Finite Group Databasebeta

← #101890

Subgroups — #101890

Order 512.

367 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 367 conjugacy classes of subgroups — too many to draw. Only its 78 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#28515C211yesmaximal, characteristic
2#23365C211yesmaximal, characteristic
3#7703C212yesmaximal
4#7639C211yesmaximal, characteristic
5#7023C212yesmaximal
6C2×#479—21no—
7C2×#479—21no—
8#2859C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2097—21no—
11#2097—21no—
12#1985—21no—
13#1984—21no—
14#1956C411yescharacteristic
15#1956C411yescharacteristic
16#1917—22no—
17#1916—22no—
18#1845C411yescharacteristic
19#1844C411yescharacteristic
20#1839C2212yes—
21C4×C4⋊C8C2211yescharacteristic
22#1745C2212yes—
23#1272—21no—
24#1272—21no—
25#1271—22no—
26#1271—22no—
27C2×C4⋊Q8C2×C411yescharacteristic
28C2×#125—21no—
29C2×C4×Q8D411yescharacteristic
30C2×C4×Q8D411yescharacteristic
31#479—42no—
32#479—42no—
33#479—42no—
34#479—42no—
35C2×#107—21no—
36C2×#107—21no—
37C2×#106—21no—
38C2×#106—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×#103—21no—
43C2×#103—21no—
44C2×#103—21no—
45C2×#103—21no—
46C2×#97—22no—
47C2×#97—21no—
48C2×C4×C8—21no—
49C2×C4×C8C2×C411yescharacteristic
50C2×C4×C8C2×C411yescharacteristic
51#391D411yescharacteristic
52#391D411yescharacteristic
53#389—22no—
54#389—22no—
55#389—22no—
56#384C2×C411yescharacteristic
57#384C2×C411yescharacteristic
58#384C2×C411yescharacteristic
59#382—21no—
60C4×C4⋊C4—22no—
61C43C2311yescharacteristic
62#336—22no—
63#336—22no—
64#336—22no—
65#336—22no—
66#336—21no—
67#336—22no—
68#336—22no—
69#336D412yes—
70#336D412yes—
71C22×Q8C22⋊C411yescharacteristic
72C22×Q8C22⋊C411yescharacteristic
73C22×C8—21no—
74C22×C8—21no—
75C22×C8—22no—
76C22×C8—22no—
77C22×C8—42no—
78C4⋊Q8—22no—
79C4⋊Q8—41no—
80#125—41no—
81#125—41no—
82#125—41no—
83#125—41no—
84C4×Q8—41no—
85C4×Q8—41no—
86C4×Q8—41no—
87C4×Q8—41no—
88C2×C4⋊C4—22no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—22no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—22no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—41no—
98C2×C4⋊C4C22⋊C411yescharacteristic
99C2×C4⋊C4C22⋊C411yescharacteristic
100C2×C42—21no—
101C2×C42—21no—
102C2×C42C22×C411yescharacteristic
103C2×C42C2×D411yescharacteristic
104C2×C42C2×D411yescharacteristic
105C2×C42C2×D412yes—
106C2×C42#4112yes—
107#107—42no—
108#107—42no—
109#106—42no—
110#106—42no—
111C4⋊C8—22no—
112C4⋊C8—22no—
113C4⋊C8—81no—
114C4⋊C8—81no—
115#103—42no—
116#103—42no—
117#103—42no—
118#103—42no—
119#97—24no—
120#97—42no—
121#97—81no—
122C4×C8—41no—
123C4×C8—41no—
124C4×C8—81no—
125#95—22no—
126#95—22no—
127#95—42no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—41no—
132C2×Q8—41no—
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8#10112yes—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—41no—
141C22×C4—41no—
142C22×C4C2×C22⋊C411yescharacteristic
143C22×C4C4×D412yes—
144C22×C4#12011yescharacteristic
145C22×C4#12112yes—
146C22×C4#12311yescharacteristic
147C2×C8—22no—
148C2×C8—22no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—41no—
152C2×C8—41no—
153C2×C8—44no—
154C2×C8—44no—
155C2×C8—44no—
156C2×C8—42no—
157C2×C8—42no—
158C2×C8—82no—
159C2×C8—82no—
160C4⋊C4—44no—
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—81no—
172C4⋊C4—81no—
173C4⋊C4—82no—
174C4⋊C4—81no—
175C4⋊C4—81no—
176C4⋊C4—81no—
177C4⋊C4—81no—
178C42—21no—
179C42—21no—
180C42—22no—
181C42—22no—
182C42—21no—
183C42—21no—
184C42—42no—
185C42—41no—
186C42—41no—
187C42—41no—
188C42—41no—
189C42—41no—
190C23#38611yescharacteristic
191Q8—42no—
192Q8—42no—
193Q8—81no—
194Q8—81no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—82no—
216C2×C4—81no—
217C2×C4—81no—
218C2×C4—82no—
219C2×C4C2×#10111yescharacteristic
220C2×C4#41311yescharacteristic
221C2×C4#44312yes—
222C2×C4#44412yes—
223C2×C4#45311yescharacteristic
224C2×C4#45311yescharacteristic
225C8—42no—
226C8—42no—
227C8—82no—
228C8—82no—
229C8—84no—
230C22#187612yes—
231C22#188711yescharacteristic
232C22#190111yescharacteristic
233C22#190512yes—
234C22#190911yescharacteristic
235C4—22no—
236C4—22no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—21no—
241C4—42no—
242C4—41no—
243C4—42no—
244C4—81no—
245C4—81no—
246C4—81no—
247C4—161no—
248C4—161no—
249C2#906911yescharacteristic
250C2#924612yes—
251C2#928012yes—
252C2#942911yescharacteristic
253C2#945511yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ 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
#285152
#233652
#77032
#76392
#70232