Finite Group Databasebeta

← #16777717

Subgroups — #16777717

Order 3328.

324 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 36 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#13129768C212yesmaximal
2#13114759C211yesmaximal, characteristic
3C23×Dic26C411yescharacteristic
4C13×#407C411yescharacteristic
5#11718868C2211yescharacteristic
6C2×#88064—22no—
7#11718284—22no—
8C23×C4×C13C2×C411yescharacteristic
9C23×Dic13C812yes—
10C22×Dic26—21no—
11C22×Dic26—21no—
12C22×Dic26—44no—
13C22×Dic26—41no—
14C22×Dic26—41no—
15C2×C13×M16—21no—
16C2×#6099D412yes—
17#88106—42no—
18C13×C22⋊C8—41no—
19C22⋊#1055—41no—
20#88064—44no—
21#7341—131nomaximal, Sylow
22C24×C13C2×C811yescharacteristic
23C22×C4×C13—21no—
24C22×C4×C13—21no—
25C22×C4×C13—42no—
26C22×C4×C13C22⋊C411yescharacteristic
27C22×C4×C13M1611yescharacteristic
28C22×Dic13—22no—
29C22×Dic13—44no—
30C22×Dic13—42no—
31C2×Dic26—24no—
32C2×Dic26—44no—
33C2×Dic26—42no—
34C2×Dic26—42no—
35C2×Dic26—48no—
36C2×Dic26—44no—
37C2×Dic26—41no—
38C2×Dic26—41no—
39C2×Dic26—44no—
40C13×M16—42no—
41C2×C8×C13—41no—
42#6099—42no—
43C2×#1055—22no—
44#6092—82no—
45#1784—131no—
46#1320—132no—
47C23×C13—21no—
48C23×C13—41no—
49C23×C13—42no—
50C23×C13C22⋊C811yescharacteristic
51C2×C4×C13—22no—
52C2×C4×C13—21no—
53C2×C4×C13—42no—
54C2×C4×C13—42no—
55C2×C4×C13—41no—
56C2×C4×C13#9911yescharacteristic
57C2×C4×C13#10011yescharacteristic
58C2×Dic13—24no—
59C2×Dic13—42no—
60C2×Dic13—44no—
61C2×Dic13—42no—
62C2×Dic13—44no—
63Dic26—44no—
64Dic26—48no—
65Dic26—44no—
66C8×C13—81no—
67#1055—42no—
68C23×Q8—131no—
69C2×#101—262no—
70#407—131no—
71#407#26111yescharacteristic
72#349—262no—
73C22×C13—22no—
74C22×C13—21no—
75C22×C13—41no—
76C22×C13—41no—
77C22×C13—42no—
78C22×C13—42no—
79C22×C13—41no—
80C22×C13#32311yescharacteristic
81C4×C13—21no—
82C4×C13—41no—
83C4×C13AΣL(1,𝔽16)12yes—
84Dic13—44no—
85C22×Q8—261no—
86C22×Q8—261no—
87C22×Q8—521no—
88C22×Q8—521no—
89C22×Q8—524no—
90C23×C4—132no—
91C23×C4C2×#26111yescharacteristic
92C2×M16—21no—
93C2×M16—132no—
94M32—522no—
95#101—524no—
96C22⋊C8—41no—
97C22⋊C8—521no—
98C2×C13—21no—
99C2×C13—42no—
100C2×C13—41no—
101C2×C13#131611yescharacteristic
102C24D13⋊C811yescharacteristic
103C2×Q8—264no—
104C2×Q8—522no—
105C2×Q8—522no—
106C2×Q8—524no—
107C2×Q8—524no—
108C2×Q8—528no—
109C2×Q8—524no—
110C2×Q8—521no—
111C2×Q8—521no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—42no—
115C22×C4—262no—
116C22×C4—524no—
117C22×C4—522no—
118C22×C4#611811yescharacteristic
119C22×C4C22⋊#26111yescharacteristic
120M16—42no—
121M16—522no—
122C2×C8—41no—
123C2×C8—262no—
124C16—1042no—
125C13#734111yescharacteristic, complemented, Sylow
126C23—21no—
127C23—41no—
128C23—42no—
129C23#8811111yescharacteristic
130Q8—524no—
131Q8—528no—
132Q8—524no—
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—42no—
136C2×C4—42no—
137C2×C4—41no—
138C2×C4—264no—
139C2×C4—522no—
140C2×C4—524no—
141C2×C4—522no—
142C2×C4—524no—
143C2×C4#8810711yescharacteristic
144C2×C4#8812111yescharacteristic
145C8—81no—
146C8—522no—
147C22—22no—
148C22—21no—
149C22—41no—
150C22—41no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22#1171828711yescharacteristic
155C4—21no—
156C4—41no—
157C4—524no—
158C4#1171823612yes—
159C2—21no—
160C2—42no—
161C2—41no—
162C2#1312976111yescharacteristic
subgroupG/H
centerC2#13129761
commutator, prime radicalC24×C13C2×C8
FrattiniC23×C4C2×#261
FittingC13×#407C4
socleC2×C13#1316
cosocle#11718868C22
hypercenter#407#261
hypocenterC13#7341
LCSG ▷ C24×C13 ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
125. C13#7341semidirect

Maximal subgroups

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

subgroupindex
#131297682
#131147592
#734113