Finite Group Databasebeta

← #46780651

Subgroups — #46780651

Order 33664.

396 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 65 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#30681794C212yesmaximal
2#379×C263C211yesmaximal, characteristic
3C2×C22⋊Dic263—22no—
4C2×C22⋊Dic263—22no—
5C2×C22⋊Dic263C414yescomplemented
6C25×C263C2211yescharacteristic
7C2×C22⋊C4×C263—22no—
8C2×C22⋊C4×C263C412yescomplemented
9C22×Dic263—24no—
10C22⋊Dic263—44no—
11C22⋊Dic263—44no—
12C22⋊Dic263—44no—
13C24×C263—42no—
14C24×C263—44no—
15C24×C263C2×C412yes—
16C24×C263C2×C411yescharacteristic
17C24×C263D412yes—
18C24×C263D411yescharacteristic
19C24×C263Q811yescharacteristic
20C22×C4×C263—22no—
21C22⋊C4×C263—44no—
22C22⋊C4×C263—42no—
23C2×Dic263—44no—
24C2×Dic263—44no—
25C2×Dic263—44no—
26C23×C263—22no—
27C23×C263—24no—
28C23×C263—24no—
29C23×C263—24no—
30C23×C263—24no—
31C23×C263—42no—
32C23×C263—42no—
33C23×C263—42no—
34C23×C263—42no—
35C23×C263—41no—
36C23×C263—42no—
37C23×C263—41no—
38C23×C263—416no—
39C23×C263C4211yescharacteristic
40C23×C263C22⋊C412yes—
41C23×C263C22⋊C411yescharacteristic
42C23×C263C4⋊C412yes—
43C23×C263C4⋊C411yescharacteristic
44C2×C4×C263—44no—
45C2×C4×C263—42no—
46C22×C263—22no—
47C22×C263—22no—
48C22×C263—22no—
49C22×C263—22no—
50C22×C263—21no—
51C22×C263—22no—
52C22×C263—22no—
53C22×C263—22no—
54C22×C263—22no—
55C22×C263—21no—
56C22×C263—44no—
57C22×C263—48no—
58C22×C263—48no—
59C22×C263—44no—
60C22×C263—44no—
61C22×C263#9511yescharacteristic
62C22×C263#9914yes—
63C22×C263#9912yes—
64C4×C263—82no—
65Dic263—84no—
66C2×C263—24no—
67C2×C263—22no—
68C2×C263—41no—
69C2×C263—42no—
70C2×C263—41no—
71C2×C263#34212yes—
72C2×C263#34211yescharacteristic
73C263#130411yescharacteristic, complemented, Sylow
74#1304—2631nomaximal, Sylow
75#379—2632no—
76#379D26311yescharacteristic
77C25C2×D26311yescharacteristic
78C2×C22⋊C4—22no—
79C2×C22⋊C4—2634no—
80C2×C22⋊C4—5262no—
81C2×C22⋊C4—5262no—
82C2×C22⋊C4Dic26312yescomplemented
83C24—44no—
84C24—42no—
85C24C4×D26312yes—
86C24C2×Dic26311yescharacteristic
87C24C22⋊D26312yes—
88C24D105211yescharacteristic
89C24Dic52611yescharacteristic
90C22×C4—22no—
91C22×C4—5264no—
92C22⋊C4—44no—
93C22⋊C4—42no—
94C22⋊C4—10524no—
95C22⋊C4—10524no—
96C22⋊C4—10524no—
97C23—24no—
98C23—24no—
99C23—24no—
100C23—22no—
101C23—24no—
102C23—42no—
103C23—42no—
104C23—42no—
105C23—42no—
106C23—41no—
107C23—42no—
108C23—41no—
109C23—416no—
110C23C4×Dic26311yescharacteristic
111C23(C2×D263)⋊C412yes—
112C23C22⋊Dic26311yescharacteristic
113C23Dic263⋊C412yes—
114C23C4⋊Dic26311yescharacteristic
115C2×C4—44no—
116C2×C4—42no—
117C2×C4—10524no—
118C2×C4—10524no—
119C2×C4—10524no—
120C22—22no—
121C22—22no—
122C22—22no—
123C22—22no—
124C22—22no—
125C22—22no—
126C22—22no—
127C22—21no—
128C22—22no—
129C22—21no—
130C22—48no—
131C22—44no—
132C22—44no—
133C22—48no—
134C22—44no—
135C22C263⋊#9511yescharacteristic
136C22#2255438414yes—
137C22#2255438512yes—
138C4—82no—
139C4—21044no—
140C2—22no—
141C2—24no—
142C2—41no—
143C2—42no—
144C2—41no—
145C2#3068170412yes—
146C2#3068170511yescharacteristic
subgroupG/H
centerC22C263⋊#95
commutatorC23×C263C42
FrattiniC25C2×D263
Fitting#379×C263C2
socleC22×C263#95
prime radical, cosocleC25×C263C22
hypercenter#379D263
hypocenterC263#1304
LCSG ▷ C23×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C25 ◁ #379

Complements

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

NH ≅ G/Ntype
5. C2×C22⋊Dic263C4semidirect
8. C2×C22⋊C4×C263C4semidirect
73. C263#1304semidirect
82. C2×C22⋊C4Dic263semidirect

Maximal subgroups

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

subgroupindex
#306817942
#379×C2632
#1304263