Finite Group Databasebeta

← #325412

Subgroups — #325412

Order 512.

522 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 162 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#33291C211yesmaximal, characteristic
2#29123C212yesmaximal
3#21712C211yesmaximal, characteristic
4#10624C212yesmaximal
5#10623C212yesmaximal
6#9900C212yesmaximal
7#8655C214yesmaximal
8C4×#335C211yesmaximal, characteristic
9C2×#446C2212yes—
10#2859C2212yes—
11C4×C4⋊Q8C2211yescharacteristic
12#2100—22no—
13#2043—22no—
14#1991—22no—
15#1991—22no—
16#1984C2212yes—
17#1939—22no—
18#1933—24no—
19#1842C2211yescharacteristic
20#1834C2211yescharacteristic
21#1834C2211yescharacteristic
22#1834C2212yes—
23#1803C2214yes—
24#1803C2214yes—
25#1770—22no—
26C4×C4⋊C8C2212yes—
27C42×C8C2211yescharacteristic
28C2×#335C2212yes—
29#1296C2214yes—
30#1296C2214yes—
31#1277C2212yes—
32C2×C4⋊Q8D411yescharacteristic
33C2×#125—22no—
34C2×C4×Q8C2312yes—
35#446—28no—
36C2×C4⋊C8—22no—
37C2×C4⋊C8—22no—
38C2×C4⋊C8C2314yes—
39C2×C4⋊C8C2312yes—
40C2×#103—24no—
41C2×#103—24no—
42C2×#97—22no—
43C2×C4×C8—22no—
44C2×C4×C8D412yes—
45C2×C4×C8D412yes—
46C2×C4×C8C2311yescharacteristic
47C2×C4×C8C2311yescharacteristic
48#391D412yes—
49#389—22no—
50#389—22no—
51#389—22no—
52#389—22no—
53#389—22no—
54#384D411yescharacteristic
55#384C2312yes—
56#384C2312yes—
57#382—22no—
58C4×C4⋊C4—22no—
59C43C2311yescharacteristic
60#340—22no—
61#340—22no—
62#340—22no—
63#340—22no—
64#340—24no—
65#340—24no—
66#336—24no—
67#336—22no—
68#335—24no—
69C22×Q8C2×D412yes—
70C22×C8—22no—
71C22×C8—24no—
72C22×C8C2×D412yes—
73C22×C8C2×D411yescharacteristic
74C22×C8C2×D411yescharacteristic
75C4⋊Q8—42no—
76#125—44no—
77#125—44no—
78C4×Q8—24no—
79C4×Q8—24no—
80C2×C4⋊C4—22no—
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—42no—
90C2×C4⋊C4—42no—
91C2×C4⋊C4C2×D412yes—
92C2×C42—22no—
93C2×C42C2×D411yescharacteristic
94C2×C42C2×D411yescharacteristic
95C2×C42C2×D412yes—
96C2×C42#4112yes—
97C2×C42C2411yescharacteristic
98C4⋊C8—24no—
99C4⋊C8—24no—
100C4⋊C8—24no—
101C4⋊C8—44no—
102C4⋊C8—44no—
103#103—48no—
104#103—84no—
105#97—44no—
106C4×C8—24no—
107C4×C8—24no—
108C4×C8—22no—
109C4×C8—82no—
110C4×C8#4114yes—
111#95—24no—
112#95—42no—
113#95—42no—
114C2×Q8—24no—
115C2×Q8—24no—
116C2×Q8—22no—
117C2×Q8—22no—
118C22×C4—22no—
119C22×C4—22no—
120C22×C4—42no—
121C22×C4—42no—
122C22×C4#12112yes—
123C22×C4#12112yes—
124C22×C4C22×D411yescharacteristic
125C22×C4C22×D411yescharacteristic
126C22×C4C2×#4111yescharacteristic
127C2×C8—22no—
128C2×C8—22no—
129C2×C8—22no—
130C2×C8—22no—
131C2×C8—22no—
132C2×C8—42no—
133C2×C8—44no—
134C2×C8—44no—
135C2×C8—44no—
136C2×C8—44no—
137C2×C8#12412yes—
138C2×C8#12412yes—
139C4⋊C4—24no—
140C4⋊C4—44no—
141C4⋊C4—44no—
142C4⋊C4—44no—
143C4⋊C4—42no—
144C4⋊C4—42no—
145C4⋊C4—42no—
146C4⋊C4—42no—
147C4⋊C4—44no—
148C4⋊C4—42no—
149C4⋊C4—42no—
150C4⋊C4—82no—
151C4⋊C4—82no—
152C4⋊C4—84no—
153C4⋊C4—84no—
154C42—22no—
155C42—21no—
156C42—21no—
157C42—42no—
158C42—42no—
159C42—42no—
160C42#13514yes—
161C42#13714yes—
162C42C2×#4112yes—
163C422−1+412yes—
164C23C2×#12111yescharacteristic
165Q8—44no—
166Q8—44no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—44no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—82no—
180C2×C4—82no—
181C2×C4—82no—
182C2×C4—82no—
183C2×C4#46414yes—
184C2×C4#46414yes—
185C2×C4C2×#12411yescharacteristic
186C2×C4#53611yescharacteristic
187C2×C4#54712yes—
188C2×C4#55612yes—
189C2×C4C2×#13512yes—
190C2×C4C2×#13712yes—
191C2×C4#57512yes—
192C2×C4#57611yescharacteristic
193C2×C4#57811yescharacteristic
194C8—22no—
195C8—22no—
196C8—42no—
197C8—84no—
198C8—82no—
199C22#254711yescharacteristic
200C22C2×#46412yes—
201C22#305411yescharacteristic
202C22#306111yescharacteristic
203C22#306712yes—
204C4—24no—
205C4—22no—
206C4—24no—
207C4—82no—
208C4—82no—
209C4—162no—
210C4—162no—
211C4#313111yescharacteristic
212C4#313911yescharacteristic
213C4#323112yes—
214C4#335212yes—
215C4#335512yes—
216C2#1915512yes—
217C2#1921712yes—
218C2#2870911yescharacteristic
219C2#2871911yescharacteristic
220C2#2873411yescharacteristic
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
#332912
#291232
#217122
#106242
#106232
#99002
#86552
C4×#3352