Finite Group Databasebeta

← #13130747

Subgroups — #13130747

Order 1664.

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

normal subgroups only

This group has 296 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
1#11719191C211yesmaximal, characteristic
2C2×#88119C212yesmaximal
3#11718238C214yesmaximal, complemented
4C22×C22⋊D13C2211yescharacteristic
5C2×C22⋊#261C2214yes—
6C2×C13×C22⋊C4C411yescharacteristic, complemented
7C2×C22⋊Dic13C411yescharacteristic, complemented
8C4×C22⋊D13—22no—
9#88135—22no—
10C22⋊C4×D13C2212yes—
11#88131C412yescomplemented
12#88119—22no—
13#88119—22no—
14C24×C13C2×C411yescharacteristic
15C23×D13C2311yescharacteristic
16C22×#261—24no—
17C22×C4×C13—21no—
18C2×C22⋊D13—24no—
19C2×C22⋊D13D412yes—
20C2×C22⋊D13D412yes—
21C22×Dic13—21no—
22C22×Dic13C2×C411yescharacteristic
23C2×C4×D13—22no—
24C22⋊#261—24no—
25C22⋊#261—24no—
26C13×C22⋊C4—21no—
27C13×C22⋊C4C2×C412yes—
28C22⋊Dic13—21no—
29C22⋊Dic13C2×C412yes—
30#6103—22no—
31#6101—22no—
32C4×Dic13—22no—
33#1828—131nomaximal, Sylow
34C23×C13—22no—
35C23×C13—81no—
36C23×C13C22⋊C411yescharacteristic
37C23×C13C22⋊C411yescharacteristic
38C23×C13C22×C411yescharacteristic
39C22×D13—81no—
40C22×D13C2×D412yes—
41C22×D13#4114yes—
42C2×#261—44no—
43C2×#261—84no—
44C2×C4×C13—22no—
45C2×C4×C13—81no—
46C22⋊D13—24no—
47C22⋊D13—24no—
48C2×Dic13—22no—
49C2×Dic13—22no—
50C2×Dic13—81no—
51C2×Dic13C22⋊C412yes—
52C4×D13—82no—
53#518—131no—
54C2×#99—132no—
55#342—134no—
56C22×C13—21no—
57C22×C13—21no—
58C22×C13—41no—
59C22×C13—41no—
60C22×C13—41no—
61C22×C13—82no—
62C22×C13C2×C22⋊C411yescharacteristic
63C22×C13#11712yes—
64C2×D13—42no—
65C2×D13—44no—
66C2×D13#12314yes—
67#261—84no—
68C4×C13—42no—
69Dic13—22no—
70Dic13—42no—
71C22×D4—131no—
72C4×D4—262no—
73C4×D4—262no—
74#117—132no—
75C2×C22⋊C4—131no—
76C2×C22⋊C4—132no—
77C2×C22⋊C4—134no—
78C2×C22⋊C4#26111yescharacteristic, complemented
79#99—262no—
80#99—262no—
81C2×C13—21no—
82C2×C13—22no—
83C2×C13—41no—
84C2×C13—41no—
85C2×C13#38111yescharacteristic
86D13—24no—
87C24—131no—
88C24C2×#26111yescharacteristic
89C2×D4—132no—
90C2×D4—132no—
91C2×D4—264no—
92C22×C4—21no—
93C22×C4—131no—
94C22×C4—262no—
95C22×C4—261no—
96C22×C4—264no—
97C4⋊C4—262no—
98C22⋊C4—21no—
99C22⋊C4—132no—
100C22⋊C4—262no—
101C22⋊C4—261no—
102C22⋊C4—264no—
103C22⋊C4—264no—
104C22⋊C4C2×#26112yes—
105C42—262no—
106C13#182811yescharacteristic, complemented, Sylow
107C23—22no—
108C23—81no—
109C23—134no—
110C23—132no—
111C23—1041no—
112C23C22⋊#26111yescharacteristic
113C23C22⋊#26111yescharacteristic
114C23C22×#26111yescharacteristic
115D4—264no—
116D4—264no—
117C2×C4—22no—
118C2×C4—81no—
119C2×C4—132no—
120C2×C4—262no—
121C2×C4—262no—
122C2×C4—524no—
123C2×C4—1042no—
124C2×C4—1041no—
125C2×C4—1044no—
126C22—21no—
127C22—21no—
128C22—41no—
129C22—41no—
130C22—41no—
131C22—82no—
132C22—134no—
133C22—522no—
134C22—524no—
135C22#8823712yes—
136C22C2×C22⋊#26111yescharacteristic
137C4—42no—
138C4—262no—
139C4—522no—
140C4—1044no—
141C2—21no—
142C2—22no—
143C2—41no—
144C2—41no—
145C2—264no—
146C2#1171913511yescharacteristic
subgroupG/H
centerC2#11719135
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C22⋊C4C4
socleC2×C13#381
prime radicalC22×C22⋊D13C22
cosocleC23×D13C23
hypercenterC2×C22⋊C4#261
hypocenterC13#1828
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #11718238C2semidirect
6. C2×C13×C22⋊C4C4semidirect
7. C2×C22⋊Dic13C4semidirect
11. #88131C4semidirect
78. C2×C22⋊C4#261semidirect
106. C13#1828semidirect

Maximal subgroups

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

subgroupindex
#117191912
C2×#881192
#117182382
#182813