Finite Group Databasebeta

← #11903874

Subgroups — #11903874

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×C4×#41C211yesmaximal, characteristic, complemented
2#10596305C211yesmaximal, characteristic, complemented
3#10596302C211yesmaximal, characteristic, complemented
4#10596047C211yesmaximal, characteristic, complemented
5C4×#3832C211yesmaximal, characteristic, complemented
6C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
7#10596040C211yesmaximal, characteristic, complemented
8#10596030C213yesmaximal, complemented
9#10596029C213yesmaximal, complemented
10#10596028C213yesmaximal, complemented
11#10596019C213yesmaximal, complemented
12#10596004C213yesmaximal, complemented
13#10596001C213yesmaximal, complemented
14#10595950C213yesmaximal, complemented
15C4×#3828C213yesmaximal, complemented
16#85842—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×#3832C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×#3828C2213yes—
21C32×C4×Q8C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic
23C32×C4×D4C2213yes—
24C32×C4×D4C2213yes—
25C32×#117C2213yes—
26C2×C32×C42C2213yes—
27Q8×C3⋊Dic3C2211yescharacteristic
28Q8×C3⋊Dic3C2211yescharacteristic
29#64149C2213yes—
30#64147C2213yes—
31#64147C2213yes—
32#64145C2213yes—
33#64139C2213yes—
34#64138C2216yes—
35C4×#638C2213yes—
36C4×#638C2213yes—
37C4×#638C2213yes—
38C4×#638C2213yes—
39C4×#638C2216yes—
40#64135C2213yes—
41#64133C2213yes—
42#64106C2213yes—
43#64104C2213yes—
44#64102C2213yes—
45#64101C2213yes—
46C4⋊C4×C3⋊D3C2213yes—
47#64099C2213yes—
48#64097C2213yes—
49#64096C2213yes—
50#64094C2216yes—
51#64093C2216yes—
52#64092C2216yes—
53#64088C2216yes—
54#64085C2216yes—
55#64084C2213yes—
56C4×C4⋊(C3⋊D3)C2213yes—
57C4×C4⋊(C3⋊D3)C2213yes—
58C4×C4⋊(C3⋊D3)C2213yes—
59#64081C2211yescharacteristic
60#64081C2213yes—
61C42×C3⋊D3C2213yes—
62C42×C3⋊D3C2213yes—
63#64079C2213yes—
64C4×#634C2213yes—
65C4×#634C2213yes—
66C4×#634C2213yes—
67C3×C4×#41D314yescomplemented
68#5834—34no—
69#5831—34no—
70#5576—34no—
71C4×#239—34no—
72C4×D3×Q8—34no—
73#5569—34no—
74#5559—312no—
75#5558—312no—
76#5557—312no—
77#5548—312no—
78#5533—312no—
79#5530—312no—
80#5479—312no—
81C4×#235—312no—
82C32×#41—24no—
83C2×C32×Q8C2311yescharacteristic
84C2×C32×D4C2313yes—
85C22×C32×C4C2313yes—
86C22×C32×C4C2313yes—
87C22×C32×C4C2313yes—
88C2×#638C2313yes—
89C2×#638C2313yes—
90C2×#638C2316yes—
91#3832—24no—
92Q8×C3⋊D3—24no—
93#3828—212no—
94C2×C4⋊(C3⋊D3)C2313yes—
95C2×C4⋊(C3⋊D3)C2313yes—
96C2×C4×C3⋊D3C2313yes—
97C2×C4×C3⋊D3C2313yes—
98C2×C4×C3⋊D3C2313yes—
99C2×C4×C3⋊D3C2313yes—
100C2×C4×C3⋊D3C2313yes—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634C2313yes—
103C2×#634C2313yes—
104C32×C4⋊C4C2313yes—
105C32×C4⋊C4C2313yes—
106C32×C22⋊C4C2316yes—
107C32×C42C2313yes—
108C32×C42C2313yes—
109C32×C42C2313yes—
110C32×C42C2311yescharacteristic
111#3757C2313yes—
112#3757C2316yes—
113#3757C2313yes—
114#3752C2311yescharacteristic
115#3752C2311yescharacteristic
116#3752C2313yes—
117#3752C2313yes—
118#3752C2316yes—
119#3752C2316yes—
120C4⋊(C3⋊Dic3)C2313yes—
121C4⋊(C3⋊Dic3)C2313yes—
122C4⋊(C3⋊Dic3)C2313yes—
123C4⋊(C3⋊Dic3)C2313yes—
124#3750C2311yescharacteristic
125#3750C2311yescharacteristic
126#3750C2313yes—
127#3750C2313yes—
128#3750C2316yes—
129#3750C2316yes—
130C4×C3⋊Dic3C2313yes—
131C4×C3⋊Dic3C2313yes—
132C4×C3⋊Dic3C2313yes—
133C4×C3⋊Dic3C2313yes—
134C4×C3⋊Dic3C2313yes—
135C4×C3⋊Dic3C2311yescharacteristic
136#3480—91noSylow
137C2×C3×#41C2×D314yes—
138C2×#239—34no—
139C2×D3×Q8—34no—
140C2×#235—312no—
141C3×C4×Q8C2×D314yes—
142C3×C4×Q8C2×D314yes—
143C3×C4×D4C2×D3112yes—
144C3×C4×D4C2×D3112yes—
145C3×#117C2×D3112yes—
146C2×C3×C42C2×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—312no—
158C4×#67—312no—
159C4×#67—324no—
160#926—312no—
161#924—312no—
162#897—312no—
163#895—312no—
164#893—312no—
165#892—312no—
166D3×C4⋊C4—312no—
167#890—312no—
168#888—312no—
169#887—312no—
170#885—324no—
171#884—324no—
172#883—324no—
173#879—324no—
174#876—324no—
175#875—312no—
176C4×D12—312no—
177C4×D12—312no—
178C4×D12—312no—
179#872—34no—
180#872—312no—
181C42×D3—312no—
182C42×D3—312no—
183#870—312no—
184C4×Dic6—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—26no—
194C2×C32×C4—43no—
195C2×C32×C4C2413yes—
196C2×C32×C4C2411yescharacteristic
197C2×C32×C4C2411yescharacteristic
198C2×C32×C4C2413yes—
199C2×C32×C4C2411yescharacteristic
200C2×C32×C4C2413yes—
201#638—26no—
202#638—26no—
203#638—46no—
204C2×C3⋊Dic3C2411yescharacteristic
205C2×C3⋊Dic3C2411yescharacteristic
206C2×C3⋊Dic3C2413yes—
207C2×C3⋊Dic3C2413yes—
208C2×C3⋊Dic3C2413yes—
209C2×C3⋊Dic3C2411yescharacteristic
210C4⋊(C3⋊D3)—26no—
211C4⋊(C3⋊D3)—26no—
212C4×C3⋊D3—26no—
213C4×C3⋊D3—26no—
214C4×C3⋊D3—26no—
215C4×C3⋊D3—43no—
216C4×C3⋊D3—43no—
217C4×C3⋊D3#4114yescomplemented
218#634—26no—
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#548—91no—
228#532—93no—
229#529—93no—
230#529—93no—
231C4×#41—91no—
232C4×#41—93no—
233C4×#41C3⋊D311yescharacteristic, complemented
234C2×C4×Q8—91no—
235C3×#41—216no—
236C2×C3×Q8C22×D314yes—
237C2×C3×D4C22×D3112yes—
238C22×C3×C4C22×D3112yes—
239C22×C3×C4C22×D3112yes—
240C22×C3×C4C22×D3112yes—
241C2×#67—312no—
242C2×#67—312no—
243C2×#67—324no—
244#239—616no—
245D3×Q8—616no—
246#235—648no—
247C2×D12—312no—
248C2×D12—312no—
249C2×C4×D3—34no—
250C2×C4×D3—312no—
251C2×C4×D3—312no—
252C2×C4×D3—312no—
253C2×C4×D3—312no—
254C2×C4×D3—312no—
255C2×Dic6—312no—
256C2×Dic6—312no—
257C3×C4⋊C4C22×D3112yes—
258C3×C4⋊C4C22×D3112yes—
259C3×C22⋊C4C22×D3124yes—
260C3×C42C22×D3112yes—
261C3×C42C22×D3112yes—
262C3×C42C22×D3112yes—
263C3×C42C22×D314yes—
264#217—312no—
265#217—324no—
266#217—312no—
267(C2×D3)⋊C4—34no—
268(C2×D3)⋊C4—34no—
269(C2×D3)⋊C4—312no—
270(C2×D3)⋊C4—312no—
271(C2×D3)⋊C4—324no—
272(C2×D3)⋊C4—324no—
273C4⋊Dic3—312no—
274C4⋊Dic3—312no—
275C4⋊Dic3—312no—
276C4⋊Dic3—312no—
277Dic3⋊C4—34no—
278Dic3⋊C4—34no—
279Dic3⋊C4—312no—
280Dic3⋊C4—312no—
281Dic3⋊C4—324no—
282Dic3⋊C4—324no—
283C4×Dic3—312no—
284C4×Dic3—312no—
285C4×Dic3—312no—
286C4×Dic3—312no—
287C4×Dic3—312no—
288C4×Dic3—34no—
289C22×C32—23no—
290C22×C32—23no—
291C22×C32—23no—
292C22×C32C2511yescharacteristic
293C2×C3⋊D3—21no—
294C2×C3⋊D3—21no—
295C2×C3⋊D3—23no—
296C2×C3⋊D3—23no—
297C2×C3⋊D3—23no—
298C2×C3⋊D3C2×#4112yes—
299C32×C4—23no—
300C32×C4—21no—
301C32×C4—23no—
302C32×C4—21no—
303C32×C4C2×#4116yes—
304C32×C4C2×#4112yes—
305C3⋊Dic3—23no—
306C3⋊Dic3—23no—
307C3⋊Dic3—21no—
308C3⋊Dic3—21no—
309C3⋊Dic3—23no—
310C3⋊Dic3C2×#4112yes—
311C2×#41—91no—
312C2×#41—93no—
313C2×#41C2×C3⋊D311yescharacteristic
314C22×Q8—91no—
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#124—93no—
324#123—96no—
325#123—96no—
326C22⋊Q8—93no—
327C22⋊Q8—93no—
328#121—93no—
329#121—93no—
330#121—93no—
331#121—93no—
332#121—96no—
333C4×Q8—91no—
334C4×Q8—91no—
335C4×Q8—93no—
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—93no—
344C4×D4—93no—
345C4×D4—96no—
346C4×D4—93no—
347C4×D4—93no—
348C4×D4—93no—
349C4×D4—93no—
350C4×D4C2×C3⋊D313yes—
351C4×D4C2×C3⋊D313yes—
352#117—93no—
353#117—93no—
354#117—91no—
355#117—93no—
356#117C2×C3⋊D313yes—
357C2×C4⋊C4—93no—
358C2×C42—93no—
359C2×C42—93no—
360C2×C42C2×C3⋊D313yes—
361C23×C3C23×D3112yes—
362C22×D3—34no—
363C22×D3—312no—
364C3×Q8#235116yescomplemented
365C3×D4—224no—
366C2×C3×C4—224no—
367C2×C3×C4—224no—
368C2×C3×C4—412no—
369C2×C3×C4C23×D3112yes—
370C2×C3×C4C23×D314yes—
371C2×C3×C4C23×D314yes—
372C2×C3×C4C23×D3112yes—
373C2×C3×C4C23×D3112yes—
374C2×C3×C4C23×D314yes—
375#67—624no—
376#67—624no—
377#67—1224no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—34no—
381C2×Dic3—312no—
382C2×Dic3—312no—
383C2×Dic3—312no—
384D12—624no—
385D12—624no—
386C4×D3—316no—
387C4×D3—624no—
388C4×D3—624no—
389C4×D3—624no—
390C4×D3—1212no—
391C4×D3—1212no—
392Dic6—624no—
393Dic6—624no—
394C2×C32—43no—
395C2×C32C22×#4111yescharacteristic
396C2×C32C22×#4111yescharacteristic
397C2×C32#58511yescharacteristic
398C3⋊D3—22no—
399C3⋊D3—43no—
400#41—24no—
401#41—1812no—
402#41—184no—
403C2×Q8—93no—
404C2×Q8—93no—
405C2×Q8—184no—
406C2×Q8C22×C3⋊D311yescharacteristic
407C2×D4—93no—
408C2×D4—93no—
409C2×D4—96no—
410C2×D4—93no—
411C2×D4—93no—
412C2×D4C22×C3⋊D313yes—
413C22×C4—91no—
414C22×C4—93no—
415C22×C4—93no—
416C22×C4—93no—
417C22×C4—93no—
418C22×C4—93no—
419C22×C4C22×C3⋊D313yes—
420C22×C4C22×C3⋊D313yes—
421C22×C4C22×C3⋊D313yes—
422C4⋊C4—93no—
423C4⋊C4—96no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—93no—
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—93no—
435C22⋊C4—93no—
436C22⋊C4—96no—
437C22⋊C4—91no—
438C22⋊C4—91no—
439C22⋊C4—93no—
440C22⋊C4—96no—
441C22⋊C4—93no—
442C22⋊C4—96no—
443C22⋊C4C22×C3⋊D316yes—
444C42—93no—
445C42—93no—
446C42—93no—
447C42—93no—
448C42—91no—
449C42—93no—
450C42C22×C3⋊D313yes—
451C42C22×C3⋊D313yes—
452C42C22×C3⋊D313yes—
453C42C22×C3⋊D311yescharacteristic
454C22×C3—212no—
455C22×C3—212no—
456C22×C3—212no—
457C22×C3C24×D314yes—
458C2×D3—38no—
459C2×D3—64no—
460C2×D3—64no—
461C2×D3—612no—
462C2×D3—612no—
463C2×D3—612no—
464C3×C4—24no—
465C3×C4—212no—
466C3×C4—212no—
467C3×C4—24no—
468C3×C4C2×#235124yes—
469C3×C4D3×#4118yes—
470Dic3—38no—
471Dic3—612no—
472Dic3—64no—
473Dic3—612no—
474Dic3—64no—
475Dic3—612no—
476C32#348011yescharacteristic, complemented, Sylow
477C23—91no—
478C23—93no—
479C23C23×C3⋊D313yes—
480Q8—186no—
481Q8—186no—
482Q8#382814yescomplemented
483D4—26no—
484D4—186no—
485D4—186no—
486D4—186no—
487D4—186no—
488D4—366no—
489C2×C4—26no—
490C2×C4—26no—
491C2×C4—43no—
492C2×C4—91no—
493C2×C4—94no—
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×C4C23×C3⋊D313yes—
505C2×C4C23×C3⋊D311yescharacteristic
506C2×C4C23×C3⋊D311yescharacteristic
507C2×C4C23×C3⋊D313yes—
508C2×C4C23×C3⋊D313yes—
509C2×C4C23×C3⋊D311yescharacteristic
510C2×C3—412no—
511C2×C3C22×#23514yes—
512C2×C3C2×D3×#4114yes—
513C2×C3#596414yes—
514D3—68no—
515D3—1212no—
516C22—23no—
517C22—23no—
518C22—23no—
519C22—92no—
520C22—181no—
521C22—181no—
522C22—183no—
523C22—183no—
524C22—183no—
525C22C24×C3⋊D311yescharacteristic
526C4—21no—
527C4—23no—
528C4—21no—
529C4—23no—
530C4—92no—
531C4—181no—
532C4—183no—
533C4—183no—
534C4—181no—
535C4—183no—
536C4C2×#382816yes—
537C4#41×C3⋊D312yes—
538C3#8584214yescomplemented
539C2—43no—
540C2—182no—
541C2—363no—
542C2C22×#382811yescharacteristic
543C2C2×#41×C3⋊D311yescharacteristic
544C2#1059675611yescharacteristic
subgroupG/H
centerC2×C4C23×C3⋊D3
commutator, socle, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC32×C4×#41C2
hypercenterC4×#41C3⋊D3
hypocenterC32#3480
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C32×C4×#41C2semidirect
2. #10596305C2semidirect
3. #10596302C2semidirect
4. #10596047C2semidirect
5. C4×#3832C2semidirect
6. C4×Q8×C3⋊D3C2semidirect
7. #10596040C2semidirect
8. #10596030C2semidirect
9. #10596029C2semidirect
10. #10596028C2semidirect
11. #10596019C2semidirect
12. #10596004C2semidirect
13. #10596001C2semidirect
14. #10595950C2semidirect
15. C4×#3828C2semidirect
67. C3×C4×#41D3semidirect
190. C32×Q8#41semidirect
217. C4×C3⋊D3#41semidirect
233. C4×#41C3⋊D3semidirect
364. C3×Q8#235semidirect
476. C32#3480semidirect
482. Q8#3828semidirect
538. C3#85842semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
#105963052
#105963022
#105960472
C4×#38322
C4×Q8×C3⋊D32
#105960402
#105960302
#105960292
#105960282
#105960192
#105960042
#105960012
#105959502
C4×#38282
#858423