Finite Group Databasebeta

← #46782050

Subgroups — #46782050

Order 33664.

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

normal subgroups only

This group has 182 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
1C263⋊#564C211yesmaximal, characteristic, complemented
2#30682304C211yesmaximal, characteristic
3#30682303C212yesmaximal
4#30681679C212yesmaximal, complemented
5#330×C263C211yesmaximal, characteristic, complemented
6#22554467C2211yescharacteristic
7#22554462C2212yes—
8#22554461—22no—
9#22554460—22no—
10#22554460—22no—
11#22554392—22no—
12#22554392—22no—
13#22554390—22no—
14#22554381C2211yescharacteristic
15#125×C263C2211yescharacteristic
16#97×C263C2212yes—
17C2×D1052—21no—
18C2×D1052—22no—
19C2×C263⋊C8—21no—
20C4⋊Dic263—22no—
21C4⋊Dic263D412yes—
22C4⋊Dic263D412yes—
23Dic263⋊C4—22no—
24Dic263⋊C4—22no—
25Dic263⋊C4—22no—
26Dic263⋊C4—22no—
27C4×Dic263—22no—
28C2×C8×C263—22no—
29C4⋊C4×C263—22no—
30C4⋊C4×C263D412yes—
31C42×C263C2311yescharacteristic
32C22×D263—41no—
33D1052—44no—
34D1052—42no—
35C2×Dic263—22no—
36C2×Dic263—22no—
37C263⋊C8—41no—
38C2×C4×C263—22no—
39C2×C4×C263C2×D412yes—
40C2×C4×C263C2×D411yescharacteristic
41C8×C263—42no—
42C22×C263#12011yescharacteristic
43C2×D263—82no—
44C2×D263—81no—
45C4×C263—22no—
46C4×C263—21no—
47C4×C263—42no—
48Dic263—42no—
49Dic263—42no—
50C2×C263#45412yes—
51C2×C263#45411yescharacteristic
52D263—161no—
53C263#165811yescharacteristic, complemented, Sylow
54#1658—2631nomaximal, Sylow
55#564—2631no—
56#490—2631no—
57#490—2632no—
58#330—2632no—
59#330D26311yescharacteristic, complemented
60#127—2631no—
61#125—2632no—
62#125—5262no—
63#125—5262no—
64#125—5262no—
65#125C2×D26311yescharacteristic
66#102—5262no—
67#102—5262no—
68#102—5262no—
69#97—2631no—
70#97C2×D26312yes—
71C2×D4—5262no—
72C2×D4—5261no—
73C2×C8—22no—
74C2×C8—5261no—
75C4⋊C4—22no—
76C4⋊C4—2632no—
77C4⋊C4—2632no—
78C4⋊C4—5262no—
79C4⋊C4—5262no—
80C4⋊C4—5262no—
81C4⋊C4—5262no—
82C4⋊C4—5262no—
83C4⋊C4D105212yes—
84C42—5262no—
85C42C22×D26311yescharacteristic
86C23—10521no—
87D4—10524no—
88D4—10522no—
89C2×C4—22no—
90C2×C4—5262no—
91C2×C4—5262no—
92C2×C4D4×D26312yes—
93C2×C4C2×D105211yescharacteristic
94C8—42no—
95C8—10521no—
96C22—21042no—
97C22—21041no—
98C22#2255444011yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—10522no—
103C4—10522no—
104C2—42081no—
105C2#3068211212yes—
106C2#3068211311yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#330×C263C2
socleC22×C263#120
prime radical#22554467C22
hypercenter#330D263
hypocenterC263#1658
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. C263⋊#564C2semidirect
4. #30681679C2semidirect
5. #330×C263C2semidirect
53. C263#1658semidirect
59. #330D263semidirect

Maximal subgroups

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

subgroupindex
C263⋊#5642
#306823042
#306823032
#306816792
#330×C2632
#1658263