Finite Group Databasebeta

← #15749552

Subgroups — #15749552

Order 3328.

188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 51 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#13112776C212yesmaximal
2C13×#1985C211yesmaximal, characteristic
3C2×C4×Q8×C13C411yescharacteristic
4C2×C13×C4⋊C8C2211yescharacteristic
5C2×C13×#97C411yescharacteristic
6C13×#336—22no—
7C22⋊#6090—22no—
8C22×Q8×C13C811yescharacteristic
9C22×C8×C13—21no—
10C22×C8×C13D412yes—
11C4×Q8×C13—41no—
12C4×Q8×C13—41no—
13C2×C13×C4⋊C4—21no—
14C2×C13×C4⋊C4C811yescharacteristic
15C2×C42×C13—21no—
16C2×C42×C13C2×C411yescharacteristic
17C13×C4⋊C8—41no—
18C13×#97—41no—
19C2×#6090—42no—
20#7061—131nomaximal, Sylow
21C2×Q8×C13—42no—
22C2×Q8×C13—41no—
23C22×C4×C13—21no—
24C22×C4×C13—21no—
25C22×C4×C13C22⋊C411yescharacteristic
26C22×C4×C13C2×C811yescharacteristic
27C22×C4×C13M1611yescharacteristic
28C2×C8×C13—22no—
29C2×C8×C13—22no—
30C2×C8×C13—41no—
31C2×C8×C13—41no—
32C2×C8×C13—42no—
33C13×C4⋊C4—41no—
34C13×C4⋊C4—42no—
35C42×C13—21no—
36C42×C13—21no—
37C42×C13—41no—
38C42×C13—41no—
39#6090—82no—
40#1985D1311yescharacteristic
41#1322—132no—
42C23×C13C22⋊C811yescharacteristic
43Q8×C13—42no—
44Q8×C13—42no—
45C2×C4×C13—21no—
46C2×C4×C13—21no—
47C2×C4×C13—22no—
48C2×C4×C13—21no—
49C2×C4×C13—21no—
50C2×C4×C13—22no—
51C2×C4×C13—41no—
52C2×C4×C13—41no—
53C2×C4×C13—41no—
54C2×C4×C13—41no—
55C2×C4×C13—42no—
56C2×C4×C13#9911yescharacteristic
57C2×C4×C13#10011yescharacteristic
58C8×C13—42no—
59C8×C13—42no—
60C2×C4×Q8Dic1311yescharacteristic
61C2×C4⋊C8C2×D1311yescharacteristic
62C2×#97Dic1311yescharacteristic
63C22⋊C16—262no—
64#336—22no—
65C22×C13—21no—
66C22×C13—21no—
67C22×C13#32311yescharacteristic
68C22×C13#35012yes—
69C4×C13—21no—
70C4×C13—41no—
71C4×C13—42no—
72C4×C13—41no—
73C4×C13—81no—
74C4×C13#35411yescharacteristic
75C4×C13#35611yescharacteristic
76C22×Q8#105511yescharacteristic
77C22×C8—21no—
78C22×C8C22⋊D1312yes—
79C4×Q8—41no—
80C4×Q8—41no—
81C2×C4⋊C4—21no—
82C2×C4⋊C4#105511yescharacteristic
83C2×C42—21no—
84C2×C42C2×Dic1311yescharacteristic
85C2×C16—522no—
86C4⋊C8—41no—
87#97—41no—
88C2×C13—22no—
89C2×C13#131511yescharacteristic
90C2×C13#131911yescharacteristic
91C2×C13#132011yescharacteristic
92C2×Q8—42no—
93C2×Q8—41no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4C2×#105511yescharacteristic
97C22×C4#609911yescharacteristic
98C22×C4C22⋊Dic1311yescharacteristic
99C2×C8—22no—
100C2×C8—22no—
101C2×C8—41no—
102C2×C8—41no—
103C2×C8—42no—
104C4⋊C4—41no—
105C4⋊C4—42no—
106C42—21no—
107C42—21no—
108C42—41no—
109C42—41no—
110C16—1042no—
111C13#706111yescharacteristic, complemented, Sylow
112C23C22⋊#105511yescharacteristic
113Q8—42no—
114Q8—42no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—42no—
125C2×C4—41no—
126C2×C4#8807311yescharacteristic
127C2×C4#8807411yescharacteristic
128C8—42no—
129C8—42no—
130C22—21no—
131C22—21no—
132C22#1171811711yescharacteristic
133C22#1171815312yes—
134C4—21no—
135C4—41no—
136C4—42no—
137C4—41no—
138C4—81no—
139C4#1171813311yescharacteristic
140C4#1171814011yescharacteristic
141C2—22no—
142C2#1311276211yescharacteristic
143C2#1311277011yescharacteristic
144C2#1311277211yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC22×C4×C13C2×C8
FrattiniC2×C4⋊C8C2×D13
FittingC13×#1985C2
socleC22×C13#323
prime radicalC23×C13C22⋊C8
cosocleC2×C13×C4⋊C8C22
hypercenter#1985D13
hypocenterC13#7061
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1985

Complements

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

NH ≅ G/Ntype
111. C13#7061semidirect

Maximal subgroups

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

subgroupindex
#131127762
C13×#19852
#706113