Finite Group Databasebeta

← C3×C4×Dic3⋊C8 #11784164

Subgroups — C3×C4×Dic3⋊C8 #11784164

Order 1152.

713 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×C8C211yesmaximal, characteristic
2C2×C3×Dic3⋊C8C212yesmaximal
3C3×C42×Dic3C211yesmaximal, characteristic
4C2×C3×C4×C3⋊C8C211yesmaximal, characteristic
5C3×#4550C212yesmaximal
6C3×C4×C4⋊C8—31nomaximal
7C4×Dic3⋊C8C311yesmaximal, characteristic, direct product factor
8C22×C32×C8C2212yes—
9C2×C32×C42C2211yescharacteristic
10C2×C3×C4×Dic3C412yes—
11C2×C3×C4×Dic3C412yes—
12C2×C3×C4×Dic3C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14C22×C3×C3⋊C8C2212yes—
15C32×C4×C8—22no—
16C3×Dic3⋊C8C418yesdirect product factor
17C3×C4×C3⋊C8—22no—
18C2×C3×C4⋊C8—32no—
19C2×C3×C4×C8—21no—
20C2×C3×C4×C8—31no—
21C2×C3×C4×C8D311yescharacteristic
22C2×C3×C4×C8C2×C311yescharacteristic
23C3×C43—31no—
24C2×Dic3⋊C8C2×C312yes—
25C42×Dic3C2×C311yescharacteristic
26C2×C4×C3⋊C8C2×C311yescharacteristic
27C3×#336—32no—
28#4550C2×C312yes—
29C22×C32×C4C2×C412yes—
30C22×C32×C4C2311yescharacteristic
31C22×C3×Dic3C2×C411yescharacteristic
32C22×C3×Dic3C2×C412yes—
33C22×C3×Dic3C2×C411yescharacteristic
34C2×C32×C8—22no—
35C2×C32×C8—22no—
36C2×C32×C8C2×C414yes—
37C32×C42D412yes—
38C32×C42Q812yes—
39C3×C4×Dic3—24no—
40C3×C4×Dic3—22no—
41C3×C4×Dic3C818yescomplemented
42C3×C4×Dic3C2×C414yes—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8—22no—
45C2×C3×C3⋊C8C2×C414yes—
46C4×C4⋊C8—31noSylow
47C22×C3×C8—22no—
48C22×C3×C8—32no—
49C22×C3×C8C2×D312yes—
50C22×C3×C8C22×C312yes—
51C2×C3×C42—21no—
52C2×C3×C42—32no—
53C2×C3×C42—31no—
54C2×C3×C42—32no—
55C2×C3×C42—31no—
56C2×C3×C42C2×D311yescharacteristic
57C2×C3×C42C22×C311yescharacteristic
58C2×C4×Dic3C3×C412yes—
59C2×C4×Dic3C3×C412yes—
60C2×C4×Dic3C22×C311yescharacteristic
61C2×C4×Dic3C22×C311yescharacteristic
62C22×C3⋊C8C22×C312yes—
63C3×C4⋊C8—38no—
64C3×C4×C8—24no—
65C3×C4×C8—22no—
66C3×C4×C8—22no—
67C3×C4×C8—62no—
68Dic3⋊C8C3×C418yesdirect product factor
69C4×C3⋊C8—22no—
70C23×C32C22×C411yescharacteristic
71C2×C32×C4C4⋊C414yes—
72C2×C32×C4C2×C814yes—
73C2×C32×C4M1614yes—
74C2×C32×C4C22×C412yes—
75C2×C32×C4C2×D411yescharacteristic
76C2×C32×C4C2×Q811yescharacteristic
77C2×C32×C4#4112yes—
78C2×C3×Dic3—22no—
79C2×C3×Dic3—22no—
80C2×C3×Dic3—22no—
81C2×C3×Dic3C4212yes—
82C2×C3×Dic3C4212yes—
83C2×C3×Dic3C2×C814yes—
84C2×C3×Dic3C2×C814yes—
85C32×C8—24no—
86C3×C3⋊C8—24no—
87C2×C4⋊C8—32no—
88C2×C4×C8—31no—
89C2×C4×C8C3×D311yescharacteristic
90C43—31no—
91#336—32no—
92C22×C3×C4—22no—
93C22×C3×C4—21no—
94C22×C3×C4—31no—
95C22×C3×C4—31no—
96C22×C3×C4—32no—
97C22×C3×C4C4×D312yes—
98C22×C3×C4C2×C3×C412yes—
99C22×C3×C4C22×D311yescharacteristic
100C22×C3×C4C23×C311yescharacteristic
101C22×Dic3C2×C3×C411yescharacteristic
102C22×Dic3C2×C3×C412yes—
103C22×Dic3C2×C3×C411yescharacteristic
104C2×C3×C8—24no—
105C2×C3×C8—24no—
106C2×C3×C8—22no—
107C2×C3×C8—22no—
108C2×C3×C8—22no—
109C2×C3×C8—22no—
110C2×C3×C8—24no—
111C2×C3×C8—34no—
112C2×C3×C8—62no—
113C2×C3×C8—62no—
114C2×C3×C8C4×D314yes—
115C2×C3×C8C2×C3×C414yes—
116C3×C42—22no—
117C3×C42—22no—
118C3×C42—38no—
119C3×C42—34no—
120C3×C42—64no—
121C3×C42—62no—
122C3×C42Dic612yes—
123C3×C42#6712yes—
124C3×C42C3×D412yes—
125C3×C42C3×Q812yes—
126C4×Dic3—24no—
127C4×Dic3—22no—
128C4×Dic3C3×C818yescomplemented
129C4×Dic3C2×C3×C414yes—
130C2×C3⋊C8—22no—
131C2×C3⋊C8—22no—
132C2×C3⋊C8C2×C3×C414yes—
133C22×C32C2×C4211yescharacteristic
134C22×C32C2×C4⋊C411yescharacteristic
135C22×C32#11711yescharacteristic
136C22×C32C22×C812yes—
137C22×C32C2×M1612yes—
138C32×C4C4⋊C818yescomplemented
139C32×C4C4×D412yes—
140C32×C4C4×Q812yes—
141C3×Dic3—22no—
142C3×Dic3—24no—
143C3×Dic3C4×C814yescomplemented
144C22×C8—32no—
145C22×C8C2×C3×D312yes—
146C2×C42—32no—
147C2×C42—31no—
148C2×C42—32no—
149C2×C42—31no—
150C2×C42C2×C3×D311yescharacteristic
151C4⋊C8—38no—
152C4×C8—22no—
153C4×C8—62no—
154C23×C3—21no—
155C23×C3C2×C4×D311yescharacteristic
156C23×C3C22×C3×C411yescharacteristic
157C2×C3×C4—24no—
158C2×C3×C4—24no—
159C2×C3×C4—24no—
160C2×C3×C4—21no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—21no—
164C2×C3×C4—32no—
165C2×C3×C4—34no—
166C2×C3×C4—32no—
167C2×C3×C4—34no—
168C2×C3×C4—62no—
169C2×C3×C4—62no—
170C2×C3×C4—62no—
171C2×C3×C4D3×C814yes—
172C2×C3×C4ΓL(1,𝔽25)14yes—
173C2×C3×C4Dic3⋊C414yes—
174C2×C3×C4C3×C4⋊C414yes—
175C2×C3×C4C2×C3×C814yes—
176C2×C3×C4C3×M1614yes—
177C2×C3×C4C2×Dic611yescharacteristic
178C2×C3×C4C2×C4×D312yes—
179C2×C3×C4#23512yes—
180C2×C3×C4C2×#6711yescharacteristic
181C2×C3×C4C22×C3×C412yes—
182C2×C3×C4C2×C3×D411yescharacteristic
183C2×C3×C4C2×C3×Q811yescharacteristic
184C2×C3×C4C3×#4112yes—
185C2×Dic3—22no—
186C2×Dic3—22no—
187C2×Dic3—22no—
188C2×Dic3C3×C4212yes—
189C2×Dic3C3×C4212yes—
190C2×Dic3C2×C3×C814yes—
191C2×Dic3C2×C3×C814yes—
192C3×C8—28no—
193C3×C8—24no—
194C3×C8—24no—
195C3×C8—64no—
196C3⋊C8—24no—
197C2×C32C4×C4⋊C411yescharacteristic
198C2×C32C2×C4×C811yescharacteristic
199C2×C32C4×M1611yescharacteristic
200C2×C32C2×C4⋊C812yes—
201C2×C32#43112yes—
202C22×C4—31no—
203C22×C4—32no—
204C22×C4—31no—
205C22×C4C3×C4×D312yes—
206C22×C4C22×C3×D311yescharacteristic
207C2×C8—22no—
208C2×C8—22no—
209C2×C8—34no—
210C2×C8—62no—
211C2×C8—62no—
212C2×C8C3×C4×D314yes—
213C42—38no—
214C42—34no—
215C42—64no—
216C42—62no—
217C42C3×Dic612yes—
218C42C3×#6712yes—
219C22×C3—22no—
220C22×C3—22no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3C42×D311yescharacteristic
225C22×C3#87211yescharacteristic
226C22×C3C2×D3×C812yes—
227C22×C3C2×ΓL(1,𝔽25)12yes—
228C22×C3C2×Dic3⋊C411yescharacteristic
229C22×C3C2×C3×C4211yescharacteristic
230C22×C3C2×C3×C4⋊C411yescharacteristic
231C22×C3C3×#11711yescharacteristic
232C22×C3C22×C3×C812yes—
233C22×C3C2×C3×M1612yes—
234C3×C4—22no—
235C3×C4—28no—
236C3×C4—22no—
237C3×C4—34no—
238C3×C4—64no—
239C3×C4—62no—
240C3×C4Dic3⋊C818yesdirect product factor
241C3×C4C3×C4⋊C818yescomplemented
242C3×C4C4×Dic612yes—
243C3×C4C4×#6712yes—
244C3×C4C3×C4×D412yes—
245C3×C4C3×C4×Q812yes—
246Dic3—22no—
247Dic3—24no—
248Dic3C3×C4×C814yescomplemented
249C32C4×C4⋊C811yescharacteristic, complemented, Sylow
250C23C2×C3×C4×D311yescharacteristic
251C2×C4—34no—
252C2×C4—32no—
253C2×C4—34no—
254C2×C4—32no—
255C2×C4—62no—
256C2×C4—62no—
257C2×C4—62no—
258C2×C4C3×D3×C814yes—
259C2×C4C3×ΓL(1,𝔽25)14yes—
260C2×C4C3×Dic3⋊C414yes—
261C2×C4C2×C3×Dic611yescharacteristic
262C2×C4C2×C3×C4×D312yes—
263C2×C4C3×#23512yes—
264C2×C4C2×C3×#6711yescharacteristic
265C8—24no—
266C8—64no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—22no—
270C2×C3—21no—
271C2×C3—22no—
272C2×C3C4×D3×C811yescharacteristic
273C2×C3#468512yes—
274C2×C3C4×ΓL(1,𝔽25)11yescharacteristic
275C2×C3C4×Dic3⋊C411yescharacteristic
276C2×C3C2×Dic3⋊C812yes—
277C2×C3C3×C4×C4⋊C411yescharacteristic
278C2×C3C2×C3×C4×C811yescharacteristic
279C2×C3C3×C4×M1611yescharacteristic
280C2×C3C2×C3×C4⋊C812yes—
281C2×C3C3×#43112yes—
282C22C3×C42×D311yescharacteristic
283C22C3×#87211yescharacteristic
284C22C2×C3×D3×C812yes—
285C22C2×C3×ΓL(1,𝔽25)12yes—
286C22C2×C3×Dic3⋊C411yescharacteristic
287C4—34no—
288C4—64no—
289C4—62no—
290C4C3×Dic3⋊C818yesdirect product factor
291C4C3×C4×Dic612yes—
292C4C3×C4×#6712yes—
293C3—21no—
294C3C4×Dic3⋊C811yescharacteristic, direct product factor
295C3C3×C4×C4⋊C811yescharacteristic, complemented
296C2C3×C4×D3×C811yescharacteristic
297C2C3×#468512yes—
298C2C3×C4×ΓL(1,𝔽25)11yescharacteristic
299C2C3×C4×Dic3⋊C411yescharacteristic
300C2C2×C3×Dic3⋊C812yes—
subgroupG/H
centerC2×C3×C42C2×D3
commutatorC2×C3C2×C3×C4×C8
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4×C8C2
socle, prime radicalC23×C32C22×C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C4×C8D3
hypocenterC3C3×C4×C4⋊C8
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C42 ◁ C2×C3×C4×C8

Complements

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

NH ≅ G/Ntype
7. C4×Dic3⋊C8C3direct (N × H)
16. C3×Dic3⋊C8C4direct (N × H)
41. C3×C4×Dic3C8semidirect
68. Dic3⋊C8C3×C4direct (N × H)
128. C4×Dic3C3×C8semidirect
138. C32×C4C4⋊C8semidirect
143. C3×Dic3C4×C8semidirect
240. C3×C4Dic3⋊C8direct (N × H)
241. C3×C4C3×C4⋊C8semidirect
248. Dic3C3×C4×C8semidirect
249. C32C4×C4⋊C8semidirect
290. C4C3×Dic3⋊C8direct (N × H)
294. C3C4×Dic3⋊C8direct (N × H)
295. C3C3×C4×C4⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×C82
C2×C3×Dic3⋊C82
C3×C42×Dic32
C2×C3×C4×C3⋊C82
C3×#45502
C3×C4×C4⋊C83
C4×Dic3⋊C83