Finite Group Databasebeta

← #137899

Subgroups — #137899

Order 512.

315 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 315 conjugacy classes of subgroups — too many to draw. Only its 90 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#33497C211yesmaximal, characteristic
2#22240C211yesmaximal, characteristic
3#11644C212yesmaximal
4#11494C211yesmaximal, characteristic
5#7143C212yesmaximal
6C2×#446C2211yescharacteristic
7C2×C8×Q8C2211yescharacteristic
8C4×C4⋊Q8C411yescharacteristic
9#2183—24no—
10#2163—21no—
11#2163C2212yes—
12#2163C2212yes—
13#2162—21no—
14#1984C411yescharacteristic
15#1984C411yescharacteristic
16#1917—21no—
17#1917—21no—
18#1916—21no—
19#1916—21no—
20#1831C411yescharacteristic
21#1744C2211yescharacteristic
22#1338—24no—
23#1322—21no—
24#1322—21no—
25C2×C4⋊Q8C811yescharacteristic
26C2×C4×Q8C2×C411yescharacteristic
27C2×C4×Q8C2×C411yescharacteristic
28#446—22no—
29#446—22no—
30C8×Q8—22no—
31C8×Q8—22no—
32C2×C4⋊C8—21no—
33C2×C4⋊C8C2×C411yescharacteristic
34C2×C4⋊C8C2×C411yescharacteristic
35C2×C4⋊C8D411yescharacteristic
36C2×C4⋊C8D411yescharacteristic
37C2×#97—21no—
38C2×C4×C8C2×C411yescharacteristic
39C2×C4×C8D411yescharacteristic
40C2×C4×C8D411yescharacteristic
41C2×C4×C8C2311yescharacteristic
42#391C811yescharacteristic
43#391C811yescharacteristic
44#389—21no—
45#389—21no—
46#384C811yescharacteristic
47C4×C4⋊C4—21no—
48C4×C4⋊C4—21no—
49C43C2×C411yescharacteristic
50C4⋊C16—22no—
51C4⋊C16—22no—
52C4⋊C16—22no—
53C4⋊C16—22no—
54C22⋊C16—22no—
55C22⋊C16—22no—
56#346—22no—
57#346—22no—
58#346D414yes—
59C4×C16—22no—
60#336—21no—
61#336—21no—
62#336—21no—
63#336—21no—
64#336—21no—
65#336—21no—
66#336—21no—
67#336—21no—
68C22×Q8C2×C811yescharacteristic
69C22×Q8C2×C811yescharacteristic
70C22×C8—21no—
71C22×C8—21no—
72C22×C8C22⋊C411yescharacteristic
73C22×C8C22⋊C411yescharacteristic
74C22×C8C2×D411yescharacteristic
75C22×C8C2×D411yescharacteristic
76C4⋊Q8—42no—
77C4×Q8—22no—
78C4×Q8—22no—
79C4×Q8—22no—
80C4×Q8—22no—
81C2×C4⋊C4—21no—
82C2×C4⋊C4—21no—
83C2×C4⋊C4—21no—
84C2×C4⋊C4—21no—
85C2×C4⋊C4—21no—
86C2×C4⋊C4C2×C811yescharacteristic
87C2×C4⋊C4C2×C811yescharacteristic
88C2×C4⋊C4M1611yescharacteristic
89C2×C4⋊C4M1611yescharacteristic
90C2×C42—21no—
91C2×C42—21no—
92C2×C42—21no—
93C2×C42C22⋊C411yescharacteristic
94C2×C42C22⋊C411yescharacteristic
95C2×C42C2×C811yescharacteristic
96C2×C42C2×C811yescharacteristic
97C2×C42C22×C411yescharacteristic
98C2×C16—24no—
99C2×C16—42no—
100C4⋊C8—22no—
101C4⋊C8—22no—
102C4⋊C8—22no—
103C4⋊C8—22no—
104C4⋊C8—41no—
105C4⋊C8—41no—
106#97—42no—
107C4×C8—21no—
108C4×C8—21no—
109C4×C8—21no—
110C4×C8—21no—
111C4×C8—22no—
112C4×C8C2×D412yes—
113C4×C8#4112yes—
114#95—21no—
115#95—21no—
116#95—21no—
117#95—21no—
118C2×Q8—22no—
119C2×Q8—22no—
120C2×Q8—22no—
121C2×Q8—41no—
122C2×Q8—41no—
123C2×Q8—41no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4C22⋊C811yescharacteristic
129C22×C4C22⋊C811yescharacteristic
130C22×C4C22⋊C811yescharacteristic
131C22×C4C22⋊C811yescharacteristic
132C22×C4C2×C22⋊C411yescharacteristic
133C22×C4C22×C811yescharacteristic
134C22×C4C2×M1611yescharacteristic
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—41no—
138C2×C8—41no—
139C2×C8—41no—
140C2×C8—41no—
141C2×C8—41no—
142C2×C8—41no—
143C2×C8—42no—
144C2×C8—41no—
145C2×C8—41no—
146C2×C8#12011yescharacteristic
147C2×C8#12112yes—
148C2×C8#12311yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—42no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C42—21no—
159C42—21no—
160C42—21no—
161C42—21no—
162C42—41no—
163C42—41no—
164C42—41no—
165C42—41no—
166C42—42no—
167C42—41no—
168C42—41no—
169C42C4×D412yes—
170C42#13112yes—
171C16—44no—
172C16—82no—
173C23C2×C22⋊C811yescharacteristic
174Q8—44no—
175Q8—82no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4#34912yes—
203C2×C4#38611yescharacteristic
204C2×C4#40811yescharacteristic
205C2×C4C8×D412yes—
206C2×C4#43512yes—
207C8—22no—
208C8—21no—
209C8—21no—
210C8—41no—
211C8—41no—
212C8—81no—
213C8—81no—
214C22—21no—
215C22—21no—
216C22#186911yescharacteristic
217C22C2×#34911yescharacteristic
218C22#211511yescharacteristic
219C4—21no—
220C4—22no—
221C4—22no—
222C4—22no—
223C4—42no—
224C4—41no—
225C4—41no—
226C4—41no—
227C4—81no—
228C4—81no—
229C4—81no—
230C4#190911yescharacteristic
231C4#191211yescharacteristic
232C2—21no—
233C2—21no—
234C2#910011yescharacteristic
235C2#1298211yescharacteristic
236C2#1298511yescharacteristic
subgroupG/H
centerC2×C4#386
commutatorC22×C4C22×C8
Frattini, cosocleC2×C4×C8C23
socleC22#1869
prime radicalC23C2×C22⋊C8
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ G
LECSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#334972
#222402
#116442
#114942
#71432