Finite Group Databasebeta

← #119485

Subgroups — #119485

Order 512.

1262 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1262 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C2×#1819C212yesmaximal
2#14341C211yesmaximal, characteristic
3C2×#1304C214yesmaximal
4C23×C22⋊C4C2211yescharacteristic
5C2×#379C2214yes—
6C2×#379C2212yes—
7#1819—28no—
8C2×#342—24no—
9#1440—24no—
10C22⋊#95C412yescomplemented
11C22⋊#95C412yescomplemented
12#1304—28no—
13C26C2311yescharacteristic
14C24×C4C2×C411yescharacteristic
15C24×C4C2×C411yescharacteristic
16C22×C22⋊C4—24no—
17C22×C22⋊C4—24no—
18C22×C22⋊C4—24no—
19C22×C22⋊C4—24no—
20C22×C22⋊C4—24no—
21C22×C22⋊C4—24no—
22C22×C22⋊C4—22no—
23C22×C22⋊C4—22no—
24C22×C22⋊C4C2×C414yes—
25C22×C22⋊C4D414yes—
26#379—24no—
27#379—24no—
28#379—24no—
29#379—24no—
30#379—24no—
31#379D418yes—
32C2×#95—24no—
33C2×#95—24no—
34#342—216no—
35C25—44no—
36C25—82no—
37C25—82no—
38C25C22×C411yescharacteristic
39C25C2×D412yes—
40C25C2×D414yes—
41C25#4114yes—
42C25#4114yes—
43C23×C4—22no—
44C23×C4—22no—
45C23×C4—24no—
46C23×C4—24no—
47C23×C4—24no—
48C23×C4—44no—
49C23×C4—82no—
50C23×C4—82no—
51C23×C4C22⋊C412yes—
52C23×C4C22⋊C412yes—
53C2×C22⋊C4—24no—
54C2×C22⋊C4—28no—
55C2×C22⋊C4—28no—
56C2×C22⋊C4—24no—
57C2×C22⋊C4—28no—
58C2×C22⋊C4—28no—
59C2×C22⋊C4—28no—
60C2×C22⋊C4—28no—
61C2×C22⋊C4—44no—
62C2×C22⋊C4—44no—
63C2×C22⋊C4—44no—
64C2×C22⋊C4—44no—
65C2×C22⋊C4—416no—
66C2×C22⋊C4—42no—
67C2×C22⋊C4—44no—
68C2×C22⋊C4—44no—
69C2×C22⋊C4—44no—
70C2×C22⋊C4—42no—
71C2×C22⋊C4—44no—
72C2×C22⋊C4—48no—
73C2×C22⋊C4—84no—
74C2×C22⋊C4—84no—
75C2×C22⋊C4—88no—
76C2×C22⋊C4—88no—
77#95—84no—
78#95—84no—
79C24—24no—
80C24—28no—
81C24—42no—
82C24—42no—
83C24—44no—
84C24—44no—
85C24—48no—
86C24—48no—
87C24—48no—
88C24—48no—
89C24—48no—
90C24—84no—
91C24—84no—
92C24—84no—
93C24—84no—
94C24—832no—
95C24C2×C22⋊C411yescharacteristic
96C24#11712yes—
97C24C4×D414yes—
98C24#12012yes—
99C24#12114yes—
100C24#12114yes—
101C24#12314yes—
102C24#12312yes—
103C24#12314yes—
104C24#12414yes—
105C24#12614yes—
106C22×C4—22no—
107C22×C4—22no—
108C22×C4—24no—
109C22×C4—24no—
110C22×C4—44no—
111C22×C4—44no—
112C22×C4—44no—
113C22×C4—44no—
114C22×C4—48no—
115C22×C4—48no—
116C22×C4—44no—
117C22×C4—48no—
118C22×C4—48no—
119C22×C4—84no—
120C22×C4—84no—
121C22×C4—88no—
122C22×C4—88no—
123C22×C4—88no—
124C22×C4—88no—
125C22×C4—88no—
126C22⋊C4—48no—
127C22⋊C4—48no—
128C22⋊C4—416no—
129C22⋊C4—88no—
130C22⋊C4—84no—
131C22⋊C4—88no—
132C22⋊C4—84no—
133C22⋊C4—88no—
134C22⋊C4—88no—
135C22⋊C4—88no—
136C22⋊C4—88no—
137C22⋊C4—88no—
138C23—22no—
139C23—22no—
140C23—28no—
141C23—24no—
142C23—24no—
143C23—24no—
144C23—28no—
145C23—28no—
146C23—28no—
147C23—24no—
148C23—28no—
149C23—24no—
150C23—44no—
151C23—44no—
152C23—42no—
153C23—44no—
154C23—44no—
155C23—44no—
156C23—42no—
157C23—44no—
158C23—44no—
159C23—44no—
160C23—44no—
161C23—44no—
162C23—44no—
163C23—42no—
164C23—44no—
165C23—42no—
166C23—44no—
167C23—44no—
168C23—44no—
169C23—44no—
170C23—416no—
171C23—816no—
172C23—832no—
173C23—832no—
174C23—832no—
175C23#38111yescharacteristic
176C23#38612yes—
177C23#38814yes—
178C23#39414yes—
179C23#39714yes—
180C23#41014yes—
181C2×C4—44no—
182C2×C4—44no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—88no—
186C2×C4—88no—
187C2×C4—84no—
188C2×C4—84no—
189C2×C4—88no—
190C2×C4—84no—
191C2×C4—84no—
192C2×C4—88no—
193C2×C4—88no—
194C2×C4—816no—
195C2×C4—84no—
196C2×C4—1616no—
197C22—28no—
198C22—22no—
199C22—22no—
200C22—24no—
201C22—24no—
202C22—24no—
203C22—24no—
204C22—24no—
205C22—24no—
206C22—24no—
207C22—24no—
208C22—24no—
209C22—416no—
210C22—416no—
211C22—48no—
212C22—84no—
213C22—88no—
214C22—84no—
215C22—88no—
216C22—88no—
217C22—88no—
218C22—88no—
219C22#144011yescharacteristic
220C22#182012yes—
221C22#182812yes—
222C22#182812yes—
223C22#189914yes—
224C4—82no—
225C4—82no—
226C4—164no—
227C4—168no—
228C2—24no—
229C2—44no—
230C2—44no—
231C2—44no—
232C2#875014yes—
233C2#1116611yescharacteristic
234C2#1116911yescharacteristic
235C2#1119711yescharacteristic
subgroupG/H
center, socleC23#381
commutatorC25C22×C4
Frattini, prime radical, cosocleC26C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C26 ◁ G
LECSG ▷ C26 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
10. C22⋊#95C4semidirect
11. C22⋊#95C4semidirect

Maximal subgroups

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

subgroupindex
C2×#18192
#143412
C2×#13042