Finite Group Databasebeta

← #120544

Subgroups — #120544

Order 512.

435 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 435 conjugacy classes of subgroups — too many to draw. Only its 132 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#21975C211yesmaximal, characteristic
2#17814C211yesmaximal, characteristic
3#8007C211yesmaximal, characteristic
4#8004C212yesmaximal
5#7960C212yesmaximal
6#2920C2212yes—
7C2×#431C2211yescharacteristic
8C2×#423C2211yescharacteristic
9C2×#423C2212yes—
10#2283C2211yescharacteristic
11#1939—22no—
12#1851—22no—
13#1843C412yes—
14#1832C412yes—
15#1571—24no—
16#1567—22no—
17#1293—22no—
18#1292—24no—
19#1286—24no—
20C22×M16—21no—
21C22×M16—22no—
22C22×C42C2311yescharacteristic
23#432—22no—
24#432—22no—
25#431—22no—
26#431—22no—
27#431—22no—
28#431Q814yes—
29#423—22no—
30#423—22no—
31#423—22no—
32#423—22no—
33#423—22no—
34#423—22no—
35#423—22no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—22no—
38C2×C4⋊C8—24no—
39C2×C4⋊C8C2×C412yes—
40C2×C4⋊C8C2×C411yescharacteristic
41C2×C4⋊C8C2×C411yescharacteristic
42C2×C4⋊C8D414yes—
43#407—22no—
44C2×C22⋊C8D412yes—
45C4×M16—22no—
46C2×C4×C8D412yes—
47#383—21no—
48#382D412yes—
49#381Q812yes—
50#380—21no—
51C4×C4⋊C4—21no—
52C4×C22⋊C4—21no—
53#376C2×C412yes—
54#336—24no—
55#335—28no—
56C23×C4C2×D411yescharacteristic
57C23×C4C2×Q811yescharacteristic
58C23×C4#4111yescharacteristic
59C2×M16—42no—
60C2×M16—42no—
61C2×M16—42no—
62C2×M16—42no—
63C2×M16—82no—
64C2×M16—84no—
65C22×C8—22no—
66C22×C8—24no—
67C22×C8C22⋊C412yes—
68C22×C8C22⋊C412yes—
69C2×C4⋊C4—22no—
70C2×C22⋊C4—22no—
71C2×C42—22no—
72C2×C42C22×C411yescharacteristic
73C2×C42C2×D412yes—
74C2×C42C2×D411yescharacteristic
75C2×C42C2×D411yescharacteristic
76C2×C42C2×Q812yes—
77C2×C42#4112yes—
78C2×C42#4112yes—
79C2×C42#4111yescharacteristic
80C4⋊C8—22no—
81C4⋊C8—22no—
82C4⋊C8—24no—
83C4⋊C8—24no—
84C4⋊C8—24no—
85C4⋊C8—24no—
86C4⋊C8—41no—
87C4⋊C8—42no—
88C4⋊C8—42no—
89C4⋊C8—41no—
90C4⋊C8—42no—
91C4⋊C8—84no—
92C22⋊C8—24no—
93C22⋊C8—24no—
94C22⋊C8—42no—
95#97—42no—
96C4×C8—22no—
97C4×C8—24no—
98C4×C8—22no—
99#95—22no—
100#95—22no—
101#95—22no—
102#95C4⋊C414yes—
103C24C22⋊Q811yescharacteristic
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—24no—
107C22×C4—41no—
108C22×C4—41no—
109C22×C4—81no—
110C22×C4C2×C22⋊C411yescharacteristic
111C22×C4C2×C4⋊C411yescharacteristic
112C22×C4#11711yescharacteristic
113C22×C4#12112yes—
114C22×C4#12111yescharacteristic
115C22×C4#12111yescharacteristic
116C22×C4C22⋊Q812yes—
117C22×C4C22⋊Q811yescharacteristic
118C22×C4#12312yes—
119C22×C4#12512yes—
120C22×C4#12512yes—
121C22×C4C4⋊Q812yes—
122M16—82no—
123M16—82no—
124M16—84no—
125M16—84no—
126M16—84no—
127C2×C8—22no—
128C2×C8—22no—
129C2×C8—42no—
130C2×C8—42no—
131C2×C8—44no—
132C2×C8—42no—
133C2×C8—44no—
134C2×C8—44no—
135C2×C8—84no—
136C4⋊C4—42no—
137C4⋊C4—42no—
138C22⋊C4—82no—
139C42—42no—
140C42—42no—
141C42C4×D412yes—
142C42C4×Q812yes—
143C42#12011yescharacteristic
144C42#12112yes—
145C42C22⋊Q812yes—
146C42C22⋊Q812yes—
147C42#12311yescharacteristic
148C42#12411yescharacteristic
149C42#12612yes—
150C42C4⋊Q811yescharacteristic
151C23—22no—
152C23—41no—
153C23—41no—
154C23#38011yescharacteristic
155C23#39812yes—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—44no—
171C2×C4—44no—
172C2×C4—44no—
173C2×C4#38611yescharacteristic
174C2×C4#38712yes—
175C2×C4#38912yes—
176C2×C4#39111yescharacteristic
177C2×C4#39411yescharacteristic
178C2×C4#39511yescharacteristic
179C2×C4#39612yes—
180C2×C4#39811yescharacteristic
181C2×C4#40011yescharacteristic
182C2×C4#47212yes—
183C2×C4#47312yes—
184C8—42no—
185C8—42no—
186C8—84no—
187C8—82no—
188C8—84no—
189C22—21no—
190C22—21no—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—82no—
195C22#144111yescharacteristic
196C22#181612yes—
197C4—22no—
198C4—21no—
199C4—22no—
200C4—21no—
201C4—21no—
202C4—22no—
203C4—84no—
204C4#190911yescharacteristic
205C4#191011yescharacteristic
206C4#204511yescharacteristic
207C4#204711yescharacteristic
208C4#208912yes—
209C2—22no—
210C2—42no—
211C2#1122511yescharacteristic
212C2#1123511yescharacteristic
213C2#1123911yescharacteristic
subgroupG/H
center, socleC22#1441
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C22⋊Q8
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#219752
#178142
#80072
#80042
#79602