Finite Group Databasebeta

← #103140

Subgroups — #103140

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#33312C211yesmaximal, characteristic
2#29208C211yesmaximal, characteristic
3#28511C211yesmaximal, characteristic
4#9896C211yesmaximal, characteristic
5#9870C211yesmaximal, characteristic
6#9691C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#500—22no—
9C2×#477—22no—
10#2868C2211yescharacteristic
11#2868C2211yescharacteristic
12C4×C4⋊Q8C2211yescharacteristic
13#2095—22no—
14#2057—22no—
15#1990—21no—
16#1956—21no—
17#1947—22no—
18#1845—22no—
19#1845—21no—
20#1845—22no—
21#1845—21no—
22#1842C2211yescharacteristic
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C42×C8C2211yescharacteristic
26C2×#333—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⋊Q8D411yescharacteristic
35C2×C4⋊Q8D412yes—
36C2×C4×Q8—21no—
37#500—48no—
38#477—44no—
39#477—44no—
40C2×#107—24no—
41C2×#107—28no—
42C2×#107—24no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8D412yes—
47C2×C4⋊C8D412yes—
48C2×#103—24no—
49C2×C4×C8—21no—
50C2×C4×C8—21no—
51C2×C4×C8—21no—
52C2×C4×C8—21no—
53C2×C4×C8D412yes—
54#391—21no—
55#389—21no—
56#389—21no—
57#384—21no—
58#384—21no—
59#384—21no—
60#384—21no—
61#384—21no—
62#384—21no—
63#384—21no—
64#384D411yescharacteristic
65#384D412yes—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C43C2311yescharacteristic
69#340—24no—
70#336—21no—
71#336—21no—
72#333—44no—
73C22×Q8—21no—
74C22×Q8—22no—
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—44no—
85C4⋊Q8—42no—
86C4⋊Q8—42no—
87C4⋊Q8—42no—
88C4⋊Q8—42no—
89C4⋊Q8—82no—
90C4⋊Q8—82no—
91C4⋊Q8Q1612yes—
92C4×Q8—42no—
93C4×Q8—42no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
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×C42—41no—
113C2×C42C2×D411yescharacteristic
114C2×C42C2×D411yescharacteristic
115C2×C42C2×D411yescharacteristic
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42#4111yescharacteristic
120#107—48no—
121#107—416no—
122#107—84no—
123C4⋊C8—22no—
124C4⋊C8—22no—
125C4⋊C8—42no—
126C4⋊C8—42no—
127C4⋊C8—42no—
128C4⋊C8D814yes—
129C4⋊C8Q1614yes—
130#103—48no—
131C4×C8—24no—
132C4×C8—24no—
133C4×C8—22no—
134C4×C8—41no—
135C4×C8—41no—
136C4×C8—41no—
137C4×C8—41no—
138C4×C8Q1614yes—
139#95—41no—
140#95—41no—
141C2×Q8—22no—
142C2×Q8—41no—
143C2×Q8—42no—
144C2×Q8—42no—
145C2×Q8—44no—
146C2×Q8—82no—
147C2×Q8—82no—
148C2×Q8—82no—
149C2×Q8—82no—
150C2×Q8—82no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4#12011yescharacteristic
156C22×C4#12011yescharacteristic
157C22×C4#12011yescharacteristic
158C22×C4#12111yescharacteristic
159C22×C4#12111yescharacteristic
160C22×C4#12111yescharacteristic
161C22×C4#12711yescharacteristic
162C2×C8—24no—
163C2×C8—24no—
164C2×C8—24no—
165C2×C8—24no—
166C2×C8—24no—
167C2×C8—42no—
168C2×C8—42no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—81no—
172C2×C8—81no—
173C2×C8—81no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—44no—
177C4⋊C4—44no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—44no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—44no—
184C4⋊C4—42no—
185C4⋊C4—82no—
186C4⋊C4—82no—
187C4⋊C4—82no—
188C4⋊C4—82no—
189C4⋊C4—82no—
190C4⋊C4—82no—
191C4⋊C4—82no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C4⋊C4—81no—
196C42—22no—
197C42—22no—
198C42—22no—
199C42—81no—
200C42—81no—
201C42C2×D812yes—
202C42C2×Q1611yescharacteristic
203C42C2×Q1612yes—
204C42C2×Q1612yes—
205C42#13511yescharacteristic
206C42AGL(1,ℤ/8)12yes—
207C42#13711yescharacteristic
208C42#13711yescharacteristic
209C42#13712yes—
210C42#13712yes—
211C23#39211yescharacteristic
212Q8—44no—
213Q8—82no—
214Q8—164no—
215Q8—164no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—81no—
224C2×C4—81no—
225C2×C4—82no—
226C2×C4—82no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—82no—
230C2×C4—82no—
231C2×C4—81no—
232C2×C4—82no—
233C2×C4—82no—
234C2×C4#44712yes—
235C2×C4#45112yes—
236C2×C4#45112yes—
237C2×C4#45111yescharacteristic
238C2×C4#45111yescharacteristic
239C2×C4#45211yescharacteristic
240C2×C4#45211yescharacteristic
241C2×C4#45312yes—
242C2×C4#45612yes—
243C2×C4#45912yes—
244C2×C4#46212yes—
245C2×C4#46212yes—
246C2×C4#46711yescharacteristic
247C2×C4#47011yescharacteristic
248C2×C4#47212yes—
249C2×C4#49311yescharacteristic
250C2×C4#49411yescharacteristic
251C2×C4#49411yescharacteristic
252C2×C4#49611yescharacteristic
253C2×C4#49711yescharacteristic
254C2×C4#49711yescharacteristic
255C8—28no—
256C8—44no—
257C8—44no—
258C8—161no—
259C22#200111yescharacteristic
260C22#200211yescharacteristic
261C22#200511yescharacteristic
262C22#201111yescharacteristic
263C22#201611yescharacteristic
264C22#201611yescharacteristic
265C22#201811yescharacteristic
266C4—22no—
267C4—22no—
268C4—22no—
269C4—82no—
270C4—161no—
271C4—162no—
272C4—162no—
273C4#163212yes—
274C4#163312yes—
275C4#164712yes—
276C4#164912yes—
277C4#167612yes—
278C4#169612yes—
279C4#171311yescharacteristic
280C4#172211yescharacteristic
281C4#172311yescharacteristic
282C4#172311yescharacteristic
283C2#1005711yescharacteristic
284C2#1007611yescharacteristic
285C2#1014411yescharacteristic
286C2#1016511yescharacteristic
287C2#1027911yescharacteristic
288C2#1029311yescharacteristic
289C2#1030911yescharacteristic
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
#333122
#292082
#285112
#98962
#98702
#96912
#70152