Finite Group Databasebeta

← #11886784

Subgroups — #11886784

Order 1152.

961 conjugacy classes of subgroups.

The subgroup lattice has 637 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5771C211yesmaximal, characteristic, complemented
2C3×#5769C211yesmaximal, characteristic, complemented
3#10595446C212yesmaximal, complemented
4#10592895C211yesmaximal, characteristic, complemented
5#10591684C212yesmaximal, complemented
6#10591681C212yesmaximal, complemented
7#10591664C212yesmaximal, complemented
8#10590930C211yesmaximal, characteristic, complemented
9#10590926C211yesmaximal, characteristic, complemented
10#10590921C211yesmaximal, characteristic, complemented
11#10590869C211yesmaximal, characteristic, complemented
12#84020—31nomaximal
13#84011—31nomaximal
14C3×#1010C2212yescomplemented
15C3×#1009C2212yes—
16C32×#135C2211yescharacteristic
17#64157C2212yescomplemented
18C3×#951C2212yescomplemented
19C3×#949C2212yes—
20C3×#919—21no—
21C3×D3×Q16—21no—
22C3×#915—22no—
23C3×#914—22no—
24C3×#912—21no—
25C3×D3×D8—21no—
26C2×C3×Dic12C2211yescharacteristic, complemented
27C2×C3×D24C2211yescharacteristic
28C3×#901C2211yescharacteristic
29C3×#901C2211yescharacteristic, complemented
30#63863C2212yescomplemented
31#63827—22no—
32#63827C2212yes—
33C2×#3715—22no—
34C2×#3715C2212yescomplemented
35#63823—22no—
36#63823C2212yescomplemented
37#63822—22no—
38#63822C2211yescharacteristic
39#63664C2212yescomplemented
40#63646C2211yescharacteristic, complemented
41C8×C3⋊Dic3C2211yescharacteristic, complemented
42#63578C2211yescharacteristic, complemented
43#63568C2211yescharacteristic
44#63568C2211yescharacteristic, complemented
45#63560C2212yescomplemented
46#63558C2212yescomplemented
47C3×#578—31no—
48C3×#576—31no—
49#5837—32no—
50#5836—32no—
51#5771D311yescharacteristic, complemented
52#5769D311yescharacteristic, complemented
53#5245—32no—
54#5242—32no—
55#5203—32no—
56#5202—32no—
57#5201—32no—
58#5200—32no—
59#5196—31no—
60#5196—31no—
61#5196—61no—
62#5192—31no—
63#5191—31no—
64#5160—31no—
65#5155—31no—
66#5144—31no—
67#5144—31no—
68#5143—31no—
69#5142—31no—
70C32×#41C2312yes—
71C3×#239—22no—
72C3×D3×Q8—22no—
73C3×#237—22no—
74C3×#237—42no—
75C3×D3×D4—22no—
76C3×D3×D4—42no—
77C3×#235—22no—
78C3×#235—22no—
79C3×#235C2311yescharacteristic
80C3×#235C2311yescharacteristic
81C2×C3×D12—22no—
82C2×C3×D12C2312yes—
83C2×C3×Dic6—22no—
84C2×C3×Dic6C2312yes—
85C32×Q16D411yescharacteristic
86C32×SD16D412yes—
87C32×D8D411yescharacteristic
88C2×C32×C8C2311yescharacteristic
89C4×C3⋊Dic3C2311yescharacteristic
90#3748—22no—
91#3748C2312yes—
92C2×C3⋊(C3⋊C8)—22no—
93C2×C3⋊(C3⋊C8)C2311yescharacteristic
94C3×#216—22no—
95C3×#215—22no—
96C3×#214—22no—
97C3×#213—22no—
98C3×#208C2311yescharacteristic
99C3×#208C2311yescharacteristic
100C3×Dic12—21no—
101C3×Dic12—21no—
102C3×D24—21no—
103C3×D24—21no—
104C3×ΓL(1,𝔽25)—21no—
105C3×ΓL(1,𝔽25)—21no—
106C3×D3×C8—21no—
107C3×D3×C8—21no—
108(C2×D3)⋊Dic3—42no—
109#3718—22no—
110#3718D411yescharacteristic
111#3715—22no—
112#3715—22no—
113#3715—22no—
114#3715—22no—
115#3715D411yescharacteristic
116#3715D411yescharacteristic
117#3713—22no—
118#3713D411yescharacteristic
119#3290—91noSylow
120C3×2−1+4—32no—
121C3×H(5,𝔽2)—32no—
122#1010C2×D312yescomplemented
123#1009C2×D312yes—
124C3×#137—32no—
125C3×#137—62no—
126C3×AGL(1,ℤ/8)—32no—
127C3×AGL(1,ℤ/8)—62no—
128C3×#135—21no—
129C3×#135—61no—
130C3×#135—61no—
131C3×#135C2×D311yescharacteristic
132C3×#135C2×D311yescharacteristic
133C2×C3×Q16—31no—
134C2×C3×Q16—61no—
135C2×C3×D8—31no—
136C2×C3×D8—61no—
137C3×#131—31no—
138C3×#131—31no—
139#951—32no—
140#951—62no—
141#951C2×D312yescomplemented
142#950—31no—
143#950—31no—
144#950—62no—
145#950—62no—
146#949—32no—
147#949—62no—
148#949C2×D312yes—
149#948—32no—
150#948—32no—
151#948—62no—
152#947—32no—
153#942—32no—
154#942—62no—
155C2×#215—32no—
156C2×#215—62no—
157#936—32no—
158C2×#214—32no—
159C2×#214—62no—
160#932—32no—
161#932—62no—
162#919—21no—
163D3×Q16—21no—
164#915—22no—
165#914—22no—
166#912—21no—
167D3×D8—21no—
168C2×Dic12C2×D311yescharacteristic, complemented
169C2×D24C2×D311yescharacteristic
170#901C2×D311yescharacteristic
171#901C2×D311yescharacteristic, complemented
172#837—32no—
173#837—32no—
174#837—31no—
175#837—31no—
176#837—62no—
177#836—32no—
178#833—32no—
179#825—31no—
180#825—31no—
181#824—32no—
182#823—32no—
183#822—31no—
184#822—31no—
185#819—31no—
186#819—31no—
187#819—61no—
188C8×Dic3—31no—
189C8×Dic3—31no—
190C8×Dic3—61no—
191C22×C3×D3—22no—
192C22×C3×D3—42no—
193C32×Q8C2×D412yes—
194C32×D4—22no—
195C32×D4C2×D412yes—
196C2×C32×C4—22no—
197C2×C32×C4C2411yescharacteristic
198C2×C3⋊Dic3—21no—
199C3×#67—21no—
200C3×#67—21no—
201C3×#67—42no—
202C3×#67—42no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—42no—
205C3×D12—22no—
206C3×D12—22no—
207C3×D12—42no—
208C3×D12C2×D411yescharacteristic
209C3×D12C2×D411yescharacteristic
210C3×C4×D3—21no—
211C3×C4×D3—21no—
212C3×C4×D3—42no—
213C3×C4×D3—42no—
214C3×Dic6—22no—
215C3×Dic6—22no—
216C3×Dic6—42no—
217C3×Dic6C2×D411yescharacteristic
218C3×Dic6C2×D411yescharacteristic
219C32×C8C2×D411yescharacteristic
220C32×C8C2×D411yescharacteristic
221C3⋊(C3⋊C8)—22no—
222C3⋊(C3⋊C8)C2×D411yescharacteristic
223C3⋊(C3⋊C8)C2×D411yescharacteristic
224C3×C3⋊C8—21no—
225C3×C3⋊C8—21no—
226#578—31no—
227#577—92no—
228#576—31no—
229#495—91no—
230#473—91no—
231#472—91no—
232#471—92no—
233#455—92no—
234#454—92no—
235#443—91no—
236#443—91no—
237C3×#41—22no—
238C3×#41—31no—
239C3×#41—31no—
240C3×#41—62no—
241C3×#41—62no—
242C3×#41—62no—
243C3×#41—62no—
244C3×#41—122no—
245C3×#41C22×D312yes—
246C3×#41C22×D312yes—
247C2×C3×Q8—32no—
248C2×C3×Q8—62no—
249C2×C3×Q8—62no—
250C2×C3×D4—32no—
251C2×C3×D4—62no—
252C2×C3×D4—62no—
253C2×C3×D4—122no—
254#239—22no—
255D3×Q8—22no—
256#237—22no—
257#237—42no—
258D3×D4—22no—
259D3×D4—42no—
260#235—22no—
261#235—22no—
262#235C22×D311yescharacteristic
263#235C22×D311yescharacteristic
264C2×D12—22no—
265C2×D12C22×D312yes—
266C2×Dic6—22no—
267C2×Dic6C22×D312yes—
268C3×Q16—21no—
269C3×Q16—62no—
270C3×Q16—61no—
271C3×Q16—61no—
272C3×Q16#6711yescharacteristic
273C3×Q16#6711yescharacteristic
274C3×SD16—22no—
275C3×SD16—62no—
276C3×SD16—62no—
277C3×SD16#6712yes—
278C3×SD16#6712yes—
279C3×D8—21no—
280C3×D8—62no—
281C3×D8—61no—
282C3×D8—61no—
283C3×D8#6711yescharacteristic
284C3×D8#6711yescharacteristic
285C3×M16—31no—
286C3×M16—31no—
287C3×M16—61no—
288C3×M16—61no—
289C2×C3×C8—21no—
290C2×C3×C8—61no—
291C2×C3×C8—61no—
292C2×C3×C8C22×D311yescharacteristic
293C2×C3×C8C22×D311yescharacteristic
294#217—122no—
295#216—22no—
296#216—31no—
297#216—31no—
298#216—62no—
299#216—62no—
300#215—22no—
301#215—31no—
302#215—31no—
303#215—62no—
304#215—62no—
305#215—62no—
306#215—62no—
307#214—22no—
308#214—31no—
309#214—31no—
310#214—62no—
311#214—62no—
312#214—62no—
313#214—62no—
314#213—22no—
315#213—31no—
316#213—31no—
317#213—62no—
318#213—62no—
319(C2×D3)⋊C4—122no—
320C4×Dic3—31no—
321C4×Dic3—31no—
322C4×Dic3—61no—
323#208—32no—
324#208—32no—
325#208—62no—
326#208—62no—
327#208—62no—
328#208—122no—
329#208C22×D311yescharacteristic
330#208C22×D311yescharacteristic
331C2×C3⋊C8—31no—
332C2×C3⋊C8—31no—
333C2×C3⋊C8—61no—
334C2×C3⋊C8—62no—
335C2×C3⋊C8—62no—
336C2×C3⋊C8—122no—
337Dic12—21no—
338Dic12—21no—
339D24—21no—
340D24—21no—
341ΓL(1,𝔽25)—21no—
342ΓL(1,𝔽25)—21no—
343D3×C8—21no—
344D3×C8—21no—
345C22×C32—22no—
346C22×C32H(5,𝔽2)11yescharacteristic
347C2×C3×D3—21no—
348C2×C3×D3—21no—
349C2×C3×D3—42no—
350C2×C3×D3—82no—
351C2×C3×D3—162no—
352C32×C4—22no—
353C32×C4C22×D411yescharacteristic
354C32×C4C22×D411yescharacteristic
355C3⋊Dic3—41no—
356C3×Dic3—21no—
357C3×Dic3—21no—
358C3×Dic3—42no—
3592−1+4—32no—
360H(5,𝔽2)—32no—
361#137—32no—
362#137—62no—
363#137—92no—
364#137—182no—
365AGL(1,ℤ/8)—32no—
366AGL(1,ℤ/8)—62no—
367AGL(1,ℤ/8)—92no—
368AGL(1,ℤ/8)—182no—
369#135—61no—
370#135—61no—
371#135—91no—
372#135—182no—
373#135D3211yescharacteristic
374C2×Q16—31no—
375C2×Q16—61no—
376C2×SD16—92no—
377C2×SD16—182no—
378C2×D8—31no—
379C2×D8—61no—
380#131—31no—
381#131—31no—
382#131—92no—
383#124—92no—
384#108—91no—
385#108—91no—
386#104—91no—
387#104—91no—
388#104—92no—
389#101—92no—
390#100—92no—
391C4×C8—91no—
392C23×C3—62no—
393C23×C3—122no—
394C22×D3—22no—
395C22×D3—42no—
396C3×Q8—22no—
397C3×Q8—31no—
398C3×Q8—31no—
399C3×Q8—62no—
400C3×Q8—62no—
401C3×Q8—122no—
402C3×Q8C2×#6712yes—
403C3×Q8C2×#6712yes—
404C3×D4—22no—
405C3×D4—22no—
406C3×D4—22no—
407C3×D4—31no—
408C3×D4—31no—
409C3×D4—42no—
410C3×D4—61no—
411C3×D4—61no—
412C3×D4—62no—
413C3×D4—62no—
414C3×D4—122no—
415C3×D4—122no—
416C3×D4—122no—
417C3×D4C2×#6712yes—
418C3×D4C2×#6712yes—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—42no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—62no—
426C2×C3×C4—122no—
427C2×C3×C4—122no—
428C2×C3×C4—122no—
429C2×C3×C4C23×D311yescharacteristic
430C2×C3×C4C23×D311yescharacteristic
431#67—21no—
432#67—21no—
433#67—42no—
434#67—42no—
435C2×Dic3—22no—
436C2×Dic3—42no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—121no—
440D12—22no—
441D12—22no—
442D12—42no—
443D12D3×D411yescharacteristic
444D12D3×D411yescharacteristic
445C4×D3—21no—
446C4×D3—21no—
447C4×D3—42no—
448C4×D3—42no—
449Dic6—22no—
450Dic6—22no—
451Dic6—42no—
452Dic6D3×D411yescharacteristic
453Dic6D3×D411yescharacteristic
454C3×C8—21no—
455C3×C8—21no—
456C3×C8—61no—
457C3×C8—61no—
458C3×C8C2×#6711yescharacteristic
459C3×C8C2×#6711yescharacteristic
460C3×C8C2×#6711yescharacteristic
461C3×C8C2×#6711yescharacteristic
462C3⋊C8—21no—
463C3⋊C8—21no—
464C3⋊C8—31no—
465C3⋊C8—31no—
466C3⋊C8—31no—
467C3⋊C8—31no—
468C3⋊C8—61no—
469C3⋊C8—61no—
470C3⋊C8—62no—
471C3⋊C8—62no—
472C3⋊C8—122no—
473C2×C32—21no—
474C2×C32—42no—
475C2×C32D4211yescharacteristic
476C3×D3—41no—
477C3×D3—41no—
478C3×D3—82no—
479#41—31no—
480#41—31no—
481#41—62no—
482#41—62no—
483#41—62no—
484#41—62no—
485#41—122no—
486#41C2×D3212yes—
487C2×Q8—32no—
488C2×Q8—62no—
489C2×Q8—62no—
490C2×D4—32no—
491C2×D4—62no—
492C2×D4—62no—
493C2×D4—122no—
494Q16—62no—
495Q16—61no—
496Q16—61no—
497Q16—91no—
498Q16—182no—
499Q16#62511yescharacteristic
500SD16—62no—
501SD16—62no—
502SD16—91no—
503SD16—91no—
504SD16—182no—
505SD16—182no—
506SD16—182no—
507SD16—182no—
508SD16#62512yes—
509D8—62no—
510D8—61no—
511D8—61no—
512D8—91no—
513D8—182no—
514D8#62511yescharacteristic
515M16—31no—
516M16—31no—
517M16—61no—
518M16—61no—
519M16—92no—
520M16—182no—
521C2×C8—61no—
522C2×C8—61no—
523C2×C8—91no—
524C2×C8—182no—
525C2×C8C2×D3211yescharacteristic
526C22⋊C4—362no—
527C42—91no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—21no—
531C22×C3—42no—
532C22×C3—61no—
533C22×C3—61no—
534C22×C3—122no—
535C22×C3—242no—
536C22×C3—482no—
537C22×C3#100411yescharacteristic
538C22×C3#100411yescharacteristic
539C2×D3—21no—
540C2×D3—21no—
541C2×D3—42no—
542C2×D3—82no—
543C2×D3—162no—
544C3×C4—22no—
545C3×C4—22no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—42no—
549C3×C4—61no—
550C3×C4—61no—
551C3×C4—122no—
552C3×C4C2×D3×D411yescharacteristic
553C3×C4C2×D3×D411yescharacteristic
554C3×C4C22×#6711yescharacteristic
555C3×C4C22×#6711yescharacteristic
556Dic3—21no—
557Dic3—21no—
558Dic3—42no—
559Dic3—121no—
560Dic3—121no—
561Dic3—122no—
562C32#329011yescharacteristic, complemented, Sylow
563C23—62no—
564C23—122no—
565Q8—31no—
566Q8—31no—
567Q8—62no—
568Q8—62no—
569Q8—122no—
570Q8C2×#62512yes—
571D4—22no—
572D4—31no—
573D4—31no—
574D4—61no—
575D4—61no—
576D4—62no—
577D4—62no—
578D4—122no—
579D4—122no—
580D4—122no—
581D4C2×#62512yes—
582C2×C4—22no—
583C2×C4—61no—
584C2×C4—61no—
585C2×C4—62no—
586C2×C4—122no—
587C2×C4—122no—
588C2×C4—122no—
589C2×C4—181no—
590C2×C4C22×D3211yescharacteristic
591C8—61no—
592C8—61no—
593C8—91no—
594C8—91no—
595C8—182no—
596C8C2×#62511yescharacteristic
597C8C2×#62511yescharacteristic
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—41no—
602C2×C3—42no—
603C2×C3—42no—
604C2×C3—82no—
605C2×C3—121no—
606C2×C3—121no—
607C2×C3—242no—
608C2×C3D4×#6711yescharacteristic
609C2×C3D4×#6711yescharacteristic
610D3—41no—
611D3—41no—
612D3—82no—
613C22—22no—
614C22—61no—
615C22—61no—
616C22—122no—
617C22—242no—
618C22—482no—
619C22#6431311yescharacteristic
620C4—22no—
621C4—61no—
622C4—61no—
623C4—122no—
624C4—361no—
625C4D32×D411yescharacteristic
626C4C22×#62511yescharacteristic
627C3—21no—
628C3#8401111yescharacteristic, complemented
629C3#8402011yescharacteristic, complemented
630C2—21no—
631C2—42no—
632C2—121no—
633C2—121no—
634C2—242no—
635C2D4×#62511yescharacteristic
subgroupG/H
centerC2D4×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#135C22
socleC2×C32D42
hypercenter#135D32
hypocenterC32#3290
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. C3×#5771C2semidirect
2. C3×#5769C2semidirect
3. #10595446C2semidirect
4. #10592895C2semidirect
5. #10591684C2semidirect
6. #10591681C2semidirect
7. #10591664C2semidirect
8. #10590930C2semidirect
9. #10590926C2semidirect
10. #10590921C2semidirect
11. #10590869C2semidirect
14. C3×#1010C22semidirect
17. #64157C22semidirect
18. C3×#951C22semidirect
26. C2×C3×Dic12C22semidirect
29. C3×#901C22semidirect
30. #63863C22semidirect
34. C2×#3715C22semidirect
36. #63823C22semidirect
39. #63664C22semidirect
40. #63646C22semidirect
41. C8×C3⋊Dic3C22semidirect
42. #63578C22semidirect
44. #63568C22semidirect
45. #63560C22semidirect
46. #63558C22semidirect
51. #5771D3semidirect
52. #5769D3semidirect
122. #1010C2×D3semidirect
141. #951C2×D3semidirect
168. C2×Dic12C2×D3semidirect
171. #901C2×D3semidirect
562. C32#3290semidirect
628. C3#84011semidirect
629. C3#84020semidirect

Maximal subgroups

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

subgroupindex
C3×#57712
C3×#57692
#105954462
#105928952
#105916842
#105916812
#105916642
#105909302
#105909262
#105909212
#105908692
#840203
#840113