Finite Group Databasebeta

← #15750577

Subgroups — #15750577

Order 3328.

102 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 49 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#13117115C211yesmaximal, characteristic
2C4⋊#88034C211yesmaximal, characteristic
3C13×#1372C211yesmaximal, characteristic
4#11718344—21no—
5C4×C13×C16C2211yescharacteristic
6C13×#335—21no—
7#11718097—21no—
8#11718096C411yescharacteristic
9#11718096C411yescharacteristic
10C2×#88034—21no—
11#88124—41no—
12C2×C13×C16C2×C411yescharacteristic
13C2×C13×C16D411yescharacteristic
14C13×C4⋊C8—41no—
15C4×C8×C13D411yescharacteristic
16#88058—21no—
17#88058—21no—
18#88057—41no—
19#88034—41no—
20#7452—131nomaximal, Sylow
21C2×C8×C13—81no—
22C2×C8×C13C22⋊C411yescharacteristic
23C2×C8×C13SD1611yescharacteristic
24C42×C13D811yescharacteristic
25C4⋊Dic13—41no—
26C4⋊Dic13—41no—
27#6101—81no—
28#6101—81no—
29C13×C16—21no—
30C13×C16SD1611yescharacteristic
31C13×C16Q1611yescharacteristic
32#2253—131no—
33C4⋊C32—131no—
34#1372D1311yescharacteristic
35C2×C4×C13#10211yescharacteristic
36C2×C4×C13D1611yescharacteristic
37C2×C4×C13SD3211yescharacteristic
38C2×Dic13—81no—
39C2×Dic13—81no—
40C8×C13—21no—
41C8×C13—161no—
42C8×C13#10111yescharacteristic
43C8×C13#10311yescharacteristic
44#499—261no—
45C2×C32—261no—
46#367—261no—
47#366—131no—
48#366—131no—
49C4×C16C2×D1311yescharacteristic
50#335—21no—
51C22×C13#35711yescharacteristic
52C4×C13—21no—
53C4×C13—21no—
54C4×C13#33211yescharacteristic
55C4×C13#36211yescharacteristic
56Dic13—161no—
57Dic13—161no—
58#125—521no—
59C2×C16C4×D1311yescharacteristic
60C2×C16D5211yescharacteristic
61#107—261no—
62#107—261no—
63#106—521no—
64C4⋊C8—41no—
65C4×C8C22⋊D1311yescharacteristic
66C32—521no—
67C2×C13#136411yescharacteristic
68C2×C13#141711yescharacteristic
69C2×C13#141811yescharacteristic
70C2×C8—81no—
71C2×C8#610311yescharacteristic
72C2×C8#610611yescharacteristic
73C4⋊C4—521no—
74C4⋊C4—521no—
75C4⋊C4—1041no—
76C4⋊C4—1041no—
77C42#610411yescharacteristic
78C16—21no—
79C16#609511yescharacteristic
80C16Dic5211yescharacteristic
81C13#745211yescharacteristic, complemented, Sylow
82C2×C4—1041no—
83C2×C4—1041no—
84C2×C4#8804911yescharacteristic
85C2×C4#8806611yescharacteristic
86C2×C4#8806811yescharacteristic
87C8—21no—
88C8—161no—
89C8#8805611yescharacteristic
90C8#8806411yescharacteristic
91C22#1171808311yescharacteristic
92C4—21no—
93C4—21no—
94C4—2081no—
95C4—2081no—
96C4#1171807411yescharacteristic
97C4#1171808811yescharacteristic
98C2#1311289211yescharacteristic
99C2#1311301911yescharacteristic
100C2#1311302211yescharacteristic
subgroupG/H
centerC22#11718083
commutatorC2×C13×C16C2×C4
FrattiniC4×C16C2×D13
FittingC13×#1372C2
socle, prime radicalC22×C13#357
cosocleC4×C13×C16C22
hypercenter#1372D13
hypocenterC13#7452
LCSG ▷ C2×C13×C16 ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×C16 ◁ #1372

Complements

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

NH ≅ G/Ntype
81. C13#7452semidirect

Maximal subgroups

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

subgroupindex
#131171152
C4⋊#880342
C13×#13722
#745213