Finite Group Databasebeta

← #11909730

Subgroups — #11909730

Order 1152.

3312 conjugacy classes of subgroups.

The subgroup lattice has 543 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
5#10596045C211yesmaximal, characteristic, complemented
6C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
7Q8×#634C211yesmaximal, characteristic, complemented
8#10596032C213yesmaximal, complemented
9#10596030C213yesmaximal, complemented
10#10596022C213yesmaximal, complemented
11#10596019C213yesmaximal, complemented
12#10596005C213yesmaximal, complemented
13#10595999C213yesmaximal, complemented
14#10595982C213yesmaximal, complemented
15#10595978C213yesmaximal, complemented
16#85908—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×#3832C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×#3828C2216yes—
21C32×C4×Q8C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic
23C32×C4×D4C2213yes—
24C32×C4×D4C2213yes—
25C32×#117C2213yes—
26C2×C32×C4⋊C4C2213yes—
27Q8×C3⋊Dic3C2211yescharacteristic
28Q8×C3⋊Dic3C2211yescharacteristic
29#64149C2213yes—
30#64147C2213yes—
31#64147C2213yes—
32#64145C2213yes—
33#64139C2213yes—
34#64138C2216yes—
35C4×#638C2213yes—
36C4×#638C2213yes—
37C4×#638C2216yes—
38#64133C2213yes—
39#64133C2216yes—
40#64107C2213yes—
41#64106C2213yes—
42#64105C2216yes—
43#64105C2211yescharacteristic
44#64104C2213yes—
45#64103C2213yes—
46#64102C2213yes—
47C4⋊C4×C3⋊D3C2213yes—
48C4⋊C4×C3⋊D3C2213yes—
49#64098C2213yes—
50#64097C2213yes—
51#64097C2213yes—
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—
71#5574—34no—
72C4×D3×Q8—34no—
73Q8×Dic6—34no—
74#5561—312no—
75#5559—312no—
76#5551—312no—
77#5548—312no—
78#5534—312no—
79#5528—312no—
80#5511—312no—
81#5507—312no—
82C32×#41—24no—
83C2×C32×Q8C2311yescharacteristic
84C2×C32×D4C2313yes—
85C22×C32×C4C2313yes—
86C22×C32×C4C2316yes—
87C2×#638C2313yes—
88C2×#638C2313yes—
89C2×#638C2316yes—
90#3832—24no—
91Q8×C3⋊D3—24no—
92#3828—412no—
93C2×C4⋊(C3⋊D3)C2313yes—
94C2×C4⋊(C3⋊D3)C2313yes—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C4×C3⋊D3C2313yes—
97C2×C4×C3⋊D3C2313yes—
98C2×C4×C3⋊D3C2313yes—
99C2×C4×C3⋊D3C2316yes—
100C2×#634C2311yescharacteristic
101C2×#634C2313yes—
102C2×#634C2316yes—
103C32×C4⋊C4C2313yes—
104C32×C4⋊C4C2313yes—
105C32×C4⋊C4C2313yes—
106C32×C4⋊C4C2311yescharacteristic
107C32×C22⋊C4C2313yes—
108C32×C22⋊C4C2313yes—
109C32×C42C2313yes—
110C32×C42C2313yes—
111#3757C2313yes—
112#3757C2313yes—
113#3757C2316yes—
114#3752C2313yes—
115#3752C2313yes—
116#3752C2311yescharacteristic
117#3752C2313yes—
118#3752C2316yes—
119#3752C2311yescharacteristic
120#3752C2313yes—
121C4⋊(C3⋊Dic3)C2313yes—
122C4⋊(C3⋊Dic3)C2313yes—
123C4⋊(C3⋊Dic3)C2313yes—
124C4⋊(C3⋊Dic3)C2313yes—
125#3750C2313yes—
126#3750C2316yes—
127#3750C2313yes—
128#3750C2311yescharacteristic
129#3750C2313yes—
130#3750C2311yescharacteristic
131#3750C2313yes—
132C4×C3⋊Dic3C2313yes—
133C4×C3⋊Dic3C2313yes—
134C4×C3⋊Dic3C2313yes—
135C4×C3⋊Dic3C2313yes—
136#3522—91noSylow
137C2×C3×#41C2×D314yes—
138C2×#239—34no—
139C2×D3×Q8—34no—
140C2×#235—324no—
141C3×C4×Q8C2×D314yes—
142C3×C4×Q8C2×D314yes—
143C3×C4×D4C2×D3112yes—
144C3×C4×D4C2×D3112yes—
145C3×#117C2×D3112yes—
146C2×C3×C4⋊C4C2×D3112yes—
147Q8×Dic3—34no—
148Q8×Dic3—34no—
149#940—312no—
150#938—312no—
151#938—312no—
152#936—312no—
153#930—312no—
154#929—324no—
155C4×#67—312no—
156C4×#67—312no—
157C4×#67—324no—
158#924—312no—
159#924—324no—
160#898—312no—
161#897—312no—
162#896—324no—
163#896—34no—
164#895—312no—
165#894—312no—
166#893—312no—
167D3×C4⋊C4—312no—
168D3×C4⋊C4—312no—
169#889—312no—
170#888—312no—
171#888—312no—
172#887—312no—
173#885—312no—
174#885—324no—
175#884—312no—
176#883—312no—
177#883—324no—
178#879—312no—
179#875—312no—
180C4×D12—312no—
181C4×D12—312no—
182#872—312no—
183C42×D3—312no—
184#869—312no—
185C4×Dic6—312no—
186C4×Dic6—312no—
187C23×C32C2413yes—
188C22×C3⋊D3C2413yes—
189C22×C3⋊D3C2411yescharacteristic
190C32×Q8#4114yescomplemented
191C32×D4—26no—
192C2×C32×C4—26no—
193C2×C32×C4—46no—
194C2×C32×C4C2411yescharacteristic
195C2×C32×C4C2413yes—
196C2×C32×C4C2411yescharacteristic
197C2×C32×C4C2413yes—
198C2×C32×C4C2411yescharacteristic
199C2×C32×C4C2413yes—
200#638—26no—
201#638—26no—
202#638—46no—
203C2×C3⋊Dic3C2411yescharacteristic
204C2×C3⋊Dic3C2413yes—
205C2×C3⋊Dic3C2413yes—
206C2×C3⋊Dic3C2413yes—
207C2×C3⋊Dic3C2411yescharacteristic
208C2×C3⋊Dic3C2411yescharacteristic
209C4⋊(C3⋊D3)—26no—
210C4⋊(C3⋊D3)—26no—
211C4×C3⋊D3—26no—
212C4×C3⋊D3—26no—
213C4×C3⋊D3—26no—
214C4×C3⋊D3—22no—
215C4×C3⋊D3—46no—
216#634—26no—
217#634—22no—
218#634—46no—
219#559—93no—
220Q82—91no—
221#554—93no—
222#550—91no—
223#548—91no—
224#548—91no—
225#547—93no—
226#547—93no—
227#542—93no—
228#542—93no—
229#532—93no—
230#529—93no—
231#520—91no—
232#520C3⋊D311yescharacteristic, complemented
233C2×C4×Q8—91no—
234C3×#41—216no—
235C2×C3×Q8C22×D314yes—
236C2×C3×D4C22×D3112yes—
237C22×C3×C4C22×D3112yes—
238C22×C3×C4C22×D3124yes—
239C2×#67—312no—
240C2×#67—312no—
241C2×#67—324no—
242#239—616no—
243D3×Q8—616no—
244#235—1248no—
245C2×D12—312no—
246C2×D12—312no—
247C2×C4×D3—34no—
248C2×C4×D3—312no—
249C2×C4×D3—312no—
250C2×C4×D3—312no—
251C2×C4×D3—324no—
252C2×Dic6—34no—
253C2×Dic6—312no—
254C2×Dic6—324no—
255C3×C4⋊C4C22×D3112yes—
256C3×C4⋊C4C22×D3112yes—
257C3×C4⋊C4C22×D3112yes—
258C3×C4⋊C4C22×D314yes—
259C3×C22⋊C4C22×D3112yes—
260C3×C22⋊C4C22×D3112yes—
261C3×C42C22×D3112yes—
262C3×C42C22×D3112yes—
263#217—312no—
264#217—312no—
265#217—324no—
266(C2×D3)⋊C4—312no—
267(C2×D3)⋊C4—312no—
268(C2×D3)⋊C4—34no—
269(C2×D3)⋊C4—312no—
270(C2×D3)⋊C4—324no—
271(C2×D3)⋊C4—34no—
272(C2×D3)⋊C4—312no—
273C4⋊Dic3—312no—
274C4⋊Dic3—312no—
275C4⋊Dic3—312no—
276C4⋊Dic3—312no—
277Dic3⋊C4—312no—
278Dic3⋊C4—324no—
279Dic3⋊C4—312no—
280Dic3⋊C4—34no—
281Dic3⋊C4—312no—
282Dic3⋊C4—34no—
283Dic3⋊C4—312no—
284C4×Dic3—312no—
285C4×Dic3—312no—
286C4×Dic3—312no—
287C4×Dic3—312no—
288C22×C32—23no—
289C22×C32—23no—
290C22×C32—23no—
291C22×C32C2511yescharacteristic
292C2×C3⋊D3—21no—
293C2×C3⋊D3—21no—
294C2×C3⋊D3—23no—
295C2×C3⋊D3—23no—
296C2×C3⋊D3—23no—
297C2×C3⋊D3H(5,𝔽2)12yes—
298C32×C4—21no—
299C32×C4—23no—
300C32×C4—23no—
301C32×C4—21no—
302C32×C4—21no—
303C32×C4C2×#4116yes—
304C3⋊Dic3—23no—
305C3⋊Dic3—21no—
306C3⋊Dic3—23no—
307C3⋊Dic3—23no—
308C3⋊Dic3—21no—
309C3⋊Dic32−1+412yes—
310C2×#41—91no—
311C2×#41—96no—
312C2×#41C2×C3⋊D311yescharacteristic
313C22×Q8—91no—
314C4⋊Q8—93no—
315C4⋊Q8—93no—
316C4⋊Q8—93no—
317#127—93no—
318#126—93no—
319#126—93no—
320#125—93no—
321#124—93no—
322#124—93no—
323#124—96no—
324#124—93no—
325#123—96no—
326#123—93no—
327#123—93no—
328#123—96no—
329C22⋊Q8—96no—
330C22⋊Q8—93no—
331C22⋊Q8—91no—
332C22⋊Q8—96no—
333C22⋊Q8—93no—
334#121—93no—
335#121—93no—
336#121—93no—
337#121—93no—
338#121—93no—
339C4×Q8—91no—
340C4×Q8—91no—
341C4×Q8—93no—
342C4×Q8—93no—
343C4×Q8—93no—
344C4×Q8C2×C3⋊D311yescharacteristic
345C4×Q8C2×C3⋊D311yescharacteristic
346C4×D4—93no—
347C4×D4—93no—
348C4×D4—96no—
349C4×D4—93no—
350C4×D4—93no—
351C4×D4—93no—
352C4×D4C2×C3⋊D313yes—
353C4×D4C2×C3⋊D313yes—
354#117—93no—
355#117C2×C3⋊D313yes—
356C2×C4⋊C4—93no—
357C2×C4⋊C4—93no—
358C2×C4⋊C4C2×C3⋊D313yes—
359C2×C42—93no—
360C23×C3C23×D3112yes—
361C22×D3—34no—
362C22×D3—312no—
363C3×Q8#235116yescomplemented
364C3×D4—224no—
365C2×C3×C4—224no—
366C2×C3×C4—424no—
367C2×C3×C4C23×D314yes—
368C2×C3×C4C23×D3112yes—
369C2×C3×C4C23×D314yes—
370C2×C3×C4C23×D3112yes—
371C2×C3×C4C23×D314yes—
372C2×C3×C4C23×D3112yes—
373#67—624no—
374#67—624no—
375#67—1224no—
376C2×Dic3—34no—
377C2×Dic3—34no—
378C2×Dic3—312no—
379C2×Dic3—312no—
380C2×Dic3—312no—
381C2×Dic3—34no—
382D12—624no—
383D12—624no—
384C4×D3—68no—
385C4×D3—624no—
386C4×D3—624no—
387C4×D3—624no—
388C4×D3—1224no—
389Dic6—68no—
390Dic6—624no—
391Dic6—1224no—
392C2×C32—43no—
393C2×C32C22×#4111yescharacteristic
394C2×C32C2×H(5,𝔽2)11yescharacteristic
395C2×C32C2×2−1+411yescharacteristic
396C3⋊D3—22no—
397C3⋊D3—43no—
398#41—24no—
399#41—184no—
400#41—3612no—
401C2×Q8—91no—
402C2×Q8—93no—
403C2×Q8—96no—
404C2×Q8—184no—
405C2×Q8C22×C3⋊D311yescharacteristic
406C2×D4—93no—
407C2×D4—93no—
408C2×D4—96no—
409C2×D4—93no—
410C2×D4—93no—
411C2×D4C22×C3⋊D313yes—
412C22×C4—91no—
413C22×C4—93no—
414C22×C4—93no—
415C22×C4—93no—
416C22×C4—96no—
417C22×C4C22×C3⋊D313yes—
418C22×C4C22×C3⋊D316yes—
419C4⋊C4—93no—
420C4⋊C4—93no—
421C4⋊C4—93no—
422C4⋊C4—96no—
423C4⋊C4—91no—
424C4⋊C4—91no—
425C4⋊C4—93no—
426C4⋊C4—93no—
427C4⋊C4—93no—
428C4⋊C4—93no—
429C4⋊C4—93no—
430C4⋊C4C22×C3⋊D313yes—
431C4⋊C4C22×C3⋊D313yes—
432C4⋊C4C22×C3⋊D313yes—
433C4⋊C4C22×C3⋊D311yescharacteristic
434C22⋊C4—93no—
435C22⋊C4—96no—
436C22⋊C4—93no—
437C22⋊C4—93no—
438C22⋊C4—93no—
439C22⋊C4—91no—
440C22⋊C4—91no—
441C22⋊C4—93no—
442C22⋊C4—96no—
443C22⋊C4—93no—
444C22⋊C4C22×C3⋊D313yes—
445C22⋊C4C22×C3⋊D313yes—
446C42—93no—
447C42—93no—
448C42—93no—
449C42—93no—
450C42C22×C3⋊D313yes—
451C42C22×C3⋊D313yes—
452C22×C3—212no—
453C22×C3—212no—
454C22×C3—212no—
455C22×C3C24×D314yes—
456C2×D3—38no—
457C2×D3—64no—
458C2×D3—64no—
459C2×D3—612no—
460C2×D3—612no—
461C2×D3—612no—
462C3×C4—24no—
463C3×C4—212no—
464C3×C4—212no—
465C3×C4—24no—
466C3×C4—24no—
467C3×C4C2×#235124yes—
468Dic3—38no—
469Dic3—612no—
470Dic3—64no—
471Dic3—612no—
472Dic3—612no—
473Dic3—64no—
474C32#352211yescharacteristic, complemented, Sylow
475C23—91no—
476C23—93no—
477C23C23×C3⋊D313yes—
478Q8—182no—
479Q8—186no—
480Q8—366no—
481Q8#382814yescomplemented
482D4—26no—
483D4—186no—
484D4—186no—
485D4—186no—
486D4—186no—
487D4—366no—
488C2×C4—26no—
489C2×C4—46no—
490C2×C4—91no—
491C2×C4—91no—
492C2×C4—93no—
493C2×C4—93no—
494C2×C4—93no—
495C2×C4—91no—
496C2×C4—182no—
497C2×C4—186no—
498C2×C4—186no—
499C2×C4—186no—
500C2×C4—366no—
501C2×C4C23×C3⋊D311yescharacteristic
502C2×C4C23×C3⋊D313yes—
503C2×C4C23×C3⋊D311yescharacteristic
504C2×C4C23×C3⋊D313yes—
505C2×C4C23×C3⋊D311yescharacteristic
506C2×C4C23×C3⋊D313yes—
507C2×C3—412no—
508C2×C3C22×#23514yes—
509C2×C3D3×H(5,𝔽2)14yes—
510C2×C3D3×2−1+414yes—
511D3—68no—
512D3—1212no—
513C22—23no—
514C22—23no—
515C22—23no—
516C22—92no—
517C22—181no—
518C22—181no—
519C22—183no—
520C22—183no—
521C22—183no—
522C22C24×C3⋊D311yescharacteristic
523C4—21no—
524C4—23no—
525C4—23no—
526C4—21no—
527C4—21no—
528C4—92no—
529C4—181no—
530C4—183no—
531C4—183no—
532C4—183no—
533C4—181no—
534C4C2×#382816yes—
535C3#8590814yescomplemented
536C2—43no—
537C2—182no—
538C2—363no—
539C2C22×#382811yescharacteristic
540C2C3⋊D3×H(5,𝔽2)11yescharacteristic
541C2C3⋊D3×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#520C2
hypercenter#520C3⋊D3
hypocenterC32#3522
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. #10596045C2semidirect
6. C4×Q8×C3⋊D3C2semidirect
7. Q8×#634C2semidirect
8. #10596032C2semidirect
9. #10596030C2semidirect
10. #10596022C2semidirect
11. #10596019C2semidirect
12. #10596005C2semidirect
13. #10595999C2semidirect
14. #10595982C2semidirect
15. #10595978C2semidirect
67. C3×#520D3semidirect
190. C32×Q8#41semidirect
232. #520C3⋊D3semidirect
363. C3×Q8#235semidirect
474. C32#3522semidirect
481. Q8#3828semidirect
535. C3#85908semidirect

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
#105960452
C4×Q8×C3⋊D32
Q8×#6342
#105960322
#105960302
#105960222
#105960192
#105960052
#105959992
#105959822
#105959782
#859083