Finite Group Databasebeta

← #105156

Subgroups — #105156

Order 512.

334 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 84 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#28723C211yesmaximal, characteristic
2#9900C211yesmaximal, characteristic
3#9605C211yesmaximal, characteristic
4#8589C211yesmaximal, characteristic
5#7660C211yesmaximal, characteristic
6#7570C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8C2×#491—21no—
9#2859C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2072—21no—
12#2072—21no—
13#1992—21no—
14#1842C2211yescharacteristic
15#1831C2211yescharacteristic
16#1805—21no—
17#1805—21no—
18#1767C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20C4×C4⋊C8C2211yescharacteristic
21C2×#334—21no—
22C2×#332—21no—
23#1296—21no—
24#1296—21no—
25#1296—21no—
26#1277—21no—
27#1271—21no—
28#1271—21no—
29#1271—21no—
30#1271—21no—
31C2×C4⋊Q8D411yescharacteristic
32C2×#125—21no—
33C2×C4×Q8—21no—
34#491—42no—
35#491—42no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8D411yescharacteristic
43C2×C4⋊C8D411yescharacteristic
44C2×#103—21no—
45C2×#103—21no—
46C2×#103—21no—
47C2×#103—21no—
48C2×#97—21no—
49C2×C4×C8—21no—
50C2×C4×C8—21no—
51#391—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#384D411yescharacteristic
59#384D411yescharacteristic
60#384D411yescharacteristic
61#382—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C43C2311yescharacteristic
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#336D411yescharacteristic
74#336D411yescharacteristic
75#334—42no—
76#332—42no—
77C22×Q8—21no—
78C22×C8—21no—
79C22×C8—21no—
80C22×C8—21no—
81C22×C8—21no—
82C22×C8—41no—
83C22×C8—41no—
84C22×C8—41no—
85C4⋊Q8—21no—
86C4⋊Q8—21no—
87C4⋊Q8—21no—
88C4⋊Q8SD1612yes—
89#125—41no—
90#125—41no—
91#125—41no—
92#125—41no—
93C4×Q8—41no—
94C4×Q8—41no—
95C4×Q8—41no—
96C4×Q8—41no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
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—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C42—41no—
112C2×C42C2×D411yescharacteristic
113C2×C42C2×D411yescharacteristic
114C2×C42C2×D411yescharacteristic
115C2×C42C2×D411yescharacteristic
116C2×C42#4111yescharacteristic
117C2×C42#4111yescharacteristic
118C2×C42#4111yescharacteristic
119C4⋊C8—22no—
120C4⋊C8—21no—
121C4⋊C8—21no—
122C4⋊C8—21no—
123C4⋊C8—21no—
124C4⋊C8—41no—
125C4⋊C8—42no—
126C4⋊C8—42no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133#103—42no—
134#103—42no—
135#103—42no—
136#103—42no—
137#97—41no—
138#97—41no—
139C4×C8—41no—
140C4×C8—41no—
141C4×C8—81no—
142#95—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146C2×Q8—22no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—41no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4#12011yescharacteristic
157C22×C4#12111yescharacteristic
158C22×C4#12111yescharacteristic
159C22×C4#12111yescharacteristic
160C22×C4#12311yescharacteristic
161C22×C4#12311yescharacteristic
162C22×C4#12411yescharacteristic
163C2×C8—22no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—42no—
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—81no—
177C2×C8—81no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C2×C8—81no—
182C2×C8—81no—
183C2×C8—81no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—81no—
197C4⋊C4—81no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C4⋊C4—81no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C4⋊C4—81no—
206C4⋊C4—81no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—41no—
212C42—41no—
213C42—41no—
214C42—81no—
215C42—81no—
216C42C2×SD1611yescharacteristic
217C42#13511yescharacteristic
218C42#13511yescharacteristic
219C42#13511yescharacteristic
220C42AGL(1,ℤ/8)11yescharacteristic
221C42AGL(1,ℤ/8)11yescharacteristic
222C42AGL(1,ℤ/8)11yescharacteristic
223C42#13711yescharacteristic
224C23#39411yescharacteristic
225Q8—42no—
226Q8—42no—
227Q8—81no—
228Q8—81no—
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—42no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4#44911yescharacteristic
255C2×C4#44911yescharacteristic
256C2×C4#45011yescharacteristic
257C2×C4#45211yescharacteristic
258C2×C4#45411yescharacteristic
259C2×C4#45611yescharacteristic
260C2×C4#46311yescharacteristic
261C2×C4#46411yescharacteristic
262C2×C4#46511yescharacteristic
263C2×C4#46911yescharacteristic
264C2×C4#47111yescharacteristic
265C2×C4#47311yescharacteristic
266C2×C4#48111yescharacteristic
267C2×C4#48211yescharacteristic
268C2×C4#48811yescharacteristic
269C2×C4#48911yescharacteristic
270C8—42no—
271C8—81no—
272C8—82no—
273C8—81no—
274C8—81no—
275C8—161no—
276C8—161no—
277C22#203411yescharacteristic
278C22#203811yescharacteristic
279C22#204211yescharacteristic
280C22#204911yescharacteristic
281C22#205011yescharacteristic
282C22#205211yescharacteristic
283C22#205311yescharacteristic
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—41no—
295C4—82no—
296C4—161no—
297C4—161no—
298C4—161no—
299C4#162811yescharacteristic
300C4#163511yescharacteristic
301C4#165011yescharacteristic
302C4#165411yescharacteristic
303C2#1041711yescharacteristic
304C2#1045911yescharacteristic
305C2#1046711yescharacteristic
306C2#1049911yescharacteristic
307C2#1051111yescharacteristic
308C2#1054711yescharacteristic
309C2#1055411yescharacteristic
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
#287232
#99002
#96052
#85892
#76602
#75702
#70222