Finite Group Databasebeta

← #16777610

Subgroups — #16777610

Order 3328.

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

normal subgroups only

This group has 212 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#13130390C211yesmaximal, characteristic
3#13114737C211yesmaximal, characteristic
4#11719129—21no—
5C2×#88062—21no—
6M16×Dic13—21no—
7C2×C8×Dic13C2211yescharacteristic
8C22⋊#6092—21no—
9#11718260C412yes—
10#11718258—21no—
11#11718255—21no—
12#11718253C412yes—
13C13×#341C411yescharacteristic
14#11718144C411yescharacteristic
15C2×#6122—41no—
16C2×C13×M16—21no—
17C22×C8×C13C2×C411yescharacteristic
18C2×C4×Dic13D411yescharacteristic
19C2×#6099—21no—
20C22×#1055D411yescharacteristic
21#88112—41no—
22C4⋊#1057—22no—
23C2×#6092—22no—
24#88062—24no—
25#88055—41no—
26C8×Dic13—41no—
27C8×Dic13C2×C411yescharacteristic
28C8×Dic13C2×C411yescharacteristic
29C8×Dic13D411yescharacteristic
30C8×Dic13Q811yescharacteristic
31#7300—131nomaximal, Sylow
32C22×C4×C13C22⋊C411yescharacteristic
33C22×Dic13SD1611yescharacteristic
34C22×Dic13Q1611yescharacteristic
35#6122—82no—
36C2×#1057—42no—
37C13×M16—22no—
38C13×M16—41no—
39C2×C8×C13—41no—
40C2×C8×C13—41no—
41C2×C8×C13C4211yescharacteristic
42C2×C8×C13C4⋊C411yescharacteristic
43C4×Dic13C22⋊C411yescharacteristic
44C4×Dic13C4⋊C411yescharacteristic
45C4×Dic13D811yescharacteristic
46C4×Dic13SD1611yescharacteristic
47#6099—22no—
48#6099—41no—
49C2×#1055—22no—
50C2×#1055—41no—
51C2×#1055C22⋊C411yescharacteristic
52C2×#1055C4⋊C411yescharacteristic
53#6092—42no—
54#2163—131no—
55C4×#108—131no—
56#1566—131no—
57C23×C13#10311yescharacteristic
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13#9511yescharacteristic
61C2×C4×C13#10211yescharacteristic
62C2×Dic13—22no—
63C2×Dic13—41no—
64C2×Dic13#10211yescharacteristic
65C2×Dic13#10311yescharacteristic
66C2×Dic13#10611yescharacteristic
67C2×Dic13#10711yescharacteristic
68#1057—82no—
69C8×C13—21no—
70C8×C13—21no—
71C8×C13—42no—
72#1055—21no—
73#1055—42no—
74#1055#10412yes—
75C2×#108—261no—
76#423—261no—
77C4×M16—261no—
78C2×C4×C8—131no—
79C4⋊C16—132no—
80C22⋊C16—261no—
81#346—261no—
82#341—131no—
83#341#26111yescharacteristic
84#334—132no—
85#334—261no—
86C22×C13—21no—
87C22×C13—21no—
88C22×C13—21no—
89C22×C13#34011yescharacteristic
90C4×C13—21no—
91C4×C13#33911yescharacteristic
92C4×C13#34411yescharacteristic
93Dic13—21no—
94Dic13—21no—
95Dic13—21no—
96Dic13#36512yes—
97C2×M16—21no—
98C2×M16—261no—
99C2×M16—521no—
100C22×C8—131no—
101C22×C8C2×#26111yescharacteristic
102C2×C42—131no—
103C2×C16—262no—
104#108—264no—
105C4⋊C8—262no—
106C4⋊C8—521no—
107#97—521no—
108C4×C8—131no—
109C4×C8—131no—
110C4×C8—131no—
111C4×C8—131no—
112C4×C8—521no—
113C2×C13—41no—
114C2×C13#130311yescharacteristic
115C2×C13#138311yescharacteristic
116C2×C13#138811yescharacteristic
117C22×C4—131no—
118C22×C4—131no—
119C22×C4C22⋊#26111yescharacteristic
120M16—22no—
121M16—41no—
122M16—262no—
123M16—521no—
124M16—1042no—
125C2×C8—41no—
126C2×C8—41no—
127C2×C8—131no—
128C2×C8—131no—
129C2×C8—262no—
130C2×C8—521no—
131C2×C8—522no—
132C2×C8C4×#26111yescharacteristic
133C2×C8C4⋊#26111yescharacteristic
134C42—131no—
135C42—131no—
136C42—131no—
137C42—131no—
138C16—522no—
139C13#730011yescharacteristic, complemented, Sylow
140C23#8811711yescharacteristic
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—131no—
144C2×C4—131no—
145C2×C4—131no—
146C2×C4—131no—
147C2×C4—262no—
148C2×C4—521no—
149C2×C4(C2×#261)⋊C411yescharacteristic
150C2×C4#8811511yescharacteristic
151C8—21no—
152C8—21no—
153C8—42no—
154C8—132no—
155C8—261no—
156C8—522no—
157C8—1042no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22#1171824611yescharacteristic
162C4—21no—
163C4—132no—
164C4—261no—
165C4—261no—
166C4—261no—
167C4#1171823411yescharacteristic
168C4#1171823911yescharacteristic
169C2—41no—
170C2#1312973411yescharacteristic
171C2#1312990211yescharacteristic
172C2#1312991311yescharacteristic
subgroupG/H
centerC22#11718246
commutatorC2×C8×C13C42
FrattiniC22×C8C2×#261
FittingC13×#341C4
socleC22×C13#340
prime radicalC23×C13#103
cosocleC2×C8×Dic13C22
hypercenter#341#261
hypocenterC13#7300
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
139. C13#7300semidirect

Maximal subgroups

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

subgroupindex
#131311982
#131303902
#131147372
#730013