Finite Group Databasebeta

← #46781372

Subgroups — #46781372

Order 33664.

196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 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#125×D263C211yesmaximal, characteristic
2#30681993C212yesmaximal
3#30681680C211yesmaximal, characteristic, complemented
4#30681679C212yesmaximal, complemented
5#330×C263C211yesmaximal, characteristic, complemented
6#22554462C2211yescharacteristic
7#22554461C412yes—
8#22554460—22no—
9C4⋊C4×D263—22no—
10C4⋊C4×D263C412yes—
11C42×D263C2211yescharacteristic
12Dic263⋊C8—22no—
13(C2×D263)⋊C8—22no—
14#22554381C2212yes—
15#125×C263C2211yescharacteristic
16#97×C263C2212yes—
17C2×C4×D263—22no—
18C2×C4×D263C2×C411yescharacteristic
19C2×C4×D263D412yes—
20C2×C263⋊C8—22no—
21C4⋊Dic263—22no—
22C4⋊Dic263C2×C412yes—
23Dic263⋊C4—22no—
24Dic263⋊C4—22no—
25Dic263⋊C4—22no—
26C4×Dic263C2×C411yescharacteristic
27C4×Dic263D412yes—
28C2×C8×C263—22no—
29C4⋊C4×C263—22no—
30C4⋊C4×C263C2×C412yes—
31C42×C263C2311yescharacteristic
32C22×D263C22⋊C411yescharacteristic
33C2×Dic263—22no—
34C2×Dic263C22⋊C412yes—
35C2×Dic263C22⋊C411yescharacteristic
36C4×D263—22no—
37C4×D263—42no—
38C4×D263—44no—
39C263⋊C8—42no—
40C2×C4×C263—22no—
41C2×C4×C263C22×C411yescharacteristic
42C2×C4×C263C2×D412yes—
43C8×C263—42no—
44C22×C263C2×C22⋊C411yescharacteristic
45C2×D263—22no—
46C2×D263#10112yes—
47C4×C263—21no—
48C4×C263—22no—
49C4×C263—42no—
50Dic263—21no—
51Dic263—22no—
52Dic263—42no—
53C2×C263C2×#10111yescharacteristic
54C2×C263#42112yes—
55D263—22no—
56C263#153411yescharacteristic, complemented, Sylow
57#1534—2631nomaximal, Sylow
58C2×#125—2631no—
59#432—2632no—
60#330—2631no—
61#330—2632no—
62#330D26311yescharacteristic, complemented
63#125—2632no—
64#125—2631no—
65#125—5262no—
66#125C2×D26311yescharacteristic
67C2×C4⋊C4—2632no—
68C2×C4⋊C4—5262no—
69C2×C42—2631no—
70C4⋊C8—5262no—
71C22⋊C8—5262no—
72#97—2632no—
73#97C2×D26312yes—
74C22×C4—2631no—
75C22×C4—2632no—
76C22×C4—5262no—
77C2×C8—22no—
78C2×C8—5262no—
79C4⋊C4—22no—
80C4⋊C4—2632no—
81C4⋊C4—5262no—
82C4⋊C4—5262no—
83C4⋊C4—5262no—
84C4⋊C4—5262no—
85C4⋊C4C4×D26312yes—
86C42—2631no—
87C42—2632no—
88C42C22×D26311yescharacteristic
89C23—2631no—
90C2×C4—22no—
91C2×C4—2631no—
92C2×C4—2632no—
93C2×C4—5262no—
94C2×C4—5262no—
95C2×C4—10522no—
96C2×C4—10524no—
97C2×C4C2×C4×D26311yescharacteristic
98C2×C4D4×D26312yes—
99C8—42no—
100C8—10522no—
101C22—2632no—
102C22—5262no—
103C22C22⋊C4×D26311yescharacteristic
104C4—21no—
105C4—22no—
106C4—42no—
107C4—5261no—
108C4—5262no—
109C4—10522no—
110C2—5262no—
111C2#101×D26311yescharacteristic
112C2#3068195312yes—
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#330×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC22×D263C22⋊C4
cosocleC42×C263C23
hypercenter#330D263
hypocenterC263#1534
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #30681680C2semidirect
4. #30681679C2semidirect
5. #330×C263C2semidirect
56. C263#1534semidirect
62. #330D263semidirect

Maximal subgroups

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

subgroupindex
#125×D2632
#306819932
#306816802
#306816792
#330×C2632
#1534263