Finite Group Databasebeta

← #103123

Subgroups — #103123

Order 512.

490 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 126 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#33289C211yesmaximal, characteristic
2#29219C211yesmaximal, characteristic
3#28511C211yesmaximal, characteristic
4#9896C211yesmaximal, characteristic
5#9870C211yesmaximal, characteristic
6#9692C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#477—22no—
9#2868C2211yescharacteristic
10#2868C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12#2099—22no—
13#2095—22no—
14#1990—22no—
15#1990—22no—
16#1990—21no—
17#1988—22no—
18#1956—21no—
19#1845—21no—
20#1842C2211yescharacteristic
21#1834—22no—
22#1834—21no—
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C42×C8C2211yescharacteristic
26C2×#332—22no—
27#1296—22no—
28#1279—22no—
29C2×C4⋊Q8—21no—
30C2×C4⋊Q8—21no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8—21no—
35C2×C4⋊Q8D411yescharacteristic
36C2×C4×Q8—21no—
37#477—44no—
38#477—44no—
39C2×#107—24no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8D412yes—
44C2×C4⋊C8D412yes—
45C2×#103—24no—
46C2×C4×C8—21no—
47C2×C4×C8—21no—
48C2×C4×C8—21no—
49C2×C4×C8—21no—
50C2×C4×C8D412yes—
51#391—21no—
52#389—21no—
53#389—21no—
54#384—21no—
55#384—21no—
56#384—21no—
57#384—21no—
58#384—21no—
59#384—21no—
60#384D411yescharacteristic
61#384D412yes—
62#384D412yes—
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C43C2311yescharacteristic
66#340—24no—
67#340—28no—
68#340—24no—
69#336—21no—
70#336—21no—
71#332—44no—
72C22×Q8—21no—
73C22×Q8—41no—
74C22×Q8—41no—
75C22×C8—22no—
76C22×C8—22no—
77C22×C8—22no—
78C22×C8—41no—
79C4⋊Q8—21no—
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82C4⋊Q8—44no—
83C4⋊Q8—42no—
84C4⋊Q8—42no—
85C4⋊Q8—42no—
86C4⋊Q8—42no—
87C4⋊Q8—42no—
88C4⋊Q8—42no—
89C4⋊Q8—42no—
90C4⋊Q8—42no—
91C4⋊Q8—82no—
92C4⋊Q8Q1612yes—
93C4×Q8—42no—
94C4×Q8—42no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C42—41no—
114C2×C42C2×D411yescharacteristic
115C2×C42C2×D411yescharacteristic
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42#4111yescharacteristic
121#107—48no—
122C4⋊C8—22no—
123C4⋊C8—22no—
124C4⋊C8—22no—
125C4⋊C8—42no—
126C4⋊C8—42no—
127C4⋊C8—42no—
128C4⋊C8D814yes—
129#103—48no—
130C4×C8—24no—
131C4×C8—22no—
132C4×C8—22no—
133C4×C8—42no—
134C4×C8—41no—
135C4×C8—41no—
136C4×C8—41no—
137C4×C8—41no—
138#95—41no—
139#95—41no—
140C2×Q8—22no—
141C2×Q8—41no—
142C2×Q8—42no—
143C2×Q8—42no—
144C2×Q8—82no—
145C2×Q8—82no—
146C2×Q8—82no—
147C2×Q8—81no—
148C2×Q8—81no—
149C2×Q8—81no—
150C2×Q8—81no—
151C2×Q8—81no—
152C2×Q8—81no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4#12011yescharacteristic
158C22×C4#12011yescharacteristic
159C22×C4#12011yescharacteristic
160C22×C4#12111yescharacteristic
161C22×C4#12111yescharacteristic
162C22×C4#12111yescharacteristic
163C22×C4#12711yescharacteristic
164C2×C8—24no—
165C2×C8—24no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—42no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—81no—
174C2×C8—81no—
175C2×C8—81no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—44no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—44no—
182C4⋊C4—42no—
183C4⋊C4—44no—
184C4⋊C4—44no—
185C4⋊C4—42no—
186C4⋊C4—44no—
187C4⋊C4—42no—
188C4⋊C4—82no—
189C4⋊C4—82no—
190C4⋊C4—82no—
191C4⋊C4—82no—
192C4⋊C4—82no—
193C4⋊C4—82no—
194C4⋊C4—82no—
195C4⋊C4—81no—
196C4⋊C4—81no—
197C42—22no—
198C42—22no—
199C42—22no—
200C42—81no—
201C42—81no—
202C42C2×D812yes—
203C42C2×Q1611yescharacteristic
204C42#13511yescharacteristic
205C42#13512yes—
206C42#13512yes—
207C42AGL(1,ℤ/8)12yes—
208C42#13711yescharacteristic
209C42#13711yescharacteristic
210C42#13712yes—
211C42#13712yes—
212C23#39211yescharacteristic
213Q8—44no—
214Q8—82no—
215Q8—164no—
216Q8—161no—
217Q8—161no—
218Q8—161no—
219Q8—161no—
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—81no—
231C2×C4—81no—
232C2×C4—82no—
233C2×C4—82no—
234C2×C4—82no—
235C2×C4—82no—
236C2×C4—81no—
237C2×C4—82no—
238C2×C4#44712yes—
239C2×C4#45111yescharacteristic
240C2×C4#45111yescharacteristic
241C2×C4#45212yes—
242C2×C4#45212yes—
243C2×C4#45211yescharacteristic
244C2×C4#45211yescharacteristic
245C2×C4#45412yes—
246C2×C4#45612yes—
247C2×C4#45912yes—
248C2×C4#46412yes—
249C2×C4#46412yes—
250C2×C4#46711yescharacteristic
251C2×C4#47011yescharacteristic
252C2×C4#47112yes—
253C2×C4#49311yescharacteristic
254C2×C4#49511yescharacteristic
255C2×C4#49511yescharacteristic
256C2×C4#49611yescharacteristic
257C2×C4#49711yescharacteristic
258C2×C4#49711yescharacteristic
259C8—44no—
260C8—44no—
261C8—82no—
262C8—161no—
263C22#200111yescharacteristic
264C22#200311yescharacteristic
265C22#200511yescharacteristic
266C22#201111yescharacteristic
267C22#201511yescharacteristic
268C22#201511yescharacteristic
269C22#201911yescharacteristic
270C4—22no—
271C4—22no—
272C4—22no—
273C4—82no—
274C4—162no—
275C4—161no—
276C4—162no—
277C4#163612yes—
278C4#163812yes—
279C4#164712yes—
280C4#164912yes—
281C4#168412yes—
282C4#170412yes—
283C4#170911yescharacteristic
284C4#172011yescharacteristic
285C4#172011yescharacteristic
286C4#172211yescharacteristic
287C2#1006111yescharacteristic
288C2#1007611yescharacteristic
289C2#1015011yescharacteristic
290C2#1017311yescharacteristic
291C2#1027711yescharacteristic
292C2#1029611yescharacteristic
293C2#1030611yescharacteristic
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
#332892
#292192
#285112
#98962
#98702
#96922
#70152