Finite Group Databasebeta

← #16777618

Subgroups — #16777618

Order 3328.

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

normal subgroups only

This group has 204 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
1C4×#88104C211yesmaximal, characteristic
2#13130397C211yesmaximal, characteristic
3#13116638C211yesmaximal, characteristic
4C2×#88104—21no—
5#11719054—21no—
6C4×#6118—21no—
7C4×C8×D13C2211yescharacteristic
8#11718268C412yes—
9#11718254—21no—
10#11718253C412yes—
11C13×C4⋊C16C411yescharacteristic
12#11718099—21no—
13#11718094—21no—
14C4⋊#6090C411yescharacteristic
15C2×#6118—22no—
16C2×C8×D13C2×C411yescharacteristic
17C2×C8×D13D411yescharacteristic
18C42×D13D411yescharacteristic
19#88111—41no—
20#88110—41no—
21#88110—41no—
22C4⋊#1057—22no—
23C4×#1057—41no—
24#88104—22no—
25#88104—22no—
26C2×C13×C16—21no—
27C4×C8×C13C2×C411yescharacteristic
28C8×Dic13C2×C411yescharacteristic
29C8×Dic13D411yescharacteristic
30C2×#6090—21no—
31C4×#1055Q811yescharacteristic
32#7303—131nomaximal, Sylow
33C2×C4×D13C22⋊C411yescharacteristic
34C2×C4×D13SD1611yescharacteristic
35C2×C4×D13Q1611yescharacteristic
36C2×#1057—42no—
37C2×#1057—42no—
38#6118—24no—
39#6118—42no—
40C2×C8×C13C4211yescharacteristic
41C2×C8×C13C22⋊C411yescharacteristic
42C42×C13C4⋊C411yescharacteristic
43C4×Dic13C22⋊C411yescharacteristic
44C4×Dic13D811yescharacteristic
45C4×Dic13SD1611yescharacteristic
46C2×#1055C4⋊C411yescharacteristic
47C2×#1055C4⋊C411yescharacteristic
48C8×D13—21no—
49C8×D13—21no—
50C8×D13—41no—
51C13×C16—41no—
52#6090—41no—
53#2163—131no—
54C4×#108—131no—
55#1568—131no—
56C22×D13#10311yescharacteristic
57C2×C4×C13#9511yescharacteristic
58C2×C4×C13#10611yescharacteristic
59C2×C4×C13#10711yescharacteristic
60C2×Dic13#10211yescharacteristic
61C2×Dic13#10211yescharacteristic
62C2×Dic13#10311yescharacteristic
63C4×D13—21no—
64C4×D13—21no—
65C4×D13—41no—
66C4×D13—41no—
67#1057—44no—
68#1057—82no—
69C8×C13—21no—
70C8×C13#10411yescharacteristic
71C8×C13#10411yescharacteristic
72#1055—21no—
73#1055—21no—
74#432—261no—
75C2×#108—261no—
76C4×M16—261no—
77C2×C4×C8—131no—
78C4⋊C16—131no—
79C4⋊C16#26111yescharacteristic
80C22⋊C16—261no—
81#346—261no—
82#341—132no—
83#335—261no—
84#334—132no—
85C22×C13#34011yescharacteristic
86C2×D13—21no—
87C2×D13—21no—
88C2×D13—21no—
89C4×C13—21no—
90C4×C13—21no—
91C4×C13#33911yescharacteristic
92C4×C13#34411yescharacteristic
93Dic13—21no—
94Dic13—21no—
95Dic13—21no—
96C2×M16—262no—
97C22×C8—131no—
98C22×C8—131no—
99C2×C42—131no—
100C2×C16—21no—
101C2×C16—261no—
102#108—262no—
103#108—262no—
104C4⋊C8—262no—
105C22⋊C8—521no—
106#97—521no—
107#97—521no—
108C4×C8—131no—
109C4×C8—131no—
110C4×C8—131no—
111C4×C8—521no—
112C4×C8C2×#26111yescharacteristic
113C2×C13#130311yescharacteristic
114C2×C13#138511yescharacteristic
115C2×C13#138911yescharacteristic
116D13—41no—
117C22×C4—131no—
118C22×C4—131no—
119C22×C4—131no—
120M16—264no—
121M16—522no—
122C2×C8—131no—
123C2×C8—131no—
124C2×C8—261no—
125C2×C8—261no—
126C2×C8—521no—
127C2×C8—522no—
128C2×C8—522no—
129C2×C8C4×#26111yescharacteristic
130C2×C8C22⋊#26111yescharacteristic
131C42—131no—
132C42—131no—
133C42—131no—
134C42C4⋊#26111yescharacteristic
135C16—41no—
136C16—521no—
137C13#730311yescharacteristic, complemented, Sylow
138C23—131no—
139C2×C4—131no—
140C2×C4—131no—
141C2×C4—131no—
142C2×C4—261no—
143C2×C4—261no—
144C2×C4—521no—
145C2×C4—521no—
146C2×C4#8810111yescharacteristic
147C2×C4#8810211yescharacteristic
148C2×C4(C2×#261)⋊C411yescharacteristic
149C8—21no—
150C8—261no—
151C8—261no—
152C8—524no—
153C8—1042no—
154C8#8811611yescharacteristic
155C8#8811811yescharacteristic
156C22—261no—
157C22—261no—
158C22—261no—
159C22#1171826511yescharacteristic
160C4—21no—
161C4—21no—
162C4—261no—
163C4—261no—
164C4—261no—
165C4#1171824711yescharacteristic
166C4#1171827411yescharacteristic
167C2—521no—
168C2#1312973311yescharacteristic
169C2#1312990611yescharacteristic
170C2#1312991711yescharacteristic
subgroupG/H
centerC22#11718265
commutatorC2×C8×C13C42
FrattiniC4×C8C2×#261
FittingC13×C4⋊C16C4
socleC22×C13#340
prime radicalC22×D13#103
cosocleC4×C8×D13C22
hypercenterC4⋊C16#261
hypocenterC13#7303
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4⋊C16

Complements

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

NH ≅ G/Ntype
137. C13#7303semidirect

Maximal subgroups

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

subgroupindex
C4×#881042
#131303972
#131166382
#730313