Finite Group Databasebeta

← #103872

Subgroups — #103872

Order 512.

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

normal subgroups only

This group has 426 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#30305C211yesmaximal, characteristic
2#29223C211yesmaximal, characteristic
3#28748C211yesmaximal, characteristic
4#9905C211yesmaximal, characteristic
5#7660C211yesmaximal, characteristic
6#7590C211yesmaximal, characteristic
7#7027C211yesmaximal, characteristic
8C2×#487—21no—
9#2868C2211yescharacteristic
10#2859C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12#2100—21no—
13#2099—21no—
14#2084—22no—
15#2058—22no—
16#2043—22no—
17#1993—21no—
18#1989—22no—
19#1981—22no—
20#1956—21no—
21#1844—21no—
22#1836—21no—
23#1834—21no—
24#1831C2211yescharacteristic
25#1767C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27#1744C2211yescharacteristic
28#1296—22no—
29#1272—22no—
30#1271—22no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8D411yescharacteristic
34C2×C4⋊Q8D412yes—
35C2×#125—21no—
36C2×C4×Q8—21no—
37#487—42no—
38#487—42no—
39C2×#106—24no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8D412yes—
43C2×#103—24no—
44C2×#103—24no—
45C2×#97—21no—
46C2×C4×C8—21no—
47C2×C4×C8—21no—
48#391—21no—
49#389—21no—
50#389—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#384—21no—
56#384—21no—
57#384—21no—
58#384—21no—
59#384D411yescharacteristic
60#384D411yescharacteristic
61#384D411yescharacteristic
62#382—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C43C2311yescharacteristic
66#340—24no—
67#340—22no—
68#340—22no—
69#340—22no—
70#340—22no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336D412yes—
76#336D412yes—
77C22×Q8—22no—
78C22×Q8—21no—
79C22×C8—22no—
80C22×C8—22no—
81C22×C8—22no—
82C22×C8—41no—
83C4⋊Q8—21no—
84C4⋊Q8—21no—
85C4⋊Q8—21no—
86C4⋊Q8—44no—
87C4⋊Q8—41no—
88C4⋊Q8—41no—
89C4⋊Q8—41no—
90C4⋊Q8—41no—
91C4⋊Q8—82no—
92C4⋊Q8SD1612yes—
93#125—42no—
94#125—42no—
95C4×Q8—82no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C42—41no—
117C2×C42C2×D411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42#4111yescharacteristic
124#106—84no—
125C4⋊C8—22no—
126C4⋊C8—22no—
127C4⋊C8—42no—
128C4⋊C8—42no—
129#103—48no—
130#103—84no—
131#97—41no—
132#97—41no—
133C4×C8—24no—
134C4×C8—41no—
135C4×C8—41no—
136#95—41no—
137#95—41no—
138#95—41no—
139#95—41no—
140C2×Q8—22no—
141C2×Q8—44no—
142C2×Q8—44no—
143C2×Q8—41no—
144C2×Q8—42no—
145C2×Q8—42no—
146C2×Q8—81no—
147C2×Q8—81no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4—42no—
153C22×C4#12011yescharacteristic
154C22×C4#12011yescharacteristic
155C22×C4#12011yescharacteristic
156C22×C4#12111yescharacteristic
157C22×C4#12111yescharacteristic
158C22×C4#12111yescharacteristic
159C22×C4#12711yescharacteristic
160C2×C8—24no—
161C2×C8—42no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—42no—
169C2×C8—81no—
170C2×C8—81no—
171C2×C8—81no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—44no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—81no—
185C4⋊C4—81no—
186C4⋊C4—82no—
187C4⋊C4—82no—
188C4⋊C4—82no—
189C4⋊C4—81no—
190C4⋊C4—81no—
191C4⋊C4—82no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C4⋊C4—82no—
195C4⋊C4—81no—
196C4⋊C4—81no—
197C42—22no—
198C42—22no—
199C42—22no—
200C42—41no—
201C42—41no—
202C42—82no—
203C42C2×SD1611yescharacteristic
204C42#13511yescharacteristic
205C42#13512yes—
206C42AGL(1,ℤ/8)11yescharacteristic
207C42#13711yescharacteristic
208C42#13712yes—
209C23#39211yescharacteristic
210Q8—82no—
211Q8—82no—
212Q8—84no—
213Q8—84no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—82no—
230C2×C4—82no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—82no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4#44811yescharacteristic
242C2×C4#44911yescharacteristic
243C2×C4#45011yescharacteristic
244C2×C4#45211yescharacteristic
245C2×C4#45212yes—
246C2×C4#45512yes—
247C2×C4#45612yes—
248C2×C4#46412yes—
249C2×C4#46511yescharacteristic
250C2×C4#46811yescharacteristic
251C2×C4#47112yes—
252C2×C4#49511yescharacteristic
253C2×C4#49711yescharacteristic
254C8—44no—
255C8—82no—
256C8—82no—
257C8—161no—
258C22#200011yescharacteristic
259C22#200411yescharacteristic
260C22#200511yescharacteristic
261C22#200811yescharacteristic
262C22#200911yescharacteristic
263C22#201511yescharacteristic
264C22#201911yescharacteristic
265C4—21no—
266C4—21no—
267C4—22no—
268C4—22no—
269C4—22no—
270C4—21no—
271C4—21no—
272C4—21no—
273C4—21no—
274C4—82no—
275C4—162no—
276C4—161no—
277C4—161no—
278C4—161no—
279C4#165212yes—
280C4#165312yes—
281C2#1006911yescharacteristic
282C2#1009911yescharacteristic
283C2#1013811yescharacteristic
284C2#1016211yescharacteristic
285C2#1018611yescharacteristic
286C2#1022311yescharacteristic
287C2#1025011yescharacteristic
subgroupG/H
center, socle, prime radicalC23#392
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
#303052
#292232
#287482
#99052
#76602
#75902
#70272