Finite Group Databasebeta

← D13×#237 #11929218

Subgroups — D13×#237 #11929218

Order 1248.

328 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 112 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#10597792C211yesmaximal, characteristic, complemented
2C13×#237C211yesmaximal, characteristic, complemented
3C3×D4×D13C211yesmaximal, characteristic, complemented
4#67×D13C212yesmaximal, complemented
5#10597746C212yesmaximal, complemented
6#10597745C212yesmaximal, complemented
7C2×Dic3×D13C212yesmaximal, complemented
8C4×D3×D13C211yesmaximal, characteristic, complemented
9#10597732C211yesmaximal, characteristic, complemented
10#10597731C211yesmaximal, characteristic, complemented
11Dic6×D13C211yesmaximal, characteristic, complemented
12#41×D13—31nomaximal, Hall
13C22×C3×D13C2212yes—
14C2×D3×D13C2211yescharacteristic
15C3×D4×C13C2211yescharacteristic, complemented
16#64625C2212yescomplemented
17C2×Dic39C2212yescomplemented
18C4×D39C2211yescharacteristic, complemented
19Dic78C2211yescharacteristic, complemented
20C13×#67C2212yescomplemented
21C2×Dic3×C13C2212yescomplemented
22C4×D3×C13C2211yescharacteristic, complemented
23C13×Dic6C2211yescharacteristic, complemented
24C3×C22⋊D13C2212yescomplemented
25C3×D52C2211yescharacteristic, complemented
26C3×C4×D13C2211yescharacteristic
27#64605C2212yescomplemented
28#64603C2212yescomplemented
29#64602C2212yescomplemented
30#64601C2211yescharacteristic, complemented
31D3×Dic13C2211yescharacteristic, complemented
32Dic3×D13C2212yes—
33Dic3×D13C2211yescharacteristic
34Dic3×D13C2212yescomplemented
35Dic3×D13C2212yescomplemented
36C13×#41—31no—
37#6131—31no—
38Q8×D13—31no—
39#6129—31no—
40#6129—32no—
41D4×D13—32no—
42D4×D13D311yescharacteristic, complemented
43#6127—32no—
44#6127—31no—
45C2×C4×D13—32no—
46C2×C4×D13—31no—
47C22×C3×C13C2312yes—
48C2×D39C2311yescharacteristic
49C2×D3×C13C2311yescharacteristic
50C2×C3×D13—24no—
51C2×C3×D13C2312yes—
52C2×C3×D13C2311yescharacteristic
53D3×D13—22no—
54C3×C4×C13C2311yescharacteristic
55Dic39C2311yescharacteristic
56Dic39C2312yes—
57C3×Dic13C2311yescharacteristic
58Dic3×C13C2311yescharacteristic
59Dic3×C13C2312yes—
60C22×D13—31no—
61C22×D13C2×D312yes—
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—32no—
71C2×Dic13—31no—
72D52—32no—
73D52C2×D311yescharacteristic, complemented
74C4×D13—31no—
75C4×D13—32no—
76C4×D13—32no—
77C4×D13—32no—
78C4×D13—31no—
79C4×D13—31no—
80C4×D13C2×D311yescharacteristic
81Dic26—31no—
82Dic26—32no—
83C2×#237—131nomaximal, Hall
84C2×C3×C13—22no—
85C2×C3×C13C2411yescharacteristic
86D39—21no—
87C3×D13—22no—
88C3×D13#4112yescomplemented
89D3×C13—21no—
90C22×C13—31no—
91C22×C13C22×D312yes—
92C2×D13—24no—
93C2×D13—31no—
94C2×D13—62no—
95C2×D13C22×D312yes—
96C2×D13C22×D311yescharacteristic
97C4×C13—32no—
98C4×C13—31no—
99C4×C13C22×D311yescharacteristic
100Dic13—32no—
101Dic13—31no—
102Dic13C22×D311yescharacteristic
103C2×C3×D4—131no—
104C2×#67—132no—
105C22×Dic3—132no—
106#237—131no—
107#237—132no—
108#237—132no—
109#237—131no—
110#237—131no—
111#237D1311yescharacteristic, direct product factor
112C2×C4×D3—131no—
113C2×Dic6—131no—
114C3×C13C2×#4111yescharacteristic, complemented, Hall
115C2×#41—391noSylow
116C2×C13—22no—
117C2×C13—61no—
118C2×C13C23×D311yescharacteristic
119D13—22no—
120D13—61no—
121D13#23712yesdirect product factor
122C23×C3—132no—
123C22×D3—131no—
124C3×D4—132no—
125C3×D4—131no—
126C3×D4C2×D1311yescharacteristic, complemented
127C2×C3×C4—131no—
128#67—132no—
129#67—132no—
130#67—132no—
131#67C2×D1312yescomplemented
132C2×Dic3—132no—
133C2×Dic3—132no—
134C2×Dic3—131no—
135C2×Dic3—132no—
136C2×Dic3—132no—
137C2×Dic3C2×D1312yescomplemented
138C4×D3—131no—
139C4×D3—131no—
140C4×D3—131no—
141C4×D3C2×D1311yescharacteristic, complemented
142Dic6—131no—
143Dic6—132no—
144Dic6C2×D1311yescharacteristic, complemented
145#41—31no—
146#41—392no—
147#41—391no—
148#41—392no—
149#41—391no—
150#41—391no—
151C2×Q8—391no—
152C2×D4—131no—
153C2×D4—392no—
154C22×C4—391no—
155C22×C4—392no—
156C13C2×#23711yescharacteristic, complemented, Sylow
157C22×C3—131no—
158C22×C3—132no—
159C22×C3—264no—
160C22×C3C22×D1312yes—
161C2×D3—131no—
162C2×D3—262no—
163C2×D3C22×D1311yescharacteristic
164C3×C4—131no—
165C3×C4C22×D1311yescharacteristic
166Dic3—132no—
167Dic3—131no—
168Dic3C22×D1312yes—
169Dic3C22×D1311yescharacteristic
170C23—132no—
171C23—391no—
172Q8—31no—
173Q8—392no—
174Q8—391no—
175D4—32no—
176D4—132no—
177D4—131no—
178D4—392no—
179D4—392no—
180D4—392no—
181D4D3×D1311yescharacteristic, complemented
182C2×C4—32no—
183C2×C4—31no—
184C2×C4—131no—
185C2×C4—391no—
186C2×C4—391no—
187C2×C4—392no—
188C2×C4—392no—
189C2×C4—392no—
190C2×C4—391no—
191C2×C4—392no—
192C2×C4—391no—
193C2×C3—22no—
194C2×C3—132no—
195C2×C3—262no—
196C2×C3C23×D1311yescharacteristic
197D3—21no—
198D3—261no—
199C22—31no—
200C22—131no—
201C22—132no—
202C22—264no—
203C22—391no—
204C22—782no—
205C22C2×D3×D1312yes—
206C4—31no—
207C4—32no—
208C4—131no—
209C4—391no—
210C4—392no—
211C4C2×D3×D1311yescharacteristic
212C3#41×D1311yescharacteristic, complemented, Sylow
213C2—22no—
214C2—61no—
215C2—132no—
216C2—262no—
217C2—781no—
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. #10597792C2semidirect
2. C13×#237C2semidirect
3. C3×D4×D13C2semidirect
4. #67×D13C2semidirect
5. #10597746C2semidirect
6. #10597745C2semidirect
7. C2×Dic3×D13C2semidirect
8. C4×D3×D13C2semidirect
9. #10597732C2semidirect
10. #10597731C2semidirect
11. Dic6×D13C2semidirect
15. C3×D4×C13C22semidirect
16. #64625C22semidirect
17. C2×Dic39C22semidirect
18. C4×D39C22semidirect
19. Dic78C22semidirect
20. C13×#67C22semidirect
21. C2×Dic3×C13C22semidirect
22. C4×D3×C13C22semidirect
23. C13×Dic6C22semidirect
24. C3×C22⋊D13C22semidirect
25. C3×D52C22semidirect
27. #64605C22semidirect
28. #64603C22semidirect
29. #64602C22semidirect
30. #64601C22semidirect
31. D3×Dic13C22semidirect
34. Dic3×D13C22semidirect
35. Dic3×D13C22semidirect
42. D4×D13D3semidirect
64. D4×C13C2×D3semidirect
69. C22⋊D13C2×D3semidirect
73. D52C2×D3semidirect
88. C3×D13#41semidirect
111. #237D13direct (N × H)
114. C3×C13C2×#41semidirect
121. D13#237direct (N × H)
126. C3×D4C2×D13semidirect
131. #67C2×D13semidirect
137. C2×Dic3C2×D13semidirect
141. C4×D3C2×D13semidirect
144. Dic6C2×D13semidirect
156. C13C2×#237semidirect
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
#105977922
C13×#2372
C3×D4×D132
#67×D132
#105977462
#105977452
C2×Dic3×D132
C4×D3×D132
#105977322
#105977312
Dic6×D132
#41×D133
C2×#23713