Finite Group Databasebeta

← #102733

Subgroups — #102733

Order 512.

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

normal subgroups only

This group has 485 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#30298C211yesmaximal, characteristic
2#29939C212yesmaximal
3#11370C211yesmaximal, characteristic
4#9711C212yesmaximal
5#7034C211yesmaximal, characteristic
6#2857C2212yes—
7#2285C2211yescharacteristic
8#2100—22no—
9#2083—22no—
10#2083—22no—
11#2076—24no—
12#2058—22no—
13#1987—22no—
14#1947—22no—
15#1809—22no—
16#1797C2212yes—
17C2×#339—22no—
18#1728C2211yescharacteristic
19C2×#328—24no—
20C4×#95C2211yescharacteristic
21C22×M16D412yes—
22C2×C4⋊Q8D412yes—
23C2×C22⋊Q8—22no—
24C2×#117—21no—
25C22×C42—21no—
26C22×C42C2311yescharacteristic
27C2×#107—22no—
28C2×#107—24no—
29C2×#106—22no—
30C2×C4⋊C8—22no—
31C2×C22⋊C8D414yes—
32#391—22no—
33#389—22no—
34#389—22no—
35#384D411yescharacteristic
36#384D412yes—
37#384D411yescharacteristic
38#382—21no—
39#380—22no—
40#380—22no—
41#380—22no—
42C4×C4⋊C4—22no—
43C2×#95—22no—
44#340—24no—
45#340—24no—
46#340—24no—
47#340—24no—
48#339—44no—
49#336—22no—
50#336—22no—
51#328—48no—
52C22×Q8—22no—
53C23×C4—41no—
54C23×C4C2×D411yescharacteristic
55C23×C4C2×D412yes—
56C2×M16—22no—
57C2×M16—42no—
58C2×M16—42no—
59C2×M16Q1614yes—
60C22×C8—22no—
61C22×C8—24no—
62C4⋊Q8—44no—
63C22⋊Q8—44no—
64C22⋊Q8—44no—
65#117—42no—
66#117—42no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—22no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—22no—
73C2×C4⋊C4—21no—
74C2×C4⋊C4—21no—
75C2×C4⋊C4—22no—
76C2×C4⋊C4—42no—
77C2×C22⋊C4—41no—
78C2×C22⋊C4—42no—
79C2×C42—22no—
80C2×C42—42no—
81C2×C42—42no—
82C2×C42—42no—
83C2×C42—41no—
84C2×C42—41no—
85C2×C42C2×D412yes—
86C2×C42C2×D411yescharacteristic
87C2×C42#4111yescharacteristic
88#107—82no—
89#107—84no—
90#106—82no—
91C4⋊C8—44no—
92C22⋊C8—44no—
93#95—24no—
94#95—42no—
95#95—42no—
96#95—42no—
97#95—42no—
98C24#12711yescharacteristic
99C2×Q8—44no—
100C2×Q8—82no—
101C2×Q8—82no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—22no—
107C22×C4—42no—
108C22×C4—42no—
109C22×C4—44no—
110C22×C4—42no—
111C22×C4—41no—
112C22×C4—41no—
113C22×C4—42no—
114C22×C4—42no—
115C22×C4—81no—
116C22×C4—82no—
117C22×C4—81no—
118C22×C4#12012yes—
119C22×C4#12011yescharacteristic
120C22×C4#12112yes—
121C22×C4#12111yescharacteristic
122C22×C4C2×Q1612yes—
123C22×C4#13712yes—
124M16—44no—
125M16—82no—
126C2×C8—24no—
127C2×C8—42no—
128C2×C8—42no—
129C2×C8—44no—
130C2×C8—44no—
131C2×C8—44no—
132C4⋊C4—44no—
133C4⋊C4—42no—
134C4⋊C4—42no—
135C4⋊C4—44no—
136C4⋊C4—44no—
137C4⋊C4—42no—
138C4⋊C4—42no—
139C4⋊C4—42no—
140C4⋊C4—42no—
141C4⋊C4—42no—
142C4⋊C4—42no—
143C4⋊C4—44no—
144C4⋊C4—82no—
145C4⋊C4—82no—
146C22⋊C4—82no—
147C22⋊C4—84no—
148C42—24no—
149C42—41no—
150C42—41no—
151C42—44no—
152C42—82no—
153C42—81no—
154C42—81no—
155C23—22no—
156C23—21no—
157C23—22no—
158C23—21no—
159C23#39211yescharacteristic
160C23#49411yescharacteristic
161C23#49711yescharacteristic
162Q8—164no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—44no—
175C2×C4—82no—
176C2×C4—82no—
177C2×C4—82no—
178C2×C4—84no—
179C2×C4—84no—
180C2×C4—82no—
181C2×C4—81no—
182C2×C4—81no—
183C2×C4—82no—
184C2×C4—82no—
185C2×C4—82no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—82no—
189C2×C4—82no—
190C2×C4—82no—
191C2×C4#45112yes—
192C2×C4#45312yes—
193C2×C4#45311yescharacteristic
194C2×C4#45412yes—
195C2×C4#45411yescharacteristic
196C2×C4#45812yes—
197C2×C4#46212yes—
198C8—44no—
199C8—84no—
200C22—22no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—42no—
206C22—41no—
207C22#200612yes—
208C22#200611yescharacteristic
209C22#200912yes—
210C22#201611yescharacteristic
211C22#202211yescharacteristic
212C4—22no—
213C4—22no—
214C4—22no—
215C4—42no—
216C4—84no—
217C4—161no—
218C4—162no—
219C4—162no—
220C4—161no—
221C4#161412yes—
222C4#161712yes—
223C2—41no—
224C2—41no—
225C2#993312yes—
226C2#997211yescharacteristic
227C2#1020312yes—
228C2#1021611yescharacteristic
229C2#1030011yescharacteristic
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
#302982
#299392
#113702
#97112
#70342