Finite Group Databasebeta

← #16777924

Subgroups — #16777924

Order 3328.

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

normal subgroups only

This group has 182 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#13129718C211yesmaximal, characteristic
3#13116353C211yesmaximal, characteristic
4D13⋊(C22⋊C8)—21no—
5#11718787—21no—
6#11718787C2211yescharacteristic
7#11718786—21no—
8#11718786C411yescharacteristic
9#11718284—21no—
10C13×#338C411yescharacteristic
11C22×C4×D13D411yescharacteristic
12C2×D13⋊C8—41no—
13C2×C13×M16—21no—
14C2×C13×M16C2×C411yescharacteristic
15C2×#6099—21no—
16C2×#6099D411yescharacteristic
17C22⋊#1057—41no—
18#88111—22no—
19#88106—41no—
20#88060—41no—
21#88060—42no—
22#88059—42no—
23#88059—41no—
24#7433—131nomaximal, Sylow
25C23×D13Q1611yescharacteristic
26C22×C4×C13C22⋊C411yescharacteristic
27C22×Dic13SD1611yescharacteristic
28C2×C4×D13—21no—
29C2×C4×D13—21no—
30C2×C4×D13—41no—
31C2×C4×D13—41no—
32C2×#1057—42no—
33D13⋊C8—81no—
34D13⋊C8—81no—
35C13×M16—41no—
36C13×M16—41no—
37C13×M16—41no—
38C2×C8×C13—22no—
39C2×C8×C13—21no—
40#6099—41no—
41#6099—41no—
42#6099—41no—
43C2×#1055—21no—
44C2×#1055—41no—
45#6092—81no—
46#2091—131no—
47#1320—131no—
48#1298—131no—
49C23×C13#10311yescharacteristic
50C22×D13—21no—
51C22×D13—42no—
52C22×D13—41no—
53C2×C4×C13—21no—
54C2×C4×C13—21no—
55C2×C4×C13#9911yescharacteristic
56C2×C4×C13#10411yescharacteristic
57C2×Dic13—21no—
58C2×Dic13—41no—
59C4×D13—41no—
60C4×D13—41no—
61C4×D13—81no—
62#1057—82no—
63C8×C13—42no—
64C8×C13—41no—
65#1055—41no—
66#1055—81no—
67#430—131no—
68#430—261no—
69#407—131no—
70#407—261no—
71C2×C22⋊C8—261no—
72#349—261no—
73#338#26111yescharacteristic
74C22×C13—21no—
75C22×C13—41no—
76C22×C13#32811yescharacteristic
77C2×D13—22no—
78C2×D13—41no—
79C2×D13—41no—
80C2×D13—42no—
81C2×D13—81no—
82C4×C13—21no—
83C4×C13#35211yescharacteristic
84C4×C13#35311yescharacteristic
85Dic13—41no—
86C23×C4—131no—
87C2×M16—21no—
88C2×M16—131no—
89C2×M16—261no—
90C2×M16C2×#26111yescharacteristic
91C22×C8—521no—
92M32—521no—
93#108—521no—
94#108—522no—
95C22⋊C8—262no—
96C22⋊C8—521no—
97C22⋊C8—522no—
98C22⋊C8—521no—
99C2×C13—21no—
100C2×C13—41no—
101C2×C13#135211yescharacteristic
102D13—42no—
103C24—131no—
104C22×C4—131no—
105C22×C4—261no—
106C22×C4—261no—
107C22×C4—521no—
108C22×C4—521no—
109C22×C4C22⋊#26111yescharacteristic
110M16—41no—
111M16—41no—
112M16—41no—
113M16—521no—
114M16—521no—
115M16—521no—
116C2×C8—22no—
117C2×C8—21no—
118C2×C8—261no—
119C2×C8—521no—
120C2×C8—522no—
121C2×C8—1041no—
122C2×C8—1041no—
123C16—1041no—
124C13#743311yescharacteristic, complemented, Sylow
125C23—261no—
126C23—521no—
127C23—522no—
128C23#8811711yescharacteristic
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—261no—
132C2×C4—521no—
133C2×C4—521no—
134C2×C4—521no—
135C2×C4—1041no—
136C2×C4#8810711yescharacteristic
137C2×C4#8811611yescharacteristic
138C8—42no—
139C8—41no—
140C8—521no—
141C8—1042no—
142C8—1041no—
143C22—21no—
144C22—41no—
145C22—262no—
146C22—521no—
147C22—522no—
148C22—521no—
149C22—1041no—
150C22#1171824111yescharacteristic
151C4—21no—
152C4—521no—
153C4#1171822511yescharacteristic
154C4#1171823711yescharacteristic
155C2—21no—
156C2—41no—
157C2—522no—
158C2#1312983211yescharacteristic
subgroupG/H
centerC4#11718225
commutatorC2×C13×M16C2×C4
FrattiniC2×M16C2×#261
FittingC13×#338C4
socleC2×C13#1352
prime radicalC23×D13Q16
cosocle#11718787C22
hypercenter#338#261
hypocenterC13#7433
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
124. C13#7433semidirect

Maximal subgroups

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

subgroupindex
#131297692
#131297182
#131163532
#743313