Finite Group Databasebeta

← #46781459

Subgroups — #46781459

Order 33664.

332 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 67 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#127×D263C211yesmaximal, characteristic
2#30681994C212yesmaximal, complemented
3#30681682C211yesmaximal, characteristic, complemented
4#30681681C212yesmaximal, complemented
5#331×C263C211yesmaximal, characteristic, complemented
6C2×D4×D263—22no—
7C2×D4×D263C412yes—
8#22554467C2211yescharacteristic
9#22554466—22no—
10#22554466C412yes—
11C42×D263C2211yescharacteristic
12C4⋊(C263⋊C8)C2212yescomplemented
13(C2×D263)⋊C8—22no—
14#22554380—22no—
15#127×C263C2211yescharacteristic
16C4⋊C8×C263C2212yescomplemented
17C23×D263—22no—
18C2×D1052—22no—
19C2×D1052C2×C412yes—
20C2×C22⋊D263—22no—
21C2×C22⋊D263—24no—
22D4×D263—44no—
23D4×D263—44no—
24D4×D263—44no—
25C2×C4×D263C2×C411yescharacteristic
26C2×C4×D263D412yes—
27C2×C263⋊C8—22no—
28C4×Dic263C2×C411yescharacteristic
29C4×Dic263D412yes—
30C2×D4×C263—22no—
31C2×D4×C263C2×C412yes—
32C2×C8×C263—22no—
33C42×C263C2311yescharacteristic
34C22×D263—22no—
35C22×D263—48no—
36C22×D263—44no—
37C22×D263C22⋊C411yescharacteristic
38D1052—42no—
39D1052—42no—
40D1052—42no—
41C22⋊D263—44no—
42C22⋊D263—48no—
43C2×Dic263C22⋊C412yes—
44C2×Dic263C22⋊C411yescharacteristic
45C4×D263—22no—
46C4×D263—22no—
47C4×D263—22no—
48C263⋊C8—42no—
49C23×C263—22no—
50D4×C263—42no—
51D4×C263—42no—
52D4×C263—42no—
53C2×C4×C263C22×C411yescharacteristic
54C2×C4×C263C2×D412yes—
55C8×C263—42no—
56C22×C263—42no—
57C22×C263—44no—
58C22×C263C2×C22⋊C411yescharacteristic
59C2×D263—22no—
60C2×D263—42no—
61C2×D263—44no—
62C2×D263—88no—
63C2×D263#10012yes—
64C4×C263—21no—
65C4×C263AGL(1,ℤ/8)12yes—
66C4×C263AGL(1,ℤ/8)12yes—
67Dic263—21no—
68Dic263—22no—
69C2×C263—82no—
70C2×C263C2×#10011yescharacteristic
71C2×C263#41812yes—
72D263—22no—
73D263—82no—
74C263#155511yescharacteristic, complemented, Sylow
75#1555—2631nomaximal, Sylow
76C2×#127—2631no—
77#432—2632no—
78#331—2631no—
79#331—2632no—
80#331D26311yescharacteristic, complemented
81C22×D4—2632no—
82C22×D4—5262no—
83#127—2632no—
84#127—2631no—
85#127—5262no—
86#127C2×D26311yescharacteristic
87C2×C42—2631no—
88C4⋊C8—2632no—
89C4⋊C8C2×D26312yescomplemented
90C22⋊C8—5262no—
91#97—5262no—
92C24—5262no—
93C2×D4—22no—
94C2×D4—2632no—
95C2×D4—5264no—
96C2×D4—5262no—
97C2×D4—5262no—
98C2×D4—10524no—
99C2×D4—10524no—
100C2×D4—10524no—
101C2×D4C4×D26312yes—
102C22×C4—2631no—
103C22×C4—2632no—
104C2×C8—22no—
105C2×C8—5262no—
106C42—2631no—
107C42—2632no—
108C42C22×D26311yescharacteristic
109C23—22no—
110C23—2631no—
111C23—5262no—
112C23—10524no—
113C23—10528no—
114D4—42no—
115D4—42no—
116D4—42no—
117D4—10522no—
118D4—10524no—
119D4—10528no—
120D4—10522no—
121D4—10522no—
122C2×C4—2631no—
123C2×C4—2632no—
124C2×C4—5262no—
125C2×C4—5262no—
126C2×C4—5262no—
127C2×C4C2×C4×D26311yescharacteristic
128C2×C4D4×D26312yes—
129C8—42no—
130C8—10522no—
131C22—42no—
132C22—44no—
133C22—2632no—
134C22—5262no—
135C22—10522no—
136C22—10524no—
137C22—21048no—
138C22C22⋊C4×D26311yescharacteristic
139C4—21no—
140C4—5261no—
141C4—5262no—
142C4#2255449412yes—
143C4#2255449712yes—
144C2—82no—
145C2—5262no—
146C2—21042no—
147C2#100×D26311yescharacteristic
148C2#3068194112yes—
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#331×C263C2
socleC22×C263C2×C22⋊C4
prime radical#127×D263C2
cosocleC42×C263C23
hypercenter#331D263
hypocenterC263#1555
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #30681994C2semidirect
3. #30681682C2semidirect
4. #30681681C2semidirect
5. #331×C263C2semidirect
12. C4⋊(C263⋊C8)C22semidirect
16. C4⋊C8×C263C22semidirect
74. C263#1555semidirect
80. #331D263semidirect
89. C4⋊C8C2×D263semidirect

Maximal subgroups

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

subgroupindex
#127×D2632
#306819942
#306816822
#306816812
#331×C2632
#1555263