Finite Group Databasebeta

← #16777132

Subgroups — #16777132

Order 3328.

218 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 82 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⋊(C4⋊C16)C211yesmaximal, characteristic
2#13130040C211yesmaximal, characteristic
3#13116590C211yesmaximal, characteristic
4C2×D13⋊C16—21no—
5#11719049C411yescharacteristic
6#11719049C411yescharacteristic
7C2×#88038—21no—
8C4×C8×D13C2211yescharacteristic
9#11718260—21no—
10#11718251—21no—
11C8×#1057—21no—
12C4⋊#6092C412yes—
13C13×C4⋊C16C411yescharacteristic
14#11718093—21no—
15C4⋊#6090C411yescharacteristic
16C2×C8×D13D411yescharacteristic
17C2×C8×D13Q811yescharacteristic
18C42×D13C2×C411yescharacteristic
19#88112—21no—
20#88112C812yes—
21#88111—21no—
22#88111C812yes—
23C4×#1057—21no—
24C4×#1057—21no—
25C2×#6092—22no—
26D13⋊C16—41no—
27D13⋊C16—41no—
28C2×C13×C16—21no—
29C4×C8×C13C2×C411yescharacteristic
30C8×Dic13D411yescharacteristic
31C8×Dic13D411yescharacteristic
32C2×#6090—21no—
33C4×#1055C2×C411yescharacteristic
34#88038—41no—
35#88038—41no—
36#7153—131nomaximal, Sylow
37C2×C4×D13C4⋊C411yescharacteristic
38C2×C4×D13C2×C811yescharacteristic
39C2×C4×D13M1611yescharacteristic
40C2×#1057—22no—
41C2×#1057—22no—
42C2×C8×C13C22⋊C411yescharacteristic
43C2×C8×C13C4⋊C411yescharacteristic
44C42×C13C4211yescharacteristic
45C4×Dic13C22⋊C411yescharacteristic
46C4×Dic13C2×C811yescharacteristic
47C4×Dic13M1611yescharacteristic
48C2×#1055C22⋊C411yescharacteristic
49C2×#1055C4⋊C411yescharacteristic
50C8×D13—21no—
51C8×D13—21no—
52C8×D13D811yescharacteristic
53C8×D13SD1611yescharacteristic
54C8×D13SD1611yescharacteristic
55C8×D13Q1611yescharacteristic
56#6092—42no—
57C13×C16—41no—
58#6090—41no—
59#2150—131no—
60C2×C4⋊C16—131no—
61#1450—131no—
62C22×D13C4⋊C811yescharacteristic
63C2×C4×C13#9511yescharacteristic
64C2×C4×C13C4×C811yescharacteristic
65C2×C4×C13#9711yescharacteristic
66C2×Dic13C22⋊C811yescharacteristic
67C2×Dic13C22⋊C811yescharacteristic
68C2×Dic13C4⋊C811yescharacteristic
69C4×D13—22no—
70C4×D13—41no—
71C4×D13#10611yescharacteristic
72C4×D13#10711yescharacteristic
73C4×D13#10811yescharacteristic
74C4×D13#10811yescharacteristic
75#1057—42no—
76#1057—42no—
77C8×C13—21no—
78C8×C13#10211yescharacteristic
79C8×C13#10311yescharacteristic
80#1055—21no—
81#1055#10211yescharacteristic
82#1055#10311yescharacteristic
83C2×M32—261no—
84C22×C16—261no—
85#431—131no—
86#431—131no—
87C2×C4×C8—131no—
88C4⋊C16—132no—
89C4⋊C16—131no—
90C4⋊C16—261no—
91C4⋊C16—261no—
92C4⋊C16#26111yescharacteristic
93#322—261no—
94C82—261no—
95C22×C13#33611yescharacteristic
96C2×D13—21no—
97C2×D13—21no—
98C2×D13#33411yescharacteristic
99C2×D13#33511yescharacteristic
100C4×C13—21no—
101C4×C13—21no—
102C4×C13#34011yescharacteristic
103C4×C13#34111yescharacteristic
104Dic13—21no—
105Dic13#33411yescharacteristic
106Dic13#33511yescharacteristic
107Dic13#35012yes—
108C22×C8—131no—
109C22×C8—131no—
110C2×C42—131no—
111M32—521no—
112M32—521no—
113C2×C16—21no—
114C2×C16—262no—
115C2×C16—261no—
116C2×C16—521no—
117C2×C16—521no—
118C4⋊C8—132no—
119C4⋊C8—261no—
120C22⋊C8—132no—
121C22⋊C8—261no—
122C4×C8—131no—
123C4×C8—131no—
124C4×C8—131no—
125C4×C8—261no—
126C4×C8—261no—
127C4×C8C2×#26111yescharacteristic
128C2×C13#127711yescharacteristic
129C2×C13#137811yescharacteristic
130C2×C13#137911yescharacteristic
131D13—21no—
132D13—21no—
133C22×C4—131no—
134C22×C4—131no—
135C22×C4—131no—
136C2×C8—131no—
137C2×C8—131no—
138C2×C8—131no—
139C2×C8—131no—
140C2×C8—131no—
141C2×C8—131no—
142C2×C8—261no—
143C2×C8—261no—
144C2×C8—262no—
145C2×C8—262no—
146C2×C8C4⋊#26111yescharacteristic
147C2×C8C22⋊#26111yescharacteristic
148C42—131no—
149C42—131no—
150C42—131no—
151C42C4×#26111yescharacteristic
152C16—41no—
153C16—522no—
154C16—521no—
155C13#715311yescharacteristic, complemented, Sylow
156C23—131no—
157C2×C4—131no—
158C2×C4—131no—
159C2×C4—131no—
160C2×C4—131no—
161C2×C4—131no—
162C2×C4—131no—
163C2×C4—131no—
164C2×C4—262no—
165C2×C4—521no—
166C2×C4C8×#26111yescharacteristic
167C2×C4#8810011yescharacteristic
168C2×C4(C2×#261)⋊C411yescharacteristic
169C8—21no—
170C8—131no—
171C8—131no—
172C8—261no—
173C8—522no—
174C8—522no—
175C8#8811511yescharacteristic
176C8#8811711yescharacteristic
177C22—131no—
178C22—131no—
179C22—261no—
180C22—261no—
181C22(C2×#261)⋊C811yescharacteristic
182C4—21no—
183C4—21no—
184C4—132no—
185C4—131no—
186C4—131no—
187C4—261no—
188C4#1171824611yescharacteristic
189C4#1171827311yescharacteristic
190C2—261no—
191C2—261no—
192C2#1312966511yescharacteristic
193C2#1312988511yescharacteristic
194C2#1312989211yescharacteristic
subgroupG/H
centerC2×C8C22⋊#261
commutatorC2×C4×C13C4×C8
FrattiniC4×C8C2×#261
FittingC13×C4⋊C16C4
socleC22×C13#336
prime radicalC22×D13C4⋊C8
cosocleC4×C8×D13C22
hypercenterC4⋊C16#261
hypocenterC13#7153
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C4⋊C16

Complements

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

NH ≅ G/Ntype
155. C13#7153semidirect

Maximal subgroups

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

subgroupindex
D13⋊(C4⋊C16)2
#131300402
#131165902
#715313