Finite Group Databasebeta

← #103887

Subgroups — #103887

Order 512.

430 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 94 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#29211C211yesmaximal, characteristic
3#28689C211yesmaximal, characteristic
4#9905C211yesmaximal, characteristic
5#7662C211yesmaximal, characteristic
6#7590C211yesmaximal, characteristic
7#7027C211yesmaximal, characteristic
8C2×#500—21no—
9#2868C2211yescharacteristic
10#2862C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12#2083—22no—
13#2072—22no—
14#2058—21no—
15#2057—21no—
16#2024—22no—
17#1993—21no—
18#1990—21no—
19#1990—21no—
20#1956—21no—
21#1949—22no—
22#1947—22no—
23#1847—21no—
24#1831C2211yescharacteristic
25#1767C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27#1744C2211yescharacteristic
28#1296—22no—
29#1272—22no—
30#1272—22no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D411yescharacteristic
36C2×C4⋊Q8D411yescharacteristic
37C2×C4×Q8—21no—
38#500—42no—
39#500—42no—
40C2×#107—24no—
41C2×#107—22no—
42C2×#106—22no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8D412yes—
46C2×#103—24no—
47C2×#97—21no—
48C2×C4×C8—21no—
49C2×C4×C8—21no—
50#391—21no—
51#391—21no—
52#391—21no—
53#391—21no—
54#391—21no—
55#389—21no—
56#389—21no—
57#384—21no—
58#384—21no—
59#384—21no—
60#384D411yescharacteristic
61#384D412yes—
62#382—21no—
63#382—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C43C2311yescharacteristic
67#340—22no—
68#340—22no—
69#340—24no—
70#340—24no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336D412yes—
76#336D412yes—
77C22×Q8—21no—
78C22×Q8—21no—
79C22×Q8—21no—
80C22×Q8—41no—
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—41no—
91C4⋊Q8—41no—
92C4⋊Q8—41no—
93C4⋊Q8—41no—
94C4⋊Q8—82no—
95C4⋊Q8—82no—
96C4⋊Q8SD1612yes—
97C4×Q8—82no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C42—41no—
115C2×C42C2×D411yescharacteristic
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42#4111yescharacteristic
122#107—48no—
123#107—82no—
124#106—82no—
125C4⋊C8—24no—
126C4⋊C8—22no—
127C4⋊C8—42no—
128C4⋊C8Q1614yes—
129#103—84no—
130#97—41no—
131#97—41no—
132C4×C8—42no—
133C4×C8—41no—
134C4×C8—41no—
135#95—41no—
136#95—41no—
137#95—41no—
138#95—41no—
139#95—41no—
140#95—41no—
141C2×Q8—22no—
142C2×Q8—42no—
143C2×Q8—42no—
144C2×Q8—41no—
145C2×Q8—42no—
146C2×Q8—42no—
147C2×Q8—82no—
148C2×Q8—82no—
149C2×Q8—81no—
150C2×Q8—81no—
151C2×Q8—81no—
152C2×Q8—81no—
153C2×Q8—81no—
154C2×Q8—81no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
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—42no—
170C2×C8—42no—
171C2×C8—42no—
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—42no—
183C4⋊C4—42no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—81no—
192C4⋊C4—81no—
193C4⋊C4—82no—
194C4⋊C4—82no—
195C4⋊C4—81no—
196C4⋊C4—81no—
197C4⋊C4—82no—
198C4⋊C4—82no—
199C42—22no—
200C42—22no—
201C42—22no—
202C42—41no—
203C42—41no—
204C42—82no—
205C42C2×SD1611yescharacteristic
206C42C2×Q1612yes—
207C42#13511yescharacteristic
208C42AGL(1,ℤ/8)11yescharacteristic
209C42#13711yescharacteristic
210C42#13712yes—
211C23#39211yescharacteristic
212Q8—82no—
213Q8—82no—
214Q8—84no—
215Q8—162no—
216Q8—162no—
217Q8—162no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
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—42no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—82no—
234C2×C4—81no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4—81no—
238C2×C4—82no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—82no—
244C2×C4—81no—
245C2×C4#44811yescharacteristic
246C2×C4#44911yescharacteristic
247C2×C4#45011yescharacteristic
248C2×C4#45112yes—
249C2×C4#45211yescharacteristic
250C2×C4#45512yes—
251C2×C4#45612yes—
252C2×C4#46212yes—
253C2×C4#46511yescharacteristic
254C2×C4#46811yescharacteristic
255C2×C4#47212yes—
256C2×C4#49411yescharacteristic
257C2×C4#49711yescharacteristic
258C8—44no—
259C8—44no—
260C8—82no—
261C8—161no—
262C22#200011yescharacteristic
263C22#200411yescharacteristic
264C22#200511yescharacteristic
265C22#200811yescharacteristic
266C22#200911yescharacteristic
267C22#201611yescharacteristic
268C22#201811yescharacteristic
269C4—21no—
270C4—21no—
271C4—22no—
272C4—22no—
273C4—22no—
274C4—21no—
275C4—21no—
276C4—21no—
277C4—21no—
278C4—82no—
279C4—161no—
280C4—161no—
281C4—161no—
282C4—162no—
283C4#164412yes—
284C4#164512yes—
285C2#1006511yescharacteristic
286C2#1010011yescharacteristic
287C2#1014011yescharacteristic
288C2#1016511yescharacteristic
289C2#1017811yescharacteristic
290C2#1022411yescharacteristic
291C2#1025111yescharacteristic
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
#292112
#286892
#99052
#76622
#75902
#70272