Finite Group Databasebeta

← C2×C3×#4814 #11869482

Subgroups — C2×C3×#4814 #11869482

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#946C211yesmaximal, characteristic
2C2×C3×#892C211yesmaximal, characteristic
3C2×C32×#103C211yesmaximal, characteristic, complemented
4C2×C3×#835C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
6C2×C3×#818C211yesmaximal, characteristic, complemented
7C2×C3×#808C211yesmaximal, characteristic, complemented
8C3×#4814C218yesmaximal, direct product factor
9C2×C3×#485—31nomaximal
10C2×#4814C311yesmaximal, characteristic, direct product factor
11C22×C32×Q8C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C3×#946—22no—
16C3×#946C2214yes—
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4—21no—
22C2×C3×C4×Dic3—21no—
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×#892—22no—
25C3×#892C2214yes—
26C32×#103C2214yescomplemented
27C3×#835C2214yescomplemented
28C3×(C2×D3)⋊C8C2214yes—
29C3×#818C2214yescomplemented
30C3×#808C2214yescomplemented
31C2×C3×C22⋊Q8—31no—
32C2×C3×#117—31no—
33C2×#946C2×C311yescharacteristic
34C2×#892C2×C311yescharacteristic
35C3×#485—38no—
36C2×C3×#107—31no—
37C2×C3×#106—31no—
38C2×C3×#103—21no—
39C2×C3×#103—31no—
40C2×C3×#103D311yescharacteristic, complemented
41C2×C3×#103C2×C311yescharacteristic, complemented
42C2×C3×C22⋊C8—31no—
43C2×#835C2×C311yescharacteristic, complemented
44C2×(C2×D3)⋊C8C2×C311yescharacteristic
45C2×#818C2×C311yescharacteristic, complemented
46C2×#808C2×C311yescharacteristic, complemented
47#4814C2×C318yesdirect product factor
48C23×C3×D3D411yescharacteristic
49C2×C32×Q8—21no—
50C2×C32×Q8—22no—
51C2×C32×Q8—22no—
52C2×C32×Q8C2312yes—
53C22×C32×C4—21no—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C2×C3×C4×D3—22no—
60C2×C3×C4×D3—22no—
61C2×C3×C4×D3D412yes—
62C2×C3×C4×D3C2312yes—
63C2×C32×C8—22no—
64C2×C32×C8C2312yes—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67C3×(C2×D3)⋊C4—24no—
68C3×(C2×D3)⋊C4—24no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4⋊Dic3C2312yes—
73C3×Dic3⋊C4—24no—
74C3×C4×Dic3—24no—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8C2312yes—
77C2×#485—31noSylow
78C22×C3×Q8—21no—
79C22×C3×Q8C2×D311yescharacteristic
80C22×C3×Q8C22×C311yescharacteristic
81C23×C3×C4—31no—
82C22×C4×D3C22×C311yescharacteristic
83C22×C3×C8—21no—
84C22×C3×C8—31no—
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C22×C311yescharacteristic
87C3×C22⋊Q8—34no—
88C3×C22⋊Q8—62no—
89C3×#117—34no—
90C3×#117—62no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—61no—
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C4⋊C4C22×C311yescharacteristic
97C2×C3×C22⋊C4—61no—
98C2×C3×C22⋊C4—61no—
99C2×C3×C42—61no—
100#946—22no—
101#946C22×C314yes—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×C4⋊Dic3C22×C311yescharacteristic
105C2×C4⋊Dic3C22×C311yescharacteristic
106C2×Dic3⋊C4—21no—
107C2×C4×Dic3—21no—
108C22×C3⋊C8C22×C311yescharacteristic
109#892—22no—
110#892C22×C314yes—
111C3×#107—34no—
112C3×#106—34no—
113C3×#103—24no—
114C3×#103—34no—
115C3×#103C2×D314yescomplemented
116C3×#103C22×C314yescomplemented
117C3×C22⋊C8—34no—
118#835C22×C314yescomplemented
119(C2×D3)⋊C8C22×C314yes—
120#818C22×C314yescomplemented
121#808C22×C314yescomplemented
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3C2×D412yes—
127C32×Q8—22no—
128C32×Q8—22no—
129C32×Q8—42no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4—42no—
133C2×C32×C4—42no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4112yes—
136C2×C32×C4#4112yes—
137C2×C32×C4C2411yescharacteristic
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3C2×D412yes—
144C3×C4×D3—24no—
145C3×C4×D3—22no—
146C3×C4×D3—22no—
147C32×C8—22no—
148C3×C3⋊C8—22no—
149C2×C22⋊Q8—31no—
150C2×#117—31no—
151#485—38no—
152C2×#107—31no—
153C2×#106—31no—
154C2×#103—31no—
155C2×#103C3×D311yescharacteristic, complemented
156C2×C22⋊C8—31no—
157C24×C3—31no—
158C23×D3C3×D411yescharacteristic
159C2×C3×Q8—21no—
160C2×C3×Q8—21no—
161C2×C3×Q8—24no—
162C2×C3×Q8—22no—
163C2×C3×Q8—22no—
164C2×C3×Q8—22no—
165C2×C3×Q8—22no—
166C2×C3×Q8—22no—
167C2×C3×Q8—41no—
168C2×C3×Q8—42no—
169C2×C3×Q8C22×D312yes—
170C2×C3×Q8C23×C312yes—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—31no—
177C22×C3×C4—32no—
178C22×C3×C4—32no—
179C22×C3×C4—41no—
180C22×C3×C4—41no—
181C22×C3×C4—62no—
182C22×C3×C4—62no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C23×C311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3C3×D411yescharacteristic
190C2×C4×D3—22no—
191C2×C4×D3—22no—
192C2×C4×D3C3×D412yes—
193C2×C4×D3C23×C312yes—
194C2×C3×C8—22no—
195C2×C3×C8—22no—
196C2×C3×C8—22no—
197C2×C3×C8—32no—
198C2×C3×C8—42no—
199C2×C3×C8—62no—
200C2×C3×C8C22×D312yes—
201C2×C3×C8C23×C312yes—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—22no—
205C3×C4⋊C4—32no—
206C3×C4⋊C4—32no—
207C3×C4⋊C4—41no—
208C3×C4⋊C4—64no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4C22×D312yes—
212C3×C4⋊C4C23×C312yes—
213C3×C22⋊C4—64no—
214C3×C22⋊C4—64no—
215C3×C42—64no—
216(C2×D3)⋊C4—24no—
217(C2×D3)⋊C4—24no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3C23×C312yes—
221C4⋊Dic3C23×C312yes—
222Dic3⋊C4—24no—
223C4×Dic3—24no—
224C2×C3⋊C8—22no—
225C2×C3⋊C8C23×C312yes—
226C22×C32#12312yes—
227C22×C32#13512yes—
228C22×C32#13712yes—
229C22×C32C22×D411yescharacteristic
230C2×C3×D3—22no—
231C2×C3×D3—22no—
232C2×C3×D3—22no—
233C2×C3×D3—44no—
234C32×C4—42no—
235C32×C4—42no—
236C32×C4#12312yes—
237C32×C4C2×#4111yescharacteristic
238C32×C4C2×#4111yescharacteristic
239C3×Dic3—22no—
240C3×Dic3—42no—
241C3×Dic3—42no—
242C22×Q8C2×C3×D311yescharacteristic
243C23×C4—31no—
244C22×C8—31no—
245C22×C8C2×C3×D311yescharacteristic
246C22⋊Q8—34no—
247C22⋊Q8—62no—
248#117—34no—
249#117—62no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—61no—
253C2×C4⋊C4C2×C3×D311yescharacteristic
254C2×C22⋊C4—61no—
255C2×C22⋊C4—61no—
256C2×C42—61no—
257#107—34no—
258#106—34no—
259#103—34no—
260#103C2×C3×D314yescomplemented
261C22⋊C8—34no—
262C23×C3—21no—
263C23×C3—32no—
264C23×C3—62no—
265C23×C3—62no—
266C23×C3—62no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×C3×D411yescharacteristic
269C22×D3—22no—
270C22×D3—22no—
271C22×D3—22no—
272C22×D3C2×C3×D412yes—
273C3×Q8—24no—
274C3×Q8—22no—
275C3×Q8—22no—
276C3×Q8—22no—
277C3×Q8—22no—
278C3×Q8—42no—
279C3×Q8—44no—
280C3×Q8—42no—
281C3×Q8—42no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—32no—
291C2×C3×C4—42no—
292C2×C3×C4—42no—
293C2×C3×C4—44no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4—62no—
299C2×C3×C4—64no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—82no—
305C2×C3×C4—122no—
306C2×C3×C4—122no—
307C2×C3×C4#23512yes—
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4#23712yes—
310C2×C3×C4C2×C3×D411yescharacteristic
311C2×C3×C4C3×#4112yes—
312C2×C3×C4C3×#4112yes—
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C24×C311yescharacteristic
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—42no—
319C2×Dic3—42no—
320C2×Dic3C2×C3×D412yes—
321C4×D3—24no—
322C4×D3—22no—
323C4×D3—22no—
324C3×C8—22no—
325C3×C8—22no—
326C3×C8—42no—
327C3×C8—62no—
328C3⋊C8—22no—
329C2×C32#48514yescomplemented
330C2×C32C2×#12311yescharacteristic
331C2×C32C2×#13511yescharacteristic
332C2×C32C2×#13711yescharacteristic
333C3×D3—42no—
334C24—31no—
335C2×Q8—21no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8C22×C3×D312yes—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—31no—
342C22×C4—32no—
343C22×C4—32no—
344C22×C4—62no—
345C22×C4—62no—
346C22×C4—61no—
347C22×C4—61no—
348C22×C4C22×C3×D311yescharacteristic
349C2×C8—22no—
350C2×C8—32no—
351C2×C8—62no—
352C2×C8C22×C3×D312yes—
353C4⋊C4—21no—
354C4⋊C4—32no—
355C4⋊C4—32no—
356C4⋊C4—64no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4C22×C3×D312yes—
360C22⋊C4—64no—
361C22⋊C4—64no—
362C42—64no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—21no—
367C22×C3—62no—
368C22×C3—62no—
369C22×C3—62no—
370C22×C3—124no—
371C22×C3#88312yes—
372C22×C3#91512yes—
373C22×C3#91912yes—
374C22×C3C3×#12312yes—
375C22×C3C3×#13512yes—
376C22×C3C3×#13712yes—
377C22×C3C2×D3×D411yescharacteristic
378C22×C3C22×C3×D411yescharacteristic
379C2×D3—22no—
380C2×D3—22no—
381C2×D3—22no—
382C2×D3—44no—
383C3×C4—22no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—44no—
387C3×C4—42no—
388C3×C4—42no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—62no—
392C3×C4—82no—
393C3×C4—122no—
394C3×C4—122no—
395C3×C4#88312yes—
396C3×C4C3×#12312yes—
397C3×C4C2×#23511yescharacteristic
398C3×C4C2×#23711yescharacteristic
399C3×C4C2×C3×#4111yescharacteristic
400C3×C4C2×C3×#4111yescharacteristic
401Dic3—22no—
402Dic3—42no—
403Dic3—42no—
404C32C2×#48511yescharacteristic, complemented, Sylow
405C23—32no—
406C23—62no—
407C23—62no—
408C23—62no—
409C23C3×D3×D411yescharacteristic
410Q8—22no—
411Q8—22no—
412Q8—42no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—32no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—62no—
419C2×C4—64no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—122no—
425C2×C4—122no—
426C2×C4C3×#23512yes—
427C2×C4C3×D3×D411yescharacteristic
428C2×C4C3×#23712yes—
429C2×C4C23×C3×D311yescharacteristic
430C8—22no—
431C8—62no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—24no—
436C2×C3—122no—
437C2×C3#481414yesdirect product factor
438C2×C3C3×#48514yescomplemented
439C2×C3C2×#88311yescharacteristic
440C2×C3C2×#91511yescharacteristic
441C2×C3C2×#91911yescharacteristic
442C2×C3C2×C3×#12311yescharacteristic
443C2×C3C2×C3×#13511yescharacteristic
444C2×C3C2×C3×#13711yescharacteristic
445D3—42no—
446C22—62no—
447C22—62no—
448C22—62no—
449C22—124no—
450C22C3×#88312yes—
451C22C3×#91512yes—
452C22C3×#91912yes—
453C22C2×C3×D3×D411yescharacteristic
454C4—42no—
455C4—42no—
456C4—62no—
457C4—122no—
458C4—122no—
459C4C3×#88312yes—
460C4C2×C3×#23511yescharacteristic
461C4C2×C3×#23711yescharacteristic
462C3—21no—
463C3C2×#481411yescharacteristic, direct product factor
464C3C2×C3×#48511yescharacteristic, complemented
465C2—122no—
466C2C3×#481414yesdirect product factor
467C2C2×C3×#88311yescharacteristic
468C2C2×C3×#91511yescharacteristic
469C2C2×C3×#91911yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC2×C3×#103D3
hypocenterC3C2×C3×#485
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
3. C2×C32×#103C2semidirect
4. C2×C3×#835C2semidirect
6. C2×C3×#818C2semidirect
7. C2×C3×#808C2semidirect
8. C3×#4814C2direct (N × H)
10. C2×#4814C3direct (N × H)
26. C32×#103C22semidirect
27. C3×#835C22semidirect
29. C3×#818C22semidirect
30. C3×#808C22semidirect
40. C2×C3×#103D3semidirect
41. C2×C3×#103C2×C3semidirect
43. C2×#835C2×C3semidirect
45. C2×#818C2×C3semidirect
46. C2×#808C2×C3semidirect
47. #4814C2×C3direct (N × H)
115. C3×#103C2×D3semidirect
116. C3×#103C22×C3semidirect
118. #835C22×C3semidirect
120. #818C22×C3semidirect
121. #808C22×C3semidirect
155. C2×#103C3×D3semidirect
260. #103C2×C3×D3semidirect
329. C2×C32#485semidirect
404. C32C2×#485semidirect
437. C2×C3#4814direct (N × H)
438. C2×C3C3×#485semidirect
463. C3C2×#4814direct (N × H)
464. C3C2×C3×#485semidirect
466. C2C3×#4814direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9462
C2×C3×#8922
C2×C32×#1032
C2×C3×#8352
C2×C3×(C2×D3)⋊C82
C2×C3×#8182
C2×C3×#8082
C3×#48142
C2×C3×#4853
C2×#48143