Finite Group Databasebeta

← #15783772

Subgroups — #15783772

Order 3328.

190 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×Dic208C211yesmaximal, characteristic, complemented
2#13116927C212yesmaximal
3#13113038C211yesmaximal, characteristic, complemented
4#13113018C212yesmaximal, complemented
5C2×C13×M64C211yesmaximal, characteristic
6C22×C13×C16C2211yescharacteristic
7#11718777—22no—
8C2×Dic104C2212yes—
9C13×M64—22no—
10C2×C13×C32C2211yescharacteristic
11C2×C13×C32C2211yescharacteristic
12#11718096C2212yes—
13#11718095—22no—
14Dic208—22no—
15C22×C8×C13D411yescharacteristic
16#88178—42no—
17C2×Dic52—22no—
18C2×C13×C16—21no—
19C2×C13×C16—21no—
20C2×C13×C16D411yescharacteristic
21C2×C13×C16C2311yescharacteristic
22#88058—22no—
23#88056—42no—
24Dic104—22no—
25Dic104—22no—
26C13×C32—21no—
27C13×C32D412yes—
28#13698—131nomaximal, Sylow
29C22×C4×C13D811yescharacteristic
30C2×Dic26—42no—
31C2×C8×C13—21no—
32C2×C8×C13—21no—
33C2×C8×C13D811yescharacteristic
34C2×C8×C13C2×D411yescharacteristic
35C22⋊Dic13—82no—
36C4⋊Dic13—42no—
37#6101—82no—
38Dic52—42no—
39Dic52—42no—
40C13×C16—21no—
41C13×C16C2×D411yescharacteristic
42C13×C16#4111yescharacteristic
43C2×Q64—131no—
44C2×M64D1311yescharacteristic
45#2216—132no—
46#1424—131no—
47#1416—132no—
48C23×C13D1611yescharacteristic
49C2×C4×C13—21no—
50C2×C4×C13—21no—
51C2×C4×C13D1611yescharacteristic
52C2×C4×C13C2×D811yescharacteristic
53C2×Dic13—82no—
54C2×Dic13—82no—
55Dic26—82no—
56Dic26—82no—
57C8×C13—21no—
58C8×C13#12111yescharacteristic
59C8×C13#13511yescharacteristic
60C2×Q32—132no—
61C22×C16C2×D1311yescharacteristic
62#467—262no—
63Q64—262no—
64M64—22no—
65C2×C32C2×D1311yescharacteristic
66C2×C32C2×D1311yescharacteristic
67#366—132no—
68#358—262no—
69C22×C13—21no—
70C22×C13—22no—
71C22×C13C2×D1611yescharacteristic
72C4×C13—21no—
73C4×C13#46611yescharacteristic
74C4×C13#50811yescharacteristic
75Dic13—162no—
76Dic13—162no—
77C2×Q16—262no—
78C22×C8D5211yescharacteristic
79C22⋊Q8—522no—
80Q32—262no—
81Q32—262no—
82C2×C16—21no—
83C2×C16—21no—
84C2×C16D5211yescharacteristic
85C2×C16C22×D1311yescharacteristic
86#107—262no—
87#103—522no—
88C32—21no—
89C32C22⋊D1312yes—
90C2×C13—41no—
91C2×C13#221511yescharacteristic
92C2×C13#226412yes—
93C2×Q8—522no—
94C22×C4D10411yescharacteristic
95Q16—522no—
96Q16—522no—
97C2×C8—21no—
98C2×C8—21no—
99C2×C8D10411yescharacteristic
100C2×C8C2×D5211yescharacteristic
101C4⋊C4—522no—
102C4⋊C4—1042no—
103C22⋊C4—1042no—
104C16—21no—
105C16#612711yescharacteristic
106C16C2×C22⋊D1311yescharacteristic
107C13#1369811yescharacteristic, complemented, Sylow
108C23D20811yescharacteristic
109Q8—1042no—
110Q8—1042no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—1042no—
114C2×C4—1042no—
115C2×C4D20811yescharacteristic
116C2×C4C2×D10411yescharacteristic
117C8—21no—
118C8#8815811yescharacteristic
119C8#8818411yescharacteristic
120C22—22no—
121C22—21no—
122C22C2×D20811yescharacteristic
123C4—21no—
124C4—2082no—
125C4—2082no—
126C4#1171856511yescharacteristic
127C4#1171877611yescharacteristic
128C2—41no—
129C2#1311692211yescharacteristic
130C2#1311715612yes—
subgroupG/H
centerC22C2×D208
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC2×C13×M64C2
socleC22×C13C2×D16
prime radicalC23×C13D16
hypercenterC2×M64D13
hypocenterC13#13698
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C2×M64

Complements

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

NH ≅ G/Ntype
1. C2×Dic208C2semidirect
3. #13113038C2semidirect
4. #13113018C2semidirect
107. C13#13698semidirect

Maximal subgroups

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

subgroupindex
C2×Dic2082
#131169272
#131130382
#131130182
C2×C13×M642
#1369813