Finite Group Databasebeta

← #100913

Subgroups — #100913

Order 512.

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

normal subgroups only

This group has 337 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#28695C211yesmaximal, characteristic
2#23265C211yesmaximal, characteristic
3#7702C211yesmaximal, characteristic
4#7702C211yesmaximal, characteristic
5#7650C211yesmaximal, characteristic
6#7043C211yesmaximal, characteristic
7#7043C211yesmaximal, characteristic
8C2×#501C411yescharacteristic
9C2×#501C411yescharacteristic
10#2862C2211yescharacteristic
11C4×#125C2211yescharacteristic
12#2085—21no—
13#2085—21no—
14#1993C411yescharacteristic
15#1993C411yescharacteristic
16#1949—21no—
17#1949—21no—
18#1917—21no—
19#1917—21no—
20#1917—21no—
21#1916—21no—
22#1839C2211yescharacteristic
23#1839C2211yescharacteristic
24#1771—21no—
25#1770—21no—
26#1767C2211yescharacteristic
27#1745C2211yescharacteristic
28#1745C2211yescharacteristic
29#1272—21no—
30#1272—21no—
31#1272—21no—
32#1272—21no—
33#1271—21no—
34#1271—21no—
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×C4⋊Q8C2×C411yescharacteristic
37C2×#125C2×C411yescharacteristic
38#501—42no—
39#501—42no—
40C2×#107—21no—
41C2×#107—21no—
42C2×#106—21no—
43C2×#106—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×#97—21no—
48C2×#97—21no—
49C2×#97—21no—
50C2×#97C2×C411yescharacteristic
51C2×#97C2×C411yescharacteristic
52C2×C4×C8—21no—
53#391—21no—
54#391—21no—
55#391—21no—
56#391—21no—
57#389D411yescharacteristic
58#389D411yescharacteristic
59#387—21no—
60#387—21no—
61#382—21no—
62#382—21no—
63#382C2×C411yescharacteristic
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4D411yescharacteristic
67C4×C4⋊C4D411yescharacteristic
68C43C2311yescharacteristic
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#336—21no—
85#336—21no—
86#336D411yescharacteristic
87#336D411yescharacteristic
88#336D411yescharacteristic
89#336D411yescharacteristic
90C22×Q8—21no—
91C22×Q8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—41no—
99C22×C8—41no—
100C4⋊Q8—41no—
101C4⋊Q8—41no—
102C4⋊Q8—41no—
103C4⋊Q8—41no—
104#125—22no—
105#125—41no—
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⋊C4C22⋊C411yescharacteristic
115C2×C4⋊C4C22⋊C411yescharacteristic
116C2×C4⋊C4C22⋊C411yescharacteristic
117C2×C4⋊C4C22⋊C411yescharacteristic
118C2×C42—21no—
119C2×C42—21no—
120C2×C42C22×C411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42#4111yescharacteristic
126C2×C42#4111yescharacteristic
127#107—42no—
128#107—42no—
129#106—42no—
130#106—42no—
131C4⋊C8—22no—
132C4⋊C8—22no—
133C4⋊C8—42no—
134C4⋊C8—42no—
135#97—41no—
136#97—41no—
137#97—42no—
138#97—42no—
139#97—42no—
140C4×C8—42no—
141#95—21no—
142#95—21no—
143#95—21no—
144#95—21no—
145#95—21no—
146#95—21no—
147#95—41no—
148#95—41no—
149#95—41no—
150#95—41no—
151C2×Q8—42no—
152C2×Q8—42no—
153C2×Q8—81no—
154C2×Q8—81no—
155C2×Q8—81no—
156C2×Q8—81no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4C2×C22⋊C411yescharacteristic
164C22×C4C4×D411yescharacteristic
165C22×C4C4×D411yescharacteristic
166C22×C4#12011yescharacteristic
167C22×C4#12111yescharacteristic
168C22×C4#12111yescharacteristic
169C22×C4#12311yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—22no—
173C2×C8—22no—
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—41no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—81no—
189C2×C8—81no—
190C2×C8—81no—
191C2×C8—81no—
192C2×C8—81no—
193C2×C8—81no—
194C4⋊C4—21no—
195C4⋊C4—21no—
196C4⋊C4—21no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—81no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C4⋊C4—81no—
209C4⋊C4#10012yes—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—41no—
215C42—41no—
216C42—41no—
217C42—41no—
218C42—41no—
219C42—41no—
220C42—41no—
221C42—41no—
222C42—41no—
223C23#38611yescharacteristic
224Q8—162no—
225Q8—162no—
226C2×C4—21no—
227C2×C4—21no—
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—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—41no—
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—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4C2×#10011yescharacteristic
264C2×C4#41311yescharacteristic
265C2×C4#45611yescharacteristic
266C2×C4#45611yescharacteristic
267C8—42no—
268C8—42no—
269C8—42no—
270C8—42no—
271C8—81no—
272C8—81no—
273C8—161no—
274C8—161no—
275C22#188111yescharacteristic
276C22#188111yescharacteristic
277C22#188611yescharacteristic
278C22#190011yescharacteristic
279C22#190611yescharacteristic
280C22#190611yescharacteristic
281C22#190911yescharacteristic
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—41no—
287C4—41no—
288C4—42no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—81no—
293C4—81no—
294C4—81no—
295C4—161no—
296C4—161no—
297C2#900611yescharacteristic
298C2#934911yescharacteristic
299C2#935011yescharacteristic
300C2#936911yescharacteristic
301C2#936911yescharacteristic
302C2#944011yescharacteristic
303C2#945211yescharacteristic
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
#286952
#232652
#77022
#76502
#70432