Finite Group Databasebeta

← #103130

Subgroups — #103130

Order 512.

534 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 134 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#33310C211yesmaximal, characteristic
2#29206C211yesmaximal, characteristic
3#28687C211yesmaximal, characteristic
4#9694C211yesmaximal, characteristic
5#9691C211yesmaximal, characteristic
6#9637C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#498—21no—
9C2×#498—22no—
10#2868C2211yescharacteristic
11#2868C2211yescharacteristic
12C4×C4⋊Q8C2211yescharacteristic
13#2084—22no—
14#2058—22no—
15#1990—21no—
16#1990—21no—
17#1948—22no—
18#1948—22no—
19#1844—22no—
20#1844—21no—
21#1844—22no—
22#1842C2211yescharacteristic
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C42×C8C2211yescharacteristic
26C2×#333—22no—
27C2×#332—22no—
28C2×Q8⋊C8—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#498—48no—
38#498—42no—
39#498—42no—
40C2×#106—24no—
41C2×#106—28no—
42C2×#106—24no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8D412yes—
47C2×C4⋊C8D412yes—
48C2×C4×C8—21no—
49C2×C4×C8—21no—
50C2×C4×C8—21no—
51C2×C4×C8—21no—
52C2×C4×C8D412yes—
53#391—21no—
54#389—21no—
55#389—21no—
56#384—21no—
57#384—21no—
58#384—21no—
59#384—21no—
60#384—21no—
61#384—21no—
62#384—21no—
63#384D411yescharacteristic
64#384D412yes—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C43C2311yescharacteristic
68#340—24no—
69#340—24no—
70#336—21no—
71#336—21no—
72#333—44no—
73#332—44no—
74Q8⋊C8—44no—
75C22×Q8—21no—
76C22×Q8—22no—
77C22×Q8—41no—
78C22×C8—22no—
79C22×C8—22no—
80C22×C8—22no—
81C22×C8—41no—
82C4⋊Q8—21no—
83C4⋊Q8—21no—
84C4⋊Q8—21no—
85C4⋊Q8—44no—
86C4⋊Q8—44no—
87C4⋊Q8—42no—
88C4⋊Q8—41no—
89C4⋊Q8—42no—
90C4⋊Q8—41no—
91C4⋊Q8—41no—
92C4⋊Q8—41no—
93C4⋊Q8—42no—
94C4⋊Q8—42no—
95C4⋊Q8—82no—
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—22no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
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
125#106—48no—
126#106—416no—
127#106—84no—
128C4⋊C8—22no—
129C4⋊C8—22no—
130C4⋊C8—42no—
131C4⋊C8—42no—
132C4⋊C8—42no—
133C4⋊C8SD1614yes—
134C4⋊C8SD1614yes—
135C4×C8—24no—
136C4×C8—24no—
137C4×C8—22no—
138C4×C8—41no—
139C4×C8—41no—
140C4×C8—41no—
141C4×C8—41no—
142C4×C8SD1614yes—
143#95—41no—
144#95—41no—
145C2×Q8—22no—
146C2×Q8—41no—
147C2×Q8—42no—
148C2×Q8—44no—
149C2×Q8—42no—
150C2×Q8—82no—
151C2×Q8—82no—
152C2×Q8—81no—
153C2×Q8—82no—
154C2×Q8—81no—
155C2×Q8—82no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—42no—
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—24no—
170C2×C8—24no—
171C2×C8—24no—
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—44no—
182C4⋊C4—44no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—44no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—44no—
192C4⋊C4—82no—
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—
203C42—22no—
204C42—22no—
205C42—22no—
206C42—81no—
207C42—81no—
208C42C2×SD1611yescharacteristic
209C42C2×SD1612yes—
210C42C2×SD1612yes—
211C42C2×SD1612yes—
212C42#13511yescharacteristic
213C42AGL(1,ℤ/8)11yescharacteristic
214C42#13711yescharacteristic
215C42#13712yes—
216C42#13712yes—
217C42#13712yes—
218C23#39211yescharacteristic
219Q8—44no—
220Q8—82no—
221Q8—164no—
222Q8—162no—
223Q8—162no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—42no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—82no—
234C2×C4—82no—
235C2×C4—82no—
236C2×C4—81no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—82no—
240C2×C4—82no—
241C2×C4—82no—
242C2×C4#44812yes—
243C2×C4#44812yes—
244C2×C4#44811yescharacteristic
245C2×C4#44812yes—
246C2×C4#44911yescharacteristic
247C2×C4#45011yescharacteristic
248C2×C4#45211yescharacteristic
249C2×C4#45312yes—
250C2×C4#45612yes—
251C2×C4#46112yes—
252C2×C4#46112yes—
253C2×C4#46112yes—
254C2×C4#46511yescharacteristic
255C2×C4#46811yescharacteristic
256C2×C4#47112yes—
257C2×C4#49211yescharacteristic
258C2×C4#49211yescharacteristic
259C2×C4#49211yescharacteristic
260C2×C4#49711yescharacteristic
261C2×C4#49711yescharacteristic
262C2×C4#49711yescharacteristic
263C8—28no—
264C8—44no—
265C8—44no—
266C8—161no—
267C22#200011yescharacteristic
268C22#200211yescharacteristic
269C22#200511yescharacteristic
270C22#201311yescharacteristic
271C22#201311yescharacteristic
272C22#201311yescharacteristic
273C22#201911yescharacteristic
274C4—22no—
275C4—22no—
276C4—22no—
277C4—82no—
278C4—161no—
279C4—162no—
280C4—162no—
281C4#162212yes—
282C4#162312yes—
283C4#165112yes—
284C4#165312yes—
285C4#167112yes—
286C4#169112yes—
287C4#170511yescharacteristic
288C4#171611yescharacteristic
289C4#171611yescharacteristic
290C4#171611yescharacteristic
291C2#1004911yescharacteristic
292C2#1007511yescharacteristic
293C2#1015311yescharacteristic
294C2#1016711yescharacteristic
295C2#1027111yescharacteristic
296C2#1028311yescharacteristic
297C2#1031611yescharacteristic
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
#333102
#292062
#286872
#96942
#96912
#96372
#70152