Finite Group Databasebeta

← C2×C3×#4795 #11865628

Subgroups — C2×C3×#4795 #11865628

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#944C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic
3C22×C3×Dic12C211yesmaximal, characteristic
4C2×C3×#887C211yesmaximal, characteristic
5C2×C32×#103C211yesmaximal, characteristic
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic
7C2×C3×#810C211yesmaximal, characteristic
8C3×#4795C218yesmaximal, direct product factor
9C2×C3×#462—31nomaximal
10C2×#4795C311yesmaximal, characteristic, direct product factor
11C22×C32×Q8C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C3×#944—22no—
17C3×#944C2214yes—
18C2×C3×#216—24no—
19C2×C3×#216C2214yes—
20C2×C3×Dic3⋊C4—21no—
21C2×C3×Dic3⋊C4—21no—
22C2×C3×Dic3⋊C4—21no—
23C2×C3×C4×Dic3—21no—
24C2×C3×C4×Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×C3×Dic12—24no—
27C2×C3×Dic12C2214yes—
28C3×#887—22no—
29C3×#887C2214yes—
30C32×#103C2214yes—
31C3×Dic3⋊C8C2214yes—
32C3×#810C2214yes—
33C22×C3×Q16—31no—
34C22×C3×Q16—31no—
35C2×C3×C4⋊Q8—31no—
36C2×C3×C4×Q8—31no—
37C2×#944C2×C311yescharacteristic
38C22×#216C2×C311yescharacteristic
39C22×Dic12C2×C311yescharacteristic
40C2×#887C2×C311yescharacteristic
41C3×#462—38no—
42C2×C3×C4⋊C8—31no—
43C2×C3×#103—21no—
44C2×C3×#103—31no—
45C2×C3×#103D311yescharacteristic
46C2×C3×#103C2×C311yescharacteristic
47C2×Dic3⋊C8C2×C311yescharacteristic
48C2×#810C2×C311yescharacteristic
49#4795C2×C318yesdirect product factor
50C2×C32×Q8—21no—
51C2×C32×Q8—22no—
52C2×C32×Q8—22no—
53C2×C32×Q8C2312yes—
54C22×C32×C4—21no—
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×#216—28no—
74C3×Dic3⋊C4—24no—
75C3×Dic3⋊C4—24no—
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×#462—31noSylow
84C22×C3×Q8—21no—
85C22×C3×Q8—31no—
86C22×C3×Q8—31no—
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×Q8C22×C311yescharacteristic
89C22×Dic6C22×C311yescharacteristic
90C22×Dic6C22×C311yescharacteristic
91C2×C3×Q16—34no—
92C2×C3×Q16—34no—
93C2×C3×Q16—64no—
94C2×C3×Q16—64no—
95C22×C3×C8—21no—
96C22×C3×C8—31no—
97C22×C3×C8C2×D311yescharacteristic
98C22×C3×C8C22×C311yescharacteristic
99C3×C4⋊Q8—34no—
100C3×C4⋊Q8—62no—
101C3×C4×Q8—34no—
102C3×C4×Q8—62no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—61no—
105C2×C3×C4⋊C4—61no—
106C2×C3×C4⋊C4—61no—
107C2×C3×C4⋊C4C2×D311yescharacteristic
108C2×C3×C4⋊C4C22×C311yescharacteristic
109C2×C3×C42—31no—
110C2×C3×C42—61no—
111#944—22no—
112#944C22×C314yes—
113C2×#216—24no—
114C2×#216C22×C314yes—
115C2×Dic3⋊C4—21no—
116C2×Dic3⋊C4—21no—
117C2×Dic3⋊C4—21no—
118C2×C4×Dic3—21no—
119C2×C4×Dic3C22×C311yescharacteristic
120C22×C3⋊C8C22×C311yescharacteristic
121C2×Dic12—24no—
122C2×Dic12C22×C314yes—
123#887—22no—
124#887C22×C314yes—
125C3×C4⋊C8—34no—
126C3×#103—24no—
127C3×#103—34no—
128C3×#103C2×D314yes—
129C3×#103C22×C314yes—
130Dic3⋊C8C22×C314yes—
131#810C22×C314yes—
132C23×C32C2×D411yescharacteristic
133C32×Q8—22no—
134C32×Q8—22no—
135C32×Q8—42no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4—42no—
139C2×C32×C4—42no—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D412yes—
142C2×C32×C4#4112yes—
143C2×C32×C4C2411yescharacteristic
144C2×C3×Dic3—24no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—42no—
149C2×C3×Dic3Q1614yescomplemented
150C2×C3×Dic3C2×D412yes—
151C2×C3×Dic3C2×D412yes—
152C3×Dic6—24no—
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6—22no—
156C3×Dic6—42no—
157C3×Dic6C2×D414yes—
158C32×C8—22no—
159C3×C3⋊C8—22no—
160C22×Q16—31no—
161C22×Q16—31no—
162C2×C4⋊Q8—31no—
163C2×C4×Q8—31no—
164#462—38no—
165C2×C4⋊C8—31no—
166C2×#103—31no—
167C2×#103C3×D311yescharacteristic
168C2×C3×Q8—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8—24no—
171C2×C3×Q8—22no—
172C2×C3×Q8—22no—
173C2×C3×Q8—22no—
174C2×C3×Q8—22no—
175C2×C3×Q8—22no—
176C2×C3×Q8—34no—
177C2×C3×Q8—32no—
178C2×C3×Q8—32no—
179C2×C3×Q8—41no—
180C2×C3×Q8—42no—
181C2×C3×Q8—62no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×Q8—62no—
185C2×C3×Q8—62no—
186C2×C3×Q8C22×D312yes—
187C2×C3×Q8C23×C312yes—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—41no—
196C22×C3×C4—41no—
197C22×C3×C4—61no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C23×C311yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3C3×D411yescharacteristic
204C22×Dic3C3×D411yescharacteristic
205C2×Dic6—21no—
206C2×Dic6—22no—
207C2×Dic6—22no—
208C2×Dic6—22no—
209C2×Dic6—21no—
210C2×Dic6C3×D414yes—
211C2×Dic6C23×C312yes—
212C2×Dic6C23×C312yes—
213C3×Q16—68no—
214C3×Q16—68no—
215C2×C3×C8—22no—
216C2×C3×C8—22no—
217C2×C3×C8—22no—
218C2×C3×C8—32no—
219C2×C3×C8—42no—
220C2×C3×C8—62no—
221C2×C3×C8C22×D312yes—
222C2×C3×C8C23×C312yes—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—41no—
227C3×C4⋊C4—64no—
228C3×C4⋊C4—64no—
229C3×C4⋊C4—64no—
230C3×C4⋊C4C22×D312yes—
231C3×C4⋊C4C23×C312yes—
232C3×C42—32no—
233C3×C42—32no—
234C3×C42—64no—
235#216—28no—
236Dic3⋊C4—24no—
237Dic3⋊C4—24no—
238Dic3⋊C4—24no—
239C4×Dic3—24no—
240C4×Dic3C3×D412yes—
241C4×Dic3C23×C312yes—
242C2×C3⋊C8—22no—
243C2×C3⋊C8C23×C312yes—
244Dic12—28no—
245C22×C32#12112yes—
246C22×C32C2×Q1612yes—
247C22×C32#13712yes—
248C22×C32C22×D411yescharacteristic
249C32×C4—42no—
250C32×C4—42no—
251C32×C4#12112yes—
252C32×C4C22×D411yescharacteristic
253C32×C4C2×#4111yescharacteristic
254C3×Dic3—24no—
255C3×Dic3—22no—
256C3×Dic3—42no—
257C3×Dic3C2×Q1614yescomplemented
258C22×Q8—31no—
259C22×Q8—31no—
260C22×Q8C2×C3×D311yescharacteristic
261C2×Q16—34no—
262C2×Q16—34no—
263C2×Q16—64no—
264C2×Q16—64no—
265C22×C8—31no—
266C22×C8C2×C3×D311yescharacteristic
267C4⋊Q8—34no—
268C4⋊Q8—62no—
269C4×Q8—34no—
270C4×Q8—62no—
271C2×C4⋊C4—61no—
272C2×C4⋊C4—61no—
273C2×C4⋊C4—61no—
274C2×C4⋊C4C2×C3×D311yescharacteristic
275C2×C42—31no—
276C2×C42—61no—
277C4⋊C8—34no—
278#103—34no—
279#103C2×C3×D314yes—
280C23×C3—21no—
281C23×C3D3×D411yescharacteristic
282C23×C3C2×C3×D411yescharacteristic
283C3×Q8—24no—
284C3×Q8—22no—
285C3×Q8—22no—
286C3×Q8—22no—
287C3×Q8—22no—
288C3×Q8—34no—
289C3×Q8—42no—
290C3×Q8—44no—
291C3×Q8—42no—
292C3×Q8—42no—
293C3×Q8—64no—
294C3×Q8—62no—
295C3×Q8—62no—
296C3×Q8—62no—
297C3×Q8—122no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—22no—
306C2×C3×C4—34no—
307C2×C3×C4—32no—
308C2×C3×C4—32no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—44no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—42no—
315C2×C3×C4—42no—
316C2×C3×C4—64no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—82no—
321C2×C3×C4—122no—
322C2×C3×C4#23512yes—
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D412yes—
325C2×C3×C4C2×C3×D411yescharacteristic
326C2×C3×C4C2×C3×D412yes—
327C2×C3×C4C3×#4112yes—
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C24×C311yescharacteristic
330C2×Dic3—24no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—42no—
335C2×Dic3C3×Q1614yescomplemented
336C2×Dic3C2×C3×D412yes—
337C2×Dic3C2×C3×D412yes—
338Dic6—24no—
339Dic6—22no—
340Dic6—22no—
341Dic6—22no—
342Dic6—42no—
343Dic6C2×C3×D414yes—
344C3×C8—22no—
345C3×C8—22no—
346C3×C8—42no—
347C3×C8—62no—
348C3⋊C8—22no—
349C2×C32#46214yescomplemented
350C2×C32C2×#12111yescharacteristic
351C2×C32C22×Q1611yescharacteristic
352C2×C32C2×#13711yescharacteristic
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—32no—
357C2×Q8—32no—
358C2×Q8—34no—
359C2×Q8—62no—
360C2×Q8—61no—
361C2×Q8—61no—
362C2×Q8—62no—
363C2×Q8—62no—
364C2×Q8C22×C3×D312yes—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—31no—
368C22×C4—31no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4C22×C3×D311yescharacteristic
372Q16—68no—
373Q16—68no—
374C2×C8—22no—
375C2×C8—32no—
376C2×C8—62no—
377C2×C8C22×C3×D312yes—
378C4⋊C4—21no—
379C4⋊C4—64no—
380C4⋊C4—64no—
381C4⋊C4—64no—
382C4⋊C4C22×C3×D312yes—
383C42—32no—
384C42—32no—
385C42—64no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—22no—
389C22×C3—21no—
390C22×C3#88412yes—
391C22×C3#91512yes—
392C22×C3D3×Q1612yes—
393C22×C3C3×#12112yes—
394C22×C3C2×C3×Q1612yes—
395C22×C3C3×#13712yes—
396C22×C3C2×D3×D411yescharacteristic
397C22×C3C22×C3×D411yescharacteristic
398C3×C4—22no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—34no—
402C3×C4—44no—
403C3×C4—42no—
404C3×C4—42no—
405C3×C4—42no—
406C3×C4—42no—
407C3×C4—64no—
408C3×C4—62no—
409C3×C4—82no—
410C3×C4—122no—
411C3×C4#88412yes—
412C3×C4C3×#12112yes—
413C3×C4C2×#23511yescharacteristic
414C3×C4C2×D3×D411yescharacteristic
415C3×C4C22×C3×D411yescharacteristic
416C3×C4C2×C3×#4111yescharacteristic
417Dic3—22no—
418Dic3—24no—
419Dic3—42no—
420Dic3C2×C3×Q1614yescomplemented
421C32C2×#46211yescharacteristic, complemented, Sylow
422C23C3×D3×D411yescharacteristic
423Q8—22no—
424Q8—22no—
425Q8—34no—
426Q8—42no—
427Q8—64no—
428Q8—62no—
429Q8—62no—
430Q8—62no—
431Q8—122no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—34no—
435C2×C4—32no—
436C2×C4—32no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—64no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—122no—
444C2×C4C3×#23512yes—
445C2×C4C3×D3×D411yescharacteristic
446C2×C4C3×D3×D412yes—
447C2×C4C23×C3×D311yescharacteristic
448C8—22no—
449C8—62no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—24no—
454C2×C3#479514yesdirect product factor
455C2×C3C3×#46214yescomplemented
456C2×C3C2×#88411yescharacteristic
457C2×C3C2×#91511yescharacteristic
458C2×C3C2×D3×Q1611yescharacteristic
459C2×C3C2×C3×#12111yescharacteristic
460C2×C3C22×C3×Q1611yescharacteristic
461C2×C3C2×C3×#13711yescharacteristic
462C22C3×#88412yes—
463C22C3×#91512yes—
464C22C3×D3×Q1612yes—
465C22C2×C3×D3×D411yescharacteristic
466C4—34no—
467C4—42no—
468C4—42no—
469C4—64no—
470C4—62no—
471C4—122no—
472C4C3×#88412yes—
473C4C2×C3×#23511yescharacteristic
474C4C2×C3×D3×D411yescharacteristic
475C3—21no—
476C3C2×#479511yescharacteristic, direct product factor
477C3C2×C3×#46211yescharacteristic, complemented
478C2C3×#479514yesdirect product factor
479C2C2×C3×#88411yescharacteristic
480C2C2×C3×#91511yescharacteristic
481C2C2×C3×D3×Q1611yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#103C2
socle, prime radicalC23×C32C2×D4
hypercenterC2×C3×#103D3
hypocenterC3C2×C3×#462
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
8. C3×#4795C2direct (N × H)
10. C2×#4795C3direct (N × H)
49. #4795C2×C3direct (N × H)
149. C2×C3×Dic3Q16semidirect
257. C3×Dic3C2×Q16semidirect
335. C2×Dic3C3×Q16semidirect
349. C2×C32#462semidirect
420. Dic3C2×C3×Q16semidirect
421. C32C2×#462semidirect
454. C2×C3#4795direct (N × H)
455. C2×C3C3×#462semidirect
476. C3C2×#4795direct (N × H)
477. C3C2×C3×#462semidirect
478. C2C3×#4795direct (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×#2162
C22×C3×Dic122
C2×C3×#8872
C2×C32×#1032
C2×C3×Dic3⋊C82
C2×C3×#8102
C3×#47952
C2×C3×#4623
C2×#47953