Finite Group Databasebeta

← C3×#81869 #11874421

Subgroups — C3×#81869 #11874421

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C212yesmaximal, complemented
2C2×C3×#916C212yesmaximal, complemented
3C3×#5725C211yesmaximal, characteristic, complemented
4C3×#5668C211yesmaximal, characteristic, complemented
5C32×#497C211yesmaximal, characteristic, complemented
6C3×#5190C212yesmaximal, complemented
7C3×#5176C212yesmaximal, complemented
8C3×#5086C211yesmaximal, characteristic, complemented
9C3×#5058C211yesmaximal, characteristic, complemented
10C3×#4712C211yesmaximal, characteristic, complemented
11C3×D3×#97C211yesmaximal, characteristic, complemented
12C3×#3150—31nomaximal
13#81869C311yesmaximal, characteristic, direct product factor
14C2×C3×#239C2212yes—
15C2×C3×#239C2211yescharacteristic
16C2×C3×#237C2211yescharacteristic
17C2×C32×Q16C2212yes—
18C2×C32×SD16C2212yes—
19C32×C4⋊Q8C2211yescharacteristic
20C32×#124C2211yescharacteristic
21C3×#947C2212yes—
22C3×#944C2211yescharacteristic
23C2×C3×#216C2212yes—
24C2×C3×#215C2212yes—
25C2×C3×#215C2212yes—
26C3×#940C2211yescharacteristic
27C2×C3×#213C2212yes—
28C3×#919—28no—
29C3×#916—28no—
30C2×C3×D24C2212yes—
31C2×C3×#204C2212yes—
32C2×C3×D3×C8C2212yes—
33C3×#895—22no—
34C3×#893—22no—
35C3×#884—22no—
36C3×#67⋊C4—22no—
37C3×#875C2211yescharacteristic
38C3×#874C2211yescharacteristic
39C3×C42×D3C2211yescharacteristic
40C32×#97C2211yescharacteristic
41C3×#815C2212yes—
42C3×#803C2211yescharacteristic
43C2×C3×#135—32no—
44C2×C3×#135—32no—
45C3×#532—31no—
46C3×#532—31no—
47C2×#919C2×C312yescomplemented
48C2×#916C2×C312yescomplemented
49#5725C2×C311yescharacteristic, complemented
50#5668C2×C311yescharacteristic, complemented
51C3×#497—21no—
52C3×#497—32no—
53C3×#497—31no—
54C3×#497D311yescharacteristic, complemented
55C3×#497C2×C311yescharacteristic, complemented
56C3×#496—32no—
57C3×#496—31no—
58C3×#496—31no—
59C2×C3×#97—31no—
60#5190C2×C312yescomplemented
61#5176C2×C312yescomplemented
62#5086C2×C311yescharacteristic, complemented
63#5058C2×C311yescharacteristic, complemented
64#4712C2×C311yescharacteristic, complemented
65D3×#97C2×C311yescharacteristic, complemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×Q8C2312yes—
68C2×C32×D4C2311yescharacteristic
69C2×C3×#67—21no—
70C2×C3×#67—22no—
71C22×C3×Dic3—21no—
72C3×#239—24no—
73C3×#239—24no—
74C3×#239—24no—
75C3×#237—24no—
76C2×C3×D12—21no—
77C2×C3×D12—22no—
78C2×C3×D12—22no—
79C2×C3×D12C2312yes—
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3—21no—
82C2×C3×C4×D3—22no—
83C2×C3×C4×D3D412yes—
84C2×C3×C4×D3C2311yescharacteristic
85C2×C3×Dic6C2311yescharacteristic
86C32×Q16—24no—
87C32×SD16—24no—
88C2×C32×C8C2312yes—
89C32×C4⋊C4—22no—
90C32×C22⋊C4—22no—
91C32×C42C2311yescharacteristic
92C3×#216—24no—
93C3×#215—24no—
94C3×#215—24no—
95C3×#213—24no—
96C3×(C2×D3)⋊C4—22no—
97C3×(C2×D3)⋊C4—24no—
98C3×Dic3⋊C4—22no—
99C3×C4×Dic3D412yes—
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102C3×D24—24no—
103C3×#204—24no—
104C3×D3×C8D418yescomplemented
105#3150—31noSylow
106C2×C3×#41—32no—
107C2×C3×#41—31no—
108C2×C3×#41—31no—
109C2×#239C22×C311yescharacteristic
110C2×#239C22×C312yes—
111C2×#237C22×C311yescharacteristic
112C3×#135—68no—
113C3×#135—68no—
114C2×C3×Q16—22no—
115C2×C3×Q16—32no—
116C2×C3×Q16C2×D312yes—
117C2×C3×Q16C22×C312yes—
118C2×C3×SD16—22no—
119C2×C3×SD16—32no—
120C2×C3×SD16—32no—
121C2×C3×SD16—32no—
122C2×C3×SD16C2×D312yes—
123C2×C3×SD16C22×C312yes—
124C2×C3×D8—32no—
125C2×C3×D8—32no—
126C22×C3×C8—32no—
127C3×C4⋊Q8—21no—
128C3×C4⋊Q8—31no—
129C3×C4⋊Q8C2×D311yescharacteristic
130C3×C4⋊Q8C22×C311yescharacteristic
131C3×#127—31no—
132C3×#127—31no—
133C3×#124—21no—
134C3×#124—32no—
135C3×#124—31no—
136C3×#124C2×D311yescharacteristic
137C3×#124C22×C311yescharacteristic
138C3×#121—62no—
139C3×#121—62no—
140C3×C4×D4—62no—
141C3×C4×D4—62no—
142C2×C3×C42—31no—
143#947C22×C312yes—
144#944C22×C311yescharacteristic
145C2×#216C22×C312yes—
146C2×#215C22×C312yes—
147C2×#215C22×C312yes—
148#940C22×C311yescharacteristic
149C2×#213C22×C312yes—
150#919—28no—
151#916—28no—
152C2×D24C22×C312yes—
153C2×#204C22×C312yes—
154C2×D3×C8C22×C312yes—
155#895—22no—
156#893—22no—
157#884—22no—
158#67⋊C4—22no—
159#875C22×C311yescharacteristic
160#874C22×C311yescharacteristic
161C42×D3C22×C311yescharacteristic
162C3×#97—21no—
163C3×#97—32no—
164C3×#97—31no—
165C3×#97C2×D311yescharacteristic
166C3×#97C22×C311yescharacteristic
167#815C22×C312yes—
168#803C22×C311yescharacteristic
169C23×C32—21no—
170C22×C3×D3—22no—
171C22×C3×D3—21no—
172C22×C3×D3C2×D411yescharacteristic
173C32×Q8—22no—
174C32×Q8—22no—
175C32×Q8—22no—
176C32×D4—22no—
177C2×C32×C4—21no—
178C2×C32×C4—22no—
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2411yescharacteristic
181C3×#67—44no—
182C3×#67—42no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—42no—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3C2×D411yescharacteristic
187C3×D12—22no—
188C3×D12—22no—
189C3×D12—22no—
190C3×D12—44no—
191C3×D12—42no—
192C3×D12—44no—
193C3×C4×D3—42no—
194C3×C4×D3—42no—
195C3×C4×D3—44no—
196C3×C4×D3C2×D414yes—
197C3×Dic6—22no—
198C32×C8C2×D414yes—
199C3×C3⋊C8C2×D414yes—
200C2×#135—32no—
201C2×#135—32no—
202#532—31no—
203#532—31no—
204#497—32no—
205#497—31no—
206#497C3×D311yescharacteristic, complemented
207#496—32no—
208#496—31no—
209#496—31no—
210C2×#97—31no—
211C3×#41—64no—
212C3×#41—64no—
213C3×#41—64no—
214C3×#41—64no—
215C2×C3×Q8—21no—
216C2×C3×Q8—22no—
217C2×C3×Q8—31no—
218C2×C3×Q8C22×D312yes—
219C2×C3×Q8C22×D311yescharacteristic
220C2×C3×Q8C23×C311yescharacteristic
221C2×C3×Q8C23×C312yes—
222C2×C3×D4—21no—
223C2×C3×D4—32no—
224C2×C3×D4—31no—
225C2×C3×D4—61no—
226C2×C3×D4—62no—
227C2×C3×D4—62no—
228C2×C3×D4—61no—
229C2×C3×D4—62no—
230C2×C3×D4C22×D311yescharacteristic
231C2×C3×D4C23×C311yescharacteristic
232C22×C3×C4—31no—
233C22×C3×C4—32no—
234C22×C3×C4—61no—
235C22×C3×C4—62no—
236C22×C3×C4—61no—
237C2×#67—21no—
238C2×#67—22no—
239C22×Dic3—21no—
240#239—24no—
241#239—24no—
242#239—24no—
243#237—24no—
244C2×D12—21no—
245C2×D12—22no—
246C2×D12—22no—
247C2×D12C23×C312yes—
248C2×D12C23×C311yescharacteristic
249C2×C4×D3—21no—
250C2×C4×D3—22no—
251C2×C4×D3C3×D412yes—
252C2×C4×D3C23×C311yescharacteristic
253C2×Dic6C23×C311yescharacteristic
254C3×Q16—24no—
255C3×Q16—24no—
256C3×Q16—44no—
257C3×Q16—64no—
258C3×SD16—24no—
259C3×SD16—24no—
260C3×SD16—44no—
261C3×SD16—64no—
262C3×SD16—64no—
263C3×SD16—64no—
264C3×D8—64no—
265C3×D8—64no—
266C2×C3×C8—22no—
267C2×C3×C8—32no—
268C2×C3×C8—38no—
269C2×C3×C8C22×D312yes—
270C2×C3×C8C23×C312yes—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—22no—
273C3×C4⋊C4—42no—
274C3×C4⋊C4—62no—
275C3×C22⋊C4—22no—
276C3×C22⋊C4—22no—
277C3×C22⋊C4—42no—
278C3×C22⋊C4—64no—
279C3×C22⋊C4—62no—
280C3×C42—21no—
281C3×C42—32no—
282C3×C42—31no—
283C3×C42C22×D311yescharacteristic
284C3×C42C23×C311yescharacteristic
285#216—24no—
286#215—24no—
287#215—24no—
288#213—24no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—24no—
291Dic3⋊C4—22no—
292C4×Dic3C3×D412yes—
293C4×Dic3C23×C311yescharacteristic
294C2×C3⋊C8C23×C312yes—
295D24—24no—
296#204—24no—
297D3×C8C3×D418yescomplemented
298C22×C32—41no—
299C22×C32—42no—
300C22×C32C22×D411yescharacteristic
301C2×C3×D3—22no—
302C2×C3×D3—42no—
303C2×C3×D3—41no—
304C2×C3×D3—44no—
305C2×C3×D3—42no—
306C2×C3×D3#12712yes—
307C32×C4—22no—
308C32×C4—41no—
309C32×C4—42no—
310C32×C4C22×D412yes—
311C3×Dic3—22no—
312C3×Dic3—41no—
313C3×Dic3#12712yes—
314C2×#41—32no—
315C2×#41—31no—
316C2×#41—31no—
317#135—68no—
318#135—68no—
319C2×Q16—32no—
320C2×Q16C2×C3×D312yes—
321C2×SD16—32no—
322C2×SD16—32no—
323C2×SD16—32no—
324C2×SD16C2×C3×D312yes—
325C2×D8—32no—
326C2×D8—32no—
327C22×C8—32no—
328C4⋊Q8—31no—
329C4⋊Q8C2×C3×D311yescharacteristic
330#127—31no—
331#127—31no—
332#124—32no—
333#124—31no—
334#124C2×C3×D311yescharacteristic
335#121—62no—
336#121—62no—
337C4×D4—62no—
338C4×D4—62no—
339C2×C42—31no—
340#97—32no—
341#97—31no—
342#97C2×C3×D311yescharacteristic
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—31no—
346C23×C3—41no—
347C23×C3—62no—
348C23×C3—61no—
349C22×D3—22no—
350C22×D3—21no—
351C22×D3C2×C3×D411yescharacteristic
352C3×Q8—22no—
353C3×Q8—22no—
354C3×Q8—22no—
355C3×Q8—22no—
356C3×Q8—22no—
357C3×Q8—22no—
358C3×Q8—42no—
359C3×Q8—42no—
360C3×Q8—42no—
361C3×Q8—62no—
362C3×D4—22no—
363C3×D4—22no—
364C3×D4—42no—
365C3×D4—62no—
366C3×D4—62no—
367C3×D4—62no—
368C3×D4—124no—
369C3×D4—122no—
370C3×D4—124no—
371C3×D4—124no—
372C3×D4—122no—
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—22no—
379C2×C3×C4—31no—
380C2×C3×C4—34no—
381C2×C3×C4—32no—
382C2×C3×C4—41no—
383C2×C3×C4—42no—
384C2×C3×C4—61no—
385C2×C3×C4—122no—
386C2×C3×C4—122no—
387C2×C3×C4—124no—
388C2×C3×C4—122no—
389C2×C3×C4D3×D412yes—
390C2×C3×C4C2×C3×D412yes—
391C2×C3×C4C23×D311yescharacteristic
392C2×C3×C4C24×C311yescharacteristic
393#67—44no—
394#67—42no—
395C2×Dic3—21no—
396C2×Dic3—42no—
397C2×Dic3C2×C3×D412yes—
398C2×Dic3C2×C3×D411yescharacteristic
399D12—22no—
400D12—22no—
401D12—22no—
402D12—44no—
403D12—42no—
404D12—44no—
405C4×D3—42no—
406C4×D3—42no—
407C4×D3—44no—
408C4×D3C2×C3×D414yes—
409Dic6—22no—
410C3×C8—24no—
411C3×C8—34no—
412C3×C8D3×D414yes—
413C3×C8C2×C3×D414yes—
414C3⋊C8C2×C3×D414yes—
415C2×C32—81no—
416C2×C32C2×#12711yescharacteristic
417C2×C32#57512yes—
418C3×D3—22no—
419C3×D3—82no—
420C3×D3—81no—
421#41—64no—
422#41—64no—
423#41—64no—
424#41—64no—
425C2×Q8—31no—
426C2×Q8C22×C3×D312yes—
427C2×Q8C22×C3×D311yescharacteristic
428C2×D4—32no—
429C2×D4—31no—
430C2×D4—61no—
431C2×D4—62no—
432C2×D4—62no—
433C2×D4—61no—
434C2×D4—62no—
435C2×D4C22×C3×D311yescharacteristic
436C22×C4—31no—
437C22×C4—32no—
438C22×C4—61no—
439C22×C4—62no—
440C22×C4—61no—
441Q16—24no—
442Q16—64no—
443SD16—24no—
444SD16—64no—
445SD16—64no—
446SD16—64no—
447D8—64no—
448D8—64no—
449C2×C8—32no—
450C2×C8—38no—
451C2×C8C22×C3×D312yes—
452C4⋊C4—22no—
453C4⋊C4—62no—
454C22⋊C4—22no—
455C22⋊C4—64no—
456C22⋊C4—62no—
457C42—31no—
458C42—32no—
459C42C22×C3×D311yescharacteristic
460C22×C3—21no—
461C22×C3—32no—
462C22×C3—42no—
463C22×C3—41no—
464C22×C3—42no—
465C22×C3—41no—
466C22×C3—62no—
467C22×C3—81no—
468C22×C3—82no—
469C22×C3—122no—
470C22×C3—121no—
471C22×C3—124no—
472C22×C3—122no—
473C22×C3C2×D3×D411yescharacteristic
474C22×C3C22×C3×D411yescharacteristic
475C2×D3—22no—
476C2×D3—44no—
477C2×D3—42no—
478C2×D3—42no—
479C2×D3—41no—
480C2×D3C3×#12712yes—
481C3×C4—22no—
482C3×C4—22no—
483C3×C4—22no—
484C3×C4—32no—
485C3×C4—42no—
486C3×C4—41no—
487C3×C4—42no—
488C3×C4—41no—
489C3×C4—42no—
490C3×C4—62no—
491C3×C4—81no—
492C3×C4—82no—
493C3×C4—121no—
494C3×C4C2×D3×D412yes—
495C3×C4C22×C3×D412yes—
496Dic3—22no—
497Dic3—41no—
498Dic3C3×#12712yes—
499C32#315011yescharacteristic, complemented, Sylow
500C23—21no—
501C23—31no—
502C23—62no—
503C23—61no—
504Q8—22no—
505Q8—22no—
506Q8—22no—
507Q8—62no—
508D4—22no—
509D4—62no—
510D4—62no—
511D4—62no—
512D4—124no—
513D4—122no—
514D4—124no—
515D4—124no—
516D4—122no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—31no—
520C2×C4—34no—
521C2×C4—32no—
522C2×C4—61no—
523C2×C4—122no—
524C2×C4—122no—
525C2×C4—124no—
526C2×C4—122no—
527C2×C4C3×D3×D412yes—
528C2×C4C23×C3×D311yescharacteristic
529C8—34no—
530C8C3×D3×D414yes—
531C2×C3—22no—
532C2×C3—21no—
533C2×C3—62no—
534C2×C3—81no—
535C2×C3—81no—
536C2×C3—161no—
537C2×C3—242no—
538C2×C3—241no—
539C2×C3D3×#12711yescharacteristic
540C2×C3#577712yes—
541C2×C3C2×C3×#12711yescharacteristic
542C2×C3C3×#57512yes—
543D3—22no—
544D3—82no—
545D3—81no—
546C22—32no—
547C22—42no—
548C22—41no—
549C22—62no—
550C22—124no—
551C22—122no—
552C22—122no—
553C22—121no—
554C22C2×C3×D3×D411yescharacteristic
555C4—22no—
556C4—32no—
557C4—41no—
558C4—42no—
559C4—62no—
560C4—121no—
561C4C2×C3×D3×D412yes—
562C3—21no—
563C3#8186911yescharacteristic, direct product factor
564C3C3×#315011yescharacteristic, complemented
565C2—62no—
566C2—81no—
567C2—242no—
568C2—241no—
569C2C3×D3×#12711yescharacteristic
570C2C3×#577712yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#497C2
socleC22×C32C22×D4
hypercenterC3×#497D3
hypocenterC3C3×#3150
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#497

Complements

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

NH ≅ G/Ntype
1. C2×C3×#919C2semidirect
2. C2×C3×#916C2semidirect
3. C3×#5725C2semidirect
4. C3×#5668C2semidirect
5. C32×#497C2semidirect
6. C3×#5190C2semidirect
7. C3×#5176C2semidirect
8. C3×#5086C2semidirect
9. C3×#5058C2semidirect
10. C3×#4712C2semidirect
11. C3×D3×#97C2semidirect
13. #81869C3direct (N × H)
47. C2×#919C2×C3semidirect
48. C2×#916C2×C3semidirect
49. #5725C2×C3semidirect
50. #5668C2×C3semidirect
54. C3×#497D3semidirect
55. C3×#497C2×C3semidirect
60. #5190C2×C3semidirect
61. #5176C2×C3semidirect
62. #5086C2×C3semidirect
63. #5058C2×C3semidirect
64. #4712C2×C3semidirect
65. D3×#97C2×C3semidirect
104. C3×D3×C8D4semidirect
206. #497C3×D3semidirect
297. D3×C8C3×D4semidirect
499. C32#3150semidirect
563. C3#81869direct (N × H)
564. C3C3×#3150semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9192
C2×C3×#9162
C3×#57252
C3×#56682
C32×#4972
C3×#51902
C3×#51762
C3×#50862
C3×#50582
C3×#47122
C3×D3×#972
C3×#31503
#818693