Finite Group Databasebeta

← #13130177

Subgroups — #13130177

Order 1664.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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×#88147C211yesmaximal, characteristic
2#11719130C211yesmaximal, characteristic, complemented
3C4×#6122C211yesmaximal, characteristic, complemented
4#11718243C214yesmaximal, complemented
5C22×D52C411yescharacteristic
6C22×C4×D13—21no—
7C2×#6122—21no—
8C2×C13×C4⋊C4C411yescharacteristic
9C2×#6103—21no—
10C2×C4×Dic13C2211yescharacteristic
11#88147—21no—
12#88147—21no—
13#88147C412yes—
14#88147C2212yes—
15C22⋊#1057—21no—
16#88110—21no—
17#88110—21no—
18C4⋊#1057C2212yescomplemented
19C4×#1057C2212yescomplemented
20C23×D13—21no—
21C22×C4×C13—21no—
22C22×C4×C13C2×C411yescharacteristic
23C22×Dic13D411yescharacteristic
24C22×Dic13D411yescharacteristic
25C2×D52—21no—
26C2×D52—24no—
27C2×D52C2×C412yes—
28C2×C4×D13—22no—
29C2×C4×D13—22no—
30C2×C4×D13—44no—
31#6122—24no—
32C2×#1057—22no—
33C2×#1057—22no—
34C13×C4⋊C4—21no—
35C13×C4⋊C4C2×C412yes—
36#6103—22no—
37#6103—22no—
38C4×Dic13C2×C411yescharacteristic
39C4×Dic13D411yescharacteristic
40C4×Dic13D411yescharacteristic
41C4×Dic13C2311yescharacteristic
42#1490—131nomaximal, Sylow
43C23×C13C22⋊C411yescharacteristic
44C22×D13—24no—
45C22×D13—22no—
46C22×D13—42no—
47C22×D13—42no—
48C2×C4×C13—22no—
49C2×C4×C13—22no—
50C2×C4×C13—42no—
51C2×C4×C13C22⋊C411yescharacteristic
52C2×C4×C13C22×C411yescharacteristic
53C2×Dic13—22no—
54C2×Dic13—22no—
55C2×Dic13C22⋊C411yescharacteristic
56C2×Dic13C22⋊C411yescharacteristic
57C2×Dic13C2×D411yescharacteristic
58C2×Dic13C2×D411yescharacteristic
59D52—24no—
60D52—22no—
61D52M1614yescomplemented
62C4×D13—44no—
63C4×D13—44no—
64#1057—24no—
65#1057—42no—
66C2×C4×D4—131no—
67#432—131no—
68C4×M16—131no—
69D4⋊C8—134no—
70C22×C13—21no—
71C22×C13—21no—
72C22×C13#10412yes—
73C22×C13C2×C22⋊C411yescharacteristic
74C2×D13—24no—
75C2×D13—48no—
76C2×D13—42no—
77C2×D13—42no—
78C4×C13—21no—
79C4×C13—42no—
80C4×C13C2×M1612yes—
81Dic13—21no—
82Dic13—21no—
83Dic13—21no—
84Dic13AGL(1,ℤ/8)12yes—
85C22×D4—131no—
86C23×C4—261no—
87C2×M16—261no—
88C4×D4—132no—
89C4×D4—132no—
90C4×D4—261no—
91C4×D4—261no—
92C2×C4⋊C4#26111yescharacteristic
93C2×C22⋊C4—261no—
94C2×C42—131no—
95C4⋊C8—132no—
96C22⋊C8—261no—
97#97—261no—
98#97—261no—
99C4×C8—132no—
100C2×C13—22no—
101C2×C13#40711yescharacteristic
102C2×C13#41811yescharacteristic
103C2×C13C2×#10411yescharacteristic
104D13—44no—
105C24—261no—
106C2×D4—132no—
107C2×D4—264no—
108C2×D4—261no—
109C22×C4—21no—
110C22×C4—131no—
111C22×C4—131no—
112C22×C4—262no—
113C22×C4—262no—
114C22×C4—524no—
115C22×C4C2×#26111yescharacteristic
116M16—264no—
117C2×C8—262no—
118C2×C8—262no—
119C4⋊C4—21no—
120C4⋊C4C2×#26112yes—
121C22⋊C4—262no—
122C22⋊C4—262no—
123C42—131no—
124C42—131no—
125C42—131no—
126C42—131no—
127C13#149011yescharacteristic, complemented, Sylow
128C23—264no—
129C23—262no—
130C23—522no—
131C23—522no—
132C23C22⋊#26111yescharacteristic
133D4—134no—
134D4—264no—
135D4—262no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—131no—
140C2×C4—131no—
141C2×C4—131no—
142C2×C4—131no—
143C2×C4—262no—
144C2×C4—262no—
145C2×C4—524no—
146C2×C4—524no—
147C2×C4C22⋊#26111yescharacteristic
148C2×C4C22×#26111yescharacteristic
149C8—264no—
150C8—522no—
151C22—21no—
152C22—21no—
153C22—264no—
154C22—528no—
155C22—522no—
156C22—522no—
157C22#8811812yes—
158C22C2×C22⋊#26111yescharacteristic
159C4—21no—
160C4—42no—
161C4—132no—
162C4—261no—
163C4—261no—
164C4—261no—
165C4D13⋊M1612yes—
166C2—22no—
167C2—524no—
168C2#1171912611yescharacteristic
169C2#1171913811yescharacteristic
170C2C2×#8811811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC2×C13×C4⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D52C4
cosocleC4×Dic13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1490
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11719130C2semidirect
3. C4×#6122C2semidirect
4. #11718243C2semidirect
18. C4⋊#1057C22semidirect
19. C4×#1057C22semidirect
61. D52M16semidirect
127. C13#1490semidirect

Maximal subgroups

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

subgroupindex
C2×#881472
#117191302
C4×#61222
#117182432
#149013