Finite Group Databasebeta

← C3×C4⋊C4×C3⋊C8 #11784252

Subgroups — C3×C4⋊C4×C3⋊C8 #11784252

Order 1152.

689 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×C4⋊C4C211yesmaximal, characteristic
2C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
3C2×C3×C4×C3⋊C8C212yesmaximal
4C2×C3×C4×C3⋊C8C211yesmaximal, characteristic
5C3×#4524C212yesmaximal
6C3×C8×C4⋊C4—31nomaximal
7C4⋊C4×C3⋊C8C311yesmaximal, characteristic, direct product factor
8C2×C32×C4⋊C4C412yes—
9C2×C32×C42C2212yes—
10C2×C32×C42C2211yescharacteristic
11C22×C3×C3⋊C8C2212yes—
12C22×C3×C3⋊C8C2211yescharacteristic
13C22×C3×C3⋊C8C2211yescharacteristic
14C32×#95C412yes—
15C3×C4⋊(C3⋊C8)C414yescomplemented
16C3×C4×C3⋊C8—24no—
17C3×C4×C3⋊C8C414yescomplemented
18C2×C3×C4⋊C8—31no—
19C2×C3×C4×C8—31no—
20C2×C3×C4×C8—32no—
21C3×C4×C4⋊C4—21no—
22C3×C4×C4⋊C4D311yescharacteristic
23C3×C4×C4⋊C4C2×C311yescharacteristic
24C2×C4⋊(C3⋊C8)C2×C311yescharacteristic
25C2×C4×C3⋊C8C2×C312yes—
26C2×C4×C3⋊C8C2×C311yescharacteristic
27C3×#336—32no—
28#4524C2×C312yes—
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4C2×C414yes—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4C2311yescharacteristic
33C32×C4⋊C4C818yescomplemented
34C32×C42—22no—
35C32×C42—22no—
36C32×C42C2×C412yes—
37C32×C42C2×C412yes—
38C2×C3×C3⋊C8—22no—
39C2×C3×C3⋊C8—21no—
40C2×C3×C3⋊C8—21no—
41C2×C3×C3⋊C8—22no—
42C2×C3×C3⋊C8C2×C412yes—
43C2×C3×C3⋊C8C2×C414yes—
44C2×C3×C3⋊C8C2×C412yes—
45C2×C3×C3⋊C8D412yes—
46C2×C3×C3⋊C8Q812yes—
47C8×C4⋊C4—31noSylow
48C22×C3×C8—31no—
49C22×C3×C8—32no—
50C22×C3×C8—31no—
51C2×C3×C4⋊C4—22no—
52C2×C3×C4⋊C4Dic312yes—
53C2×C3×C4⋊C4C3×C412yes—
54C2×C3×C42—21no—
55C2×C3×C42—22no—
56C2×C3×C42C2×D312yes—
57C2×C3×C42C2×D311yescharacteristic
58C2×C3×C42C22×C312yes—
59C2×C3×C42C22×C311yescharacteristic
60C22×C3⋊C8C22×C312yes—
61C22×C3⋊C8C22×C311yescharacteristic
62C22×C3⋊C8C22×C311yescharacteristic
63C3×C4⋊C8—34no—
64C3×C4×C8—34no—
65C3×C4×C8—64no—
66C3×#95—22no—
67C3×#95Dic312yes—
68C3×#95C3×C412yes—
69C4⋊(C3⋊C8)C3×C414yescomplemented
70C4×C3⋊C8—24no—
71C4×C3⋊C8C3×C414yescomplemented
72C23×C32C22×C411yescharacteristic
73C2×C32×C4—24no—
74C2×C32×C4—22no—
75C2×C32×C4—24no—
76C2×C32×C4C4212yes—
77C2×C32×C4C4212yes—
78C2×C32×C4C2×C818yes—
79C2×C32×C4C2×C814yes—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×Q811yescharacteristic
84C2×C32×C4#4111yescharacteristic
85C2×C32×C4#4111yescharacteristic
86C3×C3⋊C8—22no—
87C3×C3⋊C8—24no—
88C3×C3⋊C8C4⋊C414yesdirect product factor
89C2×C4⋊C8—31no—
90C2×C4×C8—31no—
91C2×C4×C8—32no—
92C4×C4⋊C4C3×D311yescharacteristic
93#336—32no—
94C22×C3×C4—21no—
95C22×C3×C4—21no—
96C22×C3×C4—24no—
97C22×C3×C4—21no—
98C22×C3×C4C2×Dic314yes—
99C22×C3×C4C2×Dic311yescharacteristic
100C22×C3×C4C2×Dic311yescharacteristic
101C22×C3×C4C2×C3×C411yescharacteristic
102C22×C3×C4C2×C3×C414yes—
103C22×C3×C4C2×C3×C411yescharacteristic
104C22×C3×C4C22×D311yescharacteristic
105C22×C3×C4C23×C311yescharacteristic
106C2×C3×C8—32no—
107C2×C3×C8—32no—
108C2×C3×C8—32no—
109C2×C3×C8—32no—
110C2×C3×C8—34no—
111C2×C3×C8—62no—
112C2×C3×C8—61no—
113C2×C3×C8—61no—
114C2×C3×C8—62no—
115C3×C4⋊C4—28no—
116C3×C4⋊C4C3⋊C818yesdirect product factor
117C3×C4⋊C4C3×C818yescomplemented
118C3×C42—22no—
119C3×C42—22no—
120C3×C42—22no—
121C3×C42—22no—
122C3×C42—22no—
123C3×C42—22no—
124C3×C42—42no—
125C3×C42—42no—
126C3×C42C4×D312yes—
127C3×C42C4×D312yes—
128C3×C42C2×C3×C412yes—
129C3×C42C2×C3×C412yes—
130C2×C3⋊C8—22no—
131C2×C3⋊C8—21no—
132C2×C3⋊C8—21no—
133C2×C3⋊C8—22no—
134C2×C3⋊C8C2×C3×C412yes—
135C2×C3⋊C8C2×C3×C414yes—
136C2×C3⋊C8C2×C3×C412yes—
137C2×C3⋊C8C3×D412yes—
138C2×C3⋊C8C3×Q812yes—
139C22×C32C2×C4211yescharacteristic
140C22×C32C4×D411yescharacteristic
141C22×C32C4×Q811yescharacteristic
142C22×C32C22×C812yes—
143C22×C32#13112yes—
144C32×C4—22no—
145C32×C4—28no—
146C32×C4C4×C814yescomplemented
147C32×C4C2×C4⋊C411yescharacteristic
148C32×C4#11711yescharacteristic
149C32×C4C4×D411yescharacteristic
150C32×C4C4×Q811yescharacteristic
151C22×C8—31no—
152C22×C8—31no—
153C22×C8—32no—
154C2×C4⋊C4C3×Dic312yes—
155C2×C42C2×C3×D312yes—
156C2×C42C2×C3×D311yescharacteristic
157C4⋊C8—34no—
158C4×C8—34no—
159C4×C8—64no—
160#95C3×Dic312yes—
161C23×C3—21no—
162C23×C3C22×Dic311yescharacteristic
163C23×C3C22×C3×C411yescharacteristic
164C2×C3×C4—24no—
165C2×C3×C4—22no—
166C2×C3×C4—24no—
167C2×C3×C4—24no—
168C2×C3×C4—22no—
169C2×C3×C4—24no—
170C2×C3×C4—24no—
171C2×C3×C4—28no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—44no—
181C2×C3×C4—42no—
182C2×C3×C4—44no—
183C2×C3×C4C2×C3⋊C818yes—
184C2×C3×C4C2×C3⋊C814yes—
185C2×C3×C4C4×Dic312yes—
186C2×C3×C4C4×Dic312yes—
187C2×C3×C4C3×C4212yes—
188C2×C3×C4C3×C4212yes—
189C2×C3×C4C2×C3×C818yes—
190C2×C3×C4C2×C3×C814yes—
191C2×C3×C4C2×C4×D311yescharacteristic
192C2×C3×C4C2×C4×D311yescharacteristic
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4#23711yescharacteristic
195C2×C3×C4D3×Q811yescharacteristic
196C2×C3×C4#23911yescharacteristic
197C2×C3×C4C22×C3×C411yescharacteristic
198C2×C3×C4C22×C3×C411yescharacteristic
199C2×C3×C4C2×C3×D411yescharacteristic
200C2×C3×C4C2×C3×Q811yescharacteristic
201C2×C3×C4C3×#4111yescharacteristic
202C2×C3×C4C3×#4111yescharacteristic
203C3×C8—34no—
204C3×C8—62no—
205C3×C8—64no—
206C3⋊C8—22no—
207C3⋊C8—24no—
208C3⋊C8C3×C4⋊C414yesdirect product factor
209C2×C32C4×C4⋊C411yescharacteristic
210C2×C32C2×C4×C811yescharacteristic
211C2×C32#40511yescharacteristic
212C2×C32C8×D412yes—
213C2×C32C8×Q812yes—
214C22×C4C2×C3×Dic314yes—
215C22×C4C2×C3×Dic311yescharacteristic
216C22×C4C2×C3×Dic311yescharacteristic
217C22×C4C22×C3×D311yescharacteristic
218C2×C8—32no—
219C2×C8—32no—
220C2×C8—32no—
221C2×C8—32no—
222C2×C8—34no—
223C2×C8—62no—
224C2×C8—61no—
225C2×C8—61no—
226C2×C8—62no—
227C4⋊C4C3×C3⋊C818yesdirect product factor
228C42—22no—
229C42—22no—
230C42C3×C4×D312yes—
231C42C3×C4×D312yes—
232C22×C3—22no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—22no—
237C22×C3C22×C3⋊C812yes—
238C22×C3C2×C4×Dic311yescharacteristic
239C22×C3D4×Dic311yescharacteristic
240C22×C3Q8×Dic311yescharacteristic
241C22×C3#94812yes—
242C22×C3C2×C3×C4211yescharacteristic
243C22×C3C3×C4×D411yescharacteristic
244C22×C3C3×C4×Q811yescharacteristic
245C22×C3C22×C3×C812yes—
246C22×C3C3×#13112yes—
247C3×C4—22no—
248C3×C4—28no—
249C3×C4—22no—
250C3×C4—28no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—24no—
256C3×C4—42no—
257C3×C4—48no—
258C3×C4C4×C3⋊C814yescomplemented
259C3×C4C3×C4×C814yescomplemented
260C3×C4#88711yescharacteristic
261C3×C4D3×C4⋊C411yescharacteristic
262C3×C4#89211yescharacteristic
263C3×C4#89311yescharacteristic
264C3×C4C2×C3×C4⋊C411yescharacteristic
265C3×C4C3×#11711yescharacteristic
266C3×C4C3×C4×D411yescharacteristic
267C3×C4C3×C4×Q811yescharacteristic
268C32C8×C4⋊C411yescharacteristic, complemented, Sylow
269C23C22×C3×Dic311yescharacteristic
270C2×C4—24no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4C2×C3×C3⋊C818yes—
274C2×C4C2×C3×C3⋊C814yes—
275C2×C4C3×C4×Dic312yes—
276C2×C4C3×C4×Dic312yes—
277C2×C4C2×C3×C4×D311yescharacteristic
278C2×C4C2×C3×C4×D311yescharacteristic
279C2×C4C3×D3×D411yescharacteristic
280C2×C4C3×#23711yescharacteristic
281C2×C4C3×D3×Q811yescharacteristic
282C2×C4C3×#23911yescharacteristic
283C8—34no—
284C8—62no—
285C8—64no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—22no—
290C2×C3—22no—
291C2×C3C2×C4×C3⋊C811yescharacteristic
292C2×C3Dic3×C4⋊C411yescharacteristic
293C2×C3#499711yescharacteristic
294C2×C3D4×C3⋊C812yes—
295C2×C3Q8×C3⋊C812yes—
296C2×C3C3×C4×C4⋊C411yescharacteristic
297C2×C3C2×C3×C4×C811yescharacteristic
298C2×C3C3×#40511yescharacteristic
299C2×C3C3×C8×D412yes—
300C2×C3C3×C8×Q812yes—
301C22C22×C3×C3⋊C812yes—
302C22C2×C3×C4×Dic311yescharacteristic
303C22C3×D4×Dic311yescharacteristic
304C22C3×Q8×Dic311yescharacteristic
305C22C3×#94812yes—
306C4—22no—
307C4—28no—
308C4C3×C4×C3⋊C814yescomplemented
309C4C3×#88711yescharacteristic
310C4C3×D3×C4⋊C411yescharacteristic
311C4C3×#89211yescharacteristic
312C4C3×#89311yescharacteristic
313C3—21no—
314C3C4⋊C4×C3⋊C811yescharacteristic, direct product factor
315C3C3×C8×C4⋊C411yescharacteristic, complemented
316C2C2×C3×C4×C3⋊C811yescharacteristic
317C2C3×Dic3×C4⋊C411yescharacteristic
318C2C3×#499711yescharacteristic
319C2C3×D4×C3⋊C812yes—
320C2C3×Q8×C3⋊C812yes—
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC2×C3C2×C3×C4×C8
FrattiniC22×C4C22×C3×D3
FittingC32×C4×C4⋊C4C2
socle, prime radicalC23×C32C22×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×C8×C4⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
7. C4⋊C4×C3⋊C8C3direct (N × H)
15. C3×C4⋊(C3⋊C8)C4semidirect
17. C3×C4×C3⋊C8C4semidirect
33. C32×C4⋊C4C8semidirect
69. C4⋊(C3⋊C8)C3×C4semidirect
71. C4×C3⋊C8C3×C4semidirect
88. C3×C3⋊C8C4⋊C4direct (N × H)
116. C3×C4⋊C4C3⋊C8direct (N × H)
117. C3×C4⋊C4C3×C8semidirect
146. C32×C4C4×C8semidirect
208. C3⋊C8C3×C4⋊C4direct (N × H)
227. C4⋊C4C3×C3⋊C8direct (N × H)
258. C3×C4C4×C3⋊C8semidirect
259. C3×C4C3×C4×C8semidirect
268. C32C8×C4⋊C4semidirect
308. C4C3×C4×C3⋊C8semidirect
314. C3C4⋊C4×C3⋊C8direct (N × H)
315. C3C3×C8×C4⋊C4semidirect

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×C4⋊(C3⋊C8)2
C2×C3×C4×C3⋊C82
C3×#45242
C3×C8×C4⋊C43
C4⋊C4×C3⋊C83