Finite Group Databasebeta

← #13130175

Subgroups — #13130175

Order 1664.

316 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 72 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×D4×Dic13C211yesmaximal, characteristic
2#11719130C211yesmaximal, characteristic, complemented
3C4×#6122C211yesmaximal, characteristic, complemented
4D4⋊#1057C214yesmaximal, complemented
5C22×D4×C13C411yescharacteristic
6C23×Dic13—21no—
7C2×#6122—21no—
8C2×C22⋊Dic13—21no—
9D4×Dic13—21no—
10D4×Dic13—21no—
11D4×Dic13C412yes—
12D4×Dic13C2212yes—
13C2×C4⋊Dic13C411yescharacteristic
14C2×C4×Dic13C2211yescharacteristic
15C22⋊#1057—21no—
16#88110—21no—
17#88110—21no—
18C4⋊#1057C2212yescomplemented
19C4×#1057C2212yescomplemented
20C24×C13—21no—
21C2×D4×C13—24no—
22C2×D4×C13—21no—
23C2×D4×C13C2×C412yes—
24C22×C4×C13C2×C411yescharacteristic
25C22×Dic13—21no—
26C22×Dic13—22no—
27C22×Dic13—22no—
28C22×Dic13—44no—
29C22×Dic13D411yescharacteristic
30C22×Dic13D411yescharacteristic
31#6122—24no—
32C2×#1057—22no—
33C2×#1057—22no—
34C22⋊Dic13—22no—
35C22⋊Dic13—22no—
36C4⋊Dic13—21no—
37C4⋊Dic13C2×C412yes—
38C4×Dic13C2×C411yescharacteristic
39C4×Dic13D411yescharacteristic
40C4×Dic13D411yescharacteristic
41C4×Dic13C2311yescharacteristic
42#1490—131nomaximal, Sylow
43C23×C13—24no—
44C23×C13—22no—
45C23×C13—42no—
46C23×C13—42no—
47C23×C13C22⋊C411yescharacteristic
48D4×C13—24no—
49D4×C13—22no—
50D4×C13M1614yescomplemented
51C2×C4×C13—22no—
52C2×C4×C13C22⋊C411yescharacteristic
53C2×C4×C13C22×C411yescharacteristic
54C2×Dic13—22no—
55C2×Dic13—22no—
56C2×Dic13—22no—
57C2×Dic13—44no—
58C2×Dic13—42no—
59C2×Dic13—44no—
60C2×Dic13C22⋊C411yescharacteristic
61C2×Dic13C22⋊C411yescharacteristic
62C2×Dic13C2×D411yescharacteristic
63C2×Dic13C2×D411yescharacteristic
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—24no—
73C22×C13—48no—
74C22×C13—42no—
75C22×C13—42no—
76C22×C13#10412yes—
77C22×C13C2×C22⋊C411yescharacteristic
78C4×C13—21no—
79C4×C13C2×M1612yes—
80Dic13—21no—
81Dic13—21no—
82Dic13—21no—
83Dic13—42no—
84Dic13AGL(1,ℤ/8)12yes—
85C22×D4#26111yescharacteristic
86C23×C4—261no—
87C2×M16—261no—
88C4×D4—132no—
89C4×D4—132no—
90C4×D4—261no—
91C4×D4—261no—
92C2×C4⋊C4—131no—
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—44no—
102C2×C13#40711yescharacteristic
103C2×C13#41811yescharacteristic
104C2×C13C2×#10411yescharacteristic
105C24—21no—
106C2×D4—24no—
107C2×D4—21no—
108C2×D4C2×#26112yes—
109C22×C4—131no—
110C22×C4—131no—
111C22×C4—262no—
112C22×C4—262no—
113C22×C4—261no—
114C22×C4—524no—
115C22×C4C2×#26111yescharacteristic
116M16—264no—
117C2×C8—262no—
118C2×C8—262no—
119C4⋊C4—132no—
120C4⋊C4—261no—
121C22⋊C4—262no—
122C22⋊C4—262no—
123C42—131no—
124C42—131no—
125C42—131no—
126C42—131no—
127C13#149011yescharacteristic, complemented, Sylow
128C23—24no—
129C23—22no—
130C23—42no—
131C23—42no—
132C23C22⋊#26111yescharacteristic
133D4—24no—
134D4—22no—
135D4#612214yescomplemented
136C2×C4—22no—
137C2×C4—131no—
138C2×C4—131no—
139C2×C4—131no—
140C2×C4—131no—
141C2×C4—262no—
142C2×C4—262no—
143C2×C4—262no—
144C2×C4—524no—
145C2×C4—524no—
146C2×C4—522no—
147C2×C4C22⋊#26111yescharacteristic
148C2×C4C22×#26111yescharacteristic
149C8—264no—
150C8—522no—
151C22—21no—
152C22—21no—
153C22—24no—
154C22—48no—
155C22—42no—
156C22—42no—
157C22#8811612yes—
158C22C2×C22⋊#26111yescharacteristic
159C4—21no—
160C4—132no—
161C4—261no—
162C4—261no—
163C4—261no—
164C4—522no—
165C4C2×#612212yes—
166C2—22no—
167C2—44no—
168C2#1171913811yescharacteristic
169C2C2×#8811611yescharacteristic
170C2#1171916911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
Fitting, prime radicalC22×D4×C13C4
socleC22×C13C2×C22⋊C4
cosocleC4×Dic13C23
hypercenterC22×D4#261
hypocenterC13#1490
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11719130C2semidirect
3. C4×#6122C2semidirect
4. D4⋊#1057C2semidirect
18. C4⋊#1057C22semidirect
19. C4×#1057C22semidirect
50. D4×C13M16semidirect
127. C13#1490semidirect
135. D4#6122semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
#117191302
C4×#61222
D4⋊#10572
#149013