Finite Group Databasebeta

← #102849

Subgroups — #102849

Order 512.

543 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 543 conjugacy classes of subgroups — too many to draw. Only its 104 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#30242C211yesmaximal, characteristic
2#27960C212yesmaximal
3#11373C211yesmaximal, characteristic
4#9885C212yesmaximal
5#7016C211yesmaximal, characteristic
6C2×#467—22no—
7#2857C2212yes—
8C2×#384C2211yescharacteristic
9#2099—24no—
10#2095—22no—
11#2016—22no—
12#1990—22no—
13#1834—22no—
14#1823—24no—
15C4×C22⋊C8C2212yes—
16C2×#340—22no—
17C2×#336C2211yescharacteristic
18C4⋊#95C2211yescharacteristic
19#1294—24no—
20C22×Q16—22no—
21C23×C8D412yes—
22C2×C4⋊Q8D412yes—
23C2×C22⋊Q8—22no—
24C22×C4⋊C4—22no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4—21no—
27C22×C42C2311yescharacteristic
28#467—44no—
29#467—44no—
30C2×#107—22no—
31C2×#103—24no—
32C2×C22⋊C8D414yes—
33C2×C4×C8—22no—
34#391—22no—
35#389—22no—
36#389—22no—
37#384—22no—
38#384—21no—
39#384D412yes—
40#384D412yes—
41#380—22no—
42#380—22no—
43C2×#95—22no—
44#340—28no—
45#340—28no—
46#340—44no—
47#336—22no—
48#336—22no—
49C22×Q8—22no—
50C23×C4—41no—
51C23×C4—41no—
52C23×C4C2×D411yescharacteristic
53C23×C4C2×D412yes—
54C2×Q16—44no—
55C2×Q16—82no—
56C2×Q16—82no—
57C22×C8—22no—
58C22×C8—22no—
59C22×C8—24no—
60C22×C8—42no—
61C22×C8—42no—
62C22×C8D814yes—
63C4⋊Q8—44no—
64C22⋊Q8—44no—
65C22⋊Q8—44no—
66C2×C4⋊C4—22no—
67C2×C4⋊C4—24no—
68C2×C4⋊C4—22no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—22no—
73C2×C4⋊C4—22no—
74C2×C4⋊C4—42no—
75C2×C4⋊C4—42no—
76C2×C4⋊C4—42no—
77C2×C4⋊C4—44no—
78C2×C4⋊C4—42no—
79C2×C4⋊C4—44no—
80C2×C4⋊C4—41no—
81C2×C4⋊C4—41no—
82C2×C4⋊C4—42no—
83C2×C4⋊C4—42no—
84C2×C22⋊C4—42no—
85C2×C42—42no—
86C2×C42C2×D412yes—
87C2×C42C2×D411yescharacteristic
88C2×C42#4111yescharacteristic
89#107—44no—
90#103—48no—
91C22⋊C8—24no—
92C22⋊C8—24no—
93C4×C8—44no—
94#95—42no—
95#95—42no—
96#95—44no—
97C24#12711yescharacteristic
98C2×Q8—44no—
99C2×Q8—42no—
100C2×Q8—42no—
101C2×Q8—44no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—22no—
105C22×C4—42no—
106C22×C4—42no—
107C22×C4—42no—
108C22×C4—42no—
109C22×C4—42no—
110C22×C4—42no—
111C22×C4—81no—
112C22×C4—82no—
113C22×C4—81no—
114C22×C4—81no—
115C22×C4—82no—
116C22×C4—82no—
117C22×C4—81no—
118C22×C4—82no—
119C22×C4#12012yes—
120C22×C4#12011yescharacteristic
121C22×C4#12111yescharacteristic
122C22×C4#12112yes—
123C22×C4C2×D812yes—
124C22×C4#13514yes—
125C22×C4AGL(1,ℤ/8)12yes—
126C22×C4#13714yes—
127Q16—88no—
128C2×C8—24no—
129C2×C8—42no—
130C2×C8—42no—
131C2×C8—44no—
132C2×C8—44no—
133C2×C8—44no—
134C2×C8—44no—
135C2×C8—82no—
136C4⋊C4—44no—
137C4⋊C4—44no—
138C4⋊C4—44no—
139C4⋊C4—44no—
140C4⋊C4—48no—
141C4⋊C4—44no—
142C4⋊C4—82no—
143C4⋊C4—82no—
144C4⋊C4—82no—
145C4⋊C4—82no—
146C4⋊C4—84no—
147C4⋊C4—84no—
148C22⋊C4—82no—
149C22⋊C4—82no—
150C42—24no—
151C42—41no—
152C42—41no—
153C23—21no—
154C23—22no—
155C23—21no—
156C23#39211yescharacteristic
157C23#49311yescharacteristic
158C23#49512yes—
159C23#49611yescharacteristic
160C23#49712yes—
161Q8—84no—
162Q8—84no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—82no—
176C2×C4—84no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—82no—
180C2×C4—82no—
181C2×C4—82no—
182C2×C4—82no—
183C2×C4—84no—
184C2×C4—82no—
185C2×C4—162no—
186C2×C4—161no—
187C2×C4—161no—
188C2×C4—161no—
189C2×C4—162no—
190C2×C4—161no—
191C2×C4#44712yes—
192C2×C4#45214yes—
193C2×C4#45511yescharacteristic
194C2×C4#45611yescharacteristic
195C2×C4#45812yes—
196C2×C4#45912yes—
197C2×C4#46414yes—
198C8—44no—
199C8—84no—
200C22—22no—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22#170911yescharacteristic
209C22#172012yes—
210C22#172211yescharacteristic
211C22#200711yescharacteristic
212C22#200912yes—
213C22#201111yescharacteristic
214C22#201512yes—
215C22#202211yescharacteristic
216C4—24no—
217C4—24no—
218C4—22no—
219C4—162no—
220C4—162no—
221C4—162no—
222C4—162no—
223C4#160712yes—
224C4#161012yes—
225C2—21no—
226C2—22no—
227C2—21no—
228C2#996112yes—
229C2#997011yescharacteristic
230C2#1020712yes—
231C2#1022511yescharacteristic
232C2#1030611yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC22×C42C23
prime radicalC24#127
LCSG ▷ C22×C42 ▷ C23 ▷ 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
#302422
#279602
#113732
#98852
#70162