Finite Group Databasebeta

← #11899733

Subgroups — #11899733

Order 1152.

762 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#10594703C211yesmaximal, characteristic, complemented
2#10594687C211yesmaximal, characteristic, complemented
3#10592600C211yesmaximal, characteristic, complemented
4C3×#4904C211yesmaximal, characteristic, complemented
5C2×C3×#800C211yesmaximal, characteristic, complemented
6#10590636C211yesmaximal, characteristic, complemented
7#10590630C211yesmaximal, characteristic, complemented
8#10590246C212yesmaximal, complemented
9#10590245C212yesmaximal, complemented
10#10590236C212yesmaximal, complemented
11#10590235C212yesmaximal, complemented
12#82032—31nomaximal
13#82024—31nomaximal
14#64307—21no—
15#64297—21no—
16#64110C2211yescharacteristic
17C2×C3×Dic12C2211yescharacteristic, complemented
18C3×#904C2211yescharacteristic
19C3×#904C2211yescharacteristic, complemented
20C2×C3×D24C2211yescharacteristic
21#63827—21no—
22#63823—21no—
23#63811—22no—
24#63810C2212yes—
25#63810C2212yescomplemented
26#63802C2212yescomplemented
27#63798—22no—
28#63797C2212yes—
29C2×C32×C16C2211yescharacteristic, complemented
30#63639C2211yescharacteristic, complemented
31#63625C2212yescomplemented
32C16×C3⋊D3C2212yescomplemented
33C3×Dic24C2211yescharacteristic, complemented
34C3×#800C2212yescomplemented
35C3×#800C2212yescomplemented
36C3×#800C2211yescharacteristic, complemented
37C3×#800C2211yescharacteristic, complemented
38C3×D48C2211yescharacteristic, complemented
39#63550C2212yescomplemented
40#63547C2212yescomplemented
41#63547C2212yescomplemented
42#63545C2212yescomplemented
43#5771—31no—
44#5769—31no—
45#5766—31no—
46#5757—31no—
47C3×#508—31no—
48C2×C3×SD32—31no—
49#5195—31no—
50#5193—31no—
51#5179—31no—
52#5147—31no—
53#4918—32no—
54#4916—32no—
55#4916—32no—
56#4915—32no—
57#4914—32no—
58D3×SD32—32no—
59D3×SD32—32no—
60#4911—32no—
61#4904D311yescharacteristic, complemented
62C2×#800D311yescharacteristic, complemented
63#4901—31no—
64#4901—31no—
65#4901—61no—
66#3828D411yescharacteristic
67C3×#235—21no—
68C3×#235—21no—
69C2×C3×D12—21no—
70C2×C3×Dic6—21no—
71D3×#67—42no—
72#3804—42no—
73#3802—22no—
74D3×D12—41no—
75#3799—41no—
76#3797—22no—
77#3796—22no—
78#3796—22no—
79#3795—41no—
80D3×Dic6—41no—
81C2×C32×C8C2311yescharacteristic
82#3748D411yescharacteristic
83#3743D412yes—
84C8×C3⋊D3C2312yes—
85C3×Dic12—21no—
86C3×Dic12C2311yescharacteristic
87C3×Dic12C2311yescharacteristic
88C3×Dic12C2312yes—
89C3×D24—21no—
90C3×D24C2312yes—
91C3×D24C2311yescharacteristic
92C3×D24C2311yescharacteristic
93C3×#204—21no—
94C3×#204—21no—
95#3718—22no—
96#3715—22no—
97#3715—22no—
98#3713—22no—
99C32×C16C2311yescharacteristic
100C32×C16C2311yescharacteristic
101C3⋊(C3⋊C16)C2312yes—
102#3416—91noSylow
103#1010—61no—
104#1009—61no—
105#1007—61no—
106#1004—61no—
107C3×#135—31no—
108C3×#135—31no—
109C2×C3×Q16—31no—
110C2×C3×D8—31no—
111#951—61no—
112#949—61no—
113#942—61no—
114#932—61no—
115#919—32no—
116#919—32no—
117#918—62no—
118D3×Q16—32no—
119D3×Q16—32no—
120#915—62no—
121#914—62no—
122#912—32no—
123#912—32no—
124#911—62no—
125D3×D8—32no—
126D3×D8—32no—
127C2×Dic12C2×D311yescharacteristic, complemented
128#904C2×D311yescharacteristic
129#904C2×D311yescharacteristic, complemented
130C2×D24C2×D311yescharacteristic
131#901—31no—
132#901—31no—
133#901—61no—
134C3×Q32—31no—
135C3×SD32—32no—
136C3×SD32—32no—
137C3×SD32—31no—
138C3×SD32—31no—
139C3×D16—31no—
140C2×C3×C16—21no—
141C2×C3×C16C2×D311yescharacteristic, complemented
142C2×C3×C16C2×D311yescharacteristic, complemented
143#829—32no—
144#829—32no—
145#828—32no—
146#828—32no—
147#827—32no—
148#827—32no—
149#826—32no—
150#826—32no—
151#812—31no—
152#812—31no—
153#812—61no—
154Dic24C2×D311yescharacteristic, complemented
155#800C2×D312yescomplemented
156#800C2×D312yescomplemented
157#800C2×D311yescharacteristic, complemented
158#800C2×D311yescharacteristic, complemented
159D48C2×D311yescharacteristic, complemented
160#798—32no—
161#798—32no—
162#798—62no—
163D3×C16—32no—
164D3×C16—32no—
165D3×C16—62no—
166C22×C3×D3—41no—
167C2×D32—42no—
168C2×C32×C4C2×D411yescharacteristic
169#638D812yes—
170C4⋊(C3⋊D3)D811yescharacteristic
171C4×C3⋊D3C2×D412yes—
172#634D811yescharacteristic
173C3×#67—41no—
174C3×#67—41no—
175C2×C3×Dic3—41no—
176C3×D12—21no—
177C3×D12—22no—
178C3×D12—21no—
179C3×D12—41no—
180C3×C4×D3—41no—
181C3×C4×D3—41no—
182C3×Dic6—21no—
183C3×Dic6—22no—
184C3×Dic6—21no—
185C3×Dic6—41no—
186#627—42no—
187#626—42no—
188#626—42no—
189#625—42no—
190#624—42no—
191D3×Dic3—42no—
192D3×Dic3—42no—
193C32×C8C2×D411yescharacteristic
194C32×C8C2411yescharacteristic
195C3⋊(C3⋊C8)C2×D412yes—
196#578—91no—
197#576—91no—
198#510—92no—
199#510—91no—
200#509—92no—
201#509—91no—
202#508—31no—
203#508—92no—
204C2×SD32—31no—
205C2×SD32—92no—
206#504—91no—
207C3×#41—61no—
208C3×#41—61no—
209C2×C3×Q8—61no—
210C2×C3×D4—61no—
211C2×#67—122no—
212#239—62no—
213#239—62no—
214#239—121no—
215D3×Q8—62no—
216D3×Q8—62no—
217D3×Q8—121no—
218#237—62no—
219#237—62no—
220#237—121no—
221#237—122no—
222D3×D4—62no—
223D3×D4—62no—
224D3×D4—121no—
225D3×D4—122no—
226#235—21no—
227#235—21no—
228#235—31no—
229#235—31no—
230#235—61no—
231#235—121no—
232#235—121no—
233#235—122no—
234C2×D12—21no—
235C2×D12—121no—
236C2×Dic6—21no—
237C2×Dic6—121no—
238C3×Q16—31no—
239C3×Q16—32no—
240C3×Q16—31no—
241C3×Q16—61no—
242C3×SD16—61no—
243C3×SD16—61no—
244C3×D8—31no—
245C3×D8—32no—
246C3×D8—31no—
247C3×D8—61no—
248C2×C3×C8—21no—
249C2×C3×C8C22×D311yescharacteristic
250C2×C3×C8C22×D311yescharacteristic
251#216—62no—
252#216—62no—
253#215—62no—
254#215—62no—
255#214—62no—
256#214—62no—
257#213—62no—
258#213—62no—
259#208—31no—
260#208—31no—
261#208—61no—
262Dic12—21no—
263Dic12C22×D312yes—
264Dic12C22×D311yescharacteristic
265Dic12C22×D311yescharacteristic
266D24—21no—
267D24C22×D311yescharacteristic
268D24C22×D311yescharacteristic
269D24C22×D312yes—
270#204—21no—
271#204—21no—
272ΓL(1,𝔽25)—32no—
273ΓL(1,𝔽25)—32no—
274ΓL(1,𝔽25)—62no—
275D3×C8—32no—
276D3×C8—32no—
277D3×C8—62no—
278C3×C16—21no—
279C3×C16—21no—
280C3×C16C22×D311yescharacteristic
281C3×C16C22×D311yescharacteristic
282C3×C16C22×D311yescharacteristic
283C3×C16C22×D311yescharacteristic
284C3⋊C16—32no—
285C3⋊C16—32no—
286C3⋊C16—62no—
287C22×C32C2×D811yescharacteristic
288C2×C3⋊D3C2×D812yes—
289C2×C3×D3—41no—
290C2×C3×D3—42no—
291C2×C3×D3—41no—
292C2×C3×D3—161no—
293D32—162no—
294C32×C4C2×D811yescharacteristic
295C32×C4C22×D411yescharacteristic
296C3⋊Dic3C2×D812yes—
297C3×Dic3—41no—
298C3×Dic3—42no—
299C3×Dic3—41no—
3002−1+4—181no—
301H(5,𝔽2)—181no—
302#137—182no—
303#137—181no—
304AGL(1,ℤ/8)—182no—
305AGL(1,ℤ/8)—181no—
306#135—31no—
307#135—31no—
308#135—92no—
309#135—92no—
310C2×Q16—31no—
311C2×Q16—92no—
312C2×D8—31no—
313C2×D8—92no—
314#131—91no—
315Q32—31no—
316Q32—92no—
317SD32—32no—
318SD32—32no—
319SD32—31no—
320SD32—31no—
321SD32—92no—
322SD32—92no—
323D16—31no—
324D16—92no—
325M32—91no—
326M32—92no—
327C2×C16—92no—
328C2×C16D3211yescharacteristic, complemented
329C23×C3—121no—
330C22×D3—41no—
331C22×D3—122no—
332C22×D3—122no—
333C3×Q8—61no—
334C3×Q8—62no—
335C3×Q8—61no—
336C3×Q8—121no—
337C3×D4—61no—
338C3×D4—62no—
339C3×D4—61no—
340C3×D4—121no—
341C3×D4—121no—
342C3×D4—121no—
343C2×C3×C4—21no—
344C2×C3×C4—121no—
345C2×C3×C4—121no—
346C2×C3×C4—121no—
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349#67—32no—
350#67—32no—
351#67—41no—
352#67—41no—
353#67—62no—
354#67—122no—
355#67—122no—
356#67—122no—
357#67—122no—
358C2×Dic3—41no—
359C2×Dic3—122no—
360C2×Dic3—122no—
361D12—21no—
362D12—21no—
363D12—22no—
364D12—31no—
365D12—31no—
366D12—41no—
367D12—61no—
368D12—122no—
369D12—122no—
370C4×D3—32no—
371C4×D3—32no—
372C4×D3—41no—
373C4×D3—41no—
374C4×D3—62no—
375C4×D3—122no—
376C4×D3—122no—
377C4×D3—122no—
378C4×D3—122no—
379Dic6—21no—
380Dic6—21no—
381Dic6—22no—
382Dic6—31no—
383Dic6—31no—
384Dic6—41no—
385Dic6—61no—
386Dic6—122no—
387Dic6—122no—
388C3×C8—21no—
389C3×C8—21no—
390C3×C8D3×D411yescharacteristic
391C3×C8D3×D411yescharacteristic
392C3×C8C23×D311yescharacteristic
393C3×C8C23×D311yescharacteristic
394C3⋊C8—32no—
395C3⋊C8—32no—
396C3⋊C8—62no—
397C2×C32—21no—
398C2×C32C22×D811yescharacteristic
399C3⋊D3—22no—
400C3×D3—81no—
401C3×D3—82no—
402C3×D3—81no—
403#41—61no—
404#41—61no—
405#41—91no—
406#41—182no—
407#41—182no—
408#41—362no—
409#41—361no—
410#41—361no—
411C2×Q8—61no—
412C2×Q8—182no—
413C2×Q8—361no—
414C2×D4—61no—
415C2×D4—182no—
416C2×D4—361no—
417C2×D4—362no—
418Q16—32no—
419Q16—31no—
420Q16—31no—
421Q16—61no—
422Q16—182no—
423SD16—61no—
424SD16—61no—
425SD16—182no—
426SD16—182no—
427D8—31no—
428D8—31no—
429D8—32no—
430D8—61no—
431D8—182no—
432M16—91no—
433M16—92no—
434C2×C8—92no—
435C2×C8C2×D3211yescharacteristic
436C16—92no—
437C16C2×D3211yescharacteristic
438C16C2×D3211yescharacteristic
439C22×C3—21no—
440C22×C3—121no—
441C22×C3—122no—
442C22×C3—121no—
443C22×C3—481no—
444C22×C3D3×D811yescharacteristic
445C22×C3D3×D811yescharacteristic
446C2×D3—32no—
447C2×D3—32no—
448C2×D3—41no—
449C2×D3—41no—
450C2×D3—42no—
451C2×D3—62no—
452C2×D3—161no—
453C2×D3—482no—
454C2×D3—482no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—121no—
458C3×C4—122no—
459C3×C4—121no—
460C3×C4D3×D811yescharacteristic
461C3×C4D3×D811yescharacteristic
462C3×C4C2×D3×D411yescharacteristic
463C3×C4C2×D3×D411yescharacteristic
464Dic3—32no—
465Dic3—32no—
466Dic3—42no—
467Dic3—41no—
468Dic3—41no—
469Dic3—62no—
470C32#341611yescharacteristic, complemented, Sylow
471C23—121no—
472C23—362no—
473Q8—61no—
474Q8—61no—
475Q8—62no—
476Q8—91no—
477Q8—121no—
478Q8—362no—
479D4—62no—
480D4—61no—
481D4—61no—
482D4—92no—
483D4—91no—
484D4—121no—
485D4—121no—
486D4—121no—
487D4—362no—
488D4—362no—
489D4—362no—
490C2×C4—92no—
491C2×C4—121no—
492C2×C4—121no—
493C2×C4—121no—
494C2×C4—362no—
495C2×C4—362no—
496C2×C4—362no—
497C2×C4#380211yescharacteristic
498C8—92no—
499C8#380211yescharacteristic
500C8C22×D3211yescharacteristic
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—41no—
505C2×C3—241no—
506C2×C3—241no—
507C2×C3—242no—
508C2×C3C2×D3×D811yescharacteristic
509C2×C3C2×D3×D811yescharacteristic
510D3—62no—
511D3—62no—
512D3—82no—
513D3—81no—
514D3—81no—
515D3—122no—
516C22—92no—
517C22—121no—
518C22—121no—
519C22—122no—
520C22—481no—
521C22—1442no—
522C22#6379711yescharacteristic
523C4—92no—
524C4—121no—
525C4—121no—
526C4—122no—
527C4#6379711yescharacteristic
528C4C2×#380211yescharacteristic
529C3—21no—
530C3#8202411yescharacteristic, complemented
531C3#8203211yescharacteristic, complemented
532C2—21no—
533C2—182no—
534C2—242no—
535C2—241no—
536C2—241no—
537C2C2×#6379711yescharacteristic
subgroupG/H
centerC2C2×#63797
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×C16C22
socleC2×C32C22×D8
hypercenterC2×C16D32
hypocenterC32#3416
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. #10594703C2semidirect
2. #10594687C2semidirect
3. #10592600C2semidirect
4. C3×#4904C2semidirect
5. C2×C3×#800C2semidirect
6. #10590636C2semidirect
7. #10590630C2semidirect
8. #10590246C2semidirect
9. #10590245C2semidirect
10. #10590236C2semidirect
11. #10590235C2semidirect
17. C2×C3×Dic12C22semidirect
19. C3×#904C22semidirect
25. #63810C22semidirect
26. #63802C22semidirect
29. C2×C32×C16C22semidirect
30. #63639C22semidirect
31. #63625C22semidirect
32. C16×C3⋊D3C22semidirect
33. C3×Dic24C22semidirect
34. C3×#800C22semidirect
35. C3×#800C22semidirect
36. C3×#800C22semidirect
37. C3×#800C22semidirect
38. C3×D48C22semidirect
39. #63550C22semidirect
40. #63547C22semidirect
41. #63547C22semidirect
42. #63545C22semidirect
61. #4904D3semidirect
62. C2×#800D3semidirect
127. C2×Dic12C2×D3semidirect
129. #904C2×D3semidirect
141. C2×C3×C16C2×D3semidirect
142. C2×C3×C16C2×D3semidirect
154. Dic24C2×D3semidirect
155. #800C2×D3semidirect
156. #800C2×D3semidirect
157. #800C2×D3semidirect
158. #800C2×D3semidirect
159. D48C2×D3semidirect
328. C2×C16D32semidirect
470. C32#3416semidirect
530. C3#82024semidirect
531. C3#82032semidirect

Maximal subgroups

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

subgroupindex
#105947032
#105946872
#105926002
C3×#49042
C2×C3×#8002
#105906362
#105906302
#105902462
#105902452
#105902362
#105902352
#820323
#820243