Finite Group Databasebeta

← #11899734

Subgroups — #11899734

Order 1152.

762 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594691C211yesmaximal, characteristic, complemented
2#10594678C211yesmaximal, characteristic, complemented
3#10592603C211yesmaximal, characteristic, complemented
4C2×C3×#800C211yesmaximal, characteristic, complemented
5C3×#4901C211yesmaximal, characteristic, complemented
6#10590642C211yesmaximal, characteristic, complemented
7#10590633C211yesmaximal, characteristic, complemented
8#10590242C212yesmaximal, complemented
9#10590239C212yesmaximal, complemented
10#10590233C212yesmaximal, complemented
11D3×#800C212yesmaximal, complemented
12#82024—31nomaximal
13#82014—31nomaximal
14#64307—21no—
15#64297—21no—
16#64113C2211yescharacteristic
17#64113C2211yescharacteristic, complemented
18C2×C3×Dic12C2211yescharacteristic, complemented
19C2×C3×D24C2211yescharacteristic
20C3×#901C2211yescharacteristic
21#63833—21no—
22#63830—21no—
23#63808C2212yescomplemented
24#63807C2212yes—
25#63801—22no—
26D3×Dic12C2212yescomplemented
27#63795—22no—
28D3×D24C2212yes—
29C2×C32×C16C2211yescharacteristic, complemented
30#63628C2211yescharacteristic, complemented
31#63627C2211yescharacteristic, complemented
32#63627C2211yescharacteristic, complemented
33#63626C2211yescharacteristic, complemented
34C3×#812C2211yescharacteristic, complemented
35C3×#800C2212yescomplemented
36C3×#800C2212yescomplemented
37C3×#798C2212yescomplemented
38C3×D3×C16C2212yescomplemented
39#63551C2212yescomplemented
40#63549C2212yescomplemented
41#63548C2212yescomplemented
42#63546C2212yescomplemented
43#5766—31no—
44#5757—31no—
45#5753—31no—
46#5752—31no—
47C2×C3×SD32—31no—
48C3×#504—31no—
49#5179—31no—
50#5147—31no—
51#4916—32no—
52#4915—32no—
53#4914—32no—
54D3×SD32—32no—
55#4909—31no—
56#4909—32no—
57#4908—31no—
58#4908—32no—
59#4904—31no—
60#4904—31no—
61#4904—32no—
62#4904—61no—
63C2×#800—32no—
64C2×#800D311yescharacteristic, complemented
65#4901D311yescharacteristic, complemented
66#3828—21no—
67#3828—21no—
68C3×#235D411yescharacteristic
69C2×C3×D12—21no—
70C2×C3×Dic6—21no—
71D3×#67—42no—
72#3804—42no—
73#3802—41no—
74D3×D12—22no—
75#3799—22no—
76#3797—41no—
77#3796—41no—
78#3796—41no—
79#3795—22no—
80D3×Dic6—22no—
81C2×C32×C8C2311yescharacteristic
82#3746C2311yescharacteristic
83#3746C2311yescharacteristic
84#3745C2311yescharacteristic
85#3745C2311yescharacteristic
86#3744—21no—
87#3744—21no—
88C3×#208D411yescharacteristic
89C3×Dic12—21no—
90C3×Dic12C2312yes—
91C3×D24—21no—
92C3×D24C2312yes—
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#1009—61no—
105#1007—61no—
106#1004—61no—
107C2×C3×Q16—31no—
108C2×C3×D8—31no—
109C3×#131—31no—
110#942—61no—
111#932—61no—
112#919—32no—
113#918—62no—
114D3×Q16—32no—
115#912—32no—
116#911—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—31no—
127#904—31no—
128#904—32no—
129#904—32no—
130#904—61no—
131#904—61no—
132C2×D24—32no—
133C2×D24C2×D311yescharacteristic
134#901C2×D311yescharacteristic
135C3×SD32—32no—
136C3×SD32—32no—
137C3×M32—31no—
138C3×M32—32no—
139C2×C3×C16—21no—
140C2×C3×C16—32no—
141C2×C3×C16C2×D311yescharacteristic, complemented
142C2×C3×C16C2×D311yescharacteristic, complemented
143#829—32no—
144#828—32no—
145#827—32no—
146#826—32no—
147#812C2×D311yescharacteristic, complemented
148Dic24—32no—
149Dic24—31no—
150Dic24—31no—
151Dic24—61no—
152#800—32no—
153#800—32no—
154#800—31no—
155#800—31no—
156#800—31no—
157#800—31no—
158#800—61no—
159#800—61no—
160#800C2×D312yescomplemented
161#800C2×D312yescomplemented
162D48—32no—
163D48—31no—
164D48—31no—
165D48—61no—
166#798C2×D312yescomplemented
167D3×C16C2×D312yescomplemented
168C22×C3×D3—41no—
169C2×D32—42no—
170C2×C32×C4C2×D411yescharacteristic
171#638—41no—
172#638—41no—
173C4⋊(C3⋊D3)—21no—
174C4⋊(C3⋊D3)—21no—
175C4×C3⋊D3—41no—
176C4×C3⋊D3—41no—
177#634—21no—
178#634—21no—
179C3×#67D812yes—
180C2×C3×Dic3—41no—
181C3×D12—22no—
182C3×D12—41no—
183C3×D12D811yescharacteristic
184C3×C4×D3C2×D412yes—
185C3×Dic6—22no—
186C3×Dic6—41no—
187C3×Dic6D811yescharacteristic
188#627—42no—
189#626—42no—
190#626—42no—
191#625—42no—
192#624—42no—
193D3×Dic3—42no—
194D3×Dic3—42no—
195C32×C8C2×D411yescharacteristic
196C32×C8C2411yescharacteristic
197C3×C3⋊C8C2×D412yes—
198#578—91no—
199#576—91no—
200#510—92no—
201#510—91no—
202#509—92no—
203#509—91no—
204#508—92no—
205#508—91no—
206C2×SD32—31no—
207C2×SD32—92no—
208#504—31no—
209C3×#41—31no—
210C2×C3×Q8—61no—
211C2×C3×D4—61no—
212C2×#67—122no—
213#239—62no—
214#239—121no—
215#239—121no—
216D3×Q8—62no—
217D3×Q8—121no—
218D3×Q8—121no—
219#237—62no—
220#237—121no—
221#237—122no—
222#237—121no—
223D3×D4—62no—
224D3×D4—121no—
225D3×D4—122no—
226D3×D4—121no—
227#235—62no—
228#235—62no—
229#235—61no—
230#235—61no—
231#235—61no—
232#235—61no—
233#235—121no—
234#235—121no—
235#235—122no—
236#235D1211yescharacteristic
237C2×D12—21no—
238C2×D12—62no—
239C2×Dic6—21no—
240C2×Dic6—62no—
241C3×Q16—32no—
242C3×Q16—61no—
243C3×D8—32no—
244C3×D8—61no—
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—21no—
257Dic12—31no—
258Dic12—31no—
259Dic12—31no—
260Dic12—31no—
261Dic12—61no—
262Dic12—61no—
263Dic12—62no—
264Dic12C22×D312yes—
265D24—21no—
266D24—31no—
267D24—31no—
268D24—31no—
269D24—31no—
270D24—61no—
271D24—61no—
272D24—62no—
273D24C22×D312yes—
274#204—62no—
275#204—62no—
276#204—61no—
277#204—61no—
278#204—61no—
279#204—61no—
280#204—121no—
281#204—121no—
282ΓL(1,𝔽25)D1212yes—
283D3×C8C22×D312yes—
284C3×C16—21no—
285C3×C16—21no—
286C3×C16—32no—
287C3×C16C22×D311yescharacteristic
288C3×C16C22×D311yescharacteristic
289C3×C16C22×D311yescharacteristic
290C3×C16C22×D311yescharacteristic
291C3⋊C16C22×D312yes—
292C22×C32C2×D811yescharacteristic
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C2×C3×D3—42no—
296C2×C3×D3—161no—
297C2×C3×D3C2×D812yes—
298D32—162no—
299C32×C4C2×D811yescharacteristic
300C32×C4C22×D411yescharacteristic
301C3⋊Dic3—41no—
302C3⋊Dic3—41no—
303C3×Dic3—42no—
304C3×Dic3C2×D812yes—
3052−1+4—181no—
306H(5,𝔽2)—181no—
307#137—182no—
308#137—181no—
309AGL(1,ℤ/8)—182no—
310AGL(1,ℤ/8)—181no—
311#135—92no—
312#135—92no—
313#135—91no—
314#135—91no—
315C2×Q16—31no—
316C2×Q16—92no—
317C2×D8—31no—
318C2×D8—92no—
319#131—31no—
320Q32—92no—
321Q32—91no—
322SD32—32no—
323SD32—32no—
324SD32—92no—
325SD32—92no—
326SD32—91no—
327SD32—91no—
328D16—92no—
329D16—91no—
330M32—31no—
331M32—32no—
332C2×C16—32no—
333C2×C16D3211yescharacteristic, complemented
334C23×C3—121no—
335C22×D3—41no—
336C22×D3—122no—
337C22×D3—122no—
338C3×Q8—31no—
339C3×Q8—62no—
340C3×Q8—121no—
341C3×D4—32no—
342C3×D4—31no—
343C3×D4—62no—
344C3×D4—121no—
345C2×C3×C4—21no—
346C2×C3×C4—32no—
347C2×C3×C4—121no—
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350#67—122no—
351#67—122no—
352#67—121no—
353#67—121no—
354#67—121no—
355#67—121no—
356#67—122no—
357#67—122no—
358#67—241no—
359#67—241no—
360#67D2412yes—
361C2×Dic3—41no—
362C2×Dic3—122no—
363C2×Dic3—122no—
364D12—22no—
365D12—41no—
366D12—61no—
367D12—61no—
368D12—61no—
369D12—61no—
370D12—121no—
371D12—121no—
372D12—122no—
373D12—122no—
374D12D2411yescharacteristic
375C4×D3—122no—
376C4×D3—122no—
377C4×D3—122no—
378C4×D3—121no—
379C4×D3—121no—
380C4×D3—121no—
381C4×D3—121no—
382C4×D3—122no—
383C4×D3—241no—
384C4×D3—241no—
385C4×D3C2×D1212yes—
386Dic6—22no—
387Dic6—41no—
388Dic6—61no—
389Dic6—61no—
390Dic6—61no—
391Dic6—61no—
392Dic6—121no—
393Dic6—121no—
394Dic6—122no—
395Dic6—122no—
396Dic6D2411yescharacteristic
397C3×C8—21no—
398C3×C8—21no—
399C3×C8—32no—
400C3×C8C2×D1211yescharacteristic
401C3×C8D3×D411yescharacteristic
402C3×C8C23×D311yescharacteristic
403C3×C8C23×D311yescharacteristic
404C3⋊C8C2×D1212yes—
405C2×C32—21no—
406C2×C32C22×D811yescharacteristic
407C3⋊D3—81no—
408C3⋊D3—81no—
409C3×D3—22no—
410C3×D3—82no—
411#41—31no—
412#41—182no—
413#41—182no—
414#41—181no—
415#41—181no—
416#41—362no—
417#41—361no—
418#41—361no—
419C2×Q8—61no—
420C2×Q8—182no—
421C2×Q8—361no—
422C2×D4—61no—
423C2×D4—182no—
424C2×D4—361no—
425C2×D4—362no—
426Q16—32no—
427Q16—61no—
428Q16—91no—
429Q16—91no—
430Q16—182no—
431SD16—182no—
432SD16—182no—
433SD16—181no—
434SD16—181no—
435D8—32no—
436D8—61no—
437D8—91no—
438D8—91no—
439D8—182no—
440M16—31no—
441M16—32no—
442C2×C8—32no—
443C2×C8C2×D3211yescharacteristic
444C16—32no—
445C16C2×D3211yescharacteristic
446C16C2×D3211yescharacteristic
447C22×C3—21no—
448C22×C3—32no—
449C22×C3—122no—
450C22×C3—481no—
451C22×C3C2×D2411yescharacteristic
452C22×C3D3×D811yescharacteristic
453C2×D3—42no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—161no—
459C2×D3—241no—
460C2×D3—241no—
461C2×D3—482no—
462C2×D3—482no—
463C2×D3C2×D2412yes—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—32no—
467C3×C4—122no—
468C3×C4C2×D2411yescharacteristic
469C3×C4D3×D811yescharacteristic
470C3×C4C22×D1211yescharacteristic
471C3×C4C2×D3×D411yescharacteristic
472Dic3—42no—
473Dic3—121no—
474Dic3—121no—
475Dic3—121no—
476Dic3—121no—
477Dic3—241no—
478Dic3—241no—
479Dic3C2×D2412yes—
480C32#341611yescharacteristic, complemented, Sylow
481C23—121no—
482C23—362no—
483Q8—31no—
484Q8—62no—
485Q8—121no—
486Q8—181no—
487Q8—181no—
488Q8—362no—
489D4—32no—
490D4—31no—
491D4—62no—
492D4—121no—
493D4—181no—
494D4—181no—
495D4—362no—
496D4—362no—
497D4—362no—
498D4—361no—
499D4—361no—
500C2×C4—32no—
501C2×C4—121no—
502C2×C4—362no—
503C2×C4—362no—
504C2×C4—362no—
505C2×C4—361no—
506C2×C4—361no—
507C2×C4D3×D1211yescharacteristic
508C8—32no—
509C8D3×D1211yescharacteristic
510C8C22×D3211yescharacteristic
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—41no—
515C2×C3—62no—
516C2×C3—242no—
517C2×C3C22×D2411yescharacteristic
518C2×C3C2×D3×D811yescharacteristic
519D3—22no—
520D3—82no—
521D3—241no—
522D3—241no—
523D3—241no—
524D3—241no—
525D3—481no—
526D3—481no—
527C22—32no—
528C22—122no—
529C22—361no—
530C22—361no—
531C22—481no—
532C22—1442no—
533C22D3×D2411yescharacteristic
534C4—32no—
535C4—122no—
536C4—361no—
537C4—361no—
538C4D3×D2411yescharacteristic
539C4C2×D3×D1211yescharacteristic
540C3—21no—
541C3#8201411yescharacteristic, complemented
542C3#8202411yescharacteristic, complemented
543C2—21no—
544C2—62no—
545C2—242no—
546C2—721no—
547C2—721no—
548C2C2×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. #10594691C2semidirect
2. #10594678C2semidirect
3. #10592603C2semidirect
4. C2×C3×#800C2semidirect
5. C3×#4901C2semidirect
6. #10590642C2semidirect
7. #10590633C2semidirect
8. #10590242C2semidirect
9. #10590239C2semidirect
10. #10590233C2semidirect
11. D3×#800C2semidirect
17. #64113C22semidirect
18. C2×C3×Dic12C22semidirect
23. #63808C22semidirect
26. D3×Dic12C22semidirect
29. C2×C32×C16C22semidirect
30. #63628C22semidirect
31. #63627C22semidirect
32. #63627C22semidirect
33. #63626C22semidirect
34. C3×#812C22semidirect
35. C3×#800C22semidirect
36. C3×#800C22semidirect
37. C3×#798C22semidirect
38. C3×D3×C16C22semidirect
39. #63551C22semidirect
40. #63549C22semidirect
41. #63548C22semidirect
42. #63546C22semidirect
64. C2×#800D3semidirect
65. #4901D3semidirect
123. C2×Dic12C2×D3semidirect
141. C2×C3×C16C2×D3semidirect
142. C2×C3×C16C2×D3semidirect
147. #812C2×D3semidirect
160. #800C2×D3semidirect
161. #800C2×D3semidirect
166. #798C2×D3semidirect
167. D3×C16C2×D3semidirect
333. C2×C16D32semidirect
480. C32#3416semidirect
541. C3#82014semidirect
542. C3#82024semidirect

Maximal subgroups

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

subgroupindex
#105946912
#105946782
#105926032
C2×C3×#8002
C3×#49012
#105906422
#105906332
#105902422
#105902392
#105902332
D3×#8002
#820243
#820143