Finite Group Databasebeta

← #102870

Subgroups — #102870

Order 512.

453 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 453 conjugacy classes of subgroups — too many to draw. Only its 96 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#23837C211yesmaximal, characteristic
2#23816C212yesmaximal
3#9874C212yesmaximal
4#9643C211yesmaximal, characteristic
5#7014C211yesmaximal, characteristic
6C4×C4⋊Q8C2211yescharacteristic
7C4×C4⋊Q8C2212yes—
8#2100—22no—
9#2084—22no—
10#2072—22no—
11#2058—22no—
12#2043—22no—
13#2024—22no—
14#1842C2211yescharacteristic
15C4×#106—22no—
16C4×#103—24no—
17#1744C2212yes—
18#1744C2211yescharacteristic
19C2×Q8⋊C8—22no—
20#1279—24no—
21C2×C4⋊Q8D412yes—
22C2×C4⋊Q8D411yescharacteristic
23C2×C4×Q8—21no—
24C2×C4×Q8—22no—
25C2×#106—24no—
26C2×C4⋊C8—21no—
27C2×C4⋊C8—22no—
28C2×#103—24no—
29C2×#103—24no—
30C2×C4×C8D414yes—
31C2×C4×C8D412yes—
32#391—22no—
33#391—21no—
34#389—22no—
35#389—22no—
36#389—22no—
37#384D411yescharacteristic
38#384D412yes—
39C4×C4⋊C4—22no—
40C4×C4⋊C4—22no—
41C4×C4⋊C4—22no—
42C43C2311yescharacteristic
43#340—22no—
44#340—24no—
45#340—22no—
46#340—24no—
47#336—22no—
48#336—22no—
49#336—22no—
50Q8⋊C8—44no—
51C22×Q8—22no—
52C22×Q8—21no—
53C22×C8—22no—
54C22×C8—24no—
55C22×C8—41no—
56C4⋊Q8—42no—
57C4⋊Q8—44no—
58C4×Q8—42no—
59C4×Q8—44no—
60C4×Q8—42no—
61C4×Q8—44no—
62C2×C4⋊C4—22no—
63C2×C4⋊C4—22no—
64C2×C4⋊C4—22no—
65C2×C4⋊C4—22no—
66C2×C4⋊C4—22no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—21no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—41no—
71C2×C4⋊C4—42no—
72C2×C42—41no—
73C2×C42—42no—
74C2×C42C2×D412yes—
75C2×C42C2×D411yescharacteristic
76C2×C42C2×D411yescharacteristic
77C2×C42C2×D412yes—
78C2×C42#4111yescharacteristic
79#106—48no—
80C4⋊C8—42no—
81C4⋊C8—44no—
82#103—48no—
83#103—48no—
84C4×C8—24no—
85C4×C8—22no—
86C4×C8—24no—
87C4×C8SD1614yes—
88#95—42no—
89#95—42no—
90#95—42no—
91C2×Q8—24no—
92C2×Q8—22no—
93C2×Q8—42no—
94C2×Q8—41no—
95C2×Q8—44no—
96C2×Q8—42no—
97C2×Q8—44no—
98C2×Q8—42no—
99C22×C4—42no—
100C22×C4—41no—
101C22×C4—41no—
102C22×C4—42no—
103C22×C4#12011yescharacteristic
104C22×C4#12012yes—
105C22×C4#12111yescharacteristic
106C22×C4#12112yes—
107C22×C4#12711yescharacteristic
108C2×C8—24no—
109C2×C8—44no—
110C2×C8—44no—
111C2×C8—44no—
112C2×C8—44no—
113C2×C8—81no—
114C2×C8—82no—
115C4⋊C4—24no—
116C4⋊C4—24no—
117C4⋊C4—24no—
118C4⋊C4—42no—
119C4⋊C4—42no—
120C4⋊C4—42no—
121C4⋊C4—44no—
122C4⋊C4—44no—
123C4⋊C4—44no—
124C4⋊C4—44no—
125C4⋊C4—42no—
126C4⋊C4—82no—
127C4⋊C4—84no—
128C42—42no—
129C42—41no—
130C42—41no—
131C42—81no—
132C42—82no—
133C42—81no—
134C42—82no—
135C42C2×SD1612yes—
136C42#13514yes—
137C42#13712yes—
138C42#13714yes—
139C23#39211yescharacteristic
140Q8—48no—
141Q8—44no—
142Q8—84no—
143Q8—82no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—44no—
152C2×C4—42no—
153C2×C4—82no—
154C2×C4—81no—
155C2×C4—82no—
156C2×C4—81no—
157C2×C4—82no—
158C2×C4—82no—
159C2×C4—81no—
160C2×C4—82no—
161C2×C4—82no—
162C2×C4#44812yes—
163C2×C4#45214yes—
164C2×C4#46112yes—
165C2×C4#46414yes—
166C2×C4#49211yescharacteristic
167C2×C4#49512yes—
168C2×C4#49712yes—
169C2×C4#49711yescharacteristic
170C8—44no—
171C8—84no—
172C8—161no—
173C22#201012yes—
174C22#201011yescharacteristic
175C22#201311yescharacteristic
176C22#201512yes—
177C22#201711yescharacteristic
178C4—22no—
179C4—24no—
180C4—24no—
181C4—22no—
182C4—84no—
183C4—82no—
184C4—161no—
185C4—162no—
186C4#170811yescharacteristic
187C4#171611yescharacteristic
188C4#171812yes—
189C2#1001411yescharacteristic
190C2#1001612yes—
191C2#1003512yes—
192C2#1003611yescharacteristic
193C2#1031711yescharacteristic
subgroupG/H
centerC22×C4#127
commutator, Frattini, cosocleC43C23
socle, prime radicalC23#392
LCSG ▷ C43 ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#238372
#238162
#98742
#96432
#70142