Finite Group Databasebeta

← #11899728

Subgroups — #11899728

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5766C211yesmaximal, characteristic, complemented
2#10594678C211yesmaximal, characteristic, complemented
3#10592878C211yesmaximal, characteristic, complemented
4C2×C3×#828C211yesmaximal, characteristic, complemented
5#10591046C212yesmaximal, complemented
6#10591045C212yesmaximal, complemented
7#10591038C212yesmaximal, complemented
8D3×#828C212yesmaximal, complemented
9#10590632C211yesmaximal, characteristic, complemented
10#10590630C211yesmaximal, characteristic, complemented
11#10590621C211yesmaximal, characteristic, complemented
12#84016—31nomaximal
13#82024—31nomaximal
14C3×#1007—21no—
15#64307—21no—
16C2×C32×Q16C2211yescharacteristic, complemented
17#64113C2211yescharacteristic
18C3×#942—21no—
19C3×#919C2212yescomplemented
20C3×#918—22no—
21C3×D3×Q16C2212yescomplemented
22C3×#904C2211yescharacteristic, complemented
23C2×C3×D24C2211yescharacteristic
24C3×#901C2211yescharacteristic
25#63830—21no—
26#63807C2212yes—
27#63795—22no—
28D3×D24C2212yes—
29#63656C2212yescomplemented
30#63655C2212yescomplemented
31#63639C2211yescharacteristic, complemented
32C3×#828C2212yescomplemented
33C3×#828C2212yescomplemented
34C2×C3×C3⋊C16C2211yescharacteristic, complemented
35#63551C2211yescharacteristic, complemented
36#63549C2211yescharacteristic, complemented
37#63548C2211yescharacteristic, complemented
38#63547C2212yescomplemented
39#63546C2211yescharacteristic, complemented
40#63545C2212yescomplemented
41#63543C2212yescomplemented
42D3×C3⋊C16C2212yescomplemented
43C3×#578—31no—
44#5766D311yescharacteristic, complemented
45#5757—31no—
46#5752—31no—
47C2×C3×SD32—31no—
48#5194—32no—
49#5194—31no—
50#5193—31no—
51#5193—32no—
52#5179—31no—
53#5179—31no—
54#5179—32no—
55#5179—61no—
56C2×#828—32no—
57C2×#828D311yescharacteristic, complemented
58#5147—31no—
59#5140—31no—
60#4916—32no—
61#4915—32no—
62#4914—32no—
63D3×SD32—32no—
64#4904—31no—
65#4901—31no—
66C2×C32×Q8—21no—
67#3828—21no—
68C3×#239—22no—
69C3×#239—41no—
70C3×D3×Q8—22no—
71C3×D3×Q8—41no—
72C3×#235—21no—
73C3×#235—42no—
74C3×#235D411yescharacteristic
75C2×C3×D12—21no—
76D3×#67—42no—
77#3802—41no—
78D3×D12—22no—
79#3796—41no—
80#3795—22no—
81C32×Q16—21no—
82C32×Q16C2312yes—
83C2×C32×C8C2311yescharacteristic
84#3746C2311yescharacteristic
85#3745C2311yescharacteristic
86#3744—21no—
87C3×#216—22no—
88C3×#215—22no—
89C3×#208D411yescharacteristic
90C3×Dic12C2311yescharacteristic
91C3×D24—21no—
92C3×D24C2312yes—
93C3×D24C2311yescharacteristic
94C3×#204—21no—
95C3×ΓL(1,𝔽25)D412yes—
96C3×D3×C8C2312yes—
97#3716—22no—
98#3714—22no—
99C3⋊(C3⋊C16)C2312yes—
100C3×C3⋊C16C2311yescharacteristic
101C3×C3⋊C16C2311yescharacteristic
102#3416—91noSylow
103C3×2−1+4—61no—
104#1009—61no—
105#1007—21no—
106#1004—61no—
107C3×#137—62no—
108C3×#137—61no—
109C3×#135—32no—
110C3×#135—31no—
111C2×C3×Q16—21no—
112C2×C3×Q16—32no—
113C2×C3×Q16C2×D311yescharacteristic, complemented
114C2×C3×Q16C2×D311yescharacteristic, complemented
115C2×C3×D8—31no—
116C3×#131—31no—
117#942—21no—
118#932—61no—
119#919C2×D312yescomplemented
120#918—22no—
121D3×Q16C2×D312yescomplemented
122#912—32no—
123#911—62no—
124D3×D8—32no—
125#908—62no—
126#908—61no—
127#904—31no—
128#904—31no—
129#904—32no—
130#904—61no—
131#904C2×D311yescharacteristic, complemented
132C2×D24—32no—
133C2×D24C2×D311yescharacteristic
134#901C2×D311yescharacteristic
135C3×SD32—32no—
136C3×SD32—32no—
137C2×C3×C16—31no—
138#829—32no—
139#829—32no—
140#829—31no—
141#829—62no—
142#828—32no—
143#828—32no—
144#828—32no—
145#828—31no—
146#828—62no—
147#828C2×D312yescomplemented
148#828C2×D312yescomplemented
149#827—32no—
150#827—31no—
151#826—32no—
152#826—32no—
153#826—31no—
154#812—31no—
155#812—31no—
156#812—32no—
157#812—61no—
158C2×C3⋊C16—32no—
159C2×C3⋊C16C2×D311yescharacteristic, complemented
160Dic24—31no—
161#800—31no—
162#800—31no—
163D48—31no—
164#798—32no—
165D3×C16—32no—
166C22×C3×D3—41no—
167C2×D32—42no—
168C32×Q8—22no—
169C32×Q8—41no—
170C2×C32×C4—41no—
171C2×C32×C4C2×D411yescharacteristic
172#638—41no—
173C4⋊(C3⋊D3)—21no—
174C4×C3⋊D3—41no—
175#634—21no—
176C3×#67—41no—
177C3×#67D812yes—
178C3×D12—22no—
179C3×D12—21no—
180C3×D12—42no—
181C3×D12—41no—
182C3×D12D811yescharacteristic
183C3×C4×D3—42no—
184C3×C4×D3—41no—
185C3×C4×D3—42no—
186C3×C4×D3C2×D412yes—
187C3×Dic6—21no—
188C3×Dic6—42no—
189C3×Dic6D811yescharacteristic
190#626—42no—
191#625—42no—
192D3×Dic3—42no—
193C32×C8C2×D411yescharacteristic
194C32×C8C2411yescharacteristic
195C3×C3⋊C8C2×D412yes—
196#578—31no—
197#576—91no—
198#510—92no—
199#510—91no—
200#509—92no—
201#509—91no—
202#508—91no—
203#508—92no—
204C2×SD32—31no—
205C2×SD32—92no—
206#504—91no—
207C3×#41—31no—
208C3×#41—62no—
209C3×#41—61no—
210C3×#41—122no—
211C3×#41—121no—
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8—41no—
215C2×C3×Q8—62no—
216C2×C3×Q8—121no—
217C2×C3×D4—61no—
218C2×#67—122no—
219#239—22no—
220#239—41no—
221#239—121no—
222D3×Q8—22no—
223D3×Q8—41no—
224#237—62no—
225#237—121no—
226D3×D4—62no—
227D3×D4—121no—
228D3×D4—122no—
229D3×D4—121no—
230#235—21no—
231#235—42no—
232#235—62no—
233#235—61no—
234#235—61no—
235#235—121no—
236#235#6711yescharacteristic
237C2×D12—21no—
238C2×D12—62no—
239C3×Q16—21no—
240C3×Q16—21no—
241C3×Q16—22no—
242C3×Q16—31no—
243C3×Q16—41no—
244C3×Q16—62no—
245C3×Q16C22×D312yes—
246C3×Q16C22×D312yes—
247C3×SD16—62no—
248C3×SD16—61no—
249C3×D8—31no—
250C3×D8—32no—
251C3×D8—61no—
252C3×M16—31no—
253C3×M16—32no—
254C2×C3×C8—21no—
255C2×C3×C8—32no—
256C2×C3×C8C22×D311yescharacteristic
257C2×C3×C8C22×D311yescharacteristic
258#216—22no—
259#215—22no—
260#214—62no—
261#213—62no—
262#208#6711yescharacteristic
263Dic12—31no—
264Dic12—31no—
265Dic12—61no—
266Dic12C22×D311yescharacteristic
267D24—21no—
268D24—31no—
269D24—31no—
270D24—61no—
271D24—62no—
272D24C22×D311yescharacteristic
273D24C22×D312yes—
274#204—21no—
275#204—62no—
276#204—61no—
277#204—61no—
278#204—121no—
279ΓL(1,𝔽25)#6712yes—
280D3×C8C22×D312yes—
281C3×C16—31no—
282C3×C16—31no—
283C3⋊C16—32no—
284C3⋊C16—32no—
285C3⋊C16—62no—
286C3⋊C16C22×D311yescharacteristic
287C3⋊C16C22×D311yescharacteristic
288C22×C32C2×D811yescharacteristic
289C2×C3⋊D3—41no—
290C2×C3×D3—42no—
291C2×C3×D3—41no—
292C2×C3×D3—161no—
293C2×C3×D3C2×D812yes—
294D32—162no—
295C32×C4—42no—
296C32×C4C2×D811yescharacteristic
297C32×C4C22×D411yescharacteristic
298C3⋊Dic3—41no—
299C3×Dic3—41no—
300C3×Dic3C2×D812yes—
3012−1+4—61no—
302H(5,𝔽2)—181no—
303#137—62no—
304#137—61no—
305AGL(1,ℤ/8)—182no—
306AGL(1,ℤ/8)—181no—
307#135—32no—
308#135—31no—
309#135—92no—
310#135—91no—
311C2×Q16—32no—
312C2×Q16D3211yescharacteristic, complemented
313C2×D8—31no—
314C2×D8—92no—
315#131—31no—
316Q32—91no—
317Q32—92no—
318SD32—32no—
319SD32—32no—
320SD32—91no—
321SD32—91no—
322SD32—92no—
323SD32—92no—
324D16—91no—
325D16—92no—
326M32—92no—
327M32—91no—
328C2×C16—31no—
329C2×C16—92no—
330C23×C3—121no—
331C22×D3—41no—
332C22×D3—122no—
333C22×D3—122no—
334C3×Q8—22no—
335C3×Q8—22no—
336C3×Q8—31no—
337C3×Q8—42no—
338C3×Q8—41no—
339C3×Q8—41no—
340C3×Q8—61no—
341C3×Q8—81no—
342C3×Q8—122no—
343C3×D4—32no—
344C3×D4—31no—
345C3×D4—61no—
346C3×D4—62no—
347C3×D4—122no—
348C3×D4—121no—
349C3×D4—121no—
350C2×C3×C4—21no—
351C2×C3×C4—32no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—81no—
355C2×C3×C4—122no—
356C2×C3×C4—122no—
357C2×C3×C4—121no—
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360#67—41no—
361#67—122no—
362#67—121no—
363#67—121no—
364#67—122no—
365#67—122no—
366#67—241no—
367#67#21312yes—
368C2×Dic3—122no—
369D12—22no—
370D12—21no—
371D12—42no—
372D12—41no—
373D12—61no—
374D12—61no—
375D12—121no—
376D12—122no—
377D12#21311yescharacteristic
378C4×D3—42no—
379C4×D3—41no—
380C4×D3—42no—
381C4×D3—122no—
382C4×D3—121no—
383C4×D3—121no—
384C4×D3—241no—
385C4×D3C2×#6712yes—
386Dic6—21no—
387Dic6—42no—
388Dic6—61no—
389Dic6—61no—
390Dic6—121no—
391Dic6#21311yescharacteristic
392C3×C8—21no—
393C3×C8—21no—
394C3×C8—32no—
395C3×C8D3×D411yescharacteristic
396C3×C8C2×#6711yescharacteristic
397C3×C8C23×D311yescharacteristic
398C3×C8C23×D311yescharacteristic
399C3⋊C8C2×#6712yes—
400C2×C32—21no—
401C2×C32C22×D811yescharacteristic
402C3⋊D3—81no—
403C3×D3—22no—
404C3×D3—82no—
405C3×D3—81no—
406#41—31no—
407#41—62no—
408#41—61no—
409#41—122no—
410#41—121no—
411#41—182no—
412#41—181no—
413#41—361no—
414C2×Q8—21no—
415C2×Q8—62no—
416C2×Q8—121no—
417C2×D4—61no—
418C2×D4—182no—
419C2×D4—361no—
420C2×D4—362no—
421Q16—21no—
422Q16—31no—
423Q16—62no—
424Q16—91no—
425Q16C2×D3212yes—
426SD16—62no—
427SD16—61no—
428SD16—182no—
429SD16—181no—
430D8—31no—
431D8—32no—
432D8—61no—
433D8—91no—
434D8—182no—
435M16—31no—
436M16—32no—
437C2×C8—32no—
438C2×C8C2×D3211yescharacteristic
439C16—31no—
440C16—31no—
441C16—92no—
442C22×C3—21no—
443C22×C3—32no—
444C22×C3—121no—
445C22×C3—122no—
446C22×C3—481no—
447C22×C3D3×D811yescharacteristic
448C22×C3C2×#21311yescharacteristic
449C2×D3—42no—
450C2×D3—41no—
451C2×D3—121no—
452C2×D3—121no—
453C2×D3—161no—
454C2×D3—241no—
455C2×D3—482no—
456C2×D3—482no—
457C2×D3C2×#21312yes—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—32no—
461C3×C4—42no—
462C3×C4—42no—
463C3×C4—82no—
464C3×C4—121no—
465C3×C4D3×D811yescharacteristic
466C3×C4C2×#21311yescharacteristic
467C3×C4C2×D3×D411yescharacteristic
468C3×C4C22×#6711yescharacteristic
469Dic3—41no—
470Dic3—121no—
471Dic3—121no—
472Dic3—241no—
473Dic3C2×#21312yes—
474C32#341611yescharacteristic, complemented, Sylow
475C23—121no—
476C23—362no—
477Q8—22no—
478Q8—31no—
479Q8—41no—
480Q8—61no—
481Q8—122no—
482Q8—181no—
483D4—32no—
484D4—31no—
485D4—62no—
486D4—61no—
487D4—122no—
488D4—121no—
489D4—121no—
490D4—181no—
491D4—362no—
492D4—362no—
493D4—361no—
494C2×C4—32no—
495C2×C4—41no—
496C2×C4—122no—
497C2×C4—122no—
498C2×C4—121no—
499C2×C4—362no—
500C2×C4—361no—
501C2×C4D3×#6711yescharacteristic
502C8—32no—
503C8D3×#6711yescharacteristic
504C8C22×D3211yescharacteristic
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—41no—
509C2×C3—62no—
510C2×C3—242no—
511C2×C3—241no—
512C2×C3C2×D3×D811yescharacteristic
513C2×C3C22×#21311yescharacteristic
514D3—22no—
515D3—81no—
516D3—82no—
517D3—241no—
518D3—241no—
519D3—481no—
520C22—32no—
521C22—121no—
522C22—122no—
523C22—361no—
524C22—481no—
525C22—1442no—
526C22D3×#21311yescharacteristic
527C4—32no—
528C4—42no—
529C4—121no—
530C4—361no—
531C4D3×#21311yescharacteristic
532C4C2×D3×#6711yescharacteristic
533C3—21no—
534C3#8202411yescharacteristic, complemented
535C3#8401611yescharacteristic, complemented
536C2—21no—
537C2—62no—
538C2—242no—
539C2—241no—
540C2—721no—
541C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC2C2×D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×Q16C22
socleC2×C32C22×D8
hypercenterC2×Q16D32
hypocenterC32#3416
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C3×#5766C2semidirect
2. #10594678C2semidirect
3. #10592878C2semidirect
4. C2×C3×#828C2semidirect
5. #10591046C2semidirect
6. #10591045C2semidirect
7. #10591038C2semidirect
8. D3×#828C2semidirect
9. #10590632C2semidirect
10. #10590630C2semidirect
11. #10590621C2semidirect
16. C2×C32×Q16C22semidirect
19. C3×#919C22semidirect
21. C3×D3×Q16C22semidirect
22. C3×#904C22semidirect
29. #63656C22semidirect
30. #63655C22semidirect
31. #63639C22semidirect
32. C3×#828C22semidirect
33. C3×#828C22semidirect
34. C2×C3×C3⋊C16C22semidirect
35. #63551C22semidirect
36. #63549C22semidirect
37. #63548C22semidirect
38. #63547C22semidirect
39. #63546C22semidirect
40. #63545C22semidirect
41. #63543C22semidirect
42. D3×C3⋊C16C22semidirect
44. #5766D3semidirect
57. C2×#828D3semidirect
113. C2×C3×Q16C2×D3semidirect
114. C2×C3×Q16C2×D3semidirect
119. #919C2×D3semidirect
121. D3×Q16C2×D3semidirect
131. #904C2×D3semidirect
147. #828C2×D3semidirect
148. #828C2×D3semidirect
159. C2×C3⋊C16C2×D3semidirect
312. C2×Q16D32semidirect
474. C32#3416semidirect
534. C3#82024semidirect
535. C3#84016semidirect

Maximal subgroups

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

subgroupindex
C3×#57662
#105946782
#105928782
C2×C3×#8282
#105910462
#105910452
#105910382
D3×#8282
#105906322
#105906302
#105906212
#840163
#820243