Finite Group Databasebeta

← #16777832

Subgroups — #16777832

Order 3328.

110 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 52 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
1C4⋊#88036C211yesmaximal, characteristic
2#13129943C211yesmaximal, characteristic
3#13116745C211yesmaximal, characteristic
4C8×Q8×C13C411yescharacteristic
5C2×#88036—21no—
6C2×#88036—21no—
7C4⋊#6090—21no—
8C4⋊#6090C411yescharacteristic
9#11718053—21no—
10C4×#6090C2211yescharacteristic
11C4×Q8×C13C811yescharacteristic
12C13×C4⋊C8—21no—
13C13×C4⋊C8C811yescharacteristic
14C4×C8×C13—21no—
15C4×C8×C13C2×C411yescharacteristic
16C2×#6090—21no—
17C2×#6090D411yescharacteristic
18C2×#6090D411yescharacteristic
19#88036—22no—
20#88036—41no—
21#7393—131nomaximal, Sylow
22C2×Q8×C13C1611yescharacteristic
23C2×C8×C13—21no—
24C2×C8×C13C22⋊C411yescharacteristic
25C2×C8×C13M1611yescharacteristic
26C13×C4⋊C4—21no—
27C13×C4⋊C4C1611yescharacteristic
28C42×C13—21no—
29C42×C13C2×C811yescharacteristic
30#6090—21no—
31#6090—41no—
32#6090SD1611yescharacteristic
33#6090Q1611yescharacteristic
34#2183—131no—
35C4⋊C32—131no—
36#1397—131no—
37Q8×C13—41no—
38C2×C4×C13—21no—
39C2×C4×C13—21no—
40C2×C4×C13C22⋊C811yescharacteristic
41C2×C4×C13C2×C1611yescharacteristic
42C2×C4×C13M3211yescharacteristic
43C8×C13—21no—
44C8×C13—41no—
45C8×C13#10311yescharacteristic
46C8×C13#10411yescharacteristic
47C8×Q8#26111yescharacteristic
48C2×C32—261no—
49C2×C32—261no—
50C4⋊C16—131no—
51C4⋊C16—261no—
52#346—261no—
53C4×C16—131no—
54C22×C13C22⋊C1611yescharacteristic
55C4×C13—21no—
56C4×C13—21no—
57C4×C13—41no—
58C4×C13—41no—
59C4×C13Q8⋊C811yescharacteristic
60C4×C13#35011yescharacteristic
61C4×Q8#105711yescharacteristic
62C2×C16—131no—
63C2×C16—131no—
64C2×C16—261no—
65C4⋊C8—21no—
66C4⋊C8#105711yescharacteristic
67C4×C8—21no—
68C4×C8C2×#26111yescharacteristic
69C32—262no—
70C32—521no—
71C2×C13Q8⋊C1611yescharacteristic
72C2×C13#140011yescharacteristic
73C2×C13#140111yescharacteristic
74C2×Q8#609211yescharacteristic
75C2×C8—21no—
76C2×C8#612211yescharacteristic
77C2×C8C22⋊#26111yescharacteristic
78C4⋊C4—21no—
79C4⋊C4#609211yescharacteristic
80C42—21no—
81C42C2×#105711yescharacteristic
82C16—131no—
83C16—131no—
84C16—261no—
85C16—521no—
86C13#739311yescharacteristic, complemented, Sylow
87Q8—41no—
88C2×C4—21no—
89C2×C4—21no—
90C2×C4C2×#609211yescharacteristic
91C2×C4#8810611yescharacteristic
92C2×C4C22⋊#105711yescharacteristic
93C8—21no—
94C8—41no—
95C8#8811711yescharacteristic
96C8#8811811yescharacteristic
97C22C22⋊#609211yescharacteristic
98C4—21no—
99C4—21no—
100C4—41no—
101C4—41no—
102C4Q8⋊#105711yescharacteristic
103C4#1171830411yescharacteristic
104C2Q8⋊#609211yescharacteristic
105C2#1312995111yescharacteristic
106C2#1312995311yescharacteristic
subgroupG/H
centerC2×C8C22⋊#261
commutatorC2×C4×C13C2×C16
FrattiniC4×C8C2×#261
FittingC8×Q8×C13C4
socle, prime radicalC22×C13C22⋊C16
cosocleC4×#6090C22
hypercenterC8×Q8#261
hypocenterC13#7393
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
86. C13#7393semidirect

Maximal subgroups

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

subgroupindex
C4⋊#880362
#131299432
#131167452
#739313