Finite Group Databasebeta

← #46781479

Subgroups — #46781479

Order 33664.

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

normal subgroups only

This group has 254 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#30682486C211yesmaximal, characteristic
2#30681960C212yesmaximal, complemented
3#30681686C212yesmaximal, complemented
4#30681682C211yesmaximal, characteristic, complemented
5#331×C263C211yesmaximal, characteristic, complemented
6C2×#16862375C412yes—
7C2×#16862359—22no—
8#22554470C2211yescharacteristic
9#22554457C412yes—
10#22554441—22no—
11D4×Dic263—22no—
12C42×D263C2211yescharacteristic
13C4⋊(C263⋊C8)C2212yes—
14Dic263⋊C8—22no—
15#127×C263C2211yescharacteristic
16C4⋊C8×C263C2212yes—
17#16862375—44no—
18C2×Dic526C2×C412yes—
19C2×C22⋊D263—22no—
20C22×Dic263—22no—
21C2×C4×D263C2×C411yescharacteristic
22C2×C4×D263D412yes—
23#16862359—44no—
24C2×C263⋊C8—22no—
25C4⋊Dic263—22no—
26C22⋊Dic263—24no—
27C4×Dic263C2×C411yescharacteristic
28C4×Dic263D412yes—
29C2×D4×C263—22no—
30C2×D4×C263C2×C412yes—
31C2×C8×C263—22no—
32C42×C263C2311yescharacteristic
33C22×D263C22⋊C411yescharacteristic
34Dic526—42no—
35C22⋊D263—44no—
36C2×Dic263—22no—
37C2×Dic263—44no—
38C2×Dic263C22⋊C412yes—
39C2×Dic263C22⋊C411yescharacteristic
40C4×D263—22no—
41C4×D263—22no—
42C4×D263—22no—
43C263⋊C8—42no—
44C23×C263—22no—
45D4×C263—42no—
46D4×C263—42no—
47D4×C263—42no—
48C2×C4×C263C22×C411yescharacteristic
49C2×C4×C263C2×D412yes—
50C8×C263—42no—
51C22×C263—42no—
52C22×C263—44no—
53C22×C263C2×C22⋊C411yescharacteristic
54C2×D263—21no—
55C2×D263—22no—
56C4×C263—21no—
57C4×C263AGL(1,ℤ/8)12yes—
58C4×C263#13712yes—
59Dic263—22no—
60Dic263—42no—
61Dic263#10012yes—
62C2×C263—82no—
63C2×C263C2×#10011yescharacteristic
64C2×C263#41712yes—
65D263—41no—
66C263#156011yescharacteristic, complemented, Sylow
67#1560—2631nomaximal, Sylow
68#532—2631no—
69#423—2632no—
70#333—2632no—
71#331—2631no—
72#331D26311yescharacteristic, complemented
73C2×#41—2632no—
74C2×M16—5262no—
75C4⋊Q8—2631no—
76#127C2×D26311yescharacteristic
77#124—2632no—
78#121—5262no—
79C4×D4—5262no—
80C2×C42—2631no—
81C4⋊C8—2632no—
82C4⋊C8—5262no—
83C4⋊C8C2×D26312yes—
84#41—10524no—
85C2×Q8—2632no—
86C2×D4—22no—
87C2×D4—5262no—
88C2×D4C4×D26312yes—
89C22×C4—2631no—
90C22×C4—2632no—
91C22×C4—5262no—
92M16—10524no—
93C2×C8—22no—
94C2×C8—5262no—
95C4⋊C4—5262no—
96C22⋊C4—5264no—
97C42—2631no—
98C42—2632no—
99C42C22×D26311yescharacteristic
100C23—22no—
101C23—2631no—
102Q8—10522no—
103D4—42no—
104D4—42no—
105D4—42no—
106D4—10524no—
107C2×C4—2631no—
108C2×C4—2632no—
109C2×C4—5262no—
110C2×C4—5262no—
111C2×C4—5262no—
112C2×C4—5262no—
113C2×C4—10524no—
114C2×C4C2×C4×D26311yescharacteristic
115C2×C4D4×D26312yes—
116C8—42no—
117C8—10522no—
118C22—42no—
119C22—44no—
120C22—5261no—
121C22—5262no—
122C22C22⋊C4×D26311yescharacteristic
123C4—21no—
124C4—2632no—
125C4—5262no—
126C4—10522no—
127C4#2255449412yes—
128C4#2255449912yes—
129C2—82no—
130C2—10521no—
131C2#100×D26311yescharacteristic
132C2#3068193612yes—
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#331×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682486C2
cosocleC42×C263C23
hypercenter#331D263
hypocenterC263#1560
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. #30681960C2semidirect
3. #30681686C2semidirect
4. #30681682C2semidirect
5. #331×C263C2semidirect
66. C263#1560semidirect
72. #331D263semidirect

Maximal subgroups

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

subgroupindex
#306824862
#306819602
#306816862
#306816822
#331×C2632
#1560263