Finite Group Databasebeta

← D3×#6129 #11929219

Subgroups — D3×#6129 #11929219

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
2D3×D4×C13C211yesmaximal, characteristic, complemented
3C3×#6129C211yesmaximal, characteristic, complemented
4D3×C22⋊D13C212yesmaximal, complemented
5#10597748C212yesmaximal, complemented
6C2×D3×Dic13C212yesmaximal, complemented
7#10597746C212yesmaximal, complemented
8C4×D3×D13C211yesmaximal, characteristic, complemented
9#10597738C211yesmaximal, characteristic, complemented
10#10597734C211yesmaximal, characteristic, complemented
11D3×Dic26C211yesmaximal, characteristic, complemented
12C2×#6129—31nomaximal, Hall
13C22×D3×C13C2212yes—
14C2×D3×D13C2211yescharacteristic
15C3×D4×C13C2211yescharacteristic, complemented
16#64625C2212yescomplemented
17C2×Dic39C2212yescomplemented
18C4×D39C2211yescharacteristic, complemented
19Dic78C2211yescharacteristic, complemented
20C13×#67C2212yescomplemented
21C13×D12C2211yescharacteristic, complemented
22C4×D3×C13C2211yescharacteristic
23C3×C22⋊D13C2212yescomplemented
24C2×C3×Dic13C2212yescomplemented
25C3×C4×D13C2211yescharacteristic, complemented
26C3×Dic26C2211yescharacteristic, complemented
27#64605C2212yescomplemented
28#64604C2212yescomplemented
29#64602C2212yescomplemented
30#64601C2211yescharacteristic, complemented
31D3×Dic13C2212yes—
32D3×Dic13C2211yescharacteristic
33D3×Dic13C2212yescomplemented
34D3×Dic13C2212yescomplemented
35Dic3×D13C2211yescharacteristic, complemented
36C2×D4×C13—31no—
37C2×C22⋊D13—32no—
38C22×Dic13—32no—
39#6129—31no—
40#6129—32no—
41#6129—32no—
42#6129—31no—
43#6129—31no—
44#6129D311yescharacteristic, direct product factor
45C2×C4×D13—31no—
46C2×Dic26—31no—
47C22×C3×C13C2312yes—
48C2×D39C2311yescharacteristic
49C2×D3×C13—24no—
50C2×D3×C13C2312yes—
51C2×D3×C13C2311yescharacteristic
52C2×C3×D13C2311yescharacteristic
53D3×D13—22no—
54C3×C4×C13C2311yescharacteristic
55Dic39C2311yescharacteristic
56Dic39C2312yes—
57C3×Dic13C2311yescharacteristic
58C3×Dic13C2312yes—
59Dic3×C13C2311yescharacteristic
60C23×C13—32no—
61C22×D13—31no—
62D4×C13—32no—
63D4×C13—31no—
64D4×C13C2×D311yescharacteristic, complemented
65C2×C4×C13—31no—
66C22⋊D13—32no—
67C22⋊D13—32no—
68C22⋊D13—32no—
69C22⋊D13C2×D312yescomplemented
70C2×Dic13—32no—
71C2×Dic13—32no—
72C2×Dic13—31no—
73C2×Dic13—32no—
74C2×Dic13—32no—
75C2×Dic13C2×D312yescomplemented
76C4×D13—31no—
77C4×D13—31no—
78C4×D13—31no—
79C4×D13C2×D311yescharacteristic, complemented
80Dic26—31no—
81Dic26—32no—
82Dic26C2×D311yescharacteristic, complemented
83D3×#41—131nomaximal, Hall
84C2×C3×C13—22no—
85C2×C3×C13C2411yescharacteristic
86D39—21no—
87C3×D13—21no—
88D3×C13—22no—
89D3×C13#4112yescomplemented
90C22×C13—31no—
91C22×C13—32no—
92C22×C13—64no—
93C22×C13C22×D312yes—
94C2×D13—31no—
95C2×D13—62no—
96C2×D13C22×D311yescharacteristic
97C4×C13—31no—
98C4×C13C22×D311yescharacteristic
99Dic13—32no—
100Dic13—31no—
101Dic13C22×D312yes—
102Dic13C22×D311yescharacteristic
103C3×#41—131no—
104#239—131no—
105D3×Q8—131no—
106#237—131no—
107#237—132no—
108D3×D4—132no—
109D3×D4D1311yescharacteristic, complemented
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—32no—
118C2×C13—62no—
119C2×C13C23×D311yescharacteristic
120D13—21no—
121D13—61no—
122C22×D3—131no—
123C22×D3C2×D1312yes—
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—132no—
133C2×Dic3—131no—
134D12—132no—
135D12C2×D1311yescharacteristic, complemented
136C4×D3—131no—
137C4×D3—132no—
138C4×D3—132no—
139C4×D3—132no—
140C4×D3—131no—
141C4×D3—131no—
142C4×D3C2×D1311yescharacteristic
143Dic6—131no—
144Dic6—132no—
145#41—131no—
146#41—392no—
147#41—391no—
148#41—392no—
149#41—391no—
150#41—391no—
151C2×Q8—391no—
152C2×D4—31no—
153C2×D4—392no—
154C22×C4—391no—
155C22×C4—392no—
156C13D3×#4111yescharacteristic, complemented, Sylow
157C22×C3—131no—
158C22×C3C22×D1312yes—
159C2×D3—24no—
160C2×D3—131no—
161C2×D3—262no—
162C2×D3C22×D1312yes—
163C2×D3C22×D1311yescharacteristic
164C3×C4—132no—
165C3×C4—131no—
166C3×C4C22×D1311yescharacteristic
167Dic3—132no—
168Dic3—131no—
169Dic3C22×D1311yescharacteristic
170C23—32no—
171C23—391no—
172Q8—131no—
173Q8—392no—
174Q8—391no—
175D4—32no—
176D4—31no—
177D4—132no—
178D4—392no—
179D4—392no—
180D4—392no—
181D4D3×D1311yescharacteristic, complemented
182C2×C4—31no—
183C2×C4—132no—
184C2×C4—131no—
185C2×C4—391no—
186C2×C4—391no—
187C2×C4—391no—
188C2×C4—392no—
189C2×C4—392no—
190C2×C4—392no—
191C2×C4—392no—
192C2×C4—391no—
193C2×C3—22no—
194C2×C3—261no—
195C2×C3C23×D1311yescharacteristic
196D3—22no—
197D3—261no—
198D3#612912yesdirect product factor
199C22—31no—
200C22—32no—
201C22—64no—
202C22—131no—
203C22—391no—
204C22—782no—
205C22C2×D3×D1312yes—
206C4—31no—
207C4—131no—
208C4—132no—
209C4—391no—
210C4—392no—
211C4C2×D3×D1311yescharacteristic
212C3C2×#612911yescharacteristic, complemented, Sylow
213C2—22no—
214C2—32no—
215C2—62no—
216C2—261no—
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. D3×D4×C13C2semidirect
3. C3×#6129C2semidirect
4. D3×C22⋊D13C2semidirect
5. #10597748C2semidirect
6. C2×D3×Dic13C2semidirect
7. #10597746C2semidirect
8. C4×D3×D13C2semidirect
9. #10597738C2semidirect
10. #10597734C2semidirect
11. D3×Dic26C2semidirect
15. C3×D4×C13C22semidirect
16. #64625C22semidirect
17. C2×Dic39C22semidirect
18. C4×D39C22semidirect
19. Dic78C22semidirect
20. C13×#67C22semidirect
21. C13×D12C22semidirect
23. C3×C22⋊D13C22semidirect
24. C2×C3×Dic13C22semidirect
25. C3×C4×D13C22semidirect
26. C3×Dic26C22semidirect
27. #64605C22semidirect
28. #64604C22semidirect
29. #64602C22semidirect
30. #64601C22semidirect
33. D3×Dic13C22semidirect
34. D3×Dic13C22semidirect
35. Dic3×D13C22semidirect
44. #6129D3direct (N × H)
64. D4×C13C2×D3semidirect
69. C22⋊D13C2×D3semidirect
75. C2×Dic13C2×D3semidirect
79. C4×D13C2×D3semidirect
82. Dic26C2×D3semidirect
89. D3×C13#41semidirect
109. D3×D4D13semidirect
114. C3×C13C2×#41semidirect
126. C3×D4C2×D13semidirect
131. #67C2×D13semidirect
135. D12C2×D13semidirect
156. C13D3×#41semidirect
181. D4D3×D13semidirect
198. D3#6129direct (N × H)
212. C3C2×#6129semidirect

Maximal subgroups

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

subgroupindex
#105977922
D3×D4×C132
C3×#61292
D3×C22⋊D132
#105977482
C2×D3×Dic132
#105977462
C4×D3×D132
#105977382
#105977342
D3×Dic262
C2×#61293
D3×#4113