Finite Group Databasebeta

← #124645

Subgroups — #124645

Order 512.

294 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 94 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#21712C211yesmaximal, characteristic
2#12894C211yesmaximal, characteristic
3#12894C211yesmaximal, characteristic
4#7128C214yesmaximal
5C2×#446C412yes—
6C4×C4⋊Q8C411yescharacteristic
7#1984C2212yes—
8#1939—21no—
9#1939—21no—
10#1842C411yescharacteristic
11#1770—21no—
12#1770—21no—
13C42×C8C2211yescharacteristic
14#1374—21no—
15#1374—21no—
16#1374—21no—
17#1374—21no—
18#1374C2212yes—
19#1374C2212yes—
20C2×C4⋊Q8C811yescharacteristic
21C2×C4×Q8C2×C412yes—
22C22×C16—22no—
23C22×C16—22no—
24#446—44no—
25C2×C4⋊C8—22no—
26C2×C4⋊C8—21no—
27C2×C4⋊C8—21no—
28C2×C4⋊C8C2×C412yes—
29C2×#97—22no—
30C2×C4×C8C2×C411yescharacteristic
31C2×C4×C8D411yescharacteristic
32C2×C4×C8D411yescharacteristic
33C2×C4×C8D411yescharacteristic
34C2×C4×C8D411yescharacteristic
35C2×C4×C8C2311yescharacteristic
36#391C812yes—
37#389—21no—
38#389—21no—
39#384C811yescharacteristic
40C4×C4⋊C4—21no—
41C4×C4⋊C4—21no—
42C43C2×C411yescharacteristic
43#336—22no—
44#336—22no—
45C22×Q8C2×C812yes—
46C22×C8—22no—
47C22×C8C22⋊C411yescharacteristic
48C22×C8C22⋊C411yescharacteristic
49C22×C8C2×D411yescharacteristic
50C22×C8C2×D411yescharacteristic
51C4⋊Q8—42no—
52C4×Q8—42no—
53C4×Q8—42no—
54C2×C4⋊C4—21no—
55C2×C4⋊C4—21no—
56C2×C4⋊C4—21no—
57C2×C4⋊C4—21no—
58C2×C4⋊C4—22no—
59C2×C4⋊C4C2×C812yes—
60C2×C42—22no—
61C2×C42C22⋊C411yescharacteristic
62C2×C42C22⋊C411yescharacteristic
63C2×C42C2×C811yescharacteristic
64C2×C42C2×C811yescharacteristic
65C2×C42M1611yescharacteristic
66C2×C42M1611yescharacteristic
67C2×C42C22×C411yescharacteristic
68C2×C16—42no—
69C2×C16—42no—
70C2×C16—42no—
71C2×C16—42no—
72C2×C16—42no—
73C2×C16—42no—
74C4⋊C8—42no—
75C4⋊C8—42no—
76C4⋊C8—42no—
77C4⋊C8—44no—
78#97—44no—
79C4×C8—22no—
80C4×C8—22no—
81C4×C8—22no—
82C4×C8—41no—
83C4×C8—41no—
84C4×C8—41no—
85#95—22no—
86#95—22no—
87C2×Q8—24no—
88C2×Q8—42no—
89C2×Q8—42no—
90C22×C4—22no—
91C22×C4—22no—
92C22×C4C22⋊C811yescharacteristic
93C22×C4C22⋊C811yescharacteristic
94C22×C4C22⋊C811yescharacteristic
95C22×C4C22⋊C811yescharacteristic
96C22×C4C2×C22⋊C411yescharacteristic
97C22×C4C22×C811yescharacteristic
98C22×C4C2×M1611yescharacteristic
99C2×C8—21no—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8—21no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—21no—
106C2×C8—21no—
107C2×C8—21no—
108C2×C8—42no—
109C2×C8—42no—
110C2×C8—42no—
111C2×C8#10012yes—
112C2×C8#13712yes—
113C2×C8#13712yes—
114C4⋊C4—42no—
115C4⋊C4—42no—
116C4⋊C4—44no—
117C4⋊C4—42no—
118C4⋊C4—42no—
119C4⋊C4—42no—
120C42—22no—
121C42—22no—
122C42—21no—
123C42—21no—
124C42—21no—
125C42—21no—
126C42—21no—
127C42—21no—
128C42—22no—
129C42—41no—
130C42—42no—
131C42—42no—
132C16—82no—
133C16—82no—
134C23C2×C22⋊C811yescharacteristic
135Q8—84no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4#34912yes—
158C2×C4#35012yes—
159C2×C4#41011yescharacteristic
160C2×C4C2×#10011yescharacteristic
161C2×C4#41911yescharacteristic
162C2×C4#41911yescharacteristic
163C2×C4#42111yescharacteristic
164C2×C4#42111yescharacteristic
165C2×C4#50412yes—
166C8—22no—
167C8—22no—
168C8—22no—
169C8—41no—
170C8—82no—
171C22#146011yescharacteristic
172C22#147911yescharacteristic
173C22#147911yescharacteristic
174C22#211311yescharacteristic
175C22C2×#34911yescharacteristic
176C22C2×#35011yescharacteristic
177C22#211711yescharacteristic
178C4—22no—
179C4—22no—
180C4—22no—
181C4—41no—
182C4—41no—
183C4—41no—
184C4—82no—
185C4—82no—
186C4#151511yescharacteristic
187C4#151511yescharacteristic
188C4#153611yescharacteristic
189C4#155811yescharacteristic
190C2#760511yescharacteristic
191C2#1148911yescharacteristic
192C2#1149211yescharacteristic
193C2#1163811yescharacteristic
194C2#1164011yescharacteristic
195C2#1164211yescharacteristic
196C2#1164411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊C4
commutatorC22×C4C22×C8
Frattini, cosocleC2×C4×C8C23
socle, prime radicalC23C2×C22⋊C8
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×C8 ◁ G
LECSG ▷ C2×C4×C8 ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#217122
#128942
#71282