Finite Group Databasebeta

← #11899643

Subgroups — #11899643

Order 1152.

773 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#912C211yesmaximal, characteristic, complemented
2D3×#904C211yesmaximal, characteristic, complemented
3#10592846C211yesmaximal, characteristic, complemented
4C3×#5147C211yesmaximal, characteristic, complemented
5#10591034C212yesmaximal, complemented
6#10591032C212yesmaximal, complemented
7#10591028C212yesmaximal, complemented
8#10591024C212yesmaximal, complemented
9#10590642C211yesmaximal, characteristic, complemented
10#10590636C211yesmaximal, characteristic, complemented
11D3×#812C211yesmaximal, characteristic, complemented
12#83894—31nomaximal
13#82035—31nomaximal
14C2×C3×#237—21no—
15D3×#235—21no—
16C2×C32×D8C2211yescharacteristic, complemented
17#64113C2211yescharacteristic
18C2×C3×#214—21no—
19C3×#912—21no—
20C3×#912—21no—
21C3×#912C2212yes—
22C3×#912C2212yescomplemented
23C2×C3×Dic12C2211yescharacteristic, complemented
24C3×#904C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26#63829—21no—
27#63808C2211yescharacteristic, complemented
28#63807C2211yescharacteristic, complemented
29#63806—21no—
30D3×Dic12C2211yescharacteristic, complemented
31D3×D24C2211yescharacteristic, complemented
32D3×#204—21no—
33#63654C2212yescomplemented
34#63653C2212yescomplemented
35#63639C2211yescharacteristic, complemented
36C3×#827C2212yescomplemented
37C3×#826C2212yescomplemented
38C3×#812C2211yescharacteristic, complemented
39#63551C2212yescomplemented
40#63550C2212yescomplemented
41#63549C2212yescomplemented
42#63547C2212yescomplemented
43#63543C2212yescomplemented
44D3×C3⋊C16C2212yescomplemented
45C2×C3×#135—31no—
46D3×#135—31no—
47C2×#912D311yescharacteristic, complemented
48C2×#904—31no—
49C3×#509—31no—
50#5195—31no—
51#5195—32no—
52#5194—32no—
53#5194—32no—
54#5193—32no—
55#5179—31no—
56#5179—31no—
57#5147—31no—
58#5147—31no—
59#5147—61no—
60#5147D311yescharacteristic, complemented
61C2×#812—31no—
62#4916—32no—
63#4915—32no—
64#4912—32no—
65#4911—32no—
66#4909—31no—
67D3×M32—31no—
68C2×C32×D4—21no—
69#3828—21no—
70C2×C3×#67—41no—
71C22×C3×Dic3—41no—
72C3×#237—22no—
73C3×#237—22no—
74C3×#237—41no—
75C3×#237—41no—
76C3×#235—21no—
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×Dic6—21no—
79D3×#67—41no—
80#3804—41no—
81D3×D12—21no—
82C4×D32—41no—
83#3799—21no—
84#3798—41no—
85#3795—21no—
86D3×Dic6—21no—
87C32×D8—21no—
88C32×D8C2312yes—
89C2×C32×C8C2311yescharacteristic
90#3746C2311yescharacteristic
91#3745C2311yescharacteristic
92#3744—21no—
93C3×#214—22no—
94C3×#214—22no—
95C2×C3×C3⋊C8D411yescharacteristic
96C3×Dic12—21no—
97C3×Dic12C2311yescharacteristic
98C3×Dic12C2312yes—
99C3×D24C2311yescharacteristic
100C3×#204—21no—
101C3×D3×C8D411yescharacteristic
102C3×D3×C8D411yescharacteristic
103C3×D3×C8C2311yescharacteristic
104C3×D3×C8C2311yescharacteristic
105#3719—21no—
106#3717—21no—
107#3716—21no—
108#3714—21no—
109C3⋊(C3⋊C16)C2312yes—
110C3×C3⋊C16C2312yes—
111#3414—91noSylow
112C2×C3×#41—61no—
113D3×#41—61no—
114C2×#237—21no—
115C2×#235—61no—
116C3×#135—32no—
117C3×#135—32no—
118C3×#135—31no—
119C3×#135—61no—
120C3×#135—61no—
121C2×C3×Q16—31no—
122C2×C3×SD16—61no—
123C2×C3×D8—21no—
124C2×C3×D8C2×D311yescharacteristic, complemented
125C2×C3×D8C2×D311yescharacteristic, complemented
126C22×C3×C8—31no—
127#950—61no—
128C2×#214—21no—
129#919—31no—
130D3×Q16—31no—
131#916—61no—
132D3×SD16—61no—
133#912—21no—
134#912—21no—
135#912—31no—
136#912C2×D312yes—
137#912C2×D312yescomplemented
138D3×D8—31no—
139C2×Dic12—31no—
140C2×Dic12C2×D311yescharacteristic, complemented
141#904—31no—
142#904—31no—
143#904—31no—
144#904—31no—
145#904—61no—
146#904—61no—
147#904—61no—
148#904C2×D311yescharacteristic
149C2×D24—31no—
150C2×#204—61no—
151C2×D3×C8C2×D311yescharacteristic
152C3×SD32—32no—
153C3×D16—32no—
154C3×M32—31no—
155#829—32no—
156#829—32no—
157#829—32no—
158#828—32no—
159#828—32no—
160#827—32no—
161#827—32no—
162#827—32no—
163#827—62no—
164#827C2×D312yescomplemented
165#826—32no—
166#826—32no—
167#826—62no—
168#826C2×D312yescomplemented
169#812—31no—
170#812—31no—
171#812—32no—
172#812—61no—
173#812C2×D311yescharacteristic, complemented
174C2×C3⋊C16—32no—
175Dic24—32no—
176#800—32no—
177#798—32no—
178D3×C16—32no—
179C23×C32—41no—
180C22×C3×D3D811yescharacteristic
181C2×D32—41no—
182C32×D4—22no—
183C32×D4—41no—
184C2×C32×C4C2×D411yescharacteristic
185#638—41no—
186C4⋊(C3⋊D3)—21no—
187C4×C3⋊D3—41no—
188#634—21no—
189C3×#67—41no—
190C3×#67—42no—
191C3×#67—42no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3—42no—
195C2×C3×Dic3D811yescharacteristic
196C3×D12—21no—
197C3×C4×D3—41no—
198C3×C4×D3D811yescharacteristic
199C3×C4×D3D811yescharacteristic
200C3×C4×D3C2×D411yescharacteristic
201C3×C4×D3C2×D411yescharacteristic
202C3×Dic6—21no—
203C3×Dic6—22no—
204C3×Dic6—41no—
205#627—41no—
206#626—41no—
207#626—41no—
208#625—41no—
209#624—41no—
210D3×Dic3—41no—
211D3×Dic3—41no—
212C32×C8C2×D411yescharacteristic
213C32×C8C2411yescharacteristic
214C3×C3⋊C8C2×D411yescharacteristic
215C3×C3⋊C8C2×D411yescharacteristic
216C2×#135—31no—
217C2×#135—91no—
218#510—91no—
219#510—92no—
220#510—91no—
221#509—31no—
222#509—92no—
223#509—91no—
224#508—92no—
225#508—92no—
226C2×M32—91no—
227C3×#41—62no—
228C3×#41—62no—
229C3×#41—61no—
230C3×#41—121no—
231C3×#41—121no—
232C2×C3×Q8—61no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—41no—
236C2×C3×D4—121no—
237C22×C3×C4—31no—
238C22×C3×C4—121no—
239C2×#67—41no—
240C2×#67—121no—
241C22×Dic3—41no—
242#239—61no—
243D3×Q8—61no—
244#237—22no—
245#237—22no—
246#237—41no—
247#237—41no—
248#237—61no—
249#237—121no—
250D3×D4—61no—
251D3×D4—121no—
252#235—21no—
253#235—61no—
254#235—61no—
255#235—61no—
256#235—61no—
257#235—121no—
258#235—121no—
259#235—121no—
260#235—121no—
261C2×D12—61no—
262C2×C4×D3—121no—
263C2×C4×D3—121no—
264C2×C4×D3#6711yescharacteristic
265C2×Dic6—21no—
266C2×Dic6—61no—
267C3×Q16—32no—
268C3×Q16—31no—
269C3×Q16—61no—
270C3×SD16—62no—
271C3×SD16—62no—
272C3×SD16—61no—
273C3×D8—21no—
274C3×D8—21no—
275C3×D8—22no—
276C3×D8—31no—
277C3×D8—41no—
278C3×D8C22×D312yes—
279C3×D8C22×D312yes—
280C2×C3×C8—21no—
281C2×C3×C8—31no—
282C2×C3×C8—31no—
283C2×C3×C8—31no—
284C2×C3×C8—31no—
285C2×C3×C8—31no—
286C2×C3×C8C22×D311yescharacteristic
287C2×C3×C8C22×D311yescharacteristic
288#216—61no—
289#215—61no—
290#214—22no—
291#214—22no—
292#214—61no—
293#213—61no—
294C2×C3⋊C8#6711yescharacteristic
295Dic12—21no—
296Dic12—31no—
297Dic12—31no—
298Dic12—61no—
299Dic12—61no—
300Dic12C22×D312yes—
301Dic12C22×D311yescharacteristic
302D24—31no—
303D24—31no—
304D24—61no—
305D24—61no—
306D24C22×D311yescharacteristic
307#204—21no—
308#204—61no—
309#204—61no—
310#204—61no—
311#204—61no—
312#204—121no—
313D3×C8#6711yescharacteristic
314D3×C8#6711yescharacteristic
315D3×C8C22×D311yescharacteristic
316D3×C8C22×D311yescharacteristic
317C3×C16—32no—
318C3⋊C16—32no—
319C3⋊C16—32no—
320C3⋊C16—62no—
321C3⋊C16C22×D312yes—
322C22×C32—42no—
323C22×C32—82no—
324C22×C32C2×D811yescharacteristic
325C2×C3⋊D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C2×C3×D3C2×D811yescharacteristic
329C2×C3×D3C2×D811yescharacteristic
330D32—82no—
331C32×C4C2×D811yescharacteristic
332C32×C4C22×D411yescharacteristic
333C3⋊Dic3—41no—
334C3×Dic3—41no—
335C3×Dic3—42no—
336C3×Dic3C2×D811yescharacteristic
337C3×Dic3C2×D811yescharacteristic
338C2×#41—61no—
339C2×#41—181no—
340#135—32no—
341#135—32no—
342#135—31no—
343#135—61no—
344#135—61no—
345#135—91no—
346#135—91no—
347#135—91no—
348#135—181no—
349#135—181no—
350C2×Q16—31no—
351C2×Q16—91no—
352C2×SD16—61no—
353C2×SD16—181no—
354C2×D8—91no—
355C2×D8D3211yescharacteristic, complemented
356C22×C8—31no—
357Q32—92no—
358Q32—92no—
359SD32—32no—
360SD32—92no—
361SD32—92no—
362SD32—92no—
363D16—32no—
364D16—92no—
365M32—31no—
366M32—92no—
367M32—91no—
368C2×C16—92no—
369C23×C3—31no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—81no—
373C22×D3—121no—
374C22×D3—121no—
375C22×D3#21311yescharacteristic
376C3×Q8—62no—
377C3×Q8—61no—
378C3×Q8—121no—
379C3×D4—22no—
380C3×D4—22no—
381C3×D4—42no—
382C3×D4—41no—
383C3×D4—41no—
384C3×D4—61no—
385C3×D4—81no—
386C3×D4—122no—
387C3×D4—122no—
388C3×D4—121no—
389C2×C3×C4—21no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—31no—
394C2×C3×C4—31no—
395C2×C3×C4—122no—
396C2×C3×C4—122no—
397C2×C3×C4—121no—
398C2×C3×C4—121no—
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4C2×#6711yescharacteristic
401#67—41no—
402#67—42no—
403#67—42no—
404#67—121no—
405#67—121no—
406#67—121no—
407#67—121no—
408#67—121no—
409#67—121no—
410#67—241no—
411C2×Dic3—41no—
412C2×Dic3—42no—
413C2×Dic3—42no—
414C2×Dic3—121no—
415C2×Dic3—121no—
416C2×Dic3#21311yescharacteristic
417D12—21no—
418D12—61no—
419D12—61no—
420D12—121no—
421D12—121no—
422D12—121no—
423C4×D3—41no—
424C4×D3—121no—
425C4×D3—121no—
426C4×D3—121no—
427C4×D3—121no—
428C4×D3—121no—
429C4×D3—121no—
430C4×D3—241no—
431C4×D3#21311yescharacteristic
432C4×D3#21311yescharacteristic
433C4×D3C2×#6711yescharacteristic
434C4×D3C2×#6711yescharacteristic
435Dic6—21no—
436Dic6—22no—
437Dic6—41no—
438Dic6—61no—
439Dic6—61no—
440Dic6—121no—
441Dic6—121no—
442Dic6—121no—
443C3×C8—21no—
444C3×C8—21no—
445C3×C8—31no—
446C3×C8—31no—
447C3×C8D3×D411yescharacteristic
448C3×C8C2×#6711yescharacteristic
449C3×C8C23×D311yescharacteristic
450C3×C8C23×D311yescharacteristic
451C3⋊C8C2×#6711yescharacteristic
452C3⋊C8C2×#6711yescharacteristic
453C2×C32—21no—
454C2×C32—82no—
455C2×C32C22×D811yescharacteristic
456C3⋊D3—81no—
457C3×D3—21no—
458C3×D3—21no—
459C3×D3—81no—
460#41—62no—
461#41—62no—
462#41—61no—
463#41—121no—
464#41—121no—
465#41—181no—
466#41—181no—
467#41—181no—
468#41—361no—
469#41—361no—
470C2×Q8—61no—
471C2×Q8—181no—
472C2×D4—21no—
473C2×D4—121no—
474C2×D4—181no—
475C2×D4—361no—
476C22×C4—31no—
477C22×C4—121no—
478C22×C4—361no—
479Q16—31no—
480Q16—32no—
481Q16—61no—
482Q16—91no—
483Q16—181no—
484SD16—62no—
485SD16—62no—
486SD16—61no—
487SD16—181no—
488SD16—181no—
489SD16—181no—
490D8—21no—
491D8—31no—
492D8—91no—
493D8—181no—
494D8C2×D3212yes—
495C2×C8—31no—
496C2×C8—31no—
497C2×C8—31no—
498C2×C8—31no—
499C2×C8—31no—
500C2×C8C2×D3211yescharacteristic
501C16—32no—
502C16—92no—
503C22×C3—21no—
504C22×C3—31no—
505C22×C3—31no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—82no—
509C22×C3—82no—
510C22×C3—82no—
511C22×C3—121no—
512C22×C3—121no—
513C22×C3—162no—
514C22×C3D3×D811yescharacteristic
515C22×C3C2×#21311yescharacteristic
516C2×D3—41no—
517C2×D3—41no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—241no—
521C2×D3—242no—
522C2×D3—242no—
523C2×D3C2×#21311yescharacteristic
524C2×D3C2×#21311yescharacteristic
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—31no—
528C3×C4—31no—
529C3×C4—122no—
530C3×C4—121no—
531C3×C4D3×D811yescharacteristic
532C3×C4C2×#21311yescharacteristic
533C3×C4C2×D3×D411yescharacteristic
534C3×C4C22×#6711yescharacteristic
535Dic3—41no—
536Dic3—42no—
537Dic3—121no—
538Dic3—121no—
539Dic3—241no—
540Dic3C2×#21311yescharacteristic
541Dic3C2×#21311yescharacteristic
542C32#341411yescharacteristic, complemented, Sylow
543C23—31no—
544C23—41no—
545C23—361no—
546Q8—62no—
547Q8—61no—
548Q8—121no—
549Q8—181no—
550Q8—361no—
551D4—22no—
552D4—41no—
553D4—61no—
554D4—122no—
555D4—122no—
556D4—121no—
557D4—181no—
558D4—361no—
559D4—361no—
560D4—361no—
561D4—361no—
562C2×C4—31no—
563C2×C4—31no—
564C2×C4—31no—
565C2×C4—31no—
566C2×C4—31no—
567C2×C4—122no—
568C2×C4—122no—
569C2×C4—121no—
570C2×C4—121no—
571C2×C4—361no—
572C2×C4—361no—
573C2×C4—361no—
574C2×C4—361no—
575C2×C4D3×#6711yescharacteristic
576C8—31no—
577C8—31no—
578C8D3×#6711yescharacteristic
579C8C22×D3211yescharacteristic
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—41no—
584C2×C3—61no—
585C2×C3—61no—
586C2×C3—82no—
587C2×C3—82no—
588C2×C3—162no—
589C2×C3—241no—
590C2×C3C2×D3×D811yescharacteristic
591C2×C3C22×#21311yescharacteristic
592D3—21no—
593D3—21no—
594D3—81no—
595D3—241no—
596D3—241no—
597D3—481no—
598C22—31no—
599C22—31no—
600C22—42no—
601C22—82no—
602C22—121no—
603C22—121no—
604C22—361no—
605C22—722no—
606C22D3×#21311yescharacteristic
607C4—31no—
608C4—31no—
609C4—122no—
610C4—121no—
611C4—361no—
612C4D3×#21311yescharacteristic
613C4C2×D3×#6711yescharacteristic
614C3—21no—
615C3#8203511yescharacteristic, complemented
616C3#8389411yescharacteristic, complemented
617C2—21no—
618C2—61no—
619C2—61no—
620C2—82no—
621C2—241no—
622C2—721no—
623C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC2C2×D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×D8C22
socleC2×C32C22×D8
hypercenterC2×D8D32
hypocenterC32#3414
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#912C2semidirect
2. D3×#904C2semidirect
3. #10592846C2semidirect
4. C3×#5147C2semidirect
5. #10591034C2semidirect
6. #10591032C2semidirect
7. #10591028C2semidirect
8. #10591024C2semidirect
9. #10590642C2semidirect
10. #10590636C2semidirect
11. D3×#812C2semidirect
16. C2×C32×D8C22semidirect
22. C3×#912C22semidirect
23. C2×C3×Dic12C22semidirect
27. #63808C22semidirect
28. #63807C22semidirect
30. D3×Dic12C22semidirect
31. D3×D24C22semidirect
33. #63654C22semidirect
34. #63653C22semidirect
35. #63639C22semidirect
36. C3×#827C22semidirect
37. C3×#826C22semidirect
38. C3×#812C22semidirect
39. #63551C22semidirect
40. #63550C22semidirect
41. #63549C22semidirect
42. #63547C22semidirect
43. #63543C22semidirect
44. D3×C3⋊C16C22semidirect
47. C2×#912D3semidirect
60. #5147D3semidirect
124. C2×C3×D8C2×D3semidirect
125. C2×C3×D8C2×D3semidirect
137. #912C2×D3semidirect
140. C2×Dic12C2×D3semidirect
164. #827C2×D3semidirect
168. #826C2×D3semidirect
173. #812C2×D3semidirect
355. C2×D8D32semidirect
542. C32#3414semidirect
615. C3#82035semidirect
616. C3#83894semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9122
D3×#9042
#105928462
C3×#51472
#105910342
#105910322
#105910282
#105910242
#105906422
#105906362
D3×#8122
#838943
#820353