Finite Group Databasebeta

← #46782842

Subgroups — #46782842

Order 33664.

300 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×C22⋊(C263⋊C8)C211yesmaximal, characteristic
2#30681798C211yesmaximal, characteristic
3#30681700C212yesmaximal, complemented
4#30681700C212yesmaximal, complemented
5C2×#117×C263C211yesmaximal, characteristic
6C22×C263⋊C8C2212yes—
7C2×C4⋊Dic263C2212yes—
8C2×C22⋊Dic263—21no—
9C22⋊(C263⋊C8)—22no—
10C263⋊#95—21no—
11C23×C4×C263C2211yescharacteristic
12#117×C263—22no—
13#117×C263C414yescomplemented
14C2×C4⋊C4×C263C2211yescharacteristic
15C2×C4⋊C4×C263C2211yescharacteristic
16C2×C22⋊C4×C263—21no—
17C2×C42×C263—21no—
18C22×Dic263—22no—
19C2×C263⋊C8—22no—
20C2×C263⋊C8—24no—
21C4⋊Dic263—24no—
22C22⋊Dic263—42no—
23C24×C263D411yescharacteristic
24C22×C4×C263—24no—
25C22×C4×C263—21no—
26C22×C4×C263—21no—
27C22×C4×C263C2×C412yes—
28C22×C4×C263D411yescharacteristic
29C22×C4×C263D412yes—
30C22×C4×C263C2311yescharacteristic
31C4⋊C4×C263—21no—
32C4⋊C4×C263—21no—
33C4⋊C4×C263C2×C412yes—
34C4⋊C4×C263C2×C412yes—
35C22⋊C4×C263—24no—
36C42×C263—24no—
37C2×Dic263—42no—
38C2×Dic263—42no—
39C2×Dic263—42no—
40C263⋊C8—42no—
41C23×C263—22no—
42C23×C263—22no—
43C23×C263—21no—
44C23×C263—21no—
45C23×C263C22⋊C412yes—
46C23×C263C2×D411yescharacteristic
47C2×C4×C263—22no—
48C2×C4×C263—24no—
49C2×C4×C263—24no—
50C2×C4×C263—22no—
51C2×C4×C263—22no—
52C2×C4×C263—42no—
53C2×C4×C263—41no—
54C2×C4×C263—41no—
55C2×C4×C263C22⋊C412yes—
56C2×C4×C263C22×C411yescharacteristic
57C2×C4×C263C2×D411yescharacteristic
58C2×C4×C263#4114yes—
59C22×C263—22no—
60C22×C263—22no—
61C22×C263—22no—
62C22×C263—42no—
63C22×C263—42no—
64C22×C263C2×C22⋊C411yescharacteristic
65C22×C263#12312yes—
66C22×C263#13512yes—
67C22×C263AGL(1,ℤ/8)11yescharacteristic
68C22×C263#13711yescharacteristic
69C4×C263—22no—
70C4×C263—42no—
71C4×C263—42no—
72C4×C263#11712yes—
73C4×C263#12312yes—
74Dic263—82no—
75C2×C263—42no—
76C2×C263#38111yescharacteristic
77C2×C263#41611yescharacteristic
78C2×C263#41711yescharacteristic
79C2×C263#48212yes—
80C2×C263#48512yes—
81C263#182511yescharacteristic, complemented, Sylow
82#1825—2631nomaximal, Sylow
83C2×#117D26311yescharacteristic
84C2×C22⋊C8—2631no—
85#380—2631no—
86#340—2632no—
87#340—2632no—
88C23×C4C2×D26311yescharacteristic
89C22×C8—2632no—
90#117—22no—
91#117Dic26314yescomplemented
92C2×C4⋊C4—2632no—
93C2×C4⋊C4C2×D26311yescharacteristic
94C2×C4⋊C4C2×D26311yescharacteristic
95C2×C22⋊C4—21no—
96C2×C22⋊C4—5261no—
97C2×C42—21no—
98C22⋊C8—5262no—
99#95—5261no—
100C24C22⋊D26311yescharacteristic
101C22×C4—24no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—5262no—
105C22×C4C2×Dic26312yes—
106C22×C4C22⋊D26311yescharacteristic
107C22×C4C22⋊D26312yes—
108C22×C4C22×D26311yescharacteristic
109C2×C8—5262no—
110C2×C8—5264no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—5264no—
114C4⋊C4C2×Dic26312yes—
115C4⋊C4C2×Dic26312yes—
116C22⋊C4—24no—
117C22⋊C4—10522no—
118C42—24no—
119C23—22no—
120C23—22no—
121C23—21no—
122C23—21no—
123C23C22⋊Dic26312yes—
124C23C2×C22⋊D26311yescharacteristic
125C2×C4—22no—
126C2×C4—24no—
127C2×C4—24no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—10522no—
134C2×C4—10522no—
135C2×C4—10522no—
136C2×C4C22⋊Dic26312yes—
137C2×C4C22×Dic26311yescharacteristic
138C2×C4C2×C22⋊D26311yescharacteristic
139C2×C4#1686237614yes—
140C8—10522no—
141C22—22no—
142C22—22no—
143C22—22no—
144C22—42no—
145C22—42no—
146C22C2×C22⋊Dic26311yescharacteristic
147C22#2255445312yes—
148C22#2255449012yes—
149C22#2255449511yescharacteristic
150C22#2255450011yescharacteristic
151C4—22no—
152C4—42no—
153C4—42no—
154C4—21042no—
155C4#2255442912yes—
156C4#2255445312yes—
157C2—42no—
158C2#3068180111yescharacteristic
159C2#3068193411yescharacteristic
160C2#3068193911yescharacteristic
161C2#3068226212yes—
162C2#3068227912yes—
subgroupG/H
centerC23C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#117×C263C2
socleC23×C263C2×D4
prime radicalC24×C263D4
cosocleC22×C4×C263C23
hypercenterC2×#117D263
hypocenterC263#1825
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #30681700C2semidirect
4. #30681700C2semidirect
13. #117×C263C4semidirect
81. C263#1825semidirect
91. #117Dic263semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊(C263⋊C8)2
#306817982
#306817002
C2×#117×C2632
#1825263