Finite Group Databasebeta

← #93479

Subgroups — #93479

Order 512.

431 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 431 conjugacy classes of subgroups — too many to draw. Only its 70 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#10763C211yesmaximal, characteristic
2#8303C211yesmaximal, characteristic
3#8303C211yesmaximal, characteristic
4C22×C4×Q8C2211yescharacteristic
5C22×#101C412yes—
6#1817—21no—
7#1817C412yes—
8C2×#343—21no—
9#1728—21no—
10C2×#324—21no—
11C2×#324—21no—
12C2×#324—21no—
13C2×#324C412yes—
14C23×Q8C2×C411yescharacteristic
15C22×M16—22no—
16C2×C4×Q8—42no—
17C2×C4×Q8—42no—
18C2×C4×Q8—42no—
19C22×C4⋊C4C2×C411yescharacteristic
20C22×C4⋊C4D411yescharacteristic
21C22×C4⋊C4D411yescharacteristic
22C22×C42C2×C411yescharacteristic
23C22×C42D411yescharacteristic
24C22×C42Q811yescharacteristic
25C2×#101—22no—
26C2×#101—42no—
27C2×#101—42no—
28C2×#101C814yescomplemented
29C2×C22⋊C8—22no—
30C2×C22⋊C8—22no—
31#343—42no—
32#336—42no—
33#336—42no—
34#336—42no—
35#324—42no—
36#324—42no—
37#324—42no—
38#324—42no—
39C22×Q8—22no—
40C22×Q8—21no—
41C22×Q8—21no—
42C22×Q8—41no—
43C22×Q8—41no—
44C22×Q8—41no—
45C22×Q8—41no—
46C22×Q8C2×C812yes—
47C22×Q8M1612yes—
48C23×C4C4211yescharacteristic
49C23×C4C22⋊C411yescharacteristic
50C23×C4C22⋊C411yescharacteristic
51C23×C4C22⋊C411yescharacteristic
52C23×C4C4⋊C411yescharacteristic
53C23×C4C4⋊C411yescharacteristic
54C23×C4C4⋊C411yescharacteristic
55C2×M16—24no—
56C2×M16—42no—
57C2×M16—42no—
58C2×M16—42no—
59C2×M16—42no—
60C2×M16—42no—
61C22×C8—42no—
62C22×C8—42no—
63C22×C8—42no—
64C4×Q8—416no—
65C2×C4⋊C4—22no—
66C2×C4⋊C4—22no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—22no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—41no—
71C2×C4⋊C4—41no—
72C2×C4⋊C4—41no—
73C2×C4⋊C4—41no—
74C2×C42—22no—
75C2×C42—22no—
76C2×C42—22no—
77C2×C42—41no—
78C2×C42—41no—
79C2×C42—41no—
80C2×C42—41no—
81C2×C42—41no—
82C2×C42—41no—
83#101—44no—
84#101—44no—
85C22⋊C8—42no—
86C22⋊C8—42no—
87C22⋊C8—42no—
88C22⋊C8—42no—
89C24#9511yescharacteristic
90C2×Q8—22no—
91C2×Q8—22no—
92C2×Q8—22no—
93C2×Q8—22no—
94C2×Q8—42no—
95C2×Q8—42no—
96C2×Q8—42no—
97C2×Q8—42no—
98C2×Q8—44no—
99C2×Q8—42no—
100C2×Q8—42no—
101C2×Q8—42no—
102C2×Q8—42no—
103C2×Q8—44no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—21no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—42no—
131C22×C4—81no—
132C22×C4—81no—
133C22×C4—81no—
134C22×C4C4×C811yescharacteristic
135C22×C4#9711yescharacteristic
136C22×C4C22⋊C812yes—
137C22×C4#9912yes—
138C22×C4#9912yes—
139C22×C4#9912yes—
140C22×C4#10011yescharacteristic
141C22×C4#10111yescharacteristic
142C22×C4C4⋊C812yes—
143M16—44no—
144M16—44no—
145M16—82no—
146M16—82no—
147C2×C8—44no—
148C2×C8—82no—
149C2×C8—82no—
150C2×C8—82no—
151C2×C8—82no—
152C2×C8—84no—
153C2×C8—84no—
154C4⋊C4—44no—
155C4⋊C4—44no—
156C4⋊C4—44no—
157C42—44no—
158C42—44no—
159C42—44no—
160C23—41no—
161C23—41no—
162C23#33611yescharacteristic
163C23#34211yescharacteristic
164C23#34211yescharacteristic
165C23#34211yescharacteristic
166C23#34311yescharacteristic
167C23#34411yescharacteristic
168C23#34411yescharacteristic
169Q8—44no—
170Q8—44no—
171Q8—44no—
172Q8—44no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—42no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—81no—
212C2×C4—81no—
213C2×C4—81no—
214C2×C4—81no—
215C2×C4—81no—
216C2×C4—81no—
217C2×C4#32312yes—
218C2×C4#32412yes—
219C8—84no—
220C8—162no—
221C8—162no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22#128011yescharacteristic
233C22#128211yescharacteristic
234C22#128211yescharacteristic
235C22#130411yescharacteristic
236C22#130511yescharacteristic
237C22#130511yescharacteristic
238C22#130611yescharacteristic
239C4—22no—
240C4—22no—
241C4—41no—
242C4—41no—
243C4—42no—
244C4—42no—
245C4—42no—
246C4—42no—
247C4—81no—
248C2—21no—
249C2—21no—
250C2—21no—
251C2—21no—
252C2—21no—
253C2—21no—
254C2#703211yescharacteristic
255C2#731311yescharacteristic
256C2#731511yescharacteristic
subgroupG/H
center, socleC22#1304
commutatorC22×C4C4×C8
Frattini, cosocleC22×C4×Q8C22
prime radicalC24#95
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4×Q8 ▷ C24 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
28. C2×#101C8semidirect

Maximal subgroups

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

subgroupindex
#107632
#83032