Finite Group Databasebeta

← #94272

Subgroups — #94272

Order 512.

197 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 197 conjugacy classes of subgroups — too many to draw. Only its 44 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#11532C212yesmaximal
2#9641C211yesmaximal, characteristic
3C4×C4⋊Q8C2211yescharacteristic
4#1831C411yescharacteristic
5#1744C411yescharacteristic
6C2×Q8⋊C8—22no—
7#1467—22no—
8#1325—22no—
9#1319C414yes—
10C2×C4⋊Q8Q811yescharacteristic
11C2×C4×Q8D412yes—
12#432—42no—
13C2×C4⋊C8—21no—
14C2×C4×C8—21no—
15#391C2×C412yes—
16#389—41no—
17#384D411yescharacteristic
18C4×C4⋊C4—41no—
19C43C2×C411yescharacteristic
20#336—41no—
21#336—41no—
22Q8⋊C8—44no—
23#324—24no—
24#324—42no—
25C22×Q8C4⋊C412yes—
26C22×C8—41no—
27C22×C8—41no—
28C4⋊Q8—22no—
29C4⋊Q8—41no—
30C4×Q8—42no—
31C4×Q8—42no—
32C2×C4⋊C4—22no—
33C2×C4⋊C4—41no—
34C2×C4⋊C4—41no—
35C2×C4⋊C4C22⋊C412yes—
36C2×C42—22no—
37C2×C42—21no—
38C2×C42—21no—
39C2×C42C4211yescharacteristic
40C2×C42C22⋊C411yescharacteristic
41C2×C42C4⋊C411yescharacteristic
42C4⋊C8—42no—
43C4⋊C8—82no—
44C22⋊C8—44no—
45#97—82no—
46C4×C8—22no—
47C4×C8—41no—
48#95—42no—
49C2×Q8—22no—
50C2×Q8—22no—
51C2×Q8—42no—
52C2×Q8—42no—
53C22×C4—21no—
54C22×C4—21no—
55C22×C4—22no—
56C22×C4—22no—
57C22×C4#9511yescharacteristic
58C22×C4#9911yescharacteristic
59C22×C4#9911yescharacteristic
60C2×C8—42no—
61C2×C8—82no—
62C2×C8—82no—
63C2×C8—84no—
64C2×C8—81no—
65C4⋊C4—42no—
66C4⋊C4—44no—
67C4⋊C4—82no—
68C4⋊C4—82no—
69C42—21no—
70C42—21no—
71C42—21no—
72C42—41no—
73C42—42no—
74C42—42no—
75C42—42no—
76C42—81no—
77C42#10812yes—
78C23#34211yescharacteristic
79Q8—44no—
80Q8—82no—
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—22no—
84C2×C4—22no—
85C2×C4—21no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4—41no—
90C2×C4—41no—
91C2×C4—42no—
92C2×C4—41no—
93C2×C4—42no—
94C2×C4—42no—
95C2×C4—42no—
96C2×C4—82no—
97C2×C4#33811yescharacteristic
98C2×C4#34111yescharacteristic
99C2×C4#35311yescharacteristic
100C2×C4#35411yescharacteristic
101C8—82no—
102C8—161no—
103C8—164no—
104C22—21no—
105C22—21no—
106C22#129311yescharacteristic
107C22#139211yescharacteristic
108C22#139311yescharacteristic
109C4—21no—
110C4—21no—
111C4—21no—
112C4—42no—
113C4—41no—
114C4—81no—
115C4—82no—
116C4—82no—
117C4#141312yes—
118C2—21no—
119C2—21no—
120C2#724911yescharacteristic
121C2#750511yescharacteristic
122C2#750611yescharacteristic
subgroupG/H
center, socleC22#1393
commutatorC2×C42C42
Frattini, cosocleC4×C4⋊Q8C22
prime radicalC23#342
LCSG ▷ C2×C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C4×C4⋊Q8 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#115322
#96412