Finite Group Databasebeta

← #93849

Subgroups — #93849

Order 512.

142 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 32 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#13450C211yesmaximal, characteristic
2#7362C211yesmaximal, characteristic
3#7242C211yesmaximal, characteristic
4C22×Q32C411yescharacteristic
5C2×C4⋊C16C2211yescharacteristic
6C2×#358—21no—
7#1969—21no—
8#1568—21no—
9C22⋊C32—21no—
10#1380C411yescharacteristic
11C22×Q16—21no—
12C2×Q32—41no—
13C2×Q32—42no—
14C22×C16C2×C411yescharacteristic
15C22×C16D411yescharacteristic
16#432—41no—
17C2×#107—21no—
18C2×#103—41no—
19C2×C4×C8D411yescharacteristic
20#391—41no—
21C2×C32—41no—
22C4⋊C16—41no—
23#358—42no—
24#335—41no—
25#334—22no—
26C22×Q8—41no—
27C2×Q16—22no—
28C2×Q16—41no—
29C2×Q16—41no—
30C2×Q16—41no—
31C2×Q16—41no—
32C2×Q16—41no—
33C22×C8C22⋊C411yescharacteristic
34C22×C8SD1611yescharacteristic
35C2×C4⋊C4—41no—
36C2×C42D811yescharacteristic
37Q32—42no—
38Q32—42no—
39C2×C16—21no—
40C2×C16—21no—
41C2×C16—41no—
42C2×C16—41no—
43#107—41no—
44#107—41no—
45C4⋊C8—42no—
46#103—82no—
47C22⋊C8—81no—
48#97—81no—
49C4×C8—21no—
50C4×C8—21no—
51#95—81no—
52#95—81no—
53C32—81no—
54C2×Q8—42no—
55C2×Q8—81no—
56C2×Q8—81no—
57C2×Q8—81no—
58C2×Q8—81no—
59C2×Q8—81no—
60C22×C4—81no—
61C22×C4—81no—
62C22×C4#10211yescharacteristic
63C22×C4D1611yescharacteristic
64C22×C4SD3211yescharacteristic
65Q16—42no—
66Q16—42no—
67Q16—81no—
68Q16—81no—
69C2×C8—21no—
70C2×C8—21no—
71C2×C8—21no—
72C2×C8—41no—
73C2×C8—82no—
74C2×C8#9911yescharacteristic
75C2×C8#10411yescharacteristic
76C4⋊C4—81no—
77C4⋊C4—81no—
78C42—21no—
79C42—21no—
80C16—41no—
81C16—41no—
82C23#35711yescharacteristic
83Q8—82no—
84Q8—82no—
85Q8—161no—
86Q8—161no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—41no—
94C2×C4—82no—
95C2×C4—161no—
96C2×C4—161no—
97C2×C4—161no—
98C2×C4—161no—
99C2×C4—161no—
100C2×C4#32711yescharacteristic
101C2×C4#36011yescharacteristic
102C8—21no—
103C8—41no—
104C8—162no—
105C8AΣL(1,𝔽16)11yescharacteristic
106C8#35511yescharacteristic
107C22—21no—
108C22—21no—
109C22#134711yescharacteristic
110C22#141711yescharacteristic
111C22#142011yescharacteristic
112C4—21no—
113C4—41no—
114C4—41no—
115C4—162no—
116C4—321no—
117C4#134111yescharacteristic
118C4#134511yescharacteristic
119C2—21no—
120C2—21no—
121C2#708811yescharacteristic
122C2#742111yescharacteristic
123C2#742311yescharacteristic
subgroupG/H
center, socleC22#1347
commutatorC22×C16C2×C4
Frattini, cosocleC2×C4⋊C16C22
prime radicalC23#357
LCSG ▷ C22×C16 ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C4⋊C16 ◁ G
LECSG ▷ C2×C4⋊C16 ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#134502
#73622
#72422