Finite Group Databasebeta

← C2×C3×#4863 #11869550

Subgroups — C2×C3×#4863 #11869550

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic
2C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C32×#106C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic, complemented
7C2×C3×#808C211yesmaximal, characteristic, complemented
8C3×#4863C218yesmaximal, direct product factor
9C2×C3×#481—31nomaximal
10C2×#4863C311yesmaximal, characteristic, direct product factor
11C22×C3×D12—21no—
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C22×C3×C4×D3C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#895—22no—
23C3×#895C2214yes—
24C3×D3×C4⋊C4—22no—
25C3×D3×C4⋊C4C2214yescomplemented
26C32×#106C2214yescomplemented
27C3×#821C2214yescomplemented
28C3×(C2×D3)⋊C8C2214yescomplemented
29C3×#809C2214yescomplemented
30C3×#808C2214yescomplemented
31C2×C3×#121—31no—
32C22×C3×C4⋊C4—31no—
33C2×#895C2×C311yescharacteristic
34C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
35C3×#481—38no—
36C2×C3×#106—21no—
37C2×C3×#106—31no—
38C2×C3×#106D311yescharacteristic, complemented
39C2×C3×#106C2×C311yescharacteristic, complemented
40C2×C3×#102—31no—
41C2×C3×#102—31no—
42C2×C3×C22⋊C8—31no—
43C2×#821C2×C311yescharacteristic, complemented
44C2×(C2×D3)⋊C8C2×C311yescharacteristic, complemented
45C2×#809C2×C311yescharacteristic, complemented
46C2×#808C2×C311yescharacteristic, complemented
47#4863C2×C318yesdirect product factor
48C23×C3×D3—21no—
49C23×C3×D3D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C2×C3×D12—22no—
56C2×C3×D12—22no—
57C2×C3×D12—24no—
58C2×C3×D12—21no—
59C2×C3×D12—44no—
60C2×C3×D12C2312yes—
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3—24no—
64C2×C3×C4×D3—44no—
65C2×C3×C4×D3D412yes—
66C2×C3×C4×D3C2312yes—
67C2×C32×C8—22no—
68C2×C32×C8C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4—21no—
71C32×C4⋊C4C2312yes—
72C32×C4⋊C4C2312yes—
73C3×(C2×D3)⋊C4—24no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3C2312yes—
76C3×Dic3⋊C4—24no—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79C2×#481—31noSylow
80C22×C3×D4—31no—
81C22×C3×D4—61no—
82C23×C3×C4—31no—
83C23×C3×C4—61no—
84C22×D12—21no—
85C22×D12C22×C311yescharacteristic
86C22×C4×D3—21no—
87C22×C4×D3C22×C311yescharacteristic
88C22×C3×C8—21no—
89C22×C3×C8—31no—
90C22×C3×C8C2×D311yescharacteristic
91C22×C3×C8C22×C311yescharacteristic
92C3×#121—34no—
93C3×#121—62no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—34no—
98C2×C3×C4⋊C4—62no—
99C2×C3×C4⋊C4—61no—
100C2×C3×C4⋊C4C2×D311yescharacteristic
101C2×C3×C4⋊C4C2×D311yescharacteristic
102C2×C3×C4⋊C4C22×C311yescharacteristic
103C2×C3×C4⋊C4C22×C311yescharacteristic
104C2×C3×C22⋊C4—61no—
105C2×(C2×D3)⋊C4—21no—
106C2×C4⋊Dic3C22×C311yescharacteristic
107C2×Dic3⋊C4—21no—
108C22×C3⋊C8C22×C311yescharacteristic
109#895—22no—
110#895C22×C314yes—
111D3×C4⋊C4—22no—
112D3×C4⋊C4C22×C314yescomplemented
113C3×#106—24no—
114C3×#106—34no—
115C3×#106C2×D314yescomplemented
116C3×#106C22×C314yescomplemented
117C3×#102—34no—
118C3×#102—34no—
119C3×C22⋊C8—34no—
120#821C22×C314yescomplemented
121(C2×D3)⋊C8C22×C314yescomplemented
122#809C22×C314yescomplemented
123#808C22×C314yescomplemented
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—22no—
126C22×C3×D3—22no—
127C22×C3×D3—22no—
128C22×C3×D3—42no—
129C22×C3×D3—42no—
130C22×C3×D3—42no—
131C22×C3×D3SD1614yes—
132C22×C3×D3C2×D412yes—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4—42no—
136C2×C32×C4—42no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4112yes—
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—42no—
144C2×C3×Dic3C2×D412yes—
145C3×D12—22no—
146C3×D12—22no—
147C3×D12—48no—
148C3×D12—42no—
149C3×C4×D3—24no—
150C3×C4×D3—22no—
151C3×C4×D3—22no—
152C3×C4×D3—48no—
153C32×C8—22no—
154C3×C3⋊C8—22no—
155C2×#121—31no—
156C22×C4⋊C4—31no—
157#481—38no—
158C2×#106—31no—
159C2×#106C3×D311yescharacteristic, complemented
160C2×#102—31no—
161C2×#102—31no—
162C2×C22⋊C8—31no—
163C24×C3—31no—
164C24×C3—61no—
165C23×D3—21no—
166C23×D3C3×D411yescharacteristic
167C2×C3×D4—32no—
168C2×C3×D4—64no—
169C2×C3×D4—62no—
170C2×C3×D4—61no—
171C2×C3×D4—62no—
172C2×C3×D4—124no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—31no—
179C22×C3×C4—32no—
180C22×C3×C4—32no—
181C22×C3×C4—41no—
182C22×C3×C4—41no—
183C22×C3×C4—64no—
184C22×C3×C4—62no—
185C22×C3×C4—62no—
186C22×C3×C4—61no—
187C22×C3×C4—124no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C23×C311yescharacteristic
190C22×Dic3—21no—
191C22×Dic3C3×D411yescharacteristic
192C2×D12—22no—
193C2×D12—22no—
194C2×D12—24no—
195C2×D12—21no—
196C2×D12—44no—
197C2×D12C23×C312yes—
198C2×C4×D3—22no—
199C2×C4×D3—22no—
200C2×C4×D3—24no—
201C2×C4×D3—44no—
202C2×C4×D3C3×D412yes—
203C2×C4×D3C23×C312yes—
204C2×C3×C8—24no—
205C2×C3×C8—22no—
206C2×C3×C8—22no—
207C2×C3×C8—22no—
208C2×C3×C8—32no—
209C2×C3×C8—62no—
210C2×C3×C8C22×D312yes—
211C2×C3×C8C23×C312yes—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—32no—
219C3×C4⋊C4—41no—
220C3×C4⋊C4—41no—
221C3×C4⋊C4—64no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4C22×D312yes—
224C3×C4⋊C4C22×D312yes—
225C3×C4⋊C4C23×C312yes—
226C3×C4⋊C4C23×C312yes—
227C3×C22⋊C4—64no—
228(C2×D3)⋊C4—24no—
229C4⋊Dic3—21no—
230C4⋊Dic3C23×C312yes—
231Dic3⋊C4—24no—
232C2×C3⋊C8—22no—
233C2×C3⋊C8C23×C312yes—
234C22×C32#12312yes—
235C22×C32C2×SD1612yes—
236C22×C32AGL(1,ℤ/8)12yes—
237C22×C32C22×D411yescharacteristic
238C2×C3×D3—22no—
239C2×C3×D3—22no—
240C2×C3×D3—28no—
241C2×C3×D3—42no—
242C2×C3×D3—42no—
243C2×C3×D3—42no—
244C2×C3×D3—84no—
245C2×C3×D3C2×SD1614yes—
246C32×C4—42no—
247C32×C4—42no—
248C32×C4#12312yes—
249C32×C4C2×#4111yescharacteristic
250C32×C4C2×#4111yescharacteristic
251C3×Dic3—22no—
252C3×Dic3—42no—
253C22×D4—31no—
254C22×D4—61no—
255C23×C4—31no—
256C23×C4—61no—
257C22×C8—31no—
258C22×C8C2×C3×D311yescharacteristic
259#121—34no—
260#121—62no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—34no—
263C2×C4⋊C4—62no—
264C2×C4⋊C4—61no—
265C2×C4⋊C4C2×C3×D311yescharacteristic
266C2×C4⋊C4C2×C3×D311yescharacteristic
267C2×C22⋊C4—61no—
268#106—34no—
269#106C2×C3×D314yescomplemented
270#102—34no—
271#102—34no—
272C22⋊C8—34no—
273C23×C3—21no—
274C23×C3—34no—
275C23×C3—32no—
276C23×C3—62no—
277C23×C3—62no—
278C23×C3—62no—
279C23×C3—122no—
280C23×C3—122no—
281C23×C3—122no—
282C23×C3D3×D411yescharacteristic
283C23×C3C2×C3×D411yescharacteristic
284C22×D3—22no—
285C22×D3—22no—
286C22×D3—22no—
287C22×D3—42no—
288C22×D3—42no—
289C22×D3—42no—
290C22×D3C3×SD1614yes—
291C22×D3C2×C3×D412yes—
292C3×D4—62no—
293C3×D4—62no—
294C3×D4—128no—
295C3×D4—122no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—32no—
305C2×C3×C4—42no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—62no—
312C2×C3×C4—64no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—82no—
317C2×C3×C4—82no—
318C2×C3×C4—128no—
319C2×C3×C4—122no—
320C2×C3×C4#23512yes—
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4#23912yes—
323C2×C3×C4C2×C3×D411yescharacteristic
324C2×C3×C4C3×#4112yes—
325C2×C3×C4C3×#4112yes—
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C24×C311yescharacteristic
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—42no—
331C2×Dic3C2×C3×D412yes—
332D12—22no—
333D12—22no—
334D12—48no—
335D12—42no—
336C4×D3—24no—
337C4×D3—22no—
338C4×D3—22no—
339C4×D3—48no—
340C3×C8—24no—
341C3×C8—22no—
342C3×C8—22no—
343C3×C8—62no—
344C3⋊C8—22no—
345C2×C32#48114yescomplemented
346C2×C32C2×#12311yescharacteristic
347C2×C32C22×SD1611yescharacteristic
348C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
349C3×D3—24no—
350C3×D3—82no—
351C24—31no—
352C24—61no—
353C2×D4—32no—
354C2×D4—64no—
355C2×D4—62no—
356C2×D4—61no—
357C2×D4—62no—
358C2×D4—124no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—31no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4—64no—
365C22×C4—62no—
366C22×C4—62no—
367C22×C4—61no—
368C22×C4—124no—
369C22×C4C22×C3×D311yescharacteristic
370C2×C8—22no—
371C2×C8—32no—
372C2×C8—62no—
373C2×C8C22×C3×D312yes—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—32no—
377C4⋊C4—64no—
378C4⋊C4—61no—
379C4⋊C4C22×C3×D312yes—
380C4⋊C4C22×C3×D312yes—
381C22⋊C4—64no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—21no—
386C22×C3—34no—
387C22×C3—62no—
388C22×C3—62no—
389C22×C3—68no—
390C22×C3—122no—
391C22×C3—122no—
392C22×C3—122no—
393C22×C3—244no—
394C22×C3#89412yes—
395C22×C3D3×SD1612yes—
396C22×C3#91412yes—
397C22×C3C3×#12312yes—
398C22×C3C2×C3×SD1612yes—
399C22×C3C3×AGL(1,ℤ/8)12yes—
400C22×C3C2×D3×D411yescharacteristic
401C22×C3C22×C3×D411yescharacteristic
402C2×D3—22no—
403C2×D3—22no—
404C2×D3—28no—
405C2×D3—42no—
406C2×D3—42no—
407C2×D3—42no—
408C2×D3—84no—
409C2×D3C2×C3×SD1614yes—
410C3×C4—22no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—42no—
414C3×C4—42no—
415C3×C4—42no—
416C3×C4—42no—
417C3×C4—62no—
418C3×C4—82no—
419C3×C4—82no—
420C3×C4—122no—
421C3×C4#89412yes—
422C3×C4C3×#12312yes—
423C3×C4C2×#23511yescharacteristic
424C3×C4C2×#23911yescharacteristic
425C3×C4C2×C3×#4111yescharacteristic
426C3×C4C2×C3×#4111yescharacteristic
427Dic3—22no—
428Dic3—42no—
429C32C2×#48111yescharacteristic, complemented, Sylow
430C23—34no—
431C23—32no—
432C23—62no—
433C23—62no—
434C23—62no—
435C23—122no—
436C23—122no—
437C23—122no—
438C23C3×D3×D411yescharacteristic
439D4—62no—
440D4—62no—
441D4—128no—
442D4—122no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—32no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—62no—
449C2×C4—64no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—128no—
454C2×C4—122no—
455C2×C4C3×#23512yes—
456C2×C4C3×D3×D411yescharacteristic
457C2×C4C3×#23912yes—
458C2×C4C23×C3×D311yescharacteristic
459C8—22no—
460C8—62no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—24no—
465C2×C3—64no—
466C2×C3—242no—
467C2×C3#486314yesdirect product factor
468C2×C3C3×#48114yescomplemented
469C2×C3C2×#89411yescharacteristic
470C2×C3C2×D3×SD1611yescharacteristic
471C2×C3C2×#91411yescharacteristic
472C2×C3C2×C3×#12311yescharacteristic
473C2×C3C22×C3×SD1611yescharacteristic
474C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
475D3—24no—
476D3—82no—
477C22—34no—
478C22—62no—
479C22—62no—
480C22—68no—
481C22—122no—
482C22—122no—
483C22—122no—
484C22—244no—
485C22C3×#89412yes—
486C22C3×D3×SD1612yes—
487C22C3×#91412yes—
488C22C2×C3×D3×D411yescharacteristic
489C4—42no—
490C4—42no—
491C4—62no—
492C4—122no—
493C4C3×#89412yes—
494C4C2×C3×#23511yescharacteristic
495C4C2×C3×#23911yescharacteristic
496C3—21no—
497C3C2×#486311yescharacteristic, direct product factor
498C3C2×C3×#48111yescharacteristic, complemented
499C2—64no—
500C2—242no—
501C2C3×#486314yesdirect product factor
502C2C2×C3×#89411yescharacteristic
503C2C2×C3×D3×SD1611yescharacteristic
504C2C2×C3×#91411yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#106C2
socleC23×C32C2×D4
prime radicalC2×C3×#895C2
hypercenterC2×C3×#106D3
hypocenterC3C2×C3×#481
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#106

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×C4⋊C4C2semidirect
3. C2×C32×#106C2semidirect
4. C2×C3×#821C2semidirect
5. C2×C3×(C2×D3)⋊C8C2semidirect
6. C2×C3×#809C2semidirect
7. C2×C3×#808C2semidirect
8. C3×#4863C2direct (N × H)
10. C2×#4863C3direct (N × H)
25. C3×D3×C4⋊C4C22semidirect
26. C32×#106C22semidirect
27. C3×#821C22semidirect
28. C3×(C2×D3)⋊C8C22semidirect
29. C3×#809C22semidirect
30. C3×#808C22semidirect
34. C2×D3×C4⋊C4C2×C3semidirect
38. C2×C3×#106D3semidirect
39. C2×C3×#106C2×C3semidirect
43. C2×#821C2×C3semidirect
44. C2×(C2×D3)⋊C8C2×C3semidirect
45. C2×#809C2×C3semidirect
46. C2×#808C2×C3semidirect
47. #4863C2×C3direct (N × H)
112. D3×C4⋊C4C22×C3semidirect
115. C3×#106C2×D3semidirect
116. C3×#106C22×C3semidirect
120. #821C22×C3semidirect
121. (C2×D3)⋊C8C22×C3semidirect
122. #809C22×C3semidirect
123. #808C22×C3semidirect
159. C2×#106C3×D3semidirect
269. #106C2×C3×D3semidirect
345. C2×C32#481semidirect
429. C32C2×#481semidirect
467. C2×C3#4863direct (N × H)
468. C2×C3C3×#481semidirect
497. C3C2×#4863direct (N × H)
498. C3C2×C3×#481semidirect
501. C2C3×#4863direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×C3×D3×C4⋊C42
C2×C32×#1062
C2×C3×#8212
C2×C3×(C2×D3)⋊C82
C2×C3×#8092
C2×C3×#8082
C3×#48632
C2×C3×#4813
C2×#48633