Finite Group Databasebeta

← C3×C4×#810 #11783972

Subgroups — C3×C4×#810 #11783972

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C32×C4×C4⋊C4C211yesmaximal, characteristic
3C2×C3×#810C212yesmaximal
4C2×C3×C4×C3⋊C8C211yesmaximal, characteristic
5C3×#4529C212yesmaximal
6C3×C4×#103—31nomaximal
7C4×#810C311yesmaximal, characteristic, direct product factor
8C22×C3×Dic6C2211yescharacteristic
9C2×C32×C4⋊C4C2212yes—
10C2×C32×C42—21no—
11C2×C32×C42C2211yescharacteristic
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C2×C3×Dic3⋊C4—21no—
14C2×C3×C4×Dic3—21no—
15C22×C3×C3⋊C8C2212yes—
16C3×C4×Dic6—22no—
17C3×C4×Dic6C414yescomplemented
18C32×#95—21no—
19C3×#810C418yesdirect product factor
20C3×C4×C3⋊C8—22no—
21C2×C3×C4×Q8—31no—
22C2×C4×Dic6C2×C311yescharacteristic
23C2×C3×#103—32no—
24C2×C3×C4×C8—31no—
25C3×C4×C4⋊C4—21no—
26C3×C4×C4⋊C4D311yescharacteristic
27C3×C4×C4⋊C4C2×C311yescharacteristic
28C2×#810C2×C312yes—
29C2×C4×C3⋊C8C2×C311yescharacteristic
30C3×#340—32no—
31#4529C2×C312yes—
32C22×C32×C4—22no—
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C2×C3×Dic6—21no—
39C2×C3×Dic6—22no—
40C2×C3×Dic6C2×C414yes—
41C2×C3×Dic6C2×C412yes—
42C32×C4⋊C4—22no—
43C32×C4⋊C4C2×C414yes—
44C32×C42—42no—
45C32×C42C2×C412yes—
46C32×C42D412yes—
47C3×C4⋊Dic3—21no—
48C3×C4⋊Dic3C2×C412yes—
49C3×Dic3⋊C4—24no—
50C3×C4×Dic3—24no—
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8—22no—
53C2×C3×C3⋊C8C2×C414yes—
54C4×#103—31noSylow
55C22×C3×Q8—31no—
56C22×Dic6C22×C311yescharacteristic
57C22×C3×C8—32no—
58C3×C4×Q8—34no—
59C3×C4×Q8—62no—
60C2×C3×C4⋊C4—22no—
61C2×C3×C4⋊C4—31no—
62C2×C3×C4⋊C4—61no—
63C2×C3×C4⋊C4C2×D312yes—
64C2×C3×C4⋊C4C22×C312yes—
65C2×C3×C42—22no—
66C2×C3×C42—21no—
67C2×C3×C42—21no—
68C2×C3×C42—21no—
69C2×C3×C42—61no—
70C2×C3×C42C2×D311yescharacteristic
71C2×C3×C42C22×C311yescharacteristic
72C2×C4⋊Dic3C22×C311yescharacteristic
73C2×Dic3⋊C4—21no—
74C2×C4×Dic3—21no—
75C22×C3⋊C8C22×C312yes—
76C4×Dic6—22no—
77C4×Dic6C3×C414yescomplemented
78C3×#103—38no—
79C3×C4×C8—62no—
80C3×#95—22no—
81C3×#95—21no—
82C3×#95—21no—
83#810C3×C418yesdirect product factor
84C4×C3⋊C8—22no—
85C23×C32C2×D411yescharacteristic
86C2×C32×C4—24no—
87C2×C32×C4—22no—
88C2×C32×C4—42no—
89C2×C32×C4—42no—
90C2×C32×C4C22⋊C412yes—
91C2×C32×C4C22⋊C412yes—
92C2×C32×C4SD1612yes—
93C2×C32×C4Q1612yes—
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C22×C412yes—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4112yes—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—42no—
102C3×Dic6—22no—
103C3×Dic6—24no—
104C3×Dic6C4214yescomplemented
105C3×C3⋊C8—24no—
106C2×C4×Q8—31no—
107C2×#103—32no—
108C2×C4×C8—31no—
109C4×C4⋊C4C3×D311yescharacteristic
110#340—32no—
111C2×C3×Q8—34no—
112C2×C3×Q8—32no—
113C2×C3×Q8—61no—
114C2×C3×Q8—62no—
115C22×C3×C4—24no—
116C22×C3×C4—22no—
117C22×C3×C4—22no—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—61no—
122C22×C3×C4—61no—
123C22×C3×C4#6711yescharacteristic
124C22×C3×C4#6711yescharacteristic
125C22×C3×C4C3×D411yescharacteristic
126C22×C3×C4C3×D411yescharacteristic
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C23×C311yescharacteristic
129C22×Dic3—21no—
130C22×Dic3—21no—
131C2×Dic6—21no—
132C2×Dic6—22no—
133C2×Dic6C2×C3×C414yes—
134C2×Dic6C2×C3×C412yes—
135C2×C3×C8—34no—
136C2×C3×C8—62no—
137C2×C3×C8—62no—
138C3×C4⋊C4—24no—
139C3×C4⋊C4—22no—
140C3×C4⋊C4—22no—
141C3×C4⋊C4—24no—
142C3×C4⋊C4—32no—
143C3×C4⋊C4—64no—
144C3×C4⋊C4—61no—
145C3×C4⋊C4C4×D314yes—
146C3×C4⋊C4C2×C3×C414yes—
147C3×C42—22no—
148C3×C42—22no—
149C3×C42—44no—
150C3×C42—42no—
151C3×C42—42no—
152C3×C42—64no—
153C3×C42C4×D312yes—
154C3×C42D1212yes—
155C3×C42C2×C3×C412yes—
156C3×C42C3×D412yes—
157C4⋊Dic3—21no—
158C4⋊Dic3C2×C3×C412yes—
159Dic3⋊C4—24no—
160C4×Dic3—24no—
161C2×C3⋊C8—22no—
162C2×C3⋊C8—22no—
163C2×C3⋊C8C2×C3×C414yes—
164C22×C32C2×C22⋊C411yescharacteristic
165C22×C32C4×D412yes—
166C22×C32C2×SD1611yescharacteristic
167C22×C32C2×Q1611yescharacteristic
168C22×C32#13512yes—
169C32×C4—22no—
170C32×C4—44no—
171C32×C4#10314yescomplemented
172C32×C4C2×C4211yescharacteristic
173C32×C4#11711yescharacteristic
174C32×C4C4×D412yes—
175C3×Dic3—24no—
176C3×Dic3—42no—
177C22×Q8—31no—
178C22×C8—32no—
179C4×Q8—34no—
180C4×Q8—62no—
181C2×C4⋊C4—31no—
182C2×C4⋊C4—61no—
183C2×C4⋊C4C2×C3×D312yes—
184C2×C42—21no—
185C2×C42—61no—
186C2×C42C2×C3×D311yescharacteristic
187#103—38no—
188C4×C8—62no—
189#95—21no—
190C23×C3—21no—
191C23×C3C2×#6711yescharacteristic
192C23×C3C2×C3×D411yescharacteristic
193C3×Q8—34no—
194C3×Q8—62no—
195C3×Q8—64no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—28no—
199C2×C3×C4—24no—
200C2×C3×C4—24no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—21no—
206C2×C3×C4—22no—
207C2×C3×C4—21no—
208C2×C3×C4—22no—
209C2×C3×C4—42no—
210C2×C3×C4—44no—
211C2×C3×C4—44no—
212C2×C3×C4—42no—
213C2×C3×C4—42no—
214C2×C3×C4—42no—
215C2×C3×C4—42no—
216C2×C3×C4—62no—
217C2×C3×C4—64no—
218C2×C3×C4—62no—
219C2×C3×C4—122no—
220C2×C3×C4(C2×D3)⋊C412yes—
221C2×C3×C4(C2×D3)⋊C412yes—
222C2×C3×C4#21412yes—
223C2×C3×C4#21612yes—
224C2×C3×C4C3×C22⋊C412yes—
225C2×C3×C4C3×C22⋊C412yes—
226C2×C3×C4C3×SD1612yes—
227C2×C3×C4C3×Q1612yes—
228C2×C3×C4C2×C4×D311yescharacteristic
229C2×C3×C4C2×C4×D312yes—
230C2×C3×C4C2×D1211yescharacteristic
231C2×C3×C4#23512yes—
232C2×C3×C4C22×C3×C411yescharacteristic
233C2×C3×C4C22×C3×C412yes—
234C2×C3×C4C2×C3×D411yescharacteristic
235C2×C3×C4C3×#4112yes—
236C2×Dic3—22no—
237C2×Dic3—24no—
238C2×Dic3—22no—
239C2×Dic3—42no—
240Dic6—22no—
241Dic6—24no—
242Dic6C3×C4214yescomplemented
243C3×C8—64no—
244C3⋊C8—24no—
245C2×C32C4×C22⋊C411yescharacteristic
246C2×C32C2×#10311yescharacteristic
247C2×C32#41611yescharacteristic
248C2×C32C4×SD1612yes—
249C2×C32C4×Q1612yes—
250C2×Q8—34no—
251C2×Q8—32no—
252C2×Q8—61no—
253C2×Q8—62no—
254C22×C4—22no—
255C22×C4—61no—
256C22×C4—61no—
257C22×C4C3×#6711yescharacteristic
258C22×C4C3×#6711yescharacteristic
259C22×C4C22×C3×D311yescharacteristic
260C2×C8—34no—
261C2×C8—62no—
262C2×C8—62no—
263C4⋊C4—22no—
264C4⋊C4—32no—
265C4⋊C4—64no—
266C4⋊C4—61no—
267C4⋊C4C3×C4×D314yes—
268C42—42no—
269C42—64no—
270C42C3×C4×D312yes—
271C42C3×D1212yes—
272C22×C3—21no—
273C22×C3—22no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—22no—
277C22×C3C2×(C2×D3)⋊C411yescharacteristic
278C22×C3C4×#6712yes—
279C22×C3C2×#21411yescharacteristic
280C22×C3C2×#21611yescharacteristic
281C22×C3#95012yes—
282C22×C3C2×C3×C22⋊C411yescharacteristic
283C22×C3C3×C4×D412yes—
284C22×C3C2×C3×SD1611yescharacteristic
285C22×C3C2×C3×Q1611yescharacteristic
286C22×C3C3×#13512yes—
287C3×C4—22no—
288C3×C4—22no—
289C3×C4—24no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—22no—
293C3×C4—42no—
294C3×C4—48no—
295C3×C4—44no—
296C3×C4—44no—
297C3×C4—64no—
298C3×C4—122no—
299C3×C4#81014yesdirect product factor
300C3×C4C3×#10314yescomplemented
301C3×C4C42×D311yescharacteristic
302C3×C4#87211yescharacteristic
303C3×C4C4×D1212yes—
304C3×C4C2×C3×C4211yescharacteristic
305C3×C4C3×#11711yescharacteristic
306C3×C4C3×C4×D412yes—
307Dic3—24no—
308Dic3—42no—
309C32C4×#10311yescharacteristic, complemented, Sylow
310C23C2×C3×#6711yescharacteristic
311Q8—34no—
312Q8—62no—
313Q8—64no—
314C2×C4—22no—
315C2×C4—24no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—62no—
319C2×C4—64no—
320C2×C4—62no—
321C2×C4—122no—
322C2×C4C3×(C2×D3)⋊C412yes—
323C2×C4C3×(C2×D3)⋊C412yes—
324C2×C4C3×#21412yes—
325C2×C4C3×#21612yes—
326C2×C4C2×C3×C4×D311yescharacteristic
327C2×C4C2×C3×C4×D312yes—
328C2×C4C2×C3×D1211yescharacteristic
329C2×C4C3×#23512yes—
330C8—64no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—22no—
335C2×C3—22no—
336C2×C3C4×(C2×D3)⋊C411yescharacteristic
337C2×C3C2×#81011yescharacteristic
338C2×C3#500211yescharacteristic
339C2×C3C4×#21412yes—
340C2×C3C4×#21612yes—
341C2×C3C3×C4×C22⋊C411yescharacteristic
342C2×C3C2×C3×#10311yescharacteristic
343C2×C3C3×#41611yescharacteristic
344C2×C3C3×C4×SD1612yes—
345C2×C3C3×C4×Q1612yes—
346C22C2×C3×(C2×D3)⋊C411yescharacteristic
347C22C3×C4×#6712yes—
348C22C2×C3×#21411yescharacteristic
349C22C2×C3×#21611yescharacteristic
350C22C3×#95012yes—
351C4—22no—
352C4—44no—
353C4—64no—
354C4—122no—
355C4C3×#81014yesdirect product factor
356C4C3×C42×D311yescharacteristic
357C4C3×#87211yescharacteristic
358C4C3×C4×D1212yes—
359C3—21no—
360C3C4×#81011yescharacteristic, direct product factor
361C3C3×C4×#10311yescharacteristic, complemented
362C2C3×C4×(C2×D3)⋊C411yescharacteristic
363C2C2×C3×#81011yescharacteristic
364C2C3×#500211yescharacteristic
365C2C3×C4×#21412yes—
366C2C3×C4×#21612yes—
subgroupG/H
centerC22×C3×C4#67
commutatorC3×C4C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC32×C4×C4⋊C4C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C3×C4C23×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×C4×#103
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
7. C4×#810C3direct (N × H)
17. C3×C4×Dic6C4semidirect
19. C3×#810C4direct (N × H)
77. C4×Dic6C3×C4semidirect
83. #810C3×C4direct (N × H)
104. C3×Dic6C42semidirect
171. C32×C4#103semidirect
242. Dic6C3×C42semidirect
299. C3×C4#810direct (N × H)
300. C3×C4C3×#103semidirect
309. C32C4×#103semidirect
355. C4C3×#810direct (N × H)
360. C3C4×#810direct (N × H)
361. C3C3×C4×#103semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
C32×C4×C4⋊C42
C2×C3×#8102
C2×C3×C4×C3⋊C82
C3×#45292
C3×C4×#1033
C4×#8103