Finite Group Databasebeta

← #119549

Subgroups — #119549

Order 512.

592 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 118 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#21830C211yesmaximal, characteristic
2#17394C211yesmaximal, characteristic
3#14289C211yesmaximal, characteristic
4#7975C212yesmaximal
5#7950C212yesmaximal
6C22×#125C2211yescharacteristic
7#2920C2212yes—
8#2920C2212yes—
9C2×#383C2211yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11#1998—24no—
12#1821—21no—
13#1821—21no—
14#1470—24no—
15#1463—22no—
16#1445—21no—
17#1445—21no—
18#1441—22no—
19#1436C414yes—
20#1288—24no—
21#1285—24no—
22C2×#125—22no—
23C2×#125—22no—
24C2×#125—22no—
25C2×#125—22no—
26C2×#125—22no—
27C2×#125—22no—
28C22×C4⋊C4—21no—
29C22×C4⋊C4C2×C412yes—
30C22×C4⋊C4D411yescharacteristic
31C22×C4⋊C4D411yescharacteristic
32C22×C4⋊C4D412yes—
33C22×C42C2×C412yes—
34C22×C42C2311yescharacteristic
35#432—22no—
36#432—22no—
37#432—22no—
38#432D414yes—
39#431—22no—
40#431—22no—
41#431—22no—
42#431—22no—
43#423—22no—
44#423—22no—
45#407—22no—
46#407—22no—
47C4×M16—22no—
48C4×M16D414yes—
49#383—22no—
50#383—22no—
51C4×C4⋊C4—22no—
52C4×C4⋊C4—22no—
53C2×#95—24no—
54C2×#95—21no—
55C2×#95—21no—
56C2×#95—21no—
57C2×#95—24no—
58C2×#95C2×C412yes—
59#343—24no—
60#343—24no—
61#324—28no—
62C23×C4—22no—
63C23×C4—22no—
64C23×C4C22⋊C412yes—
65C23×C4C22⋊C412yes—
66C23×C4C22×C411yescharacteristic
67C23×C4C2×D411yescharacteristic
68C23×C4C2×D411yescharacteristic
69C2×M16—24no—
70C2×M16—42no—
71#125—42no—
72#125—42no—
73#125—42no—
74#125—42no—
75#125—42no—
76#125—42no—
77#125—42no—
78#125—42no—
79C2×C4⋊C4—22no—
80C2×C4⋊C4—22no—
81C2×C4⋊C4—24no—
82C2×C4⋊C4—24no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—21no—
85C2×C4⋊C4—21no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—22no—
88C2×C4⋊C4—24no—
89C2×C4⋊C4—24no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4—22no—
92C2×C4⋊C4—22no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—44no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—41no—
98C2×C42—24no—
99C2×C42—82no—
100C2×C42C2×D412yes—
101C2×C42C2×D412yes—
102C2×C42#4112yes—
103C2×C42#4112yes—
104C2×C42#4112yes—
105C2×C42#4112yes—
106C4⋊C8—24no—
107C4⋊C8—42no—
108C4⋊C8—42no—
109C4⋊C8—42no—
110C22⋊C8—24no—
111C22⋊C8—42no—
112C22⋊C8—42no—
113C22⋊C8—42no—
114#97—24no—
115#97—24no—
116C4×C8—24no—
117C4×C8—42no—
118#95—24no—
119#95—48no—
120#95—41no—
121#95—42no—
122#95—42no—
123#95—41no—
124#95—84no—
125C24C2×C22⋊C411yescharacteristic
126C22×C4—24no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—41no—
134C22×C4—42no—
135C22×C4—41no—
136C22×C4—42no—
137C22×C4—42no—
138C22×C4—42no—
139C22×C4—44no—
140C22×C4—42no—
141C22×C4—44no—
142C22×C4—42no—
143C22×C4—44no—
144C22×C4—44no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—44no—
148C22×C4—42no—
149C22×C4#11711yescharacteristic
150C22×C4#11711yescharacteristic
151C22×C4C4×D412yes—
152C22×C4C4×D412yes—
153C22×C4#12011yescharacteristic
154C22×C4#12011yescharacteristic
155C22×C4#12112yes—
156C22×C4#12112yes—
157C22×C4#12312yes—
158C22×C4#12311yescharacteristic
159C22×C4#12312yes—
160C22×C4#12311yescharacteristic
161M16—48no—
162M16—84no—
163C2×C8—44no—
164C2×C8—44no—
165C4⋊C4—44no—
166C4⋊C4—44no—
167C4⋊C4—44no—
168C4⋊C4—44no—
169C4⋊C4—44no—
170C4⋊C4—42no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—44no—
174C4⋊C4—42no—
175C42—84no—
176C42#12112yes—
177C42#12112yes—
178C42#12312yes—
179C42#12312yes—
180C42#12412yes—
181C42#12412yes—
182C42#12612yes—
183C42#12612yes—
184C23—22no—
185C23—22no—
186C23—21no—
187C23—21no—
188C23#38111yescharacteristic
189C23#38611yescharacteristic
190C23#38611yescharacteristic
191C2×C4—24no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—44no—
205C2×C4—48no—
206C2×C4—44no—
207C2×C4—44no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—84no—
213C2×C4—82no—
214C2×C4—82no—
215C2×C4—82no—
216C2×C4—82no—
217C2×C4—82no—
218C2×C4—84no—
219C2×C4—84no—
220C2×C4—82no—
221C2×C4—82no—
222C2×C4—82no—
223C2×C4#38812yes—
224C2×C4#38812yes—
225C2×C4#39412yes—
226C2×C4#39412yes—
227C2×C4#39712yes—
228C2×C4#39712yes—
229C8—84no—
230C8—84no—
231C22—24no—
232C22—24no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22#144011yescharacteristic
240C22#182712yes—
241C22#191212yes—
242C22#191411yescharacteristic
243C22#191511yescharacteristic
244C4—22no—
245C4—22no—
246C4—22no—
247C4—22no—
248C4—22no—
249C4—22no—
250C4—84no—
251C4—82no—
252C4—82no—
253C4—162no—
254C2—21no—
255C2—22no—
256C2—22no—
257C2—21no—
258C2#1114911yescharacteristic
259C2#1115611yescharacteristic
260C2#1117311yescharacteristic
subgroupG/H
center, socleC22#1440
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#218302
#173942
#142892
#79752
#79502