Finite Group Databasebeta

← #11899732

Subgroups — #11899732

Order 1152.

765 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594692C211yesmaximal, characteristic, complemented
2#10594680C211yesmaximal, characteristic, complemented
3C2×#63627C211yesmaximal, characteristic, complemented
4C3×#4904C211yesmaximal, characteristic, complemented
5C3×#4901C211yesmaximal, characteristic, complemented
6#10590638C211yesmaximal, characteristic, complemented
7#10590634C211yesmaximal, characteristic, complemented
8#10590242C212yesmaximal, complemented
9#10590238C212yesmaximal, complemented
10#10590232C212yesmaximal, complemented
11D3×#800C212yesmaximal, complemented
12#82032—31nomaximal
13#82014—31nomaximal
14#64308—21no—
15#64298—21no—
16C2×#3746C2211yescharacteristic, complemented
17C2×#3745C2211yescharacteristic
18C3×#904C2211yescharacteristic
19C3×#904C2211yescharacteristic, complemented
20C3×#901C2211yescharacteristic
21#63831—21no—
22#63825—21no—
23#63808C2212yes—
24#63807C2212yescomplemented
25#63800—22no—
26D3×Dic12C2212yescomplemented
27#63794—22no—
28D3×D24C2212yes—
29C2×C32×C16C2211yescharacteristic, complemented
30#63627C2212yescomplemented
31#63627C2212yescomplemented
32C3×#812C2211yescharacteristic, complemented
33C3×Dic24C2211yescharacteristic, complemented
34C3×#800C2211yescharacteristic, complemented
35C3×#800C2211yescharacteristic, complemented
36C3×D48C2211yescharacteristic, complemented
37C3×#798C2212yescomplemented
38C3×D3×C16C2212yescomplemented
39#63551C2212yescomplemented
40#63549C2212yescomplemented
41#63548C2212yescomplemented
42#63546C2212yescomplemented
43#5771—31no—
44#5769—31no—
45#5753—31no—
46#5752—31no—
47C3×#508—31no—
48C3×#504—31no—
49#5195—31no—
50#5193—31no—
51#4918—32no—
52#4916—32no—
53D3×SD32—32no—
54#4911—32no—
55#4909—31no—
56#4909—32no—
57#4908—31no—
58#4908—32no—
59#4904—32no—
60#4904D311yescharacteristic, complemented
61C2×#800—31no—
62C2×#800—31no—
63C2×#800—32no—
64C2×#800—61no—
65#4901D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)—21no—
67C2×#634—21no—
68C3×#235—21no—
69C3×#235—21no—
70C3×#235D411yescharacteristic
71#3811—42no—
72#3805—42no—
73D3×D12—22no—
74D3×D12—41no—
75#3799—22no—
76#3799—41no—
77#3795—22no—
78#3795—41no—
79D3×Dic6—22no—
80D3×Dic6—41no—
81C2×C32×C8C2311yescharacteristic
82#3746—21no—
83#3746C2312yes—
84#3745—21no—
85#3745C2312yes—
86C3×#208D411yescharacteristic
87C3×Dic12C2311yescharacteristic
88C3×Dic12C2311yescharacteristic
89C3×D24C2311yescharacteristic
90C3×D24C2311yescharacteristic
91C3×#204—21no—
92C3×#204—21no—
93C3×ΓL(1,𝔽25)D412yes—
94C3×D3×C8C2312yes—
95#3719—22no—
96#3717—22no—
97#3716—22no—
98#3714—22no—
99C32×C16C2311yescharacteristic
100C32×C16C2311yescharacteristic
101C3×C3⋊C16C2312yes—
102#3416—91noSylow
103#1010—61no—
104#1010—61no—
105#1009—61no—
106#1009—61no—
107C3×#135—31no—
108C3×#135—31no—
109C3×#131—31no—
110#951—61no—
111#949—61no—
112#919—32no—
113D3×Q16—32no—
114#915—62no—
115#914—62no—
116#912—32no—
117D3×D8—32no—
118#909—62no—
119#909—61no—
120#908—62no—
121#908—61no—
122C2×Dic12—31no—
123C2×Dic12—31no—
124C2×Dic12—32no—
125C2×Dic12—61no—
126#904—32no—
127#904—32no—
128#904C2×D311yescharacteristic
129#904C2×D311yescharacteristic, complemented
130C2×D24—31no—
131C2×D24—31no—
132C2×D24—32no—
133C2×D24—61no—
134#901C2×D311yescharacteristic
135C3×Q32—31no—
136C3×SD32—31no—
137C3×SD32—31no—
138C3×D16—31no—
139C3×M32—31no—
140C3×M32—32no—
141C2×C3×C16—21no—
142C2×C3×C16—32no—
143C2×C3×C16C2×D311yescharacteristic, complemented
144C2×C3×C16C2×D311yescharacteristic, complemented
145#829—32no—
146#828—32no—
147#827—32no—
148#826—32no—
149#812C2×D311yescharacteristic, complemented
150Dic24—32no—
151Dic24C2×D311yescharacteristic, complemented
152#800—32no—
153#800—32no—
154#800—32no—
155#800—32no—
156#800—32no—
157#800—32no—
158#800—62no—
159#800—62no—
160#800C2×D311yescharacteristic, complemented
161#800C2×D311yescharacteristic, complemented
162D48—32no—
163D48C2×D311yescharacteristic, complemented
164#798C2×D312yescomplemented
165D3×C16C2×D312yescomplemented
166C22×C3⋊D3—41no—
167C2×D32—42no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C3⋊Dic3—41no—
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—41no—
172#634—22no—
173#634—41no—
174C3×#67—41no—
175C3×#67—41no—
176C3×#67D812yes—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12D811yescharacteristic
180C3×C4×D3—41no—
181C3×C4×D3—41no—
182C3×C4×D3C2×D412yes—
183C3×Dic6—21no—
184C3×Dic6—21no—
185C3×Dic6D811yescharacteristic
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⋊C8C2×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—92no—
205C2×SD32—91no—
206#504—31no—
207C3×#41—31no—
208C3×#41—61no—
209C3×#41—61no—
210#239—62no—
211#239—121no—
212D3×Q8—62no—
213D3×Q8—121no—
214#237—62no—
215#237—121no—
216#237—122no—
217#237—122no—
218D3×D4—62no—
219D3×D4—121no—
220D3×D4—122no—
221D3×D4—122no—
222#235—21no—
223#235—21no—
224#235—62no—
225#235—62no—
226#235—121no—
227#235—121no—
228#235D1211yescharacteristic
229C2×D12—62no—
230C2×D12—61no—
231C2×D12—61no—
232C2×D12—121no—
233C2×D12—121no—
234C2×Dic6—62no—
235C2×Dic6—61no—
236C2×Dic6—61no—
237C2×Dic6—121no—
238C2×Dic6—121no—
239C3×Q16—31no—
240C3×Q16—31no—
241C3×SD16—61no—
242C3×SD16—61no—
243C3×D8—31no—
244C3×D8—31no—
245C3×M16—31no—
246C3×M16—32no—
247C2×C3×C8—21no—
248C2×C3×C8—32no—
249C2×C3×C8C22×D311yescharacteristic
250C2×C3×C8C22×D311yescharacteristic
251#216—62no—
252#215—62no—
253#214—62no—
254#213—62no—
255#208D1211yescharacteristic
256Dic12—32no—
257Dic12—32no—
258Dic12—62no—
259Dic12—62no—
260Dic12—61no—
261Dic12—61no—
262Dic12—121no—
263Dic12C22×D311yescharacteristic
264Dic12C22×D311yescharacteristic
265D24—32no—
266D24—32no—
267D24—62no—
268D24—62no—
269D24—61no—
270D24—61no—
271D24—121no—
272D24C22×D311yescharacteristic
273D24C22×D311yescharacteristic
274#204—21no—
275#204—21no—
276#204—62no—
277#204—62no—
278ΓL(1,𝔽25)D1212yes—
279D3×C8C22×D312yes—
280C3×C16—21no—
281C3×C16—21no—
282C3×C16—32no—
283C3×C16C22×D311yescharacteristic
284C3×C16C22×D311yescharacteristic
285C3×C16C22×D311yescharacteristic
286C3×C16C22×D311yescharacteristic
287C3⋊C16C22×D312yes—
288C22×C32C2×D811yescharacteristic
289C2×C3⋊D3—42no—
290C2×C3⋊D3—161no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3C2×D812yes—
294D32—162no—
295C32×C4C2×D811yescharacteristic
296C32×C4C22×D411yescharacteristic
297C3⋊Dic3—42no—
298C3×Dic3—41no—
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—31no—
309#135—92no—
310#135—92no—
311C2×Q16—92no—
312C2×Q16—91no—
313C2×D8—92no—
314C2×D8—91no—
315#131—31no—
316Q32—31no—
317Q32—92no—
318SD32—31no—
319SD32—31no—
320SD32—92no—
321SD32—92no—
322SD32—92no—
323SD32—92no—
324D16—31no—
325D16—92no—
326M32—31no—
327M32—32no—
328C2×C16—32no—
329C2×C16D3211yescharacteristic, complemented
330C22×D3—122no—
331C22×D3—121no—
332C22×D3—121no—
333C22×D3—122no—
334C22×D3—241no—
335C3×Q8—31no—
336C3×Q8—61no—
337C3×Q8—61no—
338C3×D4—32no—
339C3×D4—31no—
340C3×D4—61no—
341C3×D4—61no—
342C3×D4—121no—
343C3×D4—121no—
344C2×C3×C4—21no—
345C2×C3×C4—32no—
346C2×C3×C4—121no—
347C2×C3×C4—121no—
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350#67—41no—
351#67—41no—
352#67—122no—
353#67—122no—
354#67—122no—
355#67—122no—
356#67D2412yes—
357C2×Dic3—122no—
358C2×Dic3—121no—
359C2×Dic3—121no—
360C2×Dic3—122no—
361C2×Dic3—241no—
362D12—21no—
363D12—21no—
364D12—62no—
365D12—62no—
366D12—122no—
367D12—122no—
368D12—122no—
369D12—121no—
370D12—121no—
371D12—241no—
372D12D2411yescharacteristic
373C4×D3—41no—
374C4×D3—41no—
375C4×D3—122no—
376C4×D3—122no—
377C4×D3—122no—
378C4×D3—122no—
379C4×D3C2×D1212yes—
380Dic6—21no—
381Dic6—21no—
382Dic6—62no—
383Dic6—62no—
384Dic6—122no—
385Dic6—122no—
386Dic6—121no—
387Dic6—121no—
388Dic6—122no—
389Dic6—241no—
390Dic6D2411yescharacteristic
391C3×C8—21no—
392C3×C8—21no—
393C3×C8—32no—
394C3×C8C2×D1211yescharacteristic
395C3×C8D3×D411yescharacteristic
396C3×C8C23×D311yescharacteristic
397C3×C8C23×D311yescharacteristic
398C3⋊C8C2×D1212yes—
399C2×C32—21no—
400C2×C32C22×D811yescharacteristic
401C3⋊D3—82no—
402C3×D3—22no—
403C3×D3—81no—
404C3×D3—81no—
405#41—31no—
406#41—61no—
407#41—61no—
408#41—182no—
409#41—182no—
410#41—361no—
411#41—361no—
412#41—362no—
413C2×Q8—182no—
414C2×Q8—181no—
415C2×Q8—361no—
416C2×D4—182no—
417C2×D4—181no—
418C2×D4—361no—
419C2×D4—362no—
420Q16—31no—
421Q16—31no—
422Q16—92no—
423Q16—182no—
424Q16—181no—
425SD16—61no—
426SD16—61no—
427SD16—182no—
428SD16—182no—
429D8—31no—
430D8—31no—
431D8—92no—
432D8—182no—
433D8—181no—
434M16—31no—
435M16—32no—
436C2×C8—32no—
437C2×C8C2×D3211yescharacteristic
438C16—32no—
439C16C2×D3211yescharacteristic
440C16C2×D3211yescharacteristic
441C22×C3—21no—
442C22×C3—32no—
443C22×C3—121no—
444C22×C3—121no—
445C22×C3C2×D2411yescharacteristic
446C22×C3D3×D811yescharacteristic
447C2×D3—41no—
448C2×D3—41no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—242no—
452C2×D3—482no—
453C2×D3—482no—
454C2×D3—481no—
455C2×D3—481no—
456C2×D3—482no—
457C2×D3C2×D2412yes—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—32no—
461C3×C4—121no—
462C3×C4—121no—
463C3×C4C2×D2411yescharacteristic
464C3×C4D3×D811yescharacteristic
465C3×C4C22×D1211yescharacteristic
466C3×C4C2×D3×D411yescharacteristic
467Dic3—41no—
468Dic3—41no—
469Dic3—122no—
470Dic3—122no—
471Dic3—242no—
472Dic3C2×D2412yes—
473C32#341611yescharacteristic, complemented, Sylow
474C23—362no—
475C23—361no—
476Q8—31no—
477Q8—61no—
478Q8—61no—
479Q8—182no—
480Q8—362no—
481Q8—361no—
482D4—32no—
483D4—31no—
484D4—61no—
485D4—61no—
486D4—121no—
487D4—121no—
488D4—182no—
489D4—362no—
490D4—362no—
491D4—362no—
492D4—361no—
493C2×C4—32no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4—362no—
497C2×C4—362no—
498C2×C4—362no—
499C2×C4—361no—
500C2×C4D3×D1211yescharacteristic
501C8—32no—
502C8D3×D1211yescharacteristic
503C8C22×D3211yescharacteristic
504C2×C3—22no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—62no—
509C2×C3—241no—
510C2×C3—241no—
511C2×C3C22×D2411yescharacteristic
512C2×C3C2×D3×D811yescharacteristic
513D3—22no—
514D3—81no—
515D3—81no—
516D3—242no—
517D3—242no—
518D3—482no—
519C22—32no—
520C22—121no—
521C22—121no—
522C22—362no—
523C22—1441no—
524C22—1442no—
525C22D3×D2411yescharacteristic
526C4—32no—
527C4—121no—
528C4—121no—
529C4—362no—
530C4D3×D2411yescharacteristic
531C4C2×D3×D1211yescharacteristic
532C3—21no—
533C3#8201411yescharacteristic, complemented
534C3#8203211yescharacteristic, complemented
535C2—21no—
536C2—62no—
537C2—241no—
538C2—241no—
539C2—722no—
540C2C2×D3×D2411yescharacteristic
subgroupG/H
centerC2C2×D3×D24
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. #10594692C2semidirect
2. #10594680C2semidirect
3. C2×#63627C2semidirect
4. C3×#4904C2semidirect
5. C3×#4901C2semidirect
6. #10590638C2semidirect
7. #10590634C2semidirect
8. #10590242C2semidirect
9. #10590238C2semidirect
10. #10590232C2semidirect
11. D3×#800C2semidirect
16. C2×#3746C22semidirect
19. C3×#904C22semidirect
24. #63807C22semidirect
26. D3×Dic12C22semidirect
29. C2×C32×C16C22semidirect
30. #63627C22semidirect
31. #63627C22semidirect
32. C3×#812C22semidirect
33. C3×Dic24C22semidirect
34. C3×#800C22semidirect
35. C3×#800C22semidirect
36. C3×D48C22semidirect
37. C3×#798C22semidirect
38. C3×D3×C16C22semidirect
39. #63551C22semidirect
40. #63549C22semidirect
41. #63548C22semidirect
42. #63546C22semidirect
60. #4904D3semidirect
65. #4901D3semidirect
129. #904C2×D3semidirect
143. C2×C3×C16C2×D3semidirect
144. C2×C3×C16C2×D3semidirect
149. #812C2×D3semidirect
151. Dic24C2×D3semidirect
160. #800C2×D3semidirect
161. #800C2×D3semidirect
163. D48C2×D3semidirect
164. #798C2×D3semidirect
165. D3×C16C2×D3semidirect
329. C2×C16D32semidirect
473. C32#3416semidirect
533. C3#82014semidirect
534. C3#82032semidirect

Maximal subgroups

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

subgroupindex
#105946922
#105946802
C2×#636272
C3×#49042
C3×#49012
#105906382
#105906342
#105902422
#105902382
#105902322
D3×#8002
#820323
#820143