Finite Group Databasebeta

← #11910211

Subgroups — #11910211

Order 1152.

2981 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#124C211yesmaximal, characteristic, complemented
2C3×#5683C212yesmaximal, complemented
3#10595439C212yesmaximal, complemented
4#10595432C212yesmaximal, complemented
5#10595278C212yesmaximal, complemented
6#10595256C212yesmaximal, complemented
7#10594309C218yesmaximal, complemented
8#10594288C214yesmaximal, complemented
9#10594258C214yesmaximal, complemented
10#10594021C212yesmaximal, complemented
11#10594009C212yesmaximal, complemented
12D3×H(3,𝔽4)—32nomaximal
13C23×D32C2212yescomplemented
14C2×Q8×C3⋊D3C2211yescharacteristic, complemented
15C2×D4×C3⋊D3C2211yescharacteristic
16C2×#3811C2214yes—
17C2×#3802C2212yes—
18C2×#3802C2212yes—
19C2×#3797C2212yescomplemented
20C32×#124C2211yescharacteristic, complemented
21#64156C2211yescharacteristic, complemented
22#64145C2211yescharacteristic, complemented
23#64094C2214yescomplemented
24C22⋊C4×C3⋊D3C2214yescomplemented
25#64084C2211yescharacteristic, complemented
26C42×C3⋊D3C2211yescharacteristic, complemented
27C3×#947C2214yescomplemented
28C3×#937C2214yescomplemented
29C3×#885C2218yescomplemented
30C3×#882C2218yescomplemented
31C3×#875C2214yescomplemented
32#63983C2214yescomplemented
33#63977C2214yescomplemented
34#63976C2218yescomplemented
35#63974C2212yescomplemented
36#63959C2218yescomplemented
37#63923C2214yescomplemented
38#63922C2218yescomplemented
39#63922C2218yescomplemented
40#63921C2214yescomplemented
41#63921C2214yescomplemented
42#63921C2214yescomplemented
43#63915C2214yescomplemented
44#63915C2214yescomplemented
45#63913C2214yescomplemented
46#63913C2214yescomplemented
47#63907C2218yescomplemented
48C4×#624C2212yescomplemented
49#63863C2214yescomplemented
50#63860C2214yescomplemented
51#63852C2218yescomplemented
52C3×H(3,𝔽4)—32no—
53#5683—34no—
54#5683—38no—
55#5683—34no—
56#5683D312yescomplemented
57D3×#124—32no—
58D3×#124—34no—
59D3×#124—38no—
60D3×#124—34no—
61D3×#124—61no—
62#5594—34no—
63#5594—38no—
64D3×#120—34no—
65D3×#120—38no—
66C23×C3⋊D3C2312yes—
67C23×C3×D3C2314yescomplemented
68C22×D32—44no—
69C22×D32—48no—
70C22×D32C2314yes—
71C22×D32C2314yescomplemented
72C2×C32×Q8C2311yescharacteristic, complemented
73C2×C32×D4C2311yescharacteristic
74C2×#638C2312yes—
75Q8×C3⋊D3—42no—
76D4×C3⋊D3—42no—
77C2×C4⋊(C3⋊D3)C2311yescharacteristic
78C2×C4×C3⋊D3C2312yes—
79C2×C4×C3⋊D3C2312yes—
80C2×C4×C3⋊D3C2311yescharacteristic
81C2×#634C2311yescharacteristic, complemented
82C2×#634C2312yescomplemented
83C2×C3×#67C2318yes—
84C2×C3×D12C2314yes—
85C2×C3×D12C2314yes—
86C2×C3×Dic6C2314yescomplemented
87#3811—48no—
88C2×#627C2314yescomplemented
89C2×#626C2318yes—
90C2×#625C2314yes—
91C2×#625C2314yes—
92C2×#624C2314yes—
93#3802—44no—
94#3802—44no—
95#3797—44no—
96C32×C22⋊C4C2314yescomplemented
97C32×C42C2311yescharacteristic, complemented
98#3757C2314yescomplemented
99#3752C2314yescomplemented
100#3752C2314yescomplemented
101C4×C3⋊Dic3C2312yescomplemented
102C4×C3⋊Dic3C2311yescharacteristic, complemented
103C3×#217C2314yescomplemented
104C3×(C2×D3)⋊C4C2318yescomplemented
105C3×(C2×D3)⋊C4C2318yescomplemented
106C3×(C2×D3)⋊C4C2318yescomplemented
107C3×C4×Dic3C2314yescomplemented
108#3722C2314yescomplemented
109(C2×D3)⋊Dic3C2318yescomplemented
110(C2×D3)⋊Dic3C2318yescomplemented
111(C2×D3)⋊Dic3C2318yescomplemented
112Dic32C2314yescomplemented
113C2×H(3,𝔽4)—91noSylow
114C24×D3—34no—
115C2×D3×Q8—32no—
116C2×D3×Q8—34no—
117C2×D3×Q8—61no—
118C2×D3×D4—32no—
119C2×D3×D4—38no—
120C2×D3×D4—34no—
121C2×D3×D4—34no—
122C2×D3×D4—61no—
123C3×#124—21no—
124C3×#124—34no—
125C3×#124—38no—
126C3×#124—34no—
127C3×#124C2×D312yescomplemented
128C3×#120—34no—
129C3×#120—38no—
130#953—38no—
131#953—34no—
132#947—32no—
133#947—34no—
134#947—38no—
135#947—61no—
136#947C2×D314yescomplemented
137#937—38no—
138#937—38no—
139#937—38no—
140#937—38no—
141#937C2×D314yescomplemented
142#936—32no—
143#936—34no—
144#936—38no—
145#936—34no—
146#936—61no—
147#885—38no—
148#885—38no—
149#885—38no—
150#885—38no—
151#885—38no—
152#885—38no—
153#885—38no—
154#885—38no—
155#885—64no—
156#885C2×D318yescomplemented
157#882—34no—
158#882—38no—
159#882—38no—
160#882—38no—
161#882C2×D318yescomplemented
162D3×C22⋊C4—38no—
163D3×C22⋊C4—34no—
164D3×C22⋊C4—38no—
165D3×C22⋊C4—38no—
166D3×C22⋊C4—38no—
167D3×C22⋊C4—64no—
168#875—34no—
169#875—32no—
170#875—38no—
171#875—61no—
172#875C2×D314yescomplemented
173C42×D3—32no—
174C42×D3—34no—
175C42×D3—61no—
176C23×C32C2412yes—
177C22×C3⋊D3—28no—
178C22×C3⋊D3—24no—
179C22×C3⋊D3C2412yes—
180C22×C3⋊D3C2411yescharacteristic
181C22×C3×D3—44no—
182C22×C3×D3—48no—
183C22×C3×D3C2418yes—
184C2×D32—28no—
185C2×D32—28no—
186C2×D32—28no—
187C2×D32—44no—
188C2×D32—48no—
189C2×D32—432no—
190C32×Q8—41no—
191C32×D4—41no—
192C2×C32×C4C2412yes—
193C2×C32×C4C2411yescharacteristic
194C2×C32×C4C2412yes—
195#638—42no—
196C2×C3⋊Dic3C2412yes—
197C2×C3⋊Dic3C2411yescharacteristic
198C2×C3⋊Dic3C2412yes—
199C4⋊(C3⋊D3)—41no—
200C4×C3⋊D3—22no—
201C4×C3⋊D3—24no—
202C4×C3⋊D3—24no—
203#634—42no—
204#634—41no—
205C3×#67—48no—
206C2×C3×Dic3C2418yes—
207C3×D12—44no—
208C3×D12—44no—
209C3×Dic6—44no—
210#627—44no—
211#626—48no—
212#625—44no—
213#625—44no—
214#624—28no—
215H(3,𝔽4)—32no—
216H(3,𝔽4)—92no—
217H(3,𝔽4)—98no—
218H(3,𝔽4)—92no—
219H(3,𝔽4)—92no—
220C2×#124—92no—
221C2×#124—94no—
222C2×#124—92no—
223C2×#124—91no—
224C2×#120—92no—
225C2×#120—94no—
226C24×C3—34no—
227C23×D3—34no—
228C23×D3—38no—
229C23×D3—38no—
230C23×D3—62no—
231C23×D3—128no—
232C23×D3—1216no—
233C23×D3C22×D314yescomplemented
234C2×C3×Q8—21no—
235C2×C3×Q8—34no—
236C2×C3×Q8C22×D312yescomplemented
237C2×C3×D4—21no—
238C2×C3×D4—38no—
239C2×C3×D4—34no—
240C2×C3×D4—34no—
241C2×C3×D4C22×D312yes—
242C2×#67—34no—
243C2×#67—38no—
244C2×#67—38no—
245C2×#67—38no—
246C2×#67—62no—
247C2×#67C22×D318yes—
248D3×Q8—128no—
249D3×Q8—124no—
250D3×Q8—124no—
251D3×D4—128no—
252D3×D4—128no—
253D3×D4—1216no—
254D3×D4—124no—
255D3×D4—124no—
256C2×D12—38no—
257C2×D12—32no—
258C2×D12—61no—
259C2×D12C22×D314yes—
260C2×D12C22×D314yes—
261C2×C4×D3—34no—
262C2×C4×D3—32no—
263C2×C4×D3—34no—
264C2×C4×D3—38no—
265C2×C4×D3—61no—
266C2×C4×D3—62no—
267C2×C4×D3—62no—
268C2×Dic6—32no—
269C2×Dic6—34no—
270C2×Dic6—38no—
271C2×Dic6—61no—
272C2×Dic6—62no—
273C2×Dic6C22×D314yescomplemented
274C3×C22⋊C4—24no—
275C3×C22⋊C4—34no—
276C3×C22⋊C4—38no—
277C3×C22⋊C4—38no—
278C3×C22⋊C4—38no—
279C3×C22⋊C4C22×D318yescomplemented
280C3×C42—21no—
281C3×C42—34no—
282C3×C42C22×D312yescomplemented
283#217—38no—
284#217—38no—
285#217—38no—
286#217—38no—
287#217—64no—
288#217C22×D314yescomplemented
289(C2×D3)⋊C4—38no—
290(C2×D3)⋊C4—38no—
291(C2×D3)⋊C4—38no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—38no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4—64no—
297(C2×D3)⋊C4C22×D318yescomplemented
298(C2×D3)⋊C4C22×D318yescomplemented
299(C2×D3)⋊C4C22×D318yescomplemented
300C4×Dic3—34no—
301C4×Dic3—32no—
302C4×Dic3—38no—
303C4×Dic3—62no—
304C4×Dic3—61no—
305C4×Dic3C22×D314yescomplemented
306C22×C32—24no—
307C22×C32—22no—
308C22×C32C2511yescharacteristic
309C2×C3⋊D3—24no—
310C2×C3⋊D3—22no—
311C2×C3⋊D3—48no—
312C2×C3⋊D3H(5,𝔽2)14yes—
313C2×C3⋊D3H(5,𝔽2)12yes—
314C2×C3×D3—28no—
315C2×C3×D3—28no—
316C2×C3×D3—28no—
317C2×C3×D3—416no—
318D32—416no—
319D32—416no—
320C32×C4—21no—
321C32×C4—22no—
322C32×C4—22no—
323C3⋊Dic3—21no—
324C3⋊Dic3—22no—
325C3⋊Dic3—22no—
326C3×Dic3—28no—
327C25—92no—
328C22×Q8—92no—
329C22×Q8—91no—
330C22×D4—94no—
331C22×D4—92no—
332C22×D4—92no—
333C22×D4—91no—
334#124—34no—
335#124—38no—
336#124—34no—
337#124—98no—
338#124—94no—
339#124—94no—
340#124—94no—
341#124—94no—
342#124—94no—
343#124—98no—
344#124—98no—
345#124—94no—
346#124—91no—
347#124—91no—
348#124—94no—
349#124—91no—
350#124D3211yescharacteristic, complemented
351#120—34no—
352#120—38no—
353#120—94no—
354#120—98no—
355#120—98no—
356#120—94no—
357#120—94no—
358#120—98no—
359C2×C22⋊C4—92no—
360C2×C22⋊C4—94no—
361C2×C22⋊C4—94no—
362C2×C22⋊C4—94no—
363C2×C22⋊C4—94no—
364C2×C42—92no—
365C2×C42—91no—
366C23×C3—22no—
367C23×C3—38no—
368C23×C3—128no—
369C23×C3—124no—
370C23×C3C23×D314yes—
371C22×D3—32no—
372C22×D3—34no—
373C22×D3—44no—
374C22×D3—48no—
375C22×D3—61no—
376C22×D3—62no—
377C22×D3—616no—
378C22×D3—616no—
379C22×D3—616no—
380C22×D3—616no—
381C22×D3—68no—
382C22×D3—124no—
383C22×D3—128no—
384C22×D3—128no—
385C22×D3—128no—
386C22×D3—128no—
387C22×D3—1264no—
388C22×D3C23×D318yes—
389C3×Q8—42no—
390C3×Q8—42no—
391C3×Q8—124no—
392C3×D4—42no—
393C3×D4—42no—
394C3×D4—124no—
395C3×D4—124no—
396C3×D4—128no—
397C2×C3×C4—21no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—38no—
401C2×C3×C4C23×D314yes—
402C2×C3×C4C23×D312yes—
403C2×C3×C4C23×D314yes—
404#67—48no—
405#67—128no—
406#67—128no—
407#67—128no—
408#67—124no—
409#67—124no—
410C2×Dic3—34no—
411C2×Dic3—32no—
412C2×Dic3—34no—
413C2×Dic3—61no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3C23×D318yes—
417D12—44no—
418D12—44no—
419D12—122no—
420D12—122no—
421D12—128no—
422C4×D3—616no—
423C4×D3—64no—
424C4×D3—68no—
425C4×D3—68no—
426C4×D3—64no—
427C4×D3—124no—
428C4×D3—124no—
429Dic6—44no—
430Dic6—128no—
431Dic6—124no—
432Dic6—122no—
433Dic6—124no—
434Dic6—122no—
435C2×C32—42no—
436C2×C32C2×H(5,𝔽2)12yes—
437C2×C32C2×H(5,𝔽2)11yescharacteristic
438C3⋊D3—42no—
439C3⋊D3H(3,𝔽4)14yescomplemented
440C3×D3—48no—
441C24—34no—
442C24—94no—
443C24—94no—
444C24—92no—
445C24—364no—
446C24—368no—
447C2×Q8—34no—
448C2×Q8—94no—
449C2×Q8—92no—
450C2×Q8—91no—
451C2×Q8—362no—
452C2×Q8—364no—
453C2×Q8C2×D3211yescharacteristic, complemented
454C2×D4—38no—
455C2×D4—34no—
456C2×D4—34no—
457C2×D4—98no—
458C2×D4—94no—
459C2×D4—94no—
460C2×D4—92no—
461C2×D4—91no—
462C2×D4—362no—
463C2×D4—364no—
464C2×D4—364no—
465C2×D4—368no—
466C2×D4C2×D3211yescharacteristic
467C22×C4—94no—
468C22×C4—91no—
469C22×C4—92no—
470C22×C4—92no—
471C22⋊C4—34no—
472C22⋊C4—38no—
473C22⋊C4—38no—
474C22⋊C4—38no—
475C22⋊C4—94no—
476C22⋊C4—98no—
477C22⋊C4—98no—
478C22⋊C4—98no—
479C22⋊C4—94no—
480C22⋊C4—94no—
481C22⋊C4—94no—
482C22⋊C4C2×D3214yescomplemented
483C42—34no—
484C42—94no—
485C42—91no—
486C42—92no—
487C42C2×D3211yescharacteristic, complemented
488C22×C3—28no—
489C22×C3—24no—
490C22×C3—21no—
491C22×C3—42no—
492C22×C3—44no—
493C22×C3—68no—
494C22×C3—68no—
495C22×C3—68no—
496C22×C3—1216no—
497C22×C3C24×D312yes—
498C2×D3—28no—
499C2×D3—28no—
500C2×D3—28no—
501C2×D3—34no—
502C2×D3—38no—
503C2×D3—416no—
504C2×D3—62no—
505C2×D3—64no—
506C2×D3—64no—
507C2×D3—68no—
508C2×D3—122no—
509C2×D3—124no—
510C2×D3—1232no—
511C2×D3—1216no—
512C2×D3—1232no—
513C2×D3—248no—
514C3×C4—22no—
515C3×C4—24no—
516C3×C4—24no—
517C3×C4—22no—
518C3×C4—42no—
519C3×C4—42no—
520C3×C4—68no—
521Dic3—28no—
522Dic3—62no—
523Dic3—62no—
524Dic3—64no—
525Dic3—64no—
526Dic3—122no—
527Dic3—122no—
528C32C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
529C23—38no—
530C23—91no—
531C23—92no—
532C23—124no—
533C23—128no—
534C23—184no—
535C23—188no—
536C23—188no—
537C23—188no—
538C23—188no—
539C23—364no—
540C23—368no—
541C23—3632no—
542C23C22×D3212yes—
543Q8—41no—
544Q8—124no—
545Q8—361no—
546Q8—362no—
547Q8—364no—
548D4—41no—
549D4—124no—
550D4—124no—
551D4—128no—
552D4—361no—
553D4—368no—
554D4—362no—
555D4—364no—
556D4—364no—
557C2×C4—38no—
558C2×C4—91no—
559C2×C4—92no—
560C2×C4—92no—
561C2×C4—182no—
562C2×C4—184no—
563C2×C4—184no—
564C2×C4—188no—
565C2×C4C22×D3212yes—
566C2×C4C22×D3211yescharacteristic
567C2×C4C22×D3212yes—
568C2×C3—21no—
569C2×C3—22no—
570C2×C3—44no—
571C2×C3—82no—
572C2×C3—128no—
573C2×C3D3×H(5,𝔽2)12yes—
574C2×C3D3×H(5,𝔽2)14yes—
575D3—38no—
576D3—48no—
577D3—64no—
578D3—124no—
579D3—242no—
580C22—22no—
581C22—24no—
582C22—68no—
583C22—68no—
584C22—68no—
585C22—92no—
586C22—94no—
587C22—1216no—
588C22—182no—
589C22—184no—
590C22—368no—
591C22—3616no—
592C22—3616no—
593C22C23×D3211yescharacteristic
594C4—21no—
595C4—22no—
596C4—22no—
597C4—68no—
598C4—181no—
599C4—182no—
600C4—182no—
601C3—21no—
602C3D3×H(3,𝔽4)12yescomplemented
603C2—42no—
604C2—94no—
605C2—128no—
606C2—362no—
607C2#1059667511yescharacteristic
608C2#1059669212yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#124C22
hypercenter#124D32
hypocenterC32C2×H(3,𝔽4)
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#124C2semidirect
2. C3×#5683C2semidirect
3. #10595439C2semidirect
4. #10595432C2semidirect
5. #10595278C2semidirect
6. #10595256C2semidirect
7. #10594309C2semidirect
8. #10594288C2semidirect
9. #10594258C2semidirect
10. #10594021C2semidirect
11. #10594009C2semidirect
13. C23×D32C22semidirect
14. C2×Q8×C3⋊D3C22semidirect
19. C2×#3797C22semidirect
20. C32×#124C22semidirect
21. #64156C22semidirect
22. #64145C22semidirect
23. #64094C22semidirect
24. C22⋊C4×C3⋊D3C22semidirect
25. #64084C22semidirect
26. C42×C3⋊D3C22semidirect
27. C3×#947C22semidirect
28. C3×#937C22semidirect
29. C3×#885C22semidirect
30. C3×#882C22semidirect
31. C3×#875C22semidirect
32. #63983C22semidirect
33. #63977C22semidirect
34. #63976C22semidirect
35. #63974C22semidirect
36. #63959C22semidirect
37. #63923C22semidirect
38. #63922C22semidirect
39. #63922C22semidirect
40. #63921C22semidirect
41. #63921C22semidirect
42. #63921C22semidirect
43. #63915C22semidirect
44. #63915C22semidirect
45. #63913C22semidirect
46. #63913C22semidirect
47. #63907C22semidirect
48. C4×#624C22semidirect
49. #63863C22semidirect
50. #63860C22semidirect
51. #63852C22semidirect
56. #5683D3semidirect
67. C23×C3×D3C23semidirect
71. C22×D32C23semidirect
72. C2×C32×Q8C23semidirect
81. C2×#634C23semidirect
82. C2×#634C23semidirect
86. C2×C3×Dic6C23semidirect
88. C2×#627C23semidirect
96. C32×C22⋊C4C23semidirect
97. C32×C42C23semidirect
98. #3757C23semidirect
99. #3752C23semidirect
100. #3752C23semidirect
101. C4×C3⋊Dic3C23semidirect
102. C4×C3⋊Dic3C23semidirect
103. C3×#217C23semidirect
104. C3×(C2×D3)⋊C4C23semidirect
105. C3×(C2×D3)⋊C4C23semidirect
106. C3×(C2×D3)⋊C4C23semidirect
107. C3×C4×Dic3C23semidirect
108. #3722C23semidirect
109. (C2×D3)⋊Dic3C23semidirect
110. (C2×D3)⋊Dic3C23semidirect
111. (C2×D3)⋊Dic3C23semidirect
112. Dic32C23semidirect
127. C3×#124C2×D3semidirect
136. #947C2×D3semidirect
141. #937C2×D3semidirect
156. #885C2×D3semidirect
161. #882C2×D3semidirect
172. #875C2×D3semidirect
233. C23×D3C22×D3semidirect
236. C2×C3×Q8C22×D3semidirect
273. C2×Dic6C22×D3semidirect
279. C3×C22⋊C4C22×D3semidirect
282. C3×C42C22×D3semidirect
288. #217C22×D3semidirect
297. (C2×D3)⋊C4C22×D3semidirect
298. (C2×D3)⋊C4C22×D3semidirect
299. (C2×D3)⋊C4C22×D3semidirect
305. C4×Dic3C22×D3semidirect
350. #124D32semidirect
439. C3⋊D3H(3,𝔽4)semidirect
453. C2×Q8C2×D32semidirect
482. C22⋊C4C2×D32semidirect
487. C42C2×D32semidirect
528. C32C2×H(3,𝔽4)semidirect
602. C3D3×H(3,𝔽4)semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1242
C3×#56832
#105954392
#105954322
#105952782
#105952562
#105943092
#105942882
#105942582
#105940212
#105940092
D3×H(3,𝔽4)3