Finite Group Databasebeta

← #46781807

Subgroups — #46781807

Order 33664.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#30682674C211yesmaximal, characteristic, complemented
2#30682314C211yesmaximal, characteristic
3#30682139C212yesmaximal, complemented
4#30681668C212yesmaximal, complemented
5#331×C263C211yesmaximal, characteristic, complemented
6C2×#16862365—22no—
7C2×#16862361—22no—
8#22554467C2211yescharacteristic
9#22554457—22no—
10#22554451—22no—
11C4×Dic526C2212yes—
12D4×Dic263—22no—
13#22554392—22no—
14C4×C263⋊C8C2211yescharacteristic
15#127×C263C2211yescharacteristic
16C4⋊C8×C263C2212yes—
17C2×Dic526D412yes—
18C2×D1052—22no—
19C2×D1052—21no—
20C22×Dic263—22no—
21#16862365—44no—
22#16862361—44no—
23C2×C263⋊C8—21no—
24C4⋊Dic263D412yes—
25Dic263⋊C4—22no—
26C22⋊Dic263—24no—
27C22⋊Dic263—22no—
28C4×Dic263—22no—
29C2×D4×C263—22no—
30C2×D4×C263D412yes—
31C2×C8×C263—22no—
32C42×C263C2311yescharacteristic
33C22×D263—41no—
34Dic526—22no—
35Dic526—22no—
36D1052—42no—
37D1052—42no—
38D1052—42no—
39C2×Dic263—22no—
40C2×Dic263—22no—
41C2×Dic263—82no—
42C263⋊C8—22no—
43C23×C263—22no—
44D4×C263—42no—
45D4×C263—42no—
46D4×C263—42no—
47C2×C4×C263C2×D412yes—
48C2×C4×C263C2×D411yescharacteristic
49C8×C263—42no—
50C22×C263—44no—
51C22×C263—42no—
52C22×C263#12011yescharacteristic
53C2×D263—82no—
54C2×D263—81no—
55C4×C263—21no—
56C4×C263#13512yes—
57C4×C263AGL(1,ℤ/8)12yes—
58Dic263—42no—
59Dic263—42no—
60C2×C263—82no—
61C2×C263#44912yes—
62C2×C263#45311yescharacteristic
63D263—161no—
64C263#162011yescharacteristic, complemented, Sylow
65#1620—2631nomaximal, Sylow
66#559—2631no—
67#493—2631no—
68#460—2632no—
69#331D26311yescharacteristic, complemented
70Q8⋊C8—2632no—
71C2×SD16—5262no—
72C2×D8—5262no—
73#127—2631no—
74#127C2×D26311yescharacteristic
75#124—5262no—
76#123—5262no—
77C4×Q8—2632no—
78C4×D4—5262no—
79C4⋊C8C2×D26312yes—
80#102—5262no—
81C4×C8—2631no—
82C2×Q8—2632no—
83C2×D4—22no—
84C2×D4—5262no—
85C2×D4—5261no—
86C2×D4D105212yes—
87C22×C4—5262no—
88SD16—10524no—
89D8—10524no—
90C2×C8—22no—
91C2×C8—5261no—
92C4⋊C4—2632no—
93C4⋊C4—5262no—
94C22⋊C4—5264no—
95C22⋊C4—5262no—
96C42—5262no—
97C42C22×D26311yescharacteristic
98C23—22no—
99C23—10521no—
100Q8—5262no—
101Q8—5262no—
102D4—42no—
103D4—42no—
104D4—42no—
105D4—10522no—
106D4—10522no—
107D4—10522no—
108C2×C4—5262no—
109C2×C4—5262no—
110C2×C4—21042no—
111C2×C4D4×D26312yes—
112C2×C4C2×D105211yescharacteristic
113C8—42no—
114C8—5262no—
115C22—44no—
116C22—42no—
117C22—21042no—
118C22—21041no—
119C22#2255444011yescharacteristic
120C4—21no—
121C4—10522no—
122C4—10522no—
123C4#2255449112yes—
124C4#2255449412yes—
125C2—82no—
126C2—42081no—
127C2#3068208412yes—
128C2#3068210811yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#331×C263C2
socleC22×C263#120
prime radical#30682314C2
hypercenter#331D263
hypocenterC263#1620
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #30682674C2semidirect
3. #30682139C2semidirect
4. #30681668C2semidirect
5. #331×C263C2semidirect
64. C263#1620semidirect
69. #331D263semidirect

Maximal subgroups

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

subgroupindex
#306826742
#306823142
#306821392
#306816682
#331×C2632
#1620263