Finite Group Databasebeta

← #100916

Subgroups — #100916

Order 512.

323 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 323 conjugacy classes of subgroups — too many to draw. Only its 74 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#29214C211yesmaximal, characteristic
2#23265C211yesmaximal, characteristic
3#7703C211yesmaximal, characteristic
4#7703C211yesmaximal, characteristic
5#7650C211yesmaximal, characteristic
6#7043C211yesmaximal, characteristic
7#7043C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9C4×#125C2211yescharacteristic
10#2059—21no—
11#2059—21no—
12#1992C411yescharacteristic
13#1992C411yescharacteristic
14#1949—21no—
15#1949—21no—
16#1917—21no—
17#1917—21no—
18#1917—21no—
19#1916—21no—
20#1847C411yescharacteristic
21#1847C411yescharacteristic
22#1839C2211yescharacteristic
23#1839C2211yescharacteristic
24#1771—21no—
25#1770—21no—
26#1767C2211yescharacteristic
27#1745C2211yescharacteristic
28#1745C2211yescharacteristic
29#1271—21no—
30#1271—21no—
31#1271—21no—
32#1271—21no—
33#1271—21no—
34#1271—21no—
35C2×#125—21no—
36C2×#125C2×C411yescharacteristic
37C2×#107—21no—
38C2×#107—21no—
39C2×#106—21no—
40C2×#106—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×#97—21no—
45C2×#97—21no—
46C2×#97—21no—
47C2×#97C2×C411yescharacteristic
48C2×#97C2×C411yescharacteristic
49C2×C4×C8—21no—
50#389—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389D411yescharacteristic
55#389D411yescharacteristic
56#387—21no—
57#387—21no—
58#384C2×C411yescharacteristic
59#384C2×C411yescharacteristic
60#382—21no—
61#382C2×C411yescharacteristic
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4D411yescharacteristic
65C4×C4⋊C4D411yescharacteristic
66C43C2311yescharacteristic
67#340—21no—
68#340—21no—
69#340—21no—
70#340—21no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336D411yescharacteristic
85#336D411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—41no—
95C22×C8—41no—
96#125—22no—
97#125—41no—
98#125—81no—
99#125—81no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
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—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4C22⋊C411yescharacteristic
113C2×C4⋊C4C22⋊C411yescharacteristic
114C2×C4⋊C4C22⋊C411yescharacteristic
115C2×C4⋊C4C22⋊C411yescharacteristic
116C2×C42—21no—
117C2×C42—21no—
118C2×C42C22×C411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42#4111yescharacteristic
124C2×C42#4111yescharacteristic
125#107—81no—
126#107—81no—
127#106—81no—
128#106—81no—
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—42no—
132C4⋊C8—42no—
133#97—41no—
134#97—41no—
135#97—42no—
136#97—42no—
137#97—42no—
138C4×C8—42no—
139#95—21no—
140#95—21no—
141#95—21no—
142#95—21no—
143#95—21no—
144#95—21no—
145#95—41no—
146#95—41no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4C2×C22⋊C411yescharacteristic
154C22×C4C4×D411yescharacteristic
155C22×C4C4×D411yescharacteristic
156C22×C4#12011yescharacteristic
157C22×C4#12111yescharacteristic
158C22×C4#12111yescharacteristic
159C22×C4#12311yescharacteristic
160C2×C8—22no—
161C2×C8—22no—
162C2×C8—22no—
163C2×C8—22no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C2×C8—81no—
182C2×C8—81no—
183C2×C8—81no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—81no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—82no—
202C4⋊C4—82no—
203C4⋊C4#10112yes—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—41no—
209C42—41no—
210C42—41no—
211C42—41no—
212C42—41no—
213C42—41no—
214C42—41no—
215C42—41no—
216C42—41no—
217C23#38611yescharacteristic
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—21no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4C2×#10111yescharacteristic
256C2×C4#41311yescharacteristic
257C2×C4#45611yescharacteristic
258C2×C4#45611yescharacteristic
259C8—42no—
260C8—42no—
261C8—42no—
262C8—42no—
263C8—81no—
264C8—81no—
265C8—161no—
266C8—161no—
267C22#188111yescharacteristic
268C22#188111yescharacteristic
269C22#188611yescharacteristic
270C22#190111yescharacteristic
271C22#190611yescharacteristic
272C22#190611yescharacteristic
273C22#191011yescharacteristic
274C4—21no—
275C4—21no—
276C4—21no—
277C4—21no—
278C4—41no—
279C4—41no—
280C4—42no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—81no—
285C4—81no—
286C4—81no—
287C4—161no—
288C4—161no—
289C2#900611yescharacteristic
290C2#935111yescharacteristic
291C2#935211yescharacteristic
292C2#937011yescharacteristic
293C2#937011yescharacteristic
294C2#944011yescharacteristic
295C2#945411yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ 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
#292142
#232652
#77032
#76502
#70432