Finite Group Databasebeta

← #49131400

Subgroups — #49131400

Order 36224.

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#31827001C211yesmaximal, characteristic, complemented
2C2×D4×Dic283C211yesmaximal, characteristic, complemented
3#31826793C211yesmaximal, characteristic, complemented
4#31826779C211yesmaximal, characteristic, complemented
5#31826763C212yesmaximal, complemented
6#31826682C212yesmaximal, complemented
7#31826599C211yesmaximal, characteristic
8#31826574C212yesmaximal, complemented
9#31826566C212yesmaximal, complemented
10#31826519C211yesmaximal, characteristic, complemented
11#450×C283C211yesmaximal, characteristic, complemented
12C23×Dic283—21no—
13C2×#17985377C2212yes—
14#22583605—21no—
15#22583601C2211yescharacteristic, complemented
16#22583599C2211yescharacteristic, complemented
17#22583594—21no—
18#22583584C2211yescharacteristic
19Q8×Dic283C2211yescharacteristic, complemented
20D4×Dic283—21no—
21D4×Dic283—21no—
22D4×Dic283C2212yes—
23D4×Dic283C2212yes—
24#22583572C2211yescharacteristic, complemented
25(C22⋊D283)⋊C4—21no—
26#22583568—21no—
27C2×C4⋊Dic283C2211yescharacteristic
28C2×C22⋊Dic283—21no—
29C2×C4×Dic283C2211yescharacteristic
30#22583544C2212yescomplemented
31#22583541C2212yescomplemented
32Dic283⋊C8C2212yescomplemented
33#22583534C2212yescomplemented
34#22583532C2212yescomplemented
35#22583531C2212yes—
36C22⋊(C283⋊C8)C2211yescharacteristic
37#22583520C2212yescomplemented
38C22×D4×C283C2211yescharacteristic
39C2×SD16×C283C2212yes—
40C22⋊Q8×C283C2211yescharacteristic
41#102×C283C2212yes—
42C22⋊C8×C283C2211yescharacteristic
43C2×D1132C2311yescharacteristic
44C2×C22⋊D283—21no—
45C22×Dic283—22no—
46C22×Dic283—22no—
47C22×Dic283—21no—
48C22×Dic283—44no—
49C22×Dic283D411yescharacteristic
50C22×Dic283D411yescharacteristic
51C2×C4×D283—21no—
52#17985377—24no—
53C2×C283⋊C8C2312yes—
54C4⋊Dic283—21no—
55C4⋊Dic283—21no—
56C4⋊Dic283—21no—
57C4⋊Dic283C2312yes—
58C4⋊Dic283C2311yescharacteristic
59Dic283⋊C4—21no—
60C22⋊Dic283—22no—
61C22⋊Dic283—22no—
62(C2×D283)⋊C4—21no—
63(C2×D283)⋊C4—21no—
64(C2×D283)⋊C4—21no—
65(C2×D283)⋊C4—21no—
66C4×Dic283—21no—
67C4×Dic283D411yescharacteristic
68C4×Dic283D411yescharacteristic
69C4×Dic283C2311yescharacteristic
70C4×Dic283C2311yescharacteristic
71C24×C283—21no—
72C2×Q8×C283C2311yescharacteristic
73C2×D4×C283—24no—
74C2×D4×C283—21no—
75C2×D4×C283C2312yes—
76C22×C4×C283C2311yescharacteristic
77SD16×C283—24no—
78C2×C8×C283C2312yes—
79C4⋊C4×C283—21no—
80C4⋊C4×C283C2311yescharacteristic
81C22⋊C4×C283—21no—
82C22×D283—21no—
83D1132—22no—
84C22⋊D283—42no—
85C2×Dic283—22no—
86C2×Dic283—21no—
87C2×Dic283—22no—
88C2×Dic283—41no—
89C2×Dic283—44no—
90C2×Dic283—44no—
91C2×Dic283—42no—
92C2×Dic283C2×D411yescharacteristic
93C2×Dic283C2×D411yescharacteristic
94C2×Dic283C2×D411yescharacteristic
95C2×Dic283C2×D411yescharacteristic
96C4×D283—42no—
97C283⋊C8—22no—
98C23×C283—24no—
99C23×C283—22no—
100C23×C283—42no—
101C23×C283—42no—
102C23×C283C2×D411yescharacteristic
103Q8×C283—22no—
104D4×C283—24no—
105D4×C283—22no—
106D4×C283#4114yes—
107C2×C4×C283—22no—
108C2×C4×C283—21no—
109C2×C4×C283—21no—
110C2×C4×C283C2×D411yescharacteristic
111C2×C4×C283C2411yescharacteristic
112C8×C283—22no—
113C22×C283—21no—
114C22×C283—21no—
115C22×C283—24no—
116C22×C283—48no—
117C22×C283—42no—
118C22×C283—42no—
119C22×C283AGL(1,ℤ/8)12yes—
120C22×C283C22×D411yescharacteristic
121C2×D283—41no—
122C2×D283—41no—
123C2×D283—41no—
124C4×C283—21no—
125C4×C283—41no—
126C4×C283—41no—
127C4×C283C2×#4112yes—
128Dic283—21no—
129Dic283—21no—
130Dic283—21no—
131Dic283—21no—
132Dic283—42no—
133Dic283—41no—
134C2×C283—22no—
135C2×C283—44no—
136C2×C283#52511yescharacteristic
137C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C283#57511yescharacteristic
139D283—81no—
140C283#311411yescharacteristic, complemented, Sylow
141#3114—2831nomaximal, Sylow
142#529—2831no—
143C2×C4×D4—2831no—
144#483—2831no—
145#480—2831no—
146#478—2832no—
147#463—2832no—
148#450D28311yescharacteristic, complemented
149#447—2831no—
150#442—2832no—
151#440—2832no—
152#432—2831no—
153C22×D4C2×D28311yescharacteristic
154C23×C4—5661no—
155C2×SD16C2×D28312yes—
156C2×D8—2832no—
157#126—5661no—
158#125—2831no—
159#124—2831no—
160#123—5661no—
161C22⋊Q8C2×D28311yescharacteristic
162#121—2831no—
163C4×Q8—2831no—
164C4×D4—2832no—
165C4×D4—2832no—
166C4×D4—2831no—
167C4×D4—5661no—
168C4×D4—5661no—
169C4×D4—5661no—
170#117—5661no—
171C2×C4⋊C4—2831no—
172C2×C22⋊C4—5661no—
173C2×C42—2831no—
174#107—2832no—
175#106—2832no—
176C4⋊C8—2832no—
177#103—2832no—
178#102—2832no—
179#102—2832no—
180#102C2×D28312yes—
181C22⋊C8—2831no—
182C22⋊C8C2×D28311yescharacteristic
183#97—2832no—
184C24—21no—
185C2×Q8C22×D28311yescharacteristic
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—2831no—
189C2×D4—5661no—
190C2×D4C22×D28312yes—
191C22×C4—2831no—
192C22×C4—2831no—
193C22×C4—5661no—
194C22×C4—5662no—
195C22×C4—5662no—
196C22×C4—5661no—
197C22×C4—11324no—
198C22×C4C22×D28311yescharacteristic
199SD16—24no—
200D8—5664no—
201C2×C8—2832no—
202C2×C8C22×D28312yes—
203C4⋊C4—21no—
204C4⋊C4—2831no—
205C4⋊C4—2832no—
206C4⋊C4—5661no—
207C4⋊C4—5661no—
208C4⋊C4—5661no—
209C4⋊C4—5661no—
210C4⋊C4C22×D28311yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—5661no—
213C22⋊C4—5661no—
214C22⋊C4—5661no—
215C22⋊C4—5662no—
216C22⋊C4—5662no—
217C22⋊C4—5661no—
218C42—2831no—
219C42—2831no—
220C42—2831no—
221C42—2831no—
222C42—5661no—
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—5661no—
228C23D4×D28311yescharacteristic
229Q8—22no—
230D4—24no—
231D4—22no—
232D4—5662no—
233D4—11322no—
234D4#1798539114yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—2831no—
239C2×C4—2831no—
240C2×C4—2831no—
241C2×C4—2831no—
242C2×C4—5662no—
243C2×C4—5661no—
244C2×C4—5662no—
245C2×C4—11322no—
246C2×C4—11321no—
247C2×C4—11324no—
248C2×C4—11324no—
249C2×C4—11322no—
250C2×C4D4×D28311yescharacteristic
251C2×C4C23×D28311yescharacteristic
252C8—22no—
253C8—5662no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—11321no—
261C22—11321no—
262C22—11321no—
263C22#2258363712yes—
264C22C2×D4×D28311yescharacteristic
265C4—21no—
266C4—41no—
267C4—41no—
268C4—5661no—
269C4—5661no—
270C4—5661no—
271C4—5661no—
272C4—11322no—
273C4—11321no—
274C4C2×#1798539112yes—
275C2—22no—
276C2—44no—
277C2—22641no—
278C2#3182697111yescharacteristic
279C2C2×#2258363711yescharacteristic
280C2#3182726111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#450×C283C2
socleC22×C283C22×D4
prime radical#31826599C2
hypercenter#450D283
hypocenterC283#3114
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #31827001C2semidirect
2. C2×D4×Dic283C2semidirect
3. #31826793C2semidirect
4. #31826779C2semidirect
5. #31826763C2semidirect
6. #31826682C2semidirect
8. #31826574C2semidirect
9. #31826566C2semidirect
10. #31826519C2semidirect
11. #450×C283C2semidirect
15. #22583601C22semidirect
16. #22583599C22semidirect
19. Q8×Dic283C22semidirect
24. #22583572C22semidirect
30. #22583544C22semidirect
31. #22583541C22semidirect
32. Dic283⋊C8C22semidirect
33. #22583534C22semidirect
34. #22583532C22semidirect
37. #22583520C22semidirect
140. C283#3114semidirect
148. #450D283semidirect

Maximal subgroups

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

subgroupindex
#318270012
C2×D4×Dic2832
#318267932
#318267792
#318267632
#318266822
#318265992
#318265742
#318265662
#318265192
#450×C2832
#3114283