Finite Group Databasebeta

← #16777520

Subgroups — #16777520

Order 3328.

208 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 72 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
1D13⋊#364C211yesmaximal, characteristic
2#13130777C211yesmaximal, characteristic
3D13×#364C211yesmaximal, characteristic
4C2×#88104—21no—
5C2×#88104—21no—
6D13⋊M32—21no—
7#11719052C412yes—
8D13×M32—21no—
9C4×C8×D13C2211yescharacteristic
10#11718261—21no—
11#11718233C412yes—
12C13×#364C411yescharacteristic
13#11718103—21no—
14#11718055C411yescharacteristic
15C2×#6118—22no—
16C2×C8×D13D411yescharacteristic
17C2×C8×D13D411yescharacteristic
18C42×D13C2×C411yescharacteristic
19C4⋊#1057—42no—
20#88106—22no—
21#88104—41no—
22#88104—41no—
23#88104—41no—
24#88104—41no—
25#88098—41no—
26D13⋊C16—41no—
27C13×M32—21no—
28C4×C8×C13C2×C411yescharacteristic
29C8×Dic13D411yescharacteristic
30C8×Dic13Q811yescharacteristic
31#88052—21no—
32C4×#1055C2×C411yescharacteristic
33#88038—41no—
34C16×D13—41no—
35#7270—131nomaximal, Sylow
36C2×C4×D13—21no—
37C2×C4×D13C22⋊C411yescharacteristic
38C2×#1057—42no—
39#6118—42no—
40#6118—42no—
41C2×C8×C13C22⋊C411yescharacteristic
42C2×C8×C13C4⋊C411yescharacteristic
43C42×C13C4211yescharacteristic
44C4×Dic13—21no—
45C4×Dic13C4⋊C411yescharacteristic
46C2×#1055C22⋊C411yescharacteristic
47C2×#1055C4⋊C411yescharacteristic
48C8×D13D811yescharacteristic
49C8×D13D811yescharacteristic
50C8×D13SD1611yescharacteristic
51C8×D13SD1611yescharacteristic
52C8×D13SD1611yescharacteristic
53C8×D13SD1611yescharacteristic
54C8×D13Q1611yescharacteristic
55C8×D13Q1611yescharacteristic
56#6092—42no—
57C13×C16—41no—
58#6090—41no—
59C2×#364—131no—
60C2×#364—131no—
61#1848—131no—
62C22×D13#10111yescharacteristic
63C2×C4×C13—21no—
64C2×C4×C13#9511yescharacteristic
65C2×Dic13—21no—
66C2×Dic13#10011yescharacteristic
67C4×D13—42no—
68C4×D13#10211yescharacteristic
69C4×D13#10211yescharacteristic
70C4×D13#10311yescharacteristic
71C4×D13#10311yescharacteristic
72#1057—82no—
73C8×C13#10211yescharacteristic
74C8×C13#10311yescharacteristic
75C8×C13#10611yescharacteristic
76C8×C13#10711yescharacteristic
77#1055#10211yescharacteristic
78#1055#10311yescharacteristic
79#1055#10611yescharacteristic
80#1055#10711yescharacteristic
81C2×M32—261no—
82C2×M32—261no—
83C2×#108—261no—
84C2×#108—261no—
85#423—132no—
86C2×C4×C8—131no—
87#364—132no—
88#364—131no—
89#364—261no—
90#364—261no—
91#364#26111yescharacteristic
92C22×C13#34311yescharacteristic
93C2×D13—41no—
94C2×D13#33211yescharacteristic
95C2×D13#33211yescharacteristic
96C4×C13—22no—
97C4×C13#34011yescharacteristic
98C4×C13#34011yescharacteristic
99Dic13—41no—
100Dic13#33111yescharacteristic
101Dic13#33311yescharacteristic
102C2×M16—262no—
103C22×C8—131no—
104C22×C8—131no—
105C2×C42—131no—
106M32—21no—
107M32—262no—
108M32—261no—
109M32—521no—
110M32—521no—
111C2×C16—521no—
112C2×C16—521no—
113#108—521no—
114#108—521no—
115#108—521no—
116#108—521no—
117C4⋊C8—522no—
118C4×C8—131no—
119C4×C8—131no—
120C4×C8—131no—
121C4×C8C2×#26111yescharacteristic
122C2×C13—21no—
123C2×C13#129611yescharacteristic
124D13—21no—
125D13—21no—
126C22×C4—131no—
127C22×C4—261no—
128M16—522no—
129M16—522no—
130C2×C8—131no—
131C2×C8—131no—
132C2×C8—131no—
133C2×C8—131no—
134C2×C8—131no—
135C2×C8—131no—
136C2×C8—131no—
137C2×C8—131no—
138C2×C8—131no—
139C2×C8—131no—
140C2×C8—522no—
141C2×C8C4⋊#26111yescharacteristic
142C2×C8C22⋊#26111yescharacteristic
143C42—131no—
144C42—261no—
145C42C4×#26111yescharacteristic
146C16—41no—
147C16—522no—
148C16—521no—
149C13#727011yescharacteristic, complemented, Sylow
150C23—131no—
151C2×C4—21no—
152C2×C4—131no—
153C2×C4—131no—
154C2×C4—131no—
155C2×C4—131no—
156C2×C4—131no—
157C2×C4—261no—
158C2×C4—522no—
159C2×C4(C2×#261)⋊C411yescharacteristic
160C8—131no—
161C8—131no—
162C8—131no—
163C8—131no—
164C8—1042no—
165C8#8810111yescharacteristic
166C8#8810211yescharacteristic
167C8#8811511yescharacteristic
168C8#8811711yescharacteristic
169C22—131no—
170C22—131no—
171C22—521no—
172C22#1171827111yescharacteristic
173C4—22no—
174C4—131no—
175C4—131no—
176C4—521no—
177C4#1171824611yescharacteristic
178C4#1171826511yescharacteristic
179C2—21no—
180C2—261no—
181C2—261no—
182C2#1312971511yescharacteristic
subgroupG/H
centerC2#13129715
commutatorC42×C13C42
FrattiniC4×C8C2×#261
FittingC13×#364C4
socleC2×C13#1296
prime radicalC22×D13#101
cosocleC4×C8×D13C22
hypercenter#364#261
hypocenterC13#7270
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #364

Complements

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

NH ≅ G/Ntype
149. C13#7270semidirect

Maximal subgroups

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

subgroupindex
D13⋊#3642
#131307772
D13×#3642
#727013