Finite Group Databasebeta

← #124878

Subgroups — #124878

Order 512.

496 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 82 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#14164C211yesmaximal, characteristic
2#7910C212yesmaximal
3#7122C214yesmaximal
4C2×#432—22no—
5C2×#383C411yescharacteristic
6C2×C4×C4⋊C4C411yescharacteristic
7C2×#376C2211yescharacteristic
8#1444C412yes—
9#1442C2212yes—
10#1436—22no—
11#1436—22no—
12#1280—22no—
13#1280C2214yes—
14C22×C4⋊C4—22no—
15C22×C4⋊C4C2×C412yes—
16C22×C42—21no—
17C22×C42C2×C411yescharacteristic
18C22×C42D412yes—
19#432—28no—
20#432—44no—
21C2×C4⋊C8—42no—
22C2×C22⋊C8—24no—
23C2×#97—42no—
24#383—24no—
25C4×C4⋊C4—42no—
26#376—42no—
27C2×#95—21no—
28C2×#95—21no—
29C2×#95—21no—
30C2×#95—22no—
31C2×#95—22no—
32C2×#95—22no—
33C2×#95C2×C412yes—
34C2×#95C2×C411yescharacteristic
35C2×#95D412yes—
36C2×#95C2311yescharacteristic
37C23×C4—22no—
38C23×C4—22no—
39C23×C4C22⋊C411yescharacteristic
40C23×C4C22⋊C412yes—
41C23×C4C22⋊C411yescharacteristic
42C23×C4C22×C411yescharacteristic
43C23×C4C2×D412yes—
44C22×C8—44no—
45C2×C4⋊C4—42no—
46C2×C4⋊C4—44no—
47C2×C4⋊C4—44no—
48C2×C4⋊C4—44no—
49C2×C4⋊C4—82no—
50C2×C42—22no—
51C2×C42—22no—
52C2×C42—22no—
53C2×C42—22no—
54C2×C42—24no—
55C2×C42—22no—
56C2×C42—22no—
57C2×C42—22no—
58C2×C42—42no—
59C2×C42—81no—
60C2×C42—81no—
61C4⋊C8—48no—
62C22⋊C8—28no—
63C22⋊C8—44no—
64#97—48no—
65#95—24no—
66#95—24no—
67#95—22no—
68#95—41no—
69#95—42no—
70#95—41no—
71#95—44no—
72#95—42no—
73#95—42no—
74#95—42no—
75#95—82no—
76#95M1614yes—
77C24C2×C22⋊C411yescharacteristic
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—22no—
83C22×C4—22no—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—22no—
87C22×C4—22no—
88C22×C4—22no—
89C22×C4—22no—
90C22×C4—24no—
91C22×C4—24no—
92C22×C4—41no—
93C22×C4—42no—
94C22×C4—41no—
95C22×C4—42no—
96C22×C4—42no—
97C22×C4—42no—
98C22×C4—42no—
99C22×C4—42no—
100C22×C4—42no—
101C22×C4—42no—
102C22×C4—42no—
103C22×C4—42no—
104C22×C4—42no—
105C22×C4—42no—
106C22×C4—42no—
107C22×C4—42no—
108C22×C4—42no—
109C22×C4—42no—
110C22×C4—42no—
111C22×C4#9912yes—
112C22×C4#10112yes—
113C22×C4#10414yes—
114C22×C4C2×M1612yes—
115C22×C4AGL(1,ℤ/8)12yes—
116C22×C4#13712yes—
117C2×C8—48no—
118C2×C8—84no—
119C2×C8—84no—
120C4⋊C4—44no—
121C4⋊C4—44no—
122C4⋊C4—88no—
123C42—24no—
124C42—24no—
125C42—28no—
126C42—24no—
127C42—24no—
128C42—84no—
129C23—22no—
130C23—21no—
131C23—21no—
132C23#40711yescharacteristic
133C23C2×#9911yescharacteristic
134C23C2×#10111yescharacteristic
135C23#41712yes—
136C23C2×#10412yes—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—24no—
144C2×C4—22no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—44no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—44no—
163C2×C4—44no—
164C2×C4—44no—
165C2×C4—44no—
166C2×C4—44no—
167C2×C4—44no—
168C2×C4—82no—
169C2×C4—82no—
170C2×C4—82no—
171C2×C4—82no—
172C2×C4—82no—
173C2×C4—82no—
174C2×C4—82no—
175C2×C4—82no—
176C2×C4—82no—
177C2×C4—82no—
178C8—88no—
179C22—22no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—21no—
187C22#146311yescharacteristic
188C22#148912yes—
189C22#150412yes—
190C22#152611yescharacteristic
191C22#156111yescharacteristic
192C22#212012yes—
193C22#212911yescharacteristic
194C22#213411yescharacteristic
195C4—42no—
196C4—42no—
197C4—42no—
198C4—44no—
199C4—42no—
200C4—42no—
201C4—84no—
202C4—84no—
203C2—22no—
204C2—21no—
205C2—21no—
206C2#763211yescharacteristic
207C2#1151511yescharacteristic
208C2#1151811yescharacteristic
209C2#1175612yes—
210C2#1176112yes—
subgroupG/H
center, socleC23C2×#99
commutatorC23×C4C22×C4
Frattini, cosocleC2×#95C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#376 ◁ G
LECSG ▷ C2×#95 ▷ C24 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#141642
#79102
#71222