Finite Group Databasebeta

← #103102

Subgroups — #103102

Order 512.

490 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 122 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#28748C211yesmaximal, characteristic
4#9898C211yesmaximal, characteristic
5#9692C211yesmaximal, characteristic
6#9637C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#487—21no—
9#2868C2211yescharacteristic
10#2868C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12#2099—22no—
13#2043—22no—
14#1990—22no—
15#1990—22no—
16#1990—21no—
17#1988—22no—
18#1981—22no—
19#1956—21no—
20#1842C2211yescharacteristic
21#1834—22no—
22#1834—21no—
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C42×C8C2211yescharacteristic
26C2×#332—22no—
27C2×Q8⋊C8—22no—
28#1296—22no—
29C2×C4⋊Q8—21no—
30C2×C4⋊Q8—21no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D412yes—
36C2×C4×Q8—21no—
37#487—42no—
38#487—42no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8D412yes—
43C2×C4⋊C8D412yes—
44C2×#103—24no—
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#384—21no—
61#384D411yescharacteristic
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—
72Q8⋊C8—44no—
73C22×Q8—22no—
74C22×Q8—21no—
75C22×Q8—41no—
76C22×C8—22no—
77C22×C8—22no—
78C22×C8—22no—
79C22×C8—41no—
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82C4⋊Q8—21no—
83C4⋊Q8—44no—
84C4⋊Q8—41no—
85C4⋊Q8—42no—
86C4⋊Q8—42no—
87C4⋊Q8—42no—
88C4⋊Q8—41no—
89C4⋊Q8—42no—
90C4⋊Q8—42no—
91C4⋊Q8—42no—
92C4⋊Q8—42no—
93C4⋊Q8—41no—
94C4⋊Q8—42no—
95C4⋊Q8—41no—
96C4⋊Q8SD1612yes—
97C4×Q8—42no—
98C4×Q8—42no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—22no—
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×C4⋊C4—41no—
117C2×C42—41no—
118C2×C42C2×D411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42#4111yescharacteristic
125C4⋊C8—22no—
126C4⋊C8—22no—
127C4⋊C8—22no—
128C4⋊C8—22no—
129C4⋊C8—42no—
130C4⋊C8—42no—
131C4⋊C8—42no—
132#103—48no—
133#103—84no—
134C4×C8—24no—
135C4×C8—22no—
136C4×C8—22no—
137C4×C8—42no—
138C4×C8—41no—
139C4×C8—41no—
140C4×C8—41no—
141C4×C8—41no—
142#95—41no—
143#95—41no—
144C2×Q8—22no—
145C2×Q8—41no—
146C2×Q8—44no—
147C2×Q8—42no—
148C2×Q8—42no—
149C2×Q8—44no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—81no—
153C2×Q8—81no—
154C2×Q8—81no—
155C2×Q8—81no—
156C2×Q8—81no—
157C2×Q8—81no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—42no—
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—24no—
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—44no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—44no—
187C4⋊C4—44no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—44no—
192C4⋊C4—82no—
193C4⋊C4—81no—
194C4⋊C4—82no—
195C4⋊C4—81no—
196C4⋊C4—82no—
197C4⋊C4—82no—
198C4⋊C4—82no—
199C4⋊C4—82no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C4⋊C4—81no—
203C4⋊C4—81no—
204C42—22no—
205C42—22no—
206C42—22no—
207C42—81no—
208C42—81no—
209C42C2×SD1611yescharacteristic
210C42#13511yescharacteristic
211C42#13512yes—
212C42#13512yes—
213C42#13512yes—
214C42AGL(1,ℤ/8)11yescharacteristic
215C42AGL(1,ℤ/8)12yes—
216C42AGL(1,ℤ/8)12yes—
217C42#13711yescharacteristic
218C42#13712yes—
219C23#39211yescharacteristic
220Q8—44no—
221Q8—82no—
222Q8—84no—
223Q8—84no—
224Q8—161no—
225Q8—161no—
226Q8—161no—
227Q8—161no—
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—81no—
242C2×C4—82no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4#44811yescharacteristic
247C2×C4#44912yes—
248C2×C4#44912yes—
249C2×C4#44911yescharacteristic
250C2×C4#45011yescharacteristic
251C2×C4#45211yescharacteristic
252C2×C4#45212yes—
253C2×C4#45512yes—
254C2×C4#45612yes—
255C2×C4#46312yes—
256C2×C4#46312yes—
257C2×C4#46412yes—
258C2×C4#46511yescharacteristic
259C2×C4#46811yescharacteristic
260C2×C4#47312yes—
261C2×C4#49511yescharacteristic
262C2×C4#49511yescharacteristic
263C2×C4#49511yescharacteristic
264C2×C4#49611yescharacteristic
265C2×C4#49611yescharacteristic
266C2×C4#49711yescharacteristic
267C8—44no—
268C8—82no—
269C8—82no—
270C8—161no—
271C22#200011yescharacteristic
272C22#200411yescharacteristic
273C22#200511yescharacteristic
274C22#201211yescharacteristic
275C22#201211yescharacteristic
276C22#201511yescharacteristic
277C22#202011yescharacteristic
278C4—22no—
279C4—22no—
280C4—22no—
281C4—82no—
282C4—161no—
283C4—162no—
284C4—162no—
285C4#164012yes—
286C4#164212yes—
287C4#165212yes—
288C4#165312yes—
289C4#167912yes—
290C4#169912yes—
291C4#171111yescharacteristic
292C4#171711yescharacteristic
293C4#171911yescharacteristic
294C4#172011yescharacteristic
295C2#1006911yescharacteristic
296C2#1007111yescharacteristic
297C2#1017111yescharacteristic
298C2#1017511yescharacteristic
299C2#1027011yescharacteristic
300C2#1028811yescharacteristic
301C2#1031111yescharacteristic
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
#287482
#98982
#96922
#96372
#70152