Finite Group Databasebeta

← #98709

Subgroups — #98709

Order 512.

552 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 112 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#59869C211yesmaximal, characteristic
2#9643C211yesmaximal, characteristic
3#8589C212yesmaximal
4#7653C211yesmaximal, characteristic
5#7588C212yesmaximal
6#2809—22no—
7#2571C412yes—
8#2568—22no—
9#2546—22no—
10#2508—24no—
11#2369C412yes—
12#2355—22no—
13C4×C4⋊Q8C2212yes—
14C4×C4⋊Q8C2211yescharacteristic
15#1842C2211yescharacteristic
16#1831C2212yes—
17#1744C2211yescharacteristic
18C2×#332—22no—
19C2×Q8⋊C8—22no—
20#1296—22no—
21#1272—22no—
22#1271—24no—
23C2×C4⋊Q8—22no—
24C2×C4⋊Q8C2×C411yescharacteristic
25C2×C4⋊Q8D412yes—
26C2×C4×Q8—22no—
27C2×C4×Q8D412yes—
28C2×C4⋊C8—22no—
29C2×C4⋊C8—22no—
30C2×C4⋊C8—21no—
31C2×C4×C8—21no—
32#400—24no—
33#400—24no—
34#398—28no—
35#391—24no—
36#391—24no—
37#391—22no—
38#391D412yes—
39#389—24no—
40#389—24no—
41#389—22no—
42#389—22no—
43#389D414yes—
44#387—28no—
45#384C2×C411yescharacteristic
46#384D412yes—
47#382—24no—
48#382—24no—
49C4×C4⋊C4—22no—
50C4×C4⋊C4—24no—
51C4×C4⋊C4—22no—
52C4×C4⋊C4—22no—
53C4×C4⋊C4C2×C414yes—
54C43C2311yescharacteristic
55#336—22no—
56#336—22no—
57#336—22no—
58#332—44no—
59Q8⋊C8—44no—
60C22×Q8—22no—
61C22×Q8C22⋊C412yes—
62C22×C8—41no—
63C22×C8—42no—
64C22×C8—41no—
65C4⋊Q8—24no—
66C4⋊Q8—22no—
67C4⋊Q8—22no—
68C4⋊Q8—22no—
69C4⋊Q8—22no—
70C4⋊Q8—82no—
71C4⋊Q8—82no—
72C4×Q8—42no—
73C4×Q8—42no—
74C4×Q8—42no—
75C4×Q8—42no—
76C4×Q8—42no—
77C4×Q8—42no—
78C2×C4⋊C4—22no—
79C2×C4⋊C4—22no—
80C2×C4⋊C4—22no—
81C2×C4⋊C4—24no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—24no—
84C2×C4⋊C4—24no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4C22⋊C414yes—
88C2×C4⋊C4C22⋊C412yes—
89C2×C4⋊C4C22⋊C414yes—
90C2×C42—24no—
91C2×C42—22no—
92C2×C42—24no—
93C2×C42C22×C411yescharacteristic
94C2×C42C2×D411yescharacteristic
95C2×C42C2×D412yes—
96C2×C42C2×D411yescharacteristic
97C2×C42C2×D412yes—
98C4⋊C8—42no—
99C4⋊C8—42no—
100C4⋊C8—42no—
101C4⋊C8—42no—
102C4⋊C8—42no—
103C4×C8—22no—
104C4×C8—41no—
105#95—24no—
106#95—28no—
107#95—28no—
108#95—24no—
109#95—24no—
110#95—24no—
111C2×Q8—22no—
112C2×Q8—42no—
113C2×Q8—42no—
114C2×Q8—42no—
115C2×Q8—42no—
116C2×Q8—42no—
117C2×Q8—42no—
118C2×Q8—42no—
119C2×Q8—42no—
120C2×Q8#10114yes—
121C22×C4—22no—
122C22×C4—24no—
123C22×C4—22no—
124C22×C4—24no—
125C22×C4C2×C22⋊C411yescharacteristic
126C22×C4C2×C22⋊C412yes—
127C22×C4#12011yescharacteristic
128C22×C4#12012yes—
129C22×C4#12011yescharacteristic
130C2×C8—42no—
131C2×C8—82no—
132C2×C8—82no—
133C2×C8—82no—
134C2×C8—82no—
135C2×C8—82no—
136C2×C8—81no—
137C4⋊C4—28no—
138C4⋊C4—24no—
139C4⋊C4—24no—
140C4⋊C4—44no—
141C4⋊C4—42no—
142C4⋊C4—44no—
143C4⋊C4—42no—
144C4⋊C4—44no—
145C4⋊C4—42no—
146C4⋊C4—42no—
147C4⋊C4—44no—
148C4⋊C4—42no—
149C4⋊C4—82no—
150C4⋊C4—82no—
151C4⋊C4—84no—
152C4⋊C4—84no—
153C42—22no—
154C42—21no—
155C42—21no—
156C42—41no—
157C42—42no—
158C42—44no—
159C42—44no—
160C42—42no—
161C42—42no—
162C42—84no—
163C42#13512yes—
164C42#13512yes—
165C42AGL(1,ℤ/8)12yes—
166C42#13712yes—
167C23#37911yescharacteristic
168Q8—44no—
169Q8—82no—
170Q8—82no—
171Q8—82no—
172Q8—82no—
173Q8—82no—
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—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—44no—
187C2×C4—44no—
188C2×C4—44no—
189C2×C4—44no—
190C2×C4—44no—
191C2×C4—44no—
192C2×C4—44no—
193C2×C4C2×#10112yes—
194C2×C4#41612yes—
195C2×C4#41712yes—
196C2×C4#44912yes—
197C2×C4#44912yes—
198C2×C4#45212yes—
199C2×C4#45212yes—
200C2×C4#45311yescharacteristic
201C2×C4#45511yescharacteristic
202C8—82no—
203C8—162no—
204C8—161no—
205C22#178411yescharacteristic
206C22#178812yes—
207C22#179211yescharacteristic
208C22#179411yescharacteristic
209C22#179612yes—
210C4—22no—
211C4—22no—
212C4—22no—
213C4—22no—
214C4—22no—
215C4—44no—
216C4—41no—
217C4—84no—
218C4—82no—
219C4—84no—
220C4#162411yescharacteristic
221C4#163411yescharacteristic
222C4#164612yes—
223C2#839012yes—
224C2#843112yes—
225C2#845211yescharacteristic
226C2#845711yescharacteristic
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
#598692
#96432
#85892
#76532
#75882