Finite Group Databasebeta

← #11861183

Subgroups — #11861183

Order 1152.

716 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596499C211yesmaximal, characteristic
2#10594722C211yesmaximal, characteristic, complemented
3#10594708C211yesmaximal, characteristic, complemented
4M16×#157C211yesmaximal, characteristic, complemented
5#10593330C211yesmaximal, characteristic, complemented
6#10593325C211yesmaximal, characteristic, complemented
7C2×#63731C211yesmaximal, characteristic, complemented
8#10593299C212yesmaximal, complemented
9#10593298C212yesmaximal, complemented
10#10593298C212yesmaximal, complemented
11#10593297C212yesmaximal, complemented
12#64306C2211yescharacteristic
13C2×#3798C2211yescharacteristic
14C2×C4×#157C2211yescharacteristic
15#64283C2211yescharacteristic
16#64239C412yescomplemented
17#64236C412yescomplemented
18#64226C411yescharacteristic, complemented
19#64226C411yescharacteristic, complemented
20#64224C411yescharacteristic, complemented
21#64224C411yescharacteristic, complemented
22#64223C2212yes—
23#64223C2212yes—
24M16×C3⋊D3C2211yescharacteristic
25C3×#907—21no—
26C3×D3×M16—21no—
27C2×#3712C2211yescharacteristic
28#63818C2211yescharacteristic
29#63814—21no—
30D3×#208—21no—
31#63805C2212yescomplemented
32#63805C2212yescomplemented
33#63804—22no—
34#63803C2212yescomplemented
35#63803C2212yescomplemented
36D3×ΓL(1,𝔽25)—22no—
37#63767C2212yescomplemented
38C8×#157C2212yescomplemented
39#63733C2212yescomplemented
40#63733C2212yescomplemented
41#63731C2211yescharacteristic, complemented
42#63731C2212yescomplemented
43#63731C2211yescharacteristic, complemented
44#63731C2211yescharacteristic, complemented
45#63731C2212yescomplemented
46#63731C2211yescharacteristic, complemented
47#5750—61no—
48#5745—61no—
49C22×#157—21no—
50C2×C4×C3⋊D3C2311yescharacteristic
51C3×#235—21no—
52C2×C3×C4×D3—21no—
53#3811—21no—
54C2×#627C2×C411yescharacteristic
55C2×#626—21no—
56C2×#625C2×C411yescharacteristic
57#3805C2×C412yes—
58#3802C2×C411yescharacteristic
59C4×D32—21no—
60#3798—21no—
61#3798—21no—
62#3798C2×C411yescharacteristic
63#3798C2×C411yescharacteristic
64#3798C2311yescharacteristic
65#3798C2311yescharacteristic
66#3798C2312yes—
67#3797C2×C411yescharacteristic
68#3796—21no—
69#3792C2×C412yes—
70C4×#157—21no—
71C4×#157C2311yescharacteristic
72C4×#157C2311yescharacteristic
73#3788C2×C411yescharacteristic
74#3788C2×C411yescharacteristic
75#3787C2312yes—
76#3776C2×C412yescomplemented
77#3776C2×C412yescomplemented
78#3775C2×C412yescomplemented
79#3775C2×C412yescomplemented
80#3775C2×C412yescomplemented
81#3775C2×C412yescomplemented
82#3774C2×C412yescomplemented
83#3774C2×C412yescomplemented
84C32×M16D411yescharacteristic
85#3748D411yescharacteristic
86#3743D412yes—
87C8×C3⋊D3C2312yes—
88C3×#208—21no—
89C2×C3×C3⋊C8—21no—
90C3×ΓL(1,𝔽25)—22no—
91C3×ΓL(1,𝔽25)—22no—
92C3×D3×C8—22no—
93C3×D3×C8—22no—
94#3712—21no—
95#3712C2311yescharacteristic
96#3712C2312yes—
97#3712C2311yescharacteristic
98#3711—22no—
99#3711—22no—
100#3710—21no—
101D3×C3⋊C8—22no—
102D3×C3⋊C8—22no—
103#2956—91nomaximal, Sylow
104D3×#41—61no—
105C2×#235—61no—
106C3×#131—61no—
107C2×C3×M16—61no—
108#948—61no—
109C2×#208—61no—
110#907—21no—
111#907—62no—
112#907—62no—
113#907—62no—
114D3×M16—21no—
115D3×M16—61no—
116D3×M16—61no—
117D3×M16—61no—
118D3×M16—62no—
119D3×M16—61no—
120#901—62no—
121#901—62no—
122#901—62no—
123#901—61no—
124C2×ΓL(1,𝔽25)—61no—
125C2×ΓL(1,𝔽25)—62no—
126C22×C3⋊D3#4111yescharacteristic
127C22×C3×D3—21no—
128C2×D32—21no—
129C2×#157—21no—
130C2×#157—21no—
131C2×#157—42no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C3⋊Dic3C22×C411yescharacteristic
134C4×C3⋊D3C22×C411yescharacteristic
135C4×C3⋊D3C2×D411yescharacteristic
136C4×C3⋊D3#4111yescharacteristic
137C4×C3⋊D3C2411yescharacteristic
138C3×#67—22no—
139C2×C3×Dic3—21no—
140C3×D12—21no—
141C3×C4×D3—21no—
142C3×C4×D3—21no—
143C3×C4×D3—21no—
144C3×C4×D3—22no—
145C3×C4×D3—21no—
146C3×Dic6—21no—
147#627—21no—
148#627C22×C412yes—
149#627C22×C411yescharacteristic
150#627C22×C411yescharacteristic
151#626—21no—
152#626—21no—
153#626—22no—
154#626—21no—
155#626—21no—
156#625—21no—
157#625C22×C411yescharacteristic
158#625C22×C411yescharacteristic
159#625C22×C412yes—
160#624—21no—
161D3×Dic3—22no—
162#622C22×C412yes—
163#622C22×C412yes—
164C32×C8C2×D412yes—
165C3⋊(C3⋊C8)C2×D412yes—
166C3×C3⋊C8—21no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—21no—
169#575—91no—
170#568—91no—
171#568—91no—
172#444—92no—
173#444—92no—
174#443—92no—
175#443—92no—
176#430—91no—
177C2×#104—91no—
178C2×#104—91no—
179C4×M16—91no—
180C3×#41—61no—
181C22×C3×C4—61no—
182C2×#67—61no—
183C2×#67—61no—
184#239—61no—
185D3×Q8—61no—
186#237—62no—
187#237—61no—
188D3×D4—61no—
189D3×D4—62no—
190#235—21no—
191#235—61no—
192#235—62no—
193#235—61no—
194#235—61no—
195#235—61no—
196#235—61no—
197#235—61no—
198#235—61no—
199#235—61no—
200C2×D12—61no—
201C2×C4×D3—21no—
202C2×C4×D3—61no—
203C2×C4×D3—61no—
204C2×C4×D3—62no—
205C2×Dic6—61no—
206C3×M16—21no—
207C3×M16—21no—
208C3×M16—62no—
209C3×M16—62no—
210C3×M16—61no—
211C2×C3×C8—62no—
212C2×C3×C8—62no—
213C2×C3×C8—61no—
214#208—21no—
215#208—61no—
216#208—61no—
217#208—62no—
218#208—62no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—62no—
221C2×C3⋊C8—62no—
222ΓL(1,𝔽25)—22no—
223ΓL(1,𝔽25)—22no—
224ΓL(1,𝔽25)—61no—
225ΓL(1,𝔽25)—61no—
226ΓL(1,𝔽25)—62no—
227ΓL(1,𝔽25)—62no—
228ΓL(1,𝔽25)—62no—
229ΓL(1,𝔽25)—61no—
230ΓL(1,𝔽25)—61no—
231ΓL(1,𝔽25)—62no—
232ΓL(1,𝔽25)—62no—
233D3×C8—22no—
234D3×C8—22no—
235D3×C8—62no—
236D3×C8—62no—
237D3×C8—62no—
238D3×C8—62no—
239D3×C8—62no—
240C22×C32C4×D411yescharacteristic
241C2×C3⋊D3—41no—
242C2×C3⋊D3C4×D411yescharacteristic
243C2×C3⋊D3C2×#4111yescharacteristic
244C2×C3×D3—22no—
245C2×C3×D3—21no—
246C2×C3×D3—21no—
247C2×C3×D3—81no—
248D32—81no—
249#157—22no—
250#157—41no—
251C32×C4C4×D411yescharacteristic
252C32×C4C22×D411yescharacteristic
253C3⋊Dic3C4×D411yescharacteristic
254C3⋊Dic3C23×C411yescharacteristic
255C3×Dic3—22no—
256C3×Dic3—21no—
257C3×Dic3—21no—
258C2×#41—91no—
259C2×#41—91no—
260#137—91no—
261#137—91no—
262#137—92no—
263AGL(1,ℤ/8)—91no—
264AGL(1,ℤ/8)—91no—
265AGL(1,ℤ/8)—92no—
266#135—92no—
267#135—92no—
268#131—61no—
269#131—92no—
270#131—92no—
271#131—92no—
272#131—92no—
273#131—182no—
274#131—181no—
275C2×M16—61no—
276C2×M16—91no—
277C2×M16—91no—
278C2×M16—91no—
279C2×M16—91no—
280C2×M16—182no—
281C2×M16—181no—
282C2×C42—91no—
283#108—92no—
284#108—92no—
285#104—91no—
286#104—91no—
287#104—92no—
288#104—91no—
289#104—91no—
290#104—92no—
291#97—92no—
292C4×C8—92no—
293C23×C3—61no—
294C22×D3—21no—
295C22×D3—61no—
296C22×D3—61no—
297C22×D3—62no—
298C3×Q8—61no—
299C3×D4—61no—
300C3×D4—62no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—61no—
304C2×C3×C4—62no—
305C2×C3×C4—61no—
306C2×C3×C4—61no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309#67—22no—
310#67—61no—
311#67—61no—
312#67—62no—
313#67—61no—
314#67—61no—
315#67—61no—
316#67—61no—
317#67—62no—
318#67—61no—
319#67—61no—
320C2×Dic3—21no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—62no—
324D12—21no—
325D12—61no—
326D12—61no—
327D12—61no—
328D12—61no—
329D12—62no—
330C4×D3—21no—
331C4×D3—22no—
332C4×D3—21no—
333C4×D3—21no—
334C4×D3—21no—
335C4×D3—61no—
336C4×D3—61no—
337C4×D3—61no—
338C4×D3—61no—
339C4×D3—61no—
340C4×D3—61no—
341C4×D3—61no—
342C4×D3—61no—
343C4×D3—62no—
344C4×D3—62no—
345Dic6—21no—
346Dic6—61no—
347Dic6—61no—
348Dic6—62no—
349Dic6—61no—
350Dic6—61no—
351C3×C8—22no—
352C3×C8—22no—
353C3×C8—61no—
354C3×C8—62no—
355C3×C8—61no—
356C3⋊C8—21no—
357C3⋊C8—22no—
358C3⋊C8—21no—
359C3⋊C8—62no—
360C3⋊C8—62no—
361C2×C32—21no—
362C2×C32C2×C4×D411yescharacteristic
363C3⋊D3—21no—
364C3⋊D3—21no—
365C3×D3—42no—
366C3×D3—41no—
367C3×D3—41no—
368#41—61no—
369#41—91no—
370#41—92no—
371#41—91no—
372#41—91no—
373#41—91no—
374#41—92no—
375#41—181no—
376#41—181no—
377#41—181no—
378C2×Q8—91no—
379C2×Q8—91no—
380C2×D4—91no—
381C2×D4—91no—
382C2×D4—181no—
383C2×D4—181no—
384C22×C4—61no—
385C22×C4—91no—
386C22×C4—181no—
387C22×C4—181no—
388Q16—92no—
389Q16—92no—
390SD16—92no—
391SD16—92no—
392SD16—92no—
393SD16—92no—
394D8—92no—
395D8—92no—
396M16—61no—
397M16—62no—
398M16—62no—
399M16—91no—
400M16—91no—
401M16—92no—
402M16—91no—
403M16—91no—
404M16—92no—
405M16—91no—
406M16—92no—
407M16—181no—
408M16—182no—
409M16—182no—
410M16GO+(4,𝔽2)11yescharacteristic
411C2×C8—61no—
412C2×C8—62no—
413C2×C8—62no—
414C2×C8—92no—
415C2×C8—92no—
416C2×C8—181no—
417C2×C8—182no—
418C2×C8—182no—
419C42—91no—
420C42—91no—
421C42—181no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—62no—
425C22×C3—61no—
426C22×C3—61no—
427C22×C3—241no—
428C2×D3—21no—
429C2×D3—21no—
430C2×D3—22no—
431C2×D3—61no—
432C2×D3—61no—
433C2×D3—61no—
434C2×D3—61no—
435C2×D3—81no—
436C2×D3—241no—
437C2×D3—241no—
438C2×D3—242no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—61no—
444C3×C4—61no—
445C3×C4—62no—
446Dic3—22no—
447Dic3—21no—
448Dic3—21no—
449Dic3—61no—
450Dic3—61no—
451Dic3—61no—
452Dic3—61no—
453C32#295611yescharacteristic, complemented, Sylow
454C23—61no—
455C23—91no—
456C23—181no—
457Q8—61no—
458Q8—91no—
459Q8—91no—
460Q8—92no—
461Q8—181no—
462D4—62no—
463D4—61no—
464D4—91no—
465D4—91no—
466D4—92no—
467D4—181no—
468D4—181no—
469D4—181no—
470D4—181no—
471D4—182no—
472D4—181no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—91no—
480C2×C4—91no—
481C2×C4—91no—
482C2×C4—91no—
483C2×C4—91no—
484C2×C4—181no—
485C2×C4—182no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—362no—
489C2×C4C2×GO+(4,𝔽2)11yescharacteristic
490C8—61no—
491C8—61no—
492C8—62no—
493C8—92no—
494C8—92no—
495C8—92no—
496C8C2×GO+(4,𝔽2)12yes—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—41no—
500C2×C3—41no—
501C2×C3—122no—
502C2×C3—121no—
503C2×C3—121no—
504D3—41no—
505D3—41no—
506D3—42no—
507D3—121no—
508D3—121no—
509D3—121no—
510D3—121no—
511C22—61no—
512C22—61no—
513C22—62no—
514C22—91no—
515C22—91no—
516C22—241no—
517C22—361no—
518C22—721no—
519C22C4×GO+(4,𝔽2)11yescharacteristic
520C4—61no—
521C4—61no—
522C4—62no—
523C4—91no—
524C4—91no—
525C4—182no—
526C4—361no—
527C4C4×GO+(4,𝔽2)11yescharacteristic
528C4C22×GO+(4,𝔽2)11yescharacteristic
529C3—21no—
530C3—21no—
531C2—21no—
532C2—121no—
533C2—121no—
534C2—122no—
535C2—181no—
536C2—181no—
537C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC4C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×M16D4
socleC2×C32C2×C4×D4
prime radical#10596499C2
cosocleC4×C3⋊D3C24
hypercenterM16GO+(4,𝔽2)
hypocenterC32#2956
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. #10594722C2semidirect
3. #10594708C2semidirect
4. M16×#157C2semidirect
5. #10593330C2semidirect
6. #10593325C2semidirect
7. C2×#63731C2semidirect
8. #10593299C2semidirect
9. #10593298C2semidirect
10. #10593298C2semidirect
11. #10593297C2semidirect
16. #64239C4semidirect
17. #64236C4semidirect
18. #64226C4semidirect
19. #64226C4semidirect
20. #64224C4semidirect
21. #64224C4semidirect
31. #63805C22semidirect
32. #63805C22semidirect
34. #63803C22semidirect
35. #63803C22semidirect
37. #63767C22semidirect
38. C8×#157C22semidirect
39. #63733C22semidirect
40. #63733C22semidirect
41. #63731C22semidirect
42. #63731C22semidirect
43. #63731C22semidirect
44. #63731C22semidirect
45. #63731C22semidirect
46. #63731C22semidirect
76. #3776C2×C4semidirect
77. #3776C2×C4semidirect
78. #3775C2×C4semidirect
79. #3775C2×C4semidirect
80. #3775C2×C4semidirect
81. #3775C2×C4semidirect
82. #3774C2×C4semidirect
83. #3774C2×C4semidirect
453. C32#2956semidirect

Maximal subgroups

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

subgroupindex
#105964992
#105947222
#105947082
M16×#1572
#105933302
#105933252
C2×#637312
#105932992
#105932982
#105932972
#29569