Finite Group Databasebeta

← #104934

Subgroups — #104934

Order 512.

314 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 76 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#32849C211yesmaximal, characteristic
2#9904C211yesmaximal, characteristic
3#9902C211yesmaximal, characteristic
4#9891C211yesmaximal, characteristic
5#9686C211yesmaximal, characteristic
6#8808C211yesmaximal, characteristic
7#7049C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9#2859C2211yescharacteristic
10#2100—21no—
11#2099—21no—
12#2088—21no—
13#2088—21no—
14#2084—21no—
15#2084—21no—
16#1842C2211yescharacteristic
17#1831C2211yescharacteristic
18#1767C2211yescharacteristic
19#1767C2211yescharacteristic
20C4×#97C2211yescharacteristic
21C2×#335—21no—
22C2×#334—21no—
23C2×#330—21no—
24C2×#330—21no—
25#1296—21no—
26#1296—21no—
27#1296—21no—
28#1296—21no—
29#1295—21no—
30#1295—21no—
31C2×#125—21no—
32C2×#125—21no—
33C2×#106—21no—
34C2×#106—21no—
35C2×C4⋊C8—21no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8D411yescharacteristic
41C2×C4⋊C8D411yescharacteristic
42C2×#97—21no—
43C2×#97—21no—
44C2×#97—21no—
45C2×#97D411yescharacteristic
46C2×#97D411yescharacteristic
47C2×C4×C8—21no—
48#389—21no—
49#389—21no—
50#389—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#384D411yescharacteristic
57#384D411yescharacteristic
58#384D411yescharacteristic
59#384D411yescharacteristic
60#382—21no—
61#382—21no—
62C43C2311yescharacteristic
63#340—21no—
64#340—21no—
65#340—21no—
66#340—21no—
67#340—21no—
68#340—21no—
69#336—21no—
70#336—21no—
71#336—21no—
72#336—21no—
73#335—42no—
74#334—42no—
75#330—42no—
76#330—42no—
77C22×C8—21no—
78C22×C8—21no—
79C22×C8—21no—
80C22×C8—21no—
81C22×C8—41no—
82C22×C8—41no—
83C22×C8—41no—
84#125—41no—
85#125—41no—
86#125—41no—
87#125—41no—
88#125—82no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C42C2×D411yescharacteristic
106C2×C42C2×D411yescharacteristic
107C2×C42C2×D411yescharacteristic
108C2×C42C2×D411yescharacteristic
109C2×C42#4111yescharacteristic
110C2×C42#4111yescharacteristic
111C2×C42#4111yescharacteristic
112#106—81no—
113#106—81no—
114C4⋊C8—22no—
115C4⋊C8—22no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—42no—
123C4⋊C8—42no—
124#97—21no—
125#97—21no—
126#97—21no—
127#97—42no—
128#97—41no—
129#97—41no—
130#97—41no—
131#97—41no—
132#97SD1612yes—
133C4×C8—22no—
134C4×C8—22no—
135#95—41no—
136#95—41no—
137#95—41no—
138#95—41no—
139C22×C4—41no—
140C22×C4—41no—
141C22×C4—41no—
142C22×C4—41no—
143C22×C4#12011yescharacteristic
144C22×C4#12111yescharacteristic
145C22×C4#12111yescharacteristic
146C22×C4#12111yescharacteristic
147C22×C4#12311yescharacteristic
148C22×C4#12311yescharacteristic
149C22×C4#12411yescharacteristic
150C2×C8—22no—
151C2×C8—22no—
152C2×C8—22no—
153C2×C8—22no—
154C2×C8—41no—
155C2×C8—41no—
156C2×C8—42no—
157C2×C8—42no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—81no—
165C2×C8—81no—
166C2×C8—81no—
167C2×C8—81no—
168C2×C8—81no—
169C2×C8—81no—
170C2×C8—81no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—81no—
184C4⋊C4—81no—
185C4⋊C4—81no—
186C4⋊C4—81no—
187C4⋊C4—81no—
188C4⋊C4—81no—
189C4⋊C4—82no—
190C4⋊C4—82no—
191C4⋊C4—81no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C42—21no—
196C42—21no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—41no—
202C42—41no—
203C42—41no—
204C42C2×SD1611yescharacteristic
205C42#13511yescharacteristic
206C42AGL(1,ℤ/8)11yescharacteristic
207C42#13711yescharacteristic
208C23#39411yescharacteristic
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4—81no—
236C2×C4#45311yescharacteristic
237C2×C4#45411yescharacteristic
238C2×C4#45411yescharacteristic
239C2×C4#45611yescharacteristic
240C2×C4#45611yescharacteristic
241C2×C4#45611yescharacteristic
242C2×C4#46011yescharacteristic
243C2×C4#46111yescharacteristic
244C2×C4#46311yescharacteristic
245C2×C4#46411yescharacteristic
246C2×C4#46511yescharacteristic
247C2×C4#46811yescharacteristic
248C8—24no—
249C8—42no—
250C8—82no—
251C8—82no—
252C8—81no—
253C8—81no—
254C8—161no—
255C22#203811yescharacteristic
256C22#203811yescharacteristic
257C22#203911yescharacteristic
258C22#204811yescharacteristic
259C22#204911yescharacteristic
260C22#205011yescharacteristic
261C22#205511yescharacteristic
262C4—21no—
263C4—21no—
264C4—21no—
265C4—21no—
266C4—21no—
267C4—21no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—161no—
272C4—161no—
273C4—161no—
274C4—161no—
275C4#165711yescharacteristic
276C4#166011yescharacteristic
277C4#166311yescharacteristic
278C4#166311yescharacteristic
279C2#1042911yescharacteristic
280C2#1049711yescharacteristic
281C2#1049911yescharacteristic
282C2#1050211yescharacteristic
283C2#1050711yescharacteristic
284C2#1052011yescharacteristic
285C2#1052611yescharacteristic
subgroupG/H
center, socle, prime radicalC23#394
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
#328492
#99042
#99022
#98912
#96862
#88082
#70492