Finite Group Databasebeta

← #11909974

Subgroups — #11909974

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×#520C211yesmaximal, characteristic, complemented
2#10596305C211yesmaximal, characteristic, complemented
3#10596302C211yesmaximal, characteristic, complemented
4#10596047C211yesmaximal, characteristic, complemented
5C4×#3832C211yesmaximal, characteristic, complemented
6#10596043C211yesmaximal, characteristic, complemented
7#10596041C211yesmaximal, characteristic, complemented
8#10596034C213yesmaximal, complemented
9#10596033C213yesmaximal, complemented
10#10596030C213yesmaximal, complemented
11#10596028C213yesmaximal, complemented
12#10596005C213yesmaximal, complemented
13#10595999C213yesmaximal, complemented
14#10595985C213yesmaximal, complemented
15#10595984C213yesmaximal, complemented
16#85898—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×#3832C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C32×C4×D4C2213yes—
23C32×C4×D4C2213yes—
24C32×#117C2213yes—
25C2×C32×C4⋊C4C2213yes—
26Q8×C3⋊Dic3C2211yescharacteristic
27Q8×C3⋊Dic3C2211yescharacteristic
28#64149C2213yes—
29#64147C2213yes—
30#64147C2213yes—
31#64145C2213yes—
32#64139C2213yes—
33#64139C2216yes—
34#64138C2216yes—
35C4×#638C2213yes—
36C4×#638C2213yes—
37C4×#638C2216yes—
38#64135C2216yes—
39#64133C2213yes—
40#64107C2216yes—
41#64107C2211yescharacteristic
42#64106C2213yes—
43#64105C2213yes—
44#64104C2213yes—
45#64103C2213yes—
46#64102C2213yes—
47#64101C2213yes—
48#64101C2213yes—
49#64099C2213yes—
50#64099C2213yes—
51#64098C2213yes—
52#64096C2213yes—
53#64094C2213yes—
54#64094C2216yes—
55#64093C2213yes—
56#64092C2213yes—
57#64092C2216yes—
58#64088C2213yes—
59#64084C2213yes—
60C4×C4⋊(C3⋊D3)C2213yes—
61C4×C4⋊(C3⋊D3)C2213yes—
62#64081C2213yes—
63C42×C3⋊D3C2213yes—
64#64078C2213yes—
65C4×#634C2213yes—
66C4×#634C2213yes—
67C3×#520D314yescomplemented
68#5834—34no—
69#5831—34no—
70#5576—34no—
71C4×#239—34no—
72#5572—34no—
73#5570—34no—
74#5563—312no—
75#5562—312no—
76#5559—312no—
77#5557—312no—
78#5534—312no—
79#5528—312no—
80#5514—312no—
81#5513—312no—
82C32×#41—24no—
83C2×C32×Q8C2311yescharacteristic
84C2×C32×D4C2313yes—
85C22×C32×C4C2313yes—
86C22×C32×C4C2316yes—
87C2×#638C2313yes—
88C2×#638C2316yes—
89C2×#638C2313yes—
90#3832—24no—
91Q8×C3⋊D3—24no—
92C2×C4⋊(C3⋊D3)C2313yes—
93C2×C4⋊(C3⋊D3)C2313yes—
94C2×C4×C3⋊D3C2313yes—
95C2×C4×C3⋊D3C2313yes—
96C2×C4×C3⋊D3C2313yes—
97C2×C4×C3⋊D3C2313yes—
98C2×#634C2313yes—
99C2×#634C2313yes—
100C32×C4⋊C4C2313yes—
101C32×C4⋊C4C2313yes—
102C32×C4⋊C4C2313yes—
103C32×C4⋊C4C2311yescharacteristic
104C32×C22⋊C4C2313yes—
105C32×C22⋊C4C2313yes—
106C32×C42C2313yes—
107C32×C42C2313yes—
108#3757C2313yes—
109#3757C2313yes—
110#3757C2316yes—
111#3752C2311yescharacteristic
112#3752C2313yes—
113#3752C2311yescharacteristic
114#3752C2313yes—
115#3752C2316yes—
116#3752C2316yes—
117#3752C2311yescharacteristic
118#3752C2313yes—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2313yes—
121C4⋊(C3⋊Dic3)C2313yes—
122C4⋊(C3⋊Dic3)C2316yes—
123C4⋊(C3⋊Dic3)C2313yes—
124#3750C2313yes—
125#3750C2313yes—
126#3750C2313yes—
127#3750C2313yes—
128#3750C2311yescharacteristic
129#3750C2313yes—
130C4×C3⋊Dic3C2313yes—
131C4×C3⋊Dic3C2313yes—
132C4×C3⋊Dic3C2316yes—
133C4×C3⋊Dic3C2311yescharacteristic
134C4×C3⋊Dic3C2313yes—
135#3524—91noSylow
136C2×C3×#41C2×D314yes—
137C2×#239—34no—
138C2×D3×Q8—34no—
139C3×C4×Q8C2×D314yes—
140C3×C4×Q8C2×D314yes—
141C3×C4×D4C2×D3112yes—
142C3×C4×D4C2×D3112yes—
143C3×#117C2×D3112yes—
144C2×C3×C4⋊C4C2×D3112yes—
145Q8×Dic3—34no—
146Q8×Dic3—34no—
147#940—312no—
148#938—312no—
149#938—312no—
150#936—312no—
151#930—312no—
152#930—324no—
153#929—324no—
154C4×#67—312no—
155C4×#67—312no—
156C4×#67—324no—
157#926—324no—
158#924—312no—
159#898—324no—
160#898—34no—
161#897—312no—
162#896—312no—
163#895—312no—
164#894—312no—
165#893—312no—
166#892—312no—
167#892—312no—
168#890—312no—
169#890—312no—
170#889—312no—
171#887—312no—
172#885—312no—
173#885—324no—
174#884—312no—
175#883—312no—
176#883—324no—
177#879—312no—
178#875—312no—
179C4×D12—312no—
180C4×D12—312no—
181#872—312no—
182C42×D3—312no—
183#869—312no—
184C4×Dic6—312no—
185C4×Dic6—312no—
186C23×C32C2413yes—
187C22×C3⋊D3C2411yescharacteristic
188C22×C3⋊D3C2413yes—
189C32×Q8#4114yes—
190C32×D4—26no—
191C2×C32×C4—26no—
192C2×C32×C4—46no—
193C2×C32×C4C2413yes—
194C2×C32×C4C2411yescharacteristic
195C2×C32×C4C2411yescharacteristic
196C2×C32×C4C2413yes—
197C2×C32×C4C2411yescharacteristic
198C2×C32×C4C2413yes—
199#638—43no—
200#638—46no—
201#638—43no—
202C2×C3⋊Dic3C2411yescharacteristic
203C2×C3⋊Dic3C2411yescharacteristic
204C2×C3⋊Dic3C2411yescharacteristic
205C2×C3⋊Dic3C2413yes—
206C2×C3⋊Dic3C2413yes—
207C2×C3⋊Dic3C2413yes—
208C4⋊(C3⋊D3)—26no—
209C4⋊(C3⋊D3)—43no—
210C4×C3⋊D3—26no—
211C4×C3⋊D3—26no—
212C4×C3⋊D3—43no—
213C4×C3⋊D3—43no—
214#634—26no—
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#548—91no—
224#542—93no—
225#540—93no—
226#529—93no—
227#529—93no—
228#520C3⋊D311yescharacteristic, complemented
229#519—91no—
230C4×#41—91no—
231C3×#41—216no—
232C2×C3×Q8C22×D314yes—
233C2×C3×D4C22×D3112yes—
234C22×C3×C4C22×D3112yes—
235C22×C3×C4C22×D3124yes—
236C2×#67—312no—
237C2×#67—324no—
238C2×#67—312no—
239#239—616no—
240D3×Q8—616no—
241C2×D12—312no—
242C2×D12—312no—
243C2×C4×D3—312no—
244C2×C4×D3—312no—
245C2×C4×D3—312no—
246C2×C4×D3—312no—
247C2×Dic6—312no—
248C2×Dic6—312no—
249C3×C4⋊C4C22×D3112yes—
250C3×C4⋊C4C22×D3112yes—
251C3×C4⋊C4C22×D3112yes—
252C3×C4⋊C4C22×D314yes—
253C3×C22⋊C4C22×D3112yes—
254C3×C22⋊C4C22×D3112yes—
255C3×C42C22×D3112yes—
256C3×C42C22×D3112yes—
257#217—312no—
258#217—312no—
259#217—324no—
260(C2×D3)⋊C4—34no—
261(C2×D3)⋊C4—312no—
262(C2×D3)⋊C4—34no—
263(C2×D3)⋊C4—312no—
264(C2×D3)⋊C4—324no—
265(C2×D3)⋊C4—324no—
266(C2×D3)⋊C4—34no—
267(C2×D3)⋊C4—312no—
268C4⋊Dic3—34no—
269C4⋊Dic3—312no—
270C4⋊Dic3—312no—
271C4⋊Dic3—324no—
272C4⋊Dic3—312no—
273Dic3⋊C4—312no—
274Dic3⋊C4—312no—
275Dic3⋊C4—312no—
276Dic3⋊C4—312no—
277Dic3⋊C4—34no—
278Dic3⋊C4—312no—
279C4×Dic3—312no—
280C4×Dic3—312no—
281C4×Dic3—324no—
282C4×Dic3—34no—
283C4×Dic3—312no—
284C22×C32—23no—
285C22×C32—23no—
286C22×C32—23no—
287C22×C32C2511yescharacteristic
288C2×C3⋊D3—21no—
289C2×C3⋊D3—23no—
290C2×C3⋊D3—23no—
291C2×C3⋊D3—23no—
292C2×C3⋊D3—21no—
293C2×C3⋊D3—21no—
294C32×C4—21no—
295C32×C4—21no—
296C32×C4—21no—
297C32×C4—23no—
298C32×C4—23no—
299C32×C4C2×#4116yes—
300C3⋊Dic3—23no—
301C3⋊Dic3—21no—
302C3⋊Dic3—23no—
303C3⋊Dic3—23no—
304C3⋊Dic3—21no—
305C3⋊Dic3—21no—
306C2×#41—91no—
307C2×#41C2×C3⋊D311yescharacteristic
308C22×Q8—91no—
309C4⋊Q8—93no—
310#127—93no—
311#126—91no—
312#126—96no—
313#126—93no—
314#125—93no—
315#125—93no—
316#125—93no—
317#124—93no—
318#124—93no—
319#124—96no—
320#124—93no—
321#123—96no—
322#123—93no—
323#123—96no—
324#123—93no—
325C22⋊Q8—93no—
326C22⋊Q8—93no—
327C22⋊Q8—93no—
328#121—93no—
329#121—93no—
330#121—96no—
331#121—93no—
332#121—93no—
333#121—93no—
334C4×Q8—91no—
335C4×Q8—91no—
336C4×Q8—93no—
337C4×Q8—93no—
338C4×Q8—93no—
339C4×Q8C2×C3⋊D311yescharacteristic
340C4×Q8C2×C3⋊D311yescharacteristic
341C4×D4—93no—
342C4×D4—93no—
343C4×D4—96no—
344C4×D4—93no—
345C4×D4—93no—
346C4×D4—93no—
347C4×D4C2×C3⋊D313yes—
348C4×D4C2×C3⋊D313yes—
349#117—96no—
350#117—93no—
351#117—93no—
352#117—93no—
353#117C2×C3⋊D313yes—
354C2×C4⋊C4C2×C3⋊D313yes—
355C2×C42—93no—
356C23×C3C23×D3112yes—
357C22×D3—34no—
358C22×D3—312no—
359C3×Q8#235116yes—
360C3×D4—224no—
361C2×C3×C4—224no—
362C2×C3×C4—424no—
363C2×C3×C4C23×D3112yes—
364C2×C3×C4C23×D314yes—
365C2×C3×C4C23×D314yes—
366C2×C3×C4C23×D3112yes—
367C2×C3×C4C23×D314yes—
368C2×C3×C4C23×D3112yes—
369#67—1212no—
370#67—1212no—
371#67—1224no—
372C2×Dic3—34no—
373C2×Dic3—34no—
374C2×Dic3—34no—
375C2×Dic3—312no—
376C2×Dic3—312no—
377C2×Dic3—312no—
378D12—624no—
379D12—1212no—
380C4×D3—624no—
381C4×D3—624no—
382C4×D3—1212no—
383C4×D3—1212no—
384Dic6—624no—
385Dic6—1212no—
386C2×C32—43no—
387C2×C32C22×#4111yescharacteristic
388C2×C32#58511yescharacteristic
389C2×C32#58511yescharacteristic
390C3⋊D3—41no—
391C3⋊D3—43no—
392#41—24no—
393#41—184no—
394C2×Q8—93no—
395C2×Q8—93no—
396C2×Q8—184no—
397C2×Q8C22×C3⋊D311yescharacteristic
398C2×D4—93no—
399C2×D4—96no—
400C2×D4—93no—
401C2×D4—93no—
402C2×D4—93no—
403C2×D4C22×C3⋊D313yes—
404C22×C4—93no—
405C22×C4—93no—
406C22×C4—93no—
407C22×C4—93no—
408C22×C4C22×C3⋊D313yes—
409C22×C4C22×C3⋊D316yes—
410C4⋊C4—93no—
411C4⋊C4—93no—
412C4⋊C4—93no—
413C4⋊C4—93no—
414C4⋊C4—93no—
415C4⋊C4—96no—
416C4⋊C4—91no—
417C4⋊C4—93no—
418C4⋊C4—93no—
419C4⋊C4—91no—
420C4⋊C4—93no—
421C4⋊C4C22×C3⋊D313yes—
422C4⋊C4C22×C3⋊D313yes—
423C4⋊C4C22×C3⋊D313yes—
424C4⋊C4C22×C3⋊D311yescharacteristic
425C22⋊C4—93no—
426C22⋊C4—96no—
427C22⋊C4—93no—
428C22⋊C4—91no—
429C22⋊C4—93no—
430C22⋊C4—96no—
431C22⋊C4—91no—
432C22⋊C4—91no—
433C22⋊C4—93no—
434C22⋊C4—96no—
435C22⋊C4—93no—
436C22⋊C4C22×C3⋊D313yes—
437C22⋊C4C22×C3⋊D313yes—
438C42—91no—
439C42—93no—
440C42—93no—
441C42—96no—
442C42—93no—
443C42C22×C3⋊D313yes—
444C42C22×C3⋊D313yes—
445C22×C3—212no—
446C22×C3—212no—
447C22×C3—212no—
448C22×C3C24×D314yes—
449C2×D3—64no—
450C2×D3—612no—
451C2×D3—612no—
452C2×D3—64no—
453C2×D3—612no—
454C2×D3—64no—
455C3×C4—24no—
456C3×C4—212no—
457C3×C4—212no—
458C3×C4—24no—
459C3×C4—24no—
460C3×C4C2×#235124yes—
461Dic3—612no—
462Dic3—64no—
463Dic3—64no—
464Dic3—64no—
465Dic3—612no—
466Dic3—612no—
467C32#352411yescharacteristic, complemented, Sylow
468C23—91no—
469C23—93no—
470C23C23×C3⋊D313yes—
471Q8—186no—
472Q8—363no—
473Q8#382814yes—
474D4—26no—
475D4—186no—
476D4—363no—
477D4—363no—
478D4—363no—
479D4—366no—
480C2×C4—26no—
481C2×C4—46no—
482C2×C4—91no—
483C2×C4—91no—
484C2×C4—93no—
485C2×C4—91no—
486C2×C4—93no—
487C2×C4—93no—
488C2×C4—186no—
489C2×C4—186no—
490C2×C4—363no—
491C2×C4—363no—
492C2×C4C23×C3⋊D313yes—
493C2×C4C23×C3⋊D311yescharacteristic
494C2×C4C23×C3⋊D311yescharacteristic
495C2×C4C23×C3⋊D313yes—
496C2×C4C23×C3⋊D311yescharacteristic
497C2×C4C23×C3⋊D313yes—
498C2×C3—412no—
499C2×C3C22×#23514yes—
500C2×C3#596614yes—
501C2×C3#596814yes—
502D3—124no—
503D3—1212no—
504C22—23no—
505C22—23no—
506C22—23no—
507C22—181no—
508C22—183no—
509C22—183no—
510C22—181no—
511C22—183no—
512C22—181no—
513C22C24×C3⋊D311yescharacteristic
514C4—21no—
515C4—23no—
516C4—23no—
517C4—21no—
518C4—21no—
519C4—181no—
520C4—183no—
521C4—181no—
522C4—181no—
523C4—183no—
524C4—183no—
525C4C2×#382816yes—
526C3#8589814yescomplemented
527C2—43no—
528C2—361no—
529C2—363no—
530C2C22×#382811yescharacteristic
531C2#1059675811yescharacteristic
532C2#1059676011yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#520C2
hypercenter#520C3⋊D3
hypocenterC32#3524
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C32×#520C2semidirect
2. #10596305C2semidirect
3. #10596302C2semidirect
4. #10596047C2semidirect
5. C4×#3832C2semidirect
6. #10596043C2semidirect
7. #10596041C2semidirect
8. #10596034C2semidirect
9. #10596033C2semidirect
10. #10596030C2semidirect
11. #10596028C2semidirect
12. #10596005C2semidirect
13. #10595999C2semidirect
14. #10595985C2semidirect
15. #10595984C2semidirect
67. C3×#520D3semidirect
228. #520C3⋊D3semidirect
467. C32#3524semidirect
526. C3#85898semidirect

Maximal subgroups

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

subgroupindex
C32×#5202
#105963052
#105963022
#105960472
C4×#38322
#105960432
#105960412
#105960342
#105960332
#105960302
#105960282
#105960052
#105959992
#105959852
#105959842
#858983