Finite Group Databasebeta

← #94651

Subgroups — #94651

Order 512.

178 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 24 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#10285C211yesmaximal, characteristic
2#7500C211yesmaximal, characteristic
3#7357C211yesmaximal, characteristic
4#3227—21no—
5#2862C411yescharacteristic, complemented
6#2126—21no—
7#1962C2211yescharacteristic
8#1549—21no—
9#1327—21no—
10#1276C411yescharacteristic, complemented
11#532D411yescharacteristic
12C2×C4⋊Q8—21no—
13#498—41no—
14#486—41no—
15#481—42no—
16#476—42no—
17#431—21no—
18#423D411yescharacteristic
19C2×#104—41no—
20#410—41no—
21#391—42no—
22#382—41no—
23C43C2×C411yescharacteristic
24#354—22no—
25#353—41no—
26#349—41no—
27#332—42no—
28C2×#41—21no—
29C22×Q8—41no—
30C2×M16—21no—
31C4⋊Q8—41no—
32C4⋊Q8—41no—
33C4⋊Q8—41no—
34C4⋊Q8—41no—
35C4⋊Q8SD1611yescharacteristic
36#127D811yescharacteristic
37#124—21no—
38#121—41no—
39C4×D4—41no—
40#117—81no—
41C2×C4⋊C4—22no—
42C2×C4⋊C4—41no—
43C2×C42—21no—
44C2×C42—41no—
45C2×C42C22⋊C411yescharacteristic
46M32—81no—
47#106—44no—
48C4⋊C8—22no—
49C4⋊C8—41no—
50#104—82no—
51#102—44no—
52#99—42no—
53#99—81no—
54C22⋊C8—41no—
55C4×C8—41no—
56#95—42no—
57#95—42no—
58#41—81no—
59#41—81no—
60C2×Q8—21no—
61C2×Q8—81no—
62C2×Q8—81no—
63C2×Q8—84no—
64C2×D4—21no—
65C2×D4—41no—
66C2×D4—41no—
67C22×C4—21no—
68C22×C4—41no—
69C22×C4—41no—
70C22×C4—42no—
71C22×C4#9911yescharacteristic
72M16—81no—
73C2×C8—42no—
74C2×C8—41no—
75C4⋊C4—41no—
76C4⋊C4—42no—
77C4⋊C4—42no—
78C4⋊C4—81no—
79C4⋊C4—81no—
80C4⋊C4—161no—
81C22⋊C4—81no—
82C22⋊C4—82no—
83C42—21no—
84C42—22no—
85C42—41no—
86C42—82no—
87C42—161no—
88C42#10211yescharacteristic
89C42#10411yescharacteristic
90C16—161no—
91C23—41no—
92C23AΣL(1,𝔽16)11yescharacteristic
93Q8—81no—
94Q8—162no—
95Q8—162no—
96D4—81no—
97D4—82no—
98D4—161no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—42no—
104C2×C4—42no—
105C2×C4—41no—
106C2×C4—82no—
107C2×C4—81no—
108C2×C4—81no—
109C2×C4—84no—
110C2×C4—82no—
111C2×C4—162no—
112C2×C4#32711yescharacteristic
113C2×C4#35311yescharacteristic
114C8—82no—
115C8—81no—
116C22—21no—
117C22—41no—
118C22—81no—
119C22—161no—
120C22#134311yescharacteristic
121C4—22no—
122C4—21no—
123C4—41no—
124C4—82no—
125C4—81no—
126C4—162no—
127C4—322no—
128C4#140711yescharacteristic
129C4#140911yescharacteristic
130C2—21no—
131C2—41no—
132C2—161no—
133C2#740311yescharacteristic
subgroupG/H
center, socleC2#7403
commutatorC43C2×C4
Frattini, cosocle#1962C22
prime radical#532D4
LCSG ▷ C43 ▷ C2×C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #1962 ◁ G
LECSG ▷ #1962 ▷ C2×C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
5. #2862C4semidirect
10. #1276C4semidirect

Maximal subgroups

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

subgroupindex
#102852
#75002
#73572