Finite Group Databasebeta

← #46780653

Subgroups — #46780653

Order 33664.

200 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 61 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#30681902C211yesmaximal, characteristic
2#30681902C211yesmaximal, characteristic
3#380×C263C211yesmaximal, characteristic
4C2×#16862360—21no—
5C2×#16862360C412yescomplemented
6C22⋊(C263⋊C8)—21no—
7C22⋊(C263⋊C8)—21no—
8C22⋊(C263⋊C8)—21no—
9C22⋊(C263⋊C8)C412yescomplemented
10C23×C4×C263C2211yescharacteristic
11C2×C4⋊C4×C263—21no—
12C2×C22⋊C4×C263C412yes—
13#95×C263—21no—
14#16862360—42no—
15#16862360—42no—
16C2×C263⋊C8—22no—
17C2×C263⋊C8—22no—
18C24×C263C2×C411yescharacteristic
19C22×C4×C263—22no—
20C22×C4×C263—42no—
21C22×C4×C263C2×C411yescharacteristic
22C22×C4×C263C2×C411yescharacteristic
23C22×C4×C263D411yescharacteristic
24C22×C4×C263D411yescharacteristic
25C22×C4×C263D411yescharacteristic
26C22×C4×C263Q811yescharacteristic
27C4⋊C4×C263—42no—
28C22⋊C4×C263—42no—
29C263⋊C8—42no—
30C263⋊C8—42no—
31C23×C263—21no—
32C23×C263—21no—
33C23×C263—41no—
34C23×C263—41no—
35C23×C263C4211yescharacteristic
36C23×C263C22⋊C411yescharacteristic
37C23×C263C4⋊C411yescharacteristic
38C2×C4×C263—22no—
39C2×C4×C263—22no—
40C2×C4×C263—22no—
41C2×C4×C263—41no—
42C2×C4×C263—41no—
43C2×C4×C263—41no—
44C2×C4×C263—42no—
45C2×C4×C263—42no—
46C2×C4×C263—42no—
47C2×C4×C263C22⋊C411yescharacteristic
48C2×C4×C263C22⋊C411yescharacteristic
49C2×C4×C263C4⋊C411yescharacteristic
50C2×C4×C263C4⋊C411yescharacteristic
51C22×C263—21no—
52C22×C263—21no—
53C22×C263—21no—
54C22×C263—21no—
55C22×C263—21no—
56C22×C263—21no—
57C22×C263—21no—
58C22×C263—21no—
59C22×C263—42no—
60C22×C263—42no—
61C22×C263#9511yescharacteristic
62C22×C263#10011yescharacteristic
63C22×C263#10111yescharacteristic
64C4×C263—21no—
65C4×C263—21no—
66C4×C263—21no—
67C4×C263—82no—
68C4×C263#9912yes—
69C2×C263—21no—
70C2×C263—21no—
71C2×C263—41no—
72C2×C263—41no—
73C2×C263#34211yescharacteristic
74C2×C263#34311yescharacteristic
75C2×C263#34411yescharacteristic
76C263#130511yescharacteristic, complemented, Sylow
77#1305—2631nomaximal, Sylow
78#407—2631no—
79#407—2631no—
80#380D26311yescharacteristic
81C23×C4C2×D26311yescharacteristic
82C2×M16—2632no—
83C2×M16—5261no—
84C2×C4⋊C4—21no—
85C2×C22⋊C4Dic26312yes—
86C22⋊C8—2632no—
87C22⋊C8—5261no—
88C22⋊C8—5261no—
89C22⋊C8—5261no—
90#95—21no—
91C24C2×Dic26311yescharacteristic
92C22×C4—22no—
93C22×C4—42no—
94C22×C4C4×D26311yescharacteristic
95C22×C4C4×D26311yescharacteristic
96C22×C4C22⋊D26311yescharacteristic
97C22×C4C22⋊D26311yescharacteristic
98C22×C4D105211yescharacteristic
99C22×C4Dic52611yescharacteristic
100M16—10522no—
101M16—10522no—
102C2×C8—5262no—
103C2×C8—5262no—
104C4⋊C4—42no—
105C22⋊C4—42no—
106C23—21no—
107C23—21no—
108C23—41no—
109C23—41no—
110C23C4×Dic26311yescharacteristic
111C23C22⋊Dic26311yescharacteristic
112C23C4⋊Dic26311yescharacteristic
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—42no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4(C2×D263)⋊C411yescharacteristic
123C2×C4(C2×D263)⋊C411yescharacteristic
124C2×C4Dic263⋊C411yescharacteristic
125C2×C4Dic263⋊C411yescharacteristic
126C8—10522no—
127C8—10522no—
128C22—21no—
129C22—21no—
130C22—21no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22—21no—
135C22—21no—
136C22—42no—
137C22—42no—
138C22C263⋊#9511yescharacteristic
139C22#2255438711yescharacteristic
140C22#2255438911yescharacteristic
141C4—21no—
142C4—21no—
143C4—21no—
144C4—82no—
145C4#2255438412yes—
146C2—21no—
147C2—21no—
148C2—41no—
149C2—41no—
150C2#3068170411yescharacteristic
151C2#3068170711yescharacteristic
152C2#3068170811yescharacteristic
subgroupG/H
centerC22C263⋊#95
commutatorC23×C263C42
FrattiniC23×C4C2×D263
Fitting#380×C263C2
socleC22×C263#95
prime radicalC24×C263C2×C4
cosocleC23×C4×C263C22
hypercenter#380D263
hypocenterC263#1305
LCSG ▷ C23×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
5. C2×#16862360C4semidirect
9. C22⋊(C263⋊C8)C4semidirect
76. C263#1305semidirect

Maximal subgroups

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

subgroupindex
#306819022
#380×C2632
#1305263