Finite Group Databasebeta

← C2×C3×#4818 #11865473

Subgroups — C2×C3×#4818 #11865473

Order 1152.

1169 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#944C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C22×C3×#204C211yesmaximal, characteristic
4C2×C3×#893C211yesmaximal, characteristic
5C2×C32×#103C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C2×C3×#810C211yesmaximal, characteristic, complemented
8C3×#4818C218yesmaximal, direct product factor
9C2×C3×#461—31nomaximal
10C2×#4818C311yesmaximal, characteristic, direct product factor
11C22×C32×Q8C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C22×C3×Dic6C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C3×#944—22no—
18C3×#944C2214yescomplemented
19C2×C3×#215—24no—
20C2×C3×#215C2214yes—
21C2×C3×(C2×D3)⋊C4—21no—
22C2×C3×Dic3⋊C4—21no—
23C2×C3×Dic3⋊C4—21no—
24C2×C3×C4×Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×C3×#204—24no—
27C2×C3×#204C2214yes—
28C3×#893—22no—
29C3×#893C2214yes—
30C32×#103C2214yescomplemented
31C3×Dic3⋊C8C2214yescomplemented
32C3×#810C2214yescomplemented
33C22×C3×SD16—31no—
34C22×C3×SD16—31no—
35C2×C3×C4⋊Q8—31no—
36C2×C3×C4×D4—31no—
37C2×#944C2×C311yescharacteristic, complemented
38C22×#215C2×C311yescharacteristic
39C22×#204C2×C311yescharacteristic
40C2×#893C2×C311yescharacteristic
41C3×#461—38no—
42C2×C3×C4⋊C8—31no—
43C2×C3×#103—21no—
44C2×C3×#103—31no—
45C2×C3×#103D311yescharacteristic, complemented
46C2×C3×#103C2×C311yescharacteristic, complemented
47C2×Dic3⋊C8C2×C311yescharacteristic, complemented
48C2×#810C2×C311yescharacteristic, complemented
49#4818C2×C318yesdirect product factor
50C23×C3×D3—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—22no—
53C2×C32×Q8—22no—
54C2×C32×Q8C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12D414yes—
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—24no—
66C2×C3×C4×D3—44no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×C32×C8—22no—
72C2×C32×C8C2312yes—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2312yes—
75C3×#215—28no—
76C3×(C2×D3)⋊C4—24no—
77C3×Dic3⋊C4—24no—
78C3×Dic3⋊C4—24no—
79C3×C4×Dic3D412yes—
80C3×C4×Dic3C2312yes—
81C2×C3×C3⋊C8—22no—
82C2×C3×C3⋊C8C2312yes—
83C3×#204—28no—
84C2×#461—31noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8—31no—
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×Q8C22×C311yescharacteristic
89C22×C3×D4—31no—
90C23×C3×C4—61no—
91C22×D12C22×C311yescharacteristic
92C22×C4×D3—21no—
93C22×Dic6C22×C311yescharacteristic
94C2×C3×SD16—34no—
95C2×C3×SD16—34no—
96C2×C3×SD16—64no—
97C2×C3×SD16—64no—
98C22×C3×C8—21no—
99C22×C3×C8—31no—
100C22×C3×C8C2×D311yescharacteristic
101C22×C3×C8C22×C311yescharacteristic
102C3×C4⋊Q8—34no—
103C3×C4⋊Q8—62no—
104C3×C4×D4—34no—
105C3×C4×D4—62no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—61no—
108C2×C3×C4⋊C4—61no—
109C2×C3×C4⋊C4C2×D311yescharacteristic
110C2×C3×C4⋊C4C22×C311yescharacteristic
111C2×C3×C22⋊C4—61no—
112C2×C3×C42—31no—
113#944—22no—
114#944C22×C314yescomplemented
115C2×#215—24no—
116C2×#215C22×C314yes—
117C2×(C2×D3)⋊C4—21no—
118C2×Dic3⋊C4—21no—
119C2×Dic3⋊C4—21no—
120C2×C4×Dic3C22×C311yescharacteristic
121C22×C3⋊C8C22×C311yescharacteristic
122C2×#204—24no—
123C2×#204C22×C314yes—
124#893—22no—
125#893C22×C314yes—
126C3×C4⋊C8—34no—
127C3×#103—24no—
128C3×#103—34no—
129C3×#103C2×D314yescomplemented
130C3×#103C22×C314yescomplemented
131Dic3⋊C8C22×C314yescomplemented
132#810C22×C314yescomplemented
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—24no—
135C22×C3×D3—22no—
136C22×C3×D3—42no—
137C22×C3×D3—42no—
138C32×Q8—22no—
139C32×Q8—22no—
140C32×Q8—42no—
141C2×C32×C4—22no—
142C2×C32×C4—22no—
143C2×C32×C4—42no—
144C2×C32×C4—42no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3SD1614yescomplemented
153C2×C3×Dic3C2×D412yes—
154C2×C3×Dic3C2×D412yes—
155C3×D12—24no—
156C3×D12—22no—
157C3×D12C2×D414yes—
158C3×C4×D3—48no—
159C3×Dic6—22no—
160C3×Dic6—22no—
161C3×Dic6—42no—
162C32×C8—22no—
163C3×C3⋊C8—22no—
164C22×SD16—31no—
165C22×SD16—31no—
166C2×C4⋊Q8—31no—
167C2×C4×D4—31no—
168#461—38no—
169C2×C4⋊C8—31no—
170C2×#103—31no—
171C2×#103C3×D311yescharacteristic, complemented
172C24×C3—61no—
173C23×D3—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—24no—
177C2×C3×Q8—22no—
178C2×C3×Q8—22no—
179C2×C3×Q8—22no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—32no—
183C2×C3×Q8—41no—
184C2×C3×Q8—42no—
185C2×C3×Q8—61no—
186C2×C3×Q8—62no—
187C2×C3×Q8—62no—
188C2×C3×Q8C22×D312yes—
189C2×C3×Q8C23×C312yes—
190C2×C3×D4—34no—
191C2×C3×D4—32no—
192C2×C3×D4—62no—
193C2×C3×D4—61no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—41no—
202C22×C3×C4—41no—
203C22×C3×C4—64no—
204C22×C3×C4—61no—
205C22×C3×C4—124no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C23×C311yescharacteristic
208C22×Dic3—21no—
209C22×Dic3C3×D411yescharacteristic
210C22×Dic3C3×D411yescharacteristic
211C2×D12—21no—
212C2×D12—22no—
213C2×D12C3×D414yes—
214C2×D12C23×C312yes—
215C2×C4×D3—24no—
216C2×C4×D3—44no—
217C2×Dic6—22no—
218C2×Dic6—22no—
219C2×Dic6—21no—
220C2×Dic6C23×C312yes—
221C3×SD16—68no—
222C3×SD16—68no—
223C2×C3×C8—22no—
224C2×C3×C8—22no—
225C2×C3×C8—22no—
226C2×C3×C8—32no—
227C2×C3×C8—42no—
228C2×C3×C8—62no—
229C2×C3×C8C22×D312yes—
230C2×C3×C8C23×C312yes—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—41no—
235C3×C4⋊C4—64no—
236C3×C4⋊C4—64no—
237C3×C4⋊C4C22×D312yes—
238C3×C4⋊C4C23×C312yes—
239C3×C22⋊C4—64no—
240C3×C42—32no—
241C3×C42—32no—
242#215—28no—
243(C2×D3)⋊C4—24no—
244Dic3⋊C4—24no—
245Dic3⋊C4—24no—
246C4×Dic3C3×D412yes—
247C4×Dic3C23×C312yes—
248C2×C3⋊C8—22no—
249C2×C3⋊C8C23×C312yes—
250#204—28no—
251C22×C32#12112yes—
252C22×C32C2×SD1612yes—
253C22×C32#13712yes—
254C22×C32C22×D411yescharacteristic
255C2×C3×D3—24no—
256C2×C3×D3—42no—
257C2×C3×D3—42no—
258C2×C3×D3—48no—
259C32×C4—42no—
260C32×C4—42no—
261C32×C4#12112yes—
262C32×C4C22×D411yescharacteristic
263C32×C4C2×#4111yescharacteristic
264C3×Dic3—22no—
265C3×Dic3—42no—
266C3×Dic3C2×SD1614yescomplemented
267C22×Q8—31no—
268C22×Q8C2×C3×D311yescharacteristic
269C22×D4—31no—
270C23×C4—61no—
271C2×SD16—34no—
272C2×SD16—34no—
273C2×SD16—64no—
274C2×SD16—64no—
275C22×C8—31no—
276C22×C8C2×C3×D311yescharacteristic
277C4⋊Q8—34no—
278C4⋊Q8—62no—
279C4×D4—34no—
280C4×D4—62no—
281C2×C4⋊C4—61no—
282C2×C4⋊C4—61no—
283C2×C4⋊C4C2×C3×D311yescharacteristic
284C2×C22⋊C4—61no—
285C2×C42—31no—
286C4⋊C8—34no—
287#103—34no—
288#103C2×C3×D314yescomplemented
289C23×C3—21no—
290C23×C3—64no—
291C23×C3—62no—
292C23×C3—122no—
293C23×C3—122no—
294C23×C3D3×D411yescharacteristic
295C23×C3C2×C3×D411yescharacteristic
296C22×D3—24no—
297C22×D3—22no—
298C22×D3—42no—
299C22×D3—42no—
300C3×Q8—24no—
301C3×Q8—22no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—42no—
306C3×Q8—44no—
307C3×Q8—42no—
308C3×Q8—42no—
309C3×Q8—62no—
310C3×Q8—62no—
311C3×Q8—122no—
312C3×D4—34no—
313C3×D4—64no—
314C3×D4—62no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—34no—
324C2×C3×C4—32no—
325C2×C3×C4—32no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—44no—
329C2×C3×C4—42no—
330C2×C3×C4—42no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—82no—
336C2×C3×C4—128no—
337C2×C3×C4—122no—
338C2×C3×C4#23512yes—
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D412yes—
341C2×C3×C4C2×C3×D411yescharacteristic
342C2×C3×C4C2×C3×D412yes—
343C2×C3×C4C3×#4112yes—
344C2×C3×C4C23×D311yescharacteristic
345C2×C3×C4C24×C311yescharacteristic
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—42no—
349C2×Dic3C3×SD1614yescomplemented
350C2×Dic3C2×C3×D412yes—
351C2×Dic3C2×C3×D412yes—
352D12—24no—
353D12—22no—
354D12C2×C3×D414yes—
355C4×D3—48no—
356Dic6—22no—
357Dic6—22no—
358Dic6—42no—
359C3×C8—22no—
360C3×C8—22no—
361C3×C8—42no—
362C3×C8—62no—
363C3⋊C8—22no—
364C2×C32#46114yescomplemented
365C2×C32C2×#12111yescharacteristic
366C2×C32C22×SD1611yescharacteristic
367C2×C32C2×#13711yescharacteristic
368C3×D3—44no—
369C24—61no—
370C2×Q8—21no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—32no—
374C2×Q8—61no—
375C2×Q8—62no—
376C2×Q8—62no—
377C2×Q8C22×C3×D312yes—
378C2×D4—32no—
379C2×D4—34no—
380C2×D4—62no—
381C2×D4—61no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—64no—
387C22×C4—61no—
388C22×C4—124no—
389C22×C4C22×C3×D311yescharacteristic
390SD16—68no—
391SD16—68no—
392C2×C8—22no—
393C2×C8—32no—
394C2×C8—62no—
395C2×C8C22×C3×D312yes—
396C4⋊C4—21no—
397C4⋊C4—64no—
398C4⋊C4—64no—
399C4⋊C4C22×C3×D312yes—
400C22⋊C4—64no—
401C42—32no—
402C42—32no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—64no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—128no—
411C22×C3#88412yes—
412C22×C3D3×SD1612yes—
413C22×C3#91812yes—
414C22×C3C3×#12112yes—
415C22×C3C2×C3×SD1612yes—
416C22×C3C3×#13712yes—
417C22×C3C2×D3×D411yescharacteristic
418C22×C3C22×C3×D411yescharacteristic
419C2×D3—24no—
420C2×D3—42no—
421C2×D3—42no—
422C2×D3—48no—
423C3×C4—22no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—34no—
427C3×C4—44no—
428C3×C4—42no—
429C3×C4—42no—
430C3×C4—42no—
431C3×C4—42no—
432C3×C4—62no—
433C3×C4—82no—
434C3×C4—122no—
435C3×C4#88412yes—
436C3×C4C3×#12112yes—
437C3×C4C2×#23511yescharacteristic
438C3×C4C2×D3×D411yescharacteristic
439C3×C4C22×C3×D411yescharacteristic
440C3×C4C2×C3×#4111yescharacteristic
441Dic3—22no—
442Dic3—42no—
443Dic3C2×C3×SD1614yescomplemented
444C32C2×#46111yescharacteristic, complemented, Sylow
445C23—64no—
446C23—62no—
447C23—122no—
448C23—122no—
449C23C3×D3×D411yescharacteristic
450Q8—22no—
451Q8—22no—
452Q8—42no—
453Q8—62no—
454Q8—62no—
455Q8—122no—
456D4—34no—
457D4—64no—
458D4—62no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—34no—
462C2×C4—32no—
463C2×C4—32no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—128no—
469C2×C4—122no—
470C2×C4C3×#23512yes—
471C2×C4C3×D3×D411yescharacteristic
472C2×C4C3×D3×D412yes—
473C2×C4C23×C3×D311yescharacteristic
474C8—22no—
475C8—62no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—24no—
480C2×C3—124no—
481C2×C3#481814yesdirect product factor
482C2×C3C3×#46114yescomplemented
483C2×C3C2×#88411yescharacteristic
484C2×C3C2×D3×SD1611yescharacteristic
485C2×C3C2×#91811yescharacteristic
486C2×C3C2×C3×#12111yescharacteristic
487C2×C3C22×C3×SD1611yescharacteristic
488C2×C3C2×C3×#13711yescharacteristic
489D3—44no—
490C22—64no—
491C22—122no—
492C22—122no—
493C22—128no—
494C22C3×#88412yes—
495C22C3×D3×SD1612yes—
496C22C3×#91812yes—
497C22C2×C3×D3×D411yescharacteristic
498C4—34no—
499C4—42no—
500C4—42no—
501C4—62no—
502C4—122no—
503C4C3×#88412yes—
504C4C2×C3×#23511yescharacteristic
505C4C2×C3×D3×D411yescharacteristic
506C3—21no—
507C3C2×#481811yescharacteristic, direct product factor
508C3C2×C3×#46111yescharacteristic, complemented
509C2—124no—
510C2C3×#481814yesdirect product factor
511C2C2×C3×#88411yescharacteristic
512C2C2×C3×D3×SD1611yescharacteristic
513C2C2×C3×#91811yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C3×#103D3
hypocenterC3C2×C3×#461
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×#944C2semidirect
5. C2×C32×#103C2semidirect
6. C2×C3×Dic3⋊C8C2semidirect
7. C2×C3×#810C2semidirect
8. C3×#4818C2direct (N × H)
10. C2×#4818C3direct (N × H)
18. C3×#944C22semidirect
30. C32×#103C22semidirect
31. C3×Dic3⋊C8C22semidirect
32. C3×#810C22semidirect
37. C2×#944C2×C3semidirect
45. C2×C3×#103D3semidirect
46. C2×C3×#103C2×C3semidirect
47. C2×Dic3⋊C8C2×C3semidirect
48. C2×#810C2×C3semidirect
49. #4818C2×C3direct (N × H)
114. #944C22×C3semidirect
129. C3×#103C2×D3semidirect
130. C3×#103C22×C3semidirect
131. Dic3⋊C8C22×C3semidirect
132. #810C22×C3semidirect
152. C2×C3×Dic3SD16semidirect
171. C2×#103C3×D3semidirect
266. C3×Dic3C2×SD16semidirect
288. #103C2×C3×D3semidirect
349. C2×Dic3C3×SD16semidirect
364. C2×C32#461semidirect
443. Dic3C2×C3×SD16semidirect
444. C32C2×#461semidirect
481. C2×C3#4818direct (N × H)
482. C2×C3C3×#461semidirect
507. C3C2×#4818direct (N × H)
508. C3C2×C3×#461semidirect
510. C2C3×#4818direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9442
C22×C3×#2152
C22×C3×#2042
C2×C3×#8932
C2×C32×#1032
C2×C3×Dic3⋊C82
C2×C3×#8102
C3×#48182
C2×C3×#4613
C2×#48183