Finite Group Databasebeta

← #25251706

Subgroups — #25251706

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#19145235C211yesmaximal, characteristic, complemented
2#19143447C211yesmaximal, characteristic, complemented
3#19136800C211yesmaximal, characteristic, complemented
4#19136787C211yesmaximal, characteristic, complemented
5#19136740C211yesmaximal, characteristic, complemented
6#19136730C211yesmaximal, characteristic, complemented
7#19136652C211yesmaximal, characteristic, complemented
8#19136652C211yesmaximal, characteristic, complemented
9#19136507C211yesmaximal, characteristic
10#19136468C211yesmaximal, characteristic, complemented
11#19136460C211yesmaximal, characteristic, complemented
12SD32×Dic43C211yesmaximal, characteristic, complemented
13#19136439C211yesmaximal, characteristic, complemented
14#19136399C211yesmaximal, characteristic, complemented
15C43×#2187C211yesmaximal, characteristic, complemented
16#14583522—21no—
17#14583374—21no—
18C2×#13063266C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20#14583303C2211yescharacteristic, complemented
21#14583284C2211yescharacteristic, complemented
22#14583260—21no—
23#14583147—21no—
24#14583135C2211yescharacteristic
25#14583011—21no—
26#14583011—21no—
27#14583002—21no—
28Q16×Dic43C2211yescharacteristic, complemented
29D8×Dic43C2211yescharacteristic
30D8×Dic43C2211yescharacteristic
31D8×Dic43C2211yescharacteristic
32D8×Dic43C2211yescharacteristic
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#14582703C2211yescharacteristic, complemented
44#14582703C2211yescharacteristic, complemented
45#14582701C2211yescharacteristic, complemented
46#14582701C2211yescharacteristic, complemented
47#14582700C2211yescharacteristic
48#14582700C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50#14582674C2211yescharacteristic, complemented
51C16×Dic43C2211yescharacteristic, complemented
52C22×D8×C43C2211yescharacteristic
53C2×SD32×C43C2211yescharacteristic
54C2×SD32×C43C2211yescharacteristic
55C43×#467C2211yescharacteristic
56C43×#357C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×C22⋊C16C2211yescharacteristic
59C2×#10621884—21no—
60C2×D344C2311yescharacteristic
61C2×#10621877D411yescharacteristic
62#13063324—21no—
63#13063320—41no—
64#13063314—21no—
65#13063311—41no—
66#13063307—41no—
67#13063305—41no—
68#13063299—21no—
69Q8×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#13063258—21no—
89#13063257—21no—
90#13063249—21no—
91#13063247—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×Q16×C43C2311yescharacteristic
103C2×D8×C43—22no—
104C2×D8×C43—22no—
105C2×D8×C43—21no—
106C2×D8×C43C2311yescharacteristic
107C2×D8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22⋊Q8×C43—21no—
110SD32×C43—22no—
111SD32×C43—22no—
112C2×C16×C43C2311yescharacteristic
113C2×C16×C43C2311yescharacteristic
114#107×C43C2311yescharacteristic
115#103×C43—21no—
116C24×C43—41no—
117C2×Q8×C43—21no—
118C2×D4×C43—24no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—42no—
122C2×D4×C43—41no—
123C22×C4×C43C2×D411yescharacteristic
124C2×C22⋊D43—41no—
125C22×Dic43—41no—
126C22×Dic43—41no—
127C22×Dic43—41no—
128C22×Dic43—41no—
129C2×D172—21no—
130C2×C4×D43—41no—
131C2×Dic86—41no—
132Q16×C43—21no—
133Q16×C43—21no—
134D8×C43—24no—
135D8×C43—21no—
136D8×C43—21no—
137D8×C43#4112yes—
138D8×C43#4112yes—
139C2×C8×C43—21no—
140C2×C8×C43—21no—
141C2×C8×C43C2×D411yescharacteristic
142C2×C8×C43C2411yescharacteristic
143C4⋊C4×C43—21no—
144C4⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C22⋊Dic43—41no—
147C22⋊Dic43—41no—
148C22⋊Dic43—41no—
149C22⋊Dic43—41no—
150C22⋊Dic43—41no—
151C22⋊Dic43D811yescharacteristic
152C22⋊Dic43D811yescharacteristic
153#10621884—42no—
154(C2×D43)⋊C4—41no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4—41no—
158C4⋊Dic43—21no—
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161C4⋊Dic43—41no—
162C4⋊Dic43D811yescharacteristic
163C4⋊Dic43D811yescharacteristic
164Dic43⋊C4—41no—
165C4×Dic43—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—161no—
182C23×C43—161no—
183C23×C43C2×D811yescharacteristic
184C22×D43—41no—
185Q8×C43—41no—
186Q8×C43—41no—
187D4×C43—22no—
188D4×C43—22no—
189D4×C43—44no—
190D4×C43—41no—
191D4×C43—41no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C22×D411yescharacteristic
198C22⋊D43—161no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202C2×Dic43—161no—
203C2×Dic43—161no—
204C2×Dic43—161no—
205C2×Dic43—161no—
206C2×Dic43C2×D811yescharacteristic
207C2×Dic43C2×D811yescharacteristic
208C2×Dic43C2×D811yescharacteristic
209C2×Dic43C2×D811yescharacteristic
210D172—41no—
211D172—41no—
212C4×D43—161no—
213Dic86—161no—
214C8×C43—21no—
215C8×C43C2×#4111yescharacteristic
216C8×C43C2×#4111yescharacteristic
217C43⋊C8—21no—
218C43⋊C8—21no—
219#33678—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—42no—
224C22×C43—42no—
225C22×C43—81no—
226C22×C43—81no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43—164no—
230C22×C43C22×D811yescharacteristic
231C2×D43—81no—
232C2×D43—81no—
233C2×D43—81no—
234C4×C43—21no—
235C4×C43—81no—
236C4×C43—81no—
237C4×C43#52511yescharacteristic
238C4×C43#57511yescharacteristic
239Dic43—21no—
240Dic43—21no—
241Dic43—21no—
242Dic43—21no—
243Dic43—81no—
244Dic43—81no—
245Dic43—81no—
246#3175—431no—
247#2948—431no—
248#2237—431no—
249#2234—431no—
250#2226—431no—
251#2224—431no—
252#2210—431no—
253#2210—431no—
254#2187D4311yescharacteristic, complemented
255#2184—431no—
256#2177—431no—
257#2175—431no—
258C4×SD32—431no—
259C4×D16—431no—
260#2164—431no—
261C2×C43—41no—
262C2×C43—82no—
263C2×C43—82no—
264C2×C43#310011yescharacteristic
265C2×C43#341511yescharacteristic
266C2×C43#341611yescharacteristic
267D43—161no—
268C22×D8C2×D4311yescharacteristic
269#542—861no—
270#518—861no—
271C2×SD32C2×D4311yescharacteristic
272C2×SD32C2×D4311yescharacteristic
273C2×D16—431no—
274C2×D16—431no—
275#500—431no—
276#495—431no—
277#489—861no—
278#468—861no—
279#467C2×D4311yescharacteristic
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×D8—431no—
290#427—431no—
291#418—861no—
292#405—431no—
293#367—431no—
294#367—431no—
295#366—431no—
296#366—431no—
297C4⋊C16—431no—
298C4⋊C16—431no—
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⋊C16C2×D4311yescharacteristic
309#346—431no—
310C4×C16—431no—
311C43#3367811yescharacteristic, complemented, Sylow
312C22×D4—21no—
313C2×Q16C22×D4311yescharacteristic
314C2×SD16—861no—
315C2×D8—22no—
316C2×D8—22no—
317C2×D8—21no—
318C2×D8—431no—
319C2×D8C22×D4311yescharacteristic
320C2×D8C22×D4311yescharacteristic
321C2×M16—431no—
322C22×C8C22×D4311yescharacteristic
323C4⋊Q8—861no—
324#126—1721no—
325#124—861no—
326#124—1721no—
327#123—1721no—
328C22⋊Q8—21no—
329C22⋊Q8—1721no—
330#121—861no—
331C4×Q8—861no—
332C4×D4—861no—
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—22no—
344SD32—22no—
345D16—862no—
346D16—862no—
347C2×C16—431no—
348C2×C16—431no—
349C2×C16C22×D4311yescharacteristic
350C2×C16C22×D4311yescharacteristic
351#107—431no—
352#107—431no—
353#107—431no—
354#107—861no—
355#107C22×D4311yescharacteristic
356#106—861no—
357#103—21no—
358#103—861no—
359#102—861no—
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×C8—431no—
369C24—41no—
370C2×Q8—21no—
371C2×Q8—1721no—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—42no—
376C2×D4—41no—
377C2×D4—861no—
378C2×D4—1721no—
379C22×C4—1721no—
380C22×C4—1721no—
381C22×C4—1721no—
382C22×C4—1721no—
383C22×C4—1721no—
384C22×C4D4×D4311yescharacteristic
385Q16—21no—
386Q16—21no—
387SD16—1722no—
388D8—24no—
389D8—21no—
390D8—21no—
391D8—861no—
392D8—861no—
393D8#1062190012yes—
394D8#1062190012yes—
395M16—1721no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—431no—
399C2×C8—431no—
400C2×C8D4×D4311yescharacteristic
401C2×C8C23×D4311yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—41no—
404C4⋊C4—431no—
405C4⋊C4—431no—
406C4⋊C4—861no—
407C4⋊C4—861no—
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—431no—
425C42—1721no—
426C42—1721no—
427C16—21no—
428C16—21no—
429C16—861no—
430C16—861no—
431C23—44no—
432C23—41no—
433C23—41no—
434C23—161no—
435C23—161no—
436C23—1721no—
437C23D8×D4311yescharacteristic
438Q8—41no—
439Q8—41no—
440Q8—6881no—
441D4—22no—
442D4—22no—
443D4—44no—
444D4—41no—
445D4—41no—
446D4—1721no—
447D4—1721no—
448D4—6881no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—431no—
454C2×C4—431no—
455C2×C4—431no—
456C2×C4—431no—
457C2×C4—1721no—
458C2×C4—1721no—
459C2×C4—1721no—
460C2×C4—6881no—
461C2×C4—6881no—
462C2×C4—6881no—
463C2×C4—6881no—
464C2×C4—6881no—
465C2×C4D8×D4311yescharacteristic
466C2×C4C2×D4×D4311yescharacteristic
467C8—21no—
468C8—861no—
469C8—861no—
470C8C2×#1062190011yescharacteristic
471C8C2×#1062190011yescharacteristic
472C22—21no—
473C22—21no—
474C22—21no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—164no—
482C22—3441no—
483C22—3441no—
484C22—3441no—
485C22C2×D8×D4311yescharacteristic
486C4—21no—
487C4—81no—
488C4—81no—
489C4—861no—
490C4—861no—
491C4—861no—
492C4—861no—
493C4—3441no—
494C4—3441no—
495C4—3441no—
496C4#1458340511yescharacteristic
497C4#1458369511yescharacteristic
498C2—41no—
499C2—82no—
500C2—82no—
501C2—6881no—
502C2#1914459011yescharacteristic
503C2#1914773511yescharacteristic
504C2#1914773711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2187C2
socleC22×C43C22×D8
prime radical#19136507C2
hypercenter#2187D43
hypocenterC43#33678
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #19145235C2semidirect
2. #19143447C2semidirect
3. #19136800C2semidirect
4. #19136787C2semidirect
5. #19136740C2semidirect
6. #19136730C2semidirect
7. #19136652C2semidirect
8. #19136652C2semidirect
10. #19136468C2semidirect
11. #19136460C2semidirect
12. SD32×Dic43C2semidirect
13. #19136439C2semidirect
14. #19136399C2semidirect
15. C43×#2187C2semidirect
20. #14583303C22semidirect
21. #14583284C22semidirect
28. Q16×Dic43C22semidirect
33. #14582981C22semidirect
37. #14582727C22semidirect
38. #14582726C22semidirect
39. #14582725C22semidirect
40. #14582724C22semidirect
41. Dic43⋊C16C22semidirect
42. Dic43⋊C16C22semidirect
43. #14582703C22semidirect
44. #14582703C22semidirect
45. #14582701C22semidirect
46. #14582701C22semidirect
50. #14582674C22semidirect
51. C16×Dic43C22semidirect
254. #2187D43semidirect
311. C43#33678semidirect

Maximal subgroups

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

subgroupindex
#191452352
#191434472
#191368002
#191367872
#191367402
#191367302
#191366522
#191365072
#191364682
#191364602
SD32×Dic432
#191364392
#191363992
C43×#21872
#3367843