Finite Group Databasebeta

← #105239

Subgroups — #105239

Order 512.

295 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 295 conjugacy classes of subgroups — too many to draw. Only its 92 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#9874C211yesmaximal, characteristic
2#9874C211yesmaximal, characteristic
3#9643C211yesmaximal, characteristic
4#8809C211yesmaximal, characteristic
5#8787C211yesmaximal, characteristic
6#8787C211yesmaximal, characteristic
7#7014C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9#1842C2211yescharacteristic
10#1842C2211yescharacteristic
11#1842C2211yescharacteristic
12#1744C2211yescharacteristic
13#1744C2211yescharacteristic
14#1744C2211yescharacteristic
15C2×#334—22no—
16C2×Q8⋊C8—22no—
17#1279—22no—
18#1279—22no—
19#1277—22no—
20#1277—22no—
21C2×C4⋊Q8Q811yescharacteristic
22C2×C4×Q8—21no—
23C2×C4⋊C8—21no—
24C2×C4⋊C8—21no—
25C2×C4⋊C8—21no—
26C2×C4⋊C8—21no—
27C2×C4⋊C8—21no—
28C2×C4⋊C8—21no—
29C2×C4⋊C8—21no—
30C2×C4⋊C8—21no—
31C2×C4⋊C8—21no—
32C2×C4×C8D412yes—
33C2×C4×C8D412yes—
34C2×C4×C8D412yes—
35#391—21no—
36#389—21no—
37#389—21no—
38#384Q811yescharacteristic
39C4×C4⋊C4—21no—
40C4×C4⋊C4—21no—
41C43C2311yescharacteristic
42#336—21no—
43#336—21no—
44#336—21no—
45#336—21no—
46#336—21no—
47#336—21no—
48#334—44no—
49Q8⋊C8—44no—
50C22×Q8—21no—
51C22×C8—22no—
52C22×C8—22no—
53C22×C8—22no—
54C22×C8—41no—
55C22×C8—41no—
56C22×C8—41no—
57C4⋊Q8—42no—
58C4×Q8—42no—
59C4×Q8—42no—
60C2×C4⋊C4—21no—
61C2×C4⋊C4—21no—
62C2×C4⋊C4—21no—
63C2×C4⋊C4—21no—
64C2×C4⋊C4—21no—
65C2×C4⋊C4—41no—
66C2×C42—41no—
67C2×C42C2×D411yescharacteristic
68C2×C42C2×D411yescharacteristic
69C2×C42C2×D411yescharacteristic
70C2×C42C2×Q811yescharacteristic
71C2×C42#4111yescharacteristic
72C2×C42#4111yescharacteristic
73C2×C42#4111yescharacteristic
74C4⋊C8—42no—
75C4⋊C8—42no—
76C4⋊C8—42no—
77C4⋊C8—42no—
78C4⋊C8—42no—
79C4⋊C8—42no—
80C4⋊C8—42no—
81C4⋊C8—42no—
82C4⋊C8—42no—
83C4×C8—22no—
84C4×C8—22no—
85C4×C8—22no—
86C4×C8—22no—
87C4×C8—22no—
88C4×C8SD1614yes—
89#95—41no—
90#95—41no—
91C2×Q8—22no—
92C2×Q8—41no—
93C2×Q8—42no—
94C2×Q8—42no—
95C22×C4—41no—
96C22×C4—41no—
97C22×C4C22⋊Q811yescharacteristic
98C22×C4C22⋊Q811yescharacteristic
99C22×C4C22⋊Q811yescharacteristic
100C22×C4#12311yescharacteristic
101C22×C4#12311yescharacteristic
102C22×C4#12311yescharacteristic
103C22×C4#12711yescharacteristic
104C2×C8—24no—
105C2×C8—42no—
106C2×C8—42no—
107C2×C8—42no—
108C2×C8—42no—
109C2×C8—42no—
110C2×C8—42no—
111C2×C8—42no—
112C2×C8—42no—
113C2×C8—81no—
114C2×C8—81no—
115C2×C8—81no—
116C2×C8—81no—
117C2×C8—81no—
118C2×C8—81no—
119C2×C8—81no—
120C2×C8—81no—
121C2×C8—81no—
122C4⋊C4—22no—
123C4⋊C4—22no—
124C4⋊C4—41no—
125C4⋊C4—41no—
126C4⋊C4—42no—
127C4⋊C4—42no—
128C4⋊C4—42no—
129C4⋊C4—82no—
130C42—41no—
131C42—41no—
132C42—41no—
133C42—41no—
134C42—81no—
135C42—81no—
136C42C2×SD1612yes—
137C42#13512yes—
138C42#13512yes—
139C42AGL(1,ℤ/8)12yes—
140C42#13712yes—
141C42#13712yes—
142C23#39911yescharacteristic
143Q8—44no—
144Q8—82no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—42no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4#47512yes—
164C2×C4#47812yes—
165C2×C4#47912yes—
166C2×C4#48212yes—
167C2×C4#48312yes—
168C2×C4#48512yes—
169C2×C4#49211yescharacteristic
170C2×C4#49511yescharacteristic
171C2×C4#49511yescharacteristic
172C2×C4#49611yescharacteristic
173C2×C4#49711yescharacteristic
174C2×C4#49711yescharacteristic
175C8—44no—
176C8—82no—
177C8—82no—
178C8—161no—
179C8—161no—
180C8—161no—
181C22#209111yescharacteristic
182C22#209211yescharacteristic
183C22#209611yescharacteristic
184C22#209711yescharacteristic
185C22#209811yescharacteristic
186C22#209811yescharacteristic
187C22#209811yescharacteristic
188C4—22no—
189C4—22no—
190C4—22no—
191C4—22no—
192C4—22no—
193C4—22no—
194C4—82no—
195C4—161no—
196C4#170811yescharacteristic
197C4#171411yescharacteristic
198C4#171811yescharacteristic
199C4#172011yescharacteristic
200C2#1065911yescharacteristic
201C2#1066311yescharacteristic
202C2#1066411yescharacteristic
203C2#1066511yescharacteristic
204C2#1066911yescharacteristic
205C2#1067011yescharacteristic
206C2#1068111yescharacteristic
subgroupG/H
centerC22×C4#127
commutator, Frattini, cosocleC43C23
socle, prime radicalC23#399
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
#98742
#96432
#88092
#87872
#70142