Finite Group Databasebeta

← #11929220

Subgroups — #11929220

Order 1248.

328 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 110 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
2C13×#237C211yesmaximal, characteristic, complemented
3C3×#6129C211yesmaximal, characteristic, complemented
4#10597756C212yesmaximal, complemented
5C2×#64601C212yesmaximal, complemented
6#10597748C212yesmaximal, complemented
7#10597745C212yesmaximal, complemented
8C4×D3×D13C211yesmaximal, characteristic, complemented
9#10597739C211yesmaximal, characteristic, complemented
10D39⋊Q8C211yesmaximal, characteristic, complemented
11#10597735C211yesmaximal, characteristic, complemented
12#41×D13—31nomaximal, Hall
13C22×D39C2212yes—
14C2×D3×D13C2211yescharacteristic
15C3×D4×C13C2211yescharacteristic, complemented
16#64625C2212yescomplemented
17D156C2211yescharacteristic, complemented
18C4×D39C2211yescharacteristic
19C13×#67C2212yescomplemented
20C2×Dic3×C13C2212yescomplemented
21C4×D3×C13C2211yescharacteristic, complemented
22C13×Dic6C2211yescharacteristic, complemented
23C3×C22⋊D13C2212yescomplemented
24C2×C3×Dic13C2212yescomplemented
25C3×C4×D13C2211yescharacteristic, complemented
26C3×Dic26C2211yescharacteristic, complemented
27#64605C2212yescomplemented
28#64604C2212yescomplemented
29#64603C2212yescomplemented
30#64601C2212yes—
31#64601C2211yescharacteristic
32#64601C2212yescomplemented
33#64601C2212yescomplemented
34D3×Dic13C2211yescharacteristic, complemented
35Dic3×D13C2211yescharacteristic, complemented
36C13×#41—31no—
37#6131—31no—
38Q8×D13—31no—
39#6129—32no—
40#6129D311yescharacteristic, complemented
41D4×D13—31no—
42D4×D13—32no—
43#6127—32no—
44#6127—31no—
45C2×C4×D13—32no—
46C2×C4×D13—31no—
47C22×C3×C13C2312yes—
48C2×D39—24no—
49C2×D39C2312yes—
50C2×D39C2311yescharacteristic
51C2×D3×C13C2311yescharacteristic
52C2×C3×D13C2311yescharacteristic
53D3×D13—22no—
54C3×C4×C13C2311yescharacteristic
55Dic39C2311yescharacteristic
56C3×Dic13C2311yescharacteristic
57C3×Dic13C2312yes—
58Dic3×C13C2311yescharacteristic
59Dic3×C13C2312yes—
60C22×D13—32no—
61C22×D13—31no—
62Q8×C13—31no—
63D4×C13—32no—
64D4×C13C2×D311yescharacteristic, complemented
65C2×C4×C13—32no—
66C2×C4×C13—31no—
67C22⋊D13—32no—
68C22⋊D13—32no—
69C22⋊D13C2×D312yescomplemented
70C2×Dic13—31no—
71C2×Dic13C2×D312yescomplemented
72D52—32no—
73D52—31no—
74C4×D13—31no—
75C4×D13—31no—
76C4×D13—31no—
77C4×D13—32no—
78C4×D13—32no—
79C4×D13—32no—
80C4×D13C2×D311yescharacteristic, complemented
81Dic26—32no—
82Dic26C2×D311yescharacteristic, complemented
83D3×#41—131nomaximal, Hall
84C2×C3×C13—22no—
85C2×C3×C13C2411yescharacteristic
86D39—22no—
87D39#4112yescomplemented
88C3×D13—21no—
89D3×C13—21no—
90C22×C13—31no—
91C22×C13C22×D312yes—
92C2×D13—31no—
93C2×D13—32no—
94C2×D13—62no—
95C2×D13—64no—
96C2×D13C22×D311yescharacteristic
97C4×C13—32no—
98C4×C13—31no—
99C4×C13C22×D311yescharacteristic
100Dic13—31no—
101Dic13C22×D312yes—
102Dic13C22×D311yescharacteristic
103C3×#41—131no—
104#239—131no—
105D3×Q8—131no—
106#237—132no—
107#237D1311yescharacteristic, complemented
108D3×D4—131no—
109D3×D4—132no—
110#235—132no—
111#235—131no—
112C2×C4×D3—132no—
113C2×C4×D3—131no—
114C3×C13C2×#4111yescharacteristic, complemented, Hall
115C2×#41—391noSylow
116C2×C13—22no—
117C2×C13—61no—
118C2×C13C23×D311yescharacteristic
119D13—21no—
120D13—32no—
121D13—62no—
122C22×D3—132no—
123C22×D3—131no—
124C3×Q8—131no—
125C3×D4—132no—
126C3×D4C2×D1311yescharacteristic, complemented
127C2×C3×C4—132no—
128C2×C3×C4—131no—
129#67—132no—
130#67—132no—
131#67C2×D1312yescomplemented
132C2×Dic3—131no—
133C2×Dic3C2×D1312yescomplemented
134D12—132no—
135D12—131no—
136C4×D3—131no—
137C4×D3—131no—
138C4×D3—131no—
139C4×D3—132no—
140C4×D3—132no—
141C4×D3—132no—
142C4×D3C2×D1311yescharacteristic, complemented
143Dic6—132no—
144Dic6C2×D1311yescharacteristic, complemented
145#41—31no—
146#41—131no—
147#41—392no—
148#41—391no—
149#41—392no—
150#41—391no—
151C2×Q8—391no—
152C2×D4—392no—
153C2×D4—391no—
154C22×C4—392no—
155C22×C4—391no—
156C13D3×#4111yescharacteristic, complemented, Sylow
157C22×C3—131no—
158C22×C3C22×D1312yes—
159C2×D3—131no—
160C2×D3—132no—
161C2×D3—262no—
162C2×D3—264no—
163C2×D3C22×D1311yescharacteristic
164C3×C4—132no—
165C3×C4—131no—
166C3×C4C22×D1311yescharacteristic
167Dic3—131no—
168Dic3C22×D1312yes—
169Dic3C22×D1311yescharacteristic
170C23—391no—
171C23—392no—
172Q8—31no—
173Q8—131no—
174Q8—392no—
175D4—32no—
176D4—132no—
177D4—392no—
178D4—392no—
179D4—392no—
180D4—391no—
181D4D3×D1311yescharacteristic, complemented
182C2×C4—32no—
183C2×C4—31no—
184C2×C4—132no—
185C2×C4—131no—
186C2×C4—391no—
187C2×C4—392no—
188C2×C4—392no—
189C2×C4—392no—
190C2×C4—391no—
191C2×C4—391no—
192C2×C4—391no—
193C2×C3—22no—
194C2×C3—261no—
195C2×C3C23×D1311yescharacteristic
196D3—21no—
197D3—132no—
198D3—262no—
199C22—31no—
200C22—131no—
201C22—391no—
202C22—392no—
203C22—784no—
204C22—782no—
205C22C2×D3×D1312yes—
206C4—31no—
207C4—32no—
208C4—131no—
209C4—132no—
210C4—391no—
211C4C2×D3×D1311yescharacteristic
212C3#41×D1311yescharacteristic, complemented, Sylow
213C2—22no—
214C2—61no—
215C2—261no—
216C2—392no—
217C2—782no—
218C2C22×D3×D1311yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×D13
commutator, socle, cosocleC2×C3×C13C24
FittingC3×D4×C13C22
hypercenterD4D3×D13
hypocenterC3×C13C2×#41
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. C13×#237C2semidirect
3. C3×#6129C2semidirect
4. #10597756C2semidirect
5. C2×#64601C2semidirect
6. #10597748C2semidirect
7. #10597745C2semidirect
8. C4×D3×D13C2semidirect
9. #10597739C2semidirect
10. D39⋊Q8C2semidirect
11. #10597735C2semidirect
15. C3×D4×C13C22semidirect
16. #64625C22semidirect
17. D156C22semidirect
19. C13×#67C22semidirect
20. C2×Dic3×C13C22semidirect
21. C4×D3×C13C22semidirect
22. C13×Dic6C22semidirect
23. C3×C22⋊D13C22semidirect
24. C2×C3×Dic13C22semidirect
25. C3×C4×D13C22semidirect
26. C3×Dic26C22semidirect
27. #64605C22semidirect
28. #64604C22semidirect
29. #64603C22semidirect
32. #64601C22semidirect
33. #64601C22semidirect
34. D3×Dic13C22semidirect
35. Dic3×D13C22semidirect
40. #6129D3semidirect
64. D4×C13C2×D3semidirect
69. C22⋊D13C2×D3semidirect
71. C2×Dic13C2×D3semidirect
80. C4×D13C2×D3semidirect
82. Dic26C2×D3semidirect
87. D39#41semidirect
107. #237D13semidirect
114. C3×C13C2×#41semidirect
126. C3×D4C2×D13semidirect
131. #67C2×D13semidirect
133. C2×Dic3C2×D13semidirect
142. C4×D3C2×D13semidirect
144. Dic6C2×D13semidirect
156. C13D3×#41semidirect
181. D4D3×D13semidirect
212. C3#41×D13semidirect

Maximal subgroups

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

subgroupindex
D4×D392
C13×#2372
C3×#61292
#105977562
C2×#646012
#105977482
#105977452
C4×D3×D132
#105977392
D39⋊Q82
#105977352
#41×D133
D3×#4113