Finite Group Databasebeta

← #101790

Subgroups — #101790

Order 512.

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

normal subgroups only

This group has 435 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#29332C211yesmaximal, characteristic
2#20540C211yesmaximal, characteristic
3#7688C212yesmaximal
4#7632C211yesmaximal, characteristic
5#7026C212yesmaximal
6C2×#433—21no—
7#2857C2211yescharacteristic
8#2296C2211yescharacteristic
9#2099C412yes—
10#2043C412yes—
11#1933—22no—
12#1873—21no—
13#1873—21no—
14#1771—22no—
15C8×C4⋊C4—22no—
16#1750—21no—
17C4×C22⋊C8C2211yescharacteristic
18C4×C22⋊C8C2212yes—
19#1728C2212yes—
20#1271—22no—
21#1271—22no—
22#1271—22no—
23C22×M16—22no—
24C2×C4⋊Q8C2×C411yescharacteristic
25C2×C22⋊Q8—21no—
26C2×#117D411yescharacteristic
27C2×#117D411yescharacteristic
28C22×C42C2311yescharacteristic
29#433—28no—
30C2×C4⋊C8—22no—
31C2×#103—22no—
32C2×#103—22no—
33C2×C22⋊C8—22no—
34C2×C22⋊C8—21no—
35C2×#97—21no—
36C2×#97—21no—
37C2×C4×C8—21no—
38C2×C4×C8—21no—
39C2×C4×C8—21no—
40C2×C4×C8—22no—
41#391—21no—
42#389—22no—
43#389C2×C412yes—
44#389D412yes—
45#385—22no—
46#384C2×C411yescharacteristic
47#380—22no—
48C4×C4⋊C4—22no—
49#340—22no—
50#340—22no—
51#336—22no—
52#336—22no—
53#336—22no—
54#336C2×C412yes—
55#336D412yes—
56#336D412yes—
57C22×Q8—21no—
58C23×C4C2×D411yescharacteristic
59C23×C4#4112yes—
60C2×M16—24no—
61C2×M16—42no—
62C2×M16—82no—
63C2×M16—82no—
64C22×C8—22no—
65C22×C8—22no—
66C22×C8—22no—
67C22×C8—42no—
68C4⋊Q8—81no—
69C22⋊Q8—44no—
70#117—24no—
71#117—81no—
72C2×C4⋊C4—22no—
73C2×C4⋊C4—22no—
74C2×C4⋊C4—21no—
75C2×C4⋊C4—22no—
76C2×C4⋊C4—22no—
77C2×C4⋊C4—41no—
78C2×C4⋊C4C22⋊C412yes—
79C2×C4⋊C4C22⋊C412yes—
80C2×C22⋊C4—21no—
81C2×C22⋊C4—21no—
82C2×C22⋊C4—41no—
83C2×C42—21no—
84C2×C42—21no—
85C2×C42—81no—
86C2×C42C22×C411yescharacteristic
87C2×C42C2×D411yescharacteristic
88C2×C42C2×D412yes—
89C4⋊C8—28no—
90#103—44no—
91#103—82no—
92C22⋊C8—28no—
93C22⋊C8—42no—
94#97—24no—
95#97—81no—
96C4×C8—24no—
97C4×C8—82no—
98C4×C8—81no—
99C4×C8—81no—
100#95—22no—
101#95—22no—
102#95—42no—
103C24#12311yescharacteristic
104C2×Q8—42no—
105C2×Q8—42no—
106C2×Q8—42no—
107C22×C4—22no—
108C22×C4—22no—
109C22×C4—22no—
110C22×C4—22no—
111C22×C4—22no—
112C22×C4—22no—
113C22×C4—22no—
114C22×C4—22no—
115C22×C4—41no—
116C22×C4—42no—
117C22×C4—41no—
118C22×C4—41no—
119C22×C4C2×C22⋊C411yescharacteristic
120C22×C4C4×D412yes—
121C22×C4#12011yescharacteristic
122C22×C4#12112yes—
123M16—84no—
124M16—84no—
125C2×C8—24no—
126C2×C8—24no—
127C2×C8—42no—
128C2×C8—42no—
129C2×C8—42no—
130C2×C8—42no—
131C2×C8—42no—
132C2×C8—42no—
133C2×C8—44no—
134C2×C8—42no—
135C2×C8—82no—
136C2×C8—82no—
137C4⋊C4—22no—
138C4⋊C4—42no—
139C4⋊C4—42no—
140C4⋊C4—42no—
141C4⋊C4—42no—
142C4⋊C4—42no—
143C4⋊C4—42no—
144C4⋊C4—42no—
145C4⋊C4—42no—
146C4⋊C4—82no—
147C4⋊C4—82no—
148C4⋊C4#10414yes—
149C22⋊C4—24no—
150C22⋊C4—81no—
151C22⋊C4—82no—
152C42—22no—
153C42—22no—
154C42—42no—
155C42—41no—
156C42—41no—
157C42—41no—
158C42—41no—
159C23—22no—
160C23—21no—
161C23—21no—
162C23—22no—
163C23—21no—
164C23#38611yescharacteristic
165Q8—84no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—44no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4C2×#10412yes—
191C2×C4#44312yes—
192C2×C4#44412yes—
193C2×C4#45412yes—
194C2×C4#47112yes—
195C2×C4#47312yes—
196C8—44no—
197C8—44no—
198C8—82no—
199C8—84no—
200C22—42no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—42no—
205C22#187612yes—
206C22#188811yescharacteristic
207C22#189611yescharacteristic
208C22#190812yes—
209C22#191311yescharacteristic
210C4—22no—
211C4—22no—
212C4—22no—
213C4—22no—
214C4—22no—
215C4—22no—
216C4—44no—
217C4—82no—
218C4—161no—
219C4—161no—
220C2—81no—
221C2#907011yescharacteristic
222C2#921212yes—
223C2#926312yes—
224C2#941011yescharacteristic
225C2#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
#205402
#76882
#76322
#70262