Finite Group Databasebeta

← C2×C3×#4819 #11865531

Subgroups — C2×C3×#4819 #11865531

Order 1152.

1209 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#947C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C22×C3×D24C211yesmaximal, characteristic
4C2×C3×#893C211yesmaximal, characteristic, complemented
5C2×C32×#103C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C2×C3×#809C211yesmaximal, characteristic, complemented
8C3×#4819C218yesmaximal, direct product factor
9C2×C3×#463—31nomaximal
10C2×#4819C311yesmaximal, characteristic, direct product factor
11C22×C32×Q8C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3—21no—
15C22×C32×C8C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C3×#947—22no—
18C3×#947C2214yescomplemented
19C2×C3×#215—24no—
20C2×C3×#215C2214yescomplemented
21C2×C3×(C2×D3)⋊C4—21no—
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×(C2×D3)⋊C4—21no—
24C2×C3×C4×Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×C3×D24—24no—
27C2×C3×D24C2214yes—
28C3×#893—22no—
29C3×#893C2214yescomplemented
30C32×#103C2214yescomplemented
31C3×Dic3⋊C8C2214yescomplemented
32C3×#809C2214yescomplemented
33C22×C3×SD16—31no—
34C22×C3×D8—31no—
35C2×C3×#124—31no—
36C2×C3×C4×D4—31no—
37C2×#947C2×C311yescharacteristic, complemented
38C22×#215C2×C311yescharacteristic, complemented
39C22×D24C2×C311yescharacteristic
40C2×#893C2×C311yescharacteristic, complemented
41C3×#463—38no—
42C2×C3×C4⋊C8—31no—
43C2×C3×#103—21no—
44C2×C3×#103D311yescharacteristic, complemented
45C2×C3×#103C2×C311yescharacteristic, complemented
46C2×C3×#102—31no—
47C2×Dic3⋊C8C2×C311yescharacteristic, complemented
48C2×#809C2×C311yescharacteristic, complemented
49#4819C2×C318yesdirect product factor
50C23×C3×D3—21no—
51C23×C3×D3—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8—22no—
54C2×C32×Q8—22no—
55C2×C32×Q8C2312yes—
56C22×C32×C4—21no—
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12D414yes—
67C2×C3×D12C2312yes—
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—24no—
70C2×C3×C4×D3—44no—
71C2×C32×C8—22no—
72C2×C32×C8C2312yes—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2312yes—
75C3×#215—28no—
76C3×(C2×D3)⋊C4—24no—
77C3×(C2×D3)⋊C4—24no—
78C3×(C2×D3)⋊C4—24no—
79C3×C4×Dic3D412yes—
80C3×C4×Dic3C2312yes—
81C2×C3×C3⋊C8—22no—
82C2×C3×C3⋊C8C2312yes—
83C3×D24—28no—
84C2×#463—31noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C22×C311yescharacteristic
88C22×C3×D4—31no—
89C22×C3×D4—31no—
90C23×C3×C4—61no—
91C22×D12C22×C311yescharacteristic
92C22×D12C22×C311yescharacteristic
93C22×C4×D3—21no—
94C2×C3×SD16—34no—
95C2×C3×SD16—64no—
96C2×C3×D8—34no—
97C2×C3×D8—64no—
98C22×C3×C8—21no—
99C22×C3×C8—31no—
100C22×C3×C8C2×D311yescharacteristic
101C22×C3×C8C22×C311yescharacteristic
102C3×#124—34no—
103C3×#124—62no—
104C3×C4×D4—34no—
105C3×C4×D4—62no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4C2×D311yescharacteristic
108C2×C3×C4⋊C4C22×C311yescharacteristic
109C2×C3×C22⋊C4—61no—
110C2×C3×C22⋊C4—61no—
111C2×C3×C22⋊C4—61no—
112C2×C3×C42—31no—
113#947—22no—
114#947C22×C314yescomplemented
115C2×#215—24no—
116C2×#215C22×C314yescomplemented
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×C4×Dic3C22×C311yescharacteristic
121C22×C3⋊C8C22×C311yescharacteristic
122C2×D24—24no—
123C2×D24C22×C314yes—
124#893—22no—
125#893C22×C314yescomplemented
126C3×C4⋊C8—34no—
127C3×#103—24no—
128C3×#103C2×D314yescomplemented
129C3×#103C22×C314yescomplemented
130C3×#102—34no—
131Dic3⋊C8C22×C314yescomplemented
132#809C22×C314yescomplemented
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—24no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C32×Q8—22no—
143C32×Q8—22no—
144C32×Q8—42no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4—42no—
148C2×C32×C4—42no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D412yes—
151C2×C32×C4#4112yes—
152C2×C32×C4C2411yescharacteristic
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3C2×D412yes—
156C2×C3×Dic3C2×D412yes—
157C3×D12—24no—
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—22no—
161C3×D12—42no—
162C3×D12C2×D414yes—
163C3×C4×D3—48no—
164C32×C8—22no—
165C3×C3⋊C8—22no—
166C22×SD16—31no—
167C22×D8—31no—
168C2×#124—31no—
169C2×C4×D4—31no—
170#463—38no—
171C2×C4⋊C8—31no—
172C2×#103C3×D311yescharacteristic, complemented
173C2×#102—31no—
174C24×C3—61no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—21no—
180C2×C3×Q8—24no—
181C2×C3×Q8—22no—
182C2×C3×Q8—22no—
183C2×C3×Q8—22no—
184C2×C3×Q8—22no—
185C2×C3×Q8—22no—
186C2×C3×Q8—41no—
187C2×C3×Q8—42no—
188C2×C3×Q8C22×D312yes—
189C2×C3×Q8C23×C312yes—
190C2×C3×D4—34no—
191C2×C3×D4—32no—
192C2×C3×D4—32no—
193C2×C3×D4—62no—
194C2×C3×D4—62no—
195C2×C3×D4—61no—
196C2×C3×D4—62no—
197C2×C3×D4—61no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—41no—
206C22×C3×C4—41no—
207C22×C3×C4—64no—
208C22×C3×C4—124no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C23×C311yescharacteristic
211C22×Dic3C3×D411yescharacteristic
212C22×Dic3C3×D411yescharacteristic
213C2×D12—21no—
214C2×D12—22no—
215C2×D12—22no—
216C2×D12—22no—
217C2×D12—21no—
218C2×D12C3×D414yes—
219C2×D12C23×C312yes—
220C2×D12C23×C312yes—
221C2×C4×D3—24no—
222C2×C4×D3—44no—
223C3×SD16—68no—
224C3×D8—68no—
225C2×C3×C8—22no—
226C2×C3×C8—22no—
227C2×C3×C8—22no—
228C2×C3×C8—32no—
229C2×C3×C8—42no—
230C2×C3×C8—62no—
231C2×C3×C8C22×D312yes—
232C2×C3×C8C23×C312yes—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—41no—
237C3×C4⋊C4C22×D312yes—
238C3×C4⋊C4C23×C312yes—
239C3×C22⋊C4—64no—
240C3×C22⋊C4—64no—
241C3×C22⋊C4—64no—
242C3×C42—32no—
243C3×C42—32no—
244#215—28no—
245(C2×D3)⋊C4—24no—
246(C2×D3)⋊C4—24no—
247(C2×D3)⋊C4—24no—
248C4×Dic3C3×D412yes—
249C4×Dic3C23×C312yes—
250C2×C3⋊C8—22no—
251C2×C3⋊C8C23×C312yes—
252D24—28no—
253C22×C32#12112yes—
254C22×C32#13512yes—
255C22×C32AGL(1,ℤ/8)12yes—
256C22×C32C22×D411yescharacteristic
257C2×C3×D3—24no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—48no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—84no—
265C32×C4—42no—
266C32×C4—42no—
267C32×C4#12112yes—
268C32×C4C22×D411yescharacteristic
269C32×C4C2×#4111yescharacteristic
270C3×Dic3—22no—
271C3×Dic3—22no—
272C22×Q8C2×C3×D311yescharacteristic
273C22×D4—31no—
274C22×D4—31no—
275C23×C4—61no—
276C2×SD16—34no—
277C2×SD16—64no—
278C2×D8—34no—
279C2×D8—64no—
280C22×C8—31no—
281C22×C8C2×C3×D311yescharacteristic
282#124—34no—
283#124—62no—
284C4×D4—34no—
285C4×D4—62no—
286C2×C4⋊C4C2×C3×D311yescharacteristic
287C2×C22⋊C4—61no—
288C2×C22⋊C4—61no—
289C2×C22⋊C4—61no—
290C2×C42—31no—
291C4⋊C8—34no—
292#103C2×C3×D314yescomplemented
293#102—34no—
294C23×C3—21no—
295C23×C3—64no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3—122no—
299C23×C3—122no—
300C23×C3—122no—
301C23×C3—122no—
302C23×C3—122no—
303C23×C3D3×D411yescharacteristic
304C23×C3C2×C3×D411yescharacteristic
305C22×D3—24no—
306C22×D3—22no—
307C22×D3—22no—
308C22×D3—42no—
309C22×D3—42no—
310C22×D3—42no—
311C22×D3—42no—
312C22×D3—42no—
313C3×Q8—24no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8—42no—
319C3×Q8—44no—
320C3×Q8—42no—
321C3×Q8—42no—
322C3×D4—34no—
323C3×D4—64no—
324C3×D4—62no—
325C3×D4—62no—
326C3×D4—62no—
327C3×D4—122no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—22no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—44no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—82no—
348C2×C3×C4—128no—
349C2×C3×C4#23512yes—
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D412yes—
352C2×C3×C4C2×C3×D411yescharacteristic
353C2×C3×C4C2×C3×D412yes—
354C2×C3×C4C3×#4112yes—
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C24×C311yescharacteristic
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3C2×C3×D412yes—
360C2×Dic3C2×C3×D412yes—
361D12—24no—
362D12—22no—
363D12—22no—
364D12—22no—
365D12—42no—
366D12C2×C3×D414yes—
367C4×D3—48no—
368C3×C8—22no—
369C3×C8—22no—
370C3×C8—42no—
371C3×C8—62no—
372C3⋊C8—22no—
373C2×C32#46314yescomplemented
374C2×C32C2×#12111yescharacteristic
375C2×C32C2×#13511yescharacteristic
376C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
377C3×D3—44no—
378C3×D3—82no—
379C24—61no—
380C24—61no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8C22×C3×D312yes—
385C2×D4—32no—
386C2×D4—32no—
387C2×D4—34no—
388C2×D4—62no—
389C2×D4—62no—
390C2×D4—61no—
391C2×D4—62no—
392C2×D4—61no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—64no—
398C22×C4—124no—
399C22×C4C22×C3×D311yescharacteristic
400SD16—68no—
401D8—68no—
402C2×C8—22no—
403C2×C8—32no—
404C2×C8—62no—
405C2×C8C22×C3×D312yes—
406C4⋊C4—21no—
407C4⋊C4C22×C3×D312yes—
408C22⋊C4—64no—
409C22⋊C4—64no—
410C22⋊C4—64no—
411C42—32no—
412C42—32no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—21no—
417C22×C3—64no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3—128no—
421C22×C3—122no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—244no—
425C22×C3#88412yes—
426C22×C3#91412yes—
427C22×C3#91912yes—
428C22×C3C3×#12112yes—
429C22×C3C3×#13512yes—
430C22×C3C3×AGL(1,ℤ/8)12yes—
431C22×C3C2×D3×D411yescharacteristic
432C22×C3C22×C3×D411yescharacteristic
433C2×D3—24no—
434C2×D3—42no—
435C2×D3—42no—
436C2×D3—48no—
437C2×D3—42no—
438C2×D3—42no—
439C2×D3—42no—
440C2×D3—84no—
441C3×C4—22no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—44no—
445C3×C4—42no—
446C3×C4—42no—
447C3×C4—42no—
448C3×C4—42no—
449C3×C4—62no—
450C3×C4—62no—
451C3×C4—82no—
452C3×C4#88412yes—
453C3×C4C3×#12112yes—
454C3×C4C2×#23511yescharacteristic
455C3×C4C2×D3×D411yescharacteristic
456C3×C4C22×C3×D411yescharacteristic
457C3×C4C2×C3×#4111yescharacteristic
458Dic3—22no—
459Dic3—22no—
460C32C2×#46311yescharacteristic, complemented, Sylow
461C23—64no—
462C23—62no—
463C23—62no—
464C23—122no—
465C23—122no—
466C23—122no—
467C23—122no—
468C23—122no—
469C23C3×D3×D411yescharacteristic
470Q8—22no—
471Q8—22no—
472Q8—42no—
473D4—34no—
474D4—64no—
475D4—62no—
476D4—62no—
477D4—62no—
478D4—122no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—32no—
482C2×C4—32no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—128no—
488C2×C4C3×#23512yes—
489C2×C4C3×D3×D411yescharacteristic
490C2×C4C3×D3×D412yes—
491C2×C4C23×C3×D311yescharacteristic
492C8—22no—
493C8—62no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—24no—
498C2×C3—124no—
499C2×C3—242no—
500C2×C3#481914yesdirect product factor
501C2×C3C3×#46314yescomplemented
502C2×C3C2×#88411yescharacteristic
503C2×C3C2×#91411yescharacteristic
504C2×C3C2×#91911yescharacteristic
505C2×C3C2×C3×#12111yescharacteristic
506C2×C3C2×C3×#13511yescharacteristic
507C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
508D3—44no—
509D3—82no—
510C22—64no—
511C22—122no—
512C22—122no—
513C22—128no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22—244no—
518C22C3×#88412yes—
519C22C3×#91412yes—
520C22C3×#91912yes—
521C22C2×C3×D3×D411yescharacteristic
522C4—42no—
523C4—42no—
524C4—62no—
525C4—62no—
526C4C3×#88412yes—
527C4C2×C3×#23511yescharacteristic
528C4C2×C3×D3×D411yescharacteristic
529C3—21no—
530C3C2×#481911yescharacteristic, direct product factor
531C3C2×C3×#46311yescharacteristic, complemented
532C2—124no—
533C2—242no—
534C2C3×#481914yesdirect product factor
535C2C2×C3×#88411yescharacteristic
536C2C2×C3×#91411yescharacteristic
537C2C2×C3×#91911yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC22×C3×D24C2
hypercenterC2×C3×#103D3
hypocenterC3C2×C3×#463
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#103

Complements

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

NH ≅ G/Ntype
1. C2×C3×#947C2semidirect
2. C22×C3×#215C2semidirect
4. C2×C3×#893C2semidirect
5. C2×C32×#103C2semidirect
6. C2×C3×Dic3⋊C8C2semidirect
7. C2×C3×#809C2semidirect
8. C3×#4819C2direct (N × H)
10. C2×#4819C3direct (N × H)
18. C3×#947C22semidirect
20. C2×C3×#215C22semidirect
29. C3×#893C22semidirect
30. C32×#103C22semidirect
31. C3×Dic3⋊C8C22semidirect
32. C3×#809C22semidirect
37. C2×#947C2×C3semidirect
38. C22×#215C2×C3semidirect
40. C2×#893C2×C3semidirect
44. C2×C3×#103D3semidirect
45. C2×C3×#103C2×C3semidirect
47. C2×Dic3⋊C8C2×C3semidirect
48. C2×#809C2×C3semidirect
49. #4819C2×C3direct (N × H)
114. #947C22×C3semidirect
116. C2×#215C22×C3semidirect
125. #893C22×C3semidirect
128. C3×#103C2×D3semidirect
129. C3×#103C22×C3semidirect
131. Dic3⋊C8C22×C3semidirect
132. #809C22×C3semidirect
172. C2×#103C3×D3semidirect
292. #103C2×C3×D3semidirect
373. C2×C32#463semidirect
460. C32C2×#463semidirect
500. C2×C3#4819direct (N × H)
501. C2×C3C3×#463semidirect
530. C3C2×#4819direct (N × H)
531. C3C2×C3×#463semidirect
534. C2C3×#4819direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9472
C22×C3×#2152
C22×C3×D242
C2×C3×#8932
C2×C32×#1032
C2×C3×Dic3⋊C82
C2×C3×#8092
C3×#48192
C2×C3×#4633
C2×#48193