Finite Group Databasebeta

← C3×C8×#239 #11861543

Subgroups — C3×C8×#239 #11861543

Order 1152.

963 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#239C211yesmaximal, characteristic
2C32×C8×Q8C211yesmaximal, characteristic, complemented
3C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4C3×#4834C213yesmaximal, complemented
5C3×#4833C213yesmaximal, complemented
6C3×C8×D12C213yesmaximal, complemented
7C3×C4×D3×C8C213yesmaximal, complemented
8C3×C8×#41—31nomaximal
9C8×#239C311yesmaximal, characteristic, direct product factor
10C2×C3×#239C411yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12C3×Q8×Dic3C411yescharacteristic
13C2×C3×D3×C8C2213yes—
14C2×C3×D3×C8C2213yes—
15C3×#893C413yes—
16C3×#892C413yes—
17C3×C4×D12C2213yes—
18C3×C42×D3C2213yes—
19C32×C4⋊C8C2213yes—
20C32×C4×C8C2213yes—
21C3×(C2×D3)⋊C8C2216yes—
22C3×C8×Dic3C2211yescharacteristic
23C3×C8×Dic3C2213yes—
24C3×C4⋊(C3⋊C8)C2213yes—
25C3×C4×C3⋊C8C2213yes—
26C3×C4×#41—31no—
27C4×#239C2×C311yescharacteristic
28C3×C8×Q8—21no—
29C3×C8×Q8—31no—
30C3×C8×Q8D311yescharacteristic, complemented
31C3×C8×Q8C2×C311yescharacteristic, complemented
32C3×C8×D4—33no—
33C3×C8×D4—33no—
34C3×#431—33no—
35C2×C3×C4×C8—33no—
36Q8×C3⋊C8C2×C311yescharacteristic, complemented
37#4834C2×C313yescomplemented
38#4833C2×C313yescomplemented
39C8×D12C2×C313yescomplemented
40C4×D3×C8C2×C313yescomplemented
41C2×C32×Q8C2×C411yescharacteristic
42C3×#239C818yesdirect product factor
43C2×C3×D12C2×C413yes—
44C2×C3×C4×D3C2×C413yes—
45C2×C3×C4×D3C2×C413yes—
46C2×C3×C4×D3C2313yes—
47C2×C32×C8C2313yes—
48C2×C32×C8C2311yescharacteristic
49C32×C4⋊C4C2×C413yes—
50C32×C42C2313yes—
51C3×(C2×D3)⋊C4C2×C416yes—
52C3×C4⋊Dic3C2×C413yes—
53C3×C4×Dic3C2×C413yes—
54C3×C4×Dic3C2×C413yes—
55C3×C4×Dic3C2311yescharacteristic
56C2×C3×C3⋊C8C2313yes—
57C2×C3×C3⋊C8C2311yescharacteristic
58C3×D3×C8—26no—
59C3×D3×C8—26no—
60C8×#41—31noSylow
61C2×C3×#41—31no—
62C2×#239C3×C411yescharacteristic
63C22×C3×C8—33no—
64C22×C3×C8—33no—
65C3×C4×Q8—21no—
66C3×C4×Q8—31no—
67C3×C4×Q8C2×D311yescharacteristic
68C3×C4×Q8C22×C311yescharacteristic
69C3×C4×D4—33no—
70C3×C4×D4—33no—
71C3×#117—33no—
72C2×C3×C42—33no—
73Q8×Dic3C3×C411yescharacteristic
74C2×D3×C8C22×C313yes—
75C2×D3×C8C22×C313yes—
76#893C3×C413yes—
77#892C3×C413yes—
78C4×D12C22×C313yes—
79C42×D3C22×C313yes—
80C3×C4⋊C8—23no—
81C3×C4⋊C8—33no—
82C3×C4⋊C8C2×D313yes—
83C3×C4⋊C8C22×C313yes—
84C3×C22⋊C8—36no—
85C3×C4×C8—23no—
86C3×C4×C8—33no—
87C3×C4×C8—31no—
88C3×C4×C8—33no—
89C3×C4×C8C2×D313yes—
90C3×C4×C8C22×C313yes—
91(C2×D3)⋊C8C22×C316yes—
92C8×Dic3C22×C311yescharacteristic
93C8×Dic3C22×C313yes—
94C4⋊(C3⋊C8)C22×C313yes—
95C4×C3⋊C8C22×C313yes—
96C22×C3×D3C22×C413yes—
97C32×Q8C2×C814yescomplemented
98C2×C32×C4C22×C413yes—
99C2×C32×C4C22×C413yes—
100C2×C32×C4C2411yescharacteristic
101C2×C3×Dic3C22×C413yes—
102C2×C3×Dic3C22×C411yescharacteristic
103C2×C3×Dic3C22×C411yescharacteristic
104C3×D12C2×C8112yescomplemented
105C3×C4×D3—23no—
106C3×C4×D3—23no—
107C3×C4×D3—26no—
108C3×C4×D3C2×C8112yescomplemented
109C32×C8—23no—
110C32×C8#4112yescomplemented
111C3×C3⋊C8—23no—
112C3×C3⋊C8#4112yescomplemented
113C4×#41—31no—
114C8×Q8—31no—
115C8×Q8C3×D311yescharacteristic, complemented
116C8×D4—33no—
117C8×D4—33no—
118#431—33no—
119C2×C4×C8—33no—
120C3×#41—38no—
121C2×C3×Q8—21no—
122C2×C3×Q8C4×D311yescharacteristic
123C2×C3×Q8C2×C3×C411yescharacteristic
124C2×C3×D4—33no—
125C22×C3×C4—33no—
126C22×C3×C4—33no—
127C22×C3×C4—33no—
128#239C3×C818yesdirect product factor
129C2×D12C2×C3×C413yes—
130C2×C4×D3C2×C3×C413yes—
131C2×C4×D3C2×C3×C413yes—
132C2×C4×D3C23×C313yes—
133C2×C3×C8—21no—
134C2×C3×C8—23no—
135C2×C3×C8—31no—
136C2×C3×C8—33no—
137C2×C3×C8—66no—
138C2×C3×C8—66no—
139C2×C3×C8C22×D313yes—
140C2×C3×C8C22×D311yescharacteristic
141C2×C3×C8C23×C313yes—
142C2×C3×C8C23×C311yescharacteristic
143C3×C4⋊C4—23no—
144C3×C4⋊C4—33no—
145C3×C4⋊C4C4×D313yes—
146C3×C4⋊C4C2×C3×C413yes—
147C3×C22⋊C4—36no—
148C3×C42—23no—
149C3×C42—33no—
150C3×C42—33no—
151C3×C42—31no—
152C3×C42C22×D313yes—
153C3×C42C23×C313yes—
154(C2×D3)⋊C4C2×C3×C416yes—
155C4⋊Dic3C2×C3×C413yes—
156C4×Dic3C2×C3×C413yes—
157C4×Dic3C2×C3×C413yes—
158C4×Dic3C23×C311yescharacteristic
159C2×C3⋊C8C23×C313yes—
160C2×C3⋊C8C23×C311yescharacteristic
161D3×C8—26no—
162D3×C8—26no—
163C22×C32C23×C411yescharacteristic
164C2×C3×D3—23no—
165C2×C3×D3—23no—
166C2×C3×D3C22×C816yes—
167C32×C4—23no—
168C32×C4C22×C816yes—
169C32×C4C2×#4111yescharacteristic
170C32×C4C2×#4111yescharacteristic
171C3×Dic3—23no—
172C3×Dic3C22×C812yes—
173C3×Dic3#13112yes—
174C2×#41—31no—
175C22×C8—33no—
176C22×C8—33no—
177C4×Q8—31no—
178C4×Q8C2×C3×D311yescharacteristic
179C4×D4—33no—
180C4×D4—33no—
181#117—33no—
182C2×C42—33no—
183C4⋊C8—33no—
184C4⋊C8C2×C3×D313yes—
185C22⋊C8—36no—
186C4×C8—31no—
187C4×C8—33no—
188C4×C8—33no—
189C4×C8C2×C3×D313yes—
190C23×C3—33no—
191C22×D3C22×C3×C413yes—
192C3×Q8—24no—
193C3×Q8D3×C814yescomplemented
194C3×Q8C2×C3×C814yescomplemented
195C3×D4—312no—
196C2×C3×C4—21no—
197C2×C3×C4—23no—
198C2×C3×C4—23no—
199C2×C3×C4—31no—
200C2×C3×C4—31no—
201C2×C3×C4—312no—
202C2×C3×C4—33no—
203C2×C3×C4—66no—
204C2×C3×C4—63no—
205C2×C3×C4—63no—
206C2×C3×C4C2×C4×D313yes—
207C2×C3×C4C2×C4×D313yes—
208C2×C3×C4C22×C3×C413yes—
209C2×C3×C4C22×C3×C413yes—
210C2×C3×C4C23×D311yescharacteristic
211C2×C3×C4C24×C311yescharacteristic
212C2×Dic3C22×C3×C413yes—
213C2×Dic3C22×C3×C411yescharacteristic
214C2×Dic3C22×C3×C411yescharacteristic
215D12C2×C3×C8112yescomplemented
216C4×D3—23no—
217C4×D3—23no—
218C4×D3—26no—
219C4×D3C2×C3×C8112yescomplemented
220C3×C8—23no—
221C3×C8—23no—
222C3×C8—22no—
223C3×C8—32no—
224C3×C8—43no—
225C3×C8—63no—
226C3×C8#23912yesdirect product factor
227C3×C8C3×#4112yescomplemented
228C3⋊C8—23no—
229C3⋊C8C3×#4112yescomplemented
230C2×C32C4×#4111yescharacteristic
231C2×C32C23×C811yescharacteristic
232C2×C32C2×#13111yescharacteristic
233C3×D3—26no—
234#41—38no—
235C2×Q8C3×C4×D311yescharacteristic
236C2×D4—33no—
237C22×C4—33no—
238C22×C4—33no—
239C22×C4—33no—
240C2×C8—31no—
241C2×C8—33no—
242C2×C8—66no—
243C2×C8—66no—
244C2×C8C22×C3×D313yes—
245C2×C8C22×C3×D311yescharacteristic
246C4⋊C4—33no—
247C4⋊C4C3×C4×D313yes—
248C22⋊C4—36no—
249C42—31no—
250C42—33no—
251C42—33no—
252C42C22×C3×D313yes—
253C22×C3—21no—
254C22×C3—36no—
255C22×C3—63no—
256C22×C3—63no—
257C22×C3C22×C4×D311yescharacteristic
258C22×C3C23×C3×C411yescharacteristic
259C2×D3—23no—
260C2×D3—23no—
261C2×D3C22×C3×C816yes—
262C3×C4—23no—
263C3×C4—23no—
264C3×C4—26no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—32no—
268C3×C4—32no—
269C3×C4—43no—
270C3×C4—63no—
271C3×C4C2×D3×C816yes—
272C3×C4C22×C3×C816yes—
273C3×C4C2×#23911yescharacteristic
274C3×C4D3×#4111yescharacteristic
275C3×C4C2×C3×#4111yescharacteristic
276C3×C4C2×C3×#4111yescharacteristic
277Dic3—23no—
278Dic3C22×C3×C812yes—
279Dic3C3×#13112yes—
280C32C8×#4111yescharacteristic, complemented, Sylow
281C23—33no—
282Q8C3×D3×C814yescomplemented
283D4—312no—
284C2×C4—31no—
285C2×C4—31no—
286C2×C4—312no—
287C2×C4—33no—
288C2×C4—66no—
289C2×C4—63no—
290C2×C4—63no—
291C2×C4C2×C3×C4×D313yes—
292C2×C4C2×C3×C4×D313yes—
293C2×C4C23×C3×D311yescharacteristic
294C8—23no—
295C8—32no—
296C8—63no—
297C8C3×#23912yesdirect product factor
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—66no—
302C2×C3C4×#23911yescharacteristic
303C2×C3C22×D3×C811yescharacteristic
304C2×C3D3×#13111yescharacteristic
305C2×C3C3×C4×#4111yescharacteristic
306C2×C3C23×C3×C811yescharacteristic
307C2×C3C2×C3×#13111yescharacteristic
308D3—26no—
309C22—36no—
310C22—63no—
311C22—63no—
312C22C22×C3×C4×D311yescharacteristic
313C4—23no—
314C4—32no—
315C4—32no—
316C4—63no—
317C4C2×C3×D3×C816yes—
318C4C2×C3×#23911yescharacteristic
319C4C3×D3×#4111yescharacteristic
320C3—21no—
321C3C8×#23911yescharacteristic, direct product factor
322C3C3×C8×#4111yescharacteristic, complemented
323C2—66no—
324C2C3×C4×#23911yescharacteristic
325C2C22×C3×D3×C811yescharacteristic
326C2C3×D3×#13111yescharacteristic
subgroupG/H
centerC2×C3×C8C22×D3
commutatorC2×C3C23×C3×C8
FrattiniC2×C4C23×C3×D3
FittingC32×C8×Q8C2
socleC22×C32C23×C4
prime radicalC2×C3×#239C4
cosocleC2×C3×C4C24×C3
hypercenterC3×C8×Q8D3
hypocenterC3C3×C8×#41
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C8 ◁ C3×C8×Q8

Complements

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

NH ≅ G/Ntype
2. C32×C8×Q8C2semidirect
3. C3×Q8×C3⋊C8C2semidirect
4. C3×#4834C2semidirect
5. C3×#4833C2semidirect
6. C3×C8×D12C2semidirect
7. C3×C4×D3×C8C2semidirect
9. C8×#239C3direct (N × H)
30. C3×C8×Q8D3semidirect
31. C3×C8×Q8C2×C3semidirect
36. Q8×C3⋊C8C2×C3semidirect
37. #4834C2×C3semidirect
38. #4833C2×C3semidirect
39. C8×D12C2×C3semidirect
40. C4×D3×C8C2×C3semidirect
42. C3×#239C8direct (N × H)
97. C32×Q8C2×C8semidirect
104. C3×D12C2×C8semidirect
108. C3×C4×D3C2×C8semidirect
110. C32×C8#41semidirect
112. C3×C3⋊C8#41semidirect
115. C8×Q8C3×D3semidirect
128. #239C3×C8direct (N × H)
193. C3×Q8D3×C8semidirect
194. C3×Q8C2×C3×C8semidirect
215. D12C2×C3×C8semidirect
219. C4×D3C2×C3×C8semidirect
226. C3×C8#239direct (N × H)
227. C3×C8C3×#41semidirect
229. C3⋊C8C3×#41semidirect
280. C32C8×#41semidirect
282. Q8C3×D3×C8semidirect
297. C8C3×#239direct (N × H)
321. C3C8×#239direct (N × H)
322. C3C3×C8×#41semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2392
C32×C8×Q82
C3×Q8×C3⋊C82
C3×#48342
C3×#48332
C3×C8×D122
C3×C4×D3×C82
C3×C8×#413
C8×#2393