Finite Group Databasebeta

← #46783032

Subgroups — #46783032

Order 33664.

260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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#30682705C211yesmaximal, characteristic
2#30681964C212yesmaximal, complemented
3#30681912C211yesmaximal, characteristic
4#30681710C212yesmaximal, complemented
5#408×C263C211yesmaximal, characteristic
6#22554477—24no—
7C2×#16862360—22no—
8C2×#16862360C2212yes—
9#22554429C2212yes—
10Dic263⋊C8—24no—
11#22554385C414yes—
12C2×#41×C263C2211yescharacteristic
13C2×M16×C263C2211yescharacteristic
14C22×C8×C263C2211yescharacteristic
15C22⋊C8×C263—22no—
16#16862360—24no—
17#16862360—22no—
18#16862360—22no—
19C2×C263⋊C8—24no—
20C2×C263⋊C8D414yes—
21C4⋊Dic263—22no—
22C22⋊Dic263C2×C414yes—
23C4×Dic263—22no—
24#41×C263—22no—
25#41×C263—22no—
26C2×Q8×C263Q811yescharacteristic
27C2×D4×C263C2×C412yes—
28C2×D4×C263Q811yescharacteristic
29C22×C4×C263D412yes—
30C22×C4×C263C2311yescharacteristic
31M16×C263—22no—
32C2×C8×C263—22no—
33C2×C8×C263—21no—
34C2×C8×C263—21no—
35C2×Dic263—24no—
36C263⋊C8—24no—
37C23×C263C4⋊C412yes—
38C23×C263C22×C411yescharacteristic
39Q8×C263—22no—
40D4×C263—24no—
41D4×C263—22no—
42C2×C4×C263—22no—
43C2×C4×C263—22no—
44C2×C4×C263C4⋊C412yes—
45C2×C4×C263C2×D412yes—
46C2×C4×C263C2×D411yescharacteristic
47C2×C4×C263C2×Q811yescharacteristic
48C2×C4×C263#4112yes—
49C8×C263—41no—
50C8×C263—41no—
51C22×C263—22no—
52C22×C263—41no—
53C22×C263—42no—
54C22×C263C2×C4⋊C411yescharacteristic
55C22×C263C4×D412yes—
56C4×C263—22no—
57C4×C263#12011yescharacteristic
58C4×C263C22⋊Q812yes—
59C4×C263#12311yescharacteristic
60Dic263—44no—
61C2×C263—22no—
62C2×C263—21no—
63C2×C263—42no—
64C2×C263#38511yescharacteristic
65C263#186811yescharacteristic, complemented, Sylow
66#1868—2631nomaximal, Sylow
67#568—2631no—
68#424—2632no—
69#410—2631no—
70#408D26311yescharacteristic
71#344—2632no—
72C2×#41C2×D26311yescharacteristic
73#131—5264no—
74C2×M16—2632no—
75C2×M16—5262no—
76C2×M16C2×D26311yescharacteristic
77C22×C8C2×D26311yescharacteristic
78#117—2632no—
79C4⋊C8—5264no—
80#99—2634no—
81C22⋊C8—22no—
82#41—22no—
83#41—22no—
84C2×Q8Dic52611yescharacteristic
85C2×D4C4×D26312yes—
86C2×D4Dic52611yescharacteristic
87C22×C4C22⋊D26312yes—
88C22×C4C22×D26311yescharacteristic
89M16—22no—
90M16—5264no—
91M16—5262no—
92M16—5262no—
93C2×C8—22no—
94C2×C8—21no—
95C2×C8—21no—
96C2×C8—2634no—
97C2×C8—5264no—
98C4⋊C4—5262no—
99C22⋊C4—2634no—
100C42—5262no—
101C23Dic263⋊C412yes—
102C23C2×C4×D26311yescharacteristic
103Q8—22no—
104D4—24no—
105D4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—5264no—
109C2×C4Dic263⋊C412yes—
110C2×C4D4×D26312yes—
111C2×C4C2×C22⋊D26311yescharacteristic
112C2×C4C2×Dic52611yescharacteristic
113C2×C4#1686237512yes—
114C8—41no—
115C8—41no—
116C8—5264no—
117C22—22no—
118C22—41no—
119C22—42no—
120C22C2×Dic263⋊C411yescharacteristic
121C22(C22⋊D263)⋊C412yes—
122C4—22no—
123C4—10524no—
124C4#2255443811yescharacteristic
125C4#2255444712yes—
126C4#2255445111yescharacteristic
127C2—22no—
128C2—21no—
129C2—42no—
130C2#3068181011yescharacteristic
subgroupG/H
centerC4#22554438
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#408×C263C2
socleC2×C263#385
prime radicalC2×#41×C263C22
cosocleC22×C4×C263C23
hypercenter#408D263
hypocenterC263#1868
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #30681964C2semidirect
4. #30681710C2semidirect
65. C263#1868semidirect

Maximal subgroups

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

subgroupindex
#306827052
#306819642
#306819122
#306817102
#408×C2632
#1868263