Finite Group Databasebeta

← #11886898

Subgroups — #11886898

Order 1152.

1428 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596245C212yesmaximal, complemented
2#10596228C211yesmaximal, characteristic, complemented
3#10596223C211yesmaximal, characteristic, complemented
4C32×#472C211yesmaximal, characteristic, complemented
5#10592897C212yesmaximal, complemented
6#10592850C211yesmaximal, characteristic, complemented
7#10592843C211yesmaximal, characteristic, complemented
8#10592596C211yesmaximal, characteristic, complemented
9#10592594C211yesmaximal, characteristic, complemented
10#10592448C212yesmaximal, complemented
11#10592446C212yesmaximal, complemented
12#80941—34nomaximal
13#64366C2212yescomplemented
14#64361C2212yescomplemented
15C32×AGL(1,ℤ/8)C2212yescomplemented
16C2×C32×D8C2211yescharacteristic, complemented
17C32×#131C2211yescharacteristic, complemented
18#64159C2211yescharacteristic
19#64149C2212yescomplemented
20#64141C2212yescomplemented
21C2×#3753C2212yescomplemented
22#64125—22no—
23#64123—22no—
24#64121—21no—
25#64120—22no—
26#64120—22no—
27D8×C3⋊D3—22no—
28D8×C3⋊D3—21no—
29#64117—22no—
30#64117C2212yescomplemented
31#64117C2212yescomplemented
32#64116C2212yescomplemented
33#64113—21no—
34#64113C2211yescharacteristic
35C2×#3745—21no—
36C2×#3745C2211yescharacteristic, complemented
37#64110C2211yescharacteristic, complemented
38C32×#108C2211yescharacteristic, complemented
39C32×#100C2212yescomplemented
40#63664C2211yescharacteristic, complemented
41#63652C2211yescharacteristic, complemented
42#63652C2212yescomplemented
43#63650C2212yescomplemented
44#63649C2211yescharacteristic, complemented
45C8×C3⋊Dic3C2211yescharacteristic, complemented
46#5774—38no—
47#5757—34no—
48#5752—34no—
49C3×#472D314yescomplemented
50#5198—38no—
51#5151—34no—
52#5144—34no—
53#4897—34no—
54#4895—34no—
55#4749—38no—
56#4747—38no—
57C32×#41C2311yescharacteristic
58C2×C32×D4C2312yes—
59C2×#638—42no—
60C2×#638—42no—
61#3832—22no—
62#3830—22no—
63#3830—22no—
64D4×C3⋊D3—22no—
65D4×C3⋊D3—22no—
66D4×C3⋊D3—22no—
67D4×C3⋊D3—42no—
68#3828—22no—
69#3828C2311yescharacteristic
70#3828C2312yes—
71C2×C4⋊(C3⋊D3)—22no—
72C2×C4⋊(C3⋊D3)C2312yes—
73C32×SD16—22no—
74C32×D8—22no—
75C32×D8—21no—
76C32×D8—21no—
77C32×M16—21no—
78C32×M16C2312yes—
79C32×M16C2311yescharacteristic
80C2×C32×C8—21no—
81C2×C32×C8C2311yescharacteristic
82#3756D411yescharacteristic, complemented
83#3755D411yescharacteristic, complemented
84#3754—22no—
85#3754D411yescharacteristic, complemented
86#3753—22no—
87#3753—22no—
88#3753—22no—
89#3753D411yescharacteristic, complemented
90C4×C3⋊Dic3C2311yescharacteristic
91#3748C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2311yescharacteristic
93#3746D411yescharacteristic, complemented
94#3745—22no—
95#3745—22no—
96#3745—21no—
97#3745—21no—
98#3745D411yescharacteristic, complemented
99#3744—22no—
100#3744—22no—
101#3744D412yescomplemented
102#3743—21no—
103#3743—22no—
104C8×C3⋊D3—21no—
105C8×C3⋊D3—22no—
106#3292—91noSylow
107#1009—38no—
108#1004—38no—
109C3×AGL(1,ℤ/8)C2×D318yescomplemented
110C2×C3×D8C2×D314yescomplemented
111C3×#131C2×D314yescomplemented
112#950—34no—
113#940—38no—
114#932—38no—
115C2×#213—38no—
116#916—68no—
117#914—68no—
118#912—64no—
119#911—68no—
120#911—68no—
121D3×D8—64no—
122D3×D8—68no—
123#908—38no—
124#908—38no—
125#908—68no—
126#907—38no—
127#904—34no—
128#904—64no—
129C2×D24—34no—
130C2×D24—64no—
131#901—34no—
132C3×#108C2×D314yescomplemented
133C3×#100C2×D318yescomplemented
134#837—34no—
135#825—34no—
136#825—38no—
137#823—38no—
138#822—34no—
139C8×Dic3—34no—
140C23×C32—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—42no—
143C22×C3⋊D3—42no—
144C32×Q8C2×D411yescharacteristic
145C32×D4—21no—
146C32×D4—22no—
147C32×D4—22no—
148C32×D4C2×D411yescharacteristic
149C2×C32×C4—21no—
150C2×C32×C4C2411yescharacteristic
151#638—22no—
152#638—21no—
153#638—42no—
154#638—42no—
155#638—42no—
156#638—84no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—42no—
159C4⋊(C3⋊D3)—22no—
160C4⋊(C3⋊D3)—22no—
161C4⋊(C3⋊D3)—42no—
162C4⋊(C3⋊D3)C2×D412yes—
163C4⋊(C3⋊D3)C2×D411yescharacteristic
164C4×C3⋊D3—21no—
165C4×C3⋊D3—22no—
166C4×C3⋊D3—42no—
167#634C2×D411yescharacteristic
168#634C2×D412yes—
169C32×C8—22no—
170C32×C8—21no—
171C32×C8C2×D411yescharacteristic
172C32×C8C2×D411yescharacteristic
173C3⋊(C3⋊C8)—21no—
174C3⋊(C3⋊C8)C2×D411yescharacteristic
175C3⋊(C3⋊C8)C2×D411yescharacteristic
176#576—92no—
177#576—91no—
178#576—91no—
179#493—91no—
180#472—91no—
181#472—92no—
182#472C3⋊D311yescharacteristic, complemented
183#453—92no—
184#453—92no—
185#443—91no—
186#443—91no—
187C3×#41C22×D314yes—
188C2×C3×D4C22×D318yes—
189C2×#67—128no—
190C2×#67—128no—
191#239—68no—
192#237—68no—
193#237—68no—
194D3×D4—68no—
195D3×D4—68no—
196D3×D4—68no—
197D3×D4—128no—
198#235—34no—
199#235—38no—
200#235—68no—
201C2×D12—38no—
202C2×D12—68no—
203C3×SD16—28no—
204C3×D8—28no—
205C3×D8—24no—
206C3×D8—24no—
207C3×M16—24no—
208C3×M16C22×D314yes—
209C3×M16C22×D318yes—
210C2×C3×C8—24no—
211C2×C3×C8C22×D314yes—
212#216—34no—
213#215—34no—
214#214—34no—
215#214—68no—
216#213—34no—
217#213—68no—
218#213—68no—
219#213—68no—
220C4×Dic3—34no—
221#208—34no—
222C2×C3⋊C8—34no—
223Dic12—34no—
224D24—34no—
225D24—68no—
226D24—68no—
227D24—64no—
228D24—64no—
229#204—38no—
230#204—68no—
231#204—68no—
232ΓL(1,𝔽25)—68no—
233ΓL(1,𝔽25)—64no—
234D3×C8—68no—
235D3×C8—64no—
236C22×C32—21no—
237C22×C32—42no—
238C22×C32—82no—
239C22×C32H(5,𝔽2)11yescharacteristic
240C2×C3⋊D3—22no—
241C2×C3⋊D3—21no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3—82no—
244C2×C3⋊D3—162no—
245C2×C3⋊D3—162no—
246C32×C4—21no—
247C32×C4C22×D411yescharacteristic
248C32×C4C22×D411yescharacteristic
249C3⋊Dic3—22no—
250C3⋊Dic3—22no—
251C3⋊Dic3—21no—
252H(5,𝔽2)—92no—
253H(5,𝔽2)—92no—
254AGL(1,ℤ/8)—92no—
255AGL(1,ℤ/8)—92no—
256AGL(1,ℤ/8)—92no—
257AGL(1,ℤ/8)—182no—
258AGL(1,ℤ/8)—182no—
259AGL(1,ℤ/8)—182no—
260AGL(1,ℤ/8)—182no—
261AGL(1,ℤ/8)C2×C3⋊D312yescomplemented
262#135—91no—
263#135—91no—
264#135—181no—
265#135—181no—
266#135—182no—
267C2×D8—92no—
268C2×D8—91no—
269C2×D8—181no—
270C2×D8—182no—
271C2×D8—181no—
272C2×D8C2×C3⋊D311yescharacteristic, complemented
273#131—92no—
274#131—91no—
275#131C2×C3⋊D311yescharacteristic, complemented
276#127—92no—
277#108—91no—
278#108C2×C3⋊D311yescharacteristic, complemented
279#104—91no—
280#104—92no—
281#104—91no—
282#100—92no—
283#100C2×C3⋊D312yescomplemented
284C4×C8—91no—
285C23×C3—28no—
286C22×D3—68no—
287C22×D3—128no—
288C22×D3—128no—
289C3×Q8D3×D414yes—
290C3×D4—24no—
291C3×D4—28no—
292C3×D4—28no—
293C3×D4D3×D414yes—
294C2×C3×C4—24no—
295C2×C3×C4C23×D314yes—
296#67—68no—
297#67—64no—
298#67—128no—
299#67—128no—
300#67—128no—
301#67—2416no—
302C2×Dic3—64no—
303C2×Dic3—128no—
304D12—38no—
305D12—34no—
306D12—68no—
307D12—68no—
308D12—128no—
309C4×D3—64no—
310C4×D3—68no—
311C4×D3—128no—
312Dic6—38no—
313Dic6—34no—
314C3×C8—28no—
315C3×C8—24no—
316C3×C8D3×D414yes—
317C3×C8D3×D414yes—
318C3⋊C8—34no—
319C3⋊C8—34no—
320C3⋊C8—64no—
321C2×C32—21no—
322C2×C32—41no—
323C2×C32—82no—
324C2×C32D4211yescharacteristic
325C3⋊D3—42no—
326C3⋊D3—41no—
327C3⋊D3—82no—
328#41—92no—
329#41—91no—
330#41—182no—
331#41—182no—
332#41—182no—
333#41—182no—
334#41C22×C3⋊D311yescharacteristic
335C2×D4—92no—
336C2×D4—182no—
337C2×D4—182no—
338C2×D4—182no—
339C2×D4—182no—
340C2×D4—362no—
341C2×D4—362no—
342C2×D4—362no—
343C2×D4C22×C3⋊D312yes—
344Q16—91no—
345Q16—91no—
346SD16—22no—
347SD16—91no—
348SD16—91no—
349SD16—92no—
350SD16—182no—
351SD16—182no—
352SD16—182no—
353D8—22no—
354D8—21no—
355D8—21no—
356D8—91no—
357D8—91no—
358D8—182no—
359D8—182no—
360D8—182no—
361D8—182no—
362D8—182no—
363D8—181no—
364D8—181no—
365M16—21no—
366M16—91no—
367M16—182no—
368M16—181no—
369M16C22×C3⋊D312yes—
370M16C22×C3⋊D311yescharacteristic
371C2×C8—21no—
372C2×C8—91no—
373C2×C8—182no—
374C2×C8—181no—
375C2×C8C22×C3⋊D311yescharacteristic
376C42—91no—
377C22×C3—24no—
378C22×C3—48no—
379C22×C3—88no—
380C22×C3#100914yes—
381C2×D3—68no—
382C2×D3—64no—
383C2×D3—128no—
384C2×D3—248no—
385C2×D3—488no—
386C2×D3—488no—
387C3×C4—24no—
388C3×C4C2×D3×D414yes—
389C3×C4C2×D3×D414yes—
390Dic3—68no—
391Dic3—68no—
392Dic3—64no—
393C32#329211yescharacteristic, complemented, Sylow
394C23—22no—
395C23—182no—
396C23—362no—
397C23—362no—
398Q8—91no—
399Q8—92no—
400Q8D4×C3⋊D311yescharacteristic
401D4—21no—
402D4—22no—
403D4—22no—
404D4—91no—
405D4—92no—
406D4—182no—
407D4—181no—
408D4—182no—
409D4—182no—
410D4—362no—
411D4—362no—
412D4—362no—
413D4—362no—
414D4—724no—
415D4D4×C3⋊D311yescharacteristic
416C2×C4—21no—
417C2×C4—181no—
418C2×C4—182no—
419C2×C4—181no—
420C2×C4—362no—
421C2×C4—362no—
422C2×C4C23×C3⋊D311yescharacteristic
423C8—21no—
424C8—22no—
425C8—91no—
426C8—91no—
427C8—181no—
428C8D4×C3⋊D311yescharacteristic
429C8D4×C3⋊D311yescharacteristic
430C2×C3—24no—
431C2×C3—44no—
432C2×C3—88no—
433C2×C3#560914yes—
434D3—128no—
435D3—124no—
436D3—248no—
437C22—21no—
438C22—42no—
439C22—82no—
440C22—182no—
441C22—181no—
442C22—362no—
443C22—722no—
444C22—1442no—
445C22—1442no—
446C22#6436611yescharacteristic
447C4—21no—
448C4—182no—
449C4—182no—
450C4—181no—
451C4C2×D4×C3⋊D311yescharacteristic
452C4C2×D4×C3⋊D311yescharacteristic
453C3#8094114yescomplemented
454C2—21no—
455C2—41no—
456C2—82no—
457C2—362no—
458C2—361no—
459C2—722no—
460C2#1059608011yescharacteristic
subgroupG/H
centerC2#10596080
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#472C2
socleC2×C32D42
hypercenter#472C3⋊D3
hypocenterC32#3292
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #10596245C2semidirect
2. #10596228C2semidirect
3. #10596223C2semidirect
4. C32×#472C2semidirect
5. #10592897C2semidirect
6. #10592850C2semidirect
7. #10592843C2semidirect
8. #10592596C2semidirect
9. #10592594C2semidirect
10. #10592448C2semidirect
11. #10592446C2semidirect
13. #64366C22semidirect
14. #64361C22semidirect
15. C32×AGL(1,ℤ/8)C22semidirect
16. C2×C32×D8C22semidirect
17. C32×#131C22semidirect
19. #64149C22semidirect
20. #64141C22semidirect
21. C2×#3753C22semidirect
30. #64117C22semidirect
31. #64117C22semidirect
32. #64116C22semidirect
36. C2×#3745C22semidirect
37. #64110C22semidirect
38. C32×#108C22semidirect
39. C32×#100C22semidirect
40. #63664C22semidirect
41. #63652C22semidirect
42. #63652C22semidirect
43. #63650C22semidirect
44. #63649C22semidirect
45. C8×C3⋊Dic3C22semidirect
49. C3×#472D3semidirect
82. #3756D4semidirect
83. #3755D4semidirect
85. #3754D4semidirect
89. #3753D4semidirect
93. #3746D4semidirect
98. #3745D4semidirect
101. #3744D4semidirect
109. C3×AGL(1,ℤ/8)C2×D3semidirect
110. C2×C3×D8C2×D3semidirect
111. C3×#131C2×D3semidirect
132. C3×#108C2×D3semidirect
133. C3×#100C2×D3semidirect
182. #472C3⋊D3semidirect
261. AGL(1,ℤ/8)C2×C3⋊D3semidirect
272. C2×D8C2×C3⋊D3semidirect
275. #131C2×C3⋊D3semidirect
278. #108C2×C3⋊D3semidirect
283. #100C2×C3⋊D3semidirect
393. C32#3292semidirect
453. C3#80941semidirect

Maximal subgroups

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

subgroupindex
#105962452
#105962282
#105962232
C32×#4722
#105928972
#105928502
#105928432
#105925962
#105925942
#105924482
#105924462
#809413