Finite Group Databasebeta

← C3×C4×#833 #11783774

Subgroups — C3×C4×#833 #11783774

Order 1152.

933 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×C32×C4×D4C211yesmaximal, characteristic
2C2×C3×#833C212yesmaximal
3C3×C4×#208C212yesmaximal, complemented
4C3×#4530C212yesmaximal, complemented
5C3×C4×#100—31nomaximal
6C4×#833C311yesmaximal, characteristic, direct product factor
7C22×C32×D4C2211yescharacteristic
8C23×C32×C4C412yes—
9C32×C4×D4—22no—
10C32×C4×D4—22no—
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C22⋊C4C412yes—
13C2×C32×C42C2211yescharacteristic
14C2×C3×#208C2214yes—
15C3×#833C418yesdirect product factor
16C3×#803—22no—
17C3×C4×C3⋊C8—22no—
18C2×C3×C4×D4—21no—
19C2×C3×C4×D4D311yescharacteristic
20C2×C3×C4×D4C2×C311yescharacteristic
21C2×C3×#100—32no—
22C3×C4×M16—32no—
23C2×#833C2×C312yes—
24C4×#208C2×C312yescomplemented
25C3×#343—32no—
26#4530C2×C312yescomplemented
27C24×C32C2×C412yes—
28C2×C32×D4—22no—
29C2×C32×D4—22no—
30C2×C32×D4C2×C414yes—
31C22×C32×C4—22no—
32C22×C32×C4—22no—
33C22×C32×C4—44no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C412yes—
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C32×C4⋊C4—22no—
39C32×C22⋊C4—24no—
40C32×C42D412yes—
41C32×C42D412yes—
42C3×#208—24no—
43C3×#208C2×C418yescomplemented
44C2×C3×C3⋊C8—24no—
45C4×#100—31noSylow
46C22×C3×D4—21no—
47C22×C3×D4C2×D311yescharacteristic
48C22×C3×D4C22×C311yescharacteristic
49C23×C3×C4—22no—
50C23×C3×C4Dic312yes—
51C23×C3×C4C3×C412yes—
52C2×C3×M16—34no—
53C3×C4×D4—24no—
54C3×C4×D4—24no—
55C3×C4×D4—22no—
56C3×C4×D4—22no—
57C3×C4×D4—22no—
58C3×C4×D4—22no—
59C2×C3×C4⋊C4—21no—
60C2×C3×C4⋊C4C2×D311yescharacteristic
61C2×C3×C4⋊C4C22×C311yescharacteristic
62C2×C3×C22⋊C4—22no—
63C2×C3×C22⋊C4Dic312yes—
64C2×C3×C22⋊C4C3×C412yes—
65C2×C3×C42—21no—
66C2×C3×C42C2×D311yescharacteristic
67C2×C3×C42C22×C311yescharacteristic
68C2×#208C22×C314yes—
69C3×#100—38no—
70C3×#97—62no—
71C3×C4×C8—62no—
72#833C3×C418yesdirect product factor
73#803—22no—
74C4×C3⋊C8—22no—
75C23×C32—22no—
76C23×C32—22no—
77C23×C32—42no—
78C23×C32—42no—
79C23×C32C4214yes—
80C23×C32C22×C411yescharacteristic
81C32×D4—28no—
82C2×C32×C4—22no—
83C2×C32×C4—22no—
84C2×C32×C4—41no—
85C2×C32×C4—44no—
86C2×C32×C4—44no—
87C2×C32×C4—42no—
88C2×C32×C4C22⋊C412yes—
89C2×C32×C4C22⋊C411yescharacteristic
90C2×C32×C4C22⋊C411yescharacteristic
91C2×C32×C4C22×C412yes—
92C2×C32×C4C2×D412yes—
93C2×C32×C4#4112yes—
94C3×C3⋊C8—28no—
95C2×C4×D4C3×D311yescharacteristic
96C2×#100—32no—
97C4×M16—32no—
98#343—32no—
99C24×C3—22no—
100C24×C3C2×Dic312yes—
101C24×C3C2×C3×C412yes—
102C2×C3×D4—24no—
103C2×C3×D4—24no—
104C2×C3×D4—22no—
105C2×C3×D4—22no—
106C2×C3×D4—22no—
107C2×C3×D4—22no—
108C2×C3×D4—24no—
109C2×C3×D4C4×D314yes—
110C2×C3×D4C2×C3×C414yes—
111C22×C3×C4—24no—
112C22×C3×C4—24no—
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×C3×C4—22no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4—22no—
120C22×C3×C4—21no—
121C22×C3×C4—48no—
122C22×C3×C4—44no—
123C22×C3×C4—44no—
124C22×C3×C4C2×Dic311yescharacteristic
125C22×C3×C4C2×Dic312yes—
126C22×C3×C4C2×Dic311yescharacteristic
127C22×C3×C4C2×C3×C411yescharacteristic
128C22×C3×C4C2×C3×C412yes—
129C22×C3×C4C2×C3×C411yescharacteristic
130C22×C3×C4C22×D311yescharacteristic
131C22×C3×C4C23×C311yescharacteristic
132C3×M16—38no—
133C3×M16—64no—
134C2×C3×C8—64no—
135C3×C4⋊C4—24no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—22no—
138C3×C22⋊C4—28no—
139C3×C22⋊C4—24no—
140C3×C22⋊C4—24no—
141C3×C42—22no—
142C3×C42—22no—
143C3×C42#6712yes—
144C3×C42#6712yes—
145C3×C42C3×D412yes—
146C3×C42C3×D412yes—
147#208—24no—
148#208C2×C3×C418yescomplemented
149C2×C3⋊C8—24no—
150C22×C32—21no—
151C22×C32—21no—
152C22×C32—24no—
153C22×C32—44no—
154C22×C32—44no—
155C22×C32—42no—
156C22×C32—42no—
157C22×C32C2×C4211yescharacteristic
158C22×C32C2×C22⋊C411yescharacteristic
159C22×C32#11711yescharacteristic
160C32×C4—21no—
161C32×C4—22no—
162C32×C4—42no—
163C32×C4#10012yescomplemented
164C32×C4C4×D414yes—
165C22×D4C2×C3×D311yescharacteristic
166C23×C4C3×Dic312yes—
167C2×M16—34no—
168C4×D4—22no—
169C4×D4—22no—
170C2×C4⋊C4C2×C3×D311yescharacteristic
171C2×C22⋊C4C3×Dic312yes—
172C2×C42C2×C3×D311yescharacteristic
173#100—38no—
174#97—62no—
175C4×C8—62no—
176C23×C3—24no—
177C23×C3—24no—
178C23×C3—22no—
179C23×C3—22no—
180C23×C3—22no—
181C23×C3—22no—
182C23×C3—24no—
183C23×C3—21no—
184C23×C3—42no—
185C23×C3—42no—
186C23×C3—42no—
187C23×C3—42no—
188C23×C3—44no—
189C23×C3—44no—
190C23×C3C4×Dic314yes—
191C23×C3C3×C4214yes—
192C23×C3C22×Dic311yescharacteristic
193C23×C3C22×C3×C411yescharacteristic
194C3×D4—216no—
195C3×D4—28no—
196C3×D4—28no—
197C2×C3×C4—24no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—24no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—48no—
212C2×C3×C4—44no—
213C2×C3×C4—44no—
214C2×C3×C4—48no—
215C2×C3×C4—42no—
216C2×C3×C4—44no—
217C2×C3×C4—44no—
218C2×C3×C4—44no—
219C2×C3×C4—42no—
220C2×C3×C4—42no—
221C2×C3×C4#21712yes—
222C2×C3×C4#21711yescharacteristic
223C2×C3×C4#21711yescharacteristic
224C2×C3×C4C3×C22⋊C412yes—
225C2×C3×C4C3×C22⋊C411yescharacteristic
226C2×C3×C4C3×C22⋊C411yescharacteristic
227C2×C3×C4C2×C4×D312yes—
228C2×C3×C4#23512yes—
229C2×C3×C4C2×#6712yes—
230C2×C3×C4C22×C3×C412yes—
231C2×C3×C4C2×C3×D412yes—
232C2×C3×C4C3×#4112yes—
233C3×C8—68no—
234C3⋊C8—28no—
235C2×C32—21no—
236C2×C32—21no—
237C2×C32—44no—
238C2×C32C4×C22⋊C411yescharacteristic
239C2×C32C2×#10011yescharacteristic
240C2×C32#41311yescharacteristic
241C24C2×C3×Dic312yes—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4C3×C4×D314yes—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—44no—
248C22×C4C2×C3×Dic311yescharacteristic
249C22×C4C2×C3×Dic312yes—
250C22×C4C2×C3×Dic311yescharacteristic
251C22×C4C22×C3×D311yescharacteristic
252M16—38no—
253M16—64no—
254C2×C8—64no—
255C4⋊C4—22no—
256C22⋊C4—24no—
257C42C3×#6712yes—
258C42C3×#6712yes—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—28no—
266C22×C3—24no—
267C22×C3—24no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—44no—
272C22×C3—44no—
273C22×C3—44no—
274C22×C3—48no—
275C22×C3—48no—
276C22×C3—44no—
277C22×C3—44no—
278C22×C3—44no—
279C22×C3—42no—
280C22×C3—42no—
281C22×C3—42no—
282C22×C3—42no—
283C22×C3C2×C4×Dic311yescharacteristic
284C22×C3#92611yescharacteristic
285C22×C3C2×#21711yescharacteristic
286C22×C3C2×C3×C4211yescharacteristic
287C22×C3C2×C3×C22⋊C411yescharacteristic
288C22×C3C3×#11711yescharacteristic
289C3×C4—22no—
290C3×C4—21no—
291C3×C4—22no—
292C3×C4—21no—
293C3×C4—22no—
294C3×C4—24no—
295C3×C4—22no—
296C3×C4—42no—
297C3×C4—44no—
298C3×C4—42no—
299C3×C4—42no—
300C3×C4#83312yesdirect product factor
301C3×C4C3×#10012yescomplemented
302C3×C4C4×#6714yes—
303C3×C4C3×C4×D414yes—
304C32C4×#10011yescharacteristic, complemented, Sylow
305C23—22no—
306C23—22no—
307C23—42no—
308C23—42no—
309C23C3×C4×Dic314yes—
310C23C22×C3×Dic311yescharacteristic
311D4—28no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—42no—
318C2×C4C3×#21712yes—
319C2×C4C3×#21711yescharacteristic
320C2×C4C3×#21711yescharacteristic
321C2×C4C2×C3×C4×D312yes—
322C2×C4C3×#23512yes—
323C2×C4C2×C3×#6712yes—
324C8—68no—
325C2×C3—22no—
326C2×C3—22no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—48no—
335C2×C3—44no—
336C2×C3—44no—
337C2×C3C4×#21711yescharacteristic
338C2×C3C2×#83311yescharacteristic
339C2×C3#523711yescharacteristic
340C2×C3C3×C4×C22⋊C411yescharacteristic
341C2×C3C2×C3×#10011yescharacteristic
342C2×C3C3×#41311yescharacteristic
343C22—21no—
344C22—21no—
345C22—24no—
346C22—44no—
347C22—44no—
348C22—42no—
349C22—42no—
350C22C2×C3×C4×Dic311yescharacteristic
351C22C3×#92611yescharacteristic
352C22C2×C3×#21711yescharacteristic
353C4—21no—
354C4—22no—
355C4—42no—
356C4C3×#83312yesdirect product factor
357C4C3×C4×#6714yes—
358C3—21no—
359C3C4×#83311yescharacteristic, direct product factor
360C3C3×C4×#10011yescharacteristic, complemented
361C2—21no—
362C2—21no—
363C2—44no—
364C2C3×C4×#21711yescharacteristic
365C2C2×C3×#83311yescharacteristic
366C2C3×#523711yescharacteristic
subgroupG/H
centerC2×C3×C4#217
commutatorC22×C3C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4×D4C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C32×D4C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×C4×#100
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
3. C3×C4×#208C2semidirect
4. C3×#4530C2semidirect
6. C4×#833C3direct (N × H)
15. C3×#833C4direct (N × H)
24. C4×#208C2×C3semidirect
26. #4530C2×C3semidirect
43. C3×#208C2×C4semidirect
72. #833C3×C4direct (N × H)
148. #208C2×C3×C4semidirect
163. C32×C4#100semidirect
300. C3×C4#833direct (N × H)
301. C3×C4C3×#100semidirect
304. C32C4×#100semidirect
356. C4C3×#833direct (N × H)
359. C3C4×#833direct (N × H)
360. C3C3×C4×#100semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#8332
C3×C4×#2082
C3×#45302
C3×C4×#1003
C4×#8333