Finite Group Databasebeta

← #13130089

Subgroups — #13130089

Order 1664.

252 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 62 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×#88126C211yesmaximal, characteristic
2#11719128C212yesmaximal, complemented
3#11718287C212yesmaximal
4#11718286C212yesmaximal, complemented
5C22×C4×D13C411yescharacteristic
6C2×C42×C13C411yescharacteristic
7C2×#6103C411yescharacteristic
8C2×#6103C2211yescharacteristic
9C2×#6101C411yescharacteristic
10C2×#6101C2211yescharacteristic
11C2×C4×Dic13C2211yescharacteristic
12#88126—22no—
13#88126—22no—
14C22⋊#1057C2214yes—
15#88112—22no—
16#88110—22no—
17C23×D13C2×C411yescharacteristic
18C22×C4×C13C2×C411yescharacteristic
19C22×C4×C13C2×C411yescharacteristic
20C22×C4×C13C2×C411yescharacteristic
21C22×Dic13C2×C411yescharacteristic
22C22×Dic13C2×C411yescharacteristic
23C22×Dic13C2311yescharacteristic
24C2×C4×D13—22no—
25C2×C4×D13—21no—
26C2×C4×D13—21no—
27C2×C4×D13—22no—
28C2×#1057—24no—
29C42×C13—21no—
30C42×C13—21no—
31#6103—22no—
32#6103—22no—
33#6101—22no—
34#6101—22no—
35C4×Dic13D412yes—
36C4×Dic13D412yes—
37#1464—131nomaximal, Sylow
38C23×C13C22×C411yescharacteristic
39C22×D13—21no—
40C22×D13—21no—
41C22×D13—41no—
42C22×D13—41no—
43C22×D13M1612yes—
44C2×C4×C13—21no—
45C2×C4×C13—21no—
46C2×C4×C13—21no—
47C2×C4×C13—21no—
48C2×C4×C13—41no—
49C2×C4×C13—41no—
50C2×C4×C13C22⋊C411yescharacteristic
51C2×C4×C13C22⋊C411yescharacteristic
52C2×Dic13—21no—
53C2×Dic13—21no—
54C2×Dic13—41no—
55C2×Dic13—41no—
56C2×Dic13C22⋊C412yes—
57C2×Dic13M1612yes—
58C2×Dic13C2×D412yes—
59C4×D13—24no—
60C4×D13—24no—
61#1057—44no—
62C2×#117—131no—
63#432—132no—
64#324—132no—
65#323—132no—
66C22×C13—21no—
67C22×C13—21no—
68C22×C13C2×C22⋊C411yescharacteristic
69C22×C13C2×M1611yescharacteristic
70C22×C13C2×M1611yescharacteristic
71C2×D13—22no—
72C2×D13—42no—
73C2×D13—41no—
74C2×D13—41no—
75C2×D13—42no—
76C4×C13—21no—
77C4×C13—21no—
78C4×C13—41no—
79C4×C13—41no—
80Dic13—22no—
81Dic13—22no—
82Dic13—22no—
83C23×C4—131no—
84#117—262no—
85#117—262no—
86C2×C4⋊C4—131no—
87C2×C4⋊C4—131no—
88C2×C22⋊C4—131no—
89C2×C22⋊C4—131no—
90C2×C42—131no—
91C2×C42#26111yescharacteristic
92C4⋊C8—262no—
93C22⋊C8—134no—
94#97—262no—
95C2×C13—21no—
96C2×C13—21no—
97C2×C13#40711yescharacteristic
98C2×C13#41011yescharacteristic
99C2×C13#41311yescharacteristic
100D13—42no—
101C24—131no—
102C22×C4—131no—
103C22×C4—131no—
104C22×C4—131no—
105C22×C4—262no—
106C22×C4—262no—
107C22×C4—261no—
108C22×C4—261no—
109C22×C4C2×#26111yescharacteristic
110C22×C4C2×#26111yescharacteristic
111C22×C4C2×#26111yescharacteristic
112C2×C8—264no—
113C4⋊C4—262no—
114C4⋊C4—262no—
115C22⋊C4—262no—
116C22⋊C4—262no—
117C42—21no—
118C42—21no—
119C42—132no—
120C42—132no—
121C13#146411yescharacteristic, complemented, Sylow
122C23—132no—
123C23—261no—
124C23—261no—
125C23—521no—
126C23—521no—
127C23C22×#26111yescharacteristic
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—132no—
135C2×C4—132no—
136C2×C4—132no—
137C2×C4—264no—
138C2×C4—264no—
139C2×C4—261no—
140C2×C4—261no—
141C2×C4—521no—
142C2×C4—521no—
143C2×C4C22⋊#26111yescharacteristic
144C2×C4C22⋊#26111yescharacteristic
145C8—524no—
146C22—21no—
147C22—21no—
148C22—262no—
149C22—522no—
150C22—522no—
151C22—521no—
152C22—521no—
153C22D13⋊M1611yescharacteristic
154C22D13⋊M1611yescharacteristic
155C22C2×C22⋊#26111yescharacteristic
156C4—21no—
157C4—21no—
158C4—41no—
159C4—41no—
160C4—262no—
161C4—262no—
162C4—262no—
163C2—21no—
164C2—21no—
165C2—522no—
166C2#1171911611yescharacteristic
167C2#1171912611yescharacteristic
168C2#1171913211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C42×C13C4
socleC22×C13C2×C22⋊C4
prime radicalC23×D13C2×C4
cosocleC22×Dic13C23
hypercenterC2×C42#261
hypocenterC13#1464
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11719128C2semidirect
4. #11718286C2semidirect
121. C13#1464semidirect

Maximal subgroups

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

subgroupindex
C2×#881262
#117191282
#117182872
#117182862
#146413