Finite Group Databasebeta

← #104913

Subgroups — #104913

Order 512.

285 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 285 conjugacy classes of subgroups — too many to draw. Only its 70 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#32849C211yesmaximal, characteristic
2#9906C211yesmaximal, characteristic
3#9906C211yesmaximal, characteristic
4#8789C211yesmaximal, characteristic
5#7683C211yesmaximal, characteristic
6#7680C211yesmaximal, characteristic
7#7042C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9#2859C2211yescharacteristic
10#2100—21no—
11#2099—21no—
12#2088—21no—
13#2088—21no—
14#2084—21no—
15#2084—21no—
16#1842C2211yescharacteristic
17#1831C2211yescharacteristic
18#1767C2211yescharacteristic
19#1767C2211yescharacteristic
20#1744C2211yescharacteristic
21#1296—21no—
22#1296—21no—
23#1296—21no—
24#1296—21no—
25#1277—21no—
26#1277—21no—
27#1271—22no—
28#1271—22no—
29C2×#125—21no—
30C2×#125—21no—
31C2×#106—21no—
32C2×#106—21no—
33C2×C4⋊C8—21no—
34C2×C4⋊C8—21no—
35C2×C4⋊C8—21no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8D411yescharacteristic
39C2×C4⋊C8D411yescharacteristic
40C2×#97—21no—
41C2×#97—21no—
42C2×C4×C8—21no—
43#389—21no—
44#389—21no—
45#389—21no—
46#389—21no—
47#389—21no—
48#389—21no—
49#389—21no—
50#389—21no—
51#384D411yescharacteristic
52#384D411yescharacteristic
53#384D411yescharacteristic
54#384D411yescharacteristic
55#382—21no—
56#382—21no—
57C43C2311yescharacteristic
58#340—21no—
59#340—21no—
60#340—21no—
61#340—21no—
62#340—21no—
63#340—21no—
64#336—21no—
65#336—21no—
66#336—21no—
67#336—21no—
68#336—21no—
69#336D412yes—
70C22×C8—21no—
71C22×C8—21no—
72C22×C8—22no—
73C22×C8—41no—
74C22×C8—41no—
75C22×C8—41no—
76#125—81no—
77#125—82no—
78#125—81no—
79C2×C4⋊C4—21no—
80C2×C4⋊C4—21no—
81C2×C4⋊C4—21no—
82C2×C4⋊C4—21no—
83C2×C4⋊C4—21no—
84C2×C4⋊C4—21no—
85C2×C4⋊C4—21no—
86C2×C4⋊C4—21no—
87C2×C4⋊C4—21no—
88C2×C4⋊C4—21no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—41no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C42C2×D411yescharacteristic
96C2×C42C2×D411yescharacteristic
97C2×C42C2×D411yescharacteristic
98C2×C42C2×D411yescharacteristic
99C2×C42#4111yescharacteristic
100C2×C42#4111yescharacteristic
101C2×C42#4111yescharacteristic
102#106—81no—
103#106—81no—
104C4⋊C8—22no—
105C4⋊C8—22no—
106C4⋊C8—41no—
107C4⋊C8—41no—
108C4⋊C8—41no—
109C4⋊C8—41no—
110C4⋊C8—42no—
111C4⋊C8—42no—
112C4⋊C8—42no—
113#97—81no—
114#97—81no—
115C4×C8—41no—
116C4×C8—41no—
117#95—41no—
118#95—41no—
119#95—41no—
120#95—41no—
121C22×C4—41no—
122C22×C4—41no—
123C22×C4—41no—
124C22×C4—41no—
125C22×C4#12011yescharacteristic
126C22×C4#12111yescharacteristic
127C22×C4#12111yescharacteristic
128C22×C4#12111yescharacteristic
129C22×C4#12311yescharacteristic
130C22×C4#12311yescharacteristic
131C22×C4#12411yescharacteristic
132C2×C8—42no—
133C2×C8—42no—
134C2×C8—42no—
135C2×C8—42no—
136C2×C8—41no—
137C2×C8—41no—
138C2×C8—41no—
139C2×C8—41no—
140C2×C8—41no—
141C2×C8—41no—
142C2×C8—42no—
143C2×C8—81no—
144C2×C8—81no—
145C2×C8—81no—
146C2×C8—81no—
147C2×C8—81no—
148C2×C8—81no—
149C2×C8—81no—
150C4⋊C4—41no—
151C4⋊C4—41no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—41no—
162C4⋊C4—81no—
163C4⋊C4—81no—
164C4⋊C4—81no—
165C4⋊C4—81no—
166C4⋊C4—81no—
167C4⋊C4—81no—
168C4⋊C4—82no—
169C4⋊C4—82no—
170C4⋊C4—81no—
171C4⋊C4—82no—
172C4⋊C4—81no—
173C42—21no—
174C42—21no—
175C42—21no—
176C42—21no—
177C42—21no—
178C42—21no—
179C42—21no—
180C42—21no—
181C42—22no—
182C42—21no—
183C42—21no—
184C42—41no—
185C23#39411yescharacteristic
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—81no—
205C2×C4—81no—
206C2×C4—81no—
207C2×C4—81no—
208C2×C4—81no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4—81no—
212C2×C4—81no—
213C2×C4#45411yescharacteristic
214C2×C4#45411yescharacteristic
215C2×C4#45411yescharacteristic
216C2×C4#45511yescharacteristic
217C2×C4#45611yescharacteristic
218C2×C4#45611yescharacteristic
219C2×C4#47111yescharacteristic
220C2×C4#47111yescharacteristic
221C2×C4#47112yes—
222C2×C4#47211yescharacteristic
223C2×C4#47311yescharacteristic
224C8—82no—
225C8—82no—
226C8—82no—
227C8—81no—
228C8—81no—
229C8—161no—
230C22#203811yescharacteristic
231C22#203811yescharacteristic
232C22#204011yescharacteristic
233C22#204611yescharacteristic
234C22#205111yescharacteristic
235C22#205211yescharacteristic
236C22#205311yescharacteristic
237C4—21no—
238C4—21no—
239C4—21no—
240C4—21no—
241C4—22no—
242C4—41no—
243C4—41no—
244C4—41no—
245C4—161no—
246C4—161no—
247C4—161no—
248C4—161no—
249C4#165811yescharacteristic
250C4#166311yescharacteristic
251C4#166411yescharacteristic
252C4#166411yescharacteristic
253C2#1042811yescharacteristic
254C2#1049111yescharacteristic
255C2#1049411yescharacteristic
256C2#1050911yescharacteristic
257C2#1051111yescharacteristic
258C2#1051511yescharacteristic
259C2#1053311yescharacteristic
subgroupG/H
center, socle, prime radicalC23#394
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ 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
#328492
#99062
#87892
#76832
#76802
#70422