Finite Group Databasebeta

← #483×D283 #49131135

Subgroups — #483×D283 #49131135

Order 36224.

460 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C22⋊Q8×D283C211yesmaximal, characteristic
2C2×C4⋊C4×D283C211yesmaximal, characteristic
3#31826797C212yesmaximal, complemented
4#31826796C211yesmaximal, characteristic, complemented
5#31826795C211yesmaximal, characteristic, complemented
6#31826794C212yesmaximal, complemented
7#31826793C211yesmaximal, characteristic, complemented
8#106×D283C212yesmaximal, complemented
9#103×D283C212yesmaximal, complemented
10C22⋊C8×D283C211yesmaximal, characteristic
11#483×C283C211yesmaximal, characteristic, complemented
12C2×Q8×D283C2211yescharacteristic
13C22×C4×D283—21no—
14C22×C4×D283C2211yescharacteristic
15C2×C8×D283C2212yes—
16#22583590C2211yescharacteristic
17#22583589C2211yescharacteristic
18#22583588—21no—
19#22583587—21no—
20#22583586C2211yescharacteristic
21C2×C4⋊Dic283C2211yescharacteristic
22C2×Dic283⋊C4—21no—
23C4⋊C4×D283—21no—
24C4⋊C4×D283—21no—
25C4⋊C4×D283—21no—
26C4⋊C4×D283C2211yescharacteristic
27C4⋊C4×D283C2212yes—
28C4⋊C4×D283C2212yes—
29C22⋊C4×D283—21no—
30#22583542C2212yescomplemented
31#22583541C2212yescomplemented
32#22583541C2212yescomplemented
33#22583535C2212yescomplemented
34#22583534C2212yescomplemented
35#22583533C2212yescomplemented
36C22⋊(C283⋊C8)C2211yescharacteristic
37(C2×D283)⋊C8C2212yes—
38C22⋊Q8×C283C2211yescharacteristic
39C2×C4⋊C4×C283C2211yescharacteristic
40#106×C283C2212yescomplemented
41#103×C283C2212yescomplemented
42C22⋊C8×C283C2211yescharacteristic
43C23×D283D411yescharacteristic
44C2×Dic566—21no—
45C2×Dic566C2311yescharacteristic
46Q8×D283—24no—
47C22×Dic283—21no—
48C22×Dic283D411yescharacteristic
49C2×C4×D283—24no—
50C2×C4×D283—21no—
51C2×C4×D283—21no—
52C2×C4×D283—22no—
53C2×C4×D283—22no—
54C2×C4×D283—44no—
55C2×C4×D283D411yescharacteristic
56C2×C4×D283D411yescharacteristic
57C2×C4×D283C2311yescharacteristic
58C2×C4×D283C2311yescharacteristic
59C2×C283⋊C8C2312yes—
60C8×D283—24no—
61C4⋊Dic283—21no—
62C4⋊Dic283—21no—
63C4⋊Dic283C2312yes—
64C4⋊Dic283C2311yescharacteristic
65Dic283⋊C4—22no—
66Dic283⋊C4—22no—
67Dic283⋊C4—21no—
68Dic283⋊C4—21no—
69Dic283⋊C4—21no—
70C22⋊Dic283—21no—
71(C2×D283)⋊C4—21no—
72(C2×D283)⋊C4—21no—
73C2×Q8×C283C2311yescharacteristic
74C22×C4×C283—21no—
75C22×C4×C283C2311yescharacteristic
76C2×C8×C283C2312yes—
77C4⋊C4×C283—21no—
78C4⋊C4×C283—21no—
79C4⋊C4×C283C2312yes—
80C4⋊C4×C283C2311yescharacteristic
81C22⋊C4×C283—21no—
82C22×D283—22no—
83C22×D283—22no—
84C22×D283SD1614yes—
85C22×D283C2×D411yescharacteristic
86C22×D283C2×D411yescharacteristic
87Dic566—22no—
88Dic566—42no—
89C2×Dic283—22no—
90C2×Dic283—21no—
91C2×Dic283—21no—
92C2×Dic283—22no—
93C2×Dic283—42no—
94C2×Dic283C2×D411yescharacteristic
95C2×Dic283C2×D411yescharacteristic
96C4×D283—22no—
97C4×D283—22no—
98C4×D283—22no—
99C4×D283—42no—
100C4×D283—44no—
101C4×D283—44no—
102C4×D283—42no—
103C4×D283#4114yes—
104C283⋊C8—22no—
105C23×C283C2×D411yescharacteristic
106Q8×C283—22no—
107C2×C4×C283—22no—
108C2×C4×C283—21no—
109C2×C4×C283—21no—
110C2×C4×C283—22no—
111C2×C4×C283—42no—
112C2×C4×C283C2×D411yescharacteristic
113C2×C4×C283C2411yescharacteristic
114C8×C283—22no—
115C22×C283—21no—
116C22×C283—21no—
117C22×C283C2×SD1612yes—
118C22×C283C22×D411yescharacteristic
119C2×D283—21no—
120C2×D283—21no—
121C2×D283—28no—
122C2×D283#12312yes—
123C2×D283C2×SD1612yes—
124C2×D283C2×SD1612yes—
125C2×D283#13712yes—
126C4×C283—21no—
127C4×C283—41no—
128C4×C283—42no—
129C4×C283—41no—
130C4×C283C2×#4112yes—
131Dic283—21no—
132Dic283—41no—
133Dic283—42no—
134Dic283—41no—
135Dic283#12312yes—
136C2×C283—22no—
137C2×C283C2×#12311yescharacteristic
138C2×C283C22×SD1611yescharacteristic
139C2×C283C2×#13711yescharacteristic
140D283—22no—
141D283#48314yesdirect product factor
142C283C2×#48311yescharacteristic, complemented, Sylow
143C2×#483—2831nomaximal, Sylow
144C2×C22⋊Q8—2831no—
145C22×C4⋊C4—2831no—
146#483—2831no—
147#483—2831no—
148#483—2832no—
149#483—2832no—
150#483—2831no—
151#483D28311yescharacteristic, direct product factor
152C2×#106—2832no—
153C2×#103—2832no—
154C2×C22⋊C8—2831no—
155C22×Q8—2831no—
156C23×C4—2831no—
157C23×C4—5661no—
158C22×C8—2832no—
159C22⋊Q8—2831no—
160C22⋊Q8—2831no—
161C22⋊Q8—2831no—
162C22⋊Q8—5661no—
163C22⋊Q8—5661no—
164C22⋊Q8C2×D28311yescharacteristic
165C2×C4⋊C4—2831no—
166C2×C4⋊C4—2832no—
167C2×C4⋊C4—2832no—
168C2×C4⋊C4—2831no—
169C2×C4⋊C4—5661no—
170C2×C4⋊C4—5661no—
171C2×C4⋊C4—5661no—
172C2×C4⋊C4—5661no—
173C2×C4⋊C4C2×D28311yescharacteristic
174C2×C22⋊C4—5661no—
175#106—2832no—
176#106—2832no—
177#106—2832no—
178#106C2×D28312yescomplemented
179#103—2832no—
180#103—2832no—
181#103—2832no—
182#103C2×D28312yescomplemented
183C22⋊C8—2831no—
184C22⋊C8—2832no—
185C22⋊C8C2×D28311yescharacteristic
186C24—2831no—
187C2×Q8—2831no—
188C2×Q8—5661no—
189C2×Q8—5664no—
190C2×Q8C22×D28311yescharacteristic
191C22×C4—21no—
192C22×C4—2831no—
193C22×C4—2831no—
194C22×C4—2831no—
195C22×C4—2831no—
196C22×C4—2831no—
197C22×C4—5664no—
198C22×C4—5661no—
199C22×C4—5661no—
200C22×C4—5662no—
201C22×C4—5662no—
202C22×C4—5661no—
203C22×C4—11324no—
204C22×C4C22×D28311yescharacteristic
205C2×C8—2832no—
206C2×C8—5664no—
207C2×C8C22×D28312yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—2832no—
211C4⋊C4—2831no—
212C4⋊C4—5662no—
213C4⋊C4—5662no—
214C4⋊C4—5661no—
215C4⋊C4—5661no—
216C4⋊C4—5661no—
217C4⋊C4—5661no—
218C4⋊C4—5661no—
219C4⋊C4C22×D28312yes—
220C4⋊C4C22×D28311yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—5661no—
223C22⋊C4—5661no—
224C22⋊C4—5661no—
225C23—2831no—
226C23—2834no—
227C23—2831no—
228C23—5662no—
229C23—5662no—
230C23D4×D28311yescharacteristic
231Q8—22no—
232Q8—5662no—
233Q8—11322no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—2831no—
240C2×C4—2834no—
241C2×C4—2831no—
242C2×C4—5662no—
243C2×C4—5662no—
244C2×C4—5662no—
245C2×C4—5662no—
246C2×C4—5661no—
247C2×C4—5661no—
248C2×C4—5662no—
249C2×C4—11324no—
250C2×C4—11324no—
251C2×C4—11322no—
252C2×C4—11322no—
253C2×C4—11322no—
254C2×C4D4×D28311yescharacteristic
255C2×C4C23×D28311yescharacteristic
256C8—22no—
257C8—5662no—
258C22—21no—
259C22—21no—
260C22—2832no—
261C22—2832no—
262C22—2832no—
263C22—2832no—
264C22—5668no—
265C22—5661no—
266C22—5661no—
267C22SD16×D28312yes—
268C22C2×D4×D28311yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—2832no—
274C4—5661no—
275C4—11321no—
276C4—11322no—
277C4—11321no—
278C4#41×D28312yes—
279C2—22no—
280C2—2834no—
281C2—5662no—
282C2#123×D28311yescharacteristic
283C2C2×SD16×D28311yescharacteristic
284C2#137×D28311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#483×C283C2
socleC22×C283C22×D4
prime radicalC23×D283D4
hypercenter#483D283
hypocenterC283C2×#483
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #31826797C2semidirect
4. #31826796C2semidirect
5. #31826795C2semidirect
6. #31826794C2semidirect
7. #31826793C2semidirect
8. #106×D283C2semidirect
9. #103×D283C2semidirect
11. #483×C283C2semidirect
30. #22583542C22semidirect
31. #22583541C22semidirect
32. #22583541C22semidirect
33. #22583535C22semidirect
34. #22583534C22semidirect
35. #22583533C22semidirect
40. #106×C283C22semidirect
41. #103×C283C22semidirect
141. D283#483direct (N × H)
142. C283C2×#483semidirect
151. #483D283direct (N × H)
178. #106C2×D283semidirect
182. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D2832
C2×C4⋊C4×D2832
#318267972
#318267962
#318267952
#318267942
#318267932
#106×D2832
#103×D2832
C22⋊C8×D2832
#483×C2832
C2×#483283