Finite Group Databasebeta

← C2×C3×#4767 #11865673

Subgroups — C2×C3×#4767 #11865673

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#936C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic
3C22×C3×Dic12C211yesmaximal, characteristic, complemented
4C2×C3×#887C211yesmaximal, characteristic, complemented
5C2×C32×#102C211yesmaximal, characteristic
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C2×C3×#810C211yesmaximal, characteristic, complemented
8C3×#4767C218yesmaximal, direct product factor
9C2×C3×#464—31nomaximal
10C2×#4767C311yesmaximal, characteristic, direct product factor
11C22×C32×D4C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C3×#217—21no—
17C2×C3×#217—21no—
18C3×#936—22no—
19C3×#936C2214yes—
20C2×C3×#214—24no—
21C2×C3×#214C2214yes—
22C2×C3×Dic3⋊C4—21no—
23C2×C3×C4×Dic3—21no—
24C2×C3×C4×Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×C3×Dic12—24no—
27C2×C3×Dic12C2214yescomplemented
28C3×#887—22no—
29C3×#887C2214yescomplemented
30C32×#102C2214yes—
31C3×Dic3⋊C8C2214yescomplemented
32C3×#810C2214yescomplemented
33C22×C3×Q16—31no—
34C22×C3×SD16—31no—
35C2×C3×#124—31no—
36C2×C3×C4×Q8—31no—
37C2×#936C2×C311yescharacteristic
38C22×#214C2×C311yescharacteristic
39C22×Dic12C2×C311yescharacteristic, complemented
40C2×#887C2×C311yescharacteristic, complemented
41C3×#464—38no—
42C2×C3×C4⋊C8—31no—
43C2×C3×#103—31no—
44C2×C3×#102—21no—
45C2×C3×#102D311yescharacteristic
46C2×C3×#102C2×C311yescharacteristic
47C2×Dic3⋊C8C2×C311yescharacteristic, complemented
48C2×#810C2×C311yescharacteristic, complemented
49#4767C2×C318yesdirect product factor
50C24×C32—21no—
51C2×C32×D4—22no—
52C2×C32×D4—21no—
53C2×C32×D4—22no—
54C2×C32×D4C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
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×C8C2312yes—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2312yes—
73C3×#217—24no—
74C3×#217—24no—
75C3×#214—28no—
76C3×Dic3⋊C4—24no—
77C3×C4×Dic3—24no—
78C3×C4×Dic3D412yes—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82C3×Dic12—28no—
83C2×#464—31noSylow
84C22×C3×Q8—31no—
85C22×C3×Q8—31no—
86C22×C3×D4—21no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C22×C311yescharacteristic
89C22×Dic6C22×C311yescharacteristic
90C22×Dic6C22×C311yescharacteristic
91C2×C3×Q16—34no—
92C2×C3×Q16—64no—
93C2×C3×SD16—34no—
94C2×C3×SD16—64no—
95C22×C3×C8—21no—
96C22×C3×C8—31no—
97C22×C3×C8C2×D311yescharacteristic
98C22×C3×C8C22×C311yescharacteristic
99C3×#124—34no—
100C3×#124—62no—
101C3×C4×Q8—34no—
102C3×C4×Q8—62no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—61no—
105C2×C3×C4⋊C4C2×D311yescharacteristic
106C2×C3×C4⋊C4C22×C311yescharacteristic
107C2×C3×C22⋊C4—61no—
108C2×C3×C22⋊C4—61no—
109C2×C3×C42—31no—
110C2×C3×C42—61no—
111C2×#217—21no—
112C2×#217—21no—
113#936—22no—
114#936C22×C314yes—
115C2×#214—24no—
116C2×#214C22×C314yes—
117C2×Dic3⋊C4—21no—
118C2×C4×Dic3—21no—
119C2×C4×Dic3C22×C311yescharacteristic
120C22×C3⋊C8C22×C311yescharacteristic
121C2×Dic12—24no—
122C2×Dic12C22×C314yescomplemented
123#887—22no—
124#887C22×C314yescomplemented
125C3×C4⋊C8—34no—
126C3×#103—34no—
127C3×#102—24no—
128C3×#102C2×D314yes—
129C3×#102C22×C314yes—
130Dic3⋊C8C22×C314yescomplemented
131#810C22×C314yescomplemented
132C23×C32—22no—
133C23×C32—42no—
134C23×C32—42no—
135C23×C32—42no—
136C23×C32C2×D411yescharacteristic
137C32×D4—22no—
138C32×D4—22no—
139C32×D4—42no—
140C2×C32×C4—22no—
141C2×C32×C4—42no—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D412yes—
144C2×C32×C4#4112yes—
145C2×C32×C4C2411yescharacteristic
146C2×C3×Dic3—24no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3C2×D412yes—
153C2×C3×Dic3C2×D412yes—
154C3×Dic6—24no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—42no—
159C3×Dic6C2×D414yes—
160C32×C8—22no—
161C3×C3⋊C8—22no—
162C22×Q16—31no—
163C22×SD16—31no—
164C2×#124—31no—
165C2×C4×Q8—31no—
166#464—38no—
167C2×C4⋊C8—31no—
168C2×#103—31no—
169C2×#102C3×D311yescharacteristic
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—41no—
173C2×C3×Q8—34no—
174C2×C3×Q8—32no—
175C2×C3×Q8—32no—
176C2×C3×Q8—62no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×Q8—62no—
180C2×C3×Q8—62no—
181C2×C3×D4—24no—
182C2×C3×D4—22no—
183C2×C3×D4—22no—
184C2×C3×D4—21no—
185C2×C3×D4—22no—
186C2×C3×D4—21no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—42no—
190C2×C3×D4—41no—
191C2×C3×D4C22×D312yes—
192C2×C3×D4C23×C312yes—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—41no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C23×C311yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3C3×D411yescharacteristic
206C22×Dic3C3×D411yescharacteristic
207C2×Dic6—21no—
208C2×Dic6—22no—
209C2×Dic6—22no—
210C2×Dic6—22no—
211C2×Dic6—21no—
212C2×Dic6C3×D414yes—
213C2×Dic6C23×C312yes—
214C2×Dic6C23×C312yes—
215C3×Q16—68no—
216C3×SD16—68no—
217C2×C3×C8—22no—
218C2×C3×C8—22no—
219C2×C3×C8—22no—
220C2×C3×C8—32no—
221C2×C3×C8—42no—
222C2×C3×C8—62no—
223C2×C3×C8C22×D312yes—
224C2×C3×C8C23×C312yes—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4—64no—
230C3×C4⋊C4C22×D312yes—
231C3×C4⋊C4C23×C312yes—
232C3×C22⋊C4—64no—
233C3×C22⋊C4—64no—
234C3×C42—32no—
235C3×C42—32no—
236C3×C42—64no—
237#217—24no—
238#217—24no—
239#214—28no—
240Dic3⋊C4—24no—
241C4×Dic3—24no—
242C4×Dic3C3×D412yes—
243C4×Dic3C23×C312yes—
244C2×C3⋊C8—22no—
245C2×C3⋊C8C23×C312yes—
246Dic12—28no—
247C22×C32—42no—
248C22×C32—42no—
249C22×C32—42no—
250C22×C32—84no—
251C22×C32#12112yes—
252C22×C32#13512yes—
253C22×C32#13712yes—
254C22×C32C22×D411yescharacteristic
255C32×C4—42no—
256C32×C4#12112yes—
257C32×C4C22×D411yescharacteristic
258C32×C4C2×#4111yescharacteristic
259C3×Dic3—24no—
260C3×Dic3—22no—
261C3×Dic3—22no—
262C3×Dic3—42no—
263C22×Q8—31no—
264C22×Q8—31no—
265C22×D4C2×C3×D311yescharacteristic
266C2×Q16—34no—
267C2×Q16—64no—
268C2×SD16—34no—
269C2×SD16—64no—
270C22×C8—31no—
271C22×C8C2×C3×D311yescharacteristic
272#124—34no—
273#124—62no—
274C4×Q8—34no—
275C4×Q8—62no—
276C2×C4⋊C4—61no—
277C2×C4⋊C4C2×C3×D311yescharacteristic
278C2×C22⋊C4—61no—
279C2×C22⋊C4—61no—
280C2×C42—31no—
281C2×C42—61no—
282C4⋊C8—34no—
283#103—34no—
284#102C2×C3×D314yes—
285C23×C3—22no—
286C23×C3—22no—
287C23×C3—21no—
288C23×C3—42no—
289C23×C3—44no—
290C23×C3—42no—
291C23×C3—42no—
292C23×C3—42no—
293C23×C3—42no—
294C23×C3—42no—
295C23×C3—42no—
296C23×C3—82no—
297C23×C3—82no—
298C23×C3D3×D411yescharacteristic
299C23×C3C2×C3×D411yescharacteristic
300C3×Q8—34no—
301C3×Q8—64no—
302C3×Q8—62no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—122no—
306C3×D4—24no—
307C3×D4—22no—
308C3×D4—22no—
309C3×D4—22no—
310C3×D4—22no—
311C3×D4—42no—
312C3×D4—44no—
313C3×D4—42no—
314C3×D4—42no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—22no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—42no—
326C2×C3×C4—64no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—82no—
332C2×C3×C4—122no—
333C2×C3×C4#23512yes—
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D412yes—
336C2×C3×C4C2×C3×D411yescharacteristic
337C2×C3×C4C2×C3×D412yes—
338C2×C3×C4C3×#4112yes—
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C24×C311yescharacteristic
341C2×Dic3—24no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—42no—
347C2×Dic3C2×C3×D412yes—
348C2×Dic3C2×C3×D412yes—
349Dic6—24no—
350Dic6—22no—
351Dic6—22no—
352Dic6—22no—
353Dic6—42no—
354Dic6C2×C3×D414yes—
355C3×C8—22no—
356C3×C8—22no—
357C3×C8—42no—
358C3×C8—62no—
359C3⋊C8—22no—
360C2×C32—82no—
361C2×C32#46414yescomplemented
362C2×C32C2×#12111yescharacteristic
363C2×C32C2×#13511yescharacteristic
364C2×C32C2×#13711yescharacteristic
365C24—21no—
366C2×Q8—32no—
367C2×Q8—32no—
368C2×Q8—34no—
369C2×Q8—62no—
370C2×Q8—61no—
371C2×Q8—61no—
372C2×Q8—62no—
373C2×Q8—62no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4C22×C3×D312yes—
378C22×C4—21no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—61no—
382C22×C4—61no—
383C22×C4C22×C3×D311yescharacteristic
384Q16—68no—
385SD16—68no—
386C2×C8—22no—
387C2×C8—32no—
388C2×C8—62no—
389C2×C8C22×C3×D312yes—
390C4⋊C4—21no—
391C4⋊C4—64no—
392C4⋊C4C22×C3×D312yes—
393C22⋊C4—64no—
394C22⋊C4—64no—
395C42—32no—
396C42—32no—
397C42—64no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—21no—
402C22×C3—44no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—82no—
410C22×C3—82no—
411C22×C3—88no—
412C22×C3—84no—
413C22×C3—84no—
414C22×C3#88412yes—
415C22×C3#91212yes—
416C22×C3#91512yes—
417C22×C3C3×#12112yes—
418C22×C3C3×#13512yes—
419C22×C3C3×#13712yes—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C22×C3×D411yescharacteristic
422C3×C4—22no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—42no—
426C3×C4—42no—
427C3×C4—64no—
428C3×C4—62no—
429C3×C4—62no—
430C3×C4—82no—
431C3×C4—122no—
432C3×C4#88412yes—
433C3×C4C3×#12112yes—
434C3×C4C2×#23511yescharacteristic
435C3×C4C2×D3×D411yescharacteristic
436C3×C4C22×C3×D411yescharacteristic
437C3×C4C2×C3×#4111yescharacteristic
438Dic3—22no—
439Dic3—22no—
440Dic3—24no—
441Dic3—42no—
442C32C2×#46411yescharacteristic, complemented, Sylow
443C23—22no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23C3×D3×D411yescharacteristic
448Q8—34no—
449Q8—64no—
450Q8—62no—
451Q8—62no—
452Q8—62no—
453Q8—122no—
454D4—22no—
455D4—22no—
456D4—42no—
457C2×C4—22no—
458C2×C4—32no—
459C2×C4—32no—
460C2×C4—42no—
461C2×C4—64no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—122no—
467C2×C4C3×#23512yes—
468C2×C4C3×D3×D411yescharacteristic
469C2×C4C3×D3×D412yes—
470C2×C4C23×C3×D311yescharacteristic
471C8—22no—
472C8—62no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—24no—
477C2×C3—84no—
478C2×C3—82no—
479C2×C3—82no—
480C2×C3#476714yesdirect product factor
481C2×C3C3×#46414yescomplemented
482C2×C3C2×#88411yescharacteristic
483C2×C3C2×#91211yescharacteristic
484C2×C3C2×#91511yescharacteristic
485C2×C3C2×C3×#12111yescharacteristic
486C2×C3C2×C3×#13511yescharacteristic
487C2×C3C2×C3×#13711yescharacteristic
488C22—42no—
489C22—42no—
490C22—42no—
491C22—84no—
492C22C3×#88412yes—
493C22C3×#91212yes—
494C22C3×#91512yes—
495C22C2×C3×D3×D411yescharacteristic
496C4—42no—
497C4—64no—
498C4—62no—
499C4—62no—
500C4—122no—
501C4C3×#88412yes—
502C4C2×C3×#23511yescharacteristic
503C4C2×C3×D3×D411yescharacteristic
504C3—21no—
505C3C2×#476711yescharacteristic, direct product factor
506C3C2×C3×#46411yescharacteristic, complemented
507C2—82no—
508C2C3×#476714yesdirect product factor
509C2C2×C3×#88411yescharacteristic
510C2C2×C3×#91211yescharacteristic
511C2C2×C3×#91511yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
hypercenterC2×C3×#102D3
hypocenterC3C2×C3×#464
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
3. C22×C3×Dic12C2semidirect
4. C2×C3×#887C2semidirect
6. C2×C3×Dic3⋊C8C2semidirect
7. C2×C3×#810C2semidirect
8. C3×#4767C2direct (N × H)
10. C2×#4767C3direct (N × H)
27. C2×C3×Dic12C22semidirect
29. C3×#887C22semidirect
31. C3×Dic3⋊C8C22semidirect
32. C3×#810C22semidirect
39. C22×Dic12C2×C3semidirect
40. C2×#887C2×C3semidirect
47. C2×Dic3⋊C8C2×C3semidirect
48. C2×#810C2×C3semidirect
49. #4767C2×C3direct (N × H)
122. C2×Dic12C22×C3semidirect
124. #887C22×C3semidirect
130. Dic3⋊C8C22×C3semidirect
131. #810C22×C3semidirect
361. C2×C32#464semidirect
442. C32C2×#464semidirect
480. C2×C3#4767direct (N × H)
481. C2×C3C3×#464semidirect
505. C3C2×#4767direct (N × H)
506. C3C2×C3×#464semidirect
508. C2C3×#4767direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9362
C22×C3×#2142
C22×C3×Dic122
C2×C3×#8872
C2×C32×#1022
C2×C3×Dic3⋊C82
C2×C3×#8102
C3×#47672
C2×C3×#4643
C2×#47673