Finite Group Databasebeta

← #46782042

Subgroups — #46782042

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#30682327C212yesmaximal, complemented
3#30682304C211yesmaximal, characteristic, complemented
4#30681677C212yesmaximal, complemented
5#330×C263C211yesmaximal, characteristic, complemented
6C2×#16862365—22no—
7C2×D2104—22no—
8#22554467C2211yescharacteristic
9#22554458C2212yes—
10#22554455—22no—
11#22554448—22no—
12#22554445—22no—
13#22554390—22no—
14#22554381C2211yescharacteristic
15#125×C263C2211yescharacteristic
16#97×C263C2212yes—
17C2×Dic526D412yes—
18C2×D1052—22no—
19C2×D1052—21no—
20C2×D1052—22no—
21C2×D1052D412yes—
22C2×C4×D263—22no—
23#16862365—44no—
24D2104—44no—
25C2×C263⋊C8—21no—
26Dic263⋊C4—22no—
27(C2×D263)⋊C4—22no—
28(C2×D263)⋊C4—22no—
29(C2×D263)⋊C4—22no—
30C2×C8×C263—22no—
31C4⋊C4×C263—22no—
32C4⋊C4×C263D412yes—
33C42×C263C2311yescharacteristic
34C22×D263—22no—
35C22×D263—41no—
36Dic526—42no—
37D1052—42no—
38D1052—42no—
39D1052—42no—
40D1052—42no—
41D1052—82no—
42C2×Dic263—22no—
43C4×D263—82no—
44C263⋊C8—41no—
45C2×C4×C263—22no—
46C2×C4×C263C2×D412yes—
47C2×C4×C263C2×D411yescharacteristic
48C8×C263—24no—
49C22×C263#12011yescharacteristic
50C2×D263—42no—
51C2×D263—42no—
52C2×D263—42no—
53C2×D263—82no—
54C2×D263—81no—
55C4×C263—22no—
56C4×C263—21no—
57C4×C263—42no—
58Dic263—42no—
59C2×C263#45312yes—
60C2×C263#45411yescharacteristic
61D263—82no—
62D263—161no—
63C263#165611yescharacteristic, complemented, Sylow
64#1656—2631nomaximal, Sylow
65#562—2631no—
66#496—2632no—
67#490—2631no—
68#330D26311yescharacteristic, complemented
69#329—2632no—
70C2×SD16—5262no—
71C2×D8—5262no—
72#127—2631no—
73#125C2×D26311yescharacteristic
74#124—2632no—
75#123—5262no—
76C22⋊Q8—5262no—
77#121—5262no—
78#102—5262no—
79#97—2631no—
80#97C2×D26312yes—
81C2×Q8—2632no—
82C2×D4—2632no—
83C2×D4—5262no—
84C2×D4—5262no—
85C2×D4—5261no—
86C22×C4—5262no—
87SD16—10524no—
88D8—10524no—
89C2×C8—22no—
90C2×C8—5261no—
91C4⋊C4—22no—
92C4⋊C4—5262no—
93C4⋊C4D105212yes—
94C22⋊C4—5262no—
95C22⋊C4—5262no—
96C22⋊C4—5262no—
97C42C22×D26311yescharacteristic
98C23—5262no—
99C23—10521no—
100Q8—10522no—
101D4—10522no—
102D4—10522no—
103D4—10522no—
104D4—10522no—
105D4—21042no—
106C2×C4—22no—
107C2×C4—5262no—
108C2×C4—21042no—
109C2×C4D4×D26312yes—
110C2×C4C2×D105211yescharacteristic
111C8—24no—
112C8—10521no—
113C22—10522no—
114C22—10522no—
115C22—10522no—
116C22—21041no—
117C22—21042no—
118C22#2255444011yescharacteristic
119C4—21no—
120C4—22no—
121C4—42no—
122C4—10522no—
123C2—21042no—
124C2—42081no—
125C2#3068210712yes—
126C2#3068211311yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#330×C263C2
socleC22×C263#120
hypercenter#330D263
hypocenterC263#1656
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #30682686C2semidirect
2. #30682327C2semidirect
3. #30682304C2semidirect
4. #30681677C2semidirect
5. #330×C263C2semidirect
63. C263#1656semidirect
68. #330D263semidirect

Maximal subgroups

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

subgroupindex
#306826862
#306823272
#306823042
#306816772
#330×C2632
#1656263