Finite Group Databasebeta

← #11910001

Subgroups — #11910001

Order 1152.

3090 conjugacy classes of subgroups.

The subgroup lattice has 534 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
5#10596283C211yesmaximal, characteristic, complemented
6#10596153C213yesmaximal, complemented
7#10596152C213yesmaximal, complemented
8#10596110C213yesmaximal, complemented
9#10596095C213yesmaximal, complemented
10#10596090C213yesmaximal, complemented
11#10596085C213yesmaximal, complemented
12#10596045C211yesmaximal, characteristic, complemented
13#10596041C211yesmaximal, characteristic, complemented
14#10596034C213yesmaximal, complemented
15#10596009C213yesmaximal, complemented
16#86723—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C22×C32×Q8C2211yescharacteristic
19C2×#3832C2211yescharacteristic
20C32×#124C2213yes—
21C32×C22⋊Q8C2213yes—
22C32×#121C2213yes—
23C32×C4×Q8C2211yescharacteristic
24C32×C4×D4C2213yes—
25#64156C2213yes—
26#64155C2213yes—
27Q8×C3⋊Dic3C2213yes—
28Q8×C3⋊Dic3C2213yes—
29Q8×C3⋊Dic3C2211yescharacteristic
30Q8×C3⋊Dic3C2211yescharacteristic
31Q8×C3⋊Dic3C2211yescharacteristic
32#64149C2213yes—
33#64148C2213yes—
34#64147C2213yes—
35#64147C2216yes—
36#64144C2213yes—
37D4×C3⋊Dic3C2213yes—
38D4×C3⋊Dic3C2213yes—
39#64139C2213yes—
40#64139C2213yes—
41C4×#638C2213yes—
42C4×#638C2213yes—
43#64135C2213yes—
44#64135C2213yes—
45#64135C2213yes—
46C2×C4×C3⋊Dic3C2213yes—
47#64107C2213yes—
48#64102C2213yes—
49#64101C2216yes—
50C4⋊C4×C3⋊D3C2213yes—
51#64099C2213yes—
52#64099C2213yes—
53#64098C2213yes—
54#64095C2213yes—
55#64095C2216yes—
56#64094C2216yes—
57#64094C2213yes—
58#64092C2216yes—
59#64090C2216yes—
60#64088C2216yes—
61#64088C2211yescharacteristic
62#64087C2213yes—
63C4×C4⋊(C3⋊D3)C2213yes—
64#64081C2213yes—
65#64078C2213yes—
66C4×#634C2213yes—
67C3×#548D314yescomplemented
68#5834—34no—
69Dic3×#41—34no—
70#5817—34no—
71#5812—34no—
72#5682—312no—
73#5681—312no—
74#5639—312no—
75#5624—312no—
76#5619—312no—
77#5614—312no—
78#5574—34no—
79#5570—34no—
80#5563—312no—
81#5538—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×#638C2316yes—
91C2×#638C2313yes—
92C2×#638C2313yes—
93C22×C3⋊Dic3C2313yes—
94C22×C3⋊Dic3C2313yes—
95#3832—24no—
96C2×C4⋊(C3⋊D3)C2313yes—
97C2×C4×C3⋊D3C2313yes—
98C2×C4×C3⋊D3C2316yes—
99C2×#634C2313yes—
100C32×C4⋊C4C2313yes—
101C32×C4⋊C4C2313yes—
102C32×C22⋊C4C2313yes—
103C32×C22⋊C4C2316yes—
104C32×C22⋊C4C2311yescharacteristic
105C32×C42C2313yes—
106#3757C2313yes—
107#3757C2316yes—
108#3757C2311yescharacteristic
109#3757C2311yescharacteristic
110#3757C2313yes—
111#3752C2313yes—
112#3752C2313yes—
113#3752C2313yes—
114#3752C2316yes—
115#3752C2313yes—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2316yes—
118C4⋊(C3⋊Dic3)C2313yes—
119C4⋊(C3⋊Dic3)C2313yes—
120C4⋊(C3⋊Dic3)C2313yes—
121C4⋊(C3⋊Dic3)C2313yes—
122C4⋊(C3⋊Dic3)C2313yes—
123#3750C2313yes—
124#3750C2313yes—
125#3750C2311yescharacteristic
126#3750C2313yes—
127#3750C2313yes—
128#3750C2311yescharacteristic
129C4×C3⋊Dic3C2313yes—
130C4×C3⋊Dic3C2313yes—
131C4×C3⋊Dic3C2313yes—
132C4×C3⋊Dic3C2316yes—
133C4×C3⋊Dic3C2311yescharacteristic
134C4×C3⋊Dic3C2313yes—
135#3524—91noSylow
136C2×C3×#41C2×D314yes—
137C22×C3×Q8C2×D314yes—
138C2×#239—34no—
139C3×#124C2×D3112yes—
140C3×C22⋊Q8C2×D3112yes—
141C3×#121C2×D3112yes—
142C3×C4×Q8C2×D314yes—
143C3×C4×D4C2×D3112yes—
144#947—312no—
145#946—312no—
146Q8×Dic3—312no—
147Q8×Dic3—312no—
148Q8×Dic3—34no—
149Q8×Dic3—34no—
150Q8×Dic3—34no—
151#940—312no—
152#939—312no—
153#938—312no—
154#938—324no—
155#935—312no—
156D4×Dic3—312no—
157D4×Dic3—312no—
158#930—312no—
159#930—312no—
160C4×#67—312no—
161C4×#67—312no—
162#926—312no—
163#926—312no—
164#926—312no—
165C2×C4×Dic3—312no—
166#898—312no—
167#893—312no—
168#892—324no—
169D3×C4⋊C4—312no—
170#890—312no—
171#890—312no—
172#889—312no—
173#886—312no—
174#886—324no—
175#885—324no—
176#885—312no—
177#883—324no—
178#67⋊C4—324no—
179#879—324no—
180#879—34no—
181#878—312no—
182C4×D12—312no—
183#872—312no—
184#869—312no—
185C4×Dic6—312no—
186C23×C32C2411yescharacteristic
187C23×C32C2413yes—
188C22×C3⋊D3C2413yes—
189C32×Q8—26no—
190C32×Q8#4114yes—
191C32×D4—26no—
192C32×D4—43no—
193C2×C32×C4—26no—
194C2×C32×C4—26no—
195C2×C32×C4C2411yescharacteristic
196C2×C32×C4C2413yes—
197C2×C32×C4C2413yes—
198C2×C32×C4C2411yescharacteristic
199C2×C32×C4C2413yes—
200#638—43no—
201#638—46no—
202#638—43no—
203C2×C3⋊Dic3—43no—
204C2×C3⋊Dic3—43no—
205C2×C3⋊Dic3C2411yescharacteristic
206C2×C3⋊Dic3C2411yescharacteristic
207C2×C3⋊Dic3C2413yes—
208C2×C3⋊Dic3C2411yescharacteristic
209C2×C3⋊Dic3C2413yes—
210C2×C3⋊Dic3C2413yes—
211C2×C3⋊Dic3C2411yescharacteristic
212C4⋊(C3⋊D3)—26no—
213C4×C3⋊D3—26no—
214C4×C3⋊D3—46no—
215#634—43no—
216#559—93no—
217#557—91no—
218#555—93no—
219#553—93no—
220#552—93no—
221#550—91no—
222#548—91no—
223#548C3⋊D311yescharacteristic, complemented
224#542—93no—
225#540—93no—
226#529—93no—
227#529—93no—
228#520—91no—
229#519—91no—
230C4×#41—91no—
231C3×#41—216no—
232C2×C3×Q8—216no—
233C2×C3×Q8C22×D3112yes—
234C2×C3×Q8C22×D314yes—
235C2×C3×D4C22×D3112yes—
236C2×C3×D4C22×D3112yes—
237C22×C3×C4C22×D3112yes—
238C22×C3×C4C22×D3112yes—
239C2×#67—324no—
240C2×#67—312no—
241C2×#67—312no—
242C22×Dic3—312no—
243C22×Dic3—312no—
244#239—616no—
245C2×D12—312no—
246C2×C4×D3—312no—
247C2×C4×D3—324no—
248C2×Dic6—312no—
249C3×C4⋊C4C22×D3112yes—
250C3×C4⋊C4C22×D3112yes—
251C3×C22⋊C4C22×D3112yes—
252C3×C22⋊C4C22×D3124yes—
253C3×C22⋊C4C22×D314yes—
254C3×C42C22×D3112yes—
255#217—312no—
256#217—324no—
257#217—34no—
258#217—34no—
259#217—312no—
260(C2×D3)⋊C4—312no—
261(C2×D3)⋊C4—312no—
262(C2×D3)⋊C4—312no—
263(C2×D3)⋊C4—324no—
264(C2×D3)⋊C4—312no—
265C4⋊Dic3—34no—
266C4⋊Dic3—324no—
267C4⋊Dic3—312no—
268C4⋊Dic3—312no—
269C4⋊Dic3—312no—
270C4⋊Dic3—312no—
271C4⋊Dic3—312no—
272Dic3⋊C4—312no—
273Dic3⋊C4—312no—
274Dic3⋊C4—34no—
275Dic3⋊C4—312no—
276Dic3⋊C4—312no—
277Dic3⋊C4—34no—
278C4×Dic3—312no—
279C4×Dic3—312no—
280C4×Dic3—312no—
281C4×Dic3—324no—
282C4×Dic3—34no—
283C4×Dic3—312no—
284C22×C32—21no—
285C22×C32—23no—
286C22×C32—23no—
287C22×C32—23no—
288C22×C32—21no—
289C22×C32—21no—
290C22×C32C2511yescharacteristic
291C2×C3⋊D3—23no—
292C2×C3⋊D3—23no—
293C2×C3⋊D3—23no—
294C32×C4—21no—
295C32×C4—23no—
296C32×C4—21no—
297C32×C4—23no—
298C32×C4C2×#4116yes—
299C3⋊Dic3—21no—
300C3⋊Dic3—23no—
301C3⋊Dic3—23no—
302C3⋊Dic3—23no—
303C3⋊Dic3—21no—
304C3⋊Dic3—21no—
305C3⋊Dic3—21no—
306C2×#41—91no—
307C2×#41C2×C3⋊D311yescharacteristic
308C22×Q8C2×C3⋊D311yescharacteristic
309C4⋊Q8—93no—
310#127—93no—
311#126—93no—
312#126—91no—
313#126—96no—
314#125—93no—
315#125—93no—
316#125—93no—
317#124—93no—
318#124—93no—
319#124—96no—
320#124C2×C3⋊D313yes—
321#123—93no—
322#123—96no—
323#123—93no—
324#123—96no—
325C22⋊Q8—93no—
326C22⋊Q8—93no—
327C22⋊Q8C2×C3⋊D313yes—
328#121—93no—
329#121—96no—
330#121—93no—
331#121—93no—
332#121—93no—
333#121C2×C3⋊D313yes—
334C4×Q8—91no—
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—96no—
347C4×D4—93no—
348C4×D4C2×C3⋊D313yes—
349#117—93no—
350#117—93no—
351#117—93no—
352#117—96no—
353#117—93no—
354C2×C4⋊C4—93no—
355C2×C42—93no—
356C23×C3C23×D314yes—
357C23×C3C23×D3112yes—
358C22×D3—312no—
359C3×Q8—224no—
360C3×Q8#237116yes—
361C3×D4—224no—
362C3×D4—412no—
363C2×C3×C4—224no—
364C2×C3×C4—224no—
365C2×C3×C4C23×D314yes—
366C2×C3×C4C23×D3112yes—
367C2×C3×C4C23×D3112yes—
368C2×C3×C4C23×D314yes—
369C2×C3×C4C23×D3112yes—
370#67—1212no—
371#67—1212no—
372#67—1224no—
373C2×Dic3—34no—
374C2×Dic3—34no—
375C2×Dic3—312no—
376C2×Dic3—34no—
377C2×Dic3—312no—
378C2×Dic3—312no—
379C2×Dic3—34no—
380C2×Dic3—1212no—
381C2×Dic3—1212no—
382D12—624no—
383C4×D3—624no—
384C4×D3—1224no—
385Dic6—1212no—
386C2×C32—41no—
387C2×C32—43no—
388C2×C32C22×#4111yescharacteristic
389C2×C32#58511yescharacteristic
390C2×C32#58511yescharacteristic
391C3⋊D3—43no—
392#41—24no—
393#41—184no—
394C2×Q8—24no—
395C2×Q8—93no—
396C2×Q8C22×C3⋊D313yes—
397C2×Q8C22×C3⋊D311yescharacteristic
398C2×D4—93no—
399C2×D4—96no—
400C2×D4—93no—
401C2×D4—93no—
402C2×D4C22×C3⋊D313yes—
403C2×D4C22×C3⋊D313yes—
404C22×C4—93no—
405C22×C4—93no—
406C22×C4—93no—
407C22×C4—96no—
408C22×C4C22×C3⋊D313yes—
409C22×C4C22×C3⋊D313yes—
410C4⋊C4—93no—
411C4⋊C4—93no—
412C4⋊C4—91no—
413C4⋊C4—93no—
414C4⋊C4—93no—
415C4⋊C4—93no—
416C4⋊C4—93no—
417C4⋊C4—96no—
418C4⋊C4—91no—
419C4⋊C4—93no—
420C4⋊C4—93no—
421C4⋊C4—91no—
422C4⋊C4—93no—
423C4⋊C4C22×C3⋊D313yes—
424C4⋊C4C22×C3⋊D313yes—
425C22⋊C4—91no—
426C22⋊C4—93no—
427C22⋊C4—96no—
428C22⋊C4—91no—
429C22⋊C4—93no—
430C22⋊C4—93no—
431C22⋊C4—93no—
432C22⋊C4—93no—
433C22⋊C4—96no—
434C22⋊C4—93no—
435C22⋊C4C22×C3⋊D316yes—
436C22⋊C4C22×C3⋊D311yescharacteristic
437C22⋊C4C22×C3⋊D313yes—
438C42—91no—
439C42—93no—
440C42—93no—
441C42—93no—
442C42—96no—
443C42—93no—
444C42C22×C3⋊D313yes—
445C22×C3—24no—
446C22×C3—212no—
447C22×C3—212no—
448C22×C3—24no—
449C22×C3—212no—
450C22×C3—24no—
451C22×C3C24×D314yes—
452C2×D3—612no—
453C2×D3—612no—
454C2×D3—612no—
455C3×C4—24no—
456C3×C4—212no—
457C3×C4—212no—
458C3×C4—24no—
459C3×C4C2×#237124yes—
460Dic3—64no—
461Dic3—612no—
462Dic3—64no—
463Dic3—64no—
464Dic3—612no—
465Dic3—612no—
466Dic3—64no—
467C32#352411yescharacteristic, complemented, Sylow
468C23—93no—
469C23C23×C3⋊D311yescharacteristic
470C23C23×C3⋊D313yes—
471Q8—26no—
472Q8—363no—
473Q8#383014yes—
474D4—26no—
475D4—43no—
476D4—186no—
477D4—363no—
478D4—363no—
479D4—366no—
480C2×C4—26no—
481C2×C4—26no—
482C2×C4—91no—
483C2×C4—93no—
484C2×C4—91no—
485C2×C4—93no—
486C2×C4—91no—
487C2×C4—93no—
488C2×C4—91no—
489C2×C4—186no—
490C2×C4—366no—
491C2×C4—363no—
492C2×C4—363no—
493C2×C4C23×C3⋊D311yescharacteristic
494C2×C4C23×C3⋊D313yes—
495C2×C4C23×C3⋊D311yescharacteristic
496C2×C4C23×C3⋊D313yes—
497C2×C4C23×C3⋊D313yes—
498C2×C3—44no—
499C2×C3—412no—
500C2×C3C22×#23714yes—
501C2×C3#596414yes—
502C2×C3#596814yes—
503D3—1212no—
504C22—21no—
505C22—23no—
506C22—23no—
507C22—21no—
508C22—23no—
509C22—21no—
510C22—183no—
511C22—183no—
512C22—183no—
513C22C24×C3⋊D311yescharacteristic
514C4—21no—
515C4—23no—
516C4—23no—
517C4—21no—
518C4—181no—
519C4—183no—
520C4—181no—
521C4—181no—
522C4—181no—
523C4—183no—
524C4—183no—
525C4C2×#383016yes—
526C3#8672314yescomplemented
527C2—41no—
528C2—43no—
529C2—363no—
530C2C22×#383011yescharacteristic
531C2#1059675611yescharacteristic
532C2#1059676011yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#548C2
hypercenter#548C3⋊D3
hypocenterC32#3524
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. #10596283C2semidirect
6. #10596153C2semidirect
7. #10596152C2semidirect
8. #10596110C2semidirect
9. #10596095C2semidirect
10. #10596090C2semidirect
11. #10596085C2semidirect
12. #10596045C2semidirect
13. #10596041C2semidirect
14. #10596034C2semidirect
15. #10596009C2semidirect
67. C3×#548D3semidirect
223. #548C3⋊D3semidirect
467. C32#3524semidirect
526. C3#86723semidirect

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
#105962832
#105961532
#105961522
#105961102
#105960952
#105960902
#105960852
#105960452
#105960412
#105960342
#105960092
#867233