Finite Group Databasebeta

← #96979

Subgroups — #96979

Order 512.

754 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 110 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#35154C211yesmaximal, characteristic
2#11380C211yesmaximal, characteristic
3#8303C211yesmaximal, characteristic
4#7579C214yesmaximal
5C2×#544C411yescharacteristic
6C22×C4×Q8C2211yescharacteristic
7#2855—22no—
8#2627—22no—
9#2453—24no—
10#2451—24no—
11#2316C411yescharacteristic
12#2310C412yes—
13#2296C2212yes—
14#1817C2212yes—
15C2×#336—22no—
16C2×#336C2212yes—
17C2×#324—22no—
18#1271—24no—
19#1271—24no—
20C23×Q8C2×C411yescharacteristic
21C23×C8—22no—
22#544—44no—
23C2×C4⋊Q8—22no—
24C2×#125—22no—
25C2×C22⋊Q8—22no—
26C2×C4×Q8—24no—
27C2×C4×Q8—44no—
28C2×#117C2×C412yes—
29C2×#117C2×C412yes—
30C22×C4⋊C4C2×C411yescharacteristic
31C22×C4⋊C4D412yes—
32C22×C42D412yes—
33C22×C42C2311yescharacteristic
34C2×C22⋊C8—22no—
35#400—24no—
36#398—28no—
37#395—24no—
38#391—24no—
39#391—22no—
40#391—24no—
41#391—22no—
42#389—24no—
43#389—24no—
44#389D414yes—
45#389D414yes—
46#387—28no—
47#385—22no—
48#385—22no—
49#381—24no—
50#380—22no—
51C4×C4⋊C4—24no—
52#336—24no—
53#336—24no—
54#336—44no—
55#324—44no—
56C22×Q8—22no—
57C22×Q8—24no—
58C22×Q8—22no—
59C22×Q8—22no—
60C22×Q8—22no—
61C22×Q8—42no—
62C23×C4C22⋊C412yes—
63C23×C4C22⋊C412yes—
64C23×C4C22×C411yescharacteristic
65C23×C4C2×D411yescharacteristic
66C23×C4C2×D411yescharacteristic
67C22×C8—24no—
68C22×C8—42no—
69C22×C8—44no—
70C22×C8—44no—
71C22×C8—42no—
72C22×C8—42no—
73C4⋊Q8—48no—
74#125—48no—
75C22⋊Q8—44no—
76C22⋊Q8—44no—
77C4×Q8—416no—
78#117—24no—
79#117—24no—
80#117—44no—
81C2×C4⋊C4—24no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—24no—
85C2×C4⋊C4—24no—
86C2×C4⋊C4—24no—
87C2×C4⋊C4—24no—
88C2×C4⋊C4—24no—
89C2×C4⋊C4—24no—
90C2×C4⋊C4—42no—
91C2×C4⋊C4C22⋊C414yes—
92C2×C4⋊C4C22⋊C412yes—
93C2×C4⋊C4C22⋊C412yes—
94C2×C22⋊C4—22no—
95C2×C22⋊C4—22no—
96C2×C42—24no—
97C2×C42—22no—
98C2×C42—22no—
99C2×C42—24no—
100C2×C42—42no—
101C2×C42—42no—
102C2×C42C2×D414yes—
103C22⋊C8—44no—
104#95—24no—
105#95—28no—
106#95—28no—
107#95—24no—
108#95—24no—
109C24C2×C22⋊C411yescharacteristic
110C2×Q8—28no—
111C2×Q8—48no—
112C2×Q8—48no—
113C2×Q8—44no—
114C2×Q8—44no—
115C2×Q8—44no—
116C2×Q8—84no—
117C22×C4—22no—
118C22×C4—22no—
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—22no—
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—24no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—42no—
135C22×C4—44no—
136C22×C4#9914yes—
137C22×C4#10114yes—
138C22×C4C2×C22⋊C412yes—
139C22×C4#12012yes—
140C22×C4#12012yes—
141C22×C4#13112yes—
142C22×C4#13112yes—
143C2×C8—48no—
144C2×C8—44no—
145C2×C8—84no—
146C2×C8—82no—
147C2×C8—82no—
148C2×C8—82no—
149C2×C8—84no—
150C4⋊C4—28no—
151C4⋊C4—28no—
152C4⋊C4—48no—
153C4⋊C4—42no—
154C4⋊C4—42no—
155C4⋊C4—44no—
156C4⋊C4—48no—
157C4⋊C4—44no—
158C4⋊C4—44no—
159C4⋊C4—84no—
160C4⋊C4—84no—
161C22⋊C4—42no—
162C22⋊C4—42no—
163C22⋊C4—44no—
164C42—44no—
165C42—48no—
166C42—44no—
167C42—44no—
168C23—22no—
169C23—22no—
170C23#37911yescharacteristic
171C23#40811yescharacteristic
172C23#40811yescharacteristic
173C23C2×#9912yes—
174C23C2×#10112yes—
175Q8—416no—
176Q8—164no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—24no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—24no—
188C2×C4—24no—
189C2×C4—24no—
190C2×C4—22no—
191C2×C4—24no—
192C2×C4—44no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—44no—
198C2×C4—44no—
199C2×C4—44no—
200C2×C4—44no—
201C2×C4—44no—
202C2×C4—44no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—82no—
206C2×C4—82no—
207C2×C4#40814yes—
208C2×C4#45412yes—
209C2×C4#45612yes—
210C8—84no—
211C8—162no—
212C22—22no—
213C22—24no—
214C22—22no—
215C22—22no—
216C22—22no—
217C22#147212yes—
218C22#147212yes—
219C22#178011yescharacteristic
220C22#178111yescharacteristic
221C22#178411yescharacteristic
222C22#179312yes—
223C22#179412yes—
224C4—22no—
225C4—22no—
226C4—24no—
227C4—42no—
228C4—44no—
229C4—44no—
230C4—82no—
231C4—82no—
232C4—84no—
233C2—22no—
234C2—22no—
235C2#830811yescharacteristic
236C2#832112yes—
237C2#845511yescharacteristic
238C2#846012yes—
239C2#846211yescharacteristic
subgroupG/H
center, socleC23#379
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#351542
#113802
#83032
#75792