Finite Group Databasebeta

← #46782822

Subgroups — #46782822

Order 33664.

300 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#22554429C211yesmaximal, characteristic
2#30681801C211yesmaximal, characteristic
3#30681704C214yesmaximal
4#381×C263C211yesmaximal, characteristic
5#22554429—22no—
6#22554429—22no—
7C2×C4⋊Dic263C412yescomplemented
8C2×C22⋊Dic263C2212yes—
9C2×C22⋊Dic263C2212yes—
10C2×C4×Dic263C412yescomplemented
11C263⋊#95—22no—
12C23×C4×C263C2211yescharacteristic
13C2×C22⋊C4×C263C2212yes—
14#95×C263—22no—
15C22×Dic263—22no—
16C22×Dic263C2×C414yes—
17C4⋊Dic263—24no—
18C22⋊Dic263—22no—
19C22⋊Dic263—22no—
20C22⋊Dic263—24no—
21C4×Dic263—24no—
22C24×C263C2311yescharacteristic
23C22×C4×C263—24no—
24C22×C4×C263—22no—
25C22×C4×C263C2×C411yescharacteristic
26C22×C4×C263C2×C411yescharacteristic
27C22×C4×C263D412yes—
28C22×C4×C263D412yes—
29C22⋊C4×C263—24no—
30C2×Dic263—24no—
31C2×Dic263—44no—
32C2×Dic263—44no—
33C2×Dic263—42no—
34C23×C263—42no—
35C23×C263C22×C411yescharacteristic
36C23×C263C2×D411yescharacteristic
37C23×C263C2×D411yescharacteristic
38C23×C263#4114yes—
39C2×C4×C263—22no—
40C2×C4×C263—22no—
41C2×C4×C263—24no—
42C2×C4×C263—24no—
43C2×C4×C263—44no—
44C2×C4×C263—42no—
45C2×C4×C263C22⋊C412yes—
46C2×C4×C263C22⋊C412yes—
47C22×C263—22no—
48C22×C263—22no—
49C22×C263—22no—
50C22×C263—44no—
51C22×C263C2×C22⋊C411yescharacteristic
52C22×C263#11712yes—
53C22×C263#12312yes—
54C22×C263#12312yes—
55C4×C263—22no—
56C4×C263—22no—
57C4×C263—82no—
58Dic263—44no—
59Dic263—82no—
60C2×C263—22no—
61C2×C263—22no—
62C2×C263—22no—
63C2×C263#38111yescharacteristic
64C2×C263#41012yes—
65C263#182011yescharacteristic, complemented, Sylow
66#1820—2631nomaximal, Sylow
67C2×#117—2631no—
68#381—2631no—
69#381D26311yescharacteristic
70#342—2634no—
71C23×C4C2×D26311yescharacteristic
72#117—5262no—
73#117—5262no—
74C2×C4⋊C4—2632no—
75C2×C22⋊C4—2632no—
76C2×C22⋊C4—2632no—
77C2×C22⋊C4C2×D26312yes—
78C2×C42—2632no—
79#95—22no—
80#95—5262no—
81C24C22×D26311yescharacteristic
82C22×C4—24no—
83C22×C4—22no—
84C22×C4—2634no—
85C22×C4—5262no—
86C22×C4C4×D26311yescharacteristic
87C22×C4C4×D26311yescharacteristic
88C22×C4C22⋊D26312yes—
89C22×C4D105212yes—
90C4⋊C4—5264no—
91C22⋊C4—24no—
92C22⋊C4—5262no—
93C22⋊C4—5262no—
94C22⋊C4—5264no—
95C42—5264no—
96C23—42no—
97C23C2×C4×D26311yescharacteristic
98C23C2×C22⋊D26311yescharacteristic
99C23C2×D105211yescharacteristic
100C23#1686237514yes—
101C2×C4—22no—
102C2×C4—22no—
103C2×C4—24no—
104C2×C4—24no—
105C2×C4—44no—
106C2×C4—42no—
107C2×C4—5264no—
108C2×C4—10524no—
109C2×C4—10524no—
110C2×C4—10522no—
111C2×C4(C2×D263)⋊C412yes—
112C2×C4(C2×D263)⋊C412yes—
113C22—22no—
114C22—22no—
115C22—22no—
116C22—44no—
117C22C2×(C2×D263)⋊C411yescharacteristic
118C22#2255442612yes—
119C22#2255445112yes—
120C22#2255445412yes—
121C4—22no—
122C4—22no—
123C4—82no—
124C4—10524no—
125C4—21042no—
126C2—22no—
127C2—22no—
128C2—22no—
129C2#3068179911yescharacteristic
130C2#3068191112yes—
subgroupG/H
centerC22C2×(C2×D263)⋊C4
commutatorC23×C263C22×C4
FrattiniC24C22×D263
Fitting#381×C263C2
socleC22×C263C2×C22⋊C4
prime radical, cosocleC24×C263C23
hypercenter#381D263
hypocenterC263#1820
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
7. C2×C4⋊Dic263C4semidirect
10. C2×C4×Dic263C4semidirect
65. C263#1820semidirect

Maximal subgroups

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

subgroupindex
C2×#225544292
#306818012
#306817042
#381×C2632
#1820263