Finite Group Databasebeta

← #93744

Subgroups — #93744

Order 512.

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

normal subgroups only

This group has 136 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#8838C211yesmaximal, characteristic
2#7128C211yesmaximal, characteristic
3#7057C211yesmaximal, characteristic
4#2983C411yescharacteristic
5#1984C2211yescharacteristic
6C4×#101C411yescharacteristic
7#1565—21no—
8#1374—21no—
9#1322—21no—
10#1278—21no—
11C2×C4×Q8C2×C411yescharacteristic
12C22×C16—41no—
13#446—41no—
14#446—41no—
15#432—41no—
16#431—21no—
17C2×C4⋊C8D411yescharacteristic
18C2×#101—21no—
19C4×M16—21no—
20C2×C4×C8D411yescharacteristic
21C22⋊C16—41no—
22#343C811yescharacteristic
23#343C811yescharacteristic
24#336—41no—
25#335—41no—
26#334—41no—
27C22×Q8M1611yescharacteristic
28C2×M16—21no—
29C2×M16—21no—
30C22×C8—21no—
31C22×C8—21no—
32C4×Q8—41no—
33C4×Q8—41no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4C2×C811yescharacteristic
36C2×C42—21no—
37C2×C42C22⋊C411yescharacteristic
38C2×C16—42no—
39C2×C16—81no—
40C2×C16—81no—
41C2×C16—81no—
42C4⋊C8—21no—
43C4⋊C8—21no—
44C4⋊C8—41no—
45C4⋊C8—41no—
46C4⋊C8—41no—
47#101—42no—
48C22⋊C8—41no—
49#97—41no—
50#97—42no—
51C4×C8—41no—
52C4×C8—41no—
53C4×C8—41no—
54C2×Q8—21no—
55C2×Q8—21no—
56C2×Q8—41no—
57C2×Q8—41no—
58C22×C4—21no—
59C22×C4—21no—
60C22×C4C22⋊C811yescharacteristic
61C22×C4#9911yescharacteristic
62C22×C4#10111yescharacteristic
63M16—22no—
64M16—41no—
65M16—41no—
66M16—41no—
67C2×C8—21no—
68C2×C8—21no—
69C2×C8—41no—
70C2×C8—41no—
71C2×C8—41no—
72C2×C8—41no—
73C2×C8—41no—
74C2×C8—41no—
75C2×C8—41no—
76C2×C8—81no—
77C4⋊C4—41no—
78C4⋊C4—42no—
79C42—21no—
80C42—21no—
81C42—41no—
82C42—41no—
83C16—82no—
84C16—161no—
85C23#32411yescharacteristic
86Q8—81no—
87Q8—81no—
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—81no—
99C2×C4#35011yescharacteristic
100C2×C4#35011yescharacteristic
101C2×C4AΣL(1,𝔽16)11yescharacteristic
102C2×C4#35211yescharacteristic
103C8—41no—
104C8—41no—
105C8—42no—
106C8—81no—
107C8—81no—
108C8—81no—
109C8—81no—
110C22—21no—
111C22—21no—
112C22#132311yescharacteristic
113C22#132611yescharacteristic
114C22#132711yescharacteristic
115C4—21no—
116C4—21no—
117C4—21no—
118C4—41no—
119C4—81no—
120C4—81no—
121C4#140411yescharacteristic
122C4#140511yescharacteristic
123C2—21no—
124C2—21no—
125C2#706711yescharacteristic
126C2#737611yescharacteristic
127C2#737711yescharacteristic
subgroupG/H
centerC2×C4AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C8
Frattini, cosocle#1984C22
socleC22#1326
prime radicalC23#324
LCSG ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #1984 ◁ G
LECSG ▷ #1984 ▷ C2×C42 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#88382
#71282
#70572