Finite Group Databasebeta

← #98421

Subgroups — #98421

Order 512.

495 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 495 conjugacy classes of subgroups — too many to draw. Only its 100 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#39635C211yesmaximal, characteristic
2#8594C211yesmaximal, characteristic
3#7720C212yesmaximal
4#7644C212yesmaximal
5#7605C211yesmaximal, characteristic
6#2859C2211yescharacteristic
7#2802—24no—
8#2647—21no—
9#2582C412yes—
10#2511—22no—
11#2507—22no—
12#2453—22no—
13Q8×C4⋊C4C412yes—
14#2327—21no—
15C4×C4⋊Q8C2211yescharacteristic
16#2295C2211yescharacteristic
17#1839C2212yes—
18#1831C2212yes—
19C2×#333—21no—
20#1296—21no—
21#1272—22no—
22#1272—22no—
23#1271—24no—
24#1271—22no—
25C2×C4⋊Q8D411yescharacteristic
26C2×#125—21no—
27C2×C4×Q8—22no—
28C2×C4×Q8C2×C412yes—
29C2×C4×Q8C2×C411yescharacteristic
30C2×C4⋊C8—22no—
31#400—24no—
32#400—24no—
33#398—24no—
34#398—24no—
35#398—24no—
36#391—22no—
37#391—22no—
38#391D412yes—
39#391D412yes—
40#389—24no—
41#389—22no—
42#389—22no—
43#389—22no—
44#389—24no—
45#389—22no—
46#389—22no—
47#389D414yes—
48#389D412yes—
49#387—24no—
50#387—24no—
51#387—24no—
52#387—22no—
53#384—22no—
54#384C2×C412yes—
55#384D411yescharacteristic
56#382—21no—
57C4×C4⋊C4—22no—
58C4×C4⋊C4—22no—
59C4×C4⋊C4—21no—
60C4×C4⋊C4C2×C411yescharacteristic
61#376—21no—
62C43C2311yescharacteristic
63#336—22no—
64#336—22no—
65#336—22no—
66#336—22no—
67#336—22no—
68#333—42no—
69C22×Q8C22⋊C411yescharacteristic
70C22×Q8C22⋊C412yes—
71C22×C8—42no—
72C22×C8—42no—
73C4⋊Q8—22no—
74C4⋊Q8SD1612yes—
75C4⋊Q8Q1612yes—
76#125—82no—
77C4×Q8—42no—
78C4×Q8—44no—
79C4×Q8—84no—
80C2×C4⋊C4—22no—
81C2×C4⋊C4—22no—
82C2×C4⋊C4—21no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—24no—
86C2×C4⋊C4—24no—
87C2×C4⋊C4—24no—
88C2×C4⋊C4—24no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4C22⋊C411yescharacteristic
92C2×C4⋊C4C22⋊C412yes—
93C2×C4⋊C4C22⋊C412yes—
94C2×C4⋊C4C22⋊C414yes—
95C2×C42—21no—
96C2×C42—21no—
97C2×C42—22no—
98C2×C42—24no—
99C2×C42C22×C411yescharacteristic
100C2×C42C2×D411yescharacteristic
101C2×C42C2×D412yes—
102C2×C42C2×D412yes—
103C2×C42C2×D411yescharacteristic
104C4⋊C8—42no—
105C4⋊C8—42no—
106#95—24no—
107#95—24no—
108#95—24no—
109#95—24no—
110#95—21no—
111#95—22no—
112#95—22no—
113#95—22no—
114#95—22no—
115#95—22no—
116#95—24no—
117C2×Q8—22no—
118C2×Q8—22no—
119C2×Q8—42no—
120C2×Q8—42no—
121C2×Q8—42no—
122C2×Q8#10314yes—
123C22×C4—22no—
124C22×C4—21no—
125C22×C4—22no—
126C22×C4—24no—
127C22×C4—21no—
128C22×C4—22no—
129C22×C4C2×C22⋊C411yescharacteristic
130C22×C4C2×C22⋊C411yescharacteristic
131C22×C4C2×C22⋊C411yescharacteristic
132C22×C4#12012yes—
133C22×C4#12012yes—
134C2×C8—82no—
135C2×C8—82no—
136C2×C8—82no—
137C2×C8—82no—
138C2×C8—82no—
139C2×C8—82no—
140C4⋊C4—24no—
141C4⋊C4—24no—
142C4⋊C4—22no—
143C4⋊C4—42no—
144C4⋊C4—44no—
145C4⋊C4—42no—
146C4⋊C4—44no—
147C4⋊C4—44no—
148C4⋊C4—42no—
149C4⋊C4—44no—
150C4⋊C4—82no—
151C4⋊C4—82no—
152C4⋊C4—84no—
153C4⋊C4—84no—
154C4⋊C4—84no—
155C4⋊C4—84no—
156C42—22no—
157C42—42no—
158C42—42no—
159C42—41no—
160C42—42no—
161C42—42no—
162C42—44no—
163C42—84no—
164C42C2×SD1611yescharacteristic
165C42C2×Q1611yescharacteristic
166C42#13712yes—
167C23#37911yescharacteristic
168Q8—44no—
169Q8—44no—
170Q8—82no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—24no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—44no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—44no—
191C2×C4—44no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4—41no—
197C2×C4#41312yes—
198C2×C4C2×#10311yescharacteristic
199C2×C4#41911yescharacteristic
200C2×C4#44812yes—
201C2×C4#45112yes—
202C8—162no—
203C8—162no—
204C22#178511yescharacteristic
205C22#178711yescharacteristic
206C22#179412yes—
207C22#179511yescharacteristic
208C22#179612yes—
209C4—22no—
210C4—21no—
211C4—21no—
212C4—22no—
213C4—22no—
214C4—41no—
215C4—42no—
216C4—44no—
217C4—81no—
218C4—82no—
219C4—84no—
220C4—82no—
221C4—81no—
222C2#839511yescharacteristic
223C2#843312yes—
224C2#847611yescharacteristic
225C2#850312yes—
226C2#852711yescharacteristic
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
#396352
#85942
#77202
#76442
#76052