Finite Group Databasebeta

← #16777922

Subgroups — #16777922

Order 3328.

210 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 32 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#13129769C211yesmaximal, characteristic
2#13129716C211yesmaximal, characteristic
3#13116353C211yesmaximal, characteristic
4C4×C22⋊#261—21no—
5#11718787—21no—
6#11718787C2211yescharacteristic
7#11718786—21no—
8#11718786C411yescharacteristic, complemented
9#11718284—21no—
10C13×#338C411yescharacteristic, complemented
11C22×C4×D13D411yescharacteristic
12C2×C22⋊#261—41no—
13C2×C4×#261—41no—
14C2×C13×M16—21no—
15C2×C13×M16C2×C411yescharacteristic
16C2×#6099—21no—
17C2×#6099D411yescharacteristic
18(C2×#261)⋊C4—22no—
19#88106—41no—
20#88060—41no—
21#88060—42no—
22#88059—42no—
23#88059—41no—
24#7432—131nomaximal, Sylow
25C23×D13SD1611yescharacteristic
26C22×#261—42no—
27C22×C4×C13C22⋊C411yescharacteristic
28C22×Dic13Q1611yescharacteristic
29C2×C4×D13—21no—
30C2×C4×D13—21no—
31C2×C4×D13—41no—
32C2×C4×D13—41no—
33C22⋊#261—44no—
34C4×#261—81no—
35C4×#261—81no—
36C13×M16—41no—
37C13×M16—41no—
38C13×M16—41no—
39C2×C8×C13—22no—
40C2×C8×C13—21no—
41#6099—41no—
42#6099—41no—
43#6099—41no—
44C2×#1055—21no—
45C2×#1055—41no—
46#6092—81no—
47#2091—131no—
48#1320—131no—
49#1297—131no—
50C23×C13#10311yescharacteristic
51C22×D13—21no—
52C22×D13—42no—
53C22×D13—41no—
54C2×#261—44no—
55C2×#261—82no—
56C2×#261—82no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13#9911yescharacteristic
60C2×C4×C13#10411yescharacteristic
61C2×Dic13—21no—
62C2×Dic13—41no—
63C4×D13—41no—
64C4×D13—41no—
65C4×D13—81no—
66C8×C13—42no—
67C8×C13—41no—
68#1055—41no—
69#1055—81no—
70#430—131no—
71#430—261no—
72#407—131no—
73#407—261no—
74C4×C22⋊C4—261no—
75#349—261no—
76#338#26111yescharacteristic, complemented
77C22×C13—21no—
78C22×C13—41no—
79C22×C13#32811yescharacteristic
80C2×D13—22no—
81C2×D13—41no—
82C2×D13—41no—
83C2×D13—42no—
84C2×D13—81no—
85#261—84no—
86C4×C13—21no—
87C4×C13#35211yescharacteristic
88C4×C13#35311yescharacteristic
89Dic13—41no—
90C23×C4—131no—
91C2×M16—21no—
92C2×M16—131no—
93C2×M16—261no—
94C2×M16C2×#26111yescharacteristic
95C2×C22⋊C4—521no—
96C2×C42—521no—
97M32—521no—
98#108—521no—
99#108—522no—
100C22⋊C8—521no—
101C22⋊C8—522no—
102#95—262no—
103C2×C13—21no—
104C2×C13—41no—
105C2×C13#135211yescharacteristic
106D13—42no—
107C24—131no—
108C22×C4—131no—
109C22×C4—261no—
110C22×C4—261no—
111C22×C4—521no—
112C22×C4—521no—
113C22×C4—522no—
114C22×C4C22⋊#26111yescharacteristic
115M16—41no—
116M16—41no—
117M16—41no—
118M16—521no—
119M16—521no—
120M16—521no—
121C2×C8—22no—
122C2×C8—21no—
123C2×C8—261no—
124C2×C8—521no—
125C22⋊C4—524no—
126C42—1041no—
127C42—1041no—
128C16—1041no—
129C13#743211yescharacteristic, complemented, Sylow
130C23—261no—
131C23—521no—
132C23—522no—
133C23#8811711yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—261no—
137C2×C4—521no—
138C2×C4—521no—
139C2×C4—521no—
140C2×C4—524no—
141C2×C4—1041no—
142C2×C4—1042no—
143C2×C4—1042no—
144C2×C4#8810711yescharacteristic
145C2×C4#8811611yescharacteristic
146C8—42no—
147C8—41no—
148C8—521no—
149C8—1041no—
150C22—21no—
151C22—41no—
152C22—262no—
153C22—521no—
154C22—522no—
155C22—521no—
156C22—1041no—
157C22#1171824111yescharacteristic
158C4—21no—
159C4—521no—
160C4—1044no—
161C4#1171822511yescharacteristic
162C4#1171823711yescharacteristic
163C2—21no—
164C2—41no—
165C2—522no—
166C2#1312983211yescharacteristic
subgroupG/H
centerC4#11718225
commutatorC2×C13×M16C2×C4
FrattiniC2×M16C2×#261
FittingC13×#338C4
socleC2×C13#1352
prime radicalC23×D13SD16
cosocle#11718787C22
hypercenter#338#261
hypocenterC13#7432
LCSG ▷ C2×C13×M16 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ #338

Complements

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

NH ≅ G/Ntype
8. #11718786C4semidirect
10. C13×#338C4semidirect
76. #338#261semidirect
129. C13#7432semidirect

Maximal subgroups

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

subgroupindex
#131297692
#131297162
#131163532
#743213