Finite Group Databasebeta

← C2×C3×#4845 #11865679

Subgroups — C2×C3×#4845 #11865679

Order 1152.

1069 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic12C211yesmaximal, characteristic, complemented
2C22×C3×#204C211yesmaximal, characteristic
3C2×C3×#875C211yesmaximal, characteristic
4C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
5C2×C32×C4⋊C8C211yesmaximal, characteristic, complemented
6C2×C3×#821C211yesmaximal, characteristic
7C2×C3×#816C211yesmaximal, characteristic, complemented
8C3×#4845C218yesmaximal, direct product factor
9C2×C3×#464—31nomaximal
10C2×#4845C311yesmaximal, characteristic, direct product factor
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C2×C3×C4×Dic3—21no—
22C2×C3×Dic12—24no—
23C2×C3×Dic12C2214yescomplemented
24C2×C3×#204—24no—
25C2×C3×#204C2214yes—
26C3×#875—22no—
27C3×#875C2214yes—
28C3×C4×Dic6—22no—
29C3×C4×Dic6C2214yescomplemented
30C32×C4⋊C8C2214yescomplemented
31C3×#821C2214yes—
32C3×#816C2214yescomplemented
33C22×C3×Q16—31no—
34C22×C3×SD16—31no—
35C2×C3×#124—31no—
36C2×C3×C4×Q8—31no—
37C22×Dic12C2×C311yescharacteristic, complemented
38C22×#204C2×C311yescharacteristic
39C2×#875C2×C311yescharacteristic
40C2×C4×Dic6C2×C311yescharacteristic, complemented
41C3×#464—38no—
42C2×C3×C4⋊C8—21no—
43C2×C3×C4⋊C8D311yescharacteristic, complemented
44C2×C3×C4⋊C8C2×C311yescharacteristic, complemented
45C2×C3×#103—31no—
46C2×C3×#102—31no—
47C2×#821C2×C311yescharacteristic
48C2×#816C2×C311yescharacteristic, complemented
49#4845C2×C318yesdirect product factor
50C23×C3×D3—21no—
51C22×C32×C4D411yescharacteristic
52C22×C32×C4D411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C2×C3×D12—22no—
58C2×C3×D12—22no—
59C2×C3×D12—21no—
60C2×C3×D12C2312yes—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6—22no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6D414yes—
67C2×C3×Dic6C2312yes—
68C2×C3×Dic6C2312yes—
69C2×C32×C8—22no—
70C2×C32×C8—22no—
71C2×C32×C8C2312yes—
72C2×C32×C8C2312yes—
73C32×C42D412yes—
74C32×C42C2312yes—
75C3×(C2×D3)⋊C4—24no—
76C3×(C2×D3)⋊C4—24no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—24no—
80C3×C4×Dic3—24no—
81C3×Dic12—28no—
82C3×#204—28no—
83C2×#464—31noSylow
84C22×C3×Q8—31no—
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×D12C22×C311yescharacteristic
88C22×Dic6C22×C311yescharacteristic
89C22×Dic6C22×C311yescharacteristic
90C2×C3×Q16—34no—
91C2×C3×Q16—64no—
92C2×C3×SD16—34no—
93C2×C3×SD16—64no—
94C22×C3×C8—21no—
95C22×C3×C8—21no—
96C22×C3×C8C2×D311yescharacteristic
97C22×C3×C8C2×D311yescharacteristic
98C22×C3×C8C22×C311yescharacteristic
99C22×C3×C8C22×C311yescharacteristic
100C3×#124—34no—
101C3×#124—62no—
102C3×C4×Q8—34no—
103C3×C4×Q8—62no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4—61no—
106C2×C3×C22⋊C4—61no—
107C2×C3×C22⋊C4—61no—
108C2×C3×C42—21no—
109C2×C3×C42—61no—
110C2×C3×C42C2×D311yescharacteristic
111C2×C3×C42C22×C311yescharacteristic
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×C4⋊Dic3C22×C311yescharacteristic
115C2×Dic3⋊C4—21no—
116C2×C4×Dic3—21no—
117C2×Dic12—24no—
118C2×Dic12C22×C314yescomplemented
119C2×#204—24no—
120C2×#204C22×C314yes—
121#875—22no—
122#875C22×C314yes—
123C4×Dic6—22no—
124C4×Dic6C22×C314yescomplemented
125C3×C4⋊C8—24no—
126C3×C4⋊C8C2×D314yescomplemented
127C3×C4⋊C8C22×C314yescomplemented
128C3×#103—34no—
129C3×#102—34no—
130#821C22×C314yes—
131#816C22×C314yescomplemented
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—42no—
135C22×C3×D3—42no—
136C22×C3×D3—42no—
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D412yes—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D412yes—
143C2×C32×C4#4112yes—
144C2×C32×C4C2411yescharacteristic
145C2×C3×Dic3—24no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3—42no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—42no—
154C3×Dic6—24no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—42no—
159C3×Dic6C2×D414yes—
160C32×C8—22no—
161C32×C8—22no—
162C22×Q16—31no—
163C22×SD16—31no—
164C2×#124—31no—
165C2×C4×Q8—31no—
166#464—38no—
167C2×C4⋊C8C3×D311yescharacteristic, complemented
168C2×#103—31no—
169C2×#102—31no—
170C24×C3—61no—
171C23×D3—21no—
172C2×C3×Q8—34no—
173C2×C3×Q8—32no—
174C2×C3×Q8—32no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—62no—
178C2×C3×Q8—62no—
179C2×C3×Q8—62no—
180C2×C3×D4—32no—
181C2×C3×D4—61no—
182C2×C3×D4—62no—
183C2×C3×D4—62no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4—61no—
190C22×C3×C4D1211yescharacteristic
191C22×C3×C4D1211yescharacteristic
192C22×C3×C4C3×D411yescharacteristic
193C22×C3×C4C3×D411yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C23×C311yescharacteristic
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—21no—
199C2×D12—22no—
200C2×D12—22no—
201C2×D12—21no—
202C2×D12C23×C312yes—
203C2×Dic6—21no—
204C2×Dic6—22no—
205C2×Dic6—22no—
206C2×Dic6—22no—
207C2×Dic6—21no—
208C2×Dic6C3×D414yes—
209C2×Dic6C23×C312yes—
210C2×Dic6C23×C312yes—
211C3×Q16—68no—
212C3×SD16—68no—
213C2×C3×C8—22no—
214C2×C3×C8—22no—
215C2×C3×C8—22no—
216C2×C3×C8—22no—
217C2×C3×C8—22no—
218C2×C3×C8—22no—
219C2×C3×C8—42no—
220C2×C3×C8—42no—
221C2×C3×C8C22×D312yes—
222C2×C3×C8C22×D312yes—
223C2×C3×C8C23×C312yes—
224C2×C3×C8C23×C312yes—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—64no—
227C3×C4⋊C4—61no—
228C3×C22⋊C4—64no—
229C3×C22⋊C4—64no—
230C3×C42—22no—
231C3×C42—22no—
232C3×C42—64no—
233C3×C42D1212yes—
234C3×C42C3×D412yes—
235C3×C42C22×D312yes—
236C3×C42C23×C312yes—
237(C2×D3)⋊C4—24no—
238(C2×D3)⋊C4—24no—
239C4⋊Dic3—21no—
240C4⋊Dic3C23×C312yes—
241Dic3⋊C4—24no—
242C4×Dic3—24no—
243Dic12—28no—
244#204—28no—
245C22×C32#12112yes—
246C22×C32#13512yes—
247C22×C32#13712yes—
248C22×C32C22×D411yescharacteristic
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—84no—
253C32×C4—22no—
254C32×C4—22no—
255C32×C4#12112yes—
256C32×C4C22×D411yescharacteristic
257C32×C4C2×#4111yescharacteristic
258C3×Dic3—24no—
259C3×Dic3—42no—
260C3×Dic3—42no—
261C22×Q8—31no—
262C22×Q8—31no—
263C22×D4—31no—
264C2×Q16—34no—
265C2×Q16—64no—
266C2×SD16—34no—
267C2×SD16—64no—
268C22×C8C2×C3×D311yescharacteristic
269C22×C8C2×C3×D311yescharacteristic
270#124—34no—
271#124—62no—
272C4×Q8—34no—
273C4×Q8—62no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—61no—
276C2×C22⋊C4—61no—
277C2×C22⋊C4—61no—
278C2×C42—61no—
279C2×C42C2×C3×D311yescharacteristic
280C4⋊C8C2×C3×D314yescomplemented
281#103—34no—
282#102—34no—
283C23×C3—21no—
284C23×C3—62no—
285C23×C3—122no—
286C23×C3—122no—
287C23×C3—122no—
288C23×C3C2×D1211yescharacteristic
289C23×C3C2×C3×D411yescharacteristic
290C22×D3—22no—
291C22×D3—42no—
292C22×D3—42no—
293C22×D3—42no—
294C3×Q8—34no—
295C3×Q8—64no—
296C3×Q8—62no—
297C3×Q8—62no—
298C3×Q8—62no—
299C3×Q8—122no—
300C3×D4—62no—
301C3×D4—62no—
302C3×D4—122no—
303C2×C3×C4—24no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—42no—
315C2×C3×C4—64no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—122no—
320C2×C3×C4—122no—
321C2×C3×C4C2×D1212yes—
322C2×C3×C4C2×D1212yes—
323C2×C3×C4C2×D1211yescharacteristic
324C2×C3×C4D3×D412yes—
325C2×C3×C4#23912yes—
326C2×C3×C4C2×C3×D412yes—
327C2×C3×C4C2×C3×D412yes—
328C2×C3×C4C2×C3×D411yescharacteristic
329C2×C3×C4C2×C3×D412yes—
330C2×C3×C4C3×#4112yes—
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C24×C311yescharacteristic
333C2×Dic3—24no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—42no—
338C2×Dic3—42no—
339D12—22no—
340D12—22no—
341D12—42no—
342Dic6—24no—
343Dic6—22no—
344Dic6—22no—
345Dic6—22no—
346Dic6—42no—
347Dic6C2×C3×D414yes—
348C3×C8—22no—
349C3×C8—22no—
350C3×C8—22no—
351C3×C8—22no—
352C3×C8—42no—
353C3×C8—42no—
354C2×C32#46414yescomplemented
355C2×C32C2×#12111yescharacteristic
356C2×C32C2×#13511yescharacteristic
357C2×C32C2×#13711yescharacteristic
358C3×D3—82no—
359C24—61no—
360C2×Q8—32no—
361C2×Q8—32no—
362C2×Q8—34no—
363C2×Q8—61no—
364C2×Q8—61no—
365C2×Q8—62no—
366C2×Q8—62no—
367C2×Q8—62no—
368C2×D4—32no—
369C2×D4—61no—
370C2×D4—62no—
371C2×D4—62no—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4—61no—
375C22×C4C3×D1211yescharacteristic
376C22×C4C3×D1211yescharacteristic
377C22×C4C22×C3×D311yescharacteristic
378Q16—68no—
379SD16—68no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8C22×C3×D312yes—
383C2×C8C22×C3×D312yes—
384C4⋊C4—32no—
385C4⋊C4—61no—
386C4⋊C4—64no—
387C22⋊C4—64no—
388C22⋊C4—64no—
389C42—64no—
390C42C3×D1212yes—
391C42C22×C3×D312yes—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—21no—
396C22×C3—122no—
397C22×C3—122no—
398C22×C3—122no—
399C22×C3—244no—
400C22×C3#89512yes—
401C22×C3#90412yes—
402C22×C3#90912yes—
403C22×C3C3×#12112yes—
404C22×C3C3×#13512yes—
405C22×C3C3×#13712yes—
406C22×C3C22×D1211yescharacteristic
407C22×C3C22×C3×D411yescharacteristic
408C2×D3—42no—
409C2×D3—42no—
410C2×D3—42no—
411C2×D3—84no—
412C3×C4—24no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—22no—
416C3×C4—22no—
417C3×C4—22no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—42no—
421C3×C4—64no—
422C3×C4—122no—
423C3×C4—122no—
424C3×C4#89512yes—
425C3×C4C3×#12112yes—
426C3×C4C2×D3×D411yescharacteristic
427C3×C4C2×#23911yescharacteristic
428C3×C4C22×C3×D411yescharacteristic
429C3×C4C2×C3×#4111yescharacteristic
430Dic3—24no—
431Dic3—42no—
432Dic3—42no—
433C32C2×#46411yescharacteristic, complemented, Sylow
434C23—62no—
435C23—122no—
436C23—122no—
437C23—122no—
438C23C2×C3×D1211yescharacteristic
439Q8—34no—
440Q8—64no—
441Q8—62no—
442Q8—62no—
443Q8—62no—
444Q8—122no—
445D4—62no—
446D4—62no—
447D4—122no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—64no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—122no—
455C2×C4—122no—
456C2×C4C2×C3×D1212yes—
457C2×C4C2×C3×D1212yes—
458C2×C4C2×C3×D1211yescharacteristic
459C2×C4C3×D3×D412yes—
460C2×C4C3×#23912yes—
461C2×C4C23×C3×D311yescharacteristic
462C8—22no—
463C8—22no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—24no—
467C2×C3—21no—
468C2×C3—242no—
469C2×C3#484514yesdirect product factor
470C2×C3C3×#46414yescomplemented
471C2×C3C2×#89511yescharacteristic
472C2×C3C2×#90411yescharacteristic
473C2×C3C2×#90911yescharacteristic
474C2×C3C2×C3×#12111yescharacteristic
475C2×C3C2×C3×#13511yescharacteristic
476C2×C3C2×C3×#13711yescharacteristic
477D3—82no—
478C22—122no—
479C22—122no—
480C22—122no—
481C22—244no—
482C22C3×#89512yes—
483C22C3×#90412yes—
484C22C3×#90912yes—
485C22C22×C3×D1211yescharacteristic
486C4—22no—
487C4—22no—
488C4—64no—
489C4—122no—
490C4—122no—
491C4C3×#89512yes—
492C4C2×C3×D3×D411yescharacteristic
493C4C2×C3×#23911yescharacteristic
494C3—21no—
495C3C2×#484511yescharacteristic, direct product factor
496C3C2×C3×#46411yescharacteristic, complemented
497C2—242no—
498C2C3×#484514yesdirect product factor
499C2C2×C3×#89511yescharacteristic
500C2C2×C3×#90411yescharacteristic
501C2C2×C3×#90911yescharacteristic
subgroupG/H
centerC23×C3C2×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4⋊C8C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C3×C4⋊C8D3
hypocenterC3C2×C3×#464
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×Dic12C2semidirect
4. C2×C3×C4×Dic6C2semidirect
5. C2×C32×C4⋊C8C2semidirect
7. C2×C3×#816C2semidirect
8. C3×#4845C2direct (N × H)
10. C2×#4845C3direct (N × H)
23. C2×C3×Dic12C22semidirect
29. C3×C4×Dic6C22semidirect
30. C32×C4⋊C8C22semidirect
32. C3×#816C22semidirect
37. C22×Dic12C2×C3semidirect
40. C2×C4×Dic6C2×C3semidirect
43. C2×C3×C4⋊C8D3semidirect
44. C2×C3×C4⋊C8C2×C3semidirect
48. C2×#816C2×C3semidirect
49. #4845C2×C3direct (N × H)
118. C2×Dic12C22×C3semidirect
124. C4×Dic6C22×C3semidirect
126. C3×C4⋊C8C2×D3semidirect
127. C3×C4⋊C8C22×C3semidirect
131. #816C22×C3semidirect
167. C2×C4⋊C8C3×D3semidirect
280. C4⋊C8C2×C3×D3semidirect
354. C2×C32#464semidirect
433. C32C2×#464semidirect
469. C2×C3#4845direct (N × H)
470. C2×C3C3×#464semidirect
495. C3C2×#4845direct (N × H)
496. C3C2×C3×#464semidirect
498. C2C3×#4845direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Dic122
C22×C3×#2042
C2×C3×#8752
C2×C3×C4×Dic62
C2×C32×C4⋊C82
C2×C3×#8212
C2×C3×#8162
C3×#48452
C2×C3×#4643
C2×#48453