Finite Group Databasebeta

← #98705

Subgroups — #98705

Order 512.

680 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 128 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#59832C211yesmaximal, characteristic
2#9643C211yesmaximal, characteristic
3#8590C212yesmaximal
4#7653C211yesmaximal, characteristic
5#7590C212yesmaximal
6C2×Q82C412yes—
7#2734—22no—
8#2582C412yes—
9#2551—22no—
10#2546—22no—
11#2451—24no—
12#2365—22no—
13C4×C4⋊Q8C2212yes—
14C4×C4⋊Q8C2211yescharacteristic
15#1842C2211yescharacteristic
16#1831C2212yes—
17#1744C2211yescharacteristic
18C2×#333—22no—
19C2×Q8⋊C8—22no—
20#1296—22no—
21#1272—24no—
22#1272—22no—
23Q82—48no—
24C2×C4⋊Q8—24no—
25C2×C4⋊Q8—22no—
26C2×C4⋊Q8—24no—
27C2×C4⋊Q8C2×C411yescharacteristic
28C2×C4⋊Q8D412yes—
29C2×C4×Q8—24no—
30C2×C4×Q8C2×C414yes—
31C2×C4×Q8D412yes—
32C2×C4⋊C8—22no—
33C2×C4⋊C8—22no—
34C2×C4⋊C8—21no—
35C2×C4×C8—21no—
36#398—24no—
37#398—24no—
38#395—28no—
39#391—24no—
40#391—24no—
41#391D414yes—
42#391D412yes—
43#389—24no—
44#389—24no—
45#389—22no—
46#389—22no—
47#389—22no—
48#387—28no—
49#384C2×C411yescharacteristic
50#384D412yes—
51C4×C4⋊C4—22no—
52C4×C4⋊C4—22no—
53C4×C4⋊C4—22no—
54C4×C4⋊C4—22no—
55C43C2311yescharacteristic
56#336—22no—
57#336—22no—
58#336—22no—
59#333—44no—
60Q8⋊C8—44no—
61C22×Q8—24no—
62C22×Q8C22⋊C412yes—
63C22×Q8C22⋊C414yes—
64C22×C8—41no—
65C22×C8—42no—
66C22×C8—41no—
67C4⋊Q8—24no—
68C4⋊Q8—22no—
69C4⋊Q8—22no—
70C4⋊Q8—416no—
71C4⋊Q8—48no—
72C4⋊Q8—48no—
73C4⋊Q8—82no—
74C4⋊Q8—82no—
75C4⋊Q8SD1614yes—
76C4⋊Q8Q1614yes—
77C4×Q8—48no—
78C4×Q8—42no—
79C4×Q8—42no—
80C4×Q8—416no—
81C2×C4⋊C4—22no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—28no—
85C2×C4⋊C4—24no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—22no—
88C2×C4⋊C4—24no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4C22⋊C414yes—
92C2×C4⋊C4C22⋊C412yes—
93C2×C42—24no—
94C2×C42—24no—
95C2×C42—22no—
96C2×C42C22×C411yescharacteristic
97C2×C42C2×D411yescharacteristic
98C2×C42C2×D412yes—
99C2×C42C2×D411yescharacteristic
100C2×C42C2×D412yes—
101C4⋊C8—42no—
102C4⋊C8—42no—
103C4⋊C8—42no—
104C4⋊C8—42no—
105C4⋊C8—42no—
106C4×C8—22no—
107C4×C8—41no—
108#95—24no—
109#95—28no—
110#95—24no—
111#95—24no—
112#95—24no—
113C2×Q8—22no—
114C2×Q8—24no—
115C2×Q8—48no—
116C2×Q8—44no—
117C2×Q8—44no—
118C2×Q8—42no—
119C2×Q8—42no—
120C2×Q8—84no—
121C2×Q8—84no—
122C2×Q8#10014yes—
123C2×Q8#10318yes—
124C22×C4—24no—
125C22×C4—22no—
126C22×C4—22no—
127C22×C4—24no—
128C22×C4C2×C22⋊C411yescharacteristic
129C22×C4C2×C22⋊C412yes—
130C22×C4#12011yescharacteristic
131C22×C4#12012yes—
132C22×C4#12011yescharacteristic
133C2×C8—42no—
134C2×C8—82no—
135C2×C8—82no—
136C2×C8—82no—
137C2×C8—82no—
138C2×C8—82no—
139C2×C8—81no—
140C4⋊C4—28no—
141C4⋊C4—24no—
142C4⋊C4—24no—
143C4⋊C4—24no—
144C4⋊C4—24no—
145C4⋊C4—42no—
146C4⋊C4—44no—
147C4⋊C4—44no—
148C4⋊C4—416no—
149C4⋊C4—48no—
150C4⋊C4—42no—
151C4⋊C4—42no—
152C4⋊C4—82no—
153C4⋊C4—82no—
154C4⋊C4—84no—
155C42—22no—
156C42—21no—
157C42—21no—
158C42—41no—
159C42—42no—
160C42—48no—
161C42—48no—
162C42—42no—
163C42—42no—
164C42C2×SD1612yes—
165C42C2×Q1612yes—
166C42#13712yes—
167C42#13712yes—
168C23#37911yescharacteristic
169Q8—44no—
170Q8—48no—
171Q8—48no—
172Q8—82no—
173Q8—168no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—28no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—44no—
187C2×C4—44no—
188C2×C4—42no—
189C2×C4—44no—
190C2×C4—44no—
191C2×C4—44no—
192C2×C4—44no—
193C2×C4C2×#10012yes—
194C2×C4C2×#10312yes—
195C2×C4#41912yes—
196C2×C4#44812yes—
197C2×C4#44812yes—
198C2×C4#45112yes—
199C2×C4#45112yes—
200C2×C4#45311yescharacteristic
201C2×C4#45511yescharacteristic
202C8—82no—
203C8—162no—
204C8—161no—
205C22#178311yescharacteristic
206C22#178712yes—
207C22#179211yescharacteristic
208C22#179411yescharacteristic
209C22#179612yes—
210C4—22no—
211C4—22no—
212C4—22no—
213C4—22no—
214C4—22no—
215C4—44no—
216C4—41no—
217C4—48no—
218C4—84no—
219C4—82no—
220C4#162311yescharacteristic
221C4#163311yescharacteristic
222C4#164512yes—
223C2#839112yes—
224C2#843312yes—
225C2#845111yescharacteristic
226C2#845611yescharacteristic
227C2#849211yescharacteristic
subgroupG/H
center, socle, prime radicalC23#379
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ 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
#598322
#96432
#85902
#76532
#75902