Finite Group Databasebeta

← C3⋊D3×#135 #10596238

Subgroups — C3⋊D3×#135 #10596238

Order 576.

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

normal subgroups only

This group has 798 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⋊D3C212yesmaximal, complemented
2C32×#135C211yesmaximal, characteristic, complemented
3#64159C212yesmaximal, complemented
4#64128C211yesmaximal, characteristic, complemented
5Q16×C3⋊D3C211yesmaximal, characteristic, complemented
6#64125C212yesmaximal, complemented
7SD16×C3⋊D3C212yesmaximal, complemented
8#64121C211yesmaximal, characteristic, complemented
9D8×C3⋊D3C211yesmaximal, characteristic, complemented
10#64113C211yesmaximal, characteristic, complemented
11C2×C8×C3⋊D3C211yesmaximal, characteristic, complemented
12D3×#135—34nomaximal
13C32×#41C2212yescomplemented
14#3832C2212yescomplemented
15Q8×C3⋊D3C2212yes—
16#3830—22no—
17#3830C2212yescomplemented
18D4×C3⋊D3—22no—
19D4×C3⋊D3C2212yes—
20#3828—22no—
21#3828C2212yescomplemented
22C2×C4×C3⋊D3—22no—
23C2×C4×C3⋊D3C2211yescharacteristic
24C32×Q16C2211yescharacteristic, complemented
25C32×SD16C2212yescomplemented
26C32×D8C2211yescharacteristic, complemented
27C2×C32×C8C2211yescharacteristic, complemented
28#3756C2212yescomplemented
29#3755C2212yescomplemented
30#3754C2212yescomplemented
31#3753C2212yescomplemented
32C2×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
33#3746C2211yescharacteristic, complemented
34#3745C2211yescharacteristic, complemented
35#3744C2212yescomplemented
36C8×C3⋊D3C2211yescharacteristic
37C8×C3⋊D3C2211yescharacteristic
38C8×C3⋊D3C2211yescharacteristic, complemented
39C8×C3⋊D3C2211yescharacteristic, complemented
40D3×#41—38no—
41C3×#135D314yescomplemented
42#950—38no—
43#919—34no—
44D3×Q16—34no—
45#916—38no—
46D3×SD16—38no—
47#912—34no—
48D3×D8—34no—
49#904—34no—
50C2×D3×C8—34no—
51C22×C3⋊D3—22no—
52C22×C3⋊D3D411yescharacteristic
53C32×Q8C2312yes—
54C32×D4—22no—
55C32×D4C2312yes—
56C2×C32×C4—22no—
57C2×C32×C4C2311yescharacteristic
58#638—22no—
59#638—22no—
60#638—22no—
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3D411yescharacteristic
63C4⋊(C3⋊D3)—22no—
64C4⋊(C3⋊D3)C2312yes—
65C4×C3⋊D3—22no—
66C4×C3⋊D3—22no—
67C4×C3⋊D3—22no—
68C4×C3⋊D3D411yescharacteristic
69C4×C3⋊D3D411yescharacteristic
70C4×C3⋊D3C2311yescharacteristic
71C4×C3⋊D3C2311yescharacteristic
72#634—22no—
73#634C2312yes—
74C32×C8C2311yescharacteristic
75C32×C8C2311yescharacteristic
76C3⋊(C3⋊C8)C2311yescharacteristic
77C3⋊(C3⋊C8)C2311yescharacteristic
78C2×#135—91noSylow
79C3×#41C2×D318yescomplemented
80#239—38no—
81D3×Q8—38no—
82#237—38no—
83#237—68no—
84D3×D4—38no—
85D3×D4—68no—
86#235—38no—
87#235—68no—
88C2×C4×D3—34no—
89C2×C4×D3—68no—
90C3×Q16C2×D314yescomplemented
91C3×SD16C2×D318yescomplemented
92C3×D8C2×D314yescomplemented
93C2×C3×C8C2×D314yescomplemented
94#216—38no—
95#215—38no—
96#214—38no—
97#213—38no—
98C2×C3⋊C8—34no—
99Dic12—34no—
100D24—34no—
101#204—38no—
102D3×C8—34no—
103D3×C8—34no—
104D3×C8—34no—
105D3×C8—34no—
106C22×C32—22no—
107C22×C32C2×D411yescharacteristic
108C2×C3⋊D3—22no—
109C2×C3⋊D3—22no—
110C2×C3⋊D3—44no—
111C2×C3⋊D3C2×D411yescharacteristic
112C2×C3⋊D3C2×D411yescharacteristic
113C32×C4—22no—
114C32×C4C2×D411yescharacteristic
115C32×C4C2411yescharacteristic
116C3⋊Dic3—22no—
117C3⋊Dic3C2×D411yescharacteristic
118C3⋊Dic3C2×D411yescharacteristic
119C2×#41—92no—
120#135—92no—
121#135—91no—
122#135—92no—
123#135—91no—
124#135—91no—
125#135C3⋊D311yescharacteristic, direct product factor
126C2×Q16—91no—
127C2×SD16—92no—
128C2×D8—91no—
129C22×C8—91no—
130C22×D3—34no—
131C22×D3—68no—
132C3×Q8C22×D318yes—
133C3×D4—28no—
134C3×D4C22×D318yes—
135C2×C3×C4—28no—
136C2×C3×C4C22×D314yes—
137#67—68no—
138#67—68no—
139#67—68no—
140C2×Dic3—34no—
141C2×Dic3—68no—
142D12—38no—
143D12—68no—
144C4×D3—34no—
145C4×D3—34no—
146C4×D3—34no—
147C4×D3—34no—
148C4×D3—68no—
149C4×D3—68no—
150C4×D3—68no—
151Dic6—38no—
152Dic6—68no—
153C3×C8C22×D314yes—
154C3×C8C22×D314yes—
155C3⋊C8—34no—
156C3⋊C8—34no—
157C2×C32—21no—
158C2×C32—42no—
159C2×C32C22×D411yescharacteristic
160C3⋊D3—21no—
161C3⋊D3—42no—
162C3⋊D3#13512yesdirect product factor
163#41—92no—
164#41—92no—
165#41—92no—
166#41—182no—
167#41—182no—
168#41C2×C3⋊D312yescomplemented
169C2×Q8—92no—
170C2×D4—92no—
171C2×D4—182no—
172C22×C4—91no—
173C22×C4—182no—
174Q16—92no—
175Q16—91no—
176Q16C2×C3⋊D311yescharacteristic, complemented
177SD16—92no—
178SD16—92no—
179SD16—92no—
180SD16C2×C3⋊D312yescomplemented
181D8—92no—
182D8—91no—
183D8C2×C3⋊D311yescharacteristic, complemented
184C2×C8—91no—
185C2×C8—91no—
186C2×C8—91no—
187C2×C8—91no—
188C2×C8—91no—
189C2×C8C2×C3⋊D311yescharacteristic, complemented
190C22×C3—28no—
191C22×C3D3×D414yes—
192C2×D3—34no—
193C2×D3—34no—
194C2×D3—68no—
195C2×D3—68no—
196C2×D3—1216no—
197C3×C4—28no—
198C3×C4D3×D414yes—
199C3×C4C23×D314yes—
200Dic3—34no—
201Dic3—34no—
202Dic3—68no—
203C32C2×#13511yescharacteristic, complemented, Sylow
204C23—91no—
205C23—182no—
206Q8—92no—
207Q8—182no—
208Q8C22×C3⋊D312yes—
209D4—22no—
210D4—92no—
211D4—182no—
212D4—182no—
213D4—182no—
214D4—182no—
215D4C22×C3⋊D312yes—
216C2×C4—22no—
217C2×C4—91no—
218C2×C4—91no—
219C2×C4—91no—
220C2×C4—91no—
221C2×C4—91no—
222C2×C4—182no—
223C2×C4—182no—
224C2×C4—182no—
225C2×C4—182no—
226C2×C4C22×C3⋊D311yescharacteristic
227C8—91no—
228C8—91no—
229C8C22×C3⋊D311yescharacteristic
230C8C22×C3⋊D311yescharacteristic
231C2×C3—24no—
232C2×C3—48no—
233C2×C3C2×D3×D414yes—
234D3—38no—
235D3—64no—
236D3—128no—
237C22—22no—
238C22—91no—
239C22—91no—
240C22—182no—
241C22—182no—
242C22—364no—
243C22D4×C3⋊D311yescharacteristic
244C4—22no—
245C4—91no—
246C4—91no—
247C4—182no—
248C4D4×C3⋊D311yescharacteristic
249C4C23×C3⋊D311yescharacteristic
250C3D3×#13514yescomplemented
251C2—21no—
252C2—42no—
253C2—92no—
254C2—181no—
255C2—362no—
256C2C2×D4×C3⋊D311yescharacteristic
subgroupG/H
centerC4D4×C3⋊D3
commutator, cosocleC32×C4C24
FrattiniC4C23×C3⋊D3
FittingC32×#135C2
socleC2×C32C22×D4
hypercenter#135C3⋊D3
hypocenterC32C2×#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊D3C2semidirect
2. C32×#135C2semidirect
3. #64159C2semidirect
4. #64128C2semidirect
5. Q16×C3⋊D3C2semidirect
6. #64125C2semidirect
7. SD16×C3⋊D3C2semidirect
8. #64121C2semidirect
9. D8×C3⋊D3C2semidirect
10. #64113C2semidirect
11. C2×C8×C3⋊D3C2semidirect
13. C32×#41C22semidirect
14. #3832C22semidirect
17. #3830C22semidirect
21. #3828C22semidirect
24. C32×Q16C22semidirect
25. C32×SD16C22semidirect
26. C32×D8C22semidirect
27. C2×C32×C8C22semidirect
28. #3756C22semidirect
29. #3755C22semidirect
30. #3754C22semidirect
31. #3753C22semidirect
32. C2×C3⋊(C3⋊C8)C22semidirect
33. #3746C22semidirect
34. #3745C22semidirect
35. #3744C22semidirect
38. C8×C3⋊D3C22semidirect
39. C8×C3⋊D3C22semidirect
41. C3×#135D3semidirect
79. C3×#41C2×D3semidirect
90. C3×Q16C2×D3semidirect
91. C3×SD16C2×D3semidirect
92. C3×D8C2×D3semidirect
93. C2×C3×C8C2×D3semidirect
125. #135C3⋊D3direct (N × H)
162. C3⋊D3#135direct (N × H)
168. #41C2×C3⋊D3semidirect
176. Q16C2×C3⋊D3semidirect
180. SD16C2×C3⋊D3semidirect
183. D8C2×C3⋊D3semidirect
189. C2×C8C2×C3⋊D3semidirect
203. C32C2×#135semidirect
250. C3D3×#135semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊D32
C32×#1352
#641592
#641282
Q16×C3⋊D32
#641252
SD16×C3⋊D32
#641212
D8×C3⋊D32
#641132
C2×C8×C3⋊D32
D3×#1353