Finite Group Databasebeta

← #496×D283 #49131691

Subgroups — #496×D283 #49131691

Order 36224.

668 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×SD16×D283C212yesmaximal, complemented
2C2×D8×D283C212yesmaximal, complemented
3#127×D283C211yesmaximal, characteristic, complemented
4#124×D283C211yesmaximal, characteristic, complemented
5#31826855C211yesmaximal, characteristic, complemented
6#31826854C211yesmaximal, characteristic, complemented
7#31826853C212yesmaximal, complemented
8#31826852C211yesmaximal, characteristic, complemented
9#31826851C212yesmaximal, complemented
10#97×D283C211yesmaximal, characteristic, complemented
11#496×C283C211yesmaximal, characteristic, complemented
12C2×Q8×D283C2211yescharacteristic
13C2×D4×D283—22no—
14C2×D4×D283C2211yescharacteristic
15C2×D4×D283C2212yes—
16C2×#17985381C2212yescomplemented
17C2×#17985380C2212yescomplemented
18C2×#17985379C2212yescomplemented
19SD16×D283—28no—
20C2×D2264C2212yescomplemented
21C2×#17985377C2212yescomplemented
22C2×#17985377C2212yescomplemented
23D8×D283—28no—
24C2×C8×D283C2212yes—
25#22583607C2211yescharacteristic, complemented
26#22583606—22no—
27#22583606C2212yescomplemented
28#22583599C2211yescharacteristic, complemented
29#22583598C2211yescharacteristic, complemented
30#22583597C2211yescharacteristic, complemented
31#22583596—22no—
32C22⋊C4×D283—22no—
33C42×D283C2211yescharacteristic
34#22583521C2211yescharacteristic, complemented
35#22583520C2212yescomplemented
36C2×SD16×C283C2212yescomplemented
37C2×D8×C283C2212yescomplemented
38#127×C283C2211yescharacteristic, complemented
39#124×C283C2211yescharacteristic, complemented
40#97×C283C2211yescharacteristic, complemented
41C23×D283—21no—
42C23×D283—22no—
43C2×Dic566—21no—
44C2×Dic566C2311yescharacteristic
45Q8×D283—24no—
46C2×D1132—22no—
47C2×D1132C2311yescharacteristic
48C2×D1132C2312yes—
49C2×C22⋊D283—21no—
50C2×C22⋊D283—22no—
51C2×C22⋊D283—24no—
52D4×D283—24no—
53D4×D283—24no—
54D4×D283—24no—
55D4×D283—48no—
56C2×C4×D283—21no—
57C2×C4×D283D412yes—
58C2×C4×D283C2311yescharacteristic
59#17985381—24no—
60#17985380—24no—
61#17985379—24no—
62D2264—24no—
63#17985377—24no—
64#17985377—24no—
65C2×C283⋊C8C2312yes—
66C8×D283D418yescomplemented
67C22⋊Dic283—22no—
68(C2×D283)⋊C4—22no—
69(C2×D283)⋊C4—22no—
70C4×Dic283D412yes—
71C4×Dic283C2311yescharacteristic
72C2×Q8×C283C2311yescharacteristic
73C2×D4×C283—22no—
74C2×D4×C283C2311yescharacteristic
75C2×D4×C283C2312yes—
76SD16×C283—24no—
77D8×C283—24no—
78C2×C8×C283C2312yes—
79C22⋊C4×C283—22no—
80C42×C283C2311yescharacteristic
81C22×D283—21no—
82C22×D283—22no—
83C22×D283—42no—
84C22×D283—44no—
85C22×D283—48no—
86C22×D283—44no—
87C22×D283C2×D411yescharacteristic
88Dic566—22no—
89Dic566—42no—
90D1132—22no—
91D1132—22no—
92D1132—22no—
93D1132—44no—
94C22⋊D283—48no—
95C22⋊D283—42no—
96C22⋊D283—44no—
97C2×Dic283—21no—
98C2×Dic283C2×D412yes—
99C2×Dic283C2×D411yescharacteristic
100C4×D283—24no—
101C4×D283—42no—
102C4×D283C2×D414yes—
103C283⋊C8C2×D414yescomplemented
104C23×C283—21no—
105C23×C283—22no—
106Q8×C283—22no—
107D4×C283—22no—
108D4×C283—22no—
109D4×C283—22no—
110D4×C283—44no—
111C2×C4×C283—21no—
112C2×C4×C283C2×D412yes—
113C2×C4×C283C2411yescharacteristic
114C8×C283C2×D414yescomplemented
115C22×C283—41no—
116C22×C283—42no—
117C22×C283—44no—
118C22×C283—42no—
119C22×C283C22×D411yescharacteristic
120C2×D283—41no—
121C2×D283—42no—
122C2×D283—44no—
123C2×D283—42no—
124C2×D283—88no—
125C2×D283—84no—
126C2×D283#12712yes—
127C2×D283AGL(1,ℤ/8)14yes—
128C4×C283—22no—
129C4×C283—41no—
130C4×C283C22×D412yes—
131Dic283—22no—
132Dic283—41no—
133Dic283#12712yes—
134C2×C283—82no—
135C2×C283—81no—
136C2×C283C2×#12711yescharacteristic
137C2×C283C2×AGL(1,ℤ/8)12yes—
138D283—82no—
139D283—81no—
140D283#49614yesdirect product factor
141C283C2×#49611yescharacteristic, complemented, Sylow
142C2×#496—2831nomaximal, Sylow
143C22×SD16—2832no—
144C22×D8—2832no—
145C2×#127—2831no—
146C2×#124—2831no—
147#496—2832no—
148#496—2832no—
149#496—2831no—
150#496—2831no—
151#496—2831no—
152#496D28311yescharacteristic, direct product factor
153C2×#97—2831no—
154C22×Q8—2831no—
155C22×D4—2831no—
156C22×D4—2832no—
157C22×D4—5662no—
158C2×SD16—2832no—
159C2×SD16—2832no—
160C2×SD16—2832no—
161C2×SD16—5668no—
162C2×SD16C2×D28312yescomplemented
163C2×D8—2832no—
164C2×D8—2832no—
165C2×D8—2832no—
166C2×D8—5668no—
167C2×D8C2×D28312yescomplemented
168C22×C8—2832no—
169#127—2832no—
170#127—2831no—
171#127—5662no—
172#127C2×D28311yescharacteristic, complemented
173#124—2831no—
174#124—2831no—
175#124—2831no—
176#124—5662no—
177#124C2×D28311yescharacteristic, complemented
178C2×C22⋊C4—5662no—
179C2×C42—2831no—
180#97—2832no—
181#97—2831no—
182#97C2×D28311yescharacteristic, complemented
183C24—5661no—
184C24—5662no—
185C2×Q8—2831no—
186C2×Q8—5661no—
187C2×Q8—5664no—
188C2×Q8C22×D28311yescharacteristic
189C2×D4—22no—
190C2×D4—2831no—
191C2×D4—2832no—
192C2×D4—5664no—
193C2×D4—5664no—
194C2×D4—5664no—
195C2×D4—5661no—
196C2×D4—5664no—
197C2×D4—5662no—
198C2×D4—5662no—
199C2×D4—11328no—
200C2×D4C22×D28311yescharacteristic
201C2×D4C22×D28312yes—
202C22×C4—2831no—
203C22×C4—2832no—
204C22×C4—5661no—
205SD16—24no—
206SD16—5664no—
207SD16—5664no—
208SD16—5664no—
209D8—24no—
210D8—5664no—
211D8—5664no—
212D8—5664no—
213C2×C8—2832no—
214C2×C8—2838no—
215C2×C8C22×D28312yes—
216C22⋊C4—22no—
217C22⋊C4—5662no—
218C22⋊C4—5662no—
219C22⋊C4—5662no—
220C42—2832no—
221C42—2831no—
222C42C22×D28311yescharacteristic
223C23—21no—
224C23—22no—
225C23—2831no—
226C23—5661no—
227C23—5662no—
228C23—11322no—
229C23—11324no—
230C23—11328no—
231C23—11324no—
232Q8—22no—
233Q8—5662no—
234Q8—11322no—
235D4—22no—
236D4—22no—
237D4—22no—
238D4—44no—
239D4—5662no—
240D4—5662no—
241D4—5662no—
242D4—11324no—
243D4—11322no—
244D4—11324no—
245D4—11328no—
246C2×C4—21no—
247C2×C4—2831no—
248C2×C4—2834no—
249C2×C4—2832no—
250C2×C4—5664no—
251C2×C4—5661no—
252C2×C4—11322no—
253C2×C4D4×D28312yes—
254C2×C4C23×D28311yescharacteristic
255C8—2834no—
256C8D4×D28314yescomplemented
257C22—44no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—2834no—
262C22—2832no—
263C22—11324no—
264C22—11322no—
265C22—11321no—
266C22—11322no—
267C22—22648no—
268C22—22644no—
269C22C2×D4×D28311yescharacteristic
270C4—22no—
271C4—41no—
272C4—2832no—
273C4—5662no—
274C4—11321no—
275C4C2×D4×D28312yes—
276C2—82no—
277C2—81no—
278C2—2834no—
279C2—22642no—
280C2—22641no—
281C2#127×D28311yescharacteristic
282C2AGL(1,ℤ/8)×D28312yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#496×C283C2
socleC22×C283C22×D4
hypercenter#496D283
hypocenterC283C2×#496
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D283C2semidirect
2. C2×D8×D283C2semidirect
3. #127×D283C2semidirect
4. #124×D283C2semidirect
5. #31826855C2semidirect
6. #31826854C2semidirect
7. #31826853C2semidirect
8. #31826852C2semidirect
9. #31826851C2semidirect
10. #97×D283C2semidirect
11. #496×C283C2semidirect
16. C2×#17985381C22semidirect
17. C2×#17985380C22semidirect
18. C2×#17985379C22semidirect
20. C2×D2264C22semidirect
21. C2×#17985377C22semidirect
22. C2×#17985377C22semidirect
25. #22583607C22semidirect
27. #22583606C22semidirect
28. #22583599C22semidirect
29. #22583598C22semidirect
30. #22583597C22semidirect
34. #22583521C22semidirect
35. #22583520C22semidirect
36. C2×SD16×C283C22semidirect
37. C2×D8×C283C22semidirect
38. #127×C283C22semidirect
39. #124×C283C22semidirect
40. #97×C283C22semidirect
66. C8×D283D4semidirect
103. C283⋊C8C2×D4semidirect
114. C8×C283C2×D4semidirect
140. D283#496direct (N × H)
141. C283C2×#496semidirect
152. #496D283direct (N × H)
162. C2×SD16C2×D283semidirect
167. C2×D8C2×D283semidirect
172. #127C2×D283semidirect
177. #124C2×D283semidirect
182. #97C2×D283semidirect
256. C8D4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D2832
C2×D8×D2832
#127×D2832
#124×D2832
#318268552
#318268542
#318268532
#318268522
#318268512
#97×D2832
#496×C2832
C2×#496283