Finite Group Databasebeta

← #46780902

Subgroups — #46780902

Order 33664.

106 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 23 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#30682120C211yesmaximal, characteristic
2#30681737C211yesmaximal, characteristic, complemented
3#333×C263C211yesmaximal, characteristic, complemented
4#22554518C411yescharacteristic
5#22554501—21no—
6#22554398—21no—
7#22554389—21no—
8#22554389C411yescharacteristic
9C4⋊Q8×C263C2211yescharacteristic
10C4⋊C8×C263—21no—
11#16862377—41no—
12#16862376—21no—
13#16862376—41no—
14Q8×D263—41no—
15#16862366—41no—
16#16862363—41no—
17#16862360—21no—
18#16862360—41no—
19C2×Q8×C263C2×C411yescharacteristic
20C2×Q8×C263D411yescharacteristic
21C2×C8×C263—41no—
22C4⋊C4×C263—41no—
23C42×C263D411yescharacteristic
24Dic526—21no—
25Dic526—41no—
26D1052—21no—
27D1052—41no—
28C22⋊D263—41no—
29C4×D263—41no—
30C4×D263—42no—
31C263⋊C8—41no—
32C263⋊C8—81no—
33Q8×C263—41no—
34Q8×C263—41no—
35C2×C4×C263—21no—
36C2×C4×C263—21no—
37C2×C4×C263—21no—
38C2×C4×C263C22⋊C411yescharacteristic
39C8×C263—81no—
40C22×C263#9911yescharacteristic
41C2×D263—41no—
42C4×C263—21no—
43C4×C263—21no—
44C4×C263—21no—
45C4×C263—41no—
46C4×C263—41no—
47Dic263—41no—
48C2×C263—21no—
49C2×C263AΣL(1,𝔽16)11yescharacteristic
50D263—81no—
51C263#140511yescharacteristic, complemented, Sylow
52#1405—2631nomaximal, Sylow
53#456—2631no—
54#356—2631no—
55#333D26311yescharacteristic, complemented
562−1+4—2631no—
57#137—5261no—
58C4⋊Q8C2×D26311yescharacteristic
59C4⋊C8—21no—
60#104—5261no—
61#101—2631no—
62#101—5261no—
63#41—5261no—
64#41—10521no—
65#41—10521no—
66C2×Q8—10521no—
67C2×Q8C4×D26311yescharacteristic
68C2×Q8D105211yescharacteristic
69Q16—10521no—
70SD16—10521no—
71M16—5261no—
72M16—10521no—
73C2×C8—41no—
74C4⋊C4—41no—
75C42C22⋊D26311yescharacteristic
76Q8—41no—
77Q8—41no—
78Q8—5261no—
79Q8—10521no—
80D4—5261no—
81D4—10521no—
82D4—10521no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—10521no—
87C2×C4—10522no—
88C2×C4(C2×D263)⋊C411yescharacteristic
89C8—81no—
90C8—10521no—
91C8—21041no—
92C22—10521no—
93C22#2255438411yescharacteristic
94C4—21no—
95C4—21no—
96C4—21no—
97C4—41no—
98C4—41no—
99C4—10521no—
100C2—21no—
101C2—21041no—
102C2#3068172611yescharacteristic
subgroupG/H
centerC2#30681726
commutatorC2×Q8×C263C2×C4
FrattiniC4⋊Q8C2×D263
Fitting#333×C263C2
socleC2×C263AΣL(1,𝔽16)
prime radical#22554518C4
cosocleC4⋊Q8×C263C22
hypercenter#333D263
hypocenterC263#1405
LCSG ▷ C2×Q8×C263 ▷ C2×C4×C263 ▷ C22×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #30681737C2semidirect
3. #333×C263C2semidirect
51. C263#1405semidirect
55. #333D263semidirect

Maximal subgroups

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

subgroupindex
#306821202
#306817372
#333×C2632
#1405263