Finite Group Databasebeta

← #103875

Subgroups — #103875

Order 512.

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

normal subgroups only

This group has 438 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#30205C211yesmaximal, characteristic
2#29147C211yesmaximal, characteristic
3#28748C211yesmaximal, characteristic
4#9905C211yesmaximal, characteristic
5#7662C211yesmaximal, characteristic
6#7588C211yesmaximal, characteristic
7#7027C211yesmaximal, characteristic
8C2×#487—21no—
9#2868C2211yescharacteristic
10#2862C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12#2072—22no—
13#2043—22no—
14#2024—21no—
15#2024—21no—
16#2024—22no—
17#1990—21no—
18#1981—22no—
19#1960—21no—
20#1956—21no—
21#1956—21no—
22#1836—21no—
23#1831C2211yescharacteristic
24#1805—22no—
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⋊Q8D411yescharacteristic
35C2×C4⋊Q8D411yescharacteristic
36C2×C4⋊Q8D412yes—
37C2×C4×Q8—21no—
38#487—42no—
39#487—42no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8D412yes—
43C2×#103—24no—
44C2×#103—22no—
45C2×#103—22no—
46C2×#103—24no—
47C2×#103—24no—
48C2×#97—21no—
49C2×C4×C8—21no—
50C2×C4×C8—21no—
51#391—21no—
52#391—21no—
53#391—21no—
54#391—21no—
55#391—21no—
56#389—21no—
57#389—21no—
58#384—21no—
59#384—21no—
60#384—21no—
61#384—21no—
62#384D411yescharacteristic
63#382—21no—
64#382—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C43C2311yescharacteristic
68#340—22no—
69#340—22no—
70#340—24no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336D412yes—
76#336D412yes—
77C22×Q8—21no—
78C22×Q8—22no—
79C22×Q8—21no—
80C22×Q8—21no—
81C22×C8—22no—
82C22×C8—22no—
83C22×C8—22no—
84C22×C8—41no—
85C4⋊Q8—21no—
86C4⋊Q8—21no—
87C4⋊Q8—21no—
88C4⋊Q8—42no—
89C4⋊Q8—42no—
90C4⋊Q8—44no—
91C4⋊Q8—41no—
92C4⋊Q8—41no—
93C4⋊Q8—41no—
94C4⋊Q8—41no—
95C4⋊Q8—82no—
96C4⋊Q8SD1612yes—
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—21no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C42—41no—
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42#4111yescharacteristic
123C4⋊C8—22no—
124C4⋊C8—22no—
125C4⋊C8—42no—
126C4⋊C8—42no—
127#103—48no—
128#103—84no—
129#103—82no—
130#103—82no—
131#103—84no—
132#97—41no—
133#97—41no—
134C4×C8—42no—
135C4×C8—41no—
136C4×C8—41no—
137#95—41no—
138#95—41no—
139#95—41no—
140#95—41no—
141#95—41no—
142#95—41no—
143C2×Q8—22no—
144C2×Q8—44no—
145C2×Q8—42no—
146C2×Q8—44no—
147C2×Q8—42no—
148C2×Q8—41no—
149C2×Q8—42no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—42no—
153C2×Q8—42no—
154C2×Q8—42no—
155C2×Q8—81no—
156C2×Q8—81no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—42no—
162C22×C4#12011yescharacteristic
163C22×C4#12011yescharacteristic
164C22×C4#12011yescharacteristic
165C22×C4#12111yescharacteristic
166C22×C4#12111yescharacteristic
167C22×C4#12111yescharacteristic
168C22×C4#12711yescharacteristic
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—44no—
190C4⋊C4—42no—
191C4⋊C4—81no—
192C4⋊C4—82no—
193C4⋊C4—81no—
194C4⋊C4—82no—
195C4⋊C4—82no—
196C4⋊C4—81no—
197C4⋊C4—81no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C42—22no—
203C42—22no—
204C42—22no—
205C42—41no—
206C42—41no—
207C42—82no—
208C42C2×SD1611yescharacteristic
209C42#13511yescharacteristic
210C42#13512yes—
211C42AGL(1,ℤ/8)11yescharacteristic
212C42#13711yescharacteristic
213C42#13712yes—
214C23#39211yescharacteristic
215Q8—44no—
216Q8—84no—
217Q8—84no—
218Q8—84no—
219Q8—82no—
220Q8—162no—
221C2×C4—21no—
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—42no—
234C2×C4—81no—
235C2×C4—81no—
236C2×C4—82no—
237C2×C4—81no—
238C2×C4—82no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—82no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4#44811yescharacteristic
249C2×C4#44911yescharacteristic
250C2×C4#45011yescharacteristic
251C2×C4#45211yescharacteristic
252C2×C4#45212yes—
253C2×C4#45512yes—
254C2×C4#45512yes—
255C2×C4#46412yes—
256C2×C4#46511yescharacteristic
257C2×C4#46811yescharacteristic
258C2×C4#47312yes—
259C2×C4#49511yescharacteristic
260C2×C4#49711yescharacteristic
261C8—82no—
262C8—82no—
263C8—82no—
264C8—161no—
265C22#200011yescharacteristic
266C22#200411yescharacteristic
267C22#200411yescharacteristic
268C22#200811yescharacteristic
269C22#200911yescharacteristic
270C22#201511yescharacteristic
271C22#202011yescharacteristic
272C4—21no—
273C4—21no—
274C4—22no—
275C4—22no—
276C4—22no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—82no—
282C4—162no—
283C4—161no—
284C4—161no—
285C4—161no—
286C4#164312yes—
287C4#164612yes—
288C2#1006411yescharacteristic
289C2#1009811yescharacteristic
290C2#1013711yescharacteristic
291C2#1017111yescharacteristic
292C2#1018711yescharacteristic
293C2#1022211yescharacteristic
294C2#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
#302052
#291472
#287482
#99052
#76622
#75882
#70272