Finite Group Databasebeta

← #11901747

Subgroups — #11901747

Order 1152.

3120 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#525C211yesmaximal, characteristic, complemented
2#10596303C211yesmaximal, characteristic, complemented
3#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#10596262C211yesmaximal, characteristic, complemented
5C2×#64135C211yesmaximal, characteristic, complemented
6#10596136C214yesmaximal, complemented
7#10596114C212yesmaximal, complemented
8#10596096C212yesmaximal, complemented
9#10596090C212yesmaximal, complemented
10#10596074C212yesmaximal, complemented
11#10596064C214yesmaximal, complemented
12#10596028C214yesmaximal, complemented
13#10596009C214yesmaximal, complemented
14#10595993C211yesmaximal, characteristic, complemented
15#10595988C211yesmaximal, characteristic, complemented
16#86019—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C23×C32×C4C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C32×#123C2212yes—
21C32×C22⋊Q8C2212yes—
22C32×#121C2212yes—
23C32×#120C2212yes—
24C32×C4×D4C2214yes—
25C32×#117C2211yescharacteristic
26#64162C2212yes—
27C2×#3757C2212yes—
28#64156C2211yescharacteristic, complemented
29Q8×C3⋊Dic3C2212yescomplemented
30#64153C2211yescharacteristic, complemented
31#64149C2211yescharacteristic, complemented
32#64148C2214yes—
33#64148C2214yes—
34#64147C2214yes—
35#64145C2214yes—
36#64145C2211yescharacteristic, complemented
37#64144C2214yes—
38D4×C3⋊Dic3C2214yes—
39D4×C3⋊Dic3C2212yescomplemented
40#64139C2212yes—
41#64138C2212yes—
42C4×#638C2214yes—
43C4×#638C2214yescomplemented
44#64135C2212yes—
45#64135C2212yes—
46#64135C2211yescharacteristic
47#64135C2212yes—
48#64135C2212yes—
49#64135C2212yescomplemented
50C2×C4⋊(C3⋊Dic3)C2212yes—
51#64133C2212yes—
52C2×C4×C3⋊Dic3C2211yescharacteristic
53C2×C4×C3⋊Dic3C2211yescharacteristic
54C2×C4×C3⋊Dic3C2212yescomplemented
55#64107C2214yescomplemented
56#64106C2214yescomplemented
57#64102C2212yescomplemented
58#64099C2214yescomplemented
59#64099C2212yescomplemented
60#64098C2214yescomplemented
61#64097C2212yescomplemented
62#64096C2212yescomplemented
63#64095C2214yescomplemented
64#64094C2214yes—
65#64092C2214yes—
66#64092C2214yescomplemented
67#64090C2214yes—
68#64088C2214yes—
69#64088C2214yes—
70#64088C2214yescomplemented
71#64087C2214yes—
72#64087C2214yescomplemented
73#64081C2212yescomplemented
74C42×C3⋊D3C2212yescomplemented
75C4×#634C2214yescomplemented
76C3×#525D314yescomplemented
77#5832—34no—
78Dic3×#41—34no—
79#5791—34no—
80C2×#926—34no—
81#5665—316no—
82#5643—38no—
83#5625—38no—
84#5619—38no—
85#5603—38no—
86#5593—316no—
87#5557—316no—
88#5538—316no—
89#5522—34no—
90#5517—34no—
91C24×C32C2311yescharacteristic
92C32×#41—24no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2312yes—
95C2×C32×D4C2311yescharacteristic
96C2×C32×D4C2314yes—
97C22×C32×C4—24no—
98C22×C32×C4C2312yes—
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2312yes—
101C22×C32×C4C2312yes—
102C22×C32×C4C2311yescharacteristic
103C2×#638C2312yes—
104C2×#638C2314yes—
105C2×#638C2314yes—
106C22×C3⋊Dic3C2312yes—
107C22×C3⋊Dic3C2314yes—
108C22×C3⋊Dic3C2312yes—
109#3828—24no—
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4×C3⋊D3C2312yes—
112C2×C4×C3⋊D3C2314yes—
113C2×#634C2311yescharacteristic
114C2×#634C2314yes—
115C32×C4⋊C4C2312yes—
116C32×C4⋊C4C2314yes—
117C32×C22⋊C4C2312yes—
118C32×C22⋊C4C2314yes—
119C32×C22⋊C4C2314yes—
120C32×C42C2312yes—
121#3757C2312yes—
122#3757C2314yes—
123#3757C2314yes—
124#3757C2312yes—
125#3757C2312yes—
126#3757C2314yes—
127#3757C2312yes—
128#3757C2312yes—
129#3752C2314yes—
130#3752C2314yes—
131#3752C2314yes—
132C4⋊(C3⋊Dic3)C2314yes—
133C4⋊(C3⋊Dic3)C2312yes—
134C4⋊(C3⋊Dic3)C2314yes—
135C4⋊(C3⋊Dic3)C2312yes—
136C4⋊(C3⋊Dic3)C2312yes—
137C4⋊(C3⋊Dic3)C2312yes—
138C4⋊(C3⋊Dic3)C2312yes—
139#3750C2314yes—
140#3750C2314yes—
141#3750C2314yes—
142#3750C2314yes—
143#3750C2314yes—
144C4×C3⋊Dic3C2312yes—
145C4×C3⋊Dic3C2312yes—
146C4×C3⋊Dic3C2311yescharacteristic
147C4×C3⋊Dic3C2314yes—
148C4×C3⋊Dic3C2311yescharacteristic
149C4×C3⋊Dic3C2314yes—
150C4×C3⋊Dic3C2312yes—
151C4×C3⋊Dic3C2311yescharacteristic
152C4×C3⋊Dic3C2311yescharacteristic
153#3455—91noSylow
154C2×C3×#41C2×D314yes—
155C23×C3×C4C2×D314yes—
156C2×#235—34no—
157C3×#123C2×D318yes—
158C3×C22⋊Q8C2×D318yes—
159C3×#121C2×D318yes—
160C3×#120C2×D318yes—
161C3×C4×D4C2×D3116yes—
162C3×#117C2×D314yes—
163#953—38no—
164C2×#217—38no—
165#947—34no—
166Q8×Dic3—38no—
167#944—34no—
168#940—34no—
169#939—316no—
170#939—316no—
171#938—316no—
172#936—316no—
173#936—34no—
174#935—316no—
175D4×Dic3—316no—
176D4×Dic3—38no—
177#930—38no—
178#929—38no—
179C4×#67—316no—
180C4×#67—316no—
181#926—38no—
182#926—34no—
183#926—38no—
184#926—38no—
185#926—38no—
186#926—38no—
187C2×C4⋊Dic3—38no—
188#924—38no—
189C2×C4×Dic3—34no—
190C2×C4×Dic3—34no—
191C2×C4×Dic3—38no—
192#898—316no—
193#897—316no—
194#893—38no—
195#890—316no—
196#890—38no—
197#889—316no—
198#888—38no—
199#887—38no—
200#886—316no—
201#885—316no—
202#883—316no—
203#883—316no—
204#67⋊C4—316no—
205#879—316no—
206#879—316no—
207#879—316no—
208#878—316no—
209#878—316no—
210#872—38no—
211C42×D3—38no—
212C4×Dic6—316no—
213C23×C32—22no—
214C23×C32—42no—
215C23×C32C2412yes—
216C23×C32C2412yes—
217C23×C32C2411yescharacteristic
218C22×C3⋊D3C2412yes—
219C32×Q8—22no—
220C32×D4—24no—
221C32×D4—22no—
222C32×D4—44no—
223C2×C32×C4—22no—
224C2×C32×C4—24no—
225C2×C32×C4—24no—
226C2×C32×C4—24no—
227C2×C32×C4#4114yes—
228C2×C32×C4C2412yes—
229C2×C32×C4C2414yes—
230C2×C32×C4C2412yes—
231C2×C32×C4C2411yescharacteristic
232C2×C32×C4C2411yescharacteristic
233#638—24no—
234#638—44no—
235#638—44no—
236C2×C3⋊Dic3—42no—
237C2×C3⋊Dic3—44no—
238C2×C3⋊Dic3—42no—
239C2×C3⋊Dic3C2412yes—
240C2×C3⋊Dic3C2412yes—
241C2×C3⋊Dic3C2412yes—
242C2×C3⋊Dic3C2412yes—
243C2×C3⋊Dic3C2414yes—
244C2×C3⋊Dic3C2412yes—
245C4⋊(C3⋊D3)—22no—
246C4×C3⋊D3—24no—
247C4×C3⋊D3—44no—
248#634—22no—
249#634—44no—
250#542—92no—
251#542—92no—
252#541—92no—
253#540—92no—
254#539—94no—
255#538—94no—
256#533—91no—
257#532—91no—
258#529—94no—
259#529—94no—
260#525—91no—
261#525C3⋊D311yescharacteristic, complemented
262C4×#41—91no—
263C4×#41—91no—
264C2×#117—91no—
265C24×C3C22×D314yes—
266C3×#41—216no—
267C2×C3×Q8C22×D314yes—
268C2×C3×D4C22×D314yes—
269C2×C3×D4C22×D318yes—
270C2×C3×D4C22×D3116yes—
271C22×C3×C4—216no—
272C22×C3×C4C22×D318yes—
273C22×C3×C4C22×D318yes—
274C22×C3×C4C22×D314yes—
275C22×C3×C4C22×D318yes—
276C22×C3×C4C22×D314yes—
277C2×#67—38no—
278C2×#67—316no—
279C2×#67—316no—
280C22×Dic3—38no—
281C22×Dic3—316no—
282C22×Dic3—38no—
283#235—616no—
284C2×D12—34no—
285C2×C4×D3—38no—
286C2×C4×D3—316no—
287C2×Dic6—34no—
288C2×Dic6—316no—
289C3×C4⋊C4C22×D318yes—
290C3×C4⋊C4C22×D3116yes—
291C3×C22⋊C4C22×D318yes—
292C3×C22⋊C4C22×D3116yes—
293C3×C22⋊C4C22×D3116yes—
294C3×C42C22×D318yes—
295#217—38no—
296#217—316no—
297#217—316no—
298#217—38no—
299#217—38no—
300#217—316no—
301#217—38no—
302#217—38no—
303(C2×D3)⋊C4—316no—
304(C2×D3)⋊C4—316no—
305(C2×D3)⋊C4—316no—
306C4⋊Dic3—316no—
307C4⋊Dic3—38no—
308C4⋊Dic3—38no—
309C4⋊Dic3—316no—
310C4⋊Dic3—38no—
311C4⋊Dic3—38no—
312C4⋊Dic3—38no—
313Dic3⋊C4—316no—
314Dic3⋊C4—316no—
315Dic3⋊C4—316no—
316Dic3⋊C4—316no—
317Dic3⋊C4—316no—
318C4×Dic3—38no—
319C4×Dic3—38no—
320C4×Dic3—34no—
321C4×Dic3—316no—
322C4×Dic3—34no—
323C4×Dic3—316no—
324C4×Dic3—38no—
325C4×Dic3—34no—
326C4×Dic3—34no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—24no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—44no—
334C22×C32C2×#4112yes—
335C22×C32C2511yescharacteristic
336C2×C3⋊D3—22no—
337C2×C3⋊D3—24no—
338C32×C4—22no—
339C32×C4—22no—
340C32×C4—24no—
341C32×C4C2×#4112yes—
342C32×C4C2×#4112yes—
343C3⋊Dic3—22no—
344C3⋊Dic3—22no—
345C3⋊Dic3—24no—
346C3⋊Dic3—22no—
347C3⋊Dic3—22no—
348C3⋊Dic3—22no—
349C2×#41—91no—
350C2×#41C2×C3⋊D311yescharacteristic
351C23×C4C2×C3⋊D311yescharacteristic
352C4⋊Q8—91no—
353C4⋊Q8—92no—
354#127—91no—
355#126—94no—
356#126—94no—
357#126—94no—
358#126—94no—
359#125—94no—
360#125—94no—
361#125—92no—
362#124—91no—
363#124—94no—
364#124—91no—
365#124—94no—
366#123—94no—
367#123—92no—
368#123—94no—
369#123—94no—
370#123—94no—
371#123C2×C3⋊D312yes—
372C22⋊Q8—92no—
373C22⋊Q8—94no—
374C22⋊Q8—94no—
375C22⋊Q8—94no—
376C22⋊Q8C2×C3⋊D312yes—
377#121—94no—
378#121—94no—
379#121—94no—
380#121—92no—
381#121C2×C3⋊D312yes—
382#120—92no—
383#120C2×C3⋊D312yes—
384C4×Q8—92no—
385C4×Q8—92no—
386C4×Q8—94no—
387C4×D4—94no—
388C4×D4—92no—
389C4×D4—94no—
390C4×D4—94no—
391C4×D4—92no—
392C4×D4—94no—
393C4×D4C2×C3⋊D314yes—
394#117—92no—
395#117—92no—
396#117—92no—
397#117—92no—
398#117—91no—
399#117—92no—
400#117—92no—
401#117C2×C3⋊D311yescharacteristic
402C2×C4⋊C4—92no—
403C2×C22⋊C4—92no—
404C2×C42—91no—
405C2×C42—91no—
406C2×C42—92no—
407C2×C42—92no—
408C23×C3—28no—
409C23×C3—48no—
410C23×C3C23×D318yes—
411C23×C3C23×D318yes—
412C23×C3C23×D314yes—
413C22×D3—38no—
414C3×Q8—28no—
415C3×D4—216no—
416C3×D4—28no—
417C3×D4—416no—
418C2×C3×C4—28no—
419C2×C3×C4—216no—
420C2×C3×C4—216no—
421C2×C3×C4—216no—
422C2×C3×C4#237116yes—
423C2×C3×C4C23×D318yes—
424C2×C3×C4C23×D3116yes—
425C2×C3×C4C23×D318yes—
426C2×C3×C4C23×D314yes—
427C2×C3×C4C23×D314yes—
428#67—616no—
429#67—1216no—
430#67—1216no—
431C2×Dic3—38no—
432C2×Dic3—38no—
433C2×Dic3—38no—
434C2×Dic3—38no—
435C2×Dic3—316no—
436C2×Dic3—38no—
437C2×Dic3—128no—
438C2×Dic3—1216no—
439C2×Dic3—128no—
440D12—68no—
441C4×D3—616no—
442C4×D3—1216no—
443Dic6—68no—
444Dic6—1216no—
445C2×C32—22no—
446C2×C32—42no—
447C2×C32—42no—
448C2×C32C22×#4111yescharacteristic
449C2×C32#58512yes—
450C3⋊D3—42no—
451C24C22×C3⋊D311yescharacteristic
452#41—24no—
453#41—184no—
454C2×Q8—91no—
455C2×Q8—94no—
456C2×Q8C22×C3⋊D311yescharacteristic
457C2×D4—92no—
458C2×D4—94no—
459C2×D4—94no—
460C2×D4—91no—
461C2×D4C22×C3⋊D312yes—
462C2×D4C22×C3⋊D311yescharacteristic
463C2×D4C22×C3⋊D314yes—
464C22×C4—24no—
465C22×C4—92no—
466C22×C4—92no—
467C22×C4—94no—
468C22×C4—92no—
469C22×C4—94no—
470C22×C4C22×C3⋊D311yescharacteristic
471C22×C4C22×C3⋊D312yes—
472C22×C4C22×C3⋊D312yes—
473C22×C4C22×C3⋊D312yes—
474C22×C4C22×C3⋊D311yescharacteristic
475C4⋊C4—92no—
476C4⋊C4—92no—
477C4⋊C4—92no—
478C4⋊C4—92no—
479C4⋊C4—92no—
480C4⋊C4—94no—
481C4⋊C4—94no—
482C4⋊C4—94no—
483C4⋊C4—94no—
484C4⋊C4—94no—
485C4⋊C4—94no—
486C4⋊C4—94no—
487C4⋊C4C22×C3⋊D312yes—
488C4⋊C4C22×C3⋊D314yes—
489C22⋊C4—92no—
490C22⋊C4—92no—
491C22⋊C4—92no—
492C22⋊C4—92no—
493C22⋊C4—92no—
494C22⋊C4—94no—
495C22⋊C4—94no—
496C22⋊C4—94no—
497C22⋊C4—94no—
498C22⋊C4—94no—
499C22⋊C4—94no—
500C22⋊C4C22×C3⋊D312yes—
501C22⋊C4C22×C3⋊D314yes—
502C22⋊C4C22×C3⋊D314yes—
503C42—92no—
504C42—91no—
505C42—91no—
506C42—94no—
507C42—94no—
508C42—91no—
509C42—91no—
510C42—92no—
511C42—92no—
512C42C22×C3⋊D312yes—
513C22×C3—28no—
514C22×C3—28no—
515C22×C3—28no—
516C22×C3—216no—
517C22×C3—28no—
518C22×C3—28no—
519C22×C3—416no—
520C22×C3C2×#23718yes—
521C22×C3C24×D314yes—
522C2×D3—68no—
523C2×D3—616no—
524C3×C4—28no—
525C3×C4—28no—
526C3×C4—216no—
527C3×C4C2×#23718yes—
528C3×C4C2×#23718yes—
529Dic3—68no—
530Dic3—68no—
531Dic3—616no—
532Dic3—68no—
533Dic3—68no—
534Dic3—68no—
535C32#345511yescharacteristic, complemented, Sylow
536C23—22no—
537C23—42no—
538C23—92no—
539C23C23×C3⋊D312yes—
540C23C23×C3⋊D312yes—
541C23C23×C3⋊D311yescharacteristic
542Q8—22no—
543Q8—182no—
544Q8—364no—
545D4—24no—
546D4—22no—
547D4—44no—
548D4—184no—
549D4—182no—
550D4—364no—
551D4—364no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—92no—
557C2×C4—92no—
558C2×C4—92no—
559C2×C4—92no—
560C2×C4—94no—
561C2×C4—92no—
562C2×C4—184no—
563C2×C4—364no—
564C2×C4—362no—
565C2×C4—364no—
566C2×C4—362no—
567C2×C4#383014yes—
568C2×C4C23×C3⋊D312yes—
569C2×C4C23×C3⋊D314yes—
570C2×C4C23×C3⋊D312yes—
571C2×C4C23×C3⋊D311yescharacteristic
572C2×C4C23×C3⋊D311yescharacteristic
573C2×C3—28no—
574C2×C3—48no—
575C2×C3—48no—
576C2×C3C22×#23714yes—
577C2×C3#596418yes—
578D3—128no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—24no—
583C22—22no—
584C22—22no—
585C22—44no—
586C22—182no—
587C22—184no—
588C22C2×#383012yes—
589C22C24×C3⋊D311yescharacteristic
590C4—22no—
591C4—22no—
592C4—24no—
593C4—182no—
594C4—182no—
595C4—182no—
596C4—182no—
597C4—184no—
598C4—182no—
599C4C2×#383012yes—
600C4C2×#383012yes—
601C3#8601914yescomplemented
602C2—22no—
603C2—42no—
604C2—42no—
605C2—362no—
606C2C22×#383011yescharacteristic
607C2#1059675612yes—
subgroupG/H
centerC2×C4C23×C3⋊D3
commutator, socle, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC32×#525C2
hypercenter#525C3⋊D3
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C32×#525C2semidirect
2. #10596303C2semidirect
3. #41×C3⋊Dic3C2semidirect
4. #10596262C2semidirect
5. C2×#64135C2semidirect
6. #10596136C2semidirect
7. #10596114C2semidirect
8. #10596096C2semidirect
9. #10596090C2semidirect
10. #10596074C2semidirect
11. #10596064C2semidirect
12. #10596028C2semidirect
13. #10596009C2semidirect
14. #10595993C2semidirect
15. #10595988C2semidirect
28. #64156C22semidirect
29. Q8×C3⋊Dic3C22semidirect
30. #64153C22semidirect
31. #64149C22semidirect
36. #64145C22semidirect
39. D4×C3⋊Dic3C22semidirect
43. C4×#638C22semidirect
49. #64135C22semidirect
54. C2×C4×C3⋊Dic3C22semidirect
55. #64107C22semidirect
56. #64106C22semidirect
57. #64102C22semidirect
58. #64099C22semidirect
59. #64099C22semidirect
60. #64098C22semidirect
61. #64097C22semidirect
62. #64096C22semidirect
63. #64095C22semidirect
66. #64092C22semidirect
70. #64088C22semidirect
72. #64087C22semidirect
73. #64081C22semidirect
74. C42×C3⋊D3C22semidirect
75. C4×#634C22semidirect
76. C3×#525D3semidirect
261. #525C3⋊D3semidirect
535. C32#3455semidirect
601. C3#86019semidirect

Maximal subgroups

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

subgroupindex
C32×#5252
#105963032
#41×C3⋊Dic32
#105962622
C2×#641352
#105961362
#105961142
#105960962
#105960902
#105960742
#105960642
#105960282
#105960092
#105959932
#105959882
#860193