Finite Group Databasebeta

← #11904210

Subgroups — #11904210

Order 1152.

2328 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×C4×#239C211yesmaximal, characteristic, complemented
3C3×#5570C211yesmaximal, characteristic, complemented
4#10595414C212yesmaximal, complemented
5Q8×#624C212yesmaximal, complemented
6#10594584C216yesmaximal, complemented
7#10594447C216yesmaximal, complemented
8C4×#3799C213yesmaximal, complemented
9#10593879C213yesmaximal, complemented
10#10593869C213yesmaximal, complemented
11#10593859C213yesmaximal, complemented
12#87017—31nomaximal
13#85844—31nomaximal
14C2×Q8×C3⋊D3C2212yes—
15C2×C3×#239C2211yescharacteristic
16C2×#3799C2213yes—
17C32×C4×Q8C2211yescharacteristic
18#64106C2216yes—
19C4×C4⋊(C3⋊D3)C2213yes—
20#64078C2213yes—
21C3×Q8×Dic3C2211yescharacteristic
22C3×Q8×Dic3C2212yes—
23C3×#893C2213yes—
24C3×#892C2213yes—
25C3×#890C2216yes—
26C3×C4×D12C2213yes—
27C3×C42×D3C2213yes—
28C3×#869C2213yes—
29C3×C4×Dic6C2213yes—
30#63916C2216yes—
31#63904C2216yes—
32C4×#626C2216yes—
33#63900C2216yes—
34#63894C2211yescharacteristic
35C4×#624C2216yes—
36#63869C2216yes—
37#63861C22112yes—
38#63860C2216yes—
39#63857C2216yes—
40#63856C2216yes—
41#63854C22112yes—
42#63844C2216yes—
43#63844C2216yes—
44Dic3×Dic6C2213yes—
45#63841C2216yes—
46#63841C2213yes—
47#63836C2216yes—
48C3×#557—31no—
49C3×C4×#41—31no—
50#5831—32no—
51#5728—33no—
52#5726—33no—
53#5694—36no—
54#5691—36no—
55#5584—33no—
56#5576—32no—
57Q8×D12—31no—
58Q8×D12—31no—
59Q8×D12—61no—
60C4×#239—33no—
61C4×#239D311yescharacteristic, complemented
62C4×D3×Q8—32no—
63C4×D3×Q8—32no—
64#5570D311yescharacteristic, complemented
65#5557—36no—
66#5551—33no—
67#5542—33no—
68#5529—36no—
69C4×#235—33no—
70#5470—33no—
71C2×C32×Q8C2311yescharacteristic
72Q8×C3⋊D3—28no—
73C2×C4⋊(C3⋊D3)C2311yescharacteristic
74C2×C4×C3⋊D3C2316yes—
75C2×#634C2316yes—
76C3×#239—24no—
77C2×C3×D12C2313yes—
78C2×C3×C4×D3C2313yes—
79C2×C3×C4×D3C2313yes—
80C2×C3×C4×D3C2313yes—
81C2×C3×Dic6C2313yes—
82C2×#626C2316yes—
83C2×#624C2316yes—
84C2×#624C2312yes—
85#3799—212no—
86C32×C4⋊C4C2313yes—
87C32×C42C2313yes—
88#3752C2316yes—
89C4⋊(C3⋊Dic3)C2313yes—
90C4⋊(C3⋊Dic3)C2316yes—
91C3×(C2×D3)⋊C4C2316yes—
92C3×C4⋊Dic3C2316yes—
93C3×C4⋊Dic3C2316yes—
94C3×C4⋊Dic3C2313yes—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4C2316yes—
97C3×C4×Dic3C2316yes—
98C3×C4×Dic3C2313yes—
99C3×C4×Dic3C2313yes—
100C3×C4×Dic3C2311yescharacteristic
101#3724C23112yes—
102Dic3⋊Dic3C2316yes—
103#3722C2312yes—
104(C2×D3)⋊Dic3C23112yes—
105(C2×D3)⋊Dic3C2316yes—
106Dic32C2316yes—
107Dic32C2316yes—
108#3482—91noSylow
109C2×C3×#41—31no—
110C2×#239—33no—
111C2×#239C2×D311yescharacteristic
112C2×D3×Q8—32no—
113C2×D3×Q8—32no—
114C2×D3×Q8—62no—
115C2×#235—33no—
116C3×C4⋊Q8—33no—
117C3×#125—36no—
118C3×C4×Q8—21no—
119C3×C4×Q8—31no—
120C3×C4×Q8—32no—
121C3×C4×Q8—33no—
122C3×C4×Q8C2×D311yescharacteristic
123C3×C4×Q8C2×D311yescharacteristic
124C3×C4×D4—33no—
125C3×C4×D4—33no—
126C3×#117—33no—
127C2×C3×C42—33no—
128#946—36no—
129Q8×Dic3—33no—
130Q8×Dic3C2×D312yes—
131Q8×Dic3C2×D311yescharacteristic
132#938—36no—
133#936—36no—
134C4×#67—36no—
135C4×#67—36no—
136#926—36no—
137#926—33no—
138#924—36no—
139#924—36no—
140#898—312no—
141#897—36no—
142#897—36no—
143#897—36no—
144#897—66no—
145#895—36no—
146#894—312no—
147#893—36no—
148#893—31no—
149#893C2×D313yes—
150#892—36no—
151#892—33no—
152#892—36no—
153#892C2×D313yes—
154D3×C4⋊C4—36no—
155D3×C4⋊C4—36no—
156#890—36no—
157#890C2×D316yes—
158#887—36no—
159#887—36no—
160#883—312no—
161#879—312no—
162#875—36no—
163C4×D12—36no—
164C4×D12—33no—
165C4×D12—33no—
166C4×D12—31no—
167C4×D12—63no—
168C4×D12C2×D313yes—
169#872—36no—
170C42×D3—36no—
171C42×D3—36no—
172C42×D3C2×D313yes—
173#870—36no—
174#869—33no—
175#869—33no—
176#869—63no—
177#869C2×D313yes—
178C4×Dic6—33no—
179C4×Dic6—36no—
180C4×Dic6—36no—
181C4×Dic6C2×D313yes—
182C22×C3⋊D3C2412yes—
183C22×C3×D3C2413yes—
184C32×Q8#4114yescomplemented
185C2×C32×C4C2413yes—
186C2×C32×C4C2413yes—
187C2×C32×C4C2411yescharacteristic
188C2×C3⋊Dic3C2416yes—
189C4⋊(C3⋊D3)#4114yescomplemented
190C4×C3⋊D3—212no—
191#634—212no—
192C2×C3×Dic3C2412yes—
193C2×C3×Dic3C2413yes—
194C2×C3×Dic3C2416yes—
195C2×C3×Dic3C2411yescharacteristic
196C2×C3×Dic3C2411yescharacteristic
197C3×D12—26no—
198C3×C4×D3—26no—
199C3×C4×D3—26no—
200C3×C4×D3—26no—
201C3×Dic6—26no—
202#626—212no—
203#624—212no—
204#624—24no—
205#557—31no—
206#556—93no—
207#552—96no—
208D4×Q8—91no—
209#548—92no—
210#547—93no—
211#533—93no—
212#529—96no—
213C4×#41—31no—
214C4×#41—93no—
215C2×C4×Q8—92no—
216C3×#41—64no—
217C2×C3×Q8—21no—
218C2×C3×Q8—33no—
219C2×C3×Q8C22×D311yescharacteristic
220C2×C3×Q8C22×D311yescharacteristic
221C2×C3×D4—33no—
222C22×C3×C4—33no—
223C22×C3×C4—33no—
224C22×C3×C4—33no—
225C2×#67—36no—
226#239—24no—
227#239—612no—
228D3×Q8—68no—
229D3×Q8—68no—
230D3×Q8—128no—
231#235—612no—
232C2×D12—31no—
233C2×D12—31no—
234C2×D12—36no—
235C2×D12—61no—
236C2×D12C22×D313yes—
237C2×C4×D3—36no—
238C2×C4×D3—36no—
239C2×C4×D3—32no—
240C2×C4×D3—32no—
241C2×C4×D3—36no—
242C2×C4×D3—36no—
243C2×C4×D3—66no—
244C2×C4×D3C22×D313yes—
245C2×C4×D3C22×D313yes—
246C2×C4×D3C22×D313yes—
247C2×Dic6—36no—
248C2×Dic6—36no—
249C2×Dic6—66no—
250C2×Dic6C22×D313yes—
251C3×C4⋊C4—23no—
252C3×C4⋊C4—33no—
253C3×C4⋊C4—36no—
254C3×C4⋊C4—36no—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—36no—
257C3×C4⋊C4C22×D313yes—
258C3×C4⋊C4C22×D313yes—
259C3×C22⋊C4—36no—
260C3×C42—23no—
261C3×C42—31no—
262C3×C42—33no—
263C3×C42—36no—
264C3×C42—33no—
265C3×C42C22×D313yes—
266C3×C42C22×D313yes—
267#217—36no—
268#217—312no—
269(C2×D3)⋊C4—36no—
270(C2×D3)⋊C4—312no—
271(C2×D3)⋊C4—36no—
272(C2×D3)⋊C4—36no—
273(C2×D3)⋊C4—32no—
274(C2×D3)⋊C4—32no—
275(C2×D3)⋊C4—66no—
276(C2×D3)⋊C4C22×D316yes—
277C4⋊Dic3—33no—
278C4⋊Dic3—33no—
279C4⋊Dic3—36no—
280C4⋊Dic3—36no—
281C4⋊Dic3—36no—
282C4⋊Dic3—63no—
283C4⋊Dic3—66no—
284C4⋊Dic3C22×D313yes—
285C4⋊Dic3C22×D316yes—
286C4⋊Dic3C22×D311yescharacteristic
287C4⋊Dic3C22×D316yes—
288Dic3⋊C4—36no—
289Dic3⋊C4—312no—
290Dic3⋊C4—312no—
291Dic3⋊C4C22×D316yes—
292C4×Dic3—36no—
293C4×Dic3—36no—
294C4×Dic3—36no—
295C4×Dic3—36no—
296C4×Dic3C22×D316yes—
297C4×Dic3C22×D313yes—
298C4×Dic3C22×D311yescharacteristic
299C4×Dic3C22×D313yes—
300C22×C32C2511yescharacteristic
301C2×C3⋊D3—22no—
302C2×C3⋊D3—22no—
303C2×C3⋊D3C2×#4114yes—
304C2×C3×D3—23no—
305C2×C3×D3—23no—
306C2×C3×D3—23no—
307C32×C4—23no—
308C32×C4C2×#4116yes—
309C32×C4C2×#4112yes—
310C3⋊Dic3—26no—
311C3×Dic3—23no—
312C3×Dic3—26no—
313C3×Dic3—21no—
314C3×Dic3—22no—
315C3×Dic32−1+412yes—
316C2×#41—31no—
317C2×#41—93no—
318C22×Q8—92no—
319C4⋊Q8—33no—
320C4⋊Q8—93no—
321#126—912no—
322#125—36no—
323#125—96no—
324#124—96no—
325#123—912no—
326C22⋊Q8—96no—
327C22⋊Q8—96no—
328C22⋊Q8—96no—
329#121—96no—
330C4×Q8—31no—
331C4×Q8—32no—
332C4×Q8—33no—
333C4×Q8—96no—
334C4×Q8—96no—
335C4×Q8—93no—
336C4×Q8D3211yescharacteristic
337C4×D4—33no—
338C4×D4—33no—
339C4×D4—91no—
340C4×D4—96no—
341C4×D4—96no—
342C4×D4—93no—
343#117—33no—
344#117—96no—
345#117—93no—
346#117—96no—
347C2×C4⋊C4—96no—
348C2×C42—33no—
349C2×C42—96no—
350C23×C3—33no—
351C22×D3—32no—
352C22×D3—32no—
353C22×D3—62no—
354C22×D3C23×D313yes—
355C3×Q8—24no—
356C3×Q8—66no—
357C3×Q8#23514yescomplemented
358C3×Q8#23914yescomplemented
359C3×D4—66no—
360C2×C3×C4—21no—
361C2×C3×C4—23no—
362C2×C3×C4—23no—
363C2×C3×C4—31no—
364C2×C3×C4—32no—
365C2×C3×C4—33no—
366C2×C3×C4—36no—
367C2×C3×C4—31no—
368C2×C3×C4—66no—
369C2×C3×C4—66no—
370C2×C3×C4—66no—
371C2×C3×C4C23×D313yes—
372C2×C3×C4C23×D313yes—
373C2×C3×C4C23×D313yes—
374C2×C3×C4C23×D313yes—
375C2×C3×C4C23×D311yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377#67—612no—
378C2×Dic3—36no—
379C2×Dic3—36no—
380C2×Dic3—66no—
381C2×Dic3C23×D312yes—
382C2×Dic3C23×D313yes—
383C2×Dic3C23×D316yes—
384C2×Dic3C23×D311yescharacteristic
385C2×Dic3C23×D311yescharacteristic
386D12—26no—
387D12—34no—
388D12—34no—
389D12—64no—
390D12—612no—
391C4×D3—26no—
392C4×D3—26no—
393C4×D3—26no—
394C4×D3—64no—
395C4×D3—612no—
396C4×D3—612no—
397C4×D3—612no—
398C4×D3—612no—
399C4×D3—64no—
400C4×D3—1212no—
401Dic6—26no—
402Dic6—612no—
403Dic6—612no—
404Dic6—1212no—
405C2×C32C22×#4111yescharacteristic
406C2×C32C22×#4111yescharacteristic
407C2×C32C2×2−1+411yescharacteristic
408C3⋊D3—24no—
409C3×D3—43no—
410#41—64no—
411#41—1812no—
412C2×Q8—33no—
413C2×Q8—96no—
414C2×Q8—188no—
415C2×Q8C2×D3211yescharacteristic
416C2×D4—33no—
417C2×D4—96no—
418C2×D4—91no—
419C22×C4—33no—
420C22×C4—33no—
421C22×C4—33no—
422C22×C4—92no—
423C22×C4—96no—
424C22×C4—96no—
425C4⋊C4—33no—
426C4⋊C4—36no—
427C4⋊C4—31no—
428C4⋊C4—36no—
429C4⋊C4—36no—
430C4⋊C4—912no—
431C4⋊C4—96no—
432C4⋊C4—93no—
433C4⋊C4—96no—
434C4⋊C4C2×D3213yes—
435C22⋊C4—36no—
436C22⋊C4—92no—
437C22⋊C4—96no—
438C22⋊C4—912no—
439C22⋊C4—96no—
440C42—31no—
441C42—33no—
442C42—33no—
443C42—36no—
444C42—96no—
445C42—96no—
446C42C2×D3213yes—
447C22×C3—21no—
448C22×C3—63no—
449C22×C3—63no—
450C22×C3—63no—
451C22×C3C24×D311yescharacteristic
452C22×C3C24×D311yescharacteristic
453C2×D3—23no—
454C2×D3—23no—
455C2×D3—23no—
456C2×D3—34no—
457C2×D3—34no—
458C2×D3—64no—
459C2×D3—62no—
460C2×D3—62no—
461C2×D3—62no—
462C2×D3—62no—
463C2×D3—122no—
464C2×D3—122no—
465C3×C4—23no—
466C3×C4—23no—
467C3×C4—26no—
468C3×C4—22no—
469C3×C4—32no—
470C3×C4—43no—
471C3×C4—61no—
472C3×C4—63no—
473C3×C4—66no—
474C3×C4—62no—
475C3×C4C2×#23516yes—
476C3×C4C2×#23916yes—
477C3×C4D3×#4112yes—
478C3×C4D3×#4112yes—
479Dic3—21no—
480Dic3—26no—
481Dic3—23no—
482Dic3—22no—
483Dic3—66no—
484Dic3—66no—
485Dic3—126no—
486Dic3#101012yes—
487C32#348211yescharacteristic, complemented, Sylow
488C23—33no—
489C23—92no—
490Q8—66no—
491Q8—1812no—
492Q8#379914yescomplemented
493D4—66no—
494D4—94no—
495D4—1812no—
496C2×C4—31no—
497C2×C4—31no—
498C2×C4—32no—
499C2×C4—33no—
500C2×C4—36no—
501C2×C4—66no—
502C2×C4—66no—
503C2×C4—66no—
504C2×C4—96no—
505C2×C4—184no—
506C2×C4—1812no—
507C2×C4—1812no—
508C2×C4C22×D3213yes—
509C2×C4C22×D3213yes—
510C2×C4C22×D3211yescharacteristic
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—123no—
515C2×C3C22×#23511yescharacteristic
516C2×C3C22×#23911yescharacteristic
517C2×C3C2×D3×#4111yescharacteristic
518C2×C3C2×D3×#4111yescharacteristic
519C2×C3C2×#101011yescharacteristic
520C2×C3D3×2−1+411yescharacteristic
521D3—43no—
522D3—64no—
523D3—64no—
524D3—124no—
525C22—63no—
526C22—63no—
527C22—63no—
528C22—94no—
529C22—182no—
530C22—182no—
531C22C23×D3211yescharacteristic
532C4—23no—
533C4—32no—
534C4—61no—
535C4—63no—
536C4—66no—
537C4—62no—
538C4—186no—
539C4C2×#379916yes—
540C4#6431912yes—
541C3—21no—
542C3#8584411yescharacteristic, complemented
543C3#8701711yescharacteristic, complemented
544C2—123no—
545C2—184no—
546C2C22×#379911yescharacteristic
547C2C2×#6431911yescharacteristic
548C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3482
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×C4⋊(C3⋊D3)C2semidirect
2. C3×C4×#239C2semidirect
3. C3×#5570C2semidirect
4. #10595414C2semidirect
5. Q8×#624C2semidirect
6. #10594584C2semidirect
7. #10594447C2semidirect
8. C4×#3799C2semidirect
9. #10593879C2semidirect
10. #10593869C2semidirect
11. #10593859C2semidirect
61. C4×#239D3semidirect
64. #5570D3semidirect
184. C32×Q8#41semidirect
189. C4⋊(C3⋊D3)#41semidirect
357. C3×Q8#235semidirect
358. C3×Q8#239semidirect
487. C32#3482semidirect
492. Q8#3799semidirect
542. C3#85844semidirect
543. C3#87017semidirect

Maximal subgroups

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

subgroupindex
Q8×C4⋊(C3⋊D3)2
C3×C4×#2392
C3×#55702
#105954142
Q8×#6242
#105945842
#105944472
C4×#37992
#105938792
#105938692
#105938592
#870173
#858443