Finite Group Databasebeta

← #11899741

Subgroups — #11899741

Order 1152.

765 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594691C211yesmaximal, characteristic, complemented
2#10594680C211yesmaximal, characteristic, complemented
3#10592607C211yesmaximal, characteristic, complemented
4C3×#4909C211yesmaximal, characteristic, complemented
5C3×#4907C211yesmaximal, characteristic, complemented
6C2×#63549C211yesmaximal, characteristic, complemented
7#10590632C211yesmaximal, characteristic, complemented
8#10590243C212yesmaximal, complemented
9#10590238C212yesmaximal, complemented
10#10590233C212yesmaximal, complemented
11D3×#800C212yesmaximal, complemented
12#82040—31nomaximal
13#82014—31nomaximal
14#64308—21no—
15#64297—21no—
16#64113C2211yescharacteristic, complemented
17C2×#3745C2211yescharacteristic
18C2×C3×Dic12C2211yescharacteristic, complemented
19C3×#904C2211yescharacteristic
20C3×#901C2211yescharacteristic
21#63833—21no—
22#63825—21no—
23#63808C2212yes—
24#63808C2212yescomplemented
25#63801—22no—
26D3×Dic12C2212yescomplemented
27#63794—22no—
28D3×D24C2212yes—
29C32×M32C2211yescharacteristic, complemented
30#63627C2212yescomplemented
31#63626C2212yescomplemented
32C2×C3×C3⋊C16C2211yescharacteristic, complemented
33C3×Dic24C2212yescomplemented
34C3×#800C2212yescomplemented
35C3×#798C2212yescomplemented
36C3×D3×C16C2212yescomplemented
37#63551C2211yescharacteristic, complemented
38#63549C2212yescomplemented
39#63549C2212yescomplemented
40#63549C2211yescharacteristic, complemented
41#63548C2211yescharacteristic, complemented
42#63546C2211yescharacteristic, complemented
43#5769—31no—
44#5766—31no—
45#5753—31no—
46#5752—31no—
47C3×#510—31no—
48C3×#504—31no—
49#5194—31no—
50C2×#828—31no—
51#4919—32no—
52#4918—32no—
53#4914—32no—
54D3×SD32—32no—
55#4909—32no—
56#4909D311yescharacteristic, complemented
57#4908—31no—
58#4908—31no—
59#4908—32no—
60#4908—61no—
61#4907D311yescharacteristic, complemented
62#4904—31no—
63#4904—32no—
64C2×#800—31no—
65C2×#800—32no—
66#3828—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C3×#235—21no—
69C3×#235D411yescharacteristic
70C2×C3×Dic6—21no—
71#3811—42no—
72#3804—42no—
73D3×D12—22no—
74D3×D12—41no—
75#3799—22no—
76#3799—22no—
77#3799—41no—
78#3797—41no—
79#3796—41no—
80D3×Dic6—22no—
81C2×C32×C8C2311yescharacteristic
82#3746C2311yescharacteristic
83#3745—21no—
84#3745C2312yes—
85#3745C2311yescharacteristic
86#3744—21no—
87C3×#208D411yescharacteristic
88C3×Dic12—21no—
89C3×Dic12C2311yescharacteristic
90C3×Dic12C2312yes—
91C3×D24C2311yescharacteristic
92C3×#204—21no—
93C3×ΓL(1,𝔽25)D412yes—
94C3×D3×C8C2312yes—
95#3719—22no—
96#3717—22no—
97#3717—22no—
98#3714—22no—
99C32×C16C2312yes—
100C3×C3⋊C16C2311yescharacteristic
101C3×C3⋊C16C2311yescharacteristic
102#3416—91noSylow
103#1010—61no—
104#1009—61no—
105#1009—61no—
106#1007—61no—
107C3×#135—31no—
108C2×C3×Q16—31no—
109C3×#131—31no—
110#949—61no—
111#942—61no—
112#919—32no—
113#919—32no—
114#918—62no—
115D3×Q16—32no—
116#914—62no—
117D3×D8—32no—
118#909—62no—
119#909—61no—
120#908—62no—
121#908—61no—
122C2×Dic12—32no—
123C2×Dic12C2×D311yescharacteristic, complemented
124#904—31no—
125#904—31no—
126#904—32no—
127#904—32no—
128#904—61no—
129#904C2×D311yescharacteristic
130C2×D24—31no—
131C2×D24—31no—
132C2×D24—32no—
133C2×D24—61no—
134#901C2×D311yescharacteristic
135C3×Q32—32no—
136C3×SD32—32no—
137C3×M32—21no—
138C3×M32—32no—
139C3×M32C2×D311yescharacteristic, complemented
140C3×M32C2×D311yescharacteristic, complemented
141C2×C3×C16—31no—
142C2×C3×C16—32no—
143#829—31no—
144#828—32no—
145#828—32no—
146#828—31no—
147#827—31no—
148#826—31no—
149C2×C3⋊C16C2×D311yescharacteristic, complemented
150Dic24—31no—
151Dic24C2×D312yescomplemented
152#800—32no—
153#800—32no—
154#800—31no—
155#800—31no—
156#800—32no—
157#800—32no—
158#800—62no—
159#800C2×D312yescomplemented
160D48—31no—
161D48—32no—
162D48—32no—
163D48—62no—
164#798C2×D312yescomplemented
165D3×C16C2×D312yescomplemented
166C22×C3⋊D3—41no—
167C2×D32—42no—
168C2×C32×C4C2×D411yescharacteristic
169#638—41no—
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—21no—
172C4⋊(C3⋊D3)—41no—
173C4×C3⋊D3—41no—
174#634—21no—
175C3×#67—41no—
176C3×#67D812yes—
177C2×C3×Dic3—41no—
178C3×D12—21no—
179C3×D12D811yescharacteristic
180C3×C4×D3—41no—
181C3×C4×D3C2×D412yes—
182C3×Dic6—21no—
183C3×Dic6—22no—
184C3×Dic6—41no—
185C3×Dic6D811yescharacteristic
186#627—42no—
187#626—42no—
188#626—42no—
189#626—42no—
190#624—42no—
191#624—42no—
192D3×Dic3—42no—
193C32×C8C2×D411yescharacteristic
194C32×C8C2411yescharacteristic
195C3×C3⋊C8C2×D412yes—
196#578—91no—
197#576—91no—
198#510—31no—
199#510—92no—
200#509—92no—
201#509—91no—
202#508—92no—
203#508—91no—
204C2×SD32—92no—
205C2×SD32—91no—
206#504—31no—
207C3×#41—31no—
208C3×#41—61no—
209C2×C3×Q8—61no—
210#239—62no—
211#239—62no—
212#239—121no—
213#239—121no—
214D3×Q8—62no—
215D3×Q8—121no—
216D3×Q8—121no—
217#237—121no—
218#237—122no—
219D3×D4—62no—
220D3×D4—121no—
221D3×D4—122no—
222D3×D4—122no—
223#235—21no—
224#235—62no—
225#235—62no—
226#235—61no—
227#235—61no—
228#235—121no—
229#235—122no—
230#235—121no—
231#235D1211yescharacteristic
232C2×D12—62no—
233C2×D12—61no—
234C2×D12—61no—
235C2×D12—121no—
236C2×D12—121no—
237C2×Dic6—21no—
238C2×Dic6—62no—
239C3×Q16—32no—
240C3×Q16—31no—
241C3×Q16—61no—
242C3×SD16—61no—
243C3×D8—31no—
244C3×M16—31no—
245C3×M16—32no—
246C2×C3×C8—21no—
247C2×C3×C8—32no—
248C2×C3×C8C22×D311yescharacteristic
249C2×C3×C8C22×D311yescharacteristic
250#216—62no—
251#215—62no—
252#215—62no—
253#213—62no—
254#208D1211yescharacteristic
255Dic12—21no—
256Dic12—31no—
257Dic12—31no—
258Dic12—61no—
259Dic12—62no—
260Dic12C22×D312yes—
261Dic12C22×D311yescharacteristic
262D24—31no—
263D24—31no—
264D24—32no—
265D24—32no—
266D24—61no—
267D24—62no—
268D24—62no—
269D24—61no—
270D24—61no—
271D24—121no—
272D24C22×D311yescharacteristic
273#204—21no—
274#204—62no—
275#204—62no—
276#204—61no—
277#204—61no—
278#204—121no—
279ΓL(1,𝔽25)D1212yes—
280D3×C8C22×D312yes—
281C3×C16—22no—
282C3×C16—31no—
283C3×C16—31no—
284C3×C16C22×D312yes—
285C3×C16C22×D312yes—
286C3⋊C16C22×D311yescharacteristic
287C3⋊C16C22×D311yescharacteristic
288C22×C32C2×D811yescharacteristic
289C2×C3⋊D3—41no—
290C2×C3⋊D3—42no—
291C2×C3⋊D3—161no—
292C2×C3×D3—41no—
293C2×C3×D3C2×D812yes—
294D32—162no—
295C32×C4C2×D811yescharacteristic
296C32×C4C22×D411yescharacteristic
297C3⋊Dic3—41no—
298C3×Dic3—42no—
299C3×Dic3—41no—
300C3×Dic3C2×D812yes—
3012−1+4—181no—
302H(5,𝔽2)—181no—
303#137—182no—
304#137—181no—
305AGL(1,ℤ/8)—182no—
306AGL(1,ℤ/8)—181no—
307#135—31no—
308#135—92no—
309#135—92no—
310#135—91no—
311C2×Q16—31no—
312C2×Q16—92no—
313C2×D8—92no—
314C2×D8—91no—
315#131—31no—
316Q32—32no—
317Q32—91no—
318SD32—32no—
319SD32—91no—
320SD32—92no—
321SD32—92no—
322SD32—91no—
323SD32—92no—
324D16—91no—
325D16—92no—
326M32—32no—
327M32D3211yescharacteristic, complemented
328C2×C16—31no—
329C2×C16—32no—
330C22×D3—122no—
331C22×D3—121no—
332C22×D3—121no—
333C22×D3—122no—
334C22×D3—241no—
335C3×Q8—31no—
336C3×Q8—61no—
337C3×Q8—62no—
338C3×Q8—121no—
339C3×D4—32no—
340C3×D4—31no—
341C3×D4—61no—
342C3×D4—121no—
343C2×C3×C4—21no—
344C2×C3×C4—32no—
345C2×C3×C4—121no—
346C2×C3×C4—121no—
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349#67—41no—
350#67—122no—
351#67—122no—
352#67—121no—
353#67—121no—
354#67—122no—
355#67—241no—
356#67D2412yes—
357C2×Dic3—41no—
358C2×Dic3—122no—
359D12—21no—
360D12—61no—
361D12—62no—
362D12—61no—
363D12—62no—
364D12—121no—
365D12—122no—
366D12—122no—
367D12—122no—
368D12—122no—
369D12—121no—
370D12—121no—
371D12—241no—
372D12D2411yescharacteristic
373C4×D3—41no—
374C4×D3—122no—
375C4×D3—122no—
376C4×D3—122no—
377C4×D3—121no—
378C4×D3—121no—
379C4×D3—122no—
380C4×D3—122no—
381C4×D3—241no—
382C4×D3C2×D1212yes—
383Dic6—21no—
384Dic6—22no—
385Dic6—41no—
386Dic6—61no—
387Dic6—61no—
388Dic6—121no—
389Dic6—122no—
390Dic6—122no—
391Dic6D2411yescharacteristic
392C3×C8—21no—
393C3×C8—21no—
394C3×C8—32no—
395C3×C8C2×D1211yescharacteristic
396C3×C8D3×D411yescharacteristic
397C3×C8C23×D311yescharacteristic
398C3×C8C23×D311yescharacteristic
399C3⋊C8C2×D1212yes—
400C2×C32—21no—
401C2×C32C22×D811yescharacteristic
402C3⋊D3—82no—
403C3⋊D3—81no—
404C3×D3—22no—
405C3×D3—81no—
406#41—31no—
407#41—61no—
408#41—182no—
409#41—182no—
410#41—181no—
411#41—362no—
412#41—361no—
413#41—361no—
414C2×Q8—61no—
415C2×Q8—182no—
416C2×Q8—361no—
417C2×D4—182no—
418C2×D4—181no—
419C2×D4—361no—
420C2×D4—362no—
421Q16—32no—
422Q16—31no—
423Q16—61no—
424Q16—91no—
425Q16—182no—
426SD16—61no—
427SD16—182no—
428SD16—182no—
429SD16—181no—
430D8—31no—
431D8—91no—
432D8—92no—
433D8—182no—
434D8—181no—
435M16—31no—
436M16—32no—
437C2×C8—32no—
438C2×C8C2×D3211yescharacteristic
439C16—31no—
440C16—31no—
441C16C2×D3212yes—
442C22×C3—21no—
443C22×C3—32no—
444C22×C3—121no—
445C22×C3C2×D2411yescharacteristic
446C22×C3D3×D811yescharacteristic
447C2×D3—41no—
448C2×D3—121no—
449C2×D3—122no—
450C2×D3—121no—
451C2×D3—122no—
452C2×D3—241no—
453C2×D3—242no—
454C2×D3—482no—
455C2×D3—482no—
456C2×D3—481no—
457C2×D3—481no—
458C2×D3—482no—
459C2×D3C2×D2412yes—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—32no—
463C3×C4—122no—
464C3×C4—121no—
465C3×C4C2×D2411yescharacteristic
466C3×C4D3×D811yescharacteristic
467C3×C4C22×D1211yescharacteristic
468C3×C4C2×D3×D411yescharacteristic
469Dic3—42no—
470Dic3—41no—
471Dic3—121no—
472Dic3—121no—
473Dic3—241no—
474Dic3C2×D2412yes—
475C32#341611yescharacteristic, complemented, Sylow
476C23—362no—
477C23—361no—
478Q8—31no—
479Q8—61no—
480Q8—62no—
481Q8—121no—
482Q8—181no—
483Q8—362no—
484D4—32no—
485D4—31no—
486D4—61no—
487D4—121no—
488D4—182no—
489D4—181no—
490D4—362no—
491D4—362no—
492D4—362no—
493D4—361no—
494D4—361no—
495C2×C4—32no—
496C2×C4—121no—
497C2×C4—121no—
498C2×C4—362no—
499C2×C4—362no—
500C2×C4—362no—
501C2×C4—361no—
502C2×C4D3×D1211yescharacteristic
503C8—32no—
504C8D3×D1211yescharacteristic
505C8C22×D3211yescharacteristic
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—41no—
510C2×C3—62no—
511C2×C3—241no—
512C2×C3C22×D2411yescharacteristic
513C2×C3C2×D3×D811yescharacteristic
514D3—22no—
515D3—81no—
516D3—242no—
517D3—241no—
518D3—242no—
519D3—241no—
520D3—482no—
521D3—481no—
522C22—32no—
523C22—121no—
524C22—361no—
525C22—362no—
526C22—1441no—
527C22—1442no—
528C22D3×D2411yescharacteristic
529C4—32no—
530C4—121no—
531C4—122no—
532C4—361no—
533C4D3×D2411yescharacteristic
534C4C2×D3×D1211yescharacteristic
535C3—21no—
536C3#8201411yescharacteristic, complemented
537C3#8204011yescharacteristic, complemented
538C2—21no—
539C2—62no—
540C2—241no—
541C2—722no—
542C2—721no—
543C2C2×D3×D2411yescharacteristic
subgroupG/H
centerC2C2×D3×D24
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×M32C22
socleC2×C32C22×D8
hypercenterM32D32
hypocenterC32#3416
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
1. #10594691C2semidirect
2. #10594680C2semidirect
3. #10592607C2semidirect
4. C3×#4909C2semidirect
5. C3×#4907C2semidirect
6. C2×#63549C2semidirect
7. #10590632C2semidirect
8. #10590243C2semidirect
9. #10590238C2semidirect
10. #10590233C2semidirect
11. D3×#800C2semidirect
16. #64113C22semidirect
18. C2×C3×Dic12C22semidirect
24. #63808C22semidirect
26. D3×Dic12C22semidirect
29. C32×M32C22semidirect
30. #63627C22semidirect
31. #63626C22semidirect
32. C2×C3×C3⋊C16C22semidirect
33. C3×Dic24C22semidirect
34. C3×#800C22semidirect
35. C3×#798C22semidirect
36. C3×D3×C16C22semidirect
37. #63551C22semidirect
38. #63549C22semidirect
39. #63549C22semidirect
40. #63549C22semidirect
41. #63548C22semidirect
42. #63546C22semidirect
56. #4909D3semidirect
61. #4907D3semidirect
123. C2×Dic12C2×D3semidirect
139. C3×M32C2×D3semidirect
140. C3×M32C2×D3semidirect
149. C2×C3⋊C16C2×D3semidirect
151. Dic24C2×D3semidirect
159. #800C2×D3semidirect
164. #798C2×D3semidirect
165. D3×C16C2×D3semidirect
327. M32D32semidirect
475. C32#3416semidirect
536. C3#82014semidirect
537. C3#82040semidirect

Maximal subgroups

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

subgroupindex
#105946912
#105946802
#105926072
C3×#49092
C3×#49072
C2×#635492
#105906322
#105902432
#105902382
#105902332
D3×#8002
#820403
#820143