Finite Group Databasebeta

← #16777436

Subgroups — #16777436

Order 3328.

200 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 66 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#13131169C211yesmaximal, characteristic
2#13130395C211yesmaximal, characteristic
3#13113593C211yesmaximal, characteristic
4C2×#88098C412yes—
5#11719052—21no—
6#11718498—21no—
7C4×C8×D13C2211yescharacteristic
8#11718260—21no—
9#11718256—21no—
10#11718256C412yes—
11C4⋊#6092—21no—
12C13×#335C411yescharacteristic
13#11718071—21no—
14#11718050C411yescharacteristic
15C2×#6118—41no—
16C2×#6094—41no—
17C2×C8×D13C2×C411yescharacteristic
18C2×C8×D13Q811yescharacteristic
19C42×D13D411yescharacteristic
20C4⋊#1057—22no—
21C4⋊#1057—41no—
22C2×#6092—22no—
23#88098—42no—
24C13×C4⋊C8—21no—
25C4×C8×C13C2×C411yescharacteristic
26#88054—41no—
27C8×Dic13C2×C411yescharacteristic
28C8×Dic13D411yescharacteristic
29C4⋊#1055—21no—
30C4×#1055D411yescharacteristic
31#7245—131nomaximal, Sylow
32C2×C4×D13C4⋊C411yescharacteristic
33C2×C4×D13SD1611yescharacteristic
34C2×C4×D13SD1611yescharacteristic
35C2×#1057—42no—
36#6118—82no—
37C2×C8×C13—41no—
38C2×C8×C13C4211yescharacteristic
39C2×C8×C13C4⋊C411yescharacteristic
40C42×C13C22⋊C411yescharacteristic
41C4×Dic13C22⋊C411yescharacteristic
42C4×Dic13D811yescharacteristic
43C4×Dic13Q1611yescharacteristic
44C2×#1055—41no—
45C2×#1055C22⋊C411yescharacteristic
46C2×#1055C4⋊C411yescharacteristic
47#6094—82no—
48C8×D13—21no—
49C8×D13—21no—
50C8×D13—41no—
51#6092—42no—
52#2150—131no—
53#1567—131no—
54#1567—131no—
55C22×D13#10611yescharacteristic
56C2×C4×C13#9511yescharacteristic
57C2×C4×C13#10211yescharacteristic
58C2×C4×C13#10311yescharacteristic
59C2×Dic13#10211yescharacteristic
60C2×Dic13#10311yescharacteristic
61C2×Dic13#10711yescharacteristic
62C4×D13—21no—
63C4×D13—21no—
64C4×D13—21no—
65C4×D13—21no—
66C4×D13—21no—
67C4×D13—21no—
68#1057—82no—
69C8×C13—21no—
70C8×C13—21no—
71C8×C13—81no—
72#1055—21no—
73#1055—81no—
74#1055#10011yescharacteristic
75#1055#10111yescharacteristic
76C2×M32—132no—
77#423—261no—
78#423—261no—
79C2×C4×C8—131no—
80C4⋊C16—261no—
81C4⋊C16—261no—
82#335—132no—
83#335—131no—
84#335—261no—
85#335—261no—
86#335#26111yescharacteristic
87C22×C13#34011yescharacteristic
88C2×D13—21no—
89C2×D13—21no—
90C2×D13—21no—
91C4×C13—21no—
92C4×C13#33811yescharacteristic
93C4×C13#34311yescharacteristic
94C4×C13#36111yescharacteristic
95C4×C13#36211yescharacteristic
96Dic13—21no—
97Dic13—21no—
98Dic13#36111yescharacteristic
99Dic13#36211yescharacteristic
100C2×M16—521no—
101C2×M16—521no—
102C22×C8—131no—
103C22×C8—131no—
104C2×C42—131no—
105M32—522no—
106C2×C16—262no—
107C4⋊C8—21no—
108C4⋊C8—262no—
109C4⋊C8—261no—
110C4⋊C8—521no—
111C4⋊C8—521no—
112C4×C8—131no—
113C4×C8—131no—
114C4×C8—131no—
115C4×C8C2×#26111yescharacteristic
116C2×C13#129211yescharacteristic
117C2×C13#138711yescharacteristic
118C2×C13#138711yescharacteristic
119D13—41no—
120C22×C4—131no—
121C22×C4—131no—
122C22×C4—131no—
123M16—1042no—
124M16—1042no—
125C2×C8—41no—
126C2×C8—131no—
127C2×C8—131no—
128C2×C8—261no—
129C2×C8—261no—
130C2×C8—521no—
131C2×C8—522no—
132C2×C8—521no—
133C2×C8C4×#26111yescharacteristic
134C2×C8C4⋊#26111yescharacteristic
135C42—131no—
136C42—131no—
137C42—131no—
138C42C22⋊#26111yescharacteristic
139C16—522no—
140C13#724511yescharacteristic, complemented, Sylow
141C23—131no—
142C2×C4—131no—
143C2×C4—131no—
144C2×C4—131no—
145C2×C4—261no—
146C2×C4—261no—
147C2×C4—261no—
148C2×C4—261no—
149C2×C4—261no—
150C2×C4—261no—
151C2×C4(C2×#261)⋊C411yescharacteristic
152C2×C4#8811511yescharacteristic
153C2×C4#8811711yescharacteristic
154C8—21no—
155C8—21no—
156C8—81no—
157C8—131no—
158C8—131no—
159C8—261no—
160C8—1042no—
161C8—1041no—
162C22—261no—
163C22—261no—
164C22—261no—
165C22#1171824611yescharacteristic
166C4—21no—
167C4—131no—
168C4—131no—
169C4—261no—
170C4—261no—
171C4#1171826911yescharacteristic
172C4#1171827111yescharacteristic
173C4#1171827811yescharacteristic
174C4#1171828211yescharacteristic
175C2—521no—
176C2#1312970511yescharacteristic
177C2#1312991011yescharacteristic
178C2#1312991211yescharacteristic
subgroupG/H
centerC22#11718246
commutatorC2×C8×C13C42
FrattiniC4×C8C2×#261
FittingC13×#335C4
socleC22×C13#340
prime radicalC22×D13#106
cosocleC4×C8×D13C22
hypercenter#335#261
hypocenterC13#7245
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #335

Complements

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

NH ≅ G/Ntype
140. C13#7245semidirect

Maximal subgroups

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

subgroupindex
#131311692
#131303952
#131135932
#724513