Finite Group Databasebeta

← #101796

Subgroups — #101796

Order 512.

387 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 387 conjugacy classes of subgroups — too many to draw. Only its 80 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#29332C211yesmaximal, characteristic
2#21913C211yesmaximal, characteristic
3#7688C212yesmaximal
4#7632C211yesmaximal, characteristic
5#7026C212yesmaximal
6#2857C2211yescharacteristic
7#2296C2211yescharacteristic
8#2099C412yes—
9#2043C412yes—
10#1933—22no—
11#1916—24no—
12#1873—21no—
13#1873—21no—
14#1818—21no—
15#1798—21no—
16C4×C22⋊C8C2211yescharacteristic
17C4×C22⋊C8C2212yes—
18#1728C2212yes—
19#1271—22no—
20#1271—24no—
21C22×M16—22no—
22C2×C4⋊Q8C2×C411yescharacteristic
23C2×C22⋊Q8—21no—
24C2×#117D411yescharacteristic
25C2×#117D411yescharacteristic
26C22×C42C2311yescharacteristic
27C2×C4⋊C8—22no—
28C2×#103—22no—
29C2×#103—22no—
30C2×C22⋊C8—22no—
31C2×C22⋊C8—21no—
32C2×C4×C8—22no—
33C2×C4×C8—21no—
34#391—21no—
35#389—22no—
36#389C2×C412yes—
37#389D412yes—
38#385—22no—
39#384C2×C411yescharacteristic
40#380—22no—
41C4×C4⋊C4—22no—
42#340—22no—
43#340—22no—
44#336—22no—
45#336—24no—
46#336—22no—
47#336—22no—
48#336C2×C412yes—
49#336D414yes—
50C22×Q8—21no—
51C23×C4C2×D411yescharacteristic
52C23×C4#4112yes—
53C2×M16—24no—
54C2×M16—42no—
55C2×M16—82no—
56C2×M16—82no—
57C22×C8—22no—
58C22×C8—24no—
59C22×C8—42no—
60C4⋊Q8—81no—
61C22⋊Q8—44no—
62#117—42no—
63#117—81no—
64C2×C4⋊C4—22no—
65C2×C4⋊C4—22no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—22no—
69C2×C4⋊C4—41no—
70C2×C4⋊C4C22⋊C412yes—
71C2×C4⋊C4C22⋊C412yes—
72C2×C22⋊C4—21no—
73C2×C22⋊C4—21no—
74C2×C22⋊C4—41no—
75C2×C42—21no—
76C2×C42—21no—
77C2×C42—81no—
78C2×C42C22×C411yescharacteristic
79C2×C42C2×D411yescharacteristic
80C2×C42C2×D412yes—
81C4⋊C8—82no—
82#103—44no—
83#103—82no—
84C22⋊C8—44no—
85C22⋊C8—42no—
86C4×C8—81no—
87C4×C8—82no—
88#95—22no—
89#95—22no—
90#95—42no—
91C24#12311yescharacteristic
92C2×Q8—42no—
93C2×Q8—42no—
94C2×Q8—42no—
95C22×C4—22no—
96C22×C4—22no—
97C22×C4—22no—
98C22×C4—22no—
99C22×C4—22no—
100C22×C4—22no—
101C22×C4—22no—
102C22×C4—22no—
103C22×C4—41no—
104C22×C4—42no—
105C22×C4—41no—
106C22×C4—41no—
107C22×C4C2×C22⋊C411yescharacteristic
108C22×C4C4×D412yes—
109C22×C4#12011yescharacteristic
110C22×C4#12112yes—
111M16—84no—
112M16—84no—
113C2×C8—42no—
114C2×C8—44no—
115C2×C8—42no—
116C2×C8—44no—
117C2×C8—44no—
118C2×C8—42no—
119C2×C8—44no—
120C2×C8—82no—
121C2×C8—82no—
122C4⋊C4—22no—
123C4⋊C4—22no—
124C4⋊C4—42no—
125C4⋊C4—42no—
126C4⋊C4—42no—
127C4⋊C4—42no—
128C4⋊C4—42no—
129C4⋊C4—42no—
130C4⋊C4—42no—
131C4⋊C4—42no—
132C4⋊C4—82no—
133C4⋊C4—82no—
134C22⋊C4—42no—
135C22⋊C4—81no—
136C22⋊C4—82no—
137C42—42no—
138C42—41no—
139C42—41no—
140C42—42no—
141C42—42no—
142C23—22no—
143C23—21no—
144C23—21no—
145C23—22no—
146C23—21no—
147C23#38611yescharacteristic
148Q8—84no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—44no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—82no—
169C2×C4—81no—
170C2×C4—81no—
171C2×C4—81no—
172C2×C4—81no—
173C2×C4#42112yes—
174C2×C4#44312yes—
175C2×C4#44412yes—
176C2×C4#45412yes—
177C2×C4#47112yes—
178C2×C4#47312yes—
179C8—84no—
180C8—82no—
181C8—84no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—42no—
187C22#187612yes—
188C22#188811yescharacteristic
189C22#189711yescharacteristic
190C22#190812yes—
191C22#191311yescharacteristic
192C4—22no—
193C4—22no—
194C4—22no—
195C4—22no—
196C4—22no—
197C4—22no—
198C4—82no—
199C4—82no—
200C4—161no—
201C4—161no—
202C2—81no—
203C2#907011yescharacteristic
204C2#921412yes—
205C2#926312yes—
206C2#941411yescharacteristic
207C2#943611yescharacteristic
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
#293322
#219132
#76882
#76322
#70262