Finite Group Databasebeta

← #25251342

Subgroups — #25251342

Order 11008.

514 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145120C211yesmaximal, characteristic, complemented
2#19143507C211yesmaximal, characteristic
3#19136772C211yesmaximal, characteristic, complemented
4#19136771C211yesmaximal, characteristic, complemented
5#19136770C211yesmaximal, characteristic, complemented
6#19136769C211yesmaximal, characteristic, complemented
7#19136765C211yesmaximal, characteristic, complemented
8#19136764C211yesmaximal, characteristic, complemented
9#19136763C211yesmaximal, characteristic, complemented
10#19136366C211yesmaximal, characteristic, complemented
11#365×D43C211yesmaximal, characteristic, complemented
12#19136359C211yesmaximal, characteristic, complemented
13#19136329C211yesmaximal, characteristic
14#360×D43C211yesmaximal, characteristic
15C43×#2230C211yesmaximal, characteristic, complemented
16#135×D43C2211yescharacteristic
17#14583664—21no—
18#14583526—21no—
19M32×D43C2211yescharacteristic
20M32×D43C2211yescharacteristic
21#14583306—21no—
22#14583305—21no—
23#14583301C2211yescharacteristic, complemented
24#14583299C2211yescharacteristic, complemented
25#14583296C2211yescharacteristic, complemented
26#14583019—21no—
27#14583018—21no—
28#14583017C2211yescharacteristic
29#14583016C2211yescharacteristic
30#14583015C2211yescharacteristic
31#108×D43C2211yescharacteristic
32#14582938—21no—
33#14582934C2211yescharacteristic
34#106×D43C2211yescharacteristic
35#14582914—21no—
36#14582853C2211yescharacteristic
37#14582723C2211yescharacteristic, complemented
38#14582723C2211yescharacteristic, complemented
39#14582722C2211yescharacteristic, complemented
40#14582722C2211yescharacteristic, complemented
41#14582721C2211yescharacteristic, complemented
42#14582721C2211yescharacteristic, complemented
43#14582720C2211yescharacteristic, complemented
44#14582719C2211yescharacteristic, complemented
45#14582719C2211yescharacteristic, complemented
46#14582710C2211yescharacteristic
47#14582710C2211yescharacteristic
48#14582709C2211yescharacteristic
49#14582709C2211yescharacteristic
50#14582708C2211yescharacteristic
51#14582708C2211yescharacteristic
52C43×#498C2211yescharacteristic, complemented
53C43×#443C2211yescharacteristic
54C43×#365C2211yescharacteristic, complemented
55C43×#365C2211yescharacteristic, complemented
56C43×#364C2211yescharacteristic, complemented
57C43×#360C2211yescharacteristic
58C43×#360C2211yescharacteristic
59#41×D43—21no—
60#13063348Q811yescharacteristic, complemented
61#13063347C2311yescharacteristic
62#13063346—21no—
63#13063345—21no—
64#13063344Q811yescharacteristic, complemented
65Q16×D43Q811yescharacteristic, complemented
66SD16×D43—21no—
67D8×D43Q811yescharacteristic, complemented
68#13063333—21no—
69#13063333—41no—
70#13063332—21no—
71#13063331—21no—
72#13063331—41no—
73C2×#10621872—41no—
74C2×#10621872D411yescharacteristic
75M16×D43—21no—
76M16×D43—41no—
77C2×C8×D43C2311yescharacteristic
78#13063324—21no—
79#13063323—41no—
80#13063317—21no—
81#13063316—21no—
82#13063315—41no—
83#13063303—41no—
84#13063301—41no—
85#13063283—21no—
86#13063282D411yescharacteristic
87C4⋊C4×D43—21no—
88#13063265C2311yescharacteristic
89#13063265C2311yescharacteristic
90#13063264—21no—
91#13063264—21no—
92C16×D43—21no—
93C16×D43—21no—
94#13063261C2311yescharacteristic
95#13063260—21no—
96#13063259—21no—
97#13063258—21no—
98#13063258—21no—
99#13063257C2311yescharacteristic
100#13063257C2311yescharacteristic
101#13063256—21no—
102#13063256—21no—
103#13063253—21no—
104#13063252—21no—
105#13063251—21no—
106#13063236D411yescharacteristic
107#13063235D411yescharacteristic
108C8×Dic43C2311yescharacteristic
109#135×C43C2311yescharacteristic
110#131×C43—21no—
111C4⋊Q8×C43—21no—
112M32×C43C2311yescharacteristic
113M32×C43C2311yescharacteristic
114#108×C43C2311yescharacteristic
115#106×C43—21no—
116#106×C43C2311yescharacteristic
117#106×C43C2311yescharacteristic
118#104×C43—21no—
119C4×C8×C43C2311yescharacteristic
120#41×C43—21no—
121C2×Q8×C43—41no—
122#10621902—21no—
123Q8×D43—21no—
124#10621900—21no—
125#10621900—41no—
126D4×D43—21no—
127D4×D43—41no—
128#10621898—21no—
129#10621898—41no—
130C2×C4×D43—41no—
131C2×C4×D43—41no—
132C2×C4×D43C2×D411yescharacteristic
133C2×Dic86—41no—
134Q16×C43C2×Q811yescharacteristic
135SD16×C43—21no—
136D8×C43C2×Q811yescharacteristic
137M16×C43—21no—
138M16×C43—41no—
139C2×C8×C43—41no—
140C2×C8×C43C2×D411yescharacteristic
141C2×C8×C43C2411yescharacteristic
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—41no—
145C42×C43C2×D411yescharacteristic
146#10621885—21no—
147#10621884—21no—
148#10621883—21no—
149#10621882—21no—
150(C2×D43)⋊C4—21no—
151(C2×D43)⋊C4—41no—
152C4⋊Dic43—21no—
153C4⋊Dic43—21no—
154C4⋊Dic43—41no—
155Dic43⋊C4—21no—
156Dic43⋊C4—41no—
157Dic43⋊C4—41no—
158Dic43⋊C4—41no—
159Dic43⋊C4—41no—
160Dic43⋊C4—41no—
161C4×Dic43—41no—
162C4×Dic43C2×D411yescharacteristic
163#10621877—21no—
164#10621877—41no—
165C2×C43⋊C8—41no—
166C2×C43⋊C8C2×D411yescharacteristic
167C2×C43⋊C8C2×D411yescharacteristic
168Dic172C2×Q811yescharacteristic
169D344C2×Q811yescharacteristic
170#10621873—21no—
171#10621872—41no—
172#10621872—41no—
173#10621872—41no—
174#10621872SD1611yescharacteristic
175#10621872SD1611yescharacteristic
176#10621872SD1611yescharacteristic
177#10621872SD1611yescharacteristic
178C8×D43—41no—
179C8×D43—41no—
180C8×D43—41no—
181C8×D43C2×Q811yescharacteristic
182C8×D43C2×Q811yescharacteristic
183C8×D43#4111yescharacteristic
184C8×D43#4111yescharacteristic
185C16×C43—21no—
186C16×C43—21no—
187C43⋊C16—21no—
188C43⋊C16—21no—
189C22×D43—41no—
190C22×D43AGL(1,ℤ/8)11yescharacteristic
191Q8×C43—21no—
192Q8×C43—161no—
193D4×C43—21no—
194D4×C43—41no—
195C2×C4×C43—21no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43C22×D411yescharacteristic
200C22⋊D43—41no—
201C22⋊D43—41no—
202C22⋊D43—41no—
203C2×Dic43—21no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43AGL(1,ℤ/8)11yescharacteristic
208D172—21no—
209D172—41no—
210C4×D43—41no—
211C4×D43—41no—
212C4×D43—41no—
213C4×D43—161no—
214C4×D43C22⋊Q811yescharacteristic
215C4×D43C22⋊Q811yescharacteristic
216C4×D43C2×SD1611yescharacteristic
217C4×D43C2×SD1611yescharacteristic
218Dic86—21no—
219Dic86—41no—
220Dic86—161no—
221C8×C43—41no—
222C8×C43C2×SD1611yescharacteristic
223C8×C43C2×SD1611yescharacteristic
224C8×C43C22×Q811yescharacteristic
225C8×C43C2×#4111yescharacteristic
226C43⋊C8—41no—
227C43⋊C8C22⋊Q811yescharacteristic
228C43⋊C8C22⋊Q811yescharacteristic
229C43⋊C8C2×SD1611yescharacteristic
230C43⋊C8C2×SD1611yescharacteristic
231#33638—431nomaximal, Sylow
232C22×C43—41no—
233C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
234C2×D43—41no—
235C2×D43—41no—
236C2×D43—161no—
237C2×D43#47611yescharacteristic
238C2×D43#47611yescharacteristic
239C4×C43—41no—
240C4×C43—41no—
241C4×C43—81no—
242C4×C43—81no—
243C4×C43C2×C22⋊Q811yescharacteristic
244C4×C43C22×SD1611yescharacteristic
245Dic43—41no—
246Dic43—41no—
247Dic43—81no—
248Dic43—81no—
249Dic43#47611yescharacteristic
250Dic43#47611yescharacteristic
251#3163—431no—
252#2957—431no—
253#2231—431no—
254#2231—431no—
255#2231—431no—
256#2231—431no—
257#2230—431no—
258#2230—431no—
259#2230—431no—
260#2230D4311yescharacteristic, complemented
261#2155—431no—
262C2×#365—431no—
263#2153—431no—
264#2145—431no—
265C2×#360—431no—
266C2×C43—21no—
267C2×C43—81no—
268C2×C43C2×#47611yescharacteristic
269D43—21no—
270D43—21no—
271D43—81no—
272C2×#135—431no—
273#568—861no—
274#544—861no—
275C2×M32—431no—
276C2×M32—431no—
277#501—861no—
278#501—861no—
279#499—431no—
280#499—431no—
281#498—431no—
282#498C2×D4311yescharacteristic, complemented
283#444—861no—
284#444—861no—
285#443—431no—
286#443—431no—
287#443—431no—
288#443C2×D4311yescharacteristic
289C2×#108—431no—
290#428—861no—
291#427—431no—
292C2×#106—431no—
293#421—861no—
294#405—431no—
295#365—431no—
296#365—431no—
297#365—431no—
298#365—431no—
299#365—431no—
300#365—431no—
301#365C2×D4311yescharacteristic, complemented
302#365C2×D4311yescharacteristic, complemented
303#364—431no—
304#364—431no—
305#364—431no—
306#364C2×D4311yescharacteristic, complemented
307#360—431no—
308#360—431no—
309#360—431no—
310#360—431no—
311#360—431no—
312#360—431no—
313#360C2×D4311yescharacteristic
314#360C2×D4311yescharacteristic
315C43#3363811yescharacteristic, complemented, Sylow
316C2×#41—861no—
317#135—431no—
318#135—431no—
319#135—431no—
320#135—861no—
321#135—861no—
322#135C22×D4311yescharacteristic
323C2×Q16—431no—
324C2×SD16—861no—
325C2×D8—431no—
326#131—21no—
327#131—861no—
328#131—861no—
329#131—861no—
330#131—1721no—
331#131—1721no—
332C2×M16—431no—
333C2×M16—861no—
334C2×M16—1721no—
335C2×M16—1721no—
336C22×C8—431no—
337C4⋊Q8—21no—
338C4⋊Q8—861no—
339C4⋊Q8—1721no—
340#125—861no—
341#125—861no—
342#125—1721no—
343C22⋊Q8—1721no—
344C22⋊Q8—1721no—
345#117—431no—
346#117—861no—
347C2×C4⋊C4—861no—
348M32—431no—
349M32—431no—
350M32—861no—
351M32—861no—
352M32C22×D4311yescharacteristic
353M32C22×D4311yescharacteristic
354C2×C16—861no—
355C2×C16—861no—
356#108—431no—
357#108—861no—
358#108C22×D4311yescharacteristic
359#107—861no—
360#107—861no—
361#107—861no—
362#106—21no—
363#106—431no—
364#106—431no—
365#106—861no—
366#106—861no—
367#106C22×D4311yescharacteristic
368#106C22×D4311yescharacteristic
369#104—21no—
370#104—861no—
371#104—861no—
372#104—861no—
373#97—431no—
374#97—431no—
375C4×C8—431no—
376C4×C8C22×D4311yescharacteristic
377#41—21no—
378#41—861no—
379#41—861no—
380#41—861no—
381#41—1721no—
382#41—1721no—
383C2×Q8—41no—
384C2×Q8—861no—
385C2×Q8—1721no—
386C2×D4—861no—
387C2×D4—1721no—
388C22×C4—431no—
389C22×C4—1721no—
390C22×C4—1721no—
391Q16—431no—
392Q16—861no—
393Q16Q8×D4311yescharacteristic
394SD16—21no—
395SD16—861no—
396SD16—861no—
397SD16—861no—
398D8—431no—
399D8—861no—
400D8Q8×D4311yescharacteristic
401M16—21no—
402M16—41no—
403M16—431no—
404M16—431no—
405M16—431no—
406M16—431no—
407M16—861no—
408M16—1721no—
409M16—1721no—
410M16—1721no—
411M16—1721no—
412C2×C8—41no—
413C2×C8—431no—
414C2×C8—431no—
415C2×C8—431no—
416C2×C8—431no—
417C2×C8—431no—
418C2×C8—431no—
419C2×C8—1721no—
420C2×C8—1721no—
421C2×C8—1721no—
422C2×C8—1721no—
423C2×C8D4×D4311yescharacteristic
424C2×C8C23×D4311yescharacteristic
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C4⋊C4—1721no—
434C4⋊C4—1721no—
435C4⋊C4—1721no—
436C4⋊C4—1721no—
437C22⋊C4—861no—
438C22⋊C4—1721no—
439C42—431no—
440C42—1721no—
441C42D4×D4311yescharacteristic
442C16—21no—
443C16—21no—
444C16—861no—
445C16—861no—
446C23—431no—
447C23—1721no—
448Q8—21no—
449Q8—161no—
450Q8—861no—
451Q8—1721no—
452Q8—6881no—
453D4—21no—
454D4—41no—
455D4—861no—
456D4—1721no—
457D4—1721no—
458D4—1721no—
459D4—1721no—
460C2×C4—21no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—431no—
465C2×C4—431no—
466C2×C4—431no—
467C2×C4—431no—
468C2×C4—431no—
469C2×C4—861no—
470C2×C4—1721no—
471C2×C4—1721no—
472C2×C4—1721no—
473C2×C4—1721no—
474C2×C4—1721no—
475C2×C4—1721no—
476C2×C4—6881no—
477C2×C4C2×D4×D4311yescharacteristic
478C8—41no—
479C8—431no—
480C8—431no—
481C8—431no—
482C8—431no—
483C8—1721no—
484C8SD16×D4311yescharacteristic
485C8SD16×D4311yescharacteristic
486C8C2×Q8×D4311yescharacteristic
487C8#41×D4311yescharacteristic
488C22—41no—
489C22—431no—
490C22—431no—
491C22—1721no—
492C22—1721no—
493C22—6881no—
494C22AGL(1,ℤ/8)×D4311yescharacteristic
495C4—41no—
496C4—41no—
497C4—81no—
498C4—81no—
499C4—431no—
500C4—431no—
501C4—3441no—
502C4—3441no—
503C4—1721no—
504C4—1721no—
505C4C22⋊Q8×D4311yescharacteristic
506C4C2×SD16×D4311yescharacteristic
507C2—21no—
508C2—81no—
509C2—861no—
510C2—861no—
511C2—3441no—
512C2#476×D4311yescharacteristic
subgroupG/H
centerC2#476×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2230C2
socleC2×C43C2×#476
prime radical#135×D43C22
hypercenter#2230D43
hypocenterC43#33638
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2230

Complements

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

NH ≅ G/Ntype
1. #19145120C2semidirect
3. #19136772C2semidirect
4. #19136771C2semidirect
5. #19136770C2semidirect
6. #19136769C2semidirect
7. #19136765C2semidirect
8. #19136764C2semidirect
9. #19136763C2semidirect
10. #19136366C2semidirect
11. #365×D43C2semidirect
12. #19136359C2semidirect
15. C43×#2230C2semidirect
23. #14583301C22semidirect
24. #14583299C22semidirect
25. #14583296C22semidirect
37. #14582723C22semidirect
38. #14582723C22semidirect
39. #14582722C22semidirect
40. #14582722C22semidirect
41. #14582721C22semidirect
42. #14582721C22semidirect
43. #14582720C22semidirect
44. #14582719C22semidirect
45. #14582719C22semidirect
52. C43×#498C22semidirect
54. C43×#365C22semidirect
55. C43×#365C22semidirect
56. C43×#364C22semidirect
60. #13063348Q8semidirect
64. #13063344Q8semidirect
65. Q16×D43Q8semidirect
67. D8×D43Q8semidirect
260. #2230D43semidirect
282. #498C2×D43semidirect
301. #365C2×D43semidirect
302. #365C2×D43semidirect
306. #364C2×D43semidirect
315. C43#33638semidirect

Maximal subgroups

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

subgroupindex
#191451202
#191435072
#191367722
#191367712
#191367702
#191367692
#191367652
#191367642
#191367632
#191363662
#365×D432
#191363592
#191363292
#360×D432
C43×#22302
#3363843