Finite Group Databasebeta

← #16777568

Subgroups — #16777568

Order 3328.

250 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 58 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#13130078C212yesmaximal
2#13115776C211yesmaximal, characteristic
3C2×C4×Dic26C2211yescharacteristic
4#11719125—22no—
5C2×C13×#97C411yescharacteristic
6C2×C4⋊#1055C411yescharacteristic
7#11718286C414yes—
8#11718285—22no—
9#11718142—22no—
10C22×Dic26Q811yescharacteristic
11C22×C8×C13—21no—
12C2×C42×C13C2×C411yescharacteristic
13C2×C4⋊Dic13D411yescharacteristic
14C2×#6101C2×C412yes—
15C2×C4×Dic13D412yes—
16C22×#1055—21no—
17C4×Dic26—41no—
18C4×Dic26—41no—
19C22⋊#1057—24no—
20#88112—42no—
21C4×#1057—42no—
22C13×#97—41no—
23C4⋊#1055—41no—
24#7286—131nomaximal, Sylow
25C22×C4×C13C4211yescharacteristic
26C22×C4×C13C22⋊C411yescharacteristic
27C22×C4×C13C4⋊C411yescharacteristic
28C22×Dic13C22⋊C412yes—
29C22×Dic13C4⋊C412yes—
30C2×Dic26—24no—
31C2×Dic26—41no—
32C2×#1057—44no—
33C2×C8×C13—22no—
34C2×C8×C13—41no—
35C2×C8×C13—41no—
36C42×C13—21no—
37C42×C13—21no—
38C4⋊Dic13—41no—
39#6101—42no—
40C4×Dic13—22no—
41C4×Dic13—22no—
42C2×#1055—42no—
43C2×#1055—41no—
44#1985—131no—
45#1461—132no—
46C23×C13#9511yescharacteristic
47C2×C4×C13—21no—
48C2×C4×C13—21no—
49C2×C4×C13—22no—
50C2×C4×C13—21no—
51C2×C4×C13—21no—
52C2×C4×C13—41no—
53C2×C4×C13#9911yescharacteristic
54C2×C4×C13#9911yescharacteristic
55C2×Dic13—22no—
56C2×Dic13—22no—
57C2×Dic13—22no—
58C2×Dic13—42no—
59C2×Dic13#10814yes—
60Dic26—44no—
61#1057—84no—
62C8×C13—42no—
63#1055—81no—
64C2×C4×Q8—131no—
65#431—262no—
66C2×C4⋊C8—131no—
67C2×#97#26111yescharacteristic
68#336—262no—
69#324—134no—
70#324—262no—
71C22×C13—21no—
72C22×C13—21no—
73C22×C13#34112yes—
74C22×C13#34211yescharacteristic
75C4×C13—21no—
76C4×C13—41no—
77C4×C13—41no—
78C4×C13#35511yescharacteristic
79C4×C13#35611yescharacteristic
80Dic13—24no—
81Dic13—42no—
82C22×Q8—131no—
83C22×C8—21no—
84C22×C8—261no—
85C4×Q8—521no—
86C4×Q8—521no—
87C2×C4⋊C4—132no—
88C2×C4⋊C4—131no—
89C2×C42—132no—
90C2×C42C2×#26111yescharacteristic
91C4⋊C8—521no—
92C4⋊C8—522no—
93C22⋊C8—264no—
94#97—41no—
95C4×C8—522no—
96C2×C13—22no—
97C2×C13#129811yescharacteristic
98C2×C13#139111yescharacteristic
99C2×C13#139411yescharacteristic
100C2×Q8—264no—
101C2×Q8—521no—
102C22×C4—132no—
103C22×C4—132no—
104C22×C4C4×#26111yescharacteristic
105C22×C4C4⋊#26111yescharacteristic
106C22×C4C22⋊#26111yescharacteristic
107C2×C8—22no—
108C2×C8—41no—
109C2×C8—41no—
110C2×C8—522no—
111C2×C8—524no—
112C2×C8—521no—
113C4⋊C4—522no—
114C4⋊C4—521no—
115C42—21no—
116C42—21no—
117C42—262no—
118C42—262no—
119C13#728611yescharacteristic, complemented, Sylow
120C23(C2×#261)⋊C411yescharacteristic
121Q8—524no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—22no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—134no—
129C2×C4—262no—
130C2×C4—262no—
131C2×C4—262no—
132C2×C4—522no—
133C2×C4#8810711yescharacteristic
134C2×C4#8811911yescharacteristic
135C8—42no—
136C8—1044no—
137C8—1041no—
138C22—21no—
139C22—21no—
140C22#1171827312yes—
141C22#1171828911yescharacteristic
142C4—21no—
143C4—41no—
144C4—41no—
145C4—264no—
146C4—522no—
147C4#1171822711yescharacteristic
148C4#1171822811yescharacteristic
149C2—22no—
150C2#1312971811yescharacteristic
151C2#1312992511yescharacteristic
152C2#1312993311yescharacteristic
subgroupG/H
centerC2×C4#88107
commutatorC22×C4×C13C42
FrattiniC2×C42C2×#261
FittingC2×C13×#97C4
socleC22×C13#342
prime radicalC23×C13#95
cosocleC2×C4×Dic26C22
hypercenterC2×#97#261
hypocenterC13#7286
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
119. C13#7286semidirect

Maximal subgroups

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

subgroupindex
#131300782
#131157762
#728613