Finite Group Databasebeta

← #93014

Subgroups — #93014

Order 512.

185 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 185 conjugacy classes of subgroups — too many to draw. Only its 56 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#13263C211yesmaximal, characteristic
2#8621C211yesmaximal, characteristic
3#8615C211yesmaximal, characteristic
4C2×C8×Q8C2211yescharacteristic
5C2×C4⋊C16C411yescharacteristic
6C2×C4×C16C411yescharacteristic
7#1801—21no—
8#1568—21no—
9#1566—21no—
10#1467—21no—
11#1374—21no—
12#1374—21no—
13#1292C412yes—
14#1290C412yes—
15C2×C4×Q8D411yescharacteristic
16C22×C16—21no—
17C22×C16—21no—
18C8×Q8—41no—
19C8×Q8—41no—
20#432—22no—
21#423—22no—
22C2×C4⋊C8C2×C411yescharacteristic
23C2×C4⋊C8C2×C411yescharacteristic
24C2×C4⋊C8Q811yescharacteristic
25C2×#101—41no—
26C2×C4×C8C2×C411yescharacteristic
27C2×C4×C8D411yescharacteristic
28C2×C4×C8D411yescharacteristic
29C4⋊C16—41no—
30C4×C16—41no—
31#343—41no—
32#335—41no—
33#334—41no—
34#334—41no—
35#334—41no—
36#324—41no—
37#324—41no—
38C22×Q8SD1611yescharacteristic
39C2×M16—42no—
40C22×C8C4211yescharacteristic
41C22×C8C22⋊C411yescharacteristic
42C22×C8C4⋊C411yescharacteristic
43C22×C8C4⋊C411yescharacteristic
44C4×Q8—41no—
45C4×Q8—41no—
46C2×C4⋊C4D811yescharacteristic
47C2×C4⋊C4SD1611yescharacteristic
48C2×C4⋊C4Q1611yescharacteristic
49C2×C42C22⋊C411yescharacteristic
50C2×C42C22⋊C411yescharacteristic
51C2×C42C4⋊C411yescharacteristic
52C2×C16—22no—
53C2×C16—41no—
54C2×C16—41no—
55C2×C16—42no—
56C2×C16—41no—
57C4⋊C8—41no—
58C4⋊C8—41no—
59C4⋊C8—41no—
60C4⋊C8—42no—
61C4⋊C8—42no—
62C4⋊C8—42no—
63#101—82no—
64C22⋊C8—42no—
65#97—42no—
66C4×C8—21no—
67C4×C8—21no—
68C4×C8—21no—
69C4×C8—21no—
70C4×C8—21no—
71C4×C8—21no—
72C2×Q8—22no—
73C2×Q8—22no—
74C2×Q8—41no—
75C22×C4#9511yescharacteristic
76C22×C4#10211yescharacteristic
77C22×C4#10211yescharacteristic
78C22×C4#10311yescharacteristic
79C22×C4#10311yescharacteristic
80C22×C4#10611yescharacteristic
81C22×C4#10711yescharacteristic
82M16—82no—
83M16—82no—
84C2×C8—21no—
85C2×C8—21no—
86C2×C8—21no—
87C2×C8—21no—
88C2×C8—21no—
89C2×C8—41no—
90C2×C8—41no—
91C2×C8—41no—
92C2×C8—82no—
93C2×C8—82no—
94C2×C8#9911yescharacteristic
95C2×C8#9911yescharacteristic
96C4⋊C4—41no—
97C4⋊C4—41no—
98C4⋊C4—41no—
99C42—21no—
100C42—21no—
101C42—21no—
102C42—21no—
103C42—21no—
104C42—21no—
105C16—42no—
106C16—81no—
107C23#34011yescharacteristic
108Q8—44no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4H(3,ℤ/4)11yescharacteristic
125C2×C4#34211yescharacteristic
126C2×C4#35912yes—
127C2×C4#36512yes—
128C8—21no—
129C8—41no—
130C8—41no—
131C8—41no—
132C8—162no—
133C8—162no—
134C8#35511yescharacteristic
135C8#35611yescharacteristic
136C22—21no—
137C22—21no—
138C22#128911yescharacteristic
139C22#138211yescharacteristic
140C22#138311yescharacteristic
141C4—22no—
142C4—22no—
143C4—21no—
144C4—41no—
145C4—41no—
146C4—41no—
147C4—41no—
148C4#139211yescharacteristic
149C4#139411yescharacteristic
150C2—21no—
151C2—21no—
152C2#722711yescharacteristic
153C2#723211yescharacteristic
154C2#723811yescharacteristic
subgroupG/H
center, socleC22#1289
commutatorC22×C8C42
Frattini, cosocleC2×C8×Q8C22
prime radicalC23#340
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C8×Q8 ◁ G
LECSG ▷ C2×C8×Q8 ▷ C22×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#132632
#86212
#86152