Finite Group Databasebeta

← #101866

Subgroups — #101866

Order 512.

545 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 545 conjugacy classes of subgroups — too many to draw. Only its 100 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#27905C211yesmaximal, characteristic
2#14424C211yesmaximal, characteristic
3#9911C212yesmaximal
4#8723C211yesmaximal, characteristic
5#7024C212yesmaximal
6C2×#483—21no—
7C2×#483—21no—
8#2857C2211yescharacteristic
9C2×#387—22no—
10C2×#384C2211yescharacteristic
11#2096—22no—
12#1956C412yescomplemented
13#1844C412yescomplemented
14#1797C2212yes—
15C4×C22⋊C8C2211yescharacteristic
16#1445—22no—
17#1441—21no—
18#1436—21no—
19#1434C2212yes—
20#1296—22no—
21#1294—22no—
22#1294—22no—
23C2×C4⋊Q8C2×C411yescharacteristic
24C2×C22⋊Q8—21no—
25C22×C4⋊C4—22no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4D411yescharacteristic
28C22×C4⋊C4D411yescharacteristic
29C22×C42—21no—
30C22×C42C2311yescharacteristic
31#483—42no—
32#483—42no—
33#483—42no—
34#483—42no—
35C2×#106—22no—
36C2×#106—22no—
37C2×C4⋊C8—22no—
38C2×#103—22no—
39C2×#103—22no—
40C2×C22⋊C8—21no—
41C2×C22⋊C8—22no—
42C2×C4×C8C2×C412yes—
43#391—21no—
44#389—22no—
45#387—44no—
46#387—44no—
47#384—22no—
48#384C2×C411yescharacteristic
49#384C2×C412yes—
50#384D412yes—
51#380—22no—
52C2×#95—22no—
53C2×#95—22no—
54C2×#95—22no—
55C2×#95—22no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95D412yes—
59C2×#95D412yes—
60#336—21no—
61#336—22no—
62C22×Q8—21no—
63C23×C4—21no—
64C23×C4—21no—
65C23×C4—22no—
66C23×C4—22no—
67C23×C4C2×D411yescharacteristic
68C23×C4C2×D412yes—
69C22×C8—22no—
70C22×C8—42no—
71C4⋊Q8—42no—
72C22⋊Q8—41no—
73C22⋊Q8—41no—
74C22⋊Q8—41no—
75C22⋊Q8—41no—
76C2×C4⋊C4—24no—
77C2×C4⋊C4—24no—
78C2×C4⋊C4—21no—
79C2×C4⋊C4—21no—
80C2×C4⋊C4—21no—
81C2×C4⋊C4—22no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—42no—
84C2×C4⋊C4—42no—
85C2×C4⋊C4—42no—
86C2×C4⋊C4—42no—
87C2×C4⋊C4—41no—
88C2×C4⋊C4—41no—
89C2×C4⋊C4—41no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4—44no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—81no—
94C2×C4⋊C4C22⋊C412yes—
95C2×C4⋊C4C22⋊C412yes—
96C2×C22⋊C4—41no—
97C2×C42—42no—
98C2×C42—44no—
99C2×C42—81no—
100C2×C42C22×C411yescharacteristic
101C2×C42C2×D411yescharacteristic
102C2×C42#4112yes—
103#106—44no—
104#106—44no—
105C4⋊C8—44no—
106#103—44no—
107#103—44no—
108C22⋊C8—22no—
109C22⋊C8—22no—
110C22⋊C8—42no—
111C22⋊C8—42no—
112C4×C8—42no—
113#95—22no—
114#95—22no—
115#95—22no—
116#95—44no—
117#95—44no—
118#95—44no—
119#95—42no—
120#95—42no—
121#95—42no—
122#95—81no—
123#95—81no—
124#95SD1614yes—
125C24#12011yescharacteristic
126C2×Q8—41no—
127C2×Q8—41no—
128C2×Q8—42no—
129C2×Q8—42no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—24no—
136C22×C4—42no—
137C22×C4—42no—
138C22×C4—41no—
139C22×C4—42no—
140C22×C4—42no—
141C22×C4—42no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—42no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—42no—
152C22×C4—41no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4C2×C22⋊C411yescharacteristic
163C22×C4C4×D412yes—
164C22×C4#12112yes—
165C22×C4#12311yescharacteristic
166C22×C4C2×SD1612yes—
167C22×C4#13512yes—
168C22×C4AGL(1,ℤ/8)12yes—
169C22×C4#13712yes—
170C2×C8—24no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—82no—
174C2×C8—82no—
175C2×C8—82no—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—44no—
181C4⋊C4—44no—
182C4⋊C4—44no—
183C4⋊C4—44no—
184C4⋊C4—81no—
185C4⋊C4—81no—
186C4⋊C4—82no—
187C4⋊C4—82no—
188C4⋊C4—81no—
189C4⋊C4—81no—
190C4⋊C4—84no—
191C22⋊C4—81no—
192C22⋊C4—81no—
193C42—22no—
194C42—22no—
195C42—42no—
196C42—84no—
197C23—21no—
198C23—22no—
199C23—21no—
200C23#38611yescharacteristic
201C23#45012yes—
202C23#45212yes—
203C23#45311yescharacteristic
204C23#45311yescharacteristic
205Q8—82no—
206Q8—82no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—44no—
223C2×C4—44no—
224C2×C4—44no—
225C2×C4—44no—
226C2×C4—44no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—82no—
230C2×C4—82no—
231C2×C4—82no—
232C2×C4—82no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4—82no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—82no—
241C2×C4—82no—
242C2×C4—82no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—82no—
250C2×C4—81no—
251C2×C4#41012yes—
252C2×C4C4×SD1612yes—
253C2×C4#44012yes—
254C2×C4#46112yes—
255C2×C4#46312yes—
256C8—44no—
257C8—162no—
258C22—22no—
259C22—22no—
260C22—22no—
261C22—22no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22#162911yescharacteristic
267C22#163011yescharacteristic
268C22#163112yes—
269C22#187712yes—
270C22#188711yescharacteristic
271C22#189911yescharacteristic
272C22#190512yes—
273C22#191211yescharacteristic
274C4—22no—
275C4—22no—
276C4—22no—
277C4—22no—
278C4—22no—
279C4—41no—
280C4—84no—
281C4—82no—
282C4—82no—
283C4—162no—
284C4—161no—
285C4—161no—
286C2—21no—
287C2—22no—
288C2—21no—
289C2#906411yescharacteristic
290C2#925612yes—
291C2#929612yes—
292C2#942911yescharacteristic
293C2#946411yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#120
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
12. #1956C4semidirect
13. #1844C4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#279052
#144242
#99112
#87232
#70242