Finite Group Databasebeta

← #100581

Subgroups — #100581

Order 512.

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

normal subgroups only

This group has 336 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#30099C211yesmaximal, characteristic
2#22383C211yesmaximal, characteristic
3#9891C211yesmaximal, characteristic
4#8227C211yesmaximal, characteristic
5#7700C211yesmaximal, characteristic
6#7043C211yesmaximal, characteristic
7#7019C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9C4×#125C2211yescharacteristic
10#2101—21no—
11#2099C411yescharacteristic
12#2099C411yescharacteristic
13#2084C411yescharacteristic
14#2083C411yescharacteristic
15#2059—21no—
16#1940—21no—
17#1921—21no—
18#1920—21no—
19#1917—21no—
20#1917—21no—
21#1916—21no—
22#1916—21no—
23#1839C2211yescharacteristic
24#1839C2211yescharacteristic
25#1770—21no—
26#1767C2211yescharacteristic
27#1745C2211yescharacteristic
28C4×#97C2211yescharacteristic
29C2×#330—21no—
30#1295—21no—
31#1295—21no—
32#1295—21no—
33#1271—21no—
34#1271—21no—
35C2×#125—21no—
36C2×#125D411yescharacteristic
37C2×#107—21no—
38C2×#106—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×#97—21no—
43C2×#97—21no—
44C2×#97—21no—
45C2×#97—21no—
46C2×#97D411yescharacteristic
47C2×#97D411yescharacteristic
48C2×C4×C8—21no—
49C2×C4×C8—21no—
50#389—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389C2×C411yescharacteristic
55#389C2×C411yescharacteristic
56#387—21no—
57#387—21no—
58#384C2×C411yescharacteristic
59#384C2×C411yescharacteristic
60#382—21no—
61#382D411yescharacteristic
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#340—21no—
72#340—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#336C2×C411yescharacteristic
85#336C2×C411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88#330—24no—
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—41no—
96C22×C8—41no—
97#125—22no—
98#125—41no—
99#125—82no—
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—42no—
126#106—42no—
127C4⋊C8—42no—
128C4⋊C8—42no—
129C4⋊C8—81no—
130#97—22no—
131#97—22no—
132#97—22no—
133#97—41no—
134#97—41no—
135#97—41no—
136#97—41no—
137#97—41no—
138#97—81no—
139C4×C8—22no—
140C4×C8—41no—
141C4×C8—42no—
142#95—21no—
143#95—21no—
144#95—21no—
145#95—21no—
146#95—21no—
147#95—21no—
148#95—41no—
149#95—41no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4C2×C22⋊C411yescharacteristic
157C22×C4C4×D411yescharacteristic
158C22×C4C4×D411yescharacteristic
159C22×C4#12011yescharacteristic
160C22×C4#12111yescharacteristic
161C22×C4#12111yescharacteristic
162C22×C4#12311yescharacteristic
163C2×C8—22no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—42no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—42no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—81no—
186C2×C8—81no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—81no—
202C4⋊C4—81no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C4⋊C4—82no—
206C4⋊C4—82no—
207C4⋊C4#10412yes—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—41no—
215C42—41no—
216C42—41no—
217C42—41no—
218C42—41no—
219C42—41no—
220C42—41no—
221C42—41no—
222C23#38611yescharacteristic
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—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4C2×#10411yescharacteristic
260C2×C4#42111yescharacteristic
261C2×C4#44311yescharacteristic
262C2×C4#44411yescharacteristic
263C2×C4#45511yescharacteristic
264C2×C4#45611yescharacteristic
265C8—42no—
266C8—44no—
267C8—81no—
268C8—81no—
269C8—81no—
270C8—81no—
271C8—81no—
272C8—82no—
273C22#187111yescharacteristic
274C22#187611yescharacteristic
275C22#188211yescharacteristic
276C22#190311yescharacteristic
277C22#190611yescharacteristic
278C22#191211yescharacteristic
279C22#191511yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4—42no—
291C4—81no—
292C4—81no—
293C4—81no—
294C4—161no—
295C4—161no—
296C2#897211yescharacteristic
297C2#916111yescharacteristic
298C2#919011yescharacteristic
299C2#926611yescharacteristic
300C2#928411yescharacteristic
301C2#933811yescharacteristic
302C2#938011yescharacteristic
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
#300992
#223832
#98912
#82272
#77002
#70432
#70192