Finite Group Databasebeta

← #13131137

Subgroups — #13131137

Order 1664.

262 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 54 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#11719230C211yesmaximal, characteristic
2#11719132C212yesmaximal, complemented
3#11718228C214yesmaximal, complemented
4C2×#6127C2211yescharacteristic
5C22×D52C411yescharacteristic
6D13⋊M16—22no—
7C13×#117C411yescharacteristic
8#88149—22no—
9#88136—22no—
10#88129C2212yes—
11#88128C412yes—
12#88121—22no—
13#88113C2214yescomplemented
14C23×D13—21no—
15C22×C4×C13C2×C411yescharacteristic
16C2×C22⋊D13D412yes—
17#6127—42no—
18C2×D52—21no—
19C2×D52—24no—
20C2×D52—42no—
21C2×D52C2×C412yes—
22C2×D52C2×C411yescharacteristic
23C2×C4×D13D412yes—
24C2×Dic26C2311yescharacteristic
25#6122—24no—
26#6118—42no—
27D13⋊C8—42no—
28C13×C4⋊C4—21no—
29C13×C22⋊C4—21no—
30C42×C13C2×C412yes—
31#6103—24no—
32#2134—131nomaximal, Sylow
33C23×C13C22⋊C411yescharacteristic
34C22×D13—22no—
35C22×D13—42no—
36C22×D13—82no—
37C22×D13C22⋊C412yes—
38C2×C4×C13—22no—
39C2×C4×C13—22no—
40C2×C4×C13C22⋊C411yescharacteristic
41C2×C4×C13C22×C411yescharacteristic
42C22⋊D13—42no—
43C2×Dic13C2×D412yes—
44D52—41no—
45D52—42no—
46D52—42no—
47D52—84no—
48C4×D13—22no—
49C4×D13—22no—
50Dic26—41no—
51#1057—44no—
52#535—131no—
53#413—132no—
54#355—134no—
55C22×C13—21no—
56C22×C13—41no—
57C22×C13C2×C22⋊C411yescharacteristic
58C2×D13—22no—
59C2×D13—42no—
60C2×D13—44no—
61C2×D13—42no—
62C2×D13—84no—
63C4×C13—21no—
64C4×C13—42no—
65C4×C13#9912yes—
66Dic13—22no—
67C2×#41—131no—
68C22×D4—131no—
69C2×M16—262no—
70#127—132no—
71#124—132no—
72#121—262no—
73#120—262no—
74#117#26111yescharacteristic
75#101—134no—
76#100—262no—
77C2×C13—21no—
78C2×C13—41no—
79C2×C13C2×#9911yescharacteristic
80D13—42no—
81D13—82no—
82C24—261no—
83#41—522no—
84C2×Q8—131no—
85C2×D4—132no—
86C2×D4—131no—
87C2×D4—132no—
88C2×D4—264no—
89C2×D4—261no—
90C2×D4—522no—
91C22×C4—132no—
92C22×C4C2×#26111yescharacteristic
93M16—264no—
94M16—522no—
95C2×C8—522no—
96C4⋊C4—21no—
97C22⋊C4—21no—
98C22⋊C4—264no—
99C42C2×#26112yes—
100C13#213411yescharacteristic, complemented, Sylow
101C23—132no—
102C23—262no—
103C23—522no—
104C23—1042no—
105C23C22⋊#26111yescharacteristic
106Q8—521no—
107D4—521no—
108D4—522no—
109D4—522no—
110D4—522no—
111D4—1044no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—132no—
115C2×C4—262no—
116C2×C4—262no—
117C2×C4C22⋊#26111yescharacteristic
118C2×C4C22×#26111yescharacteristic
119C8—524no—
120C22—21no—
121C22—41no—
122C22—262no—
123C22—522no—
124C22—524no—
125C22—522no—
126C22—1044no—
127C22C2×C22⋊#26111yescharacteristic
128C4—21no—
129C4—42no—
130C4—262no—
131C4#8810712yes—
132C2—21no—
133C2—41no—
134C2—522no—
135C2—1042no—
136C2C2×#8810711yescharacteristic
subgroupG/H
centerC2C2×#88107
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#117C4
socleC2×C13C2×#99
prime radical#11719230C2
cosocleC2×Dic26C23
hypercenter#117#261
hypocenterC13#2134
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #11719132C2semidirect
3. #11718228C2semidirect
13. #88113C22semidirect
100. C13#2134semidirect

Maximal subgroups

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

subgroupindex
#117192302
#117191322
#117182282
#213413