Finite Group Databasebeta

← #6252679

Subgroups — #6252679

Order 512.

1251 conjugacy classes of subgroups; only the 440 normal subgroups are shown.

normal subgroups only

This group has 1251 conjugacy classes of subgroups — too many to draw. Only its 440 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#17301C211yesmaximal, characteristic, complemented
2#17282C215yesmaximal
3#16967C215yesmaximal, complemented
4#16916C215yesmaximal, complemented
5#16753C215yesmaximal
6#16200C215yesmaximal
7#16141C215yesmaximal, complemented
8#1445C2215yes—
9#1445C2215yes—
10#1445C2215yes—
11#1443C2215yes—
12#1443C2215yes—
13#1443C2215yes—
14#1443C2215yes—
15#1443C2215yes—
16#1443C2215yes—
17#1442C2215yes—
18#1442C2215yes—
19#1442C2215yes—
20#1442C2215yes—
21#1442C2215yes—
22#1442C2215yes—
23#1441C2215yes—
24#1441C2215yes—
25#1441C2215yes—
26#1440C2215yes—
27#1440C2215yes—
28#1440C2215yes—
29#1439C2215yes—
30#1439C2215yes—
31#1439C2215yes—
32#1437C2215yes—
33#1436C2215yes—
34#1436C2215yes—
35#1436C2215yes—
36#1434C2215yes—
37#1434C2215yes—
38#1434C2215yes—
39C22×C4⋊C4C2315yes—
40C22×C4⋊C4C2315yes—
41C22×C4⋊C4C2315yes—
42C22×C22⋊C4C2315yes—
43C22×C22⋊C4C2315yes—
44C22×C22⋊C4C2315yes—
45C22×C42C2315yes—
46C2×#95C2315yes—
47C2×#95C2315yes—
48C2×#95C2315yes—
49C2×#95C2315yes—
50C2×#95C2315yes—
51C2×#95C2315yes—
52C2×#95C2315yes—
53C2×#95C2315yes—
54C2×#95C2315yes—
55C2×#95C2315yes—
56C2×#95C2315yes—
57C2×#95C2315yes—
58C2×#95C2315yes—
59C2×#95C2315yes—
60C2×#95C2315yes—
61C2×#95C2315yes—
62C2×#95C2315yes—
63C2×#95C2315yes—
64C2×#95C2315yes—
65C2×#95C2315yes—
66C2×#95C2315yes—
67C2×#95C2315yes—
68C2×#95C2315yes—
69C2×#95C2315yes—
70C25C2411yescharacteristic
71C23×C4C2415yes—
72C23×C4C2415yes—
73C23×C4C2415yes—
74C23×C4C2415yes—
75C23×C4C2415yes—
76C23×C4C2415yes—
77C2×C4⋊C4—45no—
78C2×C4⋊C4—45no—
79C2×C4⋊C4—45no—
80C2×C4⋊C4—45no—
81C2×C4⋊C4—45no—
82C2×C4⋊C4—45no—
83C2×C4⋊C4—45no—
84C2×C4⋊C4—45no—
85C2×C4⋊C4—45no—
86C2×C22⋊C4—45no—
87C2×C22⋊C4—45no—
88C2×C22⋊C4—45no—
89C2×C22⋊C4—45no—
90C2×C22⋊C4—45no—
91C2×C22⋊C4—45no—
92C2×C22⋊C4—45no—
93C2×C22⋊C4—45no—
94C2×C22⋊C4—45no—
95C2×C42—45no—
96C2×C42—45no—
97C2×C42—45no—
98#95—45no—
99#95—45no—
100#95—45no—
101#95—45no—
102#95—45no—
103#95—45no—
104#95—45no—
105#95—45no—
106#95—45no—
107#95—45no—
108#95—45no—
109#95—45no—
110#95—45no—
111#95—45no—
112#95—45no—
113#95—45no—
114#95—45no—
115#95—45no—
116#95—45no—
117#95—45no—
118#95—45no—
119#95—45no—
120#95—45no—
121#95—45no—
122C24—25no—
123C24—25no—
124C24—25no—
125C24C2511yescharacteristic
126C22×C4—25no—
127C22×C4—25no—
128C22×C4—25no—
129C22×C4—25no—
130C22×C4—25no—
131C22×C4—25no—
132C22×C4—25no—
133C22×C4—25no—
134C22×C4—25no—
135C22×C4—25no—
136C22×C4—25no—
137C22×C4—25no—
138C22×C4—25no—
139C22×C4—25no—
140C22×C4—25no—
141C22×C4—25no—
142C22×C4—25no—
143C22×C4—25no—
144C22×C4—25no—
145C22×C4—25no—
146C22×C4—25no—
147C22×C4—25no—
148C22×C4—25no—
149C22×C4—25no—
150C22×C4—25no—
151C22×C4—25no—
152C22×C4—25no—
153C22×C4—25no—
154C22×C4—25no—
155C22×C4—25no—
156C22×C4—25no—
157C22×C4—25no—
158C22×C4—25no—
159C22×C4—25no—
160C22×C4—25no—
161C22×C4—25no—
162C22×C4—25no—
163C22×C4—25no—
164C22×C4—25no—
165C22×C4—25no—
166C22×C4—25no—
167C22×C4—25no—
168C4⋊C4—810no—
169C4⋊C4—810no—
170C4⋊C4—810no—
171C22⋊C4—810no—
172C22⋊C4—810no—
173C22⋊C4—810no—
174C42—810no—
175C23—45no—
176C23—45no—
177C23—45no—
178C23—45no—
179C23—45no—
180C23—45no—
181C23—45no—
182C23#58515yes—
183C23#58515yes—
184C23#58515yes—
185C2×C4—45no—
186C2×C4—45no—
187C2×C4—45no—
188C2×C4—45no—
189C2×C4—45no—
190C2×C4—45no—
191C2×C4—45no—
192C2×C4—45no—
193C2×C4—45no—
194C2×C4—45no—
195C2×C4—45no—
196C2×C4—45no—
197C2×C4—45no—
198C2×C4—45no—
199C2×C4—45no—
200C2×C4—45no—
201C2×C4—45no—
202C2×C4—45no—
203C2×C4—45no—
204C2×C4—45no—
205C2×C4—45no—
206C2×C4—45no—
207C2×C4—45no—
208C2×C4—45no—
209C2×C4—45no—
210C2×C4—45no—
211C2×C4—45no—
212C2×C4—45no—
213C2×C4—45no—
214C2×C4—45no—
215C2×C4—45no—
216C2×C4—45no—
217C2×C4—45no—
218C2×C4—45no—
219C2×C4—45no—
220C2×C4—45no—
221C2×C4—45no—
222C2×C4—45no—
223C2×C4—45no—
224C2×C4—45no—
225C2×C4—45no—
226C2×C4—45no—
227C22—85no—
228C22—85no—
229C22—85no—
230C22#356615yes—
231C22#356615yes—
232C22#356615yes—
233C22#356615yes—
234C22#356615yes—
235C22#356615yes—
236C22#356615yes—
237C4—85no—
238C4—85no—
239C4—85no—
240C4—85no—
241C4—85no—
242C4—85no—
243C2—161no—
244C2#5452315yes—
245C2#5452315yes—
246C2#5452315yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #17301C2semidirect
3. #16967C2semidirect
4. #16916C2semidirect
7. #16141C2semidirect

Maximal subgroups

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

subgroupindex
#173012
#172822
#169672
#169162
#167532
#162002
#161412