Finite Group Databasebeta

← #11902852

Subgroups — #11902852

Order 1152.

3451 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C212yesmaximal, complemented
2C4×#3832C211yesmaximal, characteristic, complemented
3C3×#5576C212yesmaximal, complemented
4#10595412C211yesmaximal, characteristic, complemented
5Q8×#625C211yesmaximal, characteristic, complemented
6#10594632C216yesmaximal, complemented
7#10594618C213yesmaximal, complemented
8#10594530C213yesmaximal, complemented
9#10594007C216yesmaximal, complemented
10C4×#3802C213yesmaximal, complemented
11#10593971C213yesmaximal, complemented
12#86710—32nomaximal
13C2×#3832C2211yescharacteristic
14C2×C3×#239C2212yescomplemented
15C2×C3×D3×Q8C2212yescomplemented
16D3×#239—216no—
17C2×#3802C2213yes—
18C2×D3×D12C2216yescomplemented
19C2×C4×D32C2216yescomplemented
20C2×#3799C2216yescomplemented
21C2×#3796C2216yescomplemented
22C32×C4×Q8C2211yescharacteristic, complemented
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24#64102C2213yescomplemented
25#64101C2213yescomplemented
26C4×C4⋊(C3⋊D3)C2213yescomplemented
27C42×C3⋊D3C2213yescomplemented
28C3×#897C2216yescomplemented
29C3×#895C2216yescomplemented
30C3×#875C2216yescomplemented
31C3×C4×D12C2216yescomplemented
32#63922C22112yescomplemented
33#63921C2216yescomplemented
34#63914C2213yescomplemented
35#63912C2216yescomplemented
36#63912C2216yescomplemented
37#63908C2216yescomplemented
38#63902C2211yescharacteristic
39#63902C2216yescomplemented
40#63902C2213yescomplemented
41C4×#625C2213yes—
42C4×#625C2213yescomplemented
43#63900C2213yescomplemented
44#63898C2216yescomplemented
45#63873C2213yescomplemented
46#63856C2216yescomplemented
47#63854C22112yescomplemented
48C2×D3×#41—32no—
49C22×#239—32no—
50C3×#548—32no—
51#5834—32no—
52Q8×#67—32no—
53#5676—36no—
54#5668—36no—
55#5631—36no—
56#5627—36no—
57#5609—36no—
58#5606—36no—
59#5576D312yescomplemented
60C4×#239—32no—
61C4×#239—61no—
62#5550—36no—
63C4×D3×D4—36no—
64C22×D32C2316yes—
65C2×C32×Q8C2311yescharacteristic
66#3832D418yescomplemented
67C2×C4⋊(C3⋊D3)C2313yes—
68C2×C4×C3⋊D3C2313yes—
69C2×C4×C3⋊D3C2313yes—
70C2×C4×C3⋊D3C2313yes—
71C3×#239—28no—
72C3×D3×Q8—28no—
73C2×C3×D12C2316yes—
74C2×C3×D12C2316yes—
75C2×C3×C4×D3C2316yes—
76C2×C3×C4×D3C2316yes—
77C2×C3×Dic6C2316yes—
78C2×#626C23112yes—
79C2×#625C2313yes—
80C2×#625C2316yes—
81C2×#625C2311yescharacteristic
82C2×#624C2316yes—
83C2×D3×Dic3C2316yes—
84C2×D3×Dic3C2312yes—
85#3802—212no—
86D3×D12—224no—
87C4×D32—224no—
88#3799—224no—
89#3796—224no—
90C32×C4⋊C4C2313yes—
91C32×C42C2313yes—
92#3752C2316yes—
93C4⋊(C3⋊Dic3)C2313yes—
94C4×C3⋊Dic3C2311yescharacteristic
95C4×C3⋊Dic3C2313yes—
96C4×C3⋊Dic3C2313yes—
97C3×(C2×D3)⋊C4C23112yes—
98C3×(C2×D3)⋊C4C2312yes—
99C3×(C2×D3)⋊C4C2316yes—
100C3×C4⋊Dic3C2316yes—
101#3724C2316yes—
102#3724C2313yes—
103#3724C2311yescharacteristic
104(C2×D3)⋊Dic3C2316yes—
105(C2×D3)⋊Dic3C2316yes—
106D4×#41—91noSylow
107C2×C3×#41—32no—
108C22×C3×Q8—32no—
109D3×#41—616no—
110C2×#239—32no—
111C2×#239—36no—
112C2×#239—36no—
113C2×#239—61no—
114C2×#239—616no—
115C2×#239C2×D312yescomplemented
116C2×D3×Q8C2×D312yescomplemented
117C2×#237—36no—
118C2×D3×D4—36no—
119C2×D3×D4—36no—
120C2×#235—36no—
121C22×D12—36no—
122C22×C4×D3—36no—
123C22×C4×D3—36no—
124C3×#124—36no—
125C3×C22⋊Q8—36no—
126C3×#121—36no—
127C3×C4×Q8—21no—
128C3×C4×Q8C2×D312yescomplemented
129C3×C4×D4—36no—
130#946—36no—
131Q8×Dic3—32no—
132Q8×Dic3—61no—
133#944—36no—
134#940—36no—
135#938—36no—
136#937—312no—
137D4×Dic3—36no—
138#930—36no—
139C4×#67—36no—
140C4×#67—36no—
141#924—36no—
142#897C2×D316yescomplemented
143#895C2×D316yescomplemented
144#894—312no—
145#893—36no—
146#893—36no—
147#893—63no—
148#892—36no—
149#892—63no—
150D3×C4⋊C4—36no—
151#884—312no—
152#884—312no—
153#883—312no—
154#882—312no—
155#67⋊C4—36no—
156#67⋊C4—312no—
157#67⋊C4—32no—
158D3×C22⋊C4—36no—
159D3×C22⋊C4—36no—
160#875C2×D316yescomplemented
161C4×D12—36no—
162C4×D12—63no—
163C4×D12C2×D316yescomplemented
164C42×D3—36no—
165C42×D3—63no—
166C22×C3⋊D3C2413yes—
167C22×C3×D3C2416yes—
168C22×C3×D3C2412yes—
169C2×D32—212no—
170C2×D32—212no—
171C2×D32—46no—
172C32×Q8C2×D414yescomplemented
173C2×C32×C4C2413yes—
174C2×C32×C4C2411yescharacteristic
175C2×C32×C4C2413yes—
176C2×C3⋊Dic3C2413yes—
177C2×C3⋊Dic3C2411yescharacteristic
178C2×C3⋊Dic3C2411yescharacteristic
179C4⋊(C3⋊D3)C2×D4112yescomplemented
180C4×C3⋊D3—26no—
181C4×C3⋊D3—43no—
182C4×C3⋊D3C2×D4112yescomplemented
183C2×C3×Dic3C2412yes—
184C2×C3×Dic3C2416yes—
185C3×D12—212no—
186C3×D12—212no—
187C3×C4×D3—212no—
188C3×C4×D3—212no—
189C3×Dic6—212no—
190#626—224no—
191#625—26no—
192#625—46no—
193#625#4114yescomplemented
194#624—212no—
195D3×Dic3—212no—
196D3×Dic3—24no—
197C22×#41—92no—
198#550—91no—
199D4×Q8—91no—
200#548—32no—
201#547—93no—
202#546—96no—
203D42—93no—
204#532—93no—
205#525—96no—
206C4×#41—91no—
207C2×C4×D4—93no—
208C23×D3—36no—
209C23×D3—36no—
210C3×#41—68no—
211C2×C3×Q8—21no—
212C2×C3×Q8—36no—
213C2×C3×Q8—68no—
214C2×C3×Q8C22×D312yes—
215C2×C3×D4—36no—
216C2×C3×D4—36no—
217C22×C3×C4—36no—
218C22×C3×C4—36no—
219C2×#67—32no—
220C2×#67—36no—
221C2×#67—312no—
222C2×#67—312no—
223C22×Dic3—36no—
224C22×Dic3—32no—
225#239—28no—
226#239—316no—
227#239—68no—
228#239—624no—
229#239—624no—
230D3×Q8—28no—
231#237—624no—
232D3×D4—624no—
233D3×D4—624no—
234#235—624no—
235C2×D12—36no—
236C2×D12—312no—
237C2×D12—63no—
238C2×D12—624no—
239C2×D12C22×D316yes—
240C2×D12C22×D316yes—
241C2×C4×D3—36no—
242C2×C4×D3—36no—
243C2×C4×D3—32no—
244C2×C4×D3—36no—
245C2×C4×D3—36no—
246C2×C4×D3—36no—
247C2×C4×D3—36no—
248C2×C4×D3—63no—
249C2×C4×D3—63no—
250C2×C4×D3—63no—
251C2×C4×D3—624no—
252C2×C4×D3—624no—
253C2×C4×D3C22×D316yes—
254C2×C4×D3C22×D316yes—
255C2×Dic6C22×D316yes—
256C3×C4⋊C4—23no—
257C3×C4⋊C4—36no—
258C3×C4⋊C4C22×D316yes—
259C3×C22⋊C4—32no—
260C3×C22⋊C4—36no—
261C3×C22⋊C4—312no—
262C3×C42—23no—
263C3×C42C22×D316yes—
264#217—36no—
265#217—36no—
266(C2×D3)⋊C4—36no—
267(C2×D3)⋊C4—36no—
268(C2×D3)⋊C4—312no—
269(C2×D3)⋊C4—66no—
270(C2×D3)⋊C4C22×D312yes—
271(C2×D3)⋊C4C22×D316yes—
272(C2×D3)⋊C4C22×D3112yes—
273C4⋊Dic3—36no—
274C4⋊Dic3—63no—
275C4⋊Dic3C22×D316yes—
276Dic3⋊C4—312no—
277Dic3⋊C4—36no—
278Dic3⋊C4—32no—
279C4×Dic3—32no—
280C4×Dic3—36no—
281C4×Dic3—36no—
282C4×Dic3—61no—
283C4×Dic3—63no—
284C4×Dic3—63no—
285C22×C32C2511yescharacteristic
286C2×C3⋊D3—23no—
287C2×C3⋊D3—23no—
288C2×C3⋊D3C22×D416yes—
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C2×C3×D3—26no—
292C2×C3×D3—26no—
293C2×C3×D3—26no—
294C2×C3×D3C2×#4114yescomplemented
295D32—424no—
296C32×C4—21no—
297C32×C4—23no—
298C32×C4C22×D416yes—
299C3⋊Dic3—23no—
300C3⋊Dic3C22×D412yes—
301C3⋊Dic3C2×#4112yescomplemented
302C3×Dic3—22no—
303C3×Dic3—26no—
304C2×#41—32no—
305C2×#41—96no—
306C2×#41—96no—
307C2×#41—91no—
308C2×#41—1816no—
309C22×Q8—32no—
310C22×D4—96no—
311C22×D4—93no—
312C23×C4—96no—
313C4⋊Q8—93no—
314#127—93no—
315#124—36no—
316#123—912no—
317C22⋊Q8—36no—
318C22⋊Q8—96no—
319#121—36no—
320#121—96no—
321#121—96no—
322#121—96no—
323#120—912no—
324C4×Q8—91no—
325C4×Q8D3211yescharacteristic, complemented
326C4×D4—36no—
327C4×D4—91no—
328C4×D4—93no—
329C4×D4—96no—
330C4×D4—96no—
331C4×D4—93no—
332C4×D4—93no—
333C4×D4—93no—
334C4×D4—93no—
335#117—93no—
336C2×C4⋊C4—93no—
337C2×C22⋊C4—96no—
338C2×C42—93no—
339C23×C3—32no—
340C23×C3—36no—
341C22×D3—36no—
342C22×D3—63no—
343C22×D3—612no—
344C22×D3—612no—
345C22×D3—612no—
346C22×D3—612no—
347C22×D3—126no—
348C22×D3—126no—
349C22×D3C23×D316yes—
350C22×D3C23×D312yes—
351C3×Q8—24no—
352C3×Q8—612no—
353C3×Q8D3×D418yescomplemented
354C3×D4—612no—
355C3×D4—612no—
356C2×C3×C4—23no—
357C2×C3×C4—21no—
358C2×C3×C4—23no—
359C2×C3×C4—36no—
360C2×C3×C4—32no—
361C2×C3×C4—612no—
362C2×C3×C4—612no—
363C2×C3×C4C23×D316yes—
364C2×C3×C4C23×D312yes—
365C2×C3×C4C23×D316yes—
366#67—38no—
367#67—624no—
368#67—612no—
369#67—1212no—
370C2×Dic3—32no—
371C2×Dic3—32no—
372C2×Dic3—36no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—63no—
376C2×Dic3—64no—
377C2×Dic3—612no—
378C2×Dic3C23×D316yes—
379C2×Dic3C23×D312yes—
380D12—212no—
381D12—212no—
382D12—324no—
383D12—612no—
384D12—624no—
385C4×D3—212no—
386C4×D3—212no—
387C4×D3—324no—
388C4×D3—612no—
389C4×D3—612no—
390C4×D3—612no—
391C4×D3—612no—
392C4×D3—64no—
393C4×D3—612no—
394C4×D3—126no—
395C4×D3—126no—
396C4×D3—126no—
397Dic6—212no—
398C2×C32C23×D411yescharacteristic
399C2×C32C22×#4111yescharacteristic
400C2×C32#58511yescharacteristic
401C3⋊D3—26no—
402C3×D3—24no—
403C3×D3—46no—
404C24—96no—
405#41—68no—
406#41—98no—
407#41—1824no—
408#41—1824no—
409C2×Q8—36no—
410C2×Q8—68no—
411C2×Q8C2×D3211yescharacteristic
412C2×D4—36no—
413C2×D4—36no—
414C2×D4—912no—
415C2×D4—91no—
416C2×D4—93no—
417C2×D4—96no—
418C2×D4—93no—
419C2×D4—1824no—
420C2×D4—1812no—
421C22×C4—36no—
422C22×C4—36no—
423C22×C4—96no—
424C22×C4—92no—
425C22×C4—96no—
426C22×C4—93no—
427C22×C4—93no—
428C22×C4—93no—
429C22×C4—1824no—
430C4⋊C4—36no—
431C4⋊C4—91no—
432C4⋊C4—93no—
433C4⋊C4—96no—
434C4⋊C4—93no—
435C4⋊C4C2×D3213yes—
436C22⋊C4—32no—
437C22⋊C4—36no—
438C22⋊C4—312no—
439C22⋊C4—96no—
440C22⋊C4—96no—
441C22⋊C4—96no—
442C42—91no—
443C42—93no—
444C42—93no—
445C42C2×D3213yes—
446C22×C3—21no—
447C22×C3—34no—
448C22×C3—62no—
449C22×C3—62no—
450C22×C3—66no—
451C22×C3—66no—
452C22×C3—66no—
453C22×C3C24×D312yes—
454C2×D3—22no—
455C2×D3—22no—
456C2×D3—26no—
457C2×D3—26no—
458C2×D3—26no—
459C2×D3—312no—
460C2×D3—66no—
461C2×D3—66no—
462C2×D3—66no—
463C2×D3—123no—
464C2×D3—123no—
465C2×D3—1224no—
466C2×D3—1224no—
467C2×D3D3×#4114yescomplemented
468C3×C4—22no—
469C3×C4—26no—
470C3×C4—22no—
471C3×C4—26no—
472C3×C4—43no—
473C3×C4—62no—
474C3×C4—66no—
475C3×C4C2×D3×D4112yes—
476Dic3—26no—
477Dic3—22no—
478Dic3—34no—
479Dic3—34no—
480Dic3—62no—
481Dic3—62no—
482Dic3—66no—
483Dic3—123no—
484C32D4×#4111yescharacteristic, complemented, Sylow
485C23—32no—
486C23—36no—
487C23—93no—
488C23—1812no—
489C23—1812no—
490C23—366no—
491Q8—612no—
492Q8#380214yescomplemented
493D4—612no—
494D4—612no—
495D4—94no—
496D4—912no—
497D4—1824no—
498D4—186no—
499D4—366no—
500C2×C4—36no—
501C2×C4—32no—
502C2×C4—612no—
503C2×C4—612no—
504C2×C4—91no—
505C2×C4—91no—
506C2×C4—912no—
507C2×C4—93no—
508C2×C4—186no—
509C2×C4—1812no—
510C2×C4—184no—
511C2×C4—1812no—
512C2×C4—363no—
513C2×C4C22×D3211yescharacteristic
514C2×C4C22×D3213yes—
515C2×C4C22×D3213yes—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—64no—
520C2×C3—126no—
521C2×C3C22×D3×D412yes—
522C2×C3C2×D3×#4112yes—
523C2×C3#596812yes—
524D3—24no—
525D3—46no—
526D3—612no—
527D3—126no—
528C22—34no—
529C22—62no—
530C22—62no—
531C22—66no—
532C22—66no—
533C22—66no—
534C22—96no—
535C22—183no—
536C22—183no—
537C22—3624no—
538C22C23×D3211yescharacteristic
539C4—21no—
540C4—23no—
541C4—62no—
542C4—66no—
543C4—92no—
544C4—92no—
545C4—183no—
546C4C2×#380216yes—
547C3—21no—
548C3#8671012yescomplemented
549C2—64no—
550C2—126no—
551C2—186no—
552C2C22×#380211yescharacteristic
553C2#1059668911yescharacteristic
554C2D32×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32D4×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. C4×#3832C2semidirect
3. C3×#5576C2semidirect
4. #10595412C2semidirect
5. Q8×#625C2semidirect
6. #10594632C2semidirect
7. #10594618C2semidirect
8. #10594530C2semidirect
9. #10594007C2semidirect
10. C4×#3802C2semidirect
11. #10593971C2semidirect
14. C2×C3×#239C22semidirect
15. C2×C3×D3×Q8C22semidirect
18. C2×D3×D12C22semidirect
19. C2×C4×D32C22semidirect
20. C2×#3799C22semidirect
21. C2×#3796C22semidirect
22. C32×C4×Q8C22semidirect
23. Q8×C3⋊Dic3C22semidirect
24. #64102C22semidirect
25. #64101C22semidirect
26. C4×C4⋊(C3⋊D3)C22semidirect
27. C42×C3⋊D3C22semidirect
28. C3×#897C22semidirect
29. C3×#895C22semidirect
30. C3×#875C22semidirect
31. C3×C4×D12C22semidirect
32. #63922C22semidirect
33. #63921C22semidirect
34. #63914C22semidirect
35. #63912C22semidirect
36. #63912C22semidirect
37. #63908C22semidirect
39. #63902C22semidirect
40. #63902C22semidirect
42. C4×#625C22semidirect
43. #63900C22semidirect
44. #63898C22semidirect
45. #63873C22semidirect
46. #63856C22semidirect
47. #63854C22semidirect
59. #5576D3semidirect
66. #3832D4semidirect
115. C2×#239C2×D3semidirect
116. C2×D3×Q8C2×D3semidirect
128. C3×C4×Q8C2×D3semidirect
142. #897C2×D3semidirect
143. #895C2×D3semidirect
160. #875C2×D3semidirect
163. C4×D12C2×D3semidirect
172. C32×Q8C2×D4semidirect
179. C4⋊(C3⋊D3)C2×D4semidirect
182. C4×C3⋊D3C2×D4semidirect
193. #625#41semidirect
294. C2×C3×D3C2×#41semidirect
301. C3⋊Dic3C2×#41semidirect
325. C4×Q8D32semidirect
353. C3×Q8D3×D4semidirect
467. C2×D3D3×#41semidirect
484. C32D4×#41semidirect
492. Q8#3802semidirect
548. C3#86710semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C4×#38322
C3×#55762
#105954122
Q8×#6252
#105946322
#105946182
#105945302
#105940072
C4×#38022
#105939712
#867103