Finite Group Databasebeta

← #11870720

Subgroups — #11870720

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5596C211yesmaximal, characteristic
2C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
3#10592733C211yesmaximal, characteristic, complemented
4C3×#5040C211yesmaximal, characteristic, complemented
5#10591438C212yesmaximal, complemented
6Dic3×#214C212yesmaximal, complemented
7#10591171C211yesmaximal, characteristic, complemented
8#10591092C211yesmaximal, characteristic, complemented
9#10591053C211yesmaximal, characteristic, complemented
10#10590486C212yesmaximal, complemented
11#10590475C212yesmaximal, complemented
12#83315—31nomaximal
13#80028—31nomaximal
14C2×C3×#237—21no—
15C22×C3×Dic6C2211yescharacteristic
16C32×#121C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C3×#940C2211yescharacteristic
19C3×#939—21no—
20C3×D4×Dic3C2211yescharacteristic
21C2×C3×#214C2212yes—
22C3×#930C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C3×#893C2211yescharacteristic
25C3×#888C2211yescharacteristic
26C3×#885—21no—
27C3×#67⋊C4—21no—
28C2×Dic3⋊Dic3—21no—
29C2×Dic32—21no—
30Dic3×Dic6—21no—
31Dic3×Dic6—21no—
32Dic3×Dic6C2212yes—
33Dic3×Dic6C2212yes—
34C2×#3715C2212yes—
35#63659C2212yes—
36#63657C2211yescharacteristic
37#63635C2212yes—
38C3×#830C2211yescharacteristic
39C3×#810C2212yes—
40#63573C2212yes—
41Dic3⋊(C3⋊C8)C2212yes—
42#63565C2212yes—
43#63563C2212yes—
44Dic3×C3⋊C8C2212yes—
45C3×#532—31no—
46C2×Q8×Dic3—31no—
47#5596D311yescharacteristic
48C2×C4×Dic6—31no—
49C3×#448—31no—
50#5227—31no—
51#5163—32no—
52Dic3×SD16—32no—
53#5094—32no—
54#5075—32no—
55#5040—31no—
56#5040D311yescharacteristic, complemented
57#5034—31no—
58#5034—31no—
59#5034—31no—
60#5034—61no—
61C4×#214—32no—
62C4×#214—32no—
63#4925—31no—
64#4791—32no—
65#4788—32no—
66#4735—31no—
67#4718—31no—
68C2×C32×D4—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3—21no—
72C2×C3×#67—21no—
73C2×C3×#67—21no—
74C2×C3×#67—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C3×#237—44no—
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3—21no—
82C2×C3×Dic6—21no—
83C2×C3×Dic6—24no—
84C2×C3×Dic6—21no—
85C2×C3×Dic6C2312yes—
86C32×C4⋊C4C2311yescharacteristic
87C32×C22⋊C4—21no—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90C2×C3⋊(C3⋊C8)C2312yes—
91C3×#217—21no—
92C3×#214—24no—
93C3×(C2×D3)⋊C4—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4—21no—
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—22no—
104Dic32—22no—
105Dic32—22no—
106#3715—24no—
107#3103—91noSylow
108C2×C3×#41—61no—
109C22×C3×Q8—31no—
110C2×#237—21no—
111C22×Dic6C2×D311yescharacteristic
112C2×C3×SD16—32no—
113C3×C4⋊Q8—31no—
114C3×#127—31no—
115C3×#124—61no—
116C3×#121—21no—
117C3×#121—31no—
118C3×#121—61no—
119C3×#121C2×D311yescharacteristic
120C3×#121C2×D311yescharacteristic
121C3×C4×D4—31no—
122C3×C4×D4—31no—
123C3×C4×D4—61no—
124C2×C3×C42—31no—
125Q8×Dic3—32no—
126Q8×Dic3—32no—
127Q8×Dic3—61no—
128Q8×Dic3—61no—
129C2×#215—32no—
130#940C2×D311yescharacteristic
131#939—21no—
132D4×Dic3C2×D311yescharacteristic
133C2×#214—32no—
134C2×#214C2×D312yes—
135#930C2×D311yescharacteristic
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—61no—
139C2×C4⋊Dic3—61no—
140C2×Dic3⋊C4—61no—
141C2×C4×Dic3—61no—
142C2×C4×Dic3—61no—
143C2×C4×Dic3C2×D311yescharacteristic
144#893C2×D311yescharacteristic
145#888C2×D311yescharacteristic
146#885—21no—
147#67⋊C4—21no—
148C4×Dic6—32no—
149C4×Dic6—32no—
150C4×Dic6—61no—
151C4×Dic6—61no—
152C3×#103—32no—
153C3×C22⋊C8—31no—
154#835—32no—
155#832—32no—
156#832—32no—
157#832—32no—
158#832—62no—
159#830—31no—
160#830—31no—
161#830—61no—
162#830C2×D311yescharacteristic
163#821—32no—
164#817—32no—
165Dic3⋊C8—32no—
166C8×Dic3—32no—
167#810—32no—
168#810C2×D312yes—
169#808—32no—
170#808—32no—
171#808—32no—
172#808—62no—
173C4⋊(C3⋊C8)—32no—
174C4×C3⋊C8—32no—
175C23×C32—21no—
176C23×C32C2×D411yescharacteristic
177C22×C3×D3—21no—
178C32×D4—22no—
179C32×D4—42no—
180C2×C32×C4—22no—
181C2×C32×C4—21no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—42no—
186C3×#67—42no—
187C3×#67—42no—
188C3×#67—42no—
189C2×C3×Dic3—24no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3SD1614yescomplemented
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C3×D12—22no—
200C3×C4×D3—42no—
201C3×Dic6—24no—
202C3×Dic6—22no—
203C3×Dic6—42no—
204C3×Dic6#4114yescomplemented
205C3⋊(C3⋊C8)—22no—
206C3×C3⋊C8—22no—
207#532—31no—
208C2×C4×Q8—91no—
209#481—91no—
210#481—91no—
211#475—92no—
212#460—92no—
213#448—31no—
214#448—91no—
215C4×SD16—92no—
216C4×SD16—92no—
217#431—91no—
218C3×#41—124no—
219C2×C3×Q8—32no—
220C2×C3×Q8—61no—
221C2×C3×Q8—64no—
222C2×C3×Q8—61no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—31no—
227C2×C3×D4—41no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C2×C3×D4—61no—
231C2×C3×D4C22×D311yescharacteristic
232C2×C3×D4C22×D311yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4—31no—
235C22×C3×C4—31no—
236C22×C3×C4—61no—
237C22×C3×C4—61no—
238C22×C3×C4—61no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—21no—
242C2×#67—21no—
243C2×#67—21no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—61no—
247C22×Dic3—61no—
248C22×Dic3—121no—
249C22×Dic3#6711yescharacteristic
250C22×Dic3#6711yescharacteristic
251#237—44no—
252C2×D12C22×D311yescharacteristic
253C2×C4×D3—21no—
254C2×Dic6—21no—
255C2×Dic6—24no—
256C2×Dic6—21no—
257C2×Dic6C22×D312yes—
258C3×SD16—64no—
259C2×C3×C8—32no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4C22×D311yescharacteristic
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C22⋊C4—21no—
266C3×C22⋊C4—21no—
267C3×C22⋊C4—41no—
268C3×C22⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C42—31no—
272C3×C42—31no—
273C3×C42—31no—
274C3×C42—31no—
275#217—21no—
276#215—64no—
277#214—24no—
278#214—64no—
279(C2×D3)⋊C4—21no—
280(C2×D3)⋊C4—21no—
281C4⋊Dic3—32no—
282C4⋊Dic3—32no—
283C4⋊Dic3—62no—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3—62no—
287C4⋊Dic3—62no—
288C4⋊Dic3—121no—
289C4⋊Dic3C22×D311yescharacteristic
290Dic3⋊C4—21no—
291Dic3⋊C4—62no—
292Dic3⋊C4—62no—
293C4×Dic3—62no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C4×Dic3—62no—
297C4×Dic3#6711yescharacteristic
298C4×Dic3#6711yescharacteristic
299C4×Dic3C22×D311yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301C2×C3⋊C8—32no—
302C2×C3⋊C8—32no—
303C2×C3⋊C8—62no—
304C2×C3⋊C8C22×D312yes—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32—41no—
310C22×C32C2×SD1612yes—
311C22×C32C22×D411yescharacteristic
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C32×C4—21no—
316C32×C4—41no—
317C32×C4C2×#4112yes—
318C3⋊Dic3—42no—
319C3×Dic3—24no—
320C3×Dic3—21no—
321C3×Dic3—21no—
322C3×Dic3—41no—
323C3×Dic3C2×SD1612yes—
324C3×Dic3C2×SD1612yes—
325C2×#41—61no—
326C22×Q8—31no—
327C2×SD16—32no—
328C2×SD16—92no—
329C4⋊Q8—31no—
330#127—31no—
331#124—61no—
332#121—31no—
333#121—61no—
334#121D3211yescharacteristic
335C4×Q8—92no—
336C4×Q8—92no—
337C4×Q8—181no—
338C4×Q8—181no—
339C4×D4—31no—
340C4×D4—31no—
341C4×D4—61no—
342C2×C4⋊C4—91no—
343C2×C4⋊C4—181no—
344C2×C42—31no—
345C2×C42—181no—
346#106—92no—
347#106—92no—
348C4⋊C8—92no—
349#103—32no—
350#103—92no—
351#102—92no—
352#102—92no—
353C22⋊C8—31no—
354C22⋊C8—91no—
355C4×C8—92no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—41no—
360C23×C3—61no—
361C23×C3D3×D411yescharacteristic
362C23×C3C2×#6711yescharacteristic
363C22×D3—21no—
364C3×Q8—34no—
365C3×Q8—64no—
366C3×Q8—62no—
367C3×Q8—122no—
368C3×D4—22no—
369C3×D4—22no—
370C3×D4—42no—
371C3×D4—42no—
372C3×D4—42no—
373C3×D4—62no—
374C3×D4—82no—
375C3×D4—122no—
376C3×D4—122no—
377C3×D4—122no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—34no—
385C2×C3×C4—31no—
386C2×C3×C4—31no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—42no—
390C2×C3×C4—41no—
391C2×C3×C4—64no—
392C2×C3×C4—62no—
393C2×C3×C4—61no—
394C2×C3×C4—122no—
395C2×C3×C4—122no—
396C2×C3×C4—121no—
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401#67—42no—
402#67—42no—
403#67—42no—
404C2×Dic3—24no—
405C2×Dic3—22no—
406C2×Dic3—21no—
407C2×Dic3—41no—
408C2×Dic3—42no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—122no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3—242no—
415C2×Dic3#21414yescomplemented
416C2×Dic3C2×#6711yescharacteristic
417C2×Dic3C2×#6711yescharacteristic
418C2×Dic3C2×#6711yescharacteristic
419C2×Dic3C2×#6711yescharacteristic
420D12—22no—
421C4×D3—42no—
422Dic6—24no—
423Dic6—22no—
424Dic6—42no—
425Dic6#23714yescomplemented
426C3×C8—62no—
427C3⋊C8—22no—
428C3⋊C8—62no—
429C3⋊C8—62no—
430C3⋊C8—122no—
431C2×C32—22no—
432C2×C32—81no—
433C2×C32#52511yescharacteristic
434C2×C32C22×SD1611yescharacteristic
435C2×C32#57511yescharacteristic
436C3×D3—81no—
437#41—124no—
438C2×Q8—32no—
439C2×Q8—61no—
440C2×Q8—64no—
441C2×Q8—61no—
442C2×D4—21no—
443C2×D4—31no—
444C2×D4—61no—
445C2×D4—61no—
446C2×D4—61no—
447C2×D4C2×D3211yescharacteristic
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—61no—
451C22×C4—61no—
452C22×C4—61no—
453C22×C4—181no—
454C22×C4C2×D3211yescharacteristic
455SD16—64no—
456SD16—184no—
457C2×C8—32no—
458C2×C8—92no—
459C4⋊C4—31no—
460C4⋊C4—61no—
461C4⋊C4—92no—
462C4⋊C4—182no—
463C4⋊C4—182no—
464C4⋊C4—181no—
465C4⋊C4C2×D3211yescharacteristic
466C22⋊C4—21no—
467C22⋊C4—61no—
468C22⋊C4—61no—
469C22⋊C4—61no—
470C42—31no—
471C42—31no—
472C42—31no—
473C42—31no—
474C42—182no—
475C42—182no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—22no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—81no—
491C22×C3—81no—
492C22×C3—81no—
493C22×C3—121no—
494C22×C3—121no—
495C22×C3—121no—
496C22×C3D3×SD1612yes—
497C22×C3C2×#21412yes—
498C22×C3C2×D3×D411yescharacteristic
499C22×C3C22×#6711yescharacteristic
500C2×D3—41no—
501C2×D3—41no—
502C2×D3—41no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—22no—
506C3×C4—32no—
507C3×C4—32no—
508C3×C4—41no—
509C3×C4—41no—
510C3×C4—41no—
511C3×C4—61no—
512C3×C4—61no—
513C3×C4—64no—
514C3×C4—81no—
515C3×C4—121no—
516C3×C4C2×#23712yes—
517C3×C4D3×#4112yes—
518Dic3—21no—
519Dic3—21no—
520Dic3—24no—
521Dic3—41no—
522Dic3—122no—
523Dic3—122no—
524Dic3—242no—
525Dic3C2×#21412yes—
526Dic3C2×#21412yes—
527C32#310311yescharacteristic, complemented, Sylow
528C23—21no—
529C23—61no—
530C23D3×#6711yescharacteristic
531Q8—34no—
532Q8—64no—
533Q8—62no—
534Q8—122no—
535D4—22no—
536D4—42no—
537D4—62no—
538D4—122no—
539D4—122no—
540D4—122no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—31no—
544C2×C4—31no—
545C2×C4—34no—
546C2×C4—31no—
547C2×C4—31no—
548C2×C4—64no—
549C2×C4—62no—
550C2×C4—61no—
551C2×C4—122no—
552C2×C4—122no—
553C2×C4—121no—
554C2×C4—182no—
555C2×C4—362no—
556C2×C4D3×#6711yescharacteristic
557C2×C4C22×D3211yescharacteristic
558C8—62no—
559C8—182no—
560C2×C3—22no—
561C2×C3—22no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—42no—
566C2×C3—81no—
567C2×C3—81no—
568C2×C3—161no—
569C2×C3—241no—
570C2×C3#558611yescharacteristic
571C2×C3C2×D3×SD1611yescharacteristic
572C2×C3#577711yescharacteristic
573C2×C3C22×#21411yescharacteristic
574C2×C3#582211yescharacteristic
575C2×C3#582811yescharacteristic
576D3—81no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—121no—
583C22—121no—
584C22—121no—
585C22D3×#21412yes—
586C22C2×D3×#6711yescharacteristic
587C4—21no—
588C4—32no—
589C4—32no—
590C4—41no—
591C4—64no—
592C4—61no—
593C4—61no—
594C4—121no—
595C4—362no—
596C4D3×#23712yes—
597C3—21no—
598C3#8002811yescharacteristic, complemented
599C3#8331511yescharacteristic, complemented
600C2—22no—
601C2—81no—
602C2—241no—
603C2C2×D3×#21411yescharacteristic
604C2#1059515411yescharacteristic
605C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5596C2
hypercenter#121D32
hypocenterC32#3103
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×Dic6C2semidirect
3. #10592733C2semidirect
4. C3×#5040C2semidirect
5. #10591438C2semidirect
6. Dic3×#214C2semidirect
7. #10591171C2semidirect
8. #10591092C2semidirect
9. #10591053C2semidirect
10. #10590486C2semidirect
11. #10590475C2semidirect
56. #5040D3semidirect
194. C2×C3×Dic3SD16semidirect
204. C3×Dic6#41semidirect
415. C2×Dic3#214semidirect
425. Dic6#237semidirect
527. C32#3103semidirect
598. C3#80028semidirect
599. C3#83315semidirect

Maximal subgroups

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

subgroupindex
C3×#55962
C2×Dic3×Dic62
#105927332
C3×#50402
#105914382
Dic3×#2142
#105911712
#105910922
#105910532
#105904862
#105904752
#833153
#800283