Finite Group Databasebeta

← #94244

Subgroups — #94244

Order 512.

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

normal subgroups only

This group has 244 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#9637C211yesmaximal, characteristic
3C4×C4⋊Q8C2211yescharacteristic
4C2×#356—22no—
5#1842C411yescharacteristic
6#1801—22no—
7C42×C8C411yescharacteristic
8C2×Q8⋊C8—22no—
9#1394C414yes—
10C2×C4⋊Q8D411yescharacteristic
11C2×C4×Q8D412yes—
12#423—42no—
13C2×C4⋊C8—21no—
14C2×C4⋊C8—41no—
15C2×#101—24no—
16C2×C4×C8—21no—
17C2×C4×C8—41no—
18#391C2×C412yes—
19#389—41no—
20#384Q811yescharacteristic
21C4×C4⋊C4—41no—
22C43C2×C411yescharacteristic
23#356—42no—
24#356—42no—
25#343—42no—
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—21no—
42C2×C42—21no—
43C2×C42—22no—
44C2×C42C4211yescharacteristic
45C2×C42C22⋊C411yescharacteristic
46C2×C42C4⋊C411yescharacteristic
47C4⋊C8—42no—
48C4⋊C8—82no—
49C4⋊C8—82no—
50C4⋊C8—82no—
51#101—44no—
52#101—44no—
53C4×C8—22no—
54C4×C8—41no—
55C4×C8—44no—
56#95—42no—
57C2×Q8—22no—
58C2×Q8—42no—
59C2×Q8—42no—
60C2×Q8#10212yes—
61C2×Q8#10312yes—
62C22×C4—21no—
63C22×C4—21no—
64C22×C4—22no—
65C22×C4—22no—
66C22×C4#9511yescharacteristic
67C22×C4#9911yescharacteristic
68C22×C4#9911yescharacteristic
69M16—84no—
70M16—84no—
71C2×C8—42no—
72C2×C8—44no—
73C2×C8—82no—
74C2×C8—84no—
75C2×C8—81no—
76C4⋊C4—41no—
77C4⋊C4—42no—
78C4⋊C4—41no—
79C4⋊C4—42no—
80C4⋊C4—82no—
81C4⋊C4—82no—
82C42—22no—
83C42—22no—
84C42—21no—
85C42—21no—
86C42—21no—
87C42—41no—
88C42—42no—
89C42—42no—
90C42—42no—
91C42#10611yescharacteristic
92C42#10711yescharacteristic
93C23#34211yescharacteristic
94Q8—42no—
95Q8—42no—
96Q8—82no—
97C2×C4—22no—
98C2×C4—22no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—21no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—42no—
112C2×C4—42no—
113C2×C4—41no—
114C2×C4—42no—
115C2×C4—82no—
116C2×C4H(3,ℤ/4)11yescharacteristic
117C2×C4#34011yescharacteristic
118C2×C4#35311yescharacteristic
119C2×C4#35411yescharacteristic
120C8—44no—
121C8—164no—
122C8—161no—
123C22—21no—
124C22—21no—
125C22#128911yescharacteristic
126C22#139111yescharacteristic
127C22#139311yescharacteristic
128C4—22no—
129C4—22no—
130C4—21no—
131C4—21no—
132C4—21no—
133C4—42no—
134C4—42no—
135C4—42no—
136C4—41no—
137C4—82no—
138C4#141011yescharacteristic
139C4#141111yescharacteristic
140C2—21no—
141C2—21no—
142C2#723711yescharacteristic
143C2#749911yescharacteristic
144C2#750111yescharacteristic
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
#96372