Finite Group Databasebeta

← #94269

Subgroups — #94269

Order 512.

216 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 44 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#11532C212yesmaximal
2#9637C211yesmaximal, characteristic
3C4×C4⋊Q8C2211yescharacteristic
4#1842C411yescharacteristic
5C42×C8C411yescharacteristic
6C2×Q8⋊C8—22no—
7#1467—22no—
8#1325—22no—
9#1319C414yes—
10C2×C4⋊Q8Q811yescharacteristic
11C2×C4×Q8D412yes—
12#432—42no—
13C2×C4⋊C8—21no—
14C2×C4⋊C8—41no—
15C2×C4×C8—21no—
16C2×C4×C8—41no—
17#391C2×C412yes—
18#389—41no—
19#384D411yescharacteristic
20C4×C4⋊C4—41no—
21C43C2×C411yescharacteristic
22Q8⋊C8—44no—
23#324—24no—
24#324—42no—
25C22×Q8C4⋊C412yes—
26C22×C8—41no—
27C22×C8—41no—
28C4⋊Q8—22no—
29C4⋊Q8—41no—
30C4×Q8—42no—
31C4×Q8—42no—
32C2×C4⋊C4—22no—
33C2×C4⋊C4—41no—
34C2×C4⋊C4—41no—
35C2×C4⋊C4C22⋊C412yes—
36C2×C42—21no—
37C2×C42—21no—
38C2×C42—22no—
39C2×C42C4211yescharacteristic
40C2×C42C22⋊C411yescharacteristic
41C2×C42C4⋊C411yescharacteristic
42C4⋊C8—42no—
43C4⋊C8—82no—
44C4⋊C8—82no—
45C22⋊C8—44no—
46#97—82no—
47C4×C8—22no—
48C4×C8—41no—
49C4×C8—44no—
50#95—42no—
51C2×Q8—22no—
52C2×Q8—22no—
53C2×Q8—42no—
54C2×Q8—42no—
55C22×C4—21no—
56C22×C4—21no—
57C22×C4—22no—
58C22×C4—22no—
59C22×C4#9511yescharacteristic
60C22×C4#9911yescharacteristic
61C22×C4#9911yescharacteristic
62C2×C8—42no—
63C2×C8—44no—
64C2×C8—82no—
65C2×C8—84no—
66C2×C8—81no—
67C4⋊C4—42no—
68C4⋊C4—44no—
69C4⋊C4—82no—
70C4⋊C4—82no—
71C42—22no—
72C42—22no—
73C42—21no—
74C42—21no—
75C42—21no—
76C42—41no—
77C42—42no—
78C42—42no—
79C42—42no—
80C42#10812yes—
81C23#34211yescharacteristic
82Q8—44no—
83Q8—82no—
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—22no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—22no—
92C2×C4—21no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4—42no—
97C2×C4—42no—
98C2×C4—42no—
99C2×C4—42no—
100C2×C4—82no—
101C2×C4#33811yescharacteristic
102C2×C4#34111yescharacteristic
103C2×C4#35311yescharacteristic
104C2×C4#35411yescharacteristic
105C8—44no—
106C8—164no—
107C8—161no—
108C22—21no—
109C22—21no—
110C22#129311yescharacteristic
111C22#139211yescharacteristic
112C22#139311yescharacteristic
113C4—24no—
114C4—21no—
115C4—21no—
116C4—21no—
117C4—42no—
118C4—41no—
119C4—82no—
120C4—82no—
121C4#141011yescharacteristic
122C4#141111yescharacteristic
123C2—21no—
124C2—21no—
125C2#724911yescharacteristic
126C2#749911yescharacteristic
127C2#750011yescharacteristic
subgroupG/H
center, socleC22#1393
commutatorC2×C42C42
Frattini, cosocleC4×C4⋊Q8C22
prime radicalC23#342
LCSG ▷ C2×C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C4×C4⋊Q8 ▷ 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
#115322
#96372