Finite Group Databasebeta

← #103876

Subgroups — #103876

Order 512.

462 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 94 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#28748C211yesmaximal, characteristic
3#28518C211yesmaximal, characteristic
4#9905C211yesmaximal, characteristic
5#7660C211yesmaximal, characteristic
6#7588C211yesmaximal, characteristic
7#7027C211yesmaximal, characteristic
8C2×#487—21no—
9C2×#479—22no—
10#2868C2211yescharacteristic
11#2859C2211yescharacteristic
12C4×C4⋊Q8C2211yescharacteristic
13#2096—21no—
14#2095—21no—
15#2084—22no—
16#2058—22no—
17#2043—22no—
18#1981—22no—
19#1960—21no—
20#1956—21no—
21#1847—21no—
22#1844—21no—
23#1834—21no—
24#1831C2211yescharacteristic
25#1767C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27#1744C2211yescharacteristic
28#1296—22no—
29#1271—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—
39#479—44no—
40#479—44no—
41C2×#107—22no—
42C2×#106—22no—
43C2×#106—24no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8D412yes—
47C2×#103—22no—
48C2×#103—22no—
49C2×#103—24no—
50C2×#103—24no—
51C2×#97—21no—
52C2×C4×C8—21no—
53C2×C4×C8—21no—
54#391—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#384—21no—
62#384—21no—
63#384—21no—
64#384—21no—
65#384D411yescharacteristic
66#384D411yescharacteristic
67#384D411yescharacteristic
68#382—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C43C2311yescharacteristic
72#340—24no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336D412yes—
78#336D412yes—
79C22×Q8—21no—
80C22×Q8—22no—
81C22×C8—22no—
82C22×C8—22no—
83C22×C8—22no—
84C22×C8—41no—
85C4⋊Q8—21no—
86C4⋊Q8—21no—
87C4⋊Q8—21no—
88C4⋊Q8—44no—
89C4⋊Q8—41no—
90C4⋊Q8—41no—
91C4⋊Q8—41no—
92C4⋊Q8—41no—
93C4⋊Q8—82no—
94C4⋊Q8SD1612yes—
95#125—42no—
96#125—42no—
97C4×Q8—42no—
98C4×Q8—42no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C42—41no—
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42#4111yescharacteristic
127#107—44no—
128#106—44no—
129#106—84no—
130C4⋊C8—22no—
131C4⋊C8—42no—
132C4⋊C8—42no—
133C4⋊C8SD1614yes—
134#103—48no—
135#103—44no—
136#103—44no—
137#103—84no—
138#97—41no—
139#97—41no—
140C4×C8—24no—
141C4×C8—41no—
142C4×C8—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146#95—41no—
147C2×Q8—22no—
148C2×Q8—44no—
149C2×Q8—44no—
150C2×Q8—41no—
151C2×Q8—42no—
152C2×Q8—42no—
153C2×Q8—42no—
154C2×Q8—42no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—42no—
160C22×C4#12011yescharacteristic
161C22×C4#12011yescharacteristic
162C22×C4#12011yescharacteristic
163C22×C4#12111yescharacteristic
164C22×C4#12111yescharacteristic
165C22×C4#12111yescharacteristic
166C22×C4#12711yescharacteristic
167C2×C8—24no—
168C2×C8—24no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—81no—
177C2×C8—81no—
178C2×C8—81no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—44no—
190C4⋊C4—42no—
191C4⋊C4—81no—
192C4⋊C4—81no—
193C4⋊C4—82no—
194C4⋊C4—82no—
195C4⋊C4—82no—
196C4⋊C4—81no—
197C4⋊C4—81no—
198C4⋊C4—82no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C4⋊C4—81no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C42—22no—
206C42—22no—
207C42—22no—
208C42—41no—
209C42—41no—
210C42—82no—
211C42C2×SD1611yescharacteristic
212C42C2×SD1612yes—
213C42#13511yescharacteristic
214C42AGL(1,ℤ/8)11yescharacteristic
215C42AGL(1,ℤ/8)12yes—
216C42#13711yescharacteristic
217C23#39211yescharacteristic
218Q8—44no—
219Q8—84no—
220Q8—84no—
221Q8—82no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4—82no—
238C2×C4—82no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—82no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4#44811yescharacteristic
250C2×C4#44911yescharacteristic
251C2×C4#45011yescharacteristic
252C2×C4#45012yes—
253C2×C4#45211yescharacteristic
254C2×C4#45512yes—
255C2×C4#45612yes—
256C2×C4#46012yes—
257C2×C4#46511yescharacteristic
258C2×C4#46811yescharacteristic
259C2×C4#47312yes—
260C2×C4#49211yescharacteristic
261C2×C4#49611yescharacteristic
262C8—44no—
263C8—44no—
264C8—82no—
265C8—161no—
266C22#200011yescharacteristic
267C22#200411yescharacteristic
268C22#200511yescharacteristic
269C22#200811yescharacteristic
270C22#200911yescharacteristic
271C22#201411yescharacteristic
272C22#202011yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—22no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—82no—
283C4—162no—
284C4—161no—
285C4—161no—
286C4—161no—
287C4#165112yes—
288C4#165412yes—
289C2#1006811yescharacteristic
290C2#1009911yescharacteristic
291C2#1013911yescharacteristic
292C2#1017011yescharacteristic
293C2#1018711yescharacteristic
294C2#1022111yescharacteristic
295C2#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
#287482
#285182
#99052
#76602
#75882
#70272