Finite Group Databasebeta

← #94247

Subgroups — #94247

Order 512.

225 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 225 conjugacy classes of subgroups — too many to draw. Only its 52 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#12802C212yesmaximal
2#9641C211yesmaximal, characteristic
3C4×C4⋊Q8C2211yescharacteristic
4C2×#356—22no—
5#1831C411yescharacteristic
6#1801—22no—
7#1744C411yescharacteristic
8C2×Q8⋊C8—22no—
9#1394C414yes—
10C2×C4⋊Q8D411yescharacteristic
11C2×C4×Q8D412yes—
12#423—42no—
13C2×C4⋊C8—21no—
14C2×#101—24no—
15C2×C4×C8—21no—
16#391C2×C412yes—
17#389—41no—
18#384Q811yescharacteristic
19C4×C4⋊C4—41no—
20C43C2×C411yescharacteristic
21#356—42no—
22#356—42no—
23#343—42no—
24#336—41no—
25#336—41no—
26Q8⋊C8—44no—
27C22×Q8C22⋊C412yes—
28C2×M16—44no—
29C22×C8—41no—
30C22×C8—41no—
31C4⋊Q8—41no—
32C4⋊Q8D811yescharacteristic
33C4⋊Q8SD1612yes—
34C4⋊Q8Q1611yescharacteristic
35C4×Q8—42no—
36C4×Q8—42no—
37C2×C4⋊C4—22no—
38C2×C4⋊C4—41no—
39C2×C4⋊C4—41no—
40C2×C4⋊C4C4⋊C412yes—
41C2×C42—22no—
42C2×C42—21no—
43C2×C42—21no—
44C2×C42C4211yescharacteristic
45C2×C42C22⋊C411yescharacteristic
46C2×C42C4⋊C411yescharacteristic
47C4⋊C8—42no—
48C4⋊C8—82no—
49C4⋊C8—82no—
50#101—44no—
51#101—44no—
52C4×C8—22no—
53C4×C8—41no—
54#95—42no—
55C2×Q8—22no—
56C2×Q8—42no—
57C2×Q8—42no—
58C2×Q8#10212yes—
59C2×Q8#10312yes—
60C22×C4—22no—
61C22×C4—21no—
62C22×C4—21no—
63C22×C4—22no—
64C22×C4#9511yescharacteristic
65C22×C4#9911yescharacteristic
66C22×C4#9911yescharacteristic
67M16—84no—
68M16—84no—
69C2×C8—42no—
70C2×C8—82no—
71C2×C8—82no—
72C2×C8—84no—
73C2×C8—81no—
74C4⋊C4—41no—
75C4⋊C4—42no—
76C4⋊C4—41no—
77C4⋊C4—42no—
78C4⋊C4—82no—
79C4⋊C4—82no—
80C42—21no—
81C42—21no—
82C42—21no—
83C42—41no—
84C42—42no—
85C42—42no—
86C42—42no—
87C42—81no—
88C42#10611yescharacteristic
89C42#10711yescharacteristic
90C23#34211yescharacteristic
91Q8—42no—
92Q8—42no—
93Q8—82no—
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—22no—
97C2×C4—21no—
98C2×C4—21no—
99C2×C4—22no—
100C2×C4—22no—
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—42no—
105C2×C4—42no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—42no—
111C2×C4—82no—
112C2×C4H(3,ℤ/4)11yescharacteristic
113C2×C4#34011yescharacteristic
114C2×C4#35311yescharacteristic
115C2×C4#35411yescharacteristic
116C8—82no—
117C8—161no—
118C8—164no—
119C22—21no—
120C22—21no—
121C22#128911yescharacteristic
122C22#139111yescharacteristic
123C22#139311yescharacteristic
124C4—21no—
125C4—21no—
126C4—21no—
127C4—41no—
128C4—41no—
129C4—42no—
130C4—42no—
131C4—41no—
132C4—81no—
133C4—82no—
134C4#141312yes—
135C2—21no—
136C2—21no—
137C2#723711yescharacteristic
138C2#750511yescharacteristic
139C2#750711yescharacteristic
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
#128022
#96412