Finite Group Databasebeta

← #11929212

Subgroups — #11929212

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
1C2×C4×D39C211yesmaximal, characteristic, complemented
2C13×#235C211yesmaximal, characteristic, complemented
3C3×#6127C211yesmaximal, characteristic, complemented
4#10597756C212yesmaximal, complemented
5#10597746C212yesmaximal, complemented
6#10597743C211yesmaximal, characteristic, complemented
7C4×D3×D13C212yesmaximal, complemented
8#10597737C212yesmaximal, complemented
9D39⋊Q8C211yesmaximal, characteristic, complemented
10#10597734C211yesmaximal, characteristic, complemented
11#10597732C211yesmaximal, characteristic, complemented
12#41×D13—31nomaximal, Hall
13C22×D39C2211yescharacteristic
14C2×D3×D13C2212yes—
15C2×C3×C4×C13C2211yescharacteristic, complemented
16C2×Dic39C2211yescharacteristic, complemented
17C4×D39C2211yescharacteristic
18C4×D39C2211yescharacteristic
19C4×D39C2211yescharacteristic, complemented
20C4×D39C2211yescharacteristic, complemented
21C13×#67C2212yescomplemented
22C13×D12C2211yescharacteristic, complemented
23C4×D3×C13C2212yescomplemented
24C13×Dic6C2211yescharacteristic, complemented
25C3×C22⋊D13C2212yescomplemented
26C3×D52C2211yescharacteristic, complemented
27C3×C4×D13C2212yescomplemented
28C3×Dic26C2211yescharacteristic, complemented
29#64605C2212yescomplemented
30#64604C2212yescomplemented
31#64603C2212yescomplemented
32#64602C2212yescomplemented
33#64601C2212yes—
34D3×Dic13C2212yescomplemented
35Dic3×D13C2212yescomplemented
36C13×#41—31no—
37#6131—31no—
38Q8×D13—31no—
39#6129—32no—
40#6129—31no—
41D4×D13—32no—
42D4×D13—31no—
43#6127—32no—
44#6127D311yescharacteristic, complemented
45C2×C4×D13—31no—
46C2×C4×D13—32no—
47C22×C3×C13C2311yescharacteristic
48C2×D39—22no—
49C2×D39C2311yescharacteristic
50C2×D39C2311yescharacteristic
51C2×D3×C13C2312yes—
52C2×C3×D13C2312yes—
53D3×D13—24no—
54C3×C4×C13C2311yescharacteristic
55C3×C4×C13C2311yescharacteristic
56Dic39C2311yescharacteristic
57Dic39C2311yescharacteristic
58C3×Dic13C2312yes—
59Dic3×C13C2312yes—
60C22×D13—31no—
61C22×D13—32no—
62Q8×C13—31no—
63D4×C13—32no—
64D4×C13—31no—
65C2×C4×C13—32no—
66C2×C4×C13C2×D311yescharacteristic, complemented
67C22⋊D13—32no—
68C22⋊D13—32no—
69C22⋊D13C2×D312yescomplemented
70C2×Dic13—31no—
71C2×Dic13—32no—
72D52—32no—
73D52C2×D311yescharacteristic, complemented
74C4×D13—32no—
75C4×D13—31no—
76C4×D13—31no—
77C4×D13—31no—
78C4×D13—31no—
79C4×D13—32no—
80C4×D13C2×D312yescomplemented
81Dic26—32no—
82Dic26C2×D311yescharacteristic, complemented
83D3×#41—131nomaximal, Hall
84C2×C3×C13—21no—
85C2×C3×C13C2411yescharacteristic
86D39—21no—
87D39#4112yescomplemented
88C3×D13—22no—
89D3×C13—22no—
90C22×C13—32no—
91C22×C13C22×D311yescharacteristic
92C2×D13—31no—
93C2×D13—31no—
94C2×D13—64no—
95C2×D13—62no—
96C2×D13C22×D312yes—
97C4×C13—32no—
98C4×C13C22×D311yescharacteristic
99C4×C13C22×D311yescharacteristic
100Dic13—31no—
101Dic13—31no—
102Dic13C22×D312yes—
103C3×#41—131no—
104#239—131no—
105D3×Q8—131no—
106#237—132no—
107#237—131no—
108D3×D4—132no—
109D3×D4—131no—
110#235—132no—
111#235D1311yescharacteristic, complemented
112C2×C4×D3—131no—
113C2×C4×D3—132no—
114C3×C13C2×#4111yescharacteristic, complemented, Hall
115C2×#41—391noSylow
116C2×C13—21no—
117C2×C13—62no—
118C2×C13C23×D311yescharacteristic
119D13—22no—
120D13—32no—
121D13—61no—
122C22×D3—131no—
123C22×D3—132no—
124C3×Q8—131no—
125C3×D4—132no—
126C3×D4—131no—
127C2×C3×C4—132no—
128C2×C3×C4C2×D1311yescharacteristic, complemented
129#67—132no—
130#67—132no—
131#67C2×D1312yescomplemented
132C2×Dic3—131no—
133C2×Dic3—132no—
134D12—132no—
135D12C2×D1311yescharacteristic, complemented
136C4×D3—132no—
137C4×D3—131no—
138C4×D3—131no—
139C4×D3—131no—
140C4×D3—131no—
141C4×D3—132no—
142C4×D3C2×D1312yescomplemented
143Dic6—132no—
144Dic6C2×D1311yescharacteristic, complemented
145#41—31no—
146#41—131no—
147#41—392no—
148#41—392no—
149#41—391no—
150#41—391no—
151C2×Q8—391no—
152C2×D4—392no—
153C2×D4—391no—
154C22×C4—392no—
155C22×C4—391no—
156C13D3×#4111yescharacteristic, complemented, Sylow
157C22×C3—132no—
158C22×C3C22×D1311yescharacteristic
159C2×D3—131no—
160C2×D3—131no—
161C2×D3—264no—
162C2×D3—262no—
163C2×D3C22×D1312yes—
164C3×C4—132no—
165C3×C4C22×D1311yescharacteristic
166C3×C4C22×D1311yescharacteristic
167Dic3—131no—
168Dic3—131no—
169Dic3C22×D1312yes—
170C23—392no—
171C23—391no—
172Q8—31no—
173Q8—131no—
174Q8—392no—
175D4—32no—
176D4—31no—
177D4—132no—
178D4—131no—
179D4—392no—
180D4—392no—
181D4—392no—
182C2×C4—32no—
183C2×C4—132no—
184C2×C4—392no—
185C2×C4—392no—
186C2×C4—392no—
187C2×C4—391no—
188C2×C4—391no—
189C2×C4—391no—
190C2×C4—391no—
191C2×C4—391no—
192C2×C4D3×D1311yescharacteristic, complemented
193C2×C3—21no—
194C2×C3—262no—
195C2×C3C23×D1311yescharacteristic
196D3—22no—
197D3—132no—
198D3—261no—
199C22—32no—
200C22—132no—
201C22—391no—
202C22—391no—
203C22—782no—
204C22—784no—
205C22C2×D3×D1311yescharacteristic
206C4—32no—
207C4—132no—
208C4—391no—
209C4—391no—
210C4C2×D3×D1311yescharacteristic
211C4C2×D3×D1311yescharacteristic
212C3#41×D1311yescharacteristic, complemented, Sylow
213C2—21no—
214C2—62no—
215C2—262no—
216C2—392no—
217C2—781no—
218C2C22×D3×D1311yescharacteristic
subgroupG/H
centerC4C2×D3×D13
commutator, socle, cosocleC2×C3×C13C24
FrattiniC2C22×D3×D13
FittingC2×C3×C4×C13C22
hypercenterC2×C4D3×D13
hypocenterC3×C13C2×#41
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D39C2semidirect
2. C13×#235C2semidirect
3. C3×#6127C2semidirect
4. #10597756C2semidirect
5. #10597746C2semidirect
6. #10597743C2semidirect
7. C4×D3×D13C2semidirect
8. #10597737C2semidirect
9. D39⋊Q8C2semidirect
10. #10597734C2semidirect
11. #10597732C2semidirect
15. C2×C3×C4×C13C22semidirect
16. C2×Dic39C22semidirect
19. C4×D39C22semidirect
20. C4×D39C22semidirect
21. C13×#67C22semidirect
22. C13×D12C22semidirect
23. C4×D3×C13C22semidirect
24. C13×Dic6C22semidirect
25. C3×C22⋊D13C22semidirect
26. C3×D52C22semidirect
27. C3×C4×D13C22semidirect
28. C3×Dic26C22semidirect
29. #64605C22semidirect
30. #64604C22semidirect
31. #64603C22semidirect
32. #64602C22semidirect
34. D3×Dic13C22semidirect
35. Dic3×D13C22semidirect
44. #6127D3semidirect
66. C2×C4×C13C2×D3semidirect
69. C22⋊D13C2×D3semidirect
73. D52C2×D3semidirect
80. C4×D13C2×D3semidirect
82. Dic26C2×D3semidirect
87. D39#41semidirect
111. #235D13semidirect
114. C3×C13C2×#41semidirect
128. C2×C3×C4C2×D13semidirect
131. #67C2×D13semidirect
135. D12C2×D13semidirect
142. C4×D3C2×D13semidirect
144. Dic6C2×D13semidirect
156. C13D3×#41semidirect
192. C2×C4D3×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
C2×C4×D392
C13×#2352
C3×#61272
#105977562
#105977462
#105977432
C4×D3×D132
#105977372
D39⋊Q82
#105977342
#105977322
#41×D133
D3×#4113