Finite Group Databasebeta

← #16778109

Subgroups — #16778109

Order 3328.

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

normal subgroups only

This group has 286 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#13115664C211yesmaximal, characteristic
3#11719182C2211yescharacteristic
4#11719132—22no—
5C43×C13C411yescharacteristic
6C2×#88045—22no—
7#11718585C411yescharacteristic
8#11718228C414yescomplemented
9#11718227—22no—
10C2×#6127D412yes—
11D13⋊M16—42no—
12C2×C42×C13—21no—
13C2×C42×C13—41no—
14C2×C42×C13C2×C411yescharacteristic
15#88184—41no—
16C2×#6099—21no—
17#88129C2×C412yes—
18#88128Q811yescharacteristic
19C4×D52—41no—
20#88123D411yescharacteristic
21#88121—42no—
22#88113—24no—
23#88045—44no—
24C4⋊#1055—41no—
25#7501—131nomaximal, Sylow
26C22×C4×C13—21no—
27C22×C4×C13—41no—
28C22×C4×C13C22⋊C411yescharacteristic
29C2×C22⋊D13—22no—
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—
39C42×C13—21no—
40C42×C13—22no—
41C42×C13—41no—
42C42×C13—44no—
43C42×C13C4211yescharacteristic
44C42×C13C4⋊C411yescharacteristic
45#6103—42no—
46C4⋊Dic13—41no—
47#6099—42no—
48C2×#1055—41no—
49#2132—132no—
50#1962—131no—
51C23×C13#9911yescharacteristic
52C22×D13—22no—
53C2×C4×C13—21no—
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—42no—
58C2×C4×C13—42no—
59C2×C4×C13—44no—
60C2×C4×C13#9511yescharacteristic
61C2×C4×C13#9911yescharacteristic
62C22⋊D13—82no—
63C2×Dic13—22no—
64D52—42no—
65D52—82no—
66C4×D13—42no—
67C4×D13—42no—
68Dic26—42no—
69#1057—84no—
70#1055—81no—
71#532—131no—
72#423—131no—
73C2×#104—262no—
74#413—262no—
75C43#26111yescharacteristic
76#356—262no—
77#355—134no—
78C22×C13—21no—
79C22×C13—41no—
80C22×C13#34211yescharacteristic
81C2×D13—42no—
82C2×D13—82no—
83C4×C13—22no—
84C4×C13—21no—
85C4×C13—41no—
86C4×C13—44no—
87C4×C13#35311yescharacteristic
88C4×C13#35411yescharacteristic
89Dic13—42no—
90C2×#41—132no—
91C2×M16—261no—
92C2×M16—522no—
93C4⋊Q8—131no—
94#127—131no—
95#124—132no—
96#121—521no—
97C4×D4—521no—
98C2×C42—21no—
99C2×C42—41no—
100C2×C42C2×#26111yescharacteristic
101C4⋊C8—521no—
102#104—524no—
103#101—264no—
104#100—522no—
105C2×C13—21no—
106C2×C13—41no—
107C2×C13#139311yescharacteristic
108D13—82no—
109#41—522no—
110#41—522no—
111C2×Q8—132no—
112C2×D4—132no—
113C2×D4—262no—
114C2×D4—521no—
115C22×C4—21no—
116C22×C4—41no—
117C22×C4—262no—
118C22×C4C22⋊#26111yescharacteristic
119M16—522no—
120M16—524no—
121M16—1042no—
122C2×C8—521no—
123C2×C8—1042no—
124C4⋊C4—521no—
125C22⋊C4—522no—
126C42—21no—
127C42—22no—
128C42—41no—
129C42—44no—
130C42C4×#26111yescharacteristic
131C42C4⋊#26111yescharacteristic
132C13#750111yescharacteristic, complemented, Sylow
133C23—262no—
134C23#8811911yescharacteristic
135Q8—522no—
136D4—522no—
137D4—1042no—
138D4—1042no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—44no—
146C2×C4—262no—
147C2×C4—522no—
148C2×C4—522no—
149C2×C4#8810711yescharacteristic
150C2×C4(C2×#261)⋊C411yescharacteristic
151C8—1044no—
152C8—1041no—
153C22—21no—
154C22—41no—
155C22—522no—
156C22—1042no—
157C22#1171828911yescharacteristic
158C4—22no—
159C4—21no—
160C4—41no—
161C4—44no—
162C4—522no—
163C4#1171822511yescharacteristic
164C4#1171822611yescharacteristic
165C2—21no—
166C2—41no—
167C2—1042no—
168C2#1312993011yescharacteristic
subgroupG/H
centerC4#11718226
commutatorC42×C13C42
FrattiniC2×C42C2×#261
FittingC43×C13C4
socleC2×C13#1393
prime radical, cosocle#11719182C22
hypercenterC43#261
hypocenterC13#7501
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
8. #11718228C4semidirect
132. C13#7501semidirect

Maximal subgroups

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

subgroupindex
#131311292
#131156642
#750113