Finite Group Databasebeta

← #15750620

Subgroups — #15750620

Order 3328.

190 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 111 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×#11718096C212yesmaximal
2C22×C13×C32C211yesmaximal, characteristic
3C22×C13×C16C2211yescharacteristic
4C2×#88058—22no—
5C2×C13×C32—22no—
6C2×C13×C32C412yescomplemented
7#11718096—22no—
8#11718096C414yescomplemented
9C22×C8×C13D411yescharacteristic
10C2×C4⋊Dic13—42no—
11C2×C13×C16C2×C412yes—
12C2×C13×C16C2×C411yescharacteristic
13C2×C13×C16D412yes—
14C2×C13×C16Q811yescharacteristic
15#88058—24no—
16#88058—42no—
17C13×C32—22no—
18#7471—131nomaximal, Sylow
19C22×C4×C13D811yescharacteristic
20C22×Dic13—82no—
21C2×C8×C13C22⋊C412yes—
22C2×C8×C13C4⋊C411yescharacteristic
23C2×C8×C13SD1612yes—
24C2×C8×C13Q1611yescharacteristic
25C4⋊Dic13—44no—
26C4⋊Dic13—82no—
27C13×C16C4211yescharacteristic
28C13×C16C22⋊C411yescharacteristic
29C13×C16C4⋊C412yes—
30C22×C32D1311yescharacteristic
31C2×#366—132no—
32C23×C13D1611yescharacteristic
33C2×C4×C13#10212yes—
34C2×C4×C13#10711yescharacteristic
35C2×C4×C13SD3212yes—
36C2×C4×C13Q3211yescharacteristic
37C2×Dic13—84no—
38C2×Dic13—162no—
39C2×Dic13—162no—
40C8×C13#9511yescharacteristic
41C8×C13#10312yes—
42C8×C13#10611yescharacteristic
43C22×C16C2×D1311yescharacteristic
44C2×#107—262no—
45C2×C32—22no—
46C2×C32Dic1312yescomplemented
47#366—134no—
48#366—262no—
49C22×C13#35712yes—
50C22×C13#36611yescharacteristic
51C22×C13D3211yescharacteristic
52C22×C13SD6412yes—
53C22×C13Q6411yescharacteristic
54C4×C13#34011yescharacteristic
55C4×C13#35812yes—
56C4×C13#36711yescharacteristic
57Dic13—164no—
58C22×C8D5211yescharacteristic
59C2×C4⋊C4—522no—
60C2×C16Dic2611yescharacteristic
61C2×C16C4×D1312yes—
62C2×C16C2×Dic1311yescharacteristic
63C2×C16C22⋊D1312yes—
64#107—264no—
65#107—522no—
66C32—22no—
67C2×C13#138011yescharacteristic
68C2×C13#141512yes—
69C2×C13#141612yes—
70C2×C13#142311yescharacteristic
71C2×C13#142411yescharacteristic
72C22×C4—1042no—
73C22×C4D10411yescharacteristic
74C2×C8#609512yes—
75C2×C8Dic5211yescharacteristic
76C2×C8C4⋊Dic1311yescharacteristic
77C2×C8#610312yes—
78C4⋊C4—524no—
79C4⋊C4—1042no—
80C16C4×Dic1311yescharacteristic
81C16#610112yes—
82C16C22⋊Dic1311yescharacteristic
83C13#747111yescharacteristic, complemented, Sylow
84C23D20811yescharacteristic
85C2×C4—1044no—
86C2×C4—2082no—
87C2×C4—2082no—
88C2×C4#8804012yes—
89C2×C4Dic10411yescharacteristic
90C2×C4#8805811yescharacteristic
91C2×C4#8806112yes—
92C8#8805612yes—
93C8#8805711yescharacteristic
94C8#8807111yescharacteristic
95C22D41611yescharacteristic
96C22#1171804112yes—
97C22Dic20811yescharacteristic
98C22#1171809611yescharacteristic
99C22#1171810112yes—
100C4—2084no—
101C4#1171809512yes—
102C4#1171809711yescharacteristic
103C4#1171814311yescharacteristic
104C2#1311292811yescharacteristic
105C2#1311301512yes—
106C2#1311301812yes—
107C2#1311303611yescharacteristic
108C2#1311303811yescharacteristic
subgroupG/H
centerC23D208
commutatorC13×C16C42
FrattiniC22×C16C2×D13
FittingC22×C13×C32C2
socle, prime radicalC23×C13D16
cosocleC22×C13×C16C22
hypercenterC22×C32D13
hypocenterC13#7471
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C22×C32

Complements

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

NH ≅ G/Ntype
6. C2×C13×C32C4semidirect
8. #11718096C4semidirect
46. C2×C32Dic13semidirect
83. C13#7471semidirect

Maximal subgroups

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

subgroupindex
C2×#117180962
C22×C13×C322
#747113