Finite Group Databasebeta

← #46821018

Subgroups — #46821018

Order 34432.

450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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#31771136C211yesmaximal, characteristic, complemented
2C2×D4×Dic269C211yesmaximal, characteristic, complemented
3#31770936C211yesmaximal, characteristic, complemented
4#31770916C211yesmaximal, characteristic, complemented
5#31770907C212yesmaximal, complemented
6#31770818C212yesmaximal, complemented
7#31770756C211yesmaximal, characteristic, complemented
8#31770717C212yesmaximal, complemented
9#31770702C212yesmaximal, complemented
10#31770659C211yesmaximal, characteristic, complemented
11#447×C269C211yesmaximal, characteristic
12C23×Dic269—21no—
13C2×#16864390C2212yes—
14#22575446—21no—
15#22575444C2211yescharacteristic, complemented
16#22575440C2211yescharacteristic, complemented
17#22575434—21no—
18#22575432C2211yescharacteristic
19#22575418C2211yescharacteristic, complemented
20D4×Dic269—21no—
21D4×Dic269—21no—
22D4×Dic269—21no—
23D4×Dic269C2212yes—
24D4×Dic269C2212yes—
25D4×Dic269C2211yescharacteristic, complemented
26#22575409—21no—
27C2×C4⋊Dic269C2211yescharacteristic
28C2×C22⋊Dic269—21no—
29C2×C4×Dic269C2211yescharacteristic
30#22575386C2212yescomplemented
31#22575385C2212yescomplemented
32#22575382C2212yescomplemented
33#22575378C2212yescomplemented
34#22575374C2212yes—
35#22575374C2212yescomplemented
36C22⋊#14524130C2211yescharacteristic
37#22575363C2212yescomplemented
38C22×D4×C269C2211yescharacteristic
39C2×D8×C269C2212yes—
40#121×C269C2211yescharacteristic
41#102×C269C2212yes—
42C22⋊C8×C269C2211yescharacteristic
43C2×Dic538C2311yescharacteristic
44C22×Dic269—21no—
45C22×Dic269—22no—
46C22×Dic269—22no—
47C22×Dic269—21no—
48C22×Dic269—44no—
49C22×Dic269D411yescharacteristic
50C22×Dic269D411yescharacteristic
51#16864390—24no—
52C2×#14524130C2312yes—
53C4⋊Dic269—21no—
54C4⋊Dic269—21no—
55C4⋊Dic269C2311yescharacteristic
56C4⋊Dic269C2312yes—
57#16864381—21no—
58#16864381—21no—
59#16864381—21no—
60C22⋊Dic269—22no—
61C22⋊Dic269—22no—
62C22⋊Dic269—21no—
63C22⋊Dic269—21no—
64C22⋊Dic269—21no—
65C22⋊Dic269—21no—
66C4×Dic269—21no—
67C4×Dic269D411yescharacteristic
68C4×Dic269D411yescharacteristic
69C4×Dic269C2311yescharacteristic
70C4×Dic269C2311yescharacteristic
71C24×C269—21no—
72C2×D4×C269—24no—
73C2×D4×C269—21no—
74C2×D4×C269—21no—
75C2×D4×C269C2311yescharacteristic
76C2×D4×C269C2312yes—
77C22×C4×C269C2311yescharacteristic
78D8×C269—24no—
79C2×C8×C269C2312yes—
80C4⋊C4×C269C2311yescharacteristic
81C22⋊C4×C269—21no—
82Dic538—22no—
83C2×Dic269—22no—
84C2×Dic269—21no—
85C2×Dic269—21no—
86C2×Dic269—22no—
87C2×Dic269—41no—
88C2×Dic269—42no—
89C2×Dic269—44no—
90C2×Dic269—44no—
91C2×Dic269—42no—
92C2×Dic269C2×D411yescharacteristic
93C2×Dic269C2×D411yescharacteristic
94C2×Dic269C2×D411yescharacteristic
95C2×Dic269C2×D411yescharacteristic
96#14524130—22no—
97C23×C269—24no—
98C23×C269—22no—
99C23×C269—21no—
100C23×C269—42no—
101C23×C269—42no—
102C23×C269C2×D411yescharacteristic
103D4×C269—24no—
104D4×C269—22no—
105D4×C269—22no—
106D4×C269—42no—
107D4×C269#4114yes—
108C2×C4×C269—22no—
109C2×C4×C269—21no—
110C2×C4×C269C2×D411yescharacteristic
111C2×C4×C269C2411yescharacteristic
112C8×C269—22no—
113C22×C269—21no—
114C22×C269—21no—
115C22×C269—24no—
116C22×C269—48no—
117C22×C269—42no—
118C22×C269—42no—
119C22×C269—41no—
120C22×C269—41no—
121C22×C269—41no—
122C22×C269AGL(1,ℤ/8)12yes—
123C22×C269C22×D411yescharacteristic
124C4×C269—21no—
125C4×C269—41no—
126C4×C269C2×#4112yes—
127Dic269—21no—
128Dic269—21no—
129Dic269—21no—
130Dic269—21no—
131Dic269—41no—
132Dic269—42no—
133Dic269—41no—
134C2×C269—22no—
135C2×C269—44no—
136C2×C269—81no—
137C2×C269#52511yescharacteristic
138C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
139C2×C269#57511yescharacteristic
140C269#311411yescharacteristic, complemented, Sylow
141#3114—2691nomaximal, Sylow
142#529—2691no—
143C2×C4×D4—2691no—
144#483—2691no—
145#480—2691no—
146#478—2692no—
147#463—2692no—
148#450—2691no—
149#447D26911yescharacteristic
150#442—2692no—
151#440—2692no—
152#432—2691no—
153C22×D4C2×D26911yescharacteristic
154C23×C4—5381no—
155C2×SD16—2692no—
156C2×D8C2×D26912yes—
157#126—5381no—
158#125—2691no—
159#124—2691no—
160#123—5381no—
161C22⋊Q8—2691no—
162#121C2×D26911yescharacteristic
163C4×Q8—2691no—
164C4×D4—2692no—
165C4×D4—2692no—
166C4×D4—2691no—
167C4×D4—5381no—
168C4×D4—5381no—
169C4×D4—5381no—
170#117—5381no—
171C2×C4⋊C4—2691no—
172C2×C22⋊C4—5381no—
173C2×C42—2691no—
174#107—2692no—
175#106—2692no—
176C4⋊C8—2692no—
177#103—2692no—
178#102—2692no—
179#102—2692no—
180#102C2×D26912yes—
181C22⋊C8—2691no—
182C22⋊C8C2×D26911yescharacteristic
183#97—2692no—
184C24—21no—
185C2×Q8—2691no—
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4C22×D26911yescharacteristic
190C2×D4C22×D26912yes—
191C22×C4—2691no—
192C22×C4—2691no—
193C22×C4—5381no—
194C22×C4—5382no—
195C22×C4—5382no—
196C22×C4—5381no—
197C22×C4—10764no—
198C22×C4C22×D26911yescharacteristic
199SD16—5384no—
200D8—24no—
201C2×C8—2692no—
202C2×C8C22×D26912yes—
203C4⋊C4—2691no—
204C4⋊C4—2692no—
205C4⋊C4—5381no—
206C4⋊C4—5381no—
207C4⋊C4—5381no—
208C4⋊C4—5381no—
209C4⋊C4—5381no—
210C4⋊C4C22×D26911yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—5382no—
213C22⋊C4—5382no—
214C22⋊C4—5381no—
215C22⋊C4—5381no—
216C22⋊C4—5381no—
217C22⋊C4—5381no—
218C42—2691no—
219C42—2691no—
220C42—2691no—
221C42—2691no—
222C42—5381no—
223C23—24no—
224C23—22no—
225C23—21no—
226C23—42no—
227C23—42no—
228C23D4×D26911yescharacteristic
229Q8—5382no—
230D4—24no—
231D4—22no—
232D4—22no—
233D4—42no—
234D4#1686440114yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—2691no—
238C2×C4—2691no—
239C2×C4—2691no—
240C2×C4—2691no—
241C2×C4—5382no—
242C2×C4—5381no—
243C2×C4—5381no—
244C2×C4—5382no—
245C2×C4—10761no—
246C2×C4—10764no—
247C2×C4—10764no—
248C2×C4—10762no—
249C2×C4—10762no—
250C2×C4D4×D26911yescharacteristic
251C2×C4C23×D26911yescharacteristic
252C8—22no—
253C8—5382no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22#2257547712yes—
264C22C2×D4×D26911yescharacteristic
265C4—21no—
266C4—41no—
267C4—5381no—
268C4—5381no—
269C4—5381no—
270C4—5381no—
271C4—10761no—
272C4—10761no—
273C4—10762no—
274C4C2×#1686440112yes—
275C2—22no—
276C2—44no—
277C2—81no—
278C2#3177111111yescharacteristic
279C2C2×#2257547711yescharacteristic
280C2#3177140111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting, prime radical#447×C269C2
socleC22×C269C22×D4
hypercenter#447D269
hypocenterC269#3114
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #31771136C2semidirect
2. C2×D4×Dic269C2semidirect
3. #31770936C2semidirect
4. #31770916C2semidirect
5. #31770907C2semidirect
6. #31770818C2semidirect
7. #31770756C2semidirect
8. #31770717C2semidirect
9. #31770702C2semidirect
10. #31770659C2semidirect
15. #22575444C22semidirect
16. #22575440C22semidirect
19. #22575418C22semidirect
25. D4×Dic269C22semidirect
30. #22575386C22semidirect
31. #22575385C22semidirect
32. #22575382C22semidirect
33. #22575378C22semidirect
35. #22575374C22semidirect
37. #22575363C22semidirect
140. C269#3114semidirect

Maximal subgroups

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

subgroupindex
#317711362
C2×D4×Dic2692
#317709362
#317709162
#317709072
#317708182
#317707562
#317707172
#317707022
#317706592
#447×C2692
#3114269