yescharacteristic
50#14582674C2211yescharacteristic, complemented
51C16×Dic43C2211yescharacteristic, complemented
52C43×#500C2211yescharacteristic, complemented
53C4×D8×C43C2211yescharacteristic
54C43×#367C2211yescharacteristic, complemented
55C43×#367C2211yescharacteristic, complemented
56C43×C4⋊C16C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×D4×D43—21no—
60C2×Dic172C2311yescharacteristic
61C2×#10621873—21no—
62C2×D344C2311yescharacteristic
63C2×D344C2311yescharacteristic
64C2×#10621882—21no—
65D8×D43—22no—
66D8×D43—22no—
67C2×#10621872D411yescharacteristic
68C2×C8×D43C2311yescharacteristic
69#13063320—41no—
70#13063314—41no—
71#13063313—21no—
72#13063310—41no—
73#13063305—21no—
74#13063301—41no—
75#13063300—21no—
76#13063290—21no—
77C4×D172—21no—
78D4×Dic43—21no—
79#13063287—21no—
80#13063287—21no—
81C4×C22⋊D43—41no—
82(C22⋊D43)⋊C4—41no—
83#13063283—21no—
84#13063282D411yescharacteristic
85C2×(C2×D43)⋊C4—41no—
86C22⋊C4×D43—41no—
87#13063270—22no—
88#13063269—22no—
89D688—22no—
90#13063266—22no—
91C2×C43⋊C16C2311yescharacteristic
92C2×C43⋊C16C2311yescharacteristic
93#13063259C2311yescharacteristic
94#13063256—21no—
95#13063248—21no—
96#13063248—21no—
97#13063247—21no—
98#13063246—21no—
99#13063245—21no—
100#13063245—21no—
101#13063245—21no—
102#13063236D411yescharacteristic
103#13063235D411yescharacteristic
104C8×Dic43C2311yescharacteristic
105C2×D8×C43C2311yescharacteristic
106C4⋊Q8×C43—21no—
107C4×D4×C43—21no—
108C2×C16×C43C2311yescharacteristic
109C2×C16×C43C2311yescharacteristic
110#107×C43—21no—
111#107×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#107×C43C2311yescharacteristic
114#102×C43—21no—
115C4×C8×C43C2311yescharacteristic
116C23×D43—41no—
117C2×Q8×C43—41no—
118C2×D4×C43—21no—
119C22×C4×C43—41no—
120C2×C22⋊D43—41no—
121C22×Dic43—41no—
122D4×D43—24no—
123D4×D43—42no—
124C2×D172—21no—
125C2×D172—21no—
126C2×D172—41no—
127C2×C4×D43—41no—
128C2×C4×D43—41no—
129C2×C4×D43—41no—
130C2×C4×D43C2×D411yescharacteristic
131C2×Dic86—21no—
132D8×C43—21no—
133D8×C43#4112yes—
134C2×C8×C43C2×D411yescharacteristic
135C2×C8×C43C2411yescharacteristic
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—41no—
140C22⋊C4×C43—41no—
141C42×C43C2×D411yescharacteristic
142C22⋊Dic43—41no—
143#10621882—24no—
144(C2×D43)⋊C4—41no—
145(C2×D43)⋊C4—41no—
146(C2×D43)⋊C4—41no—
147(C2×D43)⋊C4—41no—
148(C2×D43)⋊C4—41no—
149(C2×D43)⋊C4—41no—
150(C2×D43)⋊C4—41no—
151(C2×D43)⋊C4—41no—
152(C2×D43)⋊C4D811yescharacteristic
153(C2×D43)⋊C4D811yescharacteristic
154C4⋊Dic43—21no—
155C4⋊Dic43—41no—
156Dic43⋊C4—41no—
157Dic43⋊C4D811yescharacteristic
158Dic43⋊C4D811yescharacteristic
159C4×Dic43—41no—
160C4×Dic43—41no—
161C4×Dic43C2×D411yescharacteristic
162C2×C43⋊C8C2×D411yescharacteristic
163C2×C43⋊C8C2×D411yescharacteristic
164Dic172—21no—
165Dic172—21no—
166D344—21no—
167D344—21no—
168D344—21no—
169D344#4112yes—
170#10621873—42no—
171#10621872—41no—
172C8×D43—21no—
173C8×D43—21no—
174C16×C43—21no—
175C16×C43—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43—41no—
179C22×D43—44no—
180C22×D43—41no—
181C22×D43—41no—
182C22×D43—161no—
183C22×D43—161no—
184C22×D43C2×D811yescharacteristic
185Q8×C43—161no—
186D4×C43—22no—
187D4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—161no—
192C2×C4×C43C2×D811yescharacteristic
193C2×C4×C43C2×D811yescharacteristic
194C2×C4×C43C22×D411yescharacteristic
195C22⋊D43—44no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43—161no—
199C2×Dic43C2×D811yescharacteristic
200C2×Dic43C2×D811yescharacteristic
201C2×Dic43C2×D811yescharacteristic
202D172—22no—
203D172—41no—
204D172—41no—
205D172—41no—
206D172—161no—
207C4×D43—21no—
208C4×D43—21no—
209C4×D43—161no—
210C4×D43—161no—
211C4×D43—161no—
212Dic86—41no—
213Dic86—41no—
214C8×C43—21no—
215C8×C43C2×#4111yescharacteristic
216C8×C43C2×#4111yescharacteristic
217C43⋊C8—21no—
218C43⋊C8—21no—
219#33678—431nomaximal, Sylow
220C22×C43—42no—
221C22×C43—81no—
222C22×C43—81no—
223C22×C43C22×D811yescharacteristic
224C2×D43—21no—
225C2×D43—21no—
226C2×D43—21no—
227C2×D43—42no—
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C2×D43—81no—
232C2×D43—81no—
233C2×D43—164no—
234C4×C43—21no—
235C4×C43—21no—
236C4×C43—81no—
237C4×C43—81no—
238C4×C43—81no—
239C4×C43#52511yescharacteristic
240C4×C43#57511yescharacteristic
241Dic43—21no—
242Dic43—21no—
243Dic43—21no—
244Dic43—81no—
245Dic43—81no—
246#3175—431no—
247#2948—431no—
248#2237—431no—
249#2234—431no—
250#2226D4311yescharacteristic, complemented
251#2224—431no—
252#2210—431no—
253#2210—431no—
254#2187—431no—
255#2184—431no—
256#2177—431no—
257#2175—431no—
258C4×SD32—431no—
259C4×D16—431no—
260#2164—431no—
261C2×C43—82no—
262C2×C43#310011yescharacteristic
263C2×C43#341511yescharacteristic
264C2×C43#341611yescharacteristic
265D43—41no—
266D43—82no—
267D43—161no—
268C22×D8—431no—
269#542—861no—
270#518—861no—
271C2×SD32—431no—
272C2×SD32—431no—
273C2×D16—431no—
274C2×D16—431no—
275#500C2×D4311yescharacteristic, complemented
276#495—431no—
277#489—861no—
278#468—861no—
279#467—431no—
280#466—431no—
281#442—861no—
282#442—861no—
283#440—861no—
284C4×Q16—431no—
285C4×D8—431no—
286C4×D8—431no—
287C4×D8—431no—
288C4×D8—431no—
289C4×D8C2×D4311yescharacteristic
290#427—431no—
291#418—861no—
292#405—431no—
293#367C2×D4311yescharacteristic, complemented
294#367C2×D4311yescharacteristic, complemented
295#366—431no—
296#366—431no—
297C4⋊C16—431no—
298C4⋊C16C2×D4311yescharacteristic, complemented
299#358—431no—
300#358—431no—
301#357—431no—
302#357—431no—
303#357—431no—
304#357—431no—
305#357C2×D4311yescharacteristic
306#357C2×D4311yescharacteristic
307C22⋊C16—431no—
308C22⋊C16—431no—
309#346—431no—
310C4×C16—431no—
311C43#3367811yescharacteristic, complemented, Sylow
312C22×D4—861no—
313C2×Q16—431no—
314C2×SD16—861no—
315C2×D8—431no—
316C2×D8—431no—
317C2×D8—861no—
318C2×D8—862no—
319C2×D8—862no—
320C2×D8C22×D4311yescharacteristic
321C2×M16—431no—
322C22×C8—431no—
323C4⋊Q8—21no—
324#126—1721no—
325#124—861no—
326#124—1721no—
327#123—1721no—
328C22⋊Q8—861no—
329C22⋊Q8—1721no—
330#121—861no—
331C4×Q8—861no—
332C4×D4—21no—
333C4×D4—861no—
334C4×D4—861no—
335C4×D4—861no—
336C4×D4—861no—
337C4×D4—1721no—
338C4×D4—1721no—
339#117—431no—
340#117—861no—
341C2×C22⋊C4—1721no—
342C2×C22⋊C4—1721no—
343SD32—862no—
344SD32—862no—
345D16—862no—
346D16—862no—
347C2×C16—431no—
348C2×C16—431no—
349C2×C16C22×D4311yescharacteristic
350C2×C16C22×D4311yescharacteristic
351#107—21no—
352#107—431no—
353#107C22×D4311yescharacteristic
354#107C22×D4311yescharacteristic
355#107C22×D4311yescharacteristic
356#106—861no—
357#103—861no—
358#103—861no—
359#102—21no—
360#102—861no—
361#102—861no—
362#102—861no—
363#102—861no—
364#102—861no—
365#97—431no—
366#97—431no—
367C4×C8—431no—
368C4×C8C22×D4311yescharacteristic
369C24—1721no—
370C2×Q8—41no—
371C2×Q8—861no—
372C2×D4—21no—
373C2×D4—864no—
374C2×D4—861no—
375C2×D4—861no—
376C2×D4—1721no—
377C2×D4—1721no—
378C2×D4—1722no—
379C22×C4—41no—
380C22×C4—431no—
381C22×C4—1721no—
382C22×C4—1721no—
383C22×C4—1721no—
384C22×C4—1721no—
385Q16—861no—
386Q16—861no—
387SD16—1722no—
388D8—21no—
389D8—432no—
390D8—864no—
391D8—861no—
392D8—861no—
393D8—861no—
394D8#1062190212yes—
395M16—1721no—
396C2×C8—431no—
397C2×C8—431no—
398C2×C8—861no—
399C2×C8—861no—
400C2×C8D4×D4311yescharacteristic
401C2×C8C23×D4311yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—431no—
407C4⋊C4—431no—
408C4⋊C4—861no—
409C4⋊C4—1721no—
410C4⋊C4—1721no—
411C22⋊C4—41no—
412C22⋊C4—431no—
413C22⋊C4—431no—
414C22⋊C4—1721no—
415C22⋊C4—1721no—
416C22⋊C4—1721no—
417C22⋊C4—1721no—
418C22⋊C4—1721no—
419C22⋊C4—1721no—
420C22⋊C4—1721no—
421C22⋊C4—1721no—
422C22⋊C4—1721no—
423C42—431no—
424C42—1721no—
425C42—1721no—
426C42D4×D4311yescharacteristic
427C16—21no—
428C16—21no—
429C16—861no—
430C16—861no—
431C23—41no—
432C23—431no—
433C23—1724no—
434C23—1721no—
435C23—1721no—
436C23—6881no—
437C23—6881no—
438Q8—161no—
439Q8—1721no—
440Q8—1721no—
441D4—22no—
442D4—41no—
443D4—862no—
444D4—1724no—
445D4—1721no—
446D4—1721no—
447D4—1721no—
448D4—6881no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—161no—
453C2×C4—431no—
454C2×C4—431no—
455C2×C4—431no—
456C2×C4—861no—
457C2×C4—861no—
458C2×C4—1721no—
459C2×C4—1721no—
460C2×C4—6881no—
461C2×C4—6881no—
462C2×C4—6881no—
463C2×C4—6881no—
464C2×C4D8×D4311yescharacteristic
465C2×C4D8×D4311yescharacteristic
466C2×C4C2×D4×D4311yescharacteristic
467C8—21no—
468C8—861no—
469C8—861no—
470C8#41×D4311yescharacteristic
471C8C2×#1062190211yescharacteristic
472C22—42no—
473C22—81no—
474C22—81no—
475C22—861no—
476C22—861no—
477C22—861no—
478C22—3441no—
479C22—3441no—
480C22—3441no—
481C22—3441no—
482C22—3441no—
483C22—1722no—
484C22—6884no—
485C22C2×D8×D4311yescharacteristic
486C4—21no—
487C4—21no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—861no—
492C4—861no—
493C4—861no—
494C4—3441no—
495C4—3441no—
496C4#1458341211yescharacteristic
497C4#1458369811yescharacteristic
498C2—82no—
499C2—3442no—
500C2—1721no—
501C2—6881no—
502C2#1914459711yescharacteristic
503C2#1914773511yescharacteristic
504C2#1914773711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2226C2
socleC22×C43C22×D8
prime radical#19136508C2
hypercenter#2226D43
hypocenterC43#33678
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. #19145237C2semidirect
2. #19143442C2semidirect
3. #19136806C2semidirect
4. #19136788C2semidirect
5. #19136729C2semidirect
6. #19136651C2semidirect
7. #19136650C2semidirect
8. #19136525C2semidirect
10. #19136470C2semidirect
11. #19136456C2semidirect
12. #19136446C2semidirect
13. #19136439C2semidirect
14. #19136401C2semidirect
15. C43×#2226C2semidirect
23. #14583283C22semidirect
31. #14582993C22semidirect
35. #14582981C22semidirect
39. #14582724C22semidirect
40. #14582724C22semidirect
41. C4⋊(C43⋊C16)C22semidirect
42. #14582704C22semidirect
43. #14582702C22semidirect
44. #14582701C22semidirect
47. #14582699C22semidirect
50. #14582674C22semidirect
51. C16×Dic43C22semidirect
52. C43×#500C22semidirect
54. C43×#367C22semidirect
55. C43×#367C22semidirect
56. C43×C4⋊C16C22semidirect
250. #2226D43semidirect
275. #500C2×D43semidirect
293. #367C2×D43semidirect
294. #367C2×D43semidirect
298. C4⋊C16C2×D43semidirect
311. C43#33678semidirect

Maximal subgroups

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

subgroupindex
#191452372
#191434422
#191368062
#191367882
#191367292
#191366512
#191366502
#191365252
#191365082
#191364702
#191364562
#191364462
#191364392
#191364012
C43×#22262
#3367843