Finite Group Databasebeta

← #94646

Subgroups — #94646

Order 512.

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

normal subgroups only

This group has 184 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#10014C211yesmaximal, characteristic
2#7506C211yesmaximal, characteristic
3#7356C211yesmaximal, characteristic
4#3103—21no—
5#2399C411yescharacteristic, complemented
6#2126—21no—
7#1963C2211yescharacteristic
8#1487—21no—
9#1327—21no—
10#1274C411yescharacteristic, complemented
11#532D411yescharacteristic
12C2×C4×Q8—21no—
13#481—41no—
14#475—41no—
15#460—41no—
16#448—41no—
17C4×SD16—42no—
18#431—21no—
19#423D411yescharacteristic
20C2×#104—41no—
21#410—41no—
22#398—41no—
23#395—41no—
24C4×C4⋊C4—41no—
25#376C2×C411yescharacteristic
26#354—22no—
27#353—41no—
28#349—41no—
29Q8⋊C8—42no—
30C2×#41—21no—
31C22×Q8—21no—
32C2×SD16—42no—
33C2×M16—21no—
34C4⋊Q8SD1611yescharacteristic
35#127D811yescharacteristic
36#124—21no—
37#121—41no—
38C4×Q8—41no—
39C4×Q8—41no—
40C4×Q8—41no—
41C4×Q8—41no—
42C4×D4—41no—
43#117—81no—
44C2×C4⋊C4—21no—
45C2×C4⋊C4—41no—
46C2×C4⋊C4—42no—
47C2×C42—21no—
48C2×C42—41no—
49C2×C42C22⋊C411yescharacteristic
50M32—81no—
51#106—42no—
52C4⋊C8—41no—
53C4⋊C8—41no—
54#104—82no—
55#103—42no—
56#102—42no—
57#99—42no—
58#99—81no—
59C22⋊C8—41no—
60C4×C8—22no—
61#95—41no—
62#95—41no—
63#95—41no—
64#41—81no—
65#41—81no—
66C2×Q8—21no—
67C2×Q8—41no—
68C2×Q8—41no—
69C2×Q8—82no—
70C2×D4—21no—
71C2×D4—41no—
72C2×D4—41no—
73C22×C4—21no—
74C22×C4—41no—
75C22×C4—41no—
76C22×C4—41no—
77C22×C4—41no—
78C22×C4#9911yescharacteristic
79SD16—84no—
80M16—81no—
81C2×C8—42no—
82C2×C8—41no—
83C4⋊C4—41no—
84C4⋊C4—41no—
85C4⋊C4—41no—
86C4⋊C4—81no—
87C4⋊C4—81no—
88C4⋊C4—84no—
89C4⋊C4—161no—
90C22⋊C4—81no—
91C22⋊C4—82no—
92C42—21no—
93C42—22no—
94C42—41no—
95C42—81no—
96C42—81no—
97C42—161no—
98C42#10211yescharacteristic
99C42#10411yescharacteristic
100C16—161no—
101C23—41no—
102C23AΣL(1,𝔽16)11yescharacteristic
103Q8—42no—
104Q8—42no—
105Q8—81no—
106Q8—81no—
107Q8—81no—
108D4—81no—
109D4—82no—
110D4—161no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—42no—
116C2×C4—42no—
117C2×C4—41no—
118C2×C4—81no—
119C2×C4—82no—
120C2×C4—81no—
121C2×C4—81no—
122C2×C4—81no—
123C2×C4—81no—
124C2×C4—82no—
125C2×C4—81no—
126C2×C4—162no—
127C2×C4#32711yescharacteristic
128C2×C4#35311yescharacteristic
129C8—82no—
130C8—81no—
131C22—21no—
132C22—41no—
133C22—81no—
134C22—161no—
135C22#134311yescharacteristic
136C4—21no—
137C4—41no—
138C4—41no—
139C4—82no—
140C4—82no—
141C4—81no—
142C4—161no—
143C4—322no—
144C4#140711yescharacteristic
145C4#140911yescharacteristic
146C2—21no—
147C2—41no—
148C2—161no—
149C2#740311yescharacteristic
subgroupG/H
centerC4#1409
commutator#376C2×C4
Frattini, cosocle#1963C22
socleC2#7403
prime radical#532D4
LCSG ▷ #376 ▷ C2×C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #1963 ◁ G
LECSG ▷ #1963 ▷ C2×C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #2399C4semidirect
10. #1274C4semidirect

Maximal subgroups

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

subgroupindex
#100142
#75062
#73562