Finite Group Databasebeta

← C3×C4×#807 #11784462

Subgroups — C3×C4×#807 #11784462

Order 1152.

657 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×C4⋊C4C211yesmaximal, characteristic
2C2×C3×#807C212yesmaximal
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic
4C2×C3×C4×C3⋊C8C211yesmaximal, characteristic
5C3×#4529C212yesmaximal
6C3×C4×#107—31nomaximal
7C4×#807C311yesmaximal, characteristic, direct product factor
8C2×C32×C4⋊C4C2212yes—
9C2×C32×C42—21no—
10C2×C32×C42C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×C4×Dic3—21no—
13C22×C3×C3⋊C8C2211yescharacteristic
14C22×C3×C3⋊C8C2211yescharacteristic
15C32×#95—21no—
16C3×C3⋊#95—21no—
17C3×#807C418yesdirect product factor
18C3×C4×C3⋊C8C414yescomplemented
19C2×C3×#107—32no—
20C2×C3×C4×C8—31no—
21C3×C4×C4⋊C4—21no—
22C3×C4×C4⋊C4—31no—
23C3×C4×C4⋊C4D311yescharacteristic
24C3×C4×C4⋊C4C2×C311yescharacteristic
25C2×#807C2×C312yes—
26C4×C4⋊Dic3C2×C311yescharacteristic
27C2×C4×C3⋊C8C2×C311yescharacteristic
28C3×#340—32no—
29#4529C2×C312yes—
30C22×C32×C4—22no—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3×Dic3—22no—
35C32×C4⋊C4—22no—
36C32×C4⋊C4C2×C414yes—
37C32×C42—42no—
38C32×C42C2×C412yes—
39C32×C42Q812yes—
40C3×C4⋊Dic3—22no—
41C3×C4⋊Dic3C2×C414yes—
42C3×C4×Dic3—42no—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8C2×C412yes—
45C2×C3×C3⋊C8C2×C412yes—
46C2×C3×C3⋊C8C2×C414yes—
47C4×#107—31noSylow
48C22×C3×C8—31no—
49C22×C3×C8—31no—
50C2×C3×C4⋊C4—22no—
51C2×C3×C4⋊C4—32no—
52C2×C3×C4⋊C4C2×D312yes—
53C2×C3×C4⋊C4C22×C312yes—
54C2×C3×C42—22no—
55C2×C3×C42—21no—
56C2×C3×C42—21no—
57C2×C3×C42—21no—
58C2×C3×C42—61no—
59C2×C3×C42C2×D311yescharacteristic
60C2×C3×C42C22×C311yescharacteristic
61C2×C4⋊Dic3C22×C312yes—
62C2×C4×Dic3—21no—
63C22×C3⋊C8C22×C311yescharacteristic
64C22×C3⋊C8C22×C311yescharacteristic
65C3×#107—38no—
66C3×C4×C8—34no—
67C3×#95—22no—
68C3×#95—21no—
69C3×#95—21no—
70C3×#95—61no—
71C3⋊#95—21no—
72#807C3×C418yesdirect product factor
73C4×C3⋊C8C3×C414yescomplemented
74C23×C32C2×D411yescharacteristic
75C2×C32×C4—24no—
76C2×C32×C4—22no—
77C2×C32×C4—42no—
78C2×C32×C4—42no—
79C2×C32×C4C4⋊C412yes—
80C2×C32×C4C4⋊C412yes—
81C2×C32×C4D812yes—
82C2×C32×C4Q1612yes—
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4C22×C412yes—
85C2×C32×C4C2×Q811yescharacteristic
86C2×C32×C4#4112yes—
87C2×C3×Dic3—24no—
88C2×C3×Dic3—42no—
89C2×C3×Dic3—42no—
90C3×C3⋊C8—22no—
91C3×C3⋊C8C4214yescomplemented
92C2×#107—32no—
93C2×C4×C8—31no—
94C4×C4⋊C4—31no—
95C4×C4⋊C4C3×D311yescharacteristic
96#340—32no—
97C22×C3×C4—24no—
98C22×C3×C4—22no—
99C22×C3×C4—22no—
100C22×C3×C4—21no—
101C22×C3×C4—21no—
102C22×C3×C4—21no—
103C22×C3×C4—62no—
104C22×C3×C4#6711yescharacteristic
105C22×C3×C4#6711yescharacteristic
106C22×C3×C4C3×D411yescharacteristic
107C22×C3×C4C3×D411yescharacteristic
108C22×C3×C4C22×D311yescharacteristic
109C22×C3×C4C23×C311yescharacteristic
110C22×Dic3—22no—
111C2×C3×C8—32no—
112C2×C3×C8—34no—
113C2×C3×C8—32no—
114C2×C3×C8—62no—
115C3×C4⋊C4—24no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4—24no—
119C3×C4⋊C4—34no—
120C3×C4⋊C4—62no—
121C3×C4⋊C4C4×D314yes—
122C3×C4⋊C4C2×C3×C414yes—
123C3×C42—22no—
124C3×C42—22no—
125C3×C42—44no—
126C3×C42—42no—
127C3×C42—42no—
128C3×C42—122no—
129C3×C42Dic612yes—
130C3×C42C4×D312yes—
131C3×C42C2×C3×C412yes—
132C3×C42C3×Q812yes—
133C4⋊Dic3—22no—
134C4⋊Dic3C2×C3×C414yes—
135C4×Dic3—42no—
136C2×C3⋊C8—22no—
137C2×C3⋊C8C2×C3×C412yes—
138C2×C3⋊C8C2×C3×C412yes—
139C2×C3⋊C8C2×C3×C414yes—
140C22×C32C2×C4⋊C411yescharacteristic
141C22×C32C4×D412yes—
142C22×C32C2×D811yescharacteristic
143C22×C32C2×Q1611yescharacteristic
144C22×C32#13512yes—
145C32×C4—22no—
146C32×C4—44no—
147C32×C4#10714yescomplemented
148C32×C4C2×C4211yescharacteristic
149C32×C4#11711yescharacteristic
150C32×C4C4×Q812yes—
151C3×Dic3—44no—
152C22×C8—31no—
153C22×C8—31no—
154C2×C4⋊C4—32no—
155C2×C4⋊C4C2×C3×D312yes—
156C2×C42—21no—
157C2×C42—61no—
158C2×C42C2×C3×D311yescharacteristic
159#107—38no—
160C4×C8—34no—
161#95—21no—
162#95—61no—
163C23×C3—21no—
164C23×C3C2×#6711yescharacteristic
165C23×C3C2×C3×D411yescharacteristic
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168C2×C3×C4—28no—
169C2×C3×C4—24no—
170C2×C3×C4—24no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—22no—
178C2×C3×C4—22no—
179C2×C3×C4—42no—
180C2×C3×C4—44no—
181C2×C3×C4—44no—
182C2×C3×C4—42no—
183C2×C3×C4—42no—
184C2×C3×C4—42no—
185C2×C3×C4—42no—
186C2×C3×C4—64no—
187C2×C3×C4—122no—
188C2×C3×C4—122no—
189C2×C3×C4Dic3⋊C412yes—
190C2×C3×C4Dic3⋊C412yes—
191C2×C3×C4#21312yes—
192C2×C3×C4#21612yes—
193C2×C3×C4C3×C4⋊C412yes—
194C2×C3×C4C3×C4⋊C412yes—
195C2×C3×C4C3×D812yes—
196C2×C3×C4C3×Q1612yes—
197C2×C3×C4C2×Dic611yescharacteristic
198C2×C3×C4C2×C4×D312yes—
199C2×C3×C4C2×C4×D311yescharacteristic
200C2×C3×C4#23512yes—
201C2×C3×C4C22×C3×C411yescharacteristic
202C2×C3×C4C22×C3×C412yes—
203C2×C3×C4C2×C3×Q811yescharacteristic
204C2×C3×C4C3×#4112yes—
205C2×Dic3—24no—
206C2×Dic3—42no—
207C2×Dic3—42no—
208C3×C8—34no—
209C3×C8—62no—
210C3⋊C8—22no—
211C3⋊C8C3×C4214yescomplemented
212C2×C32C4×C4⋊C411yescharacteristic
213C2×C32C2×#10711yescharacteristic
214C2×C32#42711yescharacteristic
215C2×C32C4×D812yes—
216C2×C32C4×Q1612yes—
217C22×C4—22no—
218C22×C4—62no—
219C22×C4C3×#6711yescharacteristic
220C22×C4C3×#6711yescharacteristic
221C22×C4C22×C3×D311yescharacteristic
222C2×C8—32no—
223C2×C8—34no—
224C2×C8—32no—
225C2×C8—62no—
226C4⋊C4—22no—
227C4⋊C4—34no—
228C4⋊C4—62no—
229C4⋊C4C3×C4×D314yes—
230C42—42no—
231C42—122no—
232C42C3×Dic612yes—
233C42C3×C4×D312yes—
234C22×C3—21no—
235C22×C3—22no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—22no—
239C22×C3C2×Dic3⋊C411yescharacteristic
240C22×C3C4×#6712yes—
241C22×C3C2×#21311yescharacteristic
242C22×C3C2×#21611yescharacteristic
243C22×C3#95012yes—
244C22×C3C2×C3×C4⋊C411yescharacteristic
245C22×C3C3×C4×D412yes—
246C22×C3C2×C3×D811yescharacteristic
247C22×C3C2×C3×Q1611yescharacteristic
248C22×C3C3×#13512yes—
249C3×C4—22no—
250C3×C4—22no—
251C3×C4—24no—
252C3×C4—22no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—42no—
256C3×C4—48no—
257C3×C4—44no—
258C3×C4—44no—
259C3×C4—124no—
260C3×C4#80714yesdirect product factor
261C3×C4C3×#10714yescomplemented
262C3×C4C4×Dic612yes—
263C3×C4C42×D311yescharacteristic
264C3×C4#87211yescharacteristic
265C3×C4C2×C3×C4211yescharacteristic
266C3×C4C3×#11711yescharacteristic
267C3×C4C3×C4×Q812yes—
268Dic3—44no—
269C32C4×#10711yescharacteristic, complemented, Sylow
270C23C2×C3×#6711yescharacteristic
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—64no—
276C2×C4—122no—
277C2×C4—122no—
278C2×C4C3×Dic3⋊C412yes—
279C2×C4C3×Dic3⋊C412yes—
280C2×C4C3×#21312yes—
281C2×C4C3×#21612yes—
282C2×C4C2×C3×Dic611yescharacteristic
283C2×C4C2×C3×C4×D312yes—
284C2×C4C2×C3×C4×D311yescharacteristic
285C2×C4C3×#23512yes—
286C8—34no—
287C8—62no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—22no—
292C2×C3—22no—
293C2×C3C4×Dic3⋊C411yescharacteristic
294C2×C3C2×#80711yescharacteristic
295C2×C3#499811yescharacteristic
296C2×C3C4×#21312yes—
297C2×C3C4×#21612yes—
298C2×C3C3×C4×C4⋊C411yescharacteristic
299C2×C3C2×C3×#10711yescharacteristic
300C2×C3C3×#42711yescharacteristic
301C2×C3C3×C4×D812yes—
302C2×C3C3×C4×Q1612yes—
303C22C2×C3×Dic3⋊C411yescharacteristic
304C22C3×C4×#6712yes—
305C22C2×C3×#21311yescharacteristic
306C22C2×C3×#21611yescharacteristic
307C22C3×#95012yes—
308C4—22no—
309C4—44no—
310C4—124no—
311C4C3×#80714yesdirect product factor
312C4C3×C4×Dic612yes—
313C4C3×C42×D311yescharacteristic
314C4C3×#87211yescharacteristic
315C3—21no—
316C3C4×#80711yescharacteristic, direct product factor
317C3C3×C4×#10711yescharacteristic, complemented
318C2C3×C4×Dic3⋊C411yescharacteristic
319C2C2×C3×#80711yescharacteristic
320C2C3×#499811yescharacteristic
321C2C3×C4×#21312yes—
322C2C3×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×#107
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×#807C3direct (N × H)
17. C3×#807C4direct (N × H)
18. C3×C4×C3⋊C8C4semidirect
72. #807C3×C4direct (N × H)
73. C4×C3⋊C8C3×C4semidirect
91. C3×C3⋊C8C42semidirect
147. C32×C4#107semidirect
211. C3⋊C8C3×C42semidirect
260. C3×C4#807direct (N × H)
261. C3×C4C3×#107semidirect
269. C32C4×#107semidirect
311. C4C3×#807direct (N × H)
316. C3C4×#807direct (N × H)
317. C3C3×C4×#107semidirect

Maximal subgroups

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

subgroupindex
C32×C4×C4⋊C42
C2×C3×#8072
C3×C4×C4⋊Dic32
C2×C3×C4×C3⋊C82
C3×#45292
C3×C4×#1073
C4×#8073