Finite Group Databasebeta

← #11899647

Subgroups — #11899647

Order 1152.

769 conjugacy classes of subgroups.

The subgroup lattice has 623 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63807C211yesmaximal, characteristic, complemented
2D3×#904C211yesmaximal, characteristic, complemented
3#10592608C211yesmaximal, characteristic, complemented
4C3×#4908C211yesmaximal, characteristic, complemented
5C3×D3×M32C211yesmaximal, characteristic, complemented
6#10590638C211yesmaximal, characteristic, complemented
7#10590633C211yesmaximal, characteristic, complemented
8#10590242C212yesmaximal, complemented
9#10590241C212yesmaximal, complemented
10#10590239C212yesmaximal, complemented
11#10590232C212yesmaximal, complemented
12#82035—31nomaximal
13#82009—31nomaximal
14D3×#235—21no—
15C2×#3795—21no—
16C2×#3746C2211yescharacteristic, complemented
17#64113C2211yescharacteristic
18C3×#904C2211yescharacteristic
19C2×C3×D24C2211yescharacteristic, complemented
20C2×C3×D3×C8C2211yescharacteristic
21#63829—21no—
22C2×#3716—21no—
23#63808C2211yescharacteristic, complemented
24#63807—21no—
25#63807—21no—
26#63807C2212yes—
27#63807C2211yescharacteristic, complemented
28#63807C2212yescomplemented
29#63806—21no—
30D3×Dic12C2211yescharacteristic, complemented
31D3×D24C2211yescharacteristic, complemented
32D3×#204—21no—
33C32×M32C2211yescharacteristic, complemented
34#63628C2212yescomplemented
35#63627C2212yescomplemented
36C3×#812C2211yescharacteristic, complemented
37C3×#800C2212yescomplemented
38C3×D48C2212yescomplemented
39C3×#798C2212yescomplemented
40C3×D3×C16C2212yescomplemented
41#63551C2212yescomplemented
42#63548C2212yescomplemented
43#63548C2212yescomplemented
44#63546C2212yescomplemented
45D3×#135—31no—
46C2×#912—31no—
47C2×#904—31no—
48C2×#904—31no—
49C3×#509—31no—
50C2×C3×M32—31no—
51#5195—31no—
52#5147—31no—
53#4916—32no—
54#4915—32no—
55#4912—32no—
56#4911—32no—
57#4909—31no—
58#4909—31no—
59#4909—31no—
60#4909—32no—
61#4909—61no—
62#4908—31no—
63#4908—32no—
64#4908D311yescharacteristic, complemented
65D3×M32D311yescharacteristic, complemented
66#4904—32no—
67#4904—32no—
68#3828—21no—
69C2×#634—21no—
70C3×#235—21no—
71C2×C3×D12—21no—
72C2×C3×C4×D3D411yescharacteristic
73D3×#67—41no—
74C2×#625—41no—
75#3804—41no—
76C2×D3×Dic3—41no—
77D3×D12—21no—
78C4×D32—41no—
79#3799—21no—
80#3798—41no—
81#3795—22no—
82#3795—22no—
83#3795—21no—
84#3795—41no—
85#3795—41no—
86D3×Dic6—21no—
87C2×C32×C8C2311yescharacteristic
88#3746—21no—
89#3746C2311yescharacteristic
90#3746C2312yes—
91#3745C2311yescharacteristic
92#3744—21no—
93C2×C3×C3⋊C8D411yescharacteristic
94C3×Dic12C2311yescharacteristic
95C3×D24—21no—
96C3×D24C2312yes—
97C3×D24C2311yescharacteristic
98C3×#204—21no—
99C3×D3×C8D411yescharacteristic
100C3×D3×C8D411yescharacteristic
101C3×D3×C8C2311yescharacteristic
102C3×D3×C8C2311yescharacteristic
103#3719—21no—
104#3717—21no—
105#3716—21no—
106#3716—22no—
107#3716—22no—
108#3714—21no—
109C32×C16C2312yes—
110C3×C3⋊C16C2312yes—
111#3414—91noSylow
112D3×#41—61no—
113C2×#237—61no—
114C2×#235—61no—
115C2×#235—61no—
116C3×#135—31no—
117C2×C3×D8—31no—
118C22×C3×C8—31no—
119#950—61no—
120C2×#214—61no—
121#919—31no—
122D3×Q16—31no—
123#916—61no—
124D3×SD16—61no—
125#912—32no—
126#912—31no—
127#912—32no—
128#912—61no—
129#912—61no—
130D3×D8—31no—
131C2×Dic12—31no—
132C2×Dic12—31no—
133C2×Dic12—31no—
134C2×Dic12—61no—
135#904—31no—
136#904—31no—
137#904—31no—
138#904—32no—
139#904—31no—
140#904—32no—
141#904—61no—
142#904—61no—
143#904—61no—
144#904—61no—
145#904—61no—
146#904C2×D311yescharacteristic
147C2×D24—31no—
148C2×D24C2×D311yescharacteristic, complemented
149C2×#204—61no—
150C2×#204—61no—
151C2×D3×C8C2×D311yescharacteristic
152C3×SD32—32no—
153C3×D16—32no—
154C3×M32—21no—
155C3×M32—31no—
156C3×M32—32no—
157C3×M32C2×D311yescharacteristic, complemented
158C3×M32C2×D311yescharacteristic, complemented
159C2×C3×C16—32no—
160#829—32no—
161#827—32no—
162#827—32no—
163#826—32no—
164#812C2×D311yescharacteristic, complemented
165Dic24—32no—
166Dic24—32no—
167Dic24—32no—
168Dic24—62no—
169#800—32no—
170#800—32no—
171#800—32no—
172#800—32no—
173#800—62no—
174#800C2×D312yescomplemented
175D48—32no—
176D48C2×D312yescomplemented
177#798C2×D312yescomplemented
178D3×C16C2×D312yescomplemented
179C22×C3×D3—41no—
180C22×C3×D3D811yescharacteristic
181C2×D32—41no—
182C2×C32×C4C2×D411yescharacteristic
183#638—41no—
184C2×C3⋊Dic3—41no—
185C4⋊(C3⋊D3)—21no—
186C4×C3⋊D3—41no—
187#634—22no—
188#634—21no—
189#634—41no—
190C3×#67—41no—
191C2×C3×Dic3D811yescharacteristic
192C3×D12—21no—
193C3×D12—22no—
194C3×D12—41no—
195C3×C4×D3—41no—
196C3×C4×D3D811yescharacteristic
197C3×C4×D3D811yescharacteristic
198C3×C4×D3C2×D411yescharacteristic
199C3×C4×D3C2×D411yescharacteristic
200C3×Dic6—21no—
201#627—41no—
202#626—41no—
203#626—41no—
204#625—42no—
205#625—42no—
206#625—41no—
207#624—41no—
208D3×Dic3—41no—
209D3×Dic3—42no—
210D3×Dic3—42no—
211D3×Dic3—41no—
212C32×C8C2×D411yescharacteristic
213C32×C8C2411yescharacteristic
214C3×C3⋊C8C2×D411yescharacteristic
215C3×C3⋊C8C2×D411yescharacteristic
216C2×#135—91no—
217C2×#135—91no—
218#510—92no—
219#510—91no—
220#510—91no—
221#509—31no—
222#509—92no—
223#509—91no—
224#508—92no—
225#508—92no—
226C2×M32—31no—
227C3×#41—61no—
228C2×C3×D4—61no—
229C22×C3×C4—31no—
230C2×#67—121no—
231C2×#67—121no—
232C2×#67—121no—
233C22×Dic3—121no—
234#239—61no—
235D3×Q8—61no—
236#237—62no—
237#237—62no—
238#237—61no—
239#237—121no—
240#237—121no—
241#237—121no—
242D3×D4—61no—
243D3×D4—121no—
244#235—21no—
245#235—61no—
246#235—61no—
247#235—62no—
248#235—62no—
249#235—61no—
250#235—61no—
251#235—121no—
252#235—121no—
253#235—121no—
254#235—121no—
255#235—121no—
256#235—121no—
257C2×D12—21no—
258C2×D12—61no—
259C2×C4×D3—121no—
260C2×C4×D3—121no—
261C2×C4×D3—121no—
262C2×C4×D3D1211yescharacteristic
263C2×Dic6—61no—
264C2×Dic6—61no—
265C2×Dic6—61no—
266C2×Dic6—121no—
267C3×Q16—31no—
268C3×SD16—61no—
269C3×D8—32no—
270C3×D8—31no—
271C3×D8—61no—
272C2×C3×C8—21no—
273C2×C3×C8—31no—
274C2×C3×C8—31no—
275C2×C3×C8—31no—
276C2×C3×C8—31no—
277C2×C3×C8—31no—
278C2×C3×C8C22×D311yescharacteristic
279C2×C3×C8C22×D311yescharacteristic
280#216—61no—
281#215—61no—
282#214—62no—
283#214—62no—
284#214—61no—
285#213—61no—
286C2×C3⋊C8D1211yescharacteristic
287Dic12—31no—
288Dic12—32no—
289Dic12—32no—
290Dic12—31no—
291Dic12—62no—
292Dic12—61no—
293Dic12—61no—
294Dic12—61no—
295Dic12—61no—
296Dic12—121no—
297Dic12C22×D311yescharacteristic
298D24—21no—
299D24—31no—
300D24—31no—
301D24—61no—
302D24—61no—
303D24C22×D312yes—
304D24C22×D311yescharacteristic
305#204—21no—
306#204—61no—
307#204—61no—
308#204—62no—
309#204—62no—
310#204—61no—
311#204—61no—
312#204—121no—
313D3×C8D1211yescharacteristic
314D3×C8D1211yescharacteristic
315D3×C8C22×D311yescharacteristic
316D3×C8C22×D311yescharacteristic
317C3×C16—22no—
318C3×C16—32no—
319C3×C16C22×D312yes—
320C3×C16C22×D312yes—
321C3⋊C16C22×D312yes—
322C22×C32C2×D811yescharacteristic
323C2×C3⋊D3—41no—
324C2×C3×D3—41no—
325C2×C3×D3—42no—
326C2×C3×D3—41no—
327C2×C3×D3—82no—
328C2×C3×D3C2×D811yescharacteristic
329C2×C3×D3C2×D811yescharacteristic
330D32—82no—
331C32×C4C2×D811yescharacteristic
332C32×C4C22×D411yescharacteristic
333C3⋊Dic3—42no—
334C3⋊Dic3—41no—
335C3×Dic3—41no—
336C3×Dic3C2×D811yescharacteristic
337C3×Dic3C2×D811yescharacteristic
338C2×#41—181no—
339C2×#41—181no—
340#135—31no—
341#135—91no—
342#135—92no—
343#135—92no—
344#135—91no—
345#135—91no—
346#135—181no—
347#135—181no—
348#135—181no—
349#135—181no—
350C2×Q16—91no—
351C2×Q16—91no—
352C2×SD16—181no—
353C2×SD16—181no—
354C2×D8—31no—
355C2×D8—91no—
356C22×C8—31no—
357Q32—92no—
358Q32—92no—
359SD32—32no—
360SD32—92no—
361SD32—92no—
362SD32—92no—
363D16—32no—
364D16—92no—
365M32—31no—
366M32—32no—
367M32D3211yescharacteristic, complemented
368C2×C16—32no—
369C23×C3—31no—
370C23×C3—121no—
371C22×D3—41no—
372C22×D3—121no—
373C22×D3—121no—
374C22×D3D2411yescharacteristic
375C3×Q8—61no—
376C3×D4—61no—
377C3×D4—62no—
378C3×D4—121no—
379C3×D4—121no—
380C2×C3×C4—21no—
381C2×C3×C4—31no—
382C2×C3×C4—31no—
383C2×C3×C4—31no—
384C2×C3×C4—31no—
385C2×C3×C4—31no—
386C2×C3×C4—121no—
387C2×C3×C4C2×D1211yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389#67—41no—
390#67—121no—
391#67—121no—
392#67—122no—
393#67—122no—
394#67—121no—
395#67—121no—
396#67—121no—
397#67—122no—
398#67—122no—
399#67—121no—
400#67—241no—
401C2×Dic3—121no—
402C2×Dic3—121no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C2×Dic3—241no—
408C2×Dic3D2411yescharacteristic
409D12—21no—
410D12—22no—
411D12—41no—
412D12—61no—
413D12—61no—
414D12—121no—
415D12—121no—
416D12—121no—
417C4×D3—41no—
418C4×D3—121no—
419C4×D3—122no—
420C4×D3—121no—
421C4×D3—122no—
422C4×D3—121no—
423C4×D3—121no—
424C4×D3—121no—
425C4×D3—121no—
426C4×D3—241no—
427C4×D3D2411yescharacteristic
428C4×D3D2411yescharacteristic
429C4×D3C2×D1211yescharacteristic
430C4×D3C2×D1211yescharacteristic
431Dic6—21no—
432Dic6—61no—
433Dic6—62no—
434Dic6—62no—
435Dic6—61no—
436Dic6—121no—
437Dic6—122no—
438Dic6—121no—
439Dic6—121no—
440Dic6—121no—
441Dic6—121no—
442Dic6—241no—
443C3×C8—21no—
444C3×C8—21no—
445C3×C8—31no—
446C3×C8—31no—
447C3×C8C2×D1211yescharacteristic
448C3×C8D3×D411yescharacteristic
449C3×C8C23×D311yescharacteristic
450C3×C8C23×D311yescharacteristic
451C3⋊C8C2×D1211yescharacteristic
452C3⋊C8C2×D1211yescharacteristic
453C2×C32—21no—
454C2×C32C22×D811yescharacteristic
455C3⋊D3—81no—
456C3×D3—21no—
457C3×D3—21no—
458C3×D3—81no—
459C3×D3—82no—
460#41—61no—
461#41—182no—
462#41—182no—
463#41—181no—
464#41—181no—
465#41—181no—
466#41—361no—
467#41—361no—
468#41—361no—
469#41—361no—
470C2×Q8—181no—
471C2×Q8—181no—
472C2×D4—61no—
473C2×D4—181no—
474C2×D4—361no—
475C2×D4—361no—
476C22×C4—31no—
477C22×C4—361no—
478C22×C4—361no—
479Q16—31no—
480Q16—91no—
481Q16—92no—
482Q16—181no—
483Q16—181no—
484SD16—61no—
485SD16—182no—
486SD16—182no—
487SD16—181no—
488SD16—181no—
489SD16—181no—
490D8—31no—
491D8—32no—
492D8—61no—
493D8—91no—
494D8—181no—
495C2×C8—31no—
496C2×C8—31no—
497C2×C8—31no—
498C2×C8—31no—
499C2×C8—31no—
500C2×C8C2×D3211yescharacteristic
501C16—32no—
502C16C2×D3212yes—
503C22×C3—21no—
504C22×C3—31no—
505C22×C3—31no—
506C22×C3—121no—
507C22×C3—122no—
508C22×C3—121no—
509C22×C3—242no—
510C22×C3C2×D2411yescharacteristic
511C22×C3D3×D811yescharacteristic
512C2×D3—41no—
513C2×D3—41no—
514C2×D3—42no—
515C2×D3—82no—
516C2×D3—121no—
517C2×D3—121no—
518C2×D3—241no—
519C2×D3—242no—
520C2×D3—242no—
521C2×D3C2×D2411yescharacteristic
522C2×D3C2×D2411yescharacteristic
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—31no—
526C3×C4—31no—
527C3×C4—121no—
528C3×C4C2×D2411yescharacteristic
529C3×C4D3×D811yescharacteristic
530C3×C4C22×D1211yescharacteristic
531C3×C4C2×D3×D411yescharacteristic
532Dic3—41no—
533Dic3—121no—
534Dic3—122no—
535Dic3—121no—
536Dic3—122no—
537Dic3—242no—
538Dic3—241no—
539Dic3C2×D2411yescharacteristic
540Dic3C2×D2411yescharacteristic
541C32#341411yescharacteristic, complemented, Sylow
542C23—31no—
543C23—121no—
544C23—361no—
545Q8—61no—
546Q8—182no—
547Q8—181no—
548Q8—361no—
549Q8—361no—
550D4—62no—
551D4—61no—
552D4—121no—
553D4—121no—
554D4—181no—
555D4—361no—
556D4—361no—
557D4—362no—
558D4—361no—
559D4—362no—
560D4—361no—
561C2×C4—31no—
562C2×C4—31no—
563C2×C4—31no—
564C2×C4—31no—
565C2×C4—31no—
566C2×C4—121no—
567C2×C4—361no—
568C2×C4—361no—
569C2×C4—362no—
570C2×C4—362no—
571C2×C4—361no—
572C2×C4—361no—
573C2×C4—361no—
574C2×C4D3×D1211yescharacteristic
575C8—31no—
576C8—31no—
577C8D3×D1211yescharacteristic
578C8C22×D3211yescharacteristic
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—41no—
583C2×C3—61no—
584C2×C3—61no—
585C2×C3—241no—
586C2×C3—242no—
587C2×C3C22×D2411yescharacteristic
588C2×C3C2×D3×D811yescharacteristic
589D3—21no—
590D3—21no—
591D3—82no—
592D3—81no—
593D3—241no—
594D3—241no—
595D3—481no—
596C22—31no—
597C22—31no—
598C22—121no—
599C22—121no—
600C22—122no—
601C22—242no—
602C22—361no—
603C22—722no—
604C22D3×D2411yescharacteristic
605C4—31no—
606C4—31no—
607C4—121no—
608C4—362no—
609C4—361no—
610C4D3×D2411yescharacteristic
611C4C2×D3×D1211yescharacteristic
612C3—21no—
613C3#8200911yescharacteristic, complemented
614C3#8203511yescharacteristic, complemented
615C2—21no—
616C2—61no—
617C2—61no—
618C2—242no—
619C2—241no—
620C2—721no—
621C2C2×D3×D2411yescharacteristic
subgroupG/H
centerC2C2×D3×D24
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×M32C22
socleC2×C32C22×D8
hypercenterM32D32
hypocenterC32#3414
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
1. C2×#63807C2semidirect
2. D3×#904C2semidirect
3. #10592608C2semidirect
4. C3×#4908C2semidirect
5. C3×D3×M32C2semidirect
6. #10590638C2semidirect
7. #10590633C2semidirect
8. #10590242C2semidirect
9. #10590241C2semidirect
10. #10590239C2semidirect
11. #10590232C2semidirect
16. C2×#3746C22semidirect
19. C2×C3×D24C22semidirect
23. #63808C22semidirect
27. #63807C22semidirect
28. #63807C22semidirect
30. D3×Dic12C22semidirect
31. D3×D24C22semidirect
33. C32×M32C22semidirect
34. #63628C22semidirect
35. #63627C22semidirect
36. C3×#812C22semidirect
37. C3×#800C22semidirect
38. C3×D48C22semidirect
39. C3×#798C22semidirect
40. C3×D3×C16C22semidirect
41. #63551C22semidirect
42. #63548C22semidirect
43. #63548C22semidirect
44. #63546C22semidirect
64. #4908D3semidirect
65. D3×M32D3semidirect
148. C2×D24C2×D3semidirect
157. C3×M32C2×D3semidirect
158. C3×M32C2×D3semidirect
164. #812C2×D3semidirect
174. #800C2×D3semidirect
176. D48C2×D3semidirect
177. #798C2×D3semidirect
178. D3×C16C2×D3semidirect
367. M32D32semidirect
541. C32#3414semidirect
613. C3#82009semidirect
614. C3#82035semidirect

Maximal subgroups

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

subgroupindex
C2×#638072
D3×#9042
#105926082
C3×#49082
C3×D3×M322
#105906382
#105906332
#105902422
#105902412
#105902392
#105902322
#820353
#820093