Finite Group Databasebeta

← #46781890

Subgroups — #46781890

Order 33664.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#30682654C211yesmaximal, characteristic
2#30682225C212yesmaximal, complemented
3#30681687C211yesmaximal, characteristic, complemented
4#30681667C212yesmaximal, complemented
5#494×C263C211yesmaximal, characteristic, complemented
6#22554459—22no—
7#22554445—22no—
8C4×D1052C2212yes—
9#22554428—22no—
10#22554401—22no—
11C4⋊(C263⋊C8)C2212yes—
12#22554390—22no—
13C2×Q16×C263—22no—
14C4⋊Q8×C263C2211yescharacteristic
15C4⋊Q8×C263C2211yescharacteristic
16C4×C8×C263C2211yescharacteristic
17C2×D1052—22no—
18C2×D1052D412yes—
19C2×C4×D263—22no—
20C2×C263⋊C8—22no—
21C4⋊Dic263D412yes—
22(C2×D263)⋊C4—24no—
23(C2×D263)⋊C4—22no—
24C4×Dic263—22no—
25C2×Q8×C263—21no—
26C2×Q8×C263D412yes—
27Q16×C263—44no—
28C2×C8×C263—21no—
29C4⋊C4×C263—22no—
30C4⋊C4×C263—22no—
31C42×C263C2311yescharacteristic
32C22×D263—22no—
33D1052—22no—
34D1052—22no—
35D1052—82no—
36C2×Dic263—22no—
37C4×D263—42no—
38C4×D263—42no—
39C263⋊C8—42no—
40Q8×C263—42no—
41Q8×C263—42no—
42C2×C4×C263—22no—
43C2×C4×C263—41no—
44C2×C4×C263C2×D412yes—
45C2×C4×C263C2×D411yescharacteristic
46C8×C263—22no—
47C22×C263#12011yescharacteristic
48C2×D263—42no—
49C2×D263—42no—
50C2×D263—42no—
51C4×C263—21no—
52C4×C263—42no—
53C4×C263—81no—
54C4×C263#13512yes—
55C4×C263#13712yes—
56Dic263—42no—
57C2×C263#45212yes—
58C2×C263#45311yescharacteristic
59D263—82no—
60C263#163411yescharacteristic, complemented, Sylow
61#1634—2631nomaximal, Sylow
62#555—2631no—
63#494D26311yescharacteristic, complemented
64#476—2632no—
65#333—2631no—
66D4⋊C8—2632no—
67C2×Q16—22no—
68C4⋊Q8C2×D26311yescharacteristic
69C4⋊Q8C2×D26311yescharacteristic
70#124—5262no—
71#121—5262no—
72C4×D4—2632no—
73#117—5262no—
74#106—5262no—
75C4⋊C8—2632no—
76#102—5262no—
77C4×C8C2×D26311yescharacteristic
78C2×Q8—21no—
79C2×Q8C22⋊D26312yes—
80C2×D4—2632no—
81C2×D4—5262no—
82C22×C4—5262no—
83Q16—44no—
84C2×C8—21no—
85C2×C8—5262no—
86C4⋊C4—22no—
87C4⋊C4—22no—
88C4⋊C4—2632no—
89C22⋊C4—5264no—
90C22⋊C4—5262no—
91C42—5262no—
92C42C22×D26311yescharacteristic
93C23—5262no—
94Q8—42no—
95Q8—42no—
96D4—5262no—
97D4—5262no—
98D4—21042no—
99C2×C4—22no—
100C2×C4—41no—
101C2×C4—5262no—
102C2×C4—10522no—
103C2×C4—10522no—
104C2×C4D4×D26312yes—
105C2×C4C2×C22⋊D26311yescharacteristic
106C8—22no—
107C8—10522no—
108C22—10522no—
109C22—10522no—
110C22—10522no—
111C22#2255443811yescharacteristic
112C4—21no—
113C4—42no—
114C4—81no—
115C4—10522no—
116C4#2255449312yes—
117C4#2255450212yes—
118C2—21042no—
119C2#3068209912yes—
120C2#3068210511yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#494×C263C2
socleC22×C263#120
prime radical#30682654C2
hypercenter#494D263
hypocenterC263#1634
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. #30682225C2semidirect
3. #30681687C2semidirect
4. #30681667C2semidirect
5. #494×C263C2semidirect
60. C263#1634semidirect
63. #494D263semidirect

Maximal subgroups

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

subgroupindex
#306826542
#306822252
#306816872
#306816672
#494×C2632
#1634263