Finite Group Databasebeta

← #11886801

Subgroups — #11886801

Order 1152.

958 conjugacy classes of subgroups.

The subgroup lattice has 639 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5752C211yesmaximal, characteristic, complemented
2#10595466C212yesmaximal, complemented
3#10594692C211yesmaximal, characteristic, complemented
4#10592842C211yesmaximal, characteristic, complemented
5C3×#5144C211yesmaximal, characteristic, complemented
6#10591688C212yesmaximal, complemented
7#10591019C212yesmaximal, complemented
8#10590986C212yesmaximal, complemented
9#10590926C211yesmaximal, characteristic, complemented
10#10590915C211yesmaximal, characteristic, complemented
11#10590864C211yesmaximal, characteristic, complemented
12#84011—31nomaximal
13#79891—31nomaximal
14C3×#1009C2212yes—
15#64298C2212yescomplemented
16C32×#131C2211yescharacteristic
17#64160C2212yes—
18C2×#3746C2211yescharacteristic, complemented
19C3×#950C2211yescharacteristic
20C3×#908—22no—
21C3×#908C2212yes—
22C3×#904—21no—
23C3×#904C2211yescharacteristic
24C2×C3×D24—21no—
25C2×C3×D24C2211yescharacteristic
26C3×#901C2211yescharacteristic, complemented
27#63947—22no—
28#63943—22no—
29#63932—22no—
30D3×#214—22no—
31#63860C2212yescomplemented
32#63831C2212yescomplemented
33C2×#3716C2212yescomplemented
34#63823C2212yescomplemented
35#63814C2212yescomplemented
36#63807—21no—
37#63800—22no—
38D3×Dic12—21no—
39#63651C2212yescomplemented
40#63646C2211yescharacteristic, complemented
41C3×#837C2211yescharacteristic
42C3×#825C2211yescharacteristic, complemented
43C3×#822C2211yescharacteristic, complemented
44C3×C8×Dic3C2211yescharacteristic, complemented
45#63569C2212yescomplemented
46#63558C2212yescomplemented
47C3×#576—31no—
48#5836—32no—
49#5771—31no—
50#5770—32no—
51#5753—31no—
52#5752D311yescharacteristic, complemented
53C3×#443—31no—
54#5242—32no—
55#5201—32no—
56#5200—32no—
57#5196—31no—
58#5160—31no—
59#5155—31no—
60#5144D311yescharacteristic, complemented
61#5143—31no—
62#5143—31no—
63#5143—61no—
64#5142—31no—
65#4898—32no—
66#4827—32no—
67#4825—32no—
68#4700—31no—
69#4696—31no—
70C32×#41C2311yescharacteristic
71C2×#634C2312yes—
72C3×#239—22no—
73C3×D3×D4—22no—
74C3×D3×D4—42no—
75C3×#235—22no—
76C3×#235C2311yescharacteristic
77C3×#235C2312yes—
78C2×C3×D12—22no—
79C2×C3×D12C2312yes—
80#3805—42no—
81#3795—22no—
82#3795—22no—
83D3×Dic6—22no—
84D3×Dic6—22no—
85C32×M16—21no—
86C32×M16C2311yescharacteristic
87C2×C32×C8—21no—
88C2×C32×C8C2311yescharacteristic
89#3756—22no—
90#3754—22no—
91#3748C2312yes—
92#3746—21no—
93#3746—21no—
94C3×#216D411yescharacteristic
95C3×#215D411yescharacteristic
96C3×#214D411yescharacteristic
97C3×#213D411yescharacteristic
98C3×C4×Dic3C2311yescharacteristic
99C3×#208C2311yescharacteristic
100C2×C3×C3⋊C8C2311yescharacteristic
101C3×Dic12D411yescharacteristic
102C3×D24—22no—
103C3×D24—21no—
104C3×D24—21no—
105C3×D24D411yescharacteristic
106C3×#204—22no—
107C3×#204D412yes—
108C3×ΓL(1,𝔽25)—21no—
109C3×D3×C8—21no—
110(C2×D3)⋊Dic3—42no—
111#3719—22no—
112#3716—22no—
113#3716—22no—
114#3716—22no—
115#3715—22no—
116#3713—22no—
117#3711—22no—
118D3×C3⋊C8—22no—
119#3290—91noSylow
120C3×H(5,𝔽2)—32no—
121#1010—32no—
122#1010—32no—
123#1009C2×D312yes—
124C3×AGL(1,ℤ/8)—32no—
125C3×AGL(1,ℤ/8)—62no—
126C3×#135—31no—
127C3×#135—31no—
128C3×#135—61no—
129C2×C3×D8—31no—
130C2×C3×D8—61no—
131C3×#131—21no—
132C3×#131—31no—
133C3×#131C2×D311yescharacteristic
134C3×#131C2×D311yescharacteristic
135#951—32no—
136#951—32no—
137#951—32no—
138#951—62no—
139#951—62no—
140#950—62no—
141#950C2×D311yescharacteristic
142#949—32no—
143#948—32no—
144#936—32no—
145C2×#214—32no—
146C2×#214—62no—
147#932—32no—
148#932—62no—
149#918—62no—
150D3×Q16—61no—
151#916—62no—
152#915—62no—
153D3×SD16—62no—
154#912—61no—
155#911—62no—
156#909—32no—
157#909—62no—
158#908—22no—
159#908C2×D312yes—
160C2×Dic12—31no—
161C2×Dic12—31no—
162C2×Dic12—61no—
163C2×Dic12—61no—
164#904—21no—
165#904—61no—
166#904C2×D311yescharacteristic
167C2×D24—21no—
168C2×D24C2×D311yescharacteristic
169C2×#204—32no—
170#901—32no—
171#901C2×D311yescharacteristic, complemented
172#875—32no—
173C3×#108—31no—
174C3×#104—31no—
175C3×#104—31no—
176C3×C4×C8—31no—
177#837—32no—
178#837C2×D311yescharacteristic
179#833—32no—
180#825C2×D311yescharacteristic, complemented
181#824—32no—
182#824—32no—
183#824—62no—
184#823—32no—
185#822C2×D311yescharacteristic, complemented
186#819—31no—
187#819—31no—
188#819—61no—
189C8×Dic3C2×D311yescharacteristic, complemented
190#805—32no—
191C22×C3×D3—22no—
192C22×C3×D3—42no—
193C32×Q8C2×D411yescharacteristic
194C32×D4—21no—
195C32×D4C2×D411yescharacteristic
196C2×C32×C4—21no—
197C2×C32×C4C2411yescharacteristic
198C2×C3⋊Dic3—22no—
199#634—22no—
200#634—22no—
201C3×#67—21no—
202C3×#67—22no—
203C3×#67—42no—
204C2×C3×Dic3—21no—
205C3×D12—22no—
206C3×D12—22no—
207C3×D12—42no—
208C3×D12C2×D411yescharacteristic
209C3×D12C2×D412yes—
210C3×C4×D3—22no—
211C3×C4×D3—21no—
212C3×C4×D3—42no—
213C3×Dic6C2×D411yescharacteristic
214C3×Dic6C2×D412yes—
215#627—42no—
216#625—42no—
217D3×Dic3—42no—
218D3×Dic3—42no—
219C32×C8—21no—
220C32×C8C2×D411yescharacteristic
221C32×C8C2×D411yescharacteristic
222C3⋊(C3⋊C8)—22no—
223C3×C3⋊C8—21no—
224C3×C3⋊C8C2×D411yescharacteristic
225C3×C3⋊C8C2×D411yescharacteristic
226#578—91no—
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—31no—
236#443—91no—
237C3×#41—21no—
238C3×#41—32no—
239C3×#41—31no—
240C3×#41—62no—
241C3×#41—62no—
242C3×#41C22×D311yescharacteristic
243C3×#41C22×D311yescharacteristic
244C2×C3×D4—32no—
245C2×C3×D4—62no—
246C2×C3×D4—62no—
247C2×C3×D4—122no—
248#239—22no—
249D3×Q8—62no—
250D3×Q8—62no—
251#237—62no—
252#237—62no—
253#237—122no—
254#237—122no—
255D3×D4—22no—
256D3×D4—42no—
257#235—22no—
258#235—62no—
259#235—62no—
260#235C22×D311yescharacteristic
261#235C22×D312yes—
262C2×D12—22no—
263C2×D12C22×D312yes—
264C2×Dic6—32no—
265C2×Dic6—32no—
266C2×Dic6—62no—
267C2×Dic6—62no—
268C2×Dic6—62no—
269C3×Q16—31no—
270C3×Q16—31no—
271C3×SD16—31no—
272C3×SD16—31no—
273C3×SD16—32no—
274C3×SD16—62no—
275C3×D8—31no—
276C3×D8—31no—
277C3×D8—62no—
278C3×D8—61no—
279C3×D8—61no—
280C3×M16—21no—
281C3×M16—21no—
282C3×M16—21no—
283C3×M16—31no—
284C3×M16—41no—
285C3×M16—61no—
286C3×M16C22×D311yescharacteristic
287C3×M16C22×D311yescharacteristic
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—31no—
292C2×C3×C8—41no—
293C2×C3×C8—61no—
294C2×C3×C8C22×D311yescharacteristic
295C2×C3×C8C22×D311yescharacteristic
296C3×C42—31no—
297#217—122no—
298#216—62no—
299#216—62no—
300#216—62no—
301#216—122no—
302#216D1211yescharacteristic
303#215—62no—
304#215D1211yescharacteristic
305#214—62no—
306#214—62no—
307#214—62no—
308#214—62no—
309#214—62no—
310#214—62no—
311#214—122no—
312#214D1211yescharacteristic
313#213—62no—
314#213—62no—
315#213D1211yescharacteristic
316(C2×D3)⋊C4—122no—
317C4×Dic3C22×D311yescharacteristic
318#208—32no—
319#208—32no—
320#208—62no—
321#208—62no—
322#208C22×D311yescharacteristic
323C2×C3⋊C8—62no—
324C2×C3⋊C8C22×D311yescharacteristic
325Dic12—62no—
326Dic12—61no—
327Dic12—61no—
328Dic12—61no—
329Dic12—61no—
330Dic12—121no—
331Dic12—121no—
332Dic12#6711yescharacteristic
333D24—22no—
334D24—21no—
335D24—21no—
336D24#6711yescharacteristic
337#204—22no—
338#204—62no—
339#204—62no—
340#204—62no—
341#204#6712yes—
342ΓL(1,𝔽25)—21no—
343ΓL(1,𝔽25)—62no—
344D3×C8—21no—
345D3×C8—62no—
346C22×C32—21no—
347C22×C32H(5,𝔽2)11yescharacteristic
348C2×C3×D3—21no—
349C2×C3×D3—22no—
350C2×C3×D3—42no—
351C2×C3×D3—82no—
352C2×C3×D3—162no—
353C32×C4—21no—
354C32×C4C22×D411yescharacteristic
355C32×C4C22×D411yescharacteristic
356C3⋊Dic3—42no—
357C3×Dic3—21no—
358C3×Dic3—22no—
359C3×Dic3—41no—
3602−1+4—92no—
361H(5,𝔽2)—32no—
362#137—92no—
363#137—92no—
364#137—182no—
365#137—182no—
366AGL(1,ℤ/8)—32no—
367AGL(1,ℤ/8)—62no—
368AGL(1,ℤ/8)—92no—
369AGL(1,ℤ/8)—182no—
370#135—31no—
371#135—31no—
372#135—61no—
373#135—181no—
374#135—182no—
375C2×Q16—91no—
376C2×Q16—181no—
377C2×SD16—92no—
378C2×SD16—182no—
379C2×D8—31no—
380C2×D8—61no—
381#131—31no—
382#131—92no—
383#131D3211yescharacteristic
384#124—92no—
385#108—31no—
386#108—91no—
387#104—31no—
388#104—31no—
389#104—92no—
390#101—92no—
391#100—92no—
392C4×C8—31no—
393C23×C3—62no—
394C23×C3—122no—
395C22×D3—22no—
396C22×D3—42no—
397C3×Q8—21no—
398C3×Q8—31no—
399C3×Q8—32no—
400C3×Q8C2×D1211yescharacteristic
401C3×Q8D3×D411yescharacteristic
402C3×D4—21no—
403C3×D4—21no—
404C3×D4—21no—
405C3×D4—31no—
406C3×D4—32no—
407C3×D4—41no—
408C3×D4—61no—
409C3×D4—62no—
410C3×D4—62no—
411C3×D4—62no—
412C3×D4—122no—
413C3×D4—122no—
414C3×D4C2×D1211yescharacteristic
415C3×D4D3×D411yescharacteristic
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—41no—
420C2×C3×C4—62no—
421C2×C3×C4—61no—
422C2×C3×C4—61no—
423C2×C3×C4—122no—
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426#67—22no—
427#67—21no—
428#67—42no—
429#67—122no—
430#67—122no—
431C2×Dic3—21no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—122no—
435C2×Dic3—122no—
436C2×Dic3—122no—
437D12—22no—
438D12—22no—
439D12—42no—
440D12C2×D1211yescharacteristic
441D12C2×#6712yes—
442C4×D3—21no—
443C4×D3—22no—
444C4×D3—42no—
445C4×D3—122no—
446C4×D3—122no—
447Dic6—62no—
448Dic6—62no—
449Dic6—62no—
450Dic6—62no—
451Dic6—122no—
452Dic6—122no—
453Dic6—122no—
454Dic6—122no—
455Dic6C2×D1211yescharacteristic
456Dic6C2×#6712yes—
457C3×C8—21no—
458C3×C8—21no—
459C3×C8—21no—
460C3×C8—21no—
461C3×C8—31no—
462C3×C8—31no—
463C3×C8—41no—
464C3×C8—61no—
465C3×C8D3×D411yescharacteristic
466C3×C8D3×D411yescharacteristic
467C3×C8C2×#6711yescharacteristic
468C3×C8C2×#6711yescharacteristic
469C3⋊C8—21no—
470C3⋊C8—62no—
471C3⋊C8—62no—
472C3⋊C8—122no—
473C3⋊C8C2×D1211yescharacteristic
474C3⋊C8C2×D1211yescharacteristic
475C2×C32—21no—
476C2×C32—41no—
477C2×C32D4211yescharacteristic
478C3×D3—41no—
479C3×D3—42no—
480C3×D3—82no—
481#41—31no—
482#41—32no—
483#41—62no—
484#41—62no—
485#41—182no—
486#41—182no—
487#41—362no—
488#41C2×D3211yescharacteristic
489C2×Q8—92no—
490C2×Q8—182no—
491C2×Q8—182no—
492C2×D4—32no—
493C2×D4—62no—
494C2×D4—62no—
495C2×D4—122no—
496Q16—31no—
497Q16—31no—
498Q16—182no—
499Q16—182no—
500Q16—181no—
501Q16—181no—
502SD16—31no—
503SD16—31no—
504SD16—32no—
505SD16—62no—
506SD16—182no—
507SD16—182no—
508SD16—182no—
509SD16—182no—
510SD16—182no—
511D8—31no—
512D8—31no—
513D8—62no—
514D8—61no—
515D8—61no—
516D8—182no—
517M16—21no—
518M16—31no—
519M16—61no—
520M16—92no—
521M16—182no—
522M16C2×D3211yescharacteristic
523C2×C8—21no—
524C2×C8—31no—
525C2×C8—61no—
526C2×C8—182no—
527C2×C8C2×D3211yescharacteristic
528C22⋊C4—362no—
529C42—31no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—41no—
534C22×C3—61no—
535C22×C3—62no—
536C22×C3—122no—
537C22×C3—242no—
538C22×C3—482no—
539C22×C3#100411yescharacteristic
540C22×C3#100911yescharacteristic
541C2×D3—22no—
542C2×D3—21no—
543C2×D3—42no—
544C2×D3—82no—
545C2×D3—162no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—21no—
550C3×C4—41no—
551C3×C4—61no—
552C3×C4—62no—
553C3×C4—121no—
554C3×C4C22×D1211yescharacteristic
555C3×C4C2×D3×D411yescharacteristic
556C3×C4C2×D3×D411yescharacteristic
557C3×C4C22×#6711yescharacteristic
558Dic3—22no—
559Dic3—21no—
560Dic3—41no—
561Dic3—122no—
562Dic3—122no—
563Dic3—242no—
564C32#329011yescharacteristic, complemented, Sylow
565C23—62no—
566C23—122no—
567Q8—31no—
568Q8—32no—
569Q8—182no—
570Q8—182no—
571Q8—362no—
572Q8D3×D1211yescharacteristic
573D4—21no—
574D4—31no—
575D4—32no—
576D4—62no—
577D4—61no—
578D4—62no—
579D4—62no—
580D4—122no—
581D4—122no—
582D4—362no—
583D4D3×D1211yescharacteristic
584C2×C4—21no—
585C2×C4—62no—
586C2×C4—61no—
587C2×C4—61no—
588C2×C4—122no—
589C2×C4—182no—
590C2×C4—362no—
591C2×C4—362no—
592C2×C4C22×D3211yescharacteristic
593C8—21no—
594C8—31no—
595C8—31no—
596C8—61no—
597C8—182no—
598C8D3×#6711yescharacteristic
599C8D3×#6711yescharacteristic
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—41no—
604C2×C3—41no—
605C2×C3—41no—
606C2×C3—81no—
607C2×C3—122no—
608C2×C3—121no—
609C2×C3—242no—
610C2×C3D4×D1211yescharacteristic
611C2×C3D4×#6711yescharacteristic
612D3—41no—
613D3—42no—
614D3—82no—
615C22—21no—
616C22—61no—
617C22—62no—
618C22—122no—
619C22—242no—
620C22—482no—
621C22#6430711yescharacteristic
622C4—21no—
623C4—62no—
624C4—61no—
625C4—121no—
626C4—362no—
627C4C2×D3×D1211yescharacteristic
628C4C2×D3×#6711yescharacteristic
629C3—21no—
630C3#7989111yescharacteristic, complemented
631C3#8401111yescharacteristic, complemented
632C2—21no—
633C2—41no—
634C2—122no—
635C2—121no—
636C2—242no—
637C2D12×#6711yescharacteristic
subgroupG/H
centerC2D12×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#131C22
socleC2×C32D42
hypercenter#131D32
hypocenterC32#3290
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131

Complements

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

NH ≅ G/Ntype
1. C3×#5752C2semidirect
2. #10595466C2semidirect
3. #10594692C2semidirect
4. #10592842C2semidirect
5. C3×#5144C2semidirect
6. #10591688C2semidirect
7. #10591019C2semidirect
8. #10590986C2semidirect
9. #10590926C2semidirect
10. #10590915C2semidirect
11. #10590864C2semidirect
15. #64298C22semidirect
18. C2×#3746C22semidirect
26. C3×#901C22semidirect
31. #63860C22semidirect
32. #63831C22semidirect
33. C2×#3716C22semidirect
34. #63823C22semidirect
35. #63814C22semidirect
39. #63651C22semidirect
40. #63646C22semidirect
42. C3×#825C22semidirect
43. C3×#822C22semidirect
44. C3×C8×Dic3C22semidirect
45. #63569C22semidirect
46. #63558C22semidirect
52. #5752D3semidirect
60. #5144D3semidirect
171. #901C2×D3semidirect
180. #825C2×D3semidirect
185. #822C2×D3semidirect
189. C8×Dic3C2×D3semidirect
564. C32#3290semidirect
630. C3#79891semidirect
631. C3#84011semidirect

Maximal subgroups

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

subgroupindex
C3×#57522
#105954662
#105946922
#105928422
C3×#51442
#105916882
#105910192
#105909862
#105909262
#105909152
#105908642
#840113
#798913