Finite Group Databasebeta

← #16777274

Subgroups — #16777274

Order 3328.

184 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 62 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#13131198C211yesmaximal, characteristic
2#13130049C211yesmaximal, characteristic
3#13116636C211yesmaximal, characteristic
4#11719119C411yescharacteristic
5#11719119C411yescharacteristic
6C2×C8×Dic13C2211yescharacteristic
7C22⋊#6092C412yes—
8#11718260—21no—
9#11718258—21no—
10#1057⋊C8—21no—
11#1057⋊C8—21no—
12C13×C22⋊C16C411yescharacteristic
13C22⋊#6090C411yescharacteristic
14#11718094—21no—
15#11718093—21no—
16C22×C8×C13C2×C411yescharacteristic
17C2×C4×Dic13C2×C411yescharacteristic
18C22×#1055C2×C411yescharacteristic
19C22⋊#1057C812yes—
20C22⋊#1057C812yes—
21C4⋊#1057—21no—
22C4⋊#1057—21no—
23C4×#1057—21no—
24C4×#1057—21no—
25C2×#6092—22no—
26C2×C13×C16—21no—
27C8×Dic13D411yescharacteristic
28C8×Dic13D411yescharacteristic
29C8×Dic13D411yescharacteristic
30C8×Dic13Q811yescharacteristic
31C2×#6090—21no—
32#7197—131nomaximal, Sylow
33C22×C4×C13C4211yescharacteristic
34C22×Dic13C2×C811yescharacteristic
35C22×Dic13C2×C811yescharacteristic
36C2×#1057—22no—
37C2×#1057—22no—
38C2×C8×C13—41no—
39C2×C8×C13C22⋊C411yescharacteristic
40C2×C8×C13C4⋊C411yescharacteristic
41C4×Dic13C22⋊C411yescharacteristic
42C4×Dic13C4⋊C411yescharacteristic
43C4×Dic13M1611yescharacteristic
44C4×Dic13M1611yescharacteristic
45C2×#1055—41no—
46C2×#1055C22⋊C411yescharacteristic
47C2×#1055C4⋊C411yescharacteristic
48#6092—42no—
49C13×C16—41no—
50#6090—41no—
51#2163—131no—
52#2163—131no—
53#1452—131no—
54C23×C13C4×C811yescharacteristic
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13#9511yescharacteristic
58C2×C4×C13#9711yescharacteristic
59C2×Dic13—41no—
60C2×Dic13—41no—
61C2×Dic13C22⋊C811yescharacteristic
62C2×Dic13C22⋊C811yescharacteristic
63C2×Dic13C4⋊C811yescharacteristic
64C2×Dic13C4⋊C811yescharacteristic
65#1057—42no—
66#1057—42no—
67C8×C13—21no—
68C8×C13—21no—
69#1055—21no—
70#1055—21no—
71#431—131no—
72#431—131no—
73C2×C4×C8—131no—
74C4⋊C16—261no—
75C4⋊C16—261no—
76C22⋊C16—132no—
77C22⋊C16—131no—
78C22⋊C16#26111yescharacteristic
79#346—261no—
80#346—261no—
81#322—261no—
82#322—261no—
83C22×C13—21no—
84C22×C13—21no—
85C22×C13—21no—
86C22×C13#33611yescharacteristic
87C4×C13—21no—
88C4×C13#34411yescharacteristic
89C4×C13#34411yescharacteristic
90Dic13—21no—
91Dic13—21no—
92Dic13—21no—
93Dic13—21no—
94C22×C8—131no—
95C22×C8C2×#26111yescharacteristic
96C2×C42—131no—
97C2×C16—21no—
98C2×C16—262no—
99C2×C16—261no—
100C4⋊C8—261no—
101C4⋊C8—261no—
102C22⋊C8—132no—
103C22⋊C8—132no—
104C4×C8—131no—
105C4×C8—131no—
106C4×C8—131no—
107C4×C8—131no—
108C4×C8—261no—
109C4×C8—261no—
110C2×C13—41no—
111C2×C13#128111yescharacteristic
112C2×C13#137811yescharacteristic
113C2×C13#137811yescharacteristic
114C22×C4—131no—
115C22×C4—131no—
116C22×C4C4×#26111yescharacteristic
117C2×C8—41no—
118C2×C8—131no—
119C2×C8—131no—
120C2×C8—262no—
121C2×C8—262no—
122C2×C8—521no—
123C2×C8C4⋊#26111yescharacteristic
124C2×C8C22⋊#26111yescharacteristic
125C42—131no—
126C42—131no—
127C42—131no—
128C42—131no—
129C16—41no—
130C16—521no—
131C16—522no—
132C13#719711yescharacteristic, complemented, Sylow
133C23C8×#26111yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—131no—
137C2×C4—131no—
138C2×C4—131no—
139C2×C4—131no—
140C2×C4—521no—
141C2×C4—521no—
142C2×C4#8810011yescharacteristic
143C2×C4(C2×#261)⋊C411yescharacteristic
144C8—21no—
145C8—21no—
146C8—261no—
147C8—261no—
148C8—522no—
149C8—522no—
150C22—21no—
151C22—21no—
152C22—21no—
153C22(C2×#261)⋊C811yescharacteristic
154C4—21no—
155C4—261no—
156C4—261no—
157C4—261no—
158C4—261no—
159C4#1171823911yescharacteristic
160C4#1171827411yescharacteristic
161C2—41no—
162C2#1312967511yescharacteristic
163C2#1312988511yescharacteristic
164C2#1312988811yescharacteristic
subgroupG/H
centerC2×C4(C2×#261)⋊C4
commutator, prime radicalC23×C13C4×C8
FrattiniC22×C8C2×#261
FittingC13×C22⋊C16C4
socleC22×C13#336
cosocleC2×C8×Dic13C22
hypercenterC22⋊C16#261
hypocenterC13#7197
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
132. C13#7197semidirect

Maximal subgroups

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

subgroupindex
#131311982
#131300492
#131166362
#719713