Finite Group Databasebeta

← #16776997

Subgroups — #16776997

Order 3328.

130 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 42 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#13129859C211yesmaximal, characteristic
2#13129859C211yesmaximal, characteristic
3#13114445C211yesmaximal, characteristic
4C13×#500C411yescharacteristic
5#11718754—21no—
6#11718742—21no—
7#11718343C411yescharacteristic
8C4⋊#6092—21no—
9C4⋊#6092—21no—
10C8×#1055C2211yescharacteristic
11C13×C4⋊Q8—21no—
12#88123—21no—
13C2×#6092—41no—
14C2×#6092—41no—
15C13×#107—41no—
16C4×C8×C13C2×C411yescharacteristic
17#88075—41no—
18#88075—41no—
19#88058—41no—
20#88050—41no—
21#88050—41no—
22C4×#1055D411yescharacteristic
23C4×#1055D411yescharacteristic
24#7093—131nomaximal, Sylow
25C2×Q8×C13—41no—
26C2×Dic26—41no—
27C2×C8×C13—21no—
28C13×C4⋊C4—41no—
29C13×C4⋊C4—41no—
30C42×C13C22⋊C411yescharacteristic
31C4⋊Dic13—41no—
32C4⋊Dic13—41no—
33C2×#1055D811yescharacteristic
34C2×#1055D811yescharacteristic
35C2×#1055SD1611yescharacteristic
36C2×#1055SD1611yescharacteristic
37#6092—81no—
38#6092—81no—
39#1710—131no—
40#1367—131no—
41#1367—131no—
42Q8×C13—81no—
43Q8×C13—81no—
44C2×C4×C13—81no—
45C2×C4×C13#10011yescharacteristic
46C2×C4×C13#10211yescharacteristic
47C2×C4×C13#10211yescharacteristic
48C2×Dic13—81no—
49Dic26—81no—
50Dic26—81no—
51C8×C13—22no—
52#1055—21no—
53#1055—21no—
54#1055—21no—
55#1055—21no—
56#500—131no—
57#500#26111yescharacteristic
58#487—261no—
59#487—261no—
60C4⋊C16—261no—
61C4⋊C16—261no—
62C82—131no—
63C22×C13#33111yescharacteristic
64C4×C13—21no—
65C4×C13—161no—
66C4×C13#35911yescharacteristic
67C4×C13#35911yescharacteristic
68C4×C13#36011yescharacteristic
69C4×C13#36011yescharacteristic
70Dic13—161no—
71C4⋊Q8—21no—
72C4⋊Q8—261no—
73C2×C16—521no—
74C2×C16—521no—
75#107—41no—
76#107—521no—
77#103—521no—
78#103—521no—
79#103—521no—
80#103—521no—
81C4×C8—131no—
82C4×C8—131no—
83C4×C8C2×#26111yescharacteristic
84C2×C13#135811yescharacteristic
85C2×C13#136011yescharacteristic
86C2×C13#136011yescharacteristic
87C2×Q8—41no—
88C2×Q8—521no—
89C2×C8—21no—
90C2×C8—131no—
91C2×C8—131no—
92C2×C8—131no—
93C2×C8—131no—
94C4⋊C4—41no—
95C4⋊C4—41no—
96C4⋊C4—521no—
97C4⋊C4—521no—
98C42C22⋊#26111yescharacteristic
99C16—1041no—
100C16—1041no—
101C13#709311yescharacteristic, complemented, Sylow
102Q8—81no—
103Q8—81no—
104Q8—1041no—
105Q8—1041no—
106C2×C4—81no—
107C2×C4—1041no—
108C2×C4#8811511yescharacteristic
109C2×C4#8811511yescharacteristic
110C2×C4#8812111yescharacteristic
111C8—22no—
112C8—261no—
113C8—261no—
114C8—261no—
115C8—261no—
116C22#1171829711yescharacteristic
117C4—21no—
118C4—161no—
119C4—2081no—
120C4#1171827511yescharacteristic
121C4#1171827711yescharacteristic
122C4#1171827911yescharacteristic
123C4#1171828111yescharacteristic
124C2#1312984511yescharacteristic
125C2#1312984811yescharacteristic
126C2#1312984911yescharacteristic
subgroupG/H
centerC22#11718297
commutatorC4×C8×C13C2×C4
FrattiniC4×C8C2×#261
FittingC13×#500C4
socle, prime radicalC22×C13#331
cosocleC8×#1055C22
hypercenter#500#261
hypocenterC13#7093
LCSG ▷ C4×C8×C13 ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
101. C13#7093semidirect

Maximal subgroups

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

subgroupindex
#131298592
#131144452
#709313