Finite Group Databasebeta

← #94199

Subgroups — #94199

Order 512.

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

normal subgroups only

This group has 275 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#11513C211yesmaximal, characteristic
2#10893C211yesmaximal, characteristic
3#8721C211yesmaximal, characteristic
4#2873C411yescharacteristic
5#2285C2211yescharacteristic
6#1749—21no—
7#1740C411yescharacteristic
8#1733—21no—
9C2×#339—21no—
10#1464—21no—
11#1325C412yescomplemented
12#1324—21no—
13#1295—21no—
14#1295C412yescomplemented
15C22×M16—21no—
16C2×#117—21no—
17C2×#117C2×C411yescharacteristic
18C2×#117D411yescharacteristic
19C22×C42D411yescharacteristic
20#432—41no—
21C2×C22⋊C8—41no—
22#405—42no—
23C4×M16—41no—
24C2×#97—22no—
25#384C2×C411yescharacteristic
26#384Q811yescharacteristic
27#382C2×C411yescharacteristic
28#382D411yescharacteristic
29#380—41no—
30C4×C4⋊C4—41no—
31#342—41no—
32#339—24no—
33#339—42no—
34#336—41no—
35#324—22no—
36#323—41no—
37C23×C4—21no—
38C23×C4C22⋊C411yescharacteristic
39C2×M16—22no—
40C2×M16—22no—
41C2×M16—22no—
42C2×M16—41no—
43C2×M16—41no—
44C2×M16—41no—
45C22×C8—41no—
46C22×C8—42no—
47#117—22no—
48#117—41no—
49#117—41no—
50#117—41no—
51#117—41no—
52#117—41no—
53#117—41no—
54#117—41no—
55C2×C4⋊C4—41no—
56C2×C4⋊C4—41no—
57C2×C4⋊C4—41no—
58C2×C4⋊C4C4211yescharacteristic
59C2×C4⋊C4C22⋊C411yescharacteristic
60C2×C4⋊C4C4⋊C411yescharacteristic
61C2×C4⋊C4C4⋊C411yescharacteristic
62C2×C22⋊C4—21no—
63C2×C22⋊C4—21no—
64C2×C22⋊C4—41no—
65C2×C42—22no—
66C2×C42—21no—
67C2×C42—21no—
68C2×C42—21no—
69C2×C42—41no—
70C2×C42—41no—
71C2×C42C22⋊C411yescharacteristic
72C2×C42C4⋊C411yescharacteristic
73C4⋊C8—81no—
74C22⋊C8—44no—
75C22⋊C8—42no—
76#97—42no—
77#97—42no—
78#97—42no—
79#97—81no—
80C4×C8—42no—
81#95—41no—
82#95—41no—
83C24#9911yescharacteristic
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—21no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—42no—
97C22×C4—42no—
98C22×C4—81no—
99C22×C4—81no—
100C22×C4#9511yescharacteristic
101C22×C4#9911yescharacteristic
102M16—24no—
103M16—42no—
104M16—42no—
105M16—42no—
106C2×C8—42no—
107C2×C8—42no—
108C2×C8—42no—
109C2×C8—44no—
110C2×C8—82no—
111C2×C8—82no—
112C2×C8—82no—
113C4⋊C4—41no—
114C4⋊C4—41no—
115C4⋊C4—41no—
116C4⋊C4—41no—
117C4⋊C4—42no—
118C4⋊C4—82no—
119C4⋊C4—81no—
120C4⋊C4—82no—
121C22⋊C4—42no—
122C22⋊C4—42no—
123C22⋊C4—81no—
124C22⋊C4—81no—
125C42—21no—
126C42—21no—
127C42—21no—
128C42—42no—
129C42—42no—
130C42—41no—
131C42—41no—
132C42—41no—
133C42—41no—
134C42—81no—
135C42#10412yes—
136C23—21no—
137C23—21no—
138C23—41no—
139C23—41no—
140C23#34211yescharacteristic
141C23#35511yescharacteristic
142C23#35611yescharacteristic
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—84no—
166C2×C4—81no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4—81no—
170C2×C4—82no—
171C2×C4—161no—
172C2×C4—161no—
173C2×C4H(3,ℤ/4)11yescharacteristic
174C2×C4#33911yescharacteristic
175C2×C4AΣL(1,𝔽16)11yescharacteristic
176C2×C4#35211yescharacteristic
177C8—44no—
178C8—84no—
179C8—162no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22#128411yescharacteristic
190C22#139011yescharacteristic
191C22#139411yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—42no—
197C4—42no—
198C4—81no—
199C4—81no—
200C4—81no—
201C4—81no—
202C4—162no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2#721511yescharacteristic
208C2#749211yescharacteristic
209C2#749411yescharacteristic
subgroupG/H
center, socleC22#1390
commutatorC2×C4⋊C4C42
Frattini, cosocle#2285C22
prime radicalC24#99
LCSG ▷ C2×C4⋊C4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ #2285 ◁ G
LECSG ▷ #2285 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
11. #1325C4semidirect
14. #1295C4semidirect

Maximal subgroups

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

subgroupindex
#115132
#108932
#87212