Finite Group Databasebeta

← #93499

Subgroups — #93499

Order 512.

207 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 207 conjugacy classes of subgroups — too many to draw. Only its 62 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#12845C211yesmaximal, characteristic
2#12786C211yesmaximal, characteristic
3#8157C211yesmaximal, characteristic
4C2×#405C2211yescharacteristic
5#2150—21no—
6C2×#349C412yes—
7C2×C22⋊C16C412yes—
8#1458C412yes—
9#1452—21no—
10#1377—21no—
11#1374—21no—
12#1374—21no—
13#1281—21no—
14C22×M16C2×C411yescharacteristic
15C23×C8C2×C411yescharacteristic
16C2×#117C2×C411yescharacteristic
17C2×M32—22no—
18C22×C16—22no—
19#431—22no—
20#405—42no—
21C2×#97D411yescharacteristic
22C2×#97Q811yescharacteristic
23C2×C4×C8D411yescharacteristic
24C2×C4×C8D411yescharacteristic
25C4⋊C16—42no—
26#349—42no—
27C22⋊C16—42no—
28#324C814yes—
29#323—22no—
30#322—42no—
31C23×C4C4211yescharacteristic
32C2×M16—21no—
33C2×M16—21no—
34C2×M16—41no—
35C2×M16—41no—
36C22×C8—22no—
37C22×C8—41no—
38C22×C8—41no—
39C22×C8C22⋊C411yescharacteristic
40C22×C8C22⋊C411yescharacteristic
41C22×C8C4⋊C411yescharacteristic
42C22×C8C4⋊C411yescharacteristic
43#117—41no—
44#117—41no—
45C2×C4⋊C4C2×C812yes—
46C2×C22⋊C4M1612yes—
47C2×C42C22⋊C411yescharacteristic
48C2×C42C4⋊C411yescharacteristic
49M32—42no—
50M32—42no—
51C2×C16—42no—
52C2×C16—42no—
53C2×C16—42no—
54C2×C16—42no—
55C4⋊C8—42no—
56C22⋊C8—24no—
57#97—41no—
58#97—41no—
59C4×C8—22no—
60C4×C8—22no—
61C4×C8—42no—
62C24#9711yescharacteristic
63C22×C4—21no—
64C22×C4—21no—
65C22×C4—21no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4#9511yescharacteristic
70C22×C4C4×C811yescharacteristic
71C22×C4C22⋊C812yes—
72C22×C4C4⋊C812yes—
73M16—42no—
74M16—42no—
75C2×C8—21no—
76C2×C8—21no—
77C2×C8—21no—
78C2×C8—21no—
79C2×C8—21no—
80C2×C8—21no—
81C2×C8—21no—
82C2×C8—21no—
83C2×C8—21no—
84C2×C8—21no—
85C2×C8—44no—
86C2×C8—44no—
87C2×C8#9912yes—
88C2×C8#10011yescharacteristic
89C2×C8#10111yescharacteristic
90C4⋊C4—42no—
91C22⋊C4—42no—
92C42—21no—
93C42—21no—
94C42—21no—
95C42—21no—
96C16—82no—
97C16—82no—
98C23—21no—
99C23—21no—
100C23—21no—
101C23—42no—
102C23#33611yescharacteristic
103C2×C4—21no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—42no—
113C2×C4—42no—
114C2×C4#34211yescharacteristic
115C2×C4#34311yescharacteristic
116C2×C4#34411yescharacteristic
117C2×C4#34411yescharacteristic
118C2×C4#34411yescharacteristic
119C2×C4#34411yescharacteristic
120C8—21no—
121C8—21no—
122C8—22no—
123C8—41no—
124C8—41no—
125C8—84no—
126C22—22no—
127C22—42no—
128C22—41no—
129C22—81no—
130C22—81no—
131C22#128111yescharacteristic
132C22#128211yescharacteristic
133C22#128311yescharacteristic
134C4—42no—
135C4—42no—
136C4—41no—
137C4#130511yescharacteristic
138C4#130611yescharacteristic
139C4#130711yescharacteristic
140C4#130811yescharacteristic
141C2—21no—
142C2—21no—
143C2—81no—
144C2#703311yescharacteristic
145C2#720812yes—
subgroupG/H
centerC2×C4#342
commutatorC22×C4C4×C8
Frattini, cosocleC2×#405C22
socleC22#1282
prime radicalC24#97
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#405 ◁ G
LECSG ▷ C2×#405 ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#128452
#127862
#81572