Finite Group Databasebeta

← #13130749

Subgroups — #13130749

Order 1664.

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

normal subgroups only

This group has 272 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×#88121C212yesmaximal
3#11718239C214yesmaximal, complemented
4C22×C22⋊D13C2211yescharacteristic
5C2×#6122C2214yes—
6C2×C13×C22⋊C4C411yescharacteristic
7C2×C22⋊Dic13C411yescharacteristic
8C4×C22⋊D13—22no—
9#88135—22no—
10C22⋊C4×D13C412yes—
11#88131C2212yes—
12#88121—22no—
13#88121—22no—
14C24×C13C2×C411yescharacteristic
15C23×D13C2×C411yescharacteristic
16C22×C4×C13—21no—
17C2×C22⋊D13—24no—
18C2×C22⋊D13D412yes—
19C2×C22⋊D13D412yes—
20C22×Dic13—21no—
21C22×Dic13C2311yescharacteristic
22C2×C4×D13—22no—
23#6122—24no—
24#6122—24no—
25C2×#1057—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#1829—131nomaximal, Sylow
34C23×C13—22no—
35C23×C13—81no—
36C23×C13C22⋊C411yescharacteristic
37C23×C13C22⋊C411yescharacteristic
38C23×C13C22×C411yescharacteristic
39C22×D13—22no—
40C22×D13—81no—
41C22×D13C22⋊C412yes—
42C2×C4×C13—22no—
43C2×C4×C13—81no—
44C22⋊D13—24no—
45C22⋊D13—24no—
46C2×Dic13—22no—
47C2×Dic13—81no—
48C2×Dic13C2×D412yes—
49C2×Dic13#4114yes—
50C4×D13—82no—
51#1057—44no—
52#518—131no—
53C2×#100—132no—
54#344—134no—
55C22×C13—21no—
56C22×C13—21no—
57C22×C13—41no—
58C22×C13—41no—
59C22×C13—41no—
60C22×C13—82no—
61C22×C13C2×C22⋊C411yescharacteristic
62C22×C13#11712yes—
63C2×D13—22no—
64C2×D13—42no—
65C2×D13—82no—
66C4×C13—42no—
67Dic13—42no—
68Dic13#12314yes—
69C22×D4—131no—
70C2×M16—134no—
71C4×D4—262no—
72C4×D4—262no—
73#117—132no—
74C2×C22⋊C4—131no—
75C2×C22⋊C4—132no—
76C2×C22⋊C4#26111yescharacteristic
77#100—262no—
78#100—262no—
79C2×C13—21no—
80C2×C13—22no—
81C2×C13—41no—
82C2×C13—41no—
83C2×C13#38111yescharacteristic
84D13—42no—
85C24—131no—
86C24C2×#26111yescharacteristic
87C2×D4—132no—
88C2×D4—132no—
89C2×D4—264no—
90C22×C4—21no—
91C22×C4—131no—
92C22×C4—262no—
93C22×C4—261no—
94M16—264no—
95M16—264no—
96C2×C8—264no—
97C4⋊C4—262no—
98C22⋊C4—21no—
99C22⋊C4—132no—
100C22⋊C4—262no—
101C22⋊C4—261no—
102C22⋊C4C2×#26112yes—
103C42—262no—
104C13#182911yescharacteristic, complemented, Sylow
105C23—22no—
106C23—81no—
107C23—132no—
108C23—262no—
109C23—1041no—
110C23C22⋊#26111yescharacteristic
111C23C22⋊#26111yescharacteristic
112C23C22×#26111yescharacteristic
113D4—264no—
114D4—264no—
115C2×C4—22no—
116C2×C4—81no—
117C2×C4—134no—
118C2×C4—132no—
119C2×C4—262no—
120C2×C4—1042no—
121C2×C4—1041no—
122C8—524no—
123C22—21no—
124C22—21no—
125C22—41no—
126C22—41no—
127C22—41no—
128C22—82no—
129C22—262no—
130C22—522no—
131C22—1042no—
132C22#8823712yes—
133C22C2×C22⋊#26111yescharacteristic
134C4—42no—
135C4—134no—
136C4—522no—
137C2—21no—
138C2—22no—
139C2—41no—
140C2—41no—
141C2—522no—
142C2#1171913511yescharacteristic
subgroupG/H
centerC2#11719135
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C22⋊C4C4
socleC2×C13#381
prime radicalC22×C22⋊D13C22
cosocleC22×Dic13C23
hypercenterC2×C22⋊C4#261
hypocenterC13#1829
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. #11718239C2semidirect
104. C13#1829semidirect

Maximal subgroups

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

subgroupindex
#117191912
C2×#881212
#117182392
#182913