Finite Group Databasebeta

← #11861175

Subgroups — #11861175

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594795C211yesmaximal, characteristic
2#10594780C211yesmaximal, characteristic, complemented
3#10594776C211yesmaximal, characteristic, complemented
4C2×#63632C211yesmaximal, characteristic, complemented
5C2×C3×#805C211yesmaximal, characteristic, complemented
6C3×C4×#208C211yesmaximal, characteristic, complemented
7#10591141C211yesmaximal, characteristic, complemented
8#10590342C214yesmaximal, complemented
9#10590341C214yesmaximal, complemented
10#78980—31nomaximal
11#78541—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19#63833C412yescomplemented
20#63831C412yescomplemented
21#63830C412yescomplemented
22#63829C2214yes—
23#63825C412yescomplemented
24#63818—22no—
25#63817—22no—
26#63817C2214yescomplemented
27#63815—22no—
28#63814C2214yescomplemented
29D3×#208—22no—
30#63632C2212yescomplemented
31#63632C2212yescomplemented
32C3×#805C2212yescomplemented
33C3×#805C2212yescomplemented
34C3×#803C2212yescomplemented
35C3×C4×C3⋊C8C2212yescomplemented
36#63577C2214yescomplemented
37#5822—31no—
38#5819—31no—
39#5748—31no—
40#5745—31no—
41#5745—31no—
42#5745—31no—
43C2×C3×#104—31no—
44C3×C4×M16—31no—
45#5125—31no—
46#5124—31no—
47C2×#805—31no—
48C2×#805—31no—
49C2×#805—61no—
50C2×#805D311yescharacteristic, complemented
51C4×#208D311yescharacteristic, complemented
52#4824—34no—
53#4823—34no—
54#4717—34no—
55#4700—34no—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C2×#638—21no—
59#3828—21no—
60#3828—21no—
61#3828C2×C412yes—
62#3828C2312yes—
63C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×#634C2×C411yescharacteristic
66C2×C3×#67—21no—
67C3×#235—21no—
68C3×#235—21no—
69C3×#235C2×C412yes—
70C3×#235C2312yes—
71C2×C3×D12C2×C411yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6C2×C411yescharacteristic
74C32×C42—21no—
75C32×C42C2311yescharacteristic
76C32×C42C2311yescharacteristic
77#3748—21no—
78#3748C2312yes—
79C2×C3⋊(C3⋊C8)—21no—
80C3×#208—21no—
81C3×#208C2×C412yes—
82C3×#208C2×C412yes—
83C3×#208D412yes—
84C3×#208D412yes—
85C3×#208C2312yes—
86C2×C3×C3⋊C8—21no—
87C2×C3×C3⋊C8C2312yes—
88C2×C3×C3⋊C8C2312yes—
89#3719C2×C414yescomplemented
90#3717C2×C414yescomplemented
91#3716C2×C414yescomplemented
92#3714C2×C414yescomplemented
93#3712—24no—
94#3711—24no—
95#3710—24no—
96D3×C3⋊C8—24no—
97#2956—91noSylow
98C2×C3×#41—31no—
99C2×#235—31no—
100C2×#235—31no—
101C2×#235—61no—
102C2×#235C2×D311yescharacteristic
103C2×C3×M16—31no—
104C2×C3×M16—31no—
105C2×C3×M16—31no—
106C2×C3×C42—21no—
107C2×C3×C42C2×D311yescharacteristic
108C2×C3×C42C2×D311yescharacteristic
109#951—32no—
110#950—34no—
111#949—32no—
112#948—34no—
113#948—62no—
114#942—32no—
115#932—32no—
116C2×#208—31no—
117C2×#208—31no—
118C2×#208—61no—
119C2×#208—62no—
120C2×#208C2×D311yescharacteristic
121C2×#208C2×D311yescharacteristic
122C2×#208C2×D311yescharacteristic
123#909—32no—
124#909—32no—
125#908—32no—
126#908—32no—
127#907—34no—
128#907—62no—
129#907—62no—
130D3×M16—62no—
131D3×M16—62no—
132D3×M16—62no—
133#904—34no—
134#901—34no—
135#901—34no—
136#901—62no—
137C3×#104—32no—
138C3×#104—32no—
139C3×#97—32no—
140C3×C4×C8—32no—
141#822—34no—
142#819—34no—
143#805—32no—
144#805—32no—
145#805—32no—
146#805—32no—
147#805—62no—
148#805—62no—
149#805C2×D312yescomplemented
150#805C2×D312yescomplemented
151#803C2×D312yescomplemented
152C4×C3⋊C8C2×D312yescomplemented
153C23×C32#4111yescharacteristic
154C22×C3⋊D3—21no—
155C22×C3×D3—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—42no—
159C2×C32×C4C22×C411yescharacteristic
160C2×C32×C4C22×C411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4#4111yescharacteristic
164C2×C32×C4C2411yescharacteristic
165#638—22no—
166#638—22no—
167C2×C3⋊Dic3—21no—
168C4⋊(C3⋊D3)—21no—
169C4⋊(C3⋊D3)C22×C412yes—
170C4×C3⋊D3—22no—
171C4×C3⋊D3—22no—
172#634—21no—
173#634C22×C412yes—
174C3×#67—22no—
175C3×#67—22no—
176C2×C3×Dic3—21no—
177C3×D12—21no—
178C3×D12C22×C412yes—
179C3×C4×D3—22no—
180C3×C4×D3—22no—
181C3×Dic6—21no—
182C3×Dic6C22×C412yes—
183C3⋊(C3⋊C8)—22no—
184C3×C3⋊C8—22no—
185C3×C3⋊C8C22×C414yes—
186C3×C3⋊C8C2×D414yes—
187#575—91no—
188#568—91no—
189#568—91no—
190#444—94no—
191#443—94no—
192#430—91no—
193C2×#104—31no—
194C2×#104—91no—
195C4×M16—31no—
196C3×#41—32no—
197C3×#41—32no—
198C3×#41—61no—
199C3×#41—61no—
200C2×C3×Q8—31no—
201C2×C3×D4—31no—
202C2×C3×D4—61no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—41no—
207C22×C3×C4—61no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67—21no—
211C2×#67—61no—
212C2×#67—61no—
213C2×#67—121no—
214#235—21no—
215#235—21no—
216#235—32no—
217#235—32no—
218#235—32no—
219#235—32no—
220#235—62no—
221#235—62no—
222#235—61no—
223#235—61no—
224#235—61no—
225#235—61no—
226#235—121no—
227#235—121no—
228#235C4×D312yes—
229#235C22×D312yes—
230C2×D12—31no—
231C2×D12—31no—
232C2×D12—61no—
233C2×D12C4×D311yescharacteristic
234C2×C4×D3—21no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×C4×D3—121no—
238C2×Dic6—31no—
239C2×Dic6—31no—
240C2×Dic6—61no—
241C2×Dic6C4×D311yescharacteristic
242C3×M16—32no—
243C3×M16—32no—
244C3×M16—32no—
245C3×M16—32no—
246C3×M16—32no—
247C3×M16—61no—
248C2×C3×C8—32no—
249C2×C3×C8—32no—
250C2×C3×C8—61no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42—21no—
254C3×C42—21no—
255C3×C42—41no—
256C3×C42C22×D311yescharacteristic
257C3×C42C22×D311yescharacteristic
258C3×C42C22×D311yescharacteristic
259C3×C42C22×D311yescharacteristic
260#216—34no—
261#215—34no—
262#214—34no—
263#213—34no—
264#208—21no—
265#208—32no—
266#208—32no—
267#208—62no—
268#208—61no—
269#208—61no—
270#208—64no—
271#208—121no—
272#208C4×D312yes—
273#208C4×D312yes—
274#208D1212yes—
275#208D1212yes—
276#208C22×D312yes—
277C2×C3⋊C8—21no—
278C2×C3⋊C8—61no—
279C2×C3⋊C8—61no—
280C2×C3⋊C8—64no—
281C2×C3⋊C8—121no—
282C2×C3⋊C8C22×D312yes—
283C2×C3⋊C8C22×D312yes—
284Dic12—34no—
285D24—34no—
286#204—34no—
287#204—34no—
288ΓL(1,𝔽25)—64no—
289ΓL(1,𝔽25)—64no—
290ΓL(1,𝔽25)—64no—
291D3×C8—64no—
292D3×C8—64no—
293D3×C8—64no—
294C22×C32—41no—
295C22×C32C4×D411yescharacteristic
296C22×C32C4×D411yescharacteristic
297C22×C32C2×#4111yescharacteristic
298C2×C3⋊D3—22no—
299C2×C3⋊D3—81no—
300C2×C3×D3—22no—
301C2×C3×D3—81no—
302C32×C4—22no—
303C32×C4—41no—
304C32×C4C4×D411yescharacteristic
305C32×C4C4×D411yescharacteristic
306C32×C4C23×C411yescharacteristic
307C32×C4C22×D411yescharacteristic
308C3⋊Dic3—22no—
309C3×Dic3—22no—
310C2×#41—31no—
311C2×#41—91no—
312#137—92no—
313#137—92no—
314AGL(1,ℤ/8)—92no—
315AGL(1,ℤ/8)—92no—
316#135—94no—
317#131—94no—
318#131—94no—
319#131—182no—
320#131—182no—
321C2×M16—31no—
322C2×M16—31no—
323C2×M16—31no—
324C2×M16—91no—
325C2×M16—182no—
326C2×M16—182no—
327C2×C42D3211yescharacteristic
328#108—94no—
329#104—32no—
330#104—32no—
331#104—92no—
332#104—92no—
333#97—32no—
334C4×C8—32no—
335C23×C3—21no—
336C23×C3—61no—
337C23×C3#23511yescharacteristic
338C23×C3#23711yescharacteristic
339C22×D3—21no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—121no—
343C3×Q8—32no—
344C3×Q8—61no—
345C3×D4—32no—
346C3×D4—62no—
347C3×D4—62no—
348C3×D4—61no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—44no—
364C2×C3×C4—61no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4C2×C4×D311yescharacteristic
368C2×C3×C4C2×C4×D311yescharacteristic
369C2×C3×C4C2×C4×D311yescharacteristic
370C2×C3×C4C2×C4×D311yescharacteristic
371C2×C3×C4C2×D1211yescharacteristic
372C2×C3×C4C2×D1211yescharacteristic
373C2×C3×C4#23511yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4#23711yescharacteristic
377C2×C3×C4C23×D311yescharacteristic
378C2×C3×C4C23×D311yescharacteristic
379#67—22no—
380#67—22no—
381#67—62no—
382#67—62no—
383#67—62no—
384#67—62no—
385#67—122no—
386#67—122no—
387C2×Dic3—21no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—121no—
391D12—21no—
392D12—32no—
393D12—32no—
394D12—62no—
395D12—61no—
396D12—61no—
397D12—121no—
398D12C2×C4×D312yes—
399C4×D3—22no—
400C4×D3—22no—
401C4×D3—62no—
402C4×D3—62no—
403C4×D3—62no—
404C4×D3—62no—
405C4×D3—122no—
406C4×D3—122no—
407Dic6—21no—
408Dic6—32no—
409Dic6—32no—
410Dic6—62no—
411Dic6—61no—
412Dic6—61no—
413Dic6—121no—
414Dic6C2×C4×D312yes—
415C3×C8—34no—
416C3×C8—34no—
417C3×C8—62no—
418C3⋊C8—22no—
419C3⋊C8—62no—
420C3⋊C8—62no—
421C3⋊C8—122no—
422C3⋊C8C2×C4×D314yes—
423C3⋊C8C2×D1214yes—
424C2×C32—21no—
425C2×C32—21no—
426C2×C32—21no—
427C2×C32C2×C4×D411yescharacteristic
428C3⋊D3—42no—
429C3×D3—42no—
430#41—32no—
431#41—32no—
432#41—61no—
433#41—61no—
434#41—92no—
435#41—92no—
436#41—181no—
437#41—181no—
438C2×Q8—31no—
439C2×Q8—91no—
440C2×D4—31no—
441C2×D4—61no—
442C2×D4—91no—
443C2×D4—181no—
444C22×C4—21no—
445C22×C4—61no—
446C22×C4—181no—
447C22×C4C2×D3211yescharacteristic
448Q16—94no—
449SD16—94no—
450SD16—94no—
451D8—94no—
452M16—32no—
453M16—32no—
454M16—32no—
455M16—32no—
456M16—32no—
457M16—61no—
458M16—92no—
459M16—184no—
460M16—184no—
461M16—181no—
462C2×C8—32no—
463C2×C8—32no—
464C2×C8—61no—
465C2×C8—184no—
466C2×C8—184no—
467C2×C8—181no—
468C42—21no—
469C42C2×D3211yescharacteristic
470C42C2×D3211yescharacteristic
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—41no—
475C22×C3—41no—
476C22×C3—42no—
477C22×C3—62no—
478C22×C3—241no—
479C22×C3C4×D1211yescharacteristic
480C22×C3C4×D1211yescharacteristic
481C22×C3#67⋊C411yescharacteristic
482C22×C3#67⋊C411yescharacteristic
483C22×C3C2×#23511yescharacteristic
484C22×C3C2×#23711yescharacteristic
485C2×D3—22no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—81no—
489C2×D3—122no—
490C2×D3—241no—
491C2×D3—241no—
492C2×D3—242no—
493C3×C4—22no—
494C3×C4—22no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—42no—
500C3×C4—41no—
501C3×C4—41no—
502C3×C4—42no—
503C3×C4—62no—
504C3×C4C4×D1211yescharacteristic
505C3×C4C4×D1211yescharacteristic
506C3×C4#67⋊C411yescharacteristic
507C3×C4#67⋊C411yescharacteristic
508C3×C4C22×C4×D311yescharacteristic
509C3×C4C22×C4×D311yescharacteristic
510C3×C4C22×D1211yescharacteristic
511C3×C4C2×D3×D411yescharacteristic
512Dic3—22no—
513Dic3—62no—
514Dic3—62no—
515Dic3—122no—
516C32#295611yescharacteristic, complemented, Sylow
517C23—61no—
518C23—181no—
519C23#380411yescharacteristic
520Q8—32no—
521Q8—61no—
522Q8—92no—
523Q8—181no—
524D4—32no—
525D4—62no—
526D4—62no—
527D4—61no—
528D4—92no—
529D4—182no—
530D4—182no—
531D4—181no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—42no—
535C2×C4—61no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—181no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4C4×D3211yescharacteristic
542C2×C4C4×D3211yescharacteristic
543C2×C4D3×D1211yescharacteristic
544C2×C4D3×D1211yescharacteristic
545C2×C4#380411yescharacteristic
546C2×C4C22×D3211yescharacteristic
547C8—34no—
548C8—34no—
549C8—62no—
550C8—182no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—41no—
560C2×C3—41no—
561C2×C3—122no—
562C2×C3C2×C4×D1211yescharacteristic
563C2×C3C2×#67⋊C411yescharacteristic
564D3—42no—
565D3—122no—
566D3—122no—
567D3—242no—
568C22—41no—
569C22—62no—
570C22—182no—
571C22—241no—
572C22—721no—
573C22#6388011yescharacteristic
574C22#6388011yescharacteristic
575C22C2×#380411yescharacteristic
576C4—22no—
577C4—41no—
578C4—62no—
579C4—182no—
580C4#6388011yescharacteristic
581C4#6388011yescharacteristic
582C4C2×C4×D3211yescharacteristic
583C4C2×D3×D1211yescharacteristic
584C3—21no—
585C3#7854111yescharacteristic, complemented
586C3#7898011yescharacteristic, complemented
587C2—21no—
588C2—21no—
589C2—21no—
590C2—122no—
591C2—362no—
592C2C2×#6388011yescharacteristic
subgroupG/H
centerC4C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC2×C32C2×C4×D4
prime radical#10594795C2
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32#2956
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10594780C2semidirect
3. #10594776C2semidirect
4. C2×#63632C2semidirect
5. C2×C3×#805C2semidirect
6. C3×C4×#208C2semidirect
7. #10591141C2semidirect
8. #10590342C2semidirect
9. #10590341C2semidirect
19. #63833C4semidirect
20. #63831C4semidirect
21. #63830C4semidirect
23. #63825C4semidirect
26. #63817C22semidirect
28. #63814C22semidirect
30. #63632C22semidirect
31. #63632C22semidirect
32. C3×#805C22semidirect
33. C3×#805C22semidirect
34. C3×#803C22semidirect
35. C3×C4×C3⋊C8C22semidirect
36. #63577C22semidirect
50. C2×#805D3semidirect
51. C4×#208D3semidirect
89. #3719C2×C4semidirect
90. #3717C2×C4semidirect
91. #3716C2×C4semidirect
92. #3714C2×C4semidirect
149. #805C2×D3semidirect
150. #805C2×D3semidirect
151. #803C2×D3semidirect
152. C4×C3⋊C8C2×D3semidirect
516. C32#2956semidirect
585. C3#78541semidirect
586. C3#78980semidirect

Maximal subgroups

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

subgroupindex
#105947952
#105947802
#105947762
C2×#636322
C2×C3×#8052
C3×C4×#2082
#105911412
#105903422
#105903412
#789803
#785413