Finite Group Databasebeta

← #11886924

Subgroups — #11886924

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5757C211yesmaximal, characteristic, complemented
2#10595097C212yesmaximal, complemented
3#10594680C211yesmaximal, characteristic, complemented
4#10592850C211yesmaximal, characteristic, complemented
5C3×#5160C211yesmaximal, characteristic, complemented
6#10591522C212yesmaximal, complemented
7#10591510C212yesmaximal, complemented
8#10591508C212yesmaximal, complemented
9#10590927C211yesmaximal, characteristic, complemented
10#10590921C211yesmaximal, characteristic, complemented
11#10590919C211yesmaximal, characteristic, complemented
12#84010—31nomaximal
13#80941—31nomaximal
14C3×#1004C2212yescomplemented
15#64308C2212yescomplemented
16C2×C32×D8C2211yescharacteristic, complemented
17#64149C2212yescomplemented
18C2×#3753C2212yescomplemented
19C2×#3745C2211yescharacteristic, complemented
20C3×#932C2212yescomplemented
21C3×#932C2212yescomplemented
22C3×#912—21no—
23C3×#911—22no—
24C3×D3×D8—21no—
25C3×#904C2211yescharacteristic
26C3×#901C2211yescharacteristic, complemented
27C3×#901C2211yescharacteristic, complemented
28#63935—22no—
29#63934—22no—
30#63925—22no—
31D3×#213—22no—
32#63825C2212yescomplemented
33#63825C2212yescomplemented
34#63822C2211yescharacteristic
35#63815C2212yescomplemented
36#63808—21no—
37#63794—22no—
38D3×D24—21no—
39C8×C3⋊Dic3C2211yescharacteristic, complemented
40C3×#833C2212yescomplemented
41C3×#819C2211yescharacteristic, complemented
42#63578C2211yescharacteristic, complemented
43#63568C2211yescharacteristic, complemented
44#63568C2212yescomplemented
45#63568C2211yescharacteristic, complemented
46#63559C2212yescomplemented
47C3×#576—31no—
48#5835—32no—
49#5774—32no—
50#5769—31no—
51#5757D311yescharacteristic, complemented
52#5752—31no—
53C3×#472—31no—
54#5241—32no—
55#5199—32no—
56#5198—32no—
57#5198—32no—
58#5196—31no—
59#5160D311yescharacteristic, complemented
60#5151—31no—
61#5151—31no—
62#5151—61no—
63#5144—31no—
64#5144—31no—
65#5142—31no—
66#4897—31no—
67#4895—31no—
68#4749—32no—
69#4747—32no—
70C2×C32×D4C2312yes—
71C2×#638—42no—
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×C3×#67—42no—
74C3×#237—22no—
75C3×#237—22no—
76C3×D3×D4—22no—
77C3×D3×D4—22no—
78C3×#235C2311yescharacteristic
79C3×#235C2311yescharacteristic
80C3×#235C2312yes—
81#3811—42no—
82D3×D12—22no—
83D3×D12—22no—
84#3799—22no—
85#3799—22no—
86C32×D8—21no—
87C32×D8—21no—
88C2×C32×C8C2311yescharacteristic
89#3753—22no—
90#3753—22no—
91C4×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2311yescharacteristic
93#3745—21no—
94#3745—21no—
95C3×#214—22no—
96C3×#214—22no—
97C3×#213—22no—
98C3×#213—22no—
99C3×#208C2311yescharacteristic
100C3×#208C2311yescharacteristic
101C3×#208C2312yes—
102C3×Dic12D411yescharacteristic, complemented
103C3×D24D411yescharacteristic, complemented
104C3×#204D412yescomplemented
105C3×ΓL(1,𝔽25)—21no—
106C3×ΓL(1,𝔽25)—21no—
107C3×D3×C8—21no—
108C3×D3×C8—21no—
109#3718D411yescharacteristic, complemented
110#3717—22no—
111#3717—22no—
112#3715D411yescharacteristic, complemented
113#3715D411yescharacteristic, complemented
114#3714—22no—
115#3714—22no—
116#3713D411yescharacteristic, complemented
117#3711—22no—
118D3×C3⋊C8—22no—
119#3292—91noSylow
120C3×H(5,𝔽2)—32no—
121#1009—32no—
122#1009—32no—
123#1004C2×D312yescomplemented
124C3×AGL(1,ℤ/8)—32no—
125C3×AGL(1,ℤ/8)—32no—
126C3×AGL(1,ℤ/8)—62no—
127C3×#135—31no—
128C3×#135—61no—
129C2×C3×D8—21no—
130C2×C3×D8—61no—
131C2×C3×D8C2×D311yescharacteristic, complemented
132C2×C3×D8C2×D311yescharacteristic, complemented
133C3×#131—31no—
134C3×#131—31no—
135#950—31no—
136#950—31no—
137#950—62no—
138#949—32no—
139#949—32no—
140#949—62no—
141#948—32no—
142#940—32no—
143#940—32no—
144#940—62no—
145#932—62no—
146#932C2×D312yescomplemented
147#932C2×D312yescomplemented
148C2×#213—32no—
149C2×#213—32no—
150C2×#213—62no—
151C2×#213—62no—
152#919—61no—
153#916—62no—
154#914—62no—
155#914—62no—
156#912—21no—
157#911—22no—
158#911—62no—
159D3×D8—21no—
160D3×D8—61no—
161D3×D8—62no—
162#908—32no—
163#908—32no—
164#908—62no—
165#907—32no—
166#904—61no—
167#904C2×D311yescharacteristic
168C2×D24—31no—
169C2×D24—31no—
170C2×D24—61no—
171C2×D24—61no—
172#901C2×D311yescharacteristic, complemented
173#901C2×D311yescharacteristic, complemented
174C3×#108—31no—
175C3×#100—32no—
176#837—31no—
177#837—31no—
178#837—32no—
179#833C2×D312yescomplemented
180#825—31no—
181#825—31no—
182#825—32no—
183#823—32no—
184#823—32no—
185#822—31no—
186#822—31no—
187#819C2×D311yescharacteristic, complemented
188C8×Dic3—31no—
189C8×Dic3—31no—
190C8×Dic3—61no—
191C23×C32—22no—
192C22×C3⋊D3—22no—
193C22×C3×D3—42no—
194C2×D32—42no—
195C32×D4—22no—
196C32×D4—22no—
197C2×C32×C4C2411yescharacteristic
198#638—84no—
199C2×C3⋊Dic3—21no—
200C4⋊(C3⋊D3)—22no—
201C4⋊(C3⋊D3)—22no—
202C3×#67—21no—
203C3×#67—22no—
204C3×#67—21no—
205C3×#67—42no—
206C3×#67—42no—
207C2×C3×Dic3—42no—
208C3×D12C2×D411yescharacteristic
209C3×D12C2×D411yescharacteristic
210C3×D12C2×D412yes—
211C3×C4×D3—22no—
212C3×C4×D3—21no—
213C3×C4×D3—21no—
214C3×Dic6C2×D411yescharacteristic
215C3×Dic6C2×D411yescharacteristic
216C3×Dic6C2×D412yes—
217#626—42no—
218#626—42no—
219#624—42no—
220C32×C8C2×D411yescharacteristic
221C32×C8C2×D411yescharacteristic
222C3⋊(C3⋊C8)C2×D411yescharacteristic
223C3⋊(C3⋊C8)C2×D411yescharacteristic
224C3×C3⋊C8—22no—
225C3×C3⋊C8—21no—
226C3×C3⋊C8—21no—
227#576—31no—
228#576—91no—
229#576—92no—
230#493—91no—
231#472—31no—
232#472—92no—
233#472—91no—
234#453—92no—
235#453—92no—
236#443—91no—
237#443—91no—
238C3×#41—32no—
239C3×#41—31no—
240C3×#41—31no—
241C3×#41—62no—
242C3×#41—62no—
243C2×C3×D4—22no—
244C2×C3×D4—62no—
245C2×C3×D4—62no—
246C2×C3×D4—122no—
247C2×C3×D4C22×D312yes—
248C2×C3×D4C22×D312yes—
249C2×#67—42no—
250C2×#67—122no—
251C2×#67—122no—
252C2×#67—124no—
253#239—62no—
254#239—62no—
255#237—22no—
256#237—22no—
257D3×D4—22no—
258D3×D4—22no—
259D3×D4—62no—
260D3×D4—62no—
261D3×D4—122no—
262D3×D4—122no—
263#235—62no—
264#235—62no—
265#235C22×D311yescharacteristic
266#235C22×D311yescharacteristic
267#235C22×D312yes—
268C2×D12—32no—
269C2×D12—32no—
270C2×D12—62no—
271C2×D12—62no—
272C2×D12—62no—
273C3×Q16—31no—
274C3×SD16—32no—
275C3×SD16—62no—
276C3×SD16—62no—
277C3×D8—21no—
278C3×D8—21no—
279C3×D8—21no—
280C3×D8—21no—
281C3×D8—31no—
282C3×D8—41no—
283C3×D8—41no—
284C3×D8—62no—
285C3×D8—62no—
286C3×M16—31no—
287C3×M16—31no—
288C3×M16—32no—
289C3×M16—61no—
290C3×M16—61no—
291C2×C3×C8—21no—
292C2×C3×C8—61no—
293C2×C3×C8—61no—
294C2×C3×C8C22×D311yescharacteristic
295C2×C3×C8C22×D311yescharacteristic
296#216—31no—
297#216—31no—
298#215—31no—
299#215—31no—
300#215—62no—
301#215—62no—
302#214—22no—
303#214—22no—
304#214—31no—
305#214—31no—
306#213—22no—
307#213—22no—
308#213—31no—
309#213—31no—
310#213—62no—
311#213—62no—
312#213—62no—
313#213—62no—
314#213—62no—
315#213—62no—
316#213—122no—
317#213—122no—
318C4×Dic3—31no—
319C4×Dic3—31no—
320C4×Dic3—61no—
321#208—62no—
322#208C22×D312yes—
323#208C22×D311yescharacteristic
324#208C22×D311yescharacteristic
325C2×C3⋊C8—31no—
326C2×C3⋊C8—31no—
327C2×C3⋊C8—61no—
328C2×C3⋊C8—62no—
329Dic12#6711yescharacteristic, complemented
330D24—62no—
331D24—62no—
332D24—61no—
333D24—61no—
334D24—61no—
335D24—61no—
336D24—121no—
337D24—121no—
338D24#6711yescharacteristic, complemented
339#204—62no—
340#204—62no—
341#204#6712yescomplemented
342ΓL(1,𝔽25)—21no—
343ΓL(1,𝔽25)—21no—
344ΓL(1,𝔽25)—62no—
345D3×C8—21no—
346D3×C8—21no—
347D3×C8—62no—
348C22×C32—42no—
349C22×C32—82no—
350C22×C32H(5,𝔽2)11yescharacteristic
351C2×C3⋊D3—42no—
352C2×C3⋊D3—82no—
353C2×C3×D3—21no—
354C2×C3×D3—22no—
355C2×C3×D3—21no—
356C2×C3×D3—162no—
357D32—162no—
358C32×C4C22×D411yescharacteristic
359C32×C4C22×D411yescharacteristic
360C3⋊Dic3—22no—
361C3×Dic3—21no—
362C3×Dic3—22no—
363C3×Dic3—21no—
364H(5,𝔽2)—32no—
365H(5,𝔽2)—92no—
366AGL(1,ℤ/8)—32no—
367AGL(1,ℤ/8)—32no—
368AGL(1,ℤ/8)—62no—
369AGL(1,ℤ/8)—92no—
370AGL(1,ℤ/8)—92no—
371AGL(1,ℤ/8)—182no—
372AGL(1,ℤ/8)—182no—
373AGL(1,ℤ/8)—182no—
374#135—31no—
375#135—61no—
376#135—91no—
377#135—181no—
378#135—182no—
379C2×D8—61no—
380C2×D8—92no—
381C2×D8—91no—
382C2×D8—181no—
383C2×D8—182no—
384C2×D8D3211yescharacteristic, complemented
385#131—31no—
386#131—31no—
387#131—92no—
388#127—92no—
389#108—31no—
390#108—91no—
391#104—91no—
392#104—92no—
393#104—91no—
394#100—32no—
395#100—92no—
396C4×C8—91no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—42no—
400C23×C3—122no—
401C22×D3—42no—
402C22×D3—62no—
403C22×D3—62no—
404C22×D3—122no—
405C22×D3—122no—
406C22×D3—122no—
407C3×Q8—31no—
408C3×Q8—31no—
409C3×Q8—32no—
410C3×D4—22no—
411C3×D4—22no—
412C3×D4—22no—
413C3×D4—22no—
414C3×D4—31no—
415C3×D4—31no—
416C3×D4—32no—
417C3×D4—42no—
418C3×D4—42no—
419C3×D4—61no—
420C3×D4—62no—
421C3×D4—61no—
422C3×D4—122no—
423C3×D4—122no—
424C2×C3×C4—21no—
425C2×C3×C4—62no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—122no—
429C2×C3×C4C23×D311yescharacteristic
430C2×C3×C4C23×D311yescharacteristic
431#67—22no—
432#67—21no—
433#67—21no—
434#67—42no—
435#67—42no—
436#67—122no—
437#67—122no—
438#67—244no—
439#67—244no—
440#67—248no—
441C2×Dic3—42no—
442C2×Dic3—62no—
443C2×Dic3—61no—
444C2×Dic3—61no—
445D12—62no—
446D12—62no—
447D12—62no—
448D12—62no—
449D12—122no—
450D12—122no—
451D12—122no—
452D12—122no—
453D12D3×D411yescharacteristic
454D12D3×D411yescharacteristic
455D12C2×#6712yes—
456C4×D3—21no—
457C4×D3—22no—
458C4×D3—21no—
459C4×D3—122no—
460C4×D3—122no—
461Dic6D3×D411yescharacteristic
462Dic6D3×D411yescharacteristic
463Dic6C2×#6712yes—
464C3×C8—21no—
465C3×C8—21no—
466C3×C8—62no—
467C3×C8—61no—
468C3×C8—61no—
469C3×C8D3×D411yescharacteristic
470C3×C8D3×D411yescharacteristic
471C3×C8C2×#6711yescharacteristic
472C3×C8C2×#6711yescharacteristic
473C3⋊C8—21no—
474C3⋊C8—22no—
475C3⋊C8—21no—
476C3⋊C8—31no—
477C3⋊C8—31no—
478C3⋊C8—31no—
479C3⋊C8—31no—
480C3⋊C8—61no—
481C3⋊C8—61no—
482C2×C32—21no—
483C2×C32—82no—
484C2×C32D4211yescharacteristic
485C3⋊D3—82no—
486C3×D3—41no—
487C3×D3—42no—
488C3×D3—41no—
489#41—31no—
490#41—31no—
491#41—32no—
492#41—62no—
493#41—62no—
494#41—182no—
495#41—182no—
496C2×D4—62no—
497C2×D4—62no—
498C2×D4—92no—
499C2×D4—122no—
500C2×D4—182no—
501C2×D4—182no—
502C2×D4—362no—
503C2×D4—362no—
504C2×D4C2×D3212yes—
505Q16—31no—
506Q16—91no—
507SD16—32no—
508SD16—62no—
509SD16—62no—
510SD16—91no—
511SD16—91no—
512SD16—182no—
513SD16—182no—
514D8—21no—
515D8—21no—
516D8—31no—
517D8—62no—
518D8—62no—
519D8—91no—
520D8—182no—
521D8—182no—
522D8—182no—
523D8—182no—
524D8—181no—
525D8—181no—
526M16—31no—
527M16—32no—
528M16—31no—
529M16—61no—
530M16—61no—
531M16—182no—
532C2×C8—61no—
533C2×C8—61no—
534C2×C8—91no—
535C2×C8—182no—
536C2×C8C2×D3211yescharacteristic
537C42—91no—
538C22×C3—21no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—61no—
542C22×C3—62no—
543C22×C3—61no—
544C22×C3—82no—
545C22×C3—82no—
546C22×C3—82no—
547C22×C3—84no—
548C22×C3—482no—
549C22×C3#100411yescharacteristic
550C22×C3#100911yescharacteristic
551C2×D3—22no—
552C2×D3—21no—
553C2×D3—21no—
554C2×D3—122no—
555C2×D3—122no—
556C2×D3—162no—
557C2×D3—242no—
558C2×D3—242no—
559C2×D3—242no—
560C2×D3—244no—
561C2×D3—482no—
562C2×D3—482no—
563C3×C4—21no—
564C3×C4—21no—
565C3×C4—61no—
566C3×C4—62no—
567C3×C4—61no—
568C3×C4C2×D3×D411yescharacteristic
569C3×C4C2×D3×D411yescharacteristic
570C3×C4C2×D3×D411yescharacteristic
571C3×C4C22×#6711yescharacteristic
572Dic3—21no—
573Dic3—22no—
574Dic3—21no—
575Dic3—64no—
576Dic3—62no—
577Dic3—62no—
578C32#329211yescharacteristic, complemented, Sylow
579C23—22no—
580C23—122no—
581C23—182no—
582C23—362no—
583Q8—31no—
584Q8—31no—
585Q8—32no—
586D4—22no—
587D4—22no—
588D4—31no—
589D4—31no—
590D4—32no—
591D4—61no—
592D4—62no—
593D4—61no—
594D4—122no—
595D4—122no—
596D4—182no—
597D4—182no—
598D4—362no—
599D4—362no—
600D4—724no—
601C2×C4—62no—
602C2×C4—61no—
603C2×C4—61no—
604C2×C4—122no—
605C2×C4—181no—
606C2×C4—362no—
607C2×C4C22×D3211yescharacteristic
608C8—62no—
609C8—61no—
610C8—61no—
611C8—91no—
612C8—91no—
613C8D3×#6711yescharacteristic
614C8D3×#6711yescharacteristic
615C2×C3—22no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—82no—
620C2×C3—82no—
621C2×C3—121no—
622C2×C3—122no—
623C2×C3—121no—
624C2×C3—162no—
625C2×C3#560911yescharacteristic
626C2×C3D4×#6711yescharacteristic
627D3—41no—
628D3—42no—
629D3—41no—
630D3—242no—
631D3—242no—
632D3—482no—
633C22—42no—
634C22—61no—
635C22—62no—
636C22—61no—
637C22—82no—
638C22—362no—
639C22—482no—
640C22—722no—
641C22—1442no—
642C22#6431411yescharacteristic
643C4—61no—
644C4—62no—
645C4—61no—
646C4—182no—
647C4D32×D411yescharacteristic
648C4C2×D3×#6711yescharacteristic
649C3—21no—
650C3#8094111yescharacteristic, complemented
651C3#8401011yescharacteristic, complemented
652C2—21no—
653C2—82no—
654C2—121no—
655C2—122no—
656C2—121no—
657C2—722no—
658C2#1059528811yescharacteristic
subgroupG/H
centerC2#10595288
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC2×C32D42
hypercenterC2×D8D32
hypocenterC32#3292
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C3×#5757C2semidirect
2. #10595097C2semidirect
3. #10594680C2semidirect
4. #10592850C2semidirect
5. C3×#5160C2semidirect
6. #10591522C2semidirect
7. #10591510C2semidirect
8. #10591508C2semidirect
9. #10590927C2semidirect
10. #10590921C2semidirect
11. #10590919C2semidirect
14. C3×#1004C22semidirect
15. #64308C22semidirect
16. C2×C32×D8C22semidirect
17. #64149C22semidirect
18. C2×#3753C22semidirect
19. C2×#3745C22semidirect
20. C3×#932C22semidirect
21. C3×#932C22semidirect
26. C3×#901C22semidirect
27. C3×#901C22semidirect
32. #63825C22semidirect
33. #63825C22semidirect
35. #63815C22semidirect
39. C8×C3⋊Dic3C22semidirect
40. C3×#833C22semidirect
41. C3×#819C22semidirect
42. #63578C22semidirect
43. #63568C22semidirect
44. #63568C22semidirect
45. #63568C22semidirect
46. #63559C22semidirect
51. #5757D3semidirect
59. #5160D3semidirect
102. C3×Dic12D4semidirect
103. C3×D24D4semidirect
104. C3×#204D4semidirect
109. #3718D4semidirect
112. #3715D4semidirect
113. #3715D4semidirect
116. #3713D4semidirect
123. #1004C2×D3semidirect
131. C2×C3×D8C2×D3semidirect
132. C2×C3×D8C2×D3semidirect
146. #932C2×D3semidirect
147. #932C2×D3semidirect
172. #901C2×D3semidirect
173. #901C2×D3semidirect
179. #833C2×D3semidirect
187. #819C2×D3semidirect
329. Dic12#67semidirect
338. D24#67semidirect
341. #204#67semidirect
384. C2×D8D32semidirect
578. C32#3292semidirect
650. C3#80941semidirect
651. C3#84010semidirect

Maximal subgroups

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

subgroupindex
C3×#57572
#105950972
#105946802
#105928502
C3×#51602
#105915222
#105915102
#105915082
#105909272
#105909212
#105909192
#840103
#809413