Finite Group Databasebeta

← #94480

Subgroups — #94480

Order 512.

145 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 145 conjugacy classes of subgroups — too many to draw. Only its 40 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#13270C211yesmaximal, characteristic
2#11539C211yesmaximal, characteristic
3#8639C211yesmaximal, characteristic
4#2960C2211yescharacteristic
5#2166—21no—
6#2153C411yescharacteristic
7#2110C411yescharacteristic
8#1567—21no—
9#1561C412yes—
10#1378—21no—
11#1376—21no—
12#1328C412yes—
13#1327—21no—
14#1309—21no—
15#533C2×C411yescharacteristic
16C2×M32—21no—
17C2×M32—21no—
18#446—41no—
19C8×Q8—41no—
20#424C2×C411yescharacteristic
21#424Q811yescharacteristic
22#423—22no—
23#423D411yescharacteristic
24#405C2×C411yescharacteristic
25#405D411yescharacteristic
26C2×C4×C8D411yescharacteristic
27#364—41no—
28#364—41no—
29#349—22no—
30#347—41no—
31#347—41no—
32#335—41no—
33#335—41no—
34#332—42no—
35C2×M16—42no—
36C2×M16C22⋊C411yescharacteristic
37C2×M16C4⋊C411yescharacteristic
38C22×C8C22⋊C411yescharacteristic
39C22×C8C4⋊C411yescharacteristic
40C4⋊Q8—21no—
41#125—21no—
42C22⋊Q8—41no—
43C4×Q8—41no—
44#117C4211yescharacteristic
45#117C4⋊C411yescharacteristic
46C2×C42C22⋊C411yescharacteristic
47M32—22no—
48M32—41no—
49M32—42no—
50M32—41no—
51M32—41no—
52C2×C16—41no—
53C2×C16—41no—
54C4⋊C8—41no—
55C4⋊C8—41no—
56C4⋊C8—41no—
57C4⋊C8—42no—
58C4⋊C8—42no—
59#97—21no—
60#97—21no—
61C4×C8—21no—
62C4×C8—21no—
63C4×C8—21no—
64C4×C8—21no—
65C2×Q8—41no—
66C22×C4—21no—
67C22×C4#9511yescharacteristic
68M16—41no—
69M16—41no—
70M16—162no—
71C2×C8—21no—
72C2×C8—21no—
73C2×C8—21no—
74C2×C8—21no—
75C2×C8—21no—
76C2×C8—41no—
77C2×C8—82no—
78C2×C8#9911yescharacteristic
79C2×C8#9911yescharacteristic
80C4⋊C4—21no—
81C4⋊C4—21no—
82C4⋊C4—42no—
83C4⋊C4—41no—
84C22⋊C4—21no—
85C22⋊C4—21no—
86C42—21no—
87C42—21no—
88C42—21no—
89C42#10011yescharacteristic
90C42#10111yescharacteristic
91C16—42no—
92C16—82no—
93C16—81no—
94C23#34411yescharacteristic
95Q8—81no—
96Q8—81no—
97C2×C4—21no—
98C2×C4—21no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—41no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4#34211yescharacteristic
106C2×C4#34311yescharacteristic
107C8—21no—
108C8—41no—
109C8—41no—
110C8—41no—
111C8—162no—
112C8#35511yescharacteristic
113C8#35611yescharacteristic
114C22—21no—
115C22—41no—
116C22#130511yescharacteristic
117C4—21no—
118C4—21no—
119C4—21no—
120C4—41no—
121C4—81no—
122C4—81no—
123C4#139411yescharacteristic
124C4#139511yescharacteristic
125C2—21no—
126C2—41no—
127C2#732311yescharacteristic
subgroupG/H
center, socleC2#7323
commutator#117C42
Frattini, cosocle#2960C22
prime radicalC23#344
LCSG ▷ #117 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ #2960 ◁ G
LECSG ▷ #2960 ▷ 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
#132702
#115392
#86392