Finite Group Databasebeta

← #325446

Subgroups — #325446

Order 512.

522 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 154 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#33256C211yesmaximal, characteristic
2#29132C212yesmaximal
3#21712C211yesmaximal, characteristic
4#10620C214yesmaximal
5#9906C212yesmaximal
6#8657C212yesmaximal
7#8657C212yesmaximal
8#8273C211yesmaximal, characteristic
9C2×#446C2212yes—
10#2859C2212yes—
11C4×C4⋊Q8C2211yescharacteristic
12#2099—22no—
13#2043—22no—
14#1984C2212yes—
15#1941—22no—
16#1941—22no—
17#1939—22no—
18#1935—24no—
19#1844C2212yes—
20#1842C2211yescharacteristic
21#1834C2211yescharacteristic
22#1834C2211yescharacteristic
23#1803C2214yes—
24#1803C2214yes—
25#1770—22no—
26#1767C2212yes—
27C42×C8C2211yescharacteristic
28C2×#334C2212yes—
29#1296C2214yes—
30#1296C2214yes—
31#1277C2212yes—
32C2×C4⋊Q8D411yescharacteristic
33C2×#125—22no—
34C2×C4×Q8C2312yes—
35#446—28no—
36C2×#106—22no—
37C2×#106—22no—
38C2×C4⋊C8—22no—
39C2×C4⋊C8—22no—
40C2×C4⋊C8C2314yes—
41C2×C4⋊C8C2312yes—
42C2×#103—24no—
43C2×#103—24no—
44C2×#97—22no—
45C2×#97—22no—
46C2×C4×C8D412yes—
47C2×C4×C8D412yes—
48C2×C4×C8C2311yescharacteristic
49C2×C4×C8C2311yescharacteristic
50#391D412yes—
51#389—22no—
52#389—22no—
53#389—22no—
54#389—22no—
55#389—22no—
56#384D411yescharacteristic
57#384C2312yes—
58#384C2312yes—
59#382—22no—
60C4×C4⋊C4—22no—
61C43C2311yescharacteristic
62#340—21no—
63#340—21no—
64#340—21no—
65#340—21no—
66#340—24no—
67#340—24no—
68#336—24no—
69#336—22no—
70#334—24no—
71C22×Q8C2×D412yes—
72C22×C8—22no—
73C22×C8—24no—
74C22×C8C2×D411yescharacteristic
75C22×C8C2×D411yescharacteristic
76C22×C8C2×D412yes—
77C4⋊Q8—42no—
78#125—84no—
79C4×Q8—24no—
80C4×Q8—24no—
81C2×C4⋊C4—22no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—22no—
88C2×C4⋊C4—22no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—42no—
91C2×C4⋊C4—42no—
92C2×C4⋊C4C2×D412yes—
93C2×C42—22no—
94C2×C42C2×D411yescharacteristic
95C2×C42C2×D412yes—
96C2×C42C2×D411yescharacteristic
97C2×C42#4112yes—
98C2×C42C2411yescharacteristic
99#106—44no—
100#106—44no—
101C4⋊C8—24no—
102C4⋊C8—24no—
103C4⋊C8—24no—
104C4⋊C8—44no—
105C4⋊C8—44no—
106#103—48no—
107#103—84no—
108#97—44no—
109#97—82no—
110C4×C8—24no—
111C4×C8—22no—
112C4×C8—42no—
113C4×C8#4114yes—
114#95—24no—
115#95—42no—
116#95—42no—
117C2×Q8—24no—
118C2×Q8—24no—
119C2×Q8—24no—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—42no—
123C22×C4—42no—
124C22×C4#12112yes—
125C22×C4#12112yes—
126C22×C4C22×D411yescharacteristic
127C22×C4C22×D411yescharacteristic
128C22×C4C2×#4111yescharacteristic
129C2×C8—22no—
130C2×C8—22no—
131C2×C8—22no—
132C2×C8—22no—
133C2×C8—42no—
134C2×C8—44no—
135C2×C8—44no—
136C2×C8—44no—
137C2×C8—44no—
138C2×C8#12412yes—
139C2×C8#12412yes—
140C2×C8#13714yes—
141C4⋊C4—24no—
142C4⋊C4—44no—
143C4⋊C4—44no—
144C4⋊C4—44no—
145C4⋊C4—42no—
146C4⋊C4—42no—
147C4⋊C4—44no—
148C4⋊C4—42no—
149C4⋊C4—42no—
150C4⋊C4—42no—
151C4⋊C4—42no—
152C4⋊C4—82no—
153C4⋊C4—82no—
154C4⋊C4—84no—
155C4⋊C4—84no—
156C42—22no—
157C42—22no—
158C42—22no—
159C42—22no—
160C42—24no—
161C42—42no—
162C42—42no—
163C42C2×#4112yes—
164C422−1+412yes—
165C23C2×#12111yescharacteristic
166Q8—48no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—44no—
178C2×C4—82no—
179C2×C4—82no—
180C2×C4—82no—
181C2×C4—82no—
182C2×C4—82no—
183C2×C4—82no—
184C2×C4#47114yes—
185C2×C4C2×#12411yescharacteristic
186C2×C4#53611yescharacteristic
187C2×C4#54712yes—
188C2×C4#55612yes—
189C2×C4C2×#13712yes—
190C2×C4#57512yes—
191C2×C4#57512yes—
192C2×C4#57712yes—
193C8—22no—
194C8—22no—
195C8—24no—
196C8—84no—
197C8—82no—
198C22#254711yescharacteristic
199C22#303712yes—
200C22#305411yescharacteristic
201C22#306011yescharacteristic
202C22C2×#47112yes—
203C4—22no—
204C4—24no—
205C4—42no—
206C4—82no—
207C4—82no—
208C4—162no—
209C4—162no—
210C4#313511yescharacteristic
211C4#313911yescharacteristic
212C4#323612yes—
213C4#335114yes—
214C2#1928812yes—
215C2#1934312yes—
216C2#2871011yescharacteristic
217C2#2872311yescharacteristic
218C2#2873211yescharacteristic
subgroupG/H
center, socle, prime radicalC23C2×#121
commutator, Frattini, cosocleC2×C42C24
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#332562
#291322
#217122
#106202
#99062
#86572
#82732