Finite Group Databasebeta

← #11903850

Subgroups — #11903850

Order 1152.

3336 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#548C211yesmaximal, characteristic, complemented
2#10596305C211yesmaximal, characteristic, complemented
3#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#10596288C211yesmaximal, characteristic, complemented
5C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#10596152C213yesmaximal, complemented
7#10596151C213yesmaximal, complemented
8#10596112C213yesmaximal, complemented
9#10596095C213yesmaximal, complemented
10#10596089C213yesmaximal, complemented
11#10596067C213yesmaximal, complemented
12C4×#3832C211yesmaximal, characteristic, complemented
13#10596040C211yesmaximal, characteristic, complemented
14#10596036C213yesmaximal, complemented
15C4×#3830C213yesmaximal, complemented
16#86711—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C22×C32×Q8C2211yescharacteristic
19C2×#3832C2211yescharacteristic
20C2×#3830C2213yes—
21C32×#124C2213yes—
22C32×C22⋊Q8C2213yes—
23C32×#121C2213yes—
24C32×C4×Q8C2211yescharacteristic
25C32×C4×D4C2213yes—
26#64156C2213yes—
27#64155C2213yes—
28Q8×C3⋊Dic3C2213yes—
29Q8×C3⋊Dic3C2213yes—
30Q8×C3⋊Dic3C2211yescharacteristic
31Q8×C3⋊Dic3C2211yescharacteristic
32Q8×C3⋊Dic3C2211yescharacteristic
33#64149C2213yes—
34#64148C2216yes—
35#64147C2213yes—
36D4×C3⋊Dic3C2213yes—
37D4×C3⋊Dic3C2213yes—
38D4×C3⋊Dic3C2213yes—
39#64139C2213yes—
40#64139C2213yes—
41C4×#638C2213yes—
42C4×#638C2213yes—
43#64135C2213yes—
44C2×C4⋊(C3⋊Dic3)C2213yes—
45C2×C4×C3⋊Dic3C2213yes—
46C2×C4×C3⋊Dic3C2213yes—
47#64107C2216yes—
48#64102C2213yes—
49#64101C2213yes—
50#64101C2213yes—
51#64099C2213yes—
52#64097C2213yes—
53#64096C2213yes—
54#64095C2216yes—
55#64094C2216yes—
56#64092C2216yes—
57#64090C2216yes—
58#64090C2213yes—
59#64090C2213yes—
60#64088C2216yes—
61#64086C2213yes—
62#64086C2211yescharacteristic
63C4×C4⋊(C3⋊D3)C2213yes—
64C42×C3⋊D3C2213yes—
65#64079C2213yes—
66C4×#634C2213yes—
67C3×#548D314yescomplemented
68#5834—34no—
69Dic3×#41—34no—
70#5817—34no—
71C2×Q8×Dic3—34no—
72#5681—312no—
73#5680—312no—
74#5641—312no—
75#5624—312no—
76#5618—312no—
77#5596—312no—
78C4×#239—34no—
79#5569—34no—
80#5565—312no—
81C4×#237—312no—
82C32×#41—24no—
83C2×C32×Q8—24no—
84C2×C32×Q8C2313yes—
85C2×C32×Q8C2311yescharacteristic
86C2×C32×D4C2313yes—
87C2×C32×D4C2313yes—
88C22×C32×C4C2313yes—
89C22×C32×C4C2313yes—
90C2×#638C2313yes—
91C2×#638C2313yes—
92C2×#638C2316yes—
93C22×C3⋊Dic3C2313yes—
94C22×C3⋊Dic3C2313yes—
95C22×C3⋊Dic3C2313yes—
96C22×C3⋊Dic3C2311yescharacteristic
97#3832—24no—
98#3830—212no—
99C2×C4⋊(C3⋊D3)C2313yes—
100C2×C4×C3⋊D3C2313yes—
101C2×C4×C3⋊D3C2313yes—
102C2×C4×C3⋊D3C2313yes—
103C2×#634C2313yes—
104C32×C4⋊C4C2313yes—
105C32×C4⋊C4C2313yes—
106C32×C22⋊C4C2311yescharacteristic
107C32×C22⋊C4C2313yes—
108C32×C22⋊C4C2316yes—
109C32×C42C2313yes—
110#3757C2313yes—
111#3757C2311yescharacteristic
112#3757C2316yes—
113#3752C2316yes—
114#3752C2316yes—
115#3752C2313yes—
116#3752C2313yes—
117C4⋊(C3⋊Dic3)C2313yes—
118C4⋊(C3⋊Dic3)C2313yes—
119C4⋊(C3⋊Dic3)C2313yes—
120C4⋊(C3⋊Dic3)C2313yes—
121C4⋊(C3⋊Dic3)C2316yes—
122#3750C2311yescharacteristic
123#3750C2313yes—
124#3750C2316yes—
125#3750C2313yes—
126#3750C2311yescharacteristic
127C4×C3⋊Dic3C2313yes—
128C4×C3⋊Dic3C2313yes—
129C4×C3⋊Dic3C2311yescharacteristic
130C4×C3⋊Dic3C2313yes—
131C4×C3⋊Dic3C2313yes—
132C4×C3⋊Dic3C2313yes—
133C4×C3⋊Dic3C2311yescharacteristic
134C4×C3⋊Dic3C2313yes—
135C4×C3⋊Dic3C2313yes—
136#3480—91noSylow
137C2×C3×#41C2×D314yes—
138C22×C3×Q8C2×D314yes—
139C2×#239—34no—
140C2×#237—312no—
141C3×#124C2×D3112yes—
142C3×C22⋊Q8C2×D3112yes—
143C3×#121C2×D3112yes—
144C3×C4×Q8C2×D314yes—
145C3×C4×D4C2×D3112yes—
146#947—312no—
147#946—312no—
148Q8×Dic3—312no—
149Q8×Dic3—312no—
150Q8×Dic3—34no—
151Q8×Dic3—34no—
152Q8×Dic3—34no—
153#940—312no—
154#939—324no—
155#938—312no—
156D4×Dic3—312no—
157D4×Dic3—312no—
158D4×Dic3—312no—
159#930—312no—
160#930—312no—
161C4×#67—312no—
162C4×#67—312no—
163#926—312no—
164C2×C4⋊Dic3—312no—
165C2×C4×Dic3—312no—
166C2×C4×Dic3—312no—
167#898—324no—
168#893—312no—
169#892—312no—
170#892—312no—
171#890—312no—
172#888—312no—
173#887—312no—
174#886—324no—
175#885—324no—
176#883—324no—
177#67⋊C4—324no—
178#67⋊C4—312no—
179#67⋊C4—312no—
180#879—324no—
181#877—312no—
182#877—34no—
183C4×D12—312no—
184C42×D3—312no—
185#870—312no—
186C4×Dic6—312no—
187C23×C32C2413yes—
188C23×C32C2411yescharacteristic
189C22×C3⋊D3C2413yes—
190C32×Q8—26no—
191C32×Q8#4114yescomplemented
192C32×D4—26no—
193C32×D4—26no—
194C2×C32×C4—26no—
195C2×C32×C4—26no—
196C2×C32×C4C2411yescharacteristic
197C2×C32×C4C2413yes—
198C2×C32×C4C2411yescharacteristic
199C2×C32×C4C2413yes—
200C2×C32×C4C2413yes—
201#638—26no—
202#638—26no—
203#638—46no—
204C2×C3⋊Dic3—26no—
205C2×C3⋊Dic3—43no—
206C2×C3⋊Dic3—43no—
207C2×C3⋊Dic3#4114yescomplemented
208C2×C3⋊Dic3C2411yescharacteristic
209C2×C3⋊Dic3C2411yescharacteristic
210C2×C3⋊Dic3C2413yes—
211C2×C3⋊Dic3C2413yes—
212C2×C3⋊Dic3C2413yes—
213C2×C3⋊Dic3C2411yescharacteristic
214C2×C3⋊Dic3C2411yescharacteristic
215C4⋊(C3⋊D3)—26no—
216C4×C3⋊D3—26no—
217C4×C3⋊D3—26no—
218C4×C3⋊D3—43no—
219#634—26no—
220#559—93no—
221#557—91no—
222#556—93no—
223#553—93no—
224#553—93no—
225#550—91no—
226#548—91no—
227#548C3⋊D311yescharacteristic, complemented
228#532—93no—
229#529—93no—
230#529—93no—
231C4×#41—91no—
232C4×#41—91no—
233C4×#41—93no—
234C2×C4×Q8—91no—
235C3×#41—216no—
236C2×C3×Q8—216no—
237C2×C3×Q8C22×D3112yes—
238C2×C3×Q8C22×D314yes—
239C2×C3×D4C22×D3112yes—
240C2×C3×D4C22×D3112yes—
241C22×C3×C4C22×D3112yes—
242C22×C3×C4C22×D3112yes—
243C2×#67—312no—
244C2×#67—312no—
245C2×#67—324no—
246C22×Dic3—34no—
247C22×Dic3—312no—
248C22×Dic3—312no—
249C22×Dic3—312no—
250#239—616no—
251#237—648no—
252C2×D12—312no—
253C2×C4×D3—312no—
254C2×C4×D3—312no—
255C2×C4×D3—312no—
256C2×Dic6—312no—
257C3×C4⋊C4C22×D3112yes—
258C3×C4⋊C4C22×D3112yes—
259C3×C22⋊C4C22×D314yes—
260C3×C22⋊C4C22×D3112yes—
261C3×C22⋊C4C22×D3124yes—
262C3×C42C22×D3112yes—
263#217—312no—
264#217—34no—
265#217—324no—
266(C2×D3)⋊C4—324no—
267(C2×D3)⋊C4—324no—
268(C2×D3)⋊C4—312no—
269(C2×D3)⋊C4—312no—
270C4⋊Dic3—312no—
271C4⋊Dic3—312no—
272C4⋊Dic3—312no—
273C4⋊Dic3—312no—
274C4⋊Dic3—324no—
275Dic3⋊C4—34no—
276Dic3⋊C4—312no—
277Dic3⋊C4—324no—
278Dic3⋊C4—312no—
279Dic3⋊C4—34no—
280C4×Dic3—312no—
281C4×Dic3—312no—
282C4×Dic3—34no—
283C4×Dic3—312no—
284C4×Dic3—312no—
285C4×Dic3—312no—
286C4×Dic3—34no—
287C4×Dic3—312no—
288C4×Dic3—312no—
289C22×C32—21no—
290C22×C32—21no—
291C22×C32—23no—
292C22×C32—23no—
293C22×C32—23no—
294C22×C32C2×#4112yes—
295C22×C32C2511yescharacteristic
296C2×C3⋊D3—23no—
297C2×C3⋊D3—23no—
298C2×C3⋊D3—23no—
299C32×C4—23no—
300C32×C4—21no—
301C32×C4—23no—
302C32×C4—21no—
303C32×C4C2×#4116yes—
304C3⋊Dic3—23no—
305C3⋊Dic3—21no—
306C3⋊Dic3—23no—
307C3⋊Dic3—21no—
308C3⋊Dic3—23no—
309C3⋊Dic3C2×#4112yes—
310C3⋊Dic3C2×#4112yes—
311C2×#41—91no—
312C2×#41—93no—
313C2×#41C2×C3⋊D311yescharacteristic
314C22×Q8C2×C3⋊D311yescharacteristic
315C4⋊Q8—93no—
316#127—93no—
317#126—96no—
318#126—96no—
319#125—93no—
320#125—93no—
321#124—93no—
322#124—96no—
323#124C2×C3⋊D313yes—
324#123—96no—
325#123—96no—
326C22⋊Q8—93no—
327C22⋊Q8C2×C3⋊D313yes—
328#121—93no—
329#121—96no—
330#121—93no—
331#121—93no—
332#121C2×C3⋊D313yes—
333C4×Q8—91no—
334C4×Q8—93no—
335C4×Q8—91no—
336C4×Q8—93no—
337C4×Q8—91no—
338C4×Q8—93no—
339C4×Q8—93no—
340C4×Q8C2×C3⋊D311yescharacteristic
341C4×D4—93no—
342C4×D4—93no—
343C4×D4—93no—
344C4×D4—93no—
345C4×D4—93no—
346C4×D4—93no—
347C4×D4—93no—
348C4×D4—93no—
349C4×D4—96no—
350C4×D4—93no—
351C4×D4C2×C3⋊D313yes—
352#117—93no—
353#117—93no—
354#117—93no—
355#117—91no—
356#117—93no—
357C2×C4⋊C4—93no—
358C2×C42—93no—
359C2×C42—93no—
360C2×C42—93no—
361C23×C3C23×D3112yes—
362C23×C3C23×D314yes—
363C22×D3—312no—
364C3×Q8—224no—
365C3×Q8#237116yescomplemented
366C3×D4—224no—
367C3×D4—224no—
368C2×C3×C4—224no—
369C2×C3×C4—224no—
370C2×C3×C4C23×D314yes—
371C2×C3×C4C23×D3112yes—
372C2×C3×C4C23×D314yes—
373C2×C3×C4C23×D3112yes—
374C2×C3×C4C23×D3112yes—
375#67—624no—
376#67—624no—
377#67—1224no—
378C2×Dic3—316no—
379C2×Dic3—34no—
380C2×Dic3—34no—
381C2×Dic3—34no—
382C2×Dic3—34no—
383C2×Dic3—312no—
384C2×Dic3—312no—
385C2×Dic3—312no—
386C2×Dic3—624no—
387C2×Dic3—1212no—
388C2×Dic3—1212no—
389D12—624no—
390C4×D3—624no—
391C4×D3—624no—
392C4×D3—1212no—
393Dic6—624no—
394C2×C32—22no—
395C2×C32—43no—
396C2×C32C22×#4111yescharacteristic
397C2×C32C22×#4111yescharacteristic
398C2×C32#58511yescharacteristic
399C3⋊D3—43no—
400#41—24no—
401#41—1812no—
402#41—184no—
403C2×Q8—24no—
404C2×Q8—93no—
405C2×Q8C22×C3⋊D313yes—
406C2×Q8C22×C3⋊D311yescharacteristic
407C2×D4—93no—
408C2×D4—93no—
409C2×D4—96no—
410C2×D4—93no—
411C2×D4C22×C3⋊D313yes—
412C2×D4C22×C3⋊D313yes—
413C22×C4—91no—
414C22×C4—93no—
415C22×C4—93no—
416C22×C4—93no—
417C22×C4—93no—
418C22×C4—93no—
419C22×C4—93no—
420C22×C4C22×C3⋊D313yes—
421C22×C4C22×C3⋊D313yes—
422C4⋊C4—93no—
423C4⋊C4—93no—
424C4⋊C4—96no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—93no—
428C4⋊C4—93no—
429C4⋊C4—93no—
430C4⋊C4—93no—
431C4⋊C4—96no—
432C4⋊C4C22×C3⋊D313yes—
433C4⋊C4C22×C3⋊D313yes—
434C22⋊C4—91no—
435C22⋊C4—93no—
436C22⋊C4—96no—
437C22⋊C4—93no—
438C22⋊C4—96no—
439C22⋊C4—93no—
440C22⋊C4—96no—
441C22⋊C4C22×C3⋊D311yescharacteristic
442C22⋊C4C22×C3⋊D313yes—
443C22⋊C4C22×C3⋊D316yes—
444C42—91no—
445C42—91no—
446C42—93no—
447C42—93no—
448C42—93no—
449C42—93no—
450C42—93no—
451C42—93no—
452C42—93no—
453C42C22×C3⋊D313yes—
454C22×C3—24no—
455C22×C3—24no—
456C22×C3—212no—
457C22×C3—212no—
458C22×C3—212no—
459C22×C3D3×#4118yes—
460C22×C3C24×D314yes—
461C2×D3—612no—
462C2×D3—612no—
463C2×D3—612no—
464C3×C4—24no—
465C3×C4—212no—
466C3×C4—212no—
467C3×C4—24no—
468C3×C4C2×#237124yes—
469Dic3—38no—
470Dic3—38no—
471Dic3—64no—
472Dic3—612no—
473Dic3—612no—
474Dic3—64no—
475Dic3—612no—
476C32#348011yescharacteristic, complemented, Sylow
477C23—93no—
478C23C23×C3⋊D313yes—
479C23C23×C3⋊D311yescharacteristic
480Q8—26no—
481Q8—186no—
482Q8#383014yescomplemented
483D4—26no—
484D4—26no—
485D4—186no—
486D4—186no—
487D4—186no—
488D4—366no—
489C2×C4—26no—
490C2×C4—26no—
491C2×C4—94no—
492C2×C4—91no—
493C2×C4—91no—
494C2×C4—91no—
495C2×C4—91no—
496C2×C4—93no—
497C2×C4—93no—
498C2×C4—93no—
499C2×C4—186no—
500C2×C4—186no—
501C2×C4—186no—
502C2×C4—363no—
503C2×C4—363no—
504C2×C4—363no—
505C2×C4C23×C3⋊D311yescharacteristic
506C2×C4C23×C3⋊D313yes—
507C2×C4C23×C3⋊D311yescharacteristic
508C2×C4C23×C3⋊D313yes—
509C2×C4C23×C3⋊D313yes—
510C2×C3—28no—
511C2×C3—412no—
512C2×C3C22×#23714yes—
513C2×C3C2×D3×#4114yes—
514C2×C3#596814yes—
515D3—1212no—
516C22—21no—
517C22—21no—
518C22—23no—
519C22—23no—
520C22—23no—
521C22—183no—
522C22—183no—
523C22—183no—
524C22#41×C3⋊D312yes—
525C22C24×C3⋊D311yescharacteristic
526C4—21no—
527C4—23no—
528C4—23no—
529C4—21no—
530C4—92no—
531C4—92no—
532C4—181no—
533C4—183no—
534C4—183no—
535C4—181no—
536C4—183no—
537C4C2×#383016yes—
538C3#8671114yescomplemented
539C2—22no—
540C2—43no—
541C2—363no—
542C2C22×#383011yescharacteristic
543C2C2×#41×C3⋊D311yescharacteristic
544C2#1059676011yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#548C2
hypercenter#548C3⋊D3
hypocenterC32#3480
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C32×#548C2semidirect
2. #10596305C2semidirect
3. #41×C3⋊Dic3C2semidirect
4. #10596288C2semidirect
5. C2×Q8×C3⋊Dic3C2semidirect
6. #10596152C2semidirect
7. #10596151C2semidirect
8. #10596112C2semidirect
9. #10596095C2semidirect
10. #10596089C2semidirect
11. #10596067C2semidirect
12. C4×#3832C2semidirect
13. #10596040C2semidirect
14. #10596036C2semidirect
15. C4×#3830C2semidirect
67. C3×#548D3semidirect
191. C32×Q8#41semidirect
207. C2×C3⋊Dic3#41semidirect
227. #548C3⋊D3semidirect
365. C3×Q8#237semidirect
476. C32#3480semidirect
482. Q8#3830semidirect
538. C3#86711semidirect

Maximal subgroups

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

subgroupindex
C32×#5482
#105963052
#41×C3⋊Dic32
#105962882
C2×Q8×C3⋊Dic32
#105961522
#105961512
#105961122
#105960952
#105960892
#105960672
C4×#38322
#105960402
#105960362
C4×#38302
#867113