Finite Group Databasebeta

← #102994

Subgroups — #102994

Order 512.

609 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 609 conjugacy classes of subgroups — too many to draw. Only its 84 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#27613C212yesmaximal
2#15211C211yesmaximal, characteristic
3#11359C211yesmaximal, characteristic
4#7610C212yesmaximal
5#7017C211yesmaximal, characteristic
6C2×#389—22no—
7C2×#389C2212yes—
8#2285C2211yescharacteristic
9#2100—22no—
10#2084—22no—
11#1919—24no—
12#1853—22no—
13#1823—22no—
14#1817C2212yes—
15C2×#339—22no—
16#1728C2211yescharacteristic
17#1444—22no—
18#1444—22no—
19C4×#95C2211yescharacteristic
20#1271—24no—
21C22×M16—21no—
22C2×#117—21no—
23C22×C4⋊C4—22no—
24C22×C4⋊C4—22no—
25C22×C4⋊C4—22no—
26C22×C4⋊C4D412yes—
27C22×C4⋊C4D412yes—
28C22×C42D412yes—
29C22×C42C2311yescharacteristic
30C2×#106—24no—
31C2×C22⋊C8—22no—
32#389—22no—
33#389—22no—
34#389—22no—
35#389—22no—
36#389—44no—
37#389—44no—
38#384D412yes—
39#382—21no—
40#380—22no—
41C4×C4⋊C4—22no—
42C2×#95—22no—
43C2×#95—24no—
44C2×#95—22no—
45#340—24no—
46#340—24no—
47#340—24no—
48#339—44no—
49#336—22no—
50#336—22no—
51#336D414yes—
52C23×C4—22no—
53C23×C4—22no—
54C23×C4—22no—
55C23×C4C2×D412yes—
56C23×C4C2×D411yescharacteristic
57C2×M16—22no—
58C2×M16—41no—
59C2×M16—42no—
60C2×M16—42no—
61C22×C8—24no—
62C22×C8—41no—
63#117—42no—
64#117—42no—
65C2×C4⋊C4—22no—
66C2×C4⋊C4—22no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—22no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—44no—
73C2×C4⋊C4—48no—
74C2×C4⋊C4—44no—
75C2×C4⋊C4—44no—
76C2×C4⋊C4—44no—
77C2×C4⋊C4—42no—
78C2×C4⋊C4—42no—
79C2×C4⋊C4—44no—
80C2×C4⋊C4—44no—
81C2×C4⋊C4—82no—
82C2×C4⋊C4—82no—
83C2×C22⋊C4—41no—
84C2×C42—22no—
85C2×C42—42no—
86C2×C42—42no—
87C2×C42—42no—
88C2×C42—41no—
89C2×C42SD1614yes—
90C2×C42C2×D411yescharacteristic
91C2×C42C2×D412yes—
92C2×C42#4111yescharacteristic
93#106—48no—
94C22⋊C8—44no—
95#95—28no—
96#95—48no—
97#95—42no—
98#95—42no—
99#95—42no—
100C24#12011yescharacteristic
101C22×C4—21no—
102C22×C4—21no—
103C22×C4—22no—
104C22×C4—28no—
105C22×C4—24no—
106C22×C4—24no—
107C22×C4—24no—
108C22×C4—24no—
109C22×C4—42no—
110C22×C4—44no—
111C22×C4—42no—
112C22×C4—42no—
113C22×C4—44no—
114C22×C4—42no—
115C22×C4—42no—
116C22×C4—44no—
117C22×C4—42no—
118C22×C4—42no—
119C22×C4—44no—
120C22×C4—42no—
121C22×C4—42no—
122C22×C4—44no—
123C22×C4#12012yes—
124C22×C4#12112yes—
125C22×C4#12111yescharacteristic
126C22×C4#12711yescharacteristic
127C22×C4C2×SD1612yes—
128C22×C4AGL(1,ℤ/8)12yes—
129M16—44no—
130M16—82no—
131C2×C8—44no—
132C2×C8—44no—
133C2×C8—42no—
134C2×C8—44no—
135C2×C8—81no—
136C2×C8—81no—
137C4⋊C4—24no—
138C4⋊C4—24no—
139C4⋊C4—42no—
140C4⋊C4—42no—
141C4⋊C4—44no—
142C4⋊C4—44no—
143C4⋊C4—44no—
144C4⋊C4—416no—
145C4⋊C4—44no—
146C4⋊C4—82no—
147C4⋊C4—88no—
148C4⋊C4—84no—
149C4⋊C4—82no—
150C4⋊C4—82no—
151C22⋊C4—81no—
152C22⋊C4—81no—
153C42—41no—
154C42—42no—
155C42—41no—
156C42—44no—
157C42—82no—
158C42—82no—
159C23—22no—
160C23—22no—
161C23#39211yescharacteristic
162C23#45012yes—
163C23#45311yescharacteristic
164C23#45411yescharacteristic
165C23#45812yes—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—48no—
181C2×C4—44no—
182C2×C4—48no—
183C2×C4—48no—
184C2×C4—44no—
185C2×C4—48no—
186C2×C4—44no—
187C2×C4—84no—
188C2×C4—82no—
189C2×C4—82no—
190C2×C4—84no—
191C2×C4—84no—
192C2×C4—82no—
193C2×C4—82no—
194C2×C4—82no—
195C2×C4—82no—
196C2×C4—82no—
197C2×C4—82no—
198C2×C4#45614yes—
199C2×C4#46012yes—
200C2×C4#49211yescharacteristic
201C2×C4#49611yescharacteristic
202C8—84no—
203C8—82no—
204C22—22no—
205C22—22no—
206C22—22no—
207C22—22no—
208C22—24no—
209C22#161312yes—
210C22#161612yes—
211C22#200512yes—
212C22#200611yescharacteristic
213C22#201012yes—
214C22#201411yescharacteristic
215C22#202211yescharacteristic
216C4—24no—
217C4—21no—
218C4—22no—
219C4—21no—
220C4—48no—
221C4—42no—
222C4—84no—
223C4—162no—
224C4—162no—
225C2—22no—
226C2—22no—
227C2#994512yes—
228C2#996811yescharacteristic
229C2#1000712yes—
230C2#1001511yescharacteristic
231C2#1029911yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC22×C42C23
prime radicalC24#120
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
#276132
#152112
#113592
#76102
#70172