Finite Group Databasebeta

← #16778130

Subgroups — #16778130

Order 3328.

266 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 46 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#13131129C212yesmaximal
2#13115667C211yesmaximal, characteristic
3#11719182C2211yescharacteristic
4#11719132—22no—
5C13×#423C411yescharacteristic
6C2×#88065—22no—
7#11718593C411yescharacteristic
8#11718228C414yescomplemented
9#11718227—22no—
10C2×#6127D412yes—
11D13⋊M16—42no—
12C2×C13×M16—21no—
13C2×C42×C13C2×C411yescharacteristic
14#88184—41no—
15C2×C4×Dic13—21no—
16#88129C2×C412yes—
17#88128Q811yescharacteristic
18C4×D52—41no—
19#88123D411yescharacteristic
20#88121—42no—
21#88113—24no—
22C13×C4⋊C8—41no—
23#88071—41no—
24#88065—44no—
25#7507—131nomaximal, Sylow
26C22×C4×C13—21no—
27C22×C4×C13C22⋊C411yescharacteristic
28C2×C22⋊D13—22no—
29C22×Dic13—41no—
30#6127—42no—
31#6127—42no—
32C2×D52—41no—
33C2×D52C4⋊C412yes—
34C2×C4×D13—22no—
35C2×Dic26C22⋊C412yes—
36#6122—44no—
37#6118—82no—
38D13⋊C8—82no—
39C13×M16—42no—
40C2×C8×C13—41no—
41C42×C13—21no—
42C42×C13C4211yescharacteristic
43C42×C13C4⋊C411yescharacteristic
44#6103—42no—
45C4⋊Dic13—41no—
46C4×Dic13—22no—
47C4×Dic13—41no—
48#2132—132no—
49#1963—131no—
50C23×C13#9911yescharacteristic
51C22×D13—22no—
52C2×C4×C13—21no—
53C2×C4×C13—21no—
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—81no—
57C2×C4×C13#9511yescharacteristic
58C2×C4×C13#9911yescharacteristic
59C22⋊D13—82no—
60C2×Dic13—22no—
61C2×Dic13—42no—
62C2×Dic13—82no—
63D52—42no—
64D52—82no—
65C4×D13—42no—
66C4×D13—42no—
67Dic26—42no—
68#1057—84no—
69C8×C13—81no—
70#532—131no—
71#423#26111yescharacteristic
72C2×#104—262no—
73#413—262no—
74#376—131no—
75#356—262no—
76#355—134no—
77C22×C13—21no—
78C22×C13—41no—
79C22×C13#34211yescharacteristic
80C2×D13—42no—
81C2×D13—82no—
82C4×C13—21no—
83C4×C13—41no—
84C4×C13—41no—
85C4×C13#35311yescharacteristic
86C4×C13#35411yescharacteristic
87Dic13—42no—
88Dic13—82no—
89C2×#41—132no—
90C2×M16—21no—
91C2×M16—522no—
92C4⋊Q8—131no—
93#127—131no—
94#124—132no—
95#121—521no—
96C4×D4—521no—
97C2×C42—261no—
98C2×C42C2×#26111yescharacteristic
99C4⋊C8—41no—
100#104—524no—
101#101—264no—
102#100—522no—
103#95—521no—
104C2×C13—21no—
105C2×C13—41no—
106C2×C13#139311yescharacteristic
107D13—82no—
108#41—522no—
109#41—522no—
110C2×Q8—132no—
111C2×D4—132no—
112C2×D4—262no—
113C2×D4—521no—
114C22×C4—21no—
115C22×C4—262no—
116C22×C4—521no—
117C22×C4C22⋊#26111yescharacteristic
118M16—42no—
119M16—524no—
120M16—1042no—
121C2×C8—41no—
122C2×C8—1042no—
123C4⋊C4—521no—
124C22⋊C4—522no—
125C42—21no—
126C42—262no—
127C42—521no—
128C42C4×#26111yescharacteristic
129C42C4⋊#26111yescharacteristic
130C13#750711yescharacteristic, complemented, Sylow
131C23—262no—
132C23#8810711yescharacteristic
133Q8—522no—
134D4—522no—
135D4—1042no—
136D4—1042no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—81no—
142C2×C4—262no—
143C2×C4—522no—
144C2×C4—522no—
145C2×C4—522no—
146C2×C4—1042no—
147C2×C4(C2×#261)⋊C411yescharacteristic
148C2×C4#8811911yescharacteristic
149C8—81no—
150C8—1044no—
151C22—21no—
152C22—41no—
153C22—522no—
154C22—1042no—
155C22#1171828911yescharacteristic
156C4—21no—
157C4—41no—
158C4—41no—
159C4—522no—
160C4—1042no—
161C4#1171829411yescharacteristic
162C4#1171830011yescharacteristic
163C2—21no—
164C2—41no—
165C2—1042no—
166C2#1312993111yescharacteristic
subgroupG/H
centerC4#11718294
commutatorC42×C13C42
FrattiniC2×C42C2×#261
FittingC13×#423C4
socleC2×C13#1393
prime radical, cosocle#11719182C22
hypercenter#423#261
hypocenterC13#7507
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
8. #11718228C4semidirect
130. C13#7507semidirect

Maximal subgroups

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

subgroupindex
#131311292
#131156672
#750713