Finite Group Databasebeta

← #46782039

Subgroups — #46782039

Order 33664.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#30682686C211yesmaximal, characteristic, complemented
2#30682325C212yesmaximal, complemented
3#30681680C211yesmaximal, characteristic, complemented
4#30681677C212yesmaximal, complemented
5#490×C263C211yesmaximal, characteristic, complemented
6C2×#16862364—22no—
7C2×#16862361—22no—
8#22554458C2212yes—
9#22554455—22no—
10#22554448—22no—
11#22554445—22no—
12#22554381C2212yes—
13#127×C263C2211yescharacteristic
14#125×C263C2211yescharacteristic
15#102×C263—22no—
16#97×C263C2211yescharacteristic
17C2×Dic526D412yes—
18C2×D1052—22no—
19C2×D1052D412yes—
20C2×C4×D263—22no—
21#16862364—44no—
22#16862361—44no—
23C2×C263⋊C8—22no—
24Dic263⋊C4—22no—
25(C2×D263)⋊C4—22no—
26(C2×D263)⋊C4—22no—
27(C2×D263)⋊C4—22no—
28C2×D4×C263—22no—
29C2×D4×C263—21no—
30C2×C8×C263—21no—
31C4⋊C4×C263—22no—
32C4⋊C4×C263D412yes—
33C42×C263C2311yescharacteristic
34C22×D263—22no—
35Dic526—42no—
36D1052—42no—
37D1052—82no—
38C2×Dic263—22no—
39C4×D263—82no—
40C263⋊C8—24no—
41C23×C263—41no—
42D4×C263—42no—
43D4×C263—42no—
44D4×C263—42no—
45C2×C4×C263—22no—
46C2×C4×C263C2×D412yes—
47C2×C4×C263C2×D411yescharacteristic
48C8×C263—41no—
49C22×C263—82no—
50C22×C263—81no—
51C22×C263#12011yescharacteristic
52C2×D263—42no—
53C2×D263—42no—
54C2×D263—42no—
55C4×C263—22no—
56C4×C263—21no—
57C4×C263—42no—
58Dic263—42no—
59C2×C263—161no—
60C2×C263#45312yes—
61C2×C263#45411yescharacteristic
62D263—82no—
63C263#165611yescharacteristic, complemented, Sylow
64#1656—2631nomaximal, Sylow
65#562—2631no—
66#496—2632no—
67#490D26311yescharacteristic, complemented
68#330—2631no—
69#329—2632no—
70C2×SD16—5262no—
71C2×D8—5262no—
72#127C2×D26311yescharacteristic
73#125C2×D26311yescharacteristic
74#124—2632no—
75#123—5262no—
76C22⋊Q8—5262no—
77#121—5262no—
78#102—22no—
79#97—2632no—
80#97C2×D26311yescharacteristic
81C2×Q8—2632no—
82C2×D4—22no—
83C2×D4—21no—
84C2×D4—2632no—
85C2×D4—5262no—
86C22×C4—5262no—
87SD16—10524no—
88D8—10524no—
89C2×C8—21no—
90C2×C8—5262no—
91C4⋊C4—22no—
92C4⋊C4—5262no—
93C4⋊C4C22⋊D26312yes—
94C22⋊C4—5262no—
95C22⋊C4—5262no—
96C22⋊C4—5262no—
97C42C22×D26311yescharacteristic
98C23—41no—
99C23—5262no—
100Q8—10522no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—10522no—
105D4—21042no—
106C2×C4—22no—
107C2×C4—5262no—
108C2×C4—21042no—
109C2×C4D4×D26312yes—
110C2×C4C2×C22⋊D26311yescharacteristic
111C8—41no—
112C8—5264no—
113C22—82no—
114C22—81no—
115C22—10522no—
116C22—10522no—
117C22—10522no—
118C22#2255443811yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—10522no—
123C2—161no—
124C2—21042no—
125C2#3068210412yes—
126C2#3068211011yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#490×C263C2
socleC22×C263#120
hypercenter#490D263
hypocenterC263#1656
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #30682686C2semidirect
2. #30682325C2semidirect
3. #30681680C2semidirect
4. #30681677C2semidirect
5. #490×C263C2semidirect
63. C263#1656semidirect
67. #490D263semidirect

Maximal subgroups

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

subgroupindex
#306826862
#306823252
#306816802
#306816772
#490×C2632
#1656263