Finite Group Databasebeta

← #13130340

Subgroups — #13130340

Order 1664.

246 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 60 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#11719373C211yesmaximal, characteristic
2#11719049C212yesmaximal, complemented
3#11718303C212yesmaximal, complemented
4#11718297C212yesmaximal, complemented
5C2×#6131C411yescharacteristic
6C2×#6129C411yescharacteristic
7C13×#124C411yescharacteristic
8#88198C2211yescharacteristic
9#88194C2211yescharacteristic
10#88138—22no—
11#88135—22no—
12#88129C411yescharacteristic
13C42×D13C2211yescharacteristic
14#88112C2214yes—
15#88111—22no—
16C4×#1057—22no—
17C2×Q8×C13C2×C411yescharacteristic
18C2×D4×C13C2×C411yescharacteristic
19C2×C22⋊D13—21no—
20C2×C22⋊D13—22no—
21C22×Dic13—21no—
22#6131—42no—
23#6129—42no—
24C2×D52—21no—
25C2×D52C2×C411yescharacteristic
26C2×C4×D13—21no—
27C2×C4×D13C2×C411yescharacteristic
28C2×C4×D13D412yes—
29C2×Dic26C2×C411yescharacteristic
30C2×#1057—24no—
31C13×C22⋊C4—22no—
32C42×C13C2×C411yescharacteristic
33#6103—22no—
34#6101—22no—
35C4×Dic13D412yes—
36C4×Dic13C2311yescharacteristic
37#1543—131nomaximal, Sylow
38C23×C13—21no—
39C22×D13—21no—
40C22×D13C22⋊C411yescharacteristic
41Q8×C13—41no—
42D4×C13—41no—
43C2×C4×C13—21no—
44C2×C4×C13C22⋊C412yes—
45C2×C4×C13C22×C411yescharacteristic
46C22⋊D13—42no—
47C22⋊D13—44no—
48C2×Dic13—21no—
49C2×Dic13—42no—
50C2×Dic13C22⋊C411yescharacteristic
51C2×Dic13C2×D412yes—
52D52—41no—
53D52—42no—
54C4×D13—22no—
55C4×D13—24no—
56C4×D13—42no—
57Dic26—41no—
58#1057—44no—
59#532—131no—
60#431—132no—
61#333—132no—
62#331—132no—
63C22×C13—41no—
64C22×C13—42no—
65C22×C13C2×C22⋊C411yescharacteristic
66C2×D13—21no—
67C2×D13—22no—
68C2×D13—41no—
69C2×D13—42no—
70C4×C13—21no—
71C4×C13—22no—
72C4×C13—41no—
73Dic13—41no—
74Dic13#10012yes—
75Dic13#13514yes—
76C2×#41—131no—
77C2×#41—131no—
78C4⋊Q8—131no—
79#127—131no—
80#124—131no—
81#124#26111yescharacteristic
82#121—262no—
83C4×D4—262no—
84C2×C42—131no—
85C4⋊C8—134no—
86C22⋊C8—262no—
87C4×C8—262no—
88C2×C13—81no—
89C2×C13C2×#10011yescharacteristic
90C2×C13#41612yes—
91D13—41no—
92D13—81no—
93#41—522no—
94#41—522no—
95C2×Q8—131no—
96C2×Q8C2×#26111yescharacteristic
97C2×D4—131no—
98C2×D4—261no—
99C2×D4—262no—
100C2×D4—261no—
101C2×D4C2×#26111yescharacteristic
102C22×C4—132no—
103C22×C4—131no—
104C22×C4—261no—
105C22×C4—261no—
106C2×C8—264no—
107C4⋊C4—262no—
108C22⋊C4—22no—
109C22⋊C4—262no—
110C42—132no—
111C42—131no—
112C42C2×#26111yescharacteristic
113C13#154311yescharacteristic, complemented, Sylow
114C23—21no—
115C23—131no—
116C23—261no—
117Q8—41no—
118Q8—521no—
119D4—41no—
120D4—521no—
121D4—522no—
122D4—524no—
123D4—522no—
124C2×C4—21no—
125C2×C4—132no—
126C2×C4—131no—
127C2×C4—264no—
128C2×C4—262no—
129C2×C4—261no—
130C2×C4—522no—
131C2×C4—522no—
132C2×C4C22⋊#26112yes—
133C2×C4C22×#26111yescharacteristic
134C8—524no—
135C22—41no—
136C22—42no—
137C22—261no—
138C22—262no—
139C22—521no—
140C22—522no—
141C22C2×C22⋊#26111yescharacteristic
142C4—21no—
143C4—22no—
144C4—41no—
145C4—132no—
146C4—134no—
147C4—521no—
148C2—81no—
149C2—521no—
150C2—1041no—
151C2D13⋊#10011yescharacteristic
152C2#1171916512yes—
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#124C4
socleC22×C13C2×C22⋊C4
prime radical#11719373C2
cosocleC4×Dic13C23
hypercenter#124#261
hypocenterC13#1543
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11719049C2semidirect
3. #11718303C2semidirect
4. #11718297C2semidirect
113. C13#1543semidirect

Maximal subgroups

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

subgroupindex
#117193732
#117190492
#117183032
#117182972
#154313