Finite Group Databasebeta

← #94074

Subgroups — #94074

Order 512.

462 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C2×#1317C212yesmaximal
2#10726C211yesmaximal, characteristic
3C22×#117C411yescharacteristic
4C2×#381C411yescharacteristic
5C2×#381C2211yescharacteristic
6C2×#342—22no—
7C2×#323—22no—
8#1317—22no—
9#1317C414yescomplemented
10C24×C4C2×C411yescharacteristic
11C2×#117—44no—
12C2×#117—41no—
13C2×#117—41no—
14C22×C4⋊C4C812yescomplemented
15C22×C22⋊C4—21no—
16C22×C22⋊C4—21no—
17C22×C22⋊C4D412yes—
18C22×C42—21no—
19C2×C22⋊C8—42no—
20#381—21no—
21#381—41no—
22#381—41no—
23#381C812yescomplemented
24#381C2×C412yes—
25#381D411yescharacteristic
26#381Q811yescharacteristic
27C2×#95—41no—
28C2×#95—41no—
29#342—44no—
30#323—24no—
31#323—42no—
32C25C22⋊C411yescharacteristic
33C23×C4—21no—
34C23×C4—21no—
35C23×C4—21no—
36C23×C4—21no—
37C23×C4—22no—
38C23×C4—22no—
39C23×C4—42no—
40C23×C4—42no—
41C23×C4—41no—
42C23×C4C4211yescharacteristic
43C23×C4C4⋊C411yescharacteristic
44C23×C4C2×C811yescharacteristic
45C23×C4C2×C811yescharacteristic
46C23×C4M1611yescharacteristic
47C23×C4M1611yescharacteristic
48C22×C8—82no—
49#117—48no—
50#117—44no—
51#117—44no—
52C2×C4⋊C4—42no—
53C2×C4⋊C4—44no—
54C2×C22⋊C4—24no—
55C2×C22⋊C4—22no—
56C2×C22⋊C4—22no—
57C2×C22⋊C4—42no—
58C2×C22⋊C4—41no—
59C2×C22⋊C4—41no—
60C2×C22⋊C4—42no—
61C2×C22⋊C4—42no—
62C2×C22⋊C4—42no—
63C2×C22⋊C4—42no—
64C2×C22⋊C4—41no—
65C2×C22⋊C4C22⋊C412yes—
66C2×C22⋊C4C4⋊C412yes—
67C2×C42—42no—
68C2×C42—44no—
69C22⋊C8—44no—
70C22⋊C8—82no—
71#95—42no—
72#95—41no—
73#95—41no—
74#95—42no—
75#95—42no—
76C24—22no—
77C24—22no—
78C24—82no—
79C24#9511yescharacteristic
80C24C22⋊C811yescharacteristic
81C24C22⋊C811yescharacteristic
82C24#9911yescharacteristic
83C24#9911yescharacteristic
84C24#10011yescharacteristic
85C24#10111yescharacteristic
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—21no—
97C22×C4—21no—
98C22×C4—24no—
99C22×C4—22no—
100C22×C4—22no—
101C22×C4—42no—
102C22×C4—42no—
103C22×C4—44no—
104C22×C4—44no—
105C22×C4—42no—
106C22×C4—42no—
107C22×C4—41no—
108C22×C4—41no—
109C22×C4—42no—
110C22×C4—42no—
111C22×C4—41no—
112C22×C4—42no—
113C22×C4—41no—
114C22×C4—42no—
115C22×C4—42no—
116C22×C4—42no—
117C22×C4—42no—
118C22×C4—42no—
119C22×C4—42no—
120C22×C4—84no—
121C22×C4—84no—
122C22×C4—81no—
123C22×C4—81no—
124C22×C4—84no—
125C22×C4C4×C811yescharacteristic
126C22×C4#9711yescharacteristic
127C22×C4C4⋊C811yescharacteristic
128C22×C4C4⋊C811yescharacteristic
129C2×C8—84no—
130C2×C8—164no—
131C4⋊C4—44no—
132C4⋊C4—44no—
133C22⋊C4—44no—
134C22⋊C4—44no—
135C22⋊C4—42no—
136C22⋊C4—42no—
137C22⋊C4—44no—
138C22⋊C4—82no—
139C22⋊C4—82no—
140C42—48no—
141C23—21no—
142C23—21no—
143C23—21no—
144C23—21no—
145C23—22no—
146C23—22no—
147C23—22no—
148C23—22no—
149C23—42no—
150C23—42no—
151C23—42no—
152C23—84no—
153C23—81no—
154C23—81no—
155C23—81no—
156C23—81no—
157C23—84no—
158C23#32311yescharacteristic
159C23#32311yescharacteristic
160C23#32411yescharacteristic
161C23#32411yescharacteristic
162C23#33611yescharacteristic
163C23#34211yescharacteristic
164C23#34311yescharacteristic
165C23AΣL(1,𝔽16)12yes—
166C23#35212yes—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—44no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—84no—
193C2×C4—84no—
194C2×C4—84no—
195C2×C4—82no—
196C2×C4—82no—
197C2×C4—84no—
198C2×C4—82no—
199C2×C4—84no—
200C2×C4—162no—
201C2×C4—162no—
202C2×C4—162no—
203C8—164no—
204C22—22no—
205C22—24no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22—82no—
222C22—82no—
223C22—82no—
224C22—82no—
225C22#128011yescharacteristic
226C22#131611yescharacteristic
227C22#131711yescharacteristic
228C22#132612yes—
229C22#139012yes—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—82no—
235C4—82no—
236C4—84no—
237C4—162no—
238C2—22no—
239C2—21no—
240C2—21no—
241C2—22no—
242C2—41no—
243C2—41no—
244C2—41no—
245C2—41no—
246C2#718711yescharacteristic
247C2#733912yes—
subgroupG/H
center, socleC22#1316
commutatorC22×C4C4×C8
Frattini, cosocleC2×#381C22
prime radicalC25C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C25 ◁ C2×#381 ◁ G
LECSG ▷ C2×#381 ▷ C24 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
9. #1317C4semidirect
14. C22×C4⋊C4C8semidirect
23. #381C8semidirect

Maximal subgroups

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

subgroupindex
C2×#13172
#107262