Finite Group Databasebeta

← #100849

Subgroups — #100849

Order 512.

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

normal subgroups only

This group has 332 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#29183C211yesmaximal, characteristic
2#22383C211yesmaximal, characteristic
3#9690C211yesmaximal, characteristic
4#7720C211yesmaximal, characteristic
5#7619C211yesmaximal, characteristic
6#7043C211yesmaximal, characteristic
7#7042C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9C4×#125C2211yescharacteristic
10#2088—21no—
11#2087—21no—
12#1992C411yescharacteristic
13#1992C411yescharacteristic
14#1940—21no—
15#1919—21no—
16#1918—21no—
17#1917—21no—
18#1917—21no—
19#1916—21no—
20#1916—21no—
21#1847C411yescharacteristic
22#1839C2211yescharacteristic
23#1836C411yescharacteristic
24#1831C2211yescharacteristic
25#1770—21no—
26#1767C2211yescharacteristic
27#1767C2211yescharacteristic
28#1745C2211yescharacteristic
29C2×#330—21no—
30C2×#330—21no—
31#1271—21no—
32#1271—21no—
33#1271—21no—
34#1271—21no—
35C2×#125—21no—
36C2×#125C2×C411yescharacteristic
37C2×#107—21no—
38C2×#106—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×#97—21no—
45C2×#97—21no—
46C2×#97C2×C411yescharacteristic
47C2×#97C2×C411yescharacteristic
48C2×#97D411yescharacteristic
49C2×#97D411yescharacteristic
50C2×C4×C8—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389D411yescharacteristic
56#389D411yescharacteristic
57#387—21no—
58#387—21no—
59#384C2×C411yescharacteristic
60#384C2×C411yescharacteristic
61#382—21no—
62#382C2×C411yescharacteristic
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4D411yescharacteristic
66C4×C4⋊C4D411yescharacteristic
67C43C2311yescharacteristic
68#340—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#340—21no—
73#340—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#336—21no—
85#336—21no—
86#336D411yescharacteristic
87#336D411yescharacteristic
88#330—42no—
89#330—42no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—41no—
97C22×C8—41no—
98#125—22no—
99#125—41no—
100#125—41no—
101#125—41no—
102#125—41no—
103#125—41no—
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—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4C22⋊C411yescharacteristic
117C2×C4⋊C4C22⋊C411yescharacteristic
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C4⋊C4C22⋊C411yescharacteristic
120C2×C42—21no—
121C2×C42—21no—
122C2×C42C22×C411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42#4111yescharacteristic
128C2×C42#4111yescharacteristic
129#107—42no—
130#106—42no—
131C4⋊C8—42no—
132C4⋊C8—42no—
133C4⋊C8—42no—
134C4⋊C8—81no—
135C4⋊C8—81no—
136#97—22no—
137#97—41no—
138#97—41no—
139#97—41no—
140#97—41no—
141#97—41no—
142#97—81no—
143C4×C8—42no—
144#95—21no—
145#95—21no—
146#95—21no—
147#95—21no—
148#95—21no—
149#95—21no—
150#95—41no—
151#95—41no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4C2×C22⋊C411yescharacteristic
159C22×C4C4×D411yescharacteristic
160C22×C4C4×D411yescharacteristic
161C22×C4#12011yescharacteristic
162C22×C4#12111yescharacteristic
163C22×C4#12111yescharacteristic
164C22×C4#12311yescharacteristic
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—42no—
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—81no—
185C2×C8—81no—
186C2×C8—81no—
187C2×C8—81no—
188C2×C8—81no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C4⋊C4—81no—
209C4⋊C4—81no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C4⋊C4#10112yes—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—41no—
220C42—41no—
221C42—41no—
222C42—41no—
223C42—41no—
224C42—41no—
225C42—41no—
226C42—41no—
227C23#38611yescharacteristic
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
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—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4C2×#10111yescharacteristic
265C2×C4#41311yescharacteristic
266C2×C4#45311yescharacteristic
267C2×C4#45411yescharacteristic
268C2×C4#47111yescharacteristic
269C2×C4#47311yescharacteristic
270C8—42no—
271C8—42no—
272C8—81no—
273C8—81no—
274C8—81no—
275C8—81no—
276C8—82no—
277C8—161no—
278C22#188111yescharacteristic
279C22#188311yescharacteristic
280C22#188411yescharacteristic
281C22#190111yescharacteristic
282C22#190611yescharacteristic
283C22#190811yescharacteristic
284C22#191211yescharacteristic
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—41no—
292C4—41no—
293C4—42no—
294C4—41no—
295C4—41no—
296C4—81no—
297C4—81no—
298C4—81no—
299C4—161no—
300C4—161no—
301C2#899711yescharacteristic
302C2#935111yescharacteristic
303C2#935811yescharacteristic
304C2#937411yescharacteristic
305C2#938211yescharacteristic
306C2#943111yescharacteristic
307C2#945011yescharacteristic
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
#291832
#223832
#96902
#77202
#76192
#70432
#70422