Finite Group Databasebeta

← C3⋊D3×AGL(1,ℤ/8) #10596243

Subgroups — C3⋊D3×AGL(1,ℤ/8) #10596243

Order 576.

894 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4#64158C211yesmaximal, characteristic, complemented
5#64141C211yesmaximal, characteristic, complemented
6#64123C212yesmaximal, complemented
7SD16×C3⋊D3C212yesmaximal, complemented
8#64120C212yesmaximal, complemented
9D8×C3⋊D3C212yesmaximal, complemented
10#64117C211yesmaximal, characteristic, complemented
11M16×C3⋊D3C211yesmaximal, characteristic, complemented
12D3×AGL(1,ℤ/8)—34nomaximal
13C23×C3⋊D3—21no—
14C32×#41C2211yescharacteristic, complemented
15C2×C32×D4C2211yescharacteristic, complemented
16C2×#638—21no—
17#3832C2211yescharacteristic, complemented
18Q8×C3⋊D3C2211yescharacteristic, complemented
19#3830—21no—
20#3830C2211yescharacteristic, complemented
21D4×C3⋊D3—21no—
22D4×C3⋊D3—21no—
23D4×C3⋊D3—21no—
24D4×C3⋊D3C2212yes—
25D4×C3⋊D3C2212yescomplemented
26D4×C3⋊D3C2211yescharacteristic, complemented
27#3828—21no—
28#3828C2211yescharacteristic, complemented
29C2×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3C2211yescharacteristic
32C32×SD16C2212yescomplemented
33C32×D8C2212yescomplemented
34C32×M16C2211yescharacteristic, complemented
35#3755C2212yescomplemented
36#3754C2212yescomplemented
37#3753C2212yescomplemented
38#3753C2212yescomplemented
39#3748C2211yescharacteristic, complemented
40#3745C2212yescomplemented
41#3744C2212yescomplemented
42#3743C2212yescomplemented
43C8×C3⋊D3C2212yescomplemented
44D3×#41—34no—
45C2×D3×D4—34no—
46C3×AGL(1,ℤ/8)D314yescomplemented
47#949—34no—
48#932—34no—
49#914—38no—
50D3×SD16—38no—
51#911—38no—
52D3×D8—38no—
53#908—34no—
54D3×M16—34no—
55C23×C32—21no—
56C22×C3⋊D3—21no—
57C22×C3⋊D3—22no—
58C22×C3⋊D3—22no—
59C22×C3⋊D3—21no—
60C22×C3⋊D3—44no—
61C22×C3⋊D3D411yescharacteristic
62C32×Q8C2311yescharacteristic, complemented
63C32×D4—21no—
64C32×D4—21no—
65C32×D4C2312yes—
66C32×D4C2311yescharacteristic, complemented
67C2×C32×C4—21no—
68C2×C32×C4C2311yescharacteristic
69#638—21no—
70#638—21no—
71#638—21no—
72#638—22no—
73#638—22no—
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3D411yescharacteristic
76C4⋊(C3⋊D3)—21no—
77C4⋊(C3⋊D3)—21no—
78C4⋊(C3⋊D3)C2312yes—
79C4⋊(C3⋊D3)C2311yescharacteristic, complemented
80C4×C3⋊D3—21no—
81C4×C3⋊D3—21no—
82C4×C3⋊D3—21no—
83C4×C3⋊D3D411yescharacteristic
84C4×C3⋊D3D411yescharacteristic
85C4×C3⋊D3C2311yescharacteristic
86C4×C3⋊D3C2311yescharacteristic
87#634—21no—
88#634C2311yescharacteristic, complemented
89C32×C8C2312yescomplemented
90C3⋊(C3⋊C8)C2312yescomplemented
91C2×AGL(1,ℤ/8)—91noSylow
92C23×D3—64no—
93C3×#41C2×D314yescomplemented
94C2×C3×D4C2×D314yescomplemented
95C2×#67—64no—
96#239—34no—
97D3×Q8—34no—
98#237—34no—
99#237—64no—
100D3×D4—38no—
101D3×D4—38no—
102D3×D4—34no—
103D3×D4—64no—
104D3×D4—64no—
105D3×D4—64no—
106#235—34no—
107#235—64no—
108C2×D12—34no—
109C2×C4×D3—34no—
110C2×C4×D3—64no—
111C3×SD16C2×D318yescomplemented
112C3×D8C2×D318yescomplemented
113C3×M16C2×D314yescomplemented
114#215—38no—
115#214—38no—
116#213—38no—
117#213—38no—
118#208—34no—
119D24—38no—
120#204—38no—
121ΓL(1,𝔽25)—38no—
122D3×C8—38no—
123C22×C32—21no—
124C22×C32—22no—
125C22×C32—42no—
126C22×C32C2×D411yescharacteristic
127C2×C3⋊D3—22no—
128C2×C3⋊D3—21no—
129C2×C3⋊D3—22no—
130C2×C3⋊D3—44no—
131C2×C3⋊D3—42no—
132C2×C3⋊D3—42no—
133C2×C3⋊D3—44no—
134C2×C3⋊D3C2×D411yescharacteristic
135C2×C3⋊D3C2×D411yescharacteristic
136C32×C4—21no—
137C32×C4C2×D411yescharacteristic
138C32×C4C2411yescharacteristic
139C3⋊Dic3—21no—
140C3⋊Dic3C2×D411yescharacteristic
141C3⋊Dic3C2×D411yescharacteristic
142C2×#41—91no—
143C22×D4—91no—
144AGL(1,ℤ/8)—91no—
145AGL(1,ℤ/8)—91no—
146AGL(1,ℤ/8)—92no—
147AGL(1,ℤ/8)—92no—
148AGL(1,ℤ/8)—91no—
149AGL(1,ℤ/8)C3⋊D311yescharacteristic, direct product factor
150C2×SD16—92no—
151C2×D8—92no—
152C2×M16—91no—
153C23×C3—24no—
154C22×D3—34no—
155C22×D3—64no—
156C22×D3—68no—
157C22×D3—68no—
158C22×D3—64no—
159C22×D3—1216no—
160C3×Q8C22×D314yescomplemented
161C3×D4—24no—
162C3×D4—24no—
163C3×D4C22×D318yes—
164C3×D4C22×D314yescomplemented
165C2×C3×C4—24no—
166C2×C3×C4C22×D314yes—
167#67—64no—
168#67—68no—
169#67—68no—
170#67—64no—
171#67—64no—
172C2×Dic3—34no—
173C2×Dic3—64no—
174D12—38no—
175D12—34no—
176D12—64no—
177D12—64no—
178C4×D3—34no—
179C4×D3—34no—
180C4×D3—34no—
181C4×D3—34no—
182C4×D3—64no—
183C4×D3—64no—
184C4×D3—64no—
185Dic6—34no—
186Dic6—64no—
187C3×C8C22×D318yescomplemented
188C3⋊C8—38no—
189C2×C32—21no—
190C2×C32—42no—
191C2×C32—41no—
192C2×C32C22×D411yescharacteristic
193C3⋊D3—21no—
194C3⋊D3—41no—
195C3⋊D3—42no—
196C3⋊D3AGL(1,ℤ/8)12yesdirect product factor
197C24—181no—
198#41—91no—
199#41—91no—
200#41—91no—
201#41—181no—
202#41—181no—
203#41C2×C3⋊D311yescharacteristic, complemented
204C2×Q8—91no—
205C2×D4—92no—
206C2×D4—92no—
207C2×D4—91no—
208C2×D4—91no—
209C2×D4—181no—
210C2×D4—181no—
211C2×D4—181no—
212C2×D4—181no—
213C2×D4C2×C3⋊D311yescharacteristic, complemented
214C22×C4—91no—
215C22×C4—181no—
216SD16—92no—
217SD16—92no—
218SD16—92no—
219SD16C2×C3⋊D312yescomplemented
220D8—92no—
221D8—92no—
222D8—92no—
223D8C2×C3⋊D312yescomplemented
224M16—91no—
225M16—92no—
226M16C2×C3⋊D311yescharacteristic, complemented
227C2×C8—92no—
228C22×C3—24no—
229C22×C3—28no—
230C22×C3—48no—
231C22×C3D3×D414yes—
232C2×D3—34no—
233C2×D3—34no—
234C2×D3—68no—
235C2×D3—64no—
236C2×D3—68no—
237C2×D3—1216no—
238C2×D3—128no—
239C2×D3—1216no—
240C2×D3—128no—
241C3×C4—24no—
242C3×C4D3×D414yes—
243C3×C4C23×D314yes—
244Dic3—34no—
245Dic3—34no—
246Dic3—64no—
247C32C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
248C23—21no—
249C23—91no—
250C23—181no—
251C23—182no—
252C23—182no—
253C23—181no—
254C23—364no—
255Q8—91no—
256Q8—181no—
257Q8C22×C3⋊D311yescharacteristic, complemented
258D4—21no—
259D4—21no—
260D4—91no—
261D4—92no—
262D4—181no—
263D4—182no—
264D4—182no—
265D4—181no—
266D4—181no—
267D4—181no—
268D4—181no—
269D4C22×C3⋊D312yes—
270D4C22×C3⋊D311yescharacteristic, complemented
271C2×C4—21no—
272C2×C4—91no—
273C2×C4—91no—
274C2×C4—91no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—181no—
278C2×C4—181no—
279C2×C4—181no—
280C2×C4—181no—
281C2×C4C22×C3⋊D311yescharacteristic
282C8—92no—
283C8C22×C3⋊D312yescomplemented
284C2×C3—24no—
285C2×C3—48no—
286C2×C3—44no—
287C2×C3C2×D3×D414yes—
288D3—38no—
289D3—64no—
290D3—128no—
291D3—124no—
292C22—21no—
293C22—22no—
294C22—42no—
295C22—91no—
296C22—91no—
297C22—182no—
298C22—181no—
299C22—182no—
300C22—362no—
301C22—364no—
302C22—362no—
303C22—364no—
304C22D4×C3⋊D311yescharacteristic
305C4—21no—
306C4—91no—
307C4—91no—
308C4—181no—
309C4D4×C3⋊D311yescharacteristic
310C4C23×C3⋊D311yescharacteristic
311C3D3×AGL(1,ℤ/8)14yescomplemented
312C2—21no—
313C2—42no—
314C2—41no—
315C2—92no—
316C2—181no—
317C2—362no—
318C2—361no—
319C2C2×D4×C3⋊D311yescharacteristic
subgroupG/H
centerC2C2×D4×C3⋊D3
commutator, cosocleC32×C4C24
FrattiniC4C23×C3⋊D3
FittingC32×AGL(1,ℤ/8)C2
socleC2×C32C22×D4
hypercenterAGL(1,ℤ/8)C3⋊D3
hypocenterC32C2×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊D3C2semidirect
2. C2×D4×C3⋊D3C2semidirect
3. C32×AGL(1,ℤ/8)C2semidirect
4. #64158C2semidirect
5. #64141C2semidirect
6. #64123C2semidirect
7. SD16×C3⋊D3C2semidirect
8. #64120C2semidirect
9. D8×C3⋊D3C2semidirect
10. #64117C2semidirect
11. M16×C3⋊D3C2semidirect
14. C32×#41C22semidirect
15. C2×C32×D4C22semidirect
17. #3832C22semidirect
18. Q8×C3⋊D3C22semidirect
20. #3830C22semidirect
25. D4×C3⋊D3C22semidirect
26. D4×C3⋊D3C22semidirect
28. #3828C22semidirect
29. C2×C4⋊(C3⋊D3)C22semidirect
32. C32×SD16C22semidirect
33. C32×D8C22semidirect
34. C32×M16C22semidirect
35. #3755C22semidirect
36. #3754C22semidirect
37. #3753C22semidirect
38. #3753C22semidirect
39. #3748C22semidirect
40. #3745C22semidirect
41. #3744C22semidirect
42. #3743C22semidirect
43. C8×C3⋊D3C22semidirect
46. C3×AGL(1,ℤ/8)D3semidirect
62. C32×Q8C23semidirect
66. C32×D4C23semidirect
79. C4⋊(C3⋊D3)C23semidirect
88. #634C23semidirect
89. C32×C8C23semidirect
90. C3⋊(C3⋊C8)C23semidirect
93. C3×#41C2×D3semidirect
94. C2×C3×D4C2×D3semidirect
111. C3×SD16C2×D3semidirect
112. C3×D8C2×D3semidirect
113. C3×M16C2×D3semidirect
149. AGL(1,ℤ/8)C3⋊D3direct (N × H)
160. C3×Q8C22×D3semidirect
164. C3×D4C22×D3semidirect
187. C3×C8C22×D3semidirect
196. C3⋊D3AGL(1,ℤ/8)direct (N × H)
203. #41C2×C3⋊D3semidirect
213. C2×D4C2×C3⋊D3semidirect
219. SD16C2×C3⋊D3semidirect
223. D8C2×C3⋊D3semidirect
226. M16C2×C3⋊D3semidirect
247. C32C2×AGL(1,ℤ/8)semidirect
257. Q8C22×C3⋊D3semidirect
270. D4C22×C3⋊D3semidirect
283. C8C22×C3⋊D3semidirect
311. C3D3×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊D32
C2×D4×C3⋊D32
C32×AGL(1,ℤ/8)2
#641582
#641412
#641232
SD16×C3⋊D32
#641202
D8×C3⋊D32
#641172
M16×C3⋊D32
D3×AGL(1,ℤ/8)3