Finite Group Databasebeta

← #101276

Subgroups — #101276

Order 512.

393 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 393 conjugacy classes of subgroups — too many to draw. Only its 90 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#23745C211yesmaximal, characteristic
2#21921C211yesmaximal, characteristic
3#8724C212yesmaximal
4#7598C211yesmaximal, characteristic
5#7045C212yesmaximal
6#2296C2211yescharacteristic
7C2×#384C2211yescharacteristic
8#2100C414yes—
9#2099—22no—
10#1917—22no—
11#1916—22no—
12#1818—21no—
13#1797C2212yes—
14#1797C2212yes—
15#1750—21no—
16#1736—21no—
17#1736—21no—
18#1728C2211yescharacteristic
19#1296—22no—
20#1296—22no—
21#1271—22no—
22C22×M16—21no—
23C2×#117D411yescharacteristic
24C2×#117D411yescharacteristic
25C22×C4⋊C4—21no—
26C22×C4⋊C4—22no—
27C22×C42C2311yescharacteristic
28C2×C4⋊C8—22no—
29C2×C4⋊C8D412yes—
30C2×C4⋊C8D412yes—
31C2×C22⋊C8—22no—
32C2×C22⋊C8—22no—
33C2×#97—21no—
34C2×C4×C8—21no—
35#389C2×C412yes—
36#389D412yes—
37#385—22no—
38#384—22no—
39#384—21no—
40#384C2×C412yes—
41C4×C4⋊C4—22no—
42#340—24no—
43#340—24no—
44#336—21no—
45#336—22no—
46#336—21no—
47#336—22no—
48#336—22no—
49#336—21no—
50#336—22no—
51#336C2×C412yes—
52C23×C4—41no—
53C23×C4C2×D411yescharacteristic
54C23×C4#4112yes—
55C2×M16—42no—
56C2×M16—41no—
57C2×M16—41no—
58C2×M16—42no—
59C22×C8—22no—
60C22×C8—22no—
61C22×C8—22no—
62C22×C8—42no—
63#117—22no—
64#117—22no—
65#117—41no—
66#117—41no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—22no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—24no—
71C2×C4⋊C4—44no—
72C2×C4⋊C4—41no—
73C2×C4⋊C4—42no—
74C2×C4⋊C4—82no—
75C2×C4⋊C4—82no—
76C2×C4⋊C4C22⋊C412yes—
77C2×C4⋊C4C22⋊C412yes—
78C2×C22⋊C4—21no—
79C2×C22⋊C4—21no—
80C2×C42—21no—
81C2×C42—21no—
82C2×C42—41no—
83C2×C42—41no—
84C2×C42C22×C411yescharacteristic
85C2×C42C2×D412yes—
86C2×C42C2×D411yescharacteristic
87C4⋊C8—42no—
88C4⋊C8—42no—
89C4⋊C8—42no—
90C4⋊C8—42no—
91C22⋊C8—42no—
92C22⋊C8—42no—
93C22⋊C8—82no—
94#97—81no—
95C4×C8—81no—
96#95—22no—
97#95—22no—
98C24#12311yescharacteristic
99C22×C4—22no—
100C22×C4—21no—
101C22×C4—21no—
102C22×C4—22no—
103C22×C4—22no—
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—42no—
107C22×C4—42no—
108C22×C4—42no—
109C22×C4—82no—
110C22×C4—84no—
111C22×C4C2×C22⋊C411yescharacteristic
112C22×C4C4×D412yes—
113C22×C4#12011yescharacteristic
114C22×C4#12112yes—
115C22×C4#13512yes—
116C22×C4#13712yes—
117M16—82no—
118M16—82no—
119C2×C8—42no—
120C2×C8—42no—
121C2×C8—42no—
122C2×C8—42no—
123C2×C8—42no—
124C2×C8—42no—
125C2×C8—42no—
126C2×C8—42no—
127C2×C8—42no—
128C2×C8—82no—
129C2×C8—82no—
130C2×C8—82no—
131C4⋊C4—22no—
132C4⋊C4—22no—
133C4⋊C4—42no—
134C4⋊C4—44no—
135C4⋊C4—42no—
136C4⋊C4—42no—
137C4⋊C4—82no—
138C4⋊C4—84no—
139C4⋊C4—82no—
140C4⋊C4—82no—
141C4⋊C4—82no—
142C22⋊C4—42no—
143C22⋊C4—81no—
144C42—22no—
145C42—22no—
146C42—41no—
147C42—41no—
148C42—42no—
149C42—41no—
150C42—41no—
151C23—21no—
152C23—21no—
153C23—22no—
154C23—22no—
155C23#38611yescharacteristic
156C23#48512yes—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—44no—
169C2×C4—44no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—82no—
177C2×C4—84no—
178C2×C4—164no—
179C2×C4#41611yescharacteristic
180C2×C4#41911yescharacteristic
181C2×C4#45212yes—
182C2×C4#45412yes—
183C2×C4#45811yescharacteristic
184C2×C4#45811yescharacteristic
185C2×C4#47112yes—
186C2×C4#47212yes—
187C8—82no—
188C8—82no—
189C8—82no—
190C8—162no—
191C22—22no—
192C22—24no—
193C22—42no—
194C22—41no—
195C22—41no—
196C22#187311yescharacteristic
197C22#188811yescharacteristic
198C22#189011yescharacteristic
199C22#190212yes—
200C22#190712yes—
201C4—22no—
202C4—22no—
203C4—21no—
204C4—21no—
205C4—42no—
206C4—82no—
207C4—82no—
208C4—162no—
209C4#161512yes—
210C4#161512yes—
211C2—42no—
212C2#902211yescharacteristic
213C2#916812yes—
214C2#942211yescharacteristic
215C2#943811yescharacteristic
216C2#952212yes—
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×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
#237452
#219212
#87242
#75982
#70452