Finite Group Databasebeta

← #11929223

Subgroups — #11929223

Order 1248.

332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 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
1D4×D39C211yesmaximal, characteristic, complemented
2D3×D4×C13C211yesmaximal, characteristic, complemented
3C3×#6129C211yesmaximal, characteristic, complemented
4#10597756C212yesmaximal, complemented
5D3×C22⋊D13C212yesmaximal, complemented
6C2×#64604C212yesmaximal, complemented
7#10597748C212yesmaximal, complemented
8D12×D13C211yesmaximal, characteristic, complemented
9#10597737C211yesmaximal, characteristic, complemented
10#10597735C211yesmaximal, characteristic, complemented
11#10597734C211yesmaximal, characteristic, complemented
12#88251—31nomaximal, Hall
13C22×D39C2212yescomplemented
14C22×D3×C13C2212yescomplemented
15C2×D3×D13C2212yescomplemented
16C3×D4×C13C2211yescharacteristic, complemented
17#64625C2212yescomplemented
18D156C2211yescharacteristic, complemented
19C4×D39C2211yescharacteristic, complemented
20C13×#67C2212yescomplemented
21C13×D12C2211yescharacteristic, complemented
22C4×D3×C13C2211yescharacteristic, complemented
23C3×C22⋊D13C2212yescomplemented
24C2×C3×Dic13C2212yescomplemented
25C3×C4×D13C2211yescharacteristic, complemented
26C3×Dic26C2211yescharacteristic, complemented
27#64605C2211yescharacteristic, complemented
28#64604C2212yescomplemented
29#64604C2212yescomplemented
30#64604C2211yescharacteristic, complemented
31#64604C2212yescomplemented
32#64603C2211yescharacteristic, complemented
33#64602C2211yescharacteristic, complemented
34#64601C2212yescomplemented
35D3×Dic13C2212yescomplemented
36C2×D4×C13—31no—
37C2×C22⋊D13—32no—
38C2×C22⋊D13—32no—
39#6129—32no—
40#6129—31no—
41#6129D311yescharacteristic, complemented
42D4×D13—31no—
43D4×D13—32no—
44D4×D13—31no—
45#6127—31no—
46#6127—31no—
47C22×C3×C13C2312yes—
48C2×D39—42no—
49C2×D39C2312yes—
50C2×D39C2311yescharacteristic
51C2×D3×C13—42no—
52C2×D3×C13C2312yes—
53C2×D3×C13C2311yescharacteristic
54C2×C3×D13C2311yescharacteristic
55D3×D13—42no—
56C3×C4×C13C2311yescharacteristic
57Dic39C2311yescharacteristic
58C3×Dic13C2312yes—
59C3×Dic13C2311yescharacteristic
60Dic3×C13C2311yescharacteristic
61C23×C13—32no—
62C22×D13—32no—
63C22×D13—32no—
64D4×C13—32no—
65D4×C13—31no—
66D4×C13C2×D311yescharacteristic, complemented
67C2×C4×C13—31no—
68C22⋊D13—32no—
69C22⋊D13—31no—
70C22⋊D13—31no—
71C22⋊D13—32no—
72C22⋊D13—32no—
73C22⋊D13—32no—
74C22⋊D13C2×D312yescomplemented
75C2×Dic13—32no—
76C2×Dic13C2×D312yescomplemented
77D52—31no—
78D52—31no—
79C4×D13—31no—
80C4×D13—32no—
81C4×D13C2×D311yescharacteristic, complemented
82Dic26—31no—
83Dic26C2×D311yescharacteristic, complemented
84#1009—131nomaximal, Hall
85C2×C3×C13—22no—
86C2×C3×C13C2411yescharacteristic
87D39—22no—
88D39—21no—
89C3×D13—21no—
90D3×C13—22no—
91D3×C13—21no—
92C22×C13—32no—
93C22×C13—31no—
94C22×C13—122no—
95C22×C13C22×D312yes—
96C2×D13—31no—
97C2×D13—32no—
98C2×D13—122no—
99C2×D13—122no—
100C2×D13C22×D311yescharacteristic
101C4×C13—31no—
102C4×C13C22×D311yescharacteristic
103Dic13—31no—
104Dic13C22×D311yescharacteristic
105Dic13C22×D312yes—
106C3×#41—131no—
107#239—131no—
108#239—131no—
109D3×D4—132no—
110D3×D4—131no—
111D3×D4—132no—
112D3×D4D1311yescharacteristic, complemented
113#235—132no—
114#235—131no—
115C2×D12—132no—
116C2×D12—131no—
117C3×C13H(5,𝔽2)11yescharacteristic, complemented, Hall
118H(5,𝔽2)—391noSylow
119C2×C13—22no—
120C2×C13—62no—
121C2×C13—61no—
122C2×C13C23×D311yescharacteristic
123D13—21no—
124D13—62no—
125D13—61no—
126C22×D3—132no—
127C22×D3—132no—
128C22×D3C2×D1312yescomplemented
129C3×Q8—131no—
130C3×D4—132no—
131C3×D4C2×D1311yescharacteristic, complemented
132C2×C3×C4—132no—
133C2×C3×C4—131no—
134#67—132no—
135#67—131no—
136#67—131no—
137#67C2×D1312yescomplemented
138D12—132no—
139D12—131no—
140D12—132no—
141D12—132no—
142D12—131no—
143D12C2×D1311yescharacteristic, complemented
144C4×D3—132no—
145C4×D3—131no—
146C4×D3—132no—
147C4×D3C2×D1311yescharacteristic, complemented
148Dic6—131no—
149#41—131no—
150#41—391no—
151#41—391no—
152#41—392no—
153#41—391no—
154C2×D4—31no—
155C2×D4—391no—
156C2×D4—392no—
157C2×D4—392no—
158C2×D4—392no—
159C2×D4—391no—
160C13#100911yescharacteristic, complemented, Sylow
161C22×C3—131no—
162C22×C3C22×D1312yes—
163C2×D3—42no—
164C2×D3—131no—
165C2×D3—132no—
166C2×D3—522no—
167C2×D3—522no—
168C2×D3C22×D1312yes—
169C2×D3C22×D1311yescharacteristic
170C3×C4—131no—
171C3×C4—132no—
172C3×C4C22×D1311yescharacteristic
173Dic3—131no—
174Dic3C22×D1311yescharacteristic
175C23—32no—
176C23—392no—
177C23—392no—
178Q8—131no—
179Q8—391no—
180D4—32no—
181D4—31no—
182D4—132no—
183D4—391no—
184D4—391no—
185D4—392no—
186D4—392no—
187D4—392no—
188D4—391no—
189D4—392no—
190D4—391no—
191D4D3×D1311yescharacteristic, complemented
192C2×C4—31no—
193C2×C4—132no—
194C2×C4—131no—
195C2×C4—392no—
196C2×C4—392no—
197C2×C4—391no—
198C2×C3—22no—
199C2×C3—261no—
200C2×C3C23×D1311yescharacteristic
201D3—21no—
202D3—22no—
203D3—262no—
204D3—261no—
205C22—31no—
206C22—32no—
207C22—122no—
208C22—131no—
209C22—392no—
210C22—391no—
211C22—1562no—
212C22—1562no—
213C22C2×D3×D1312yes—
214C4—31no—
215C4—131no—
216C4—132no—
217C4—391no—
218C4C2×D3×D1311yescharacteristic
219C3#8825111yescharacteristic, complemented, Sylow
220C2—22no—
221C2—61no—
222C2—62no—
223C2—261no—
224C2—781no—
225C2—782no—
226C2C22×D3×D1311yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×D13
commutator, socle, cosocleC2×C3×C13C24
FittingC3×D4×C13C22
hypercenterD4D3×D13
hypocenterC3×C13H(5,𝔽2)
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. D4×D39C2semidirect
2. D3×D4×C13C2semidirect
3. C3×#6129C2semidirect
4. #10597756C2semidirect
5. D3×C22⋊D13C2semidirect
6. C2×#64604C2semidirect
7. #10597748C2semidirect
8. D12×D13C2semidirect
9. #10597737C2semidirect
10. #10597735C2semidirect
11. #10597734C2semidirect
13. C22×D39C22semidirect
14. C22×D3×C13C22semidirect
15. C2×D3×D13C22semidirect
16. C3×D4×C13C22semidirect
17. #64625C22semidirect
18. D156C22semidirect
19. C4×D39C22semidirect
20. C13×#67C22semidirect
21. C13×D12C22semidirect
22. C4×D3×C13C22semidirect
23. C3×C22⋊D13C22semidirect
24. C2×C3×Dic13C22semidirect
25. C3×C4×D13C22semidirect
26. C3×Dic26C22semidirect
27. #64605C22semidirect
28. #64604C22semidirect
29. #64604C22semidirect
30. #64604C22semidirect
31. #64604C22semidirect
32. #64603C22semidirect
33. #64602C22semidirect
34. #64601C22semidirect
35. D3×Dic13C22semidirect
41. #6129D3semidirect
66. D4×C13C2×D3semidirect
74. C22⋊D13C2×D3semidirect
76. C2×Dic13C2×D3semidirect
81. C4×D13C2×D3semidirect
83. Dic26C2×D3semidirect
112. D3×D4D13semidirect
117. C3×C13H(5,𝔽2)semidirect
128. C22×D3C2×D13semidirect
131. C3×D4C2×D13semidirect
137. #67C2×D13semidirect
143. D12C2×D13semidirect
147. C4×D3C2×D13semidirect
160. C13#1009semidirect
191. D4D3×D13semidirect
219. C3#88251semidirect

Maximal subgroups

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

subgroupindex
D4×D392
D3×D4×C132
C3×#61292
#105977562
D3×C22⋊D132
C2×#646042
#105977482
D12×D132
#105977372
#105977352
#105977342
#882513
#100913