Finite Group Databasebeta

← #489×D283 #49131587

Subgroups — #489×D283 #49131587

Order 36224.

436 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C4⋊Q8×D283C211yesmaximal, characteristic, complemented
2#124×D283C211yesmaximal, characteristic
3#31826827C211yesmaximal, characteristic, complemented
4#31826826C212yesmaximal, complemented
5#31826825C211yesmaximal, characteristic, complemented
6#31826824C211yesmaximal, characteristic, complemented
7#31826823C212yesmaximal, complemented
8#103×D283C212yesmaximal, complemented
9#102×D283C212yesmaximal
10#97×D283C211yesmaximal, characteristic, complemented
11#489×C283C211yesmaximal, characteristic, complemented
12C2×Q8×D283—21no—
13C2×Q8×D283C2211yescharacteristic
14C2×D4×D283C2211yescharacteristic
15C2×C8×D283C2212yes—
16#22583610C2211yescharacteristic, complemented
17#22583609—21no—
18#22583609C2212yescomplemented
19#22583608—21no—
20#22583599C2211yescharacteristic
21#22583598C2211yescharacteristic
22#22583597C2211yescharacteristic
23#22583596—21no—
24#22583596—21no—
25C4⋊C4×D283—21no—
26C4⋊C4×D283C2212yes—
27C22⋊C4×D283—21no—
28C22⋊C4×D283—21no—
29C42×D283C2211yescharacteristic
30#22583535C2212yescomplemented
31#22583534C2212yescomplemented
32#22583533C2212yescomplemented
33#22583532C2212yes—
34#22583531C2212yes—
35#22583530C2212yes—
36#22583521C2211yescharacteristic, complemented
37#22583520C2212yescomplemented
38C4⋊Q8×C283C2211yescharacteristic, complemented
39#124×C283C2211yescharacteristic
40#103×C283C2212yescomplemented
41#102×C283C2212yes—
42#97×C283C2211yescharacteristic, complemented
43C23×D283—21no—
44C2×Dic566—21no—
45C2×Dic566—22no—
46C2×Dic566—21no—
47C2×Dic566C2311yescharacteristic
48Q8×D283—24no—
49Q8×D283—44no—
50C2×D1132C2311yescharacteristic
51C2×C22⋊D283—21no—
52D4×D283—24no—
53C2×C4×D283—21no—
54C2×C4×D283—22no—
55C2×C4×D283D411yescharacteristic
56C2×C4×D283D411yescharacteristic
57C2×C4×D283C2311yescharacteristic
58C2×C283⋊C8C2312yes—
59C8×D283—24no—
60C4⋊Dic283—21no—
61C4⋊Dic283C2312yes—
62Dic283⋊C4—22no—
63Dic283⋊C4—22no—
64C22⋊Dic283—21no—
65C22⋊Dic283—21no—
66(C2×D283)⋊C4—21no—
67(C2×D283)⋊C4—21no—
68(C2×D283)⋊C4—21no—
69(C2×D283)⋊C4—21no—
70C4×Dic283D411yescharacteristic
71C4×Dic283D411yescharacteristic
72C4×Dic283C2311yescharacteristic
73C2×Q8×C283—21no—
74C2×Q8×C283C2311yescharacteristic
75C2×D4×C283C2311yescharacteristic
76C2×C8×C283C2312yes—
77C4⋊C4×C283—21no—
78C4⋊C4×C283C2312yes—
79C22⋊C4×C283—21no—
80C22⋊C4×C283—21no—
81C42×C283C2311yescharacteristic
82C22×D283—21no—
83C22×D283—42no—
84C22×D283—42no—
85C22×D283—42no—
86C22×D283C2×D411yescharacteristic
87Dic566—22no—
88Dic566—44no—
89Dic566—42no—
90Dic566—42no—
91D1132—22no—
92C22⋊D283—42no—
93C2×Dic283—21no—
94C2×Dic283—22no—
95C2×Dic283C2×D411yescharacteristic
96C2×Dic283C2×D411yescharacteristic
97C2×Dic283C2×D411yescharacteristic
98C4×D283—22no—
99C4×D283—22no—
100C4×D283—42no—
101C4×D283—44no—
102C4×D283#4114yes—
103C283⋊C8—22no—
104C23×C283—21no—
105Q8×C283—22no—
106Q8×C283—42no—
107D4×C283—22no—
108C2×C4×C283—21no—
109C2×C4×C283—22no—
110C2×C4×C283C2×D411yescharacteristic
111C2×C4×C283C2×D411yescharacteristic
112C2×C4×C283C2411yescharacteristic
113C8×C283—22no—
114C22×C283—41no—
115C22×C283—41no—
116C22×C283—41no—
117C22×C283C22×D411yescharacteristic
118C2×D283—41no—
119C2×D283—41no—
120C2×D283—41no—
121C2×D283—84no—
122C2×D283#12412yes—
123C2×D283AGL(1,ℤ/8)12yes—
124C2×D283#13712yes—
125C4×C283—21no—
126C4×C283—21no—
127C4×C283—41no—
128C4×C283—42no—
129C4×C283C2×#4112yes—
130Dic283—21no—
131Dic283—21no—
132Dic283—41no—
133Dic283—42no—
134Dic283#12412yes—
135C2×C283—81no—
136C2×C283C2×#12411yescharacteristic
137C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C283C2×#13711yescharacteristic
139D283—81no—
140D283#48914yesdirect product factor
141C283C2×#48911yescharacteristic, complemented, Sylow
142C2×#489—2831nomaximal, Sylow
143C2×C4⋊Q8—2831no—
144C2×#124—2831no—
145#489—2831no—
146#489—2831no—
147#489—2832no—
148#489—2832no—
149#489—2831no—
150#489D28311yescharacteristic, direct product factor
151C2×#103—2832no—
152C2×#102—2832no—
153C2×#97—2831no—
154C22×Q8—2831no—
155C22×Q8—5661no—
156C22×D4—2831no—
157C22×C8—2832no—
158C4⋊Q8—2832no—
159C4⋊Q8—2831no—
160C4⋊Q8—5661no—
161C4⋊Q8—5661no—
162C4⋊Q8C2×D28311yescharacteristic, complemented
163#124—2831no—
164#124—2831no—
165#124—2831no—
166#124—5661no—
167#124—5661no—
168#124C2×D28311yescharacteristic
169C2×C4⋊C4—2832no—
170C2×C4⋊C4—5661no—
171C2×C22⋊C4—5661no—
172C2×C22⋊C4—5661no—
173C2×C42—2831no—
174#103—2832no—
175#103—2832no—
176#103—2832no—
177#103C2×D28312yescomplemented
178#102—2832no—
179#102—2832no—
180#102—2832no—
181#102C2×D28312yes—
182#97—2832no—
183#97—2831no—
184#97C2×D28311yescharacteristic, complemented
185C24—5661no—
186C2×Q8—21no—
187C2×Q8—2831no—
188C2×Q8—5661no—
189C2×Q8—5662no—
190C2×Q8—5664no—
191C2×Q8—5661no—
192C2×Q8—11324no—
193C2×Q8C22×D28311yescharacteristic
194C2×D4—2831no—
195C2×D4—5664no—
196C2×D4—5661no—
197C2×D4C22×D28311yescharacteristic
198C22×C4—2831no—
199C22×C4—2831no—
200C22×C4—2831no—
201C22×C4—5661no—
202C22×C4—5662no—
203C2×C8—2832no—
204C2×C8—5664no—
205C2×C8C22×D28312yes—
206C4⋊C4—21no—
207C4⋊C4—2832no—
208C4⋊C4—5662no—
209C4⋊C4—5662no—
210C4⋊C4—5661no—
211C4⋊C4C22×D28312yes—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—5661no—
215C22⋊C4—5661no—
216C22⋊C4—5661no—
217C22⋊C4—5661no—
218C22⋊C4—5661no—
219C22⋊C4—5661no—
220C42—2831no—
221C42—2831no—
222C42—2831no—
223C42C22×D28311yescharacteristic
224C23—21no—
225C23—2831no—
226C23—5661no—
227C23—11322no—
228C23—11322no—
229C23—11322no—
230Q8—22no—
231Q8—42no—
232Q8—5662no—
233Q8—11322no—
234Q8—11322no—
235Q8—11324no—
236D4—22no—
237D4—5662no—
238D4—11322no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—2831no—
242C2×C4—2834no—
243C2×C4—2831no—
244C2×C4—2831no—
245C2×C4—5662no—
246C2×C4—5662no—
247C2×C4—5661no—
248C2×C4—5662no—
249C2×C4—11322no—
250C2×C4—11324no—
251C2×C4D4×D28311yescharacteristic
252C2×C4D4×D28311yescharacteristic
253C2×C4C23×D28311yescharacteristic
254C8—22no—
255C8—5662no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—2832no—
260C22—2832no—
261C22—2832no—
262C22—11321no—
263C22—11321no—
264C22—11321no—
265C22—22644no—
266C22C2×D4×D28311yescharacteristic
267C4—21no—
268C4—21no—
269C4—41no—
270C4—42no—
271C4—2832no—
272C4—5661no—
273C4—5661no—
274C4—11321no—
275C4—11322no—
276C4#41×D28312yes—
277C2—81no—
278C2—2834no—
279C2—22641no—
280C2#124×D28311yescharacteristic
281C2AGL(1,ℤ/8)×D28311yescharacteristic
282C2#137×D28311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#489×C283C2
socleC22×C283C22×D4
prime radicalC2×D4×D283C22
hypercenter#489D283
hypocenterC283C2×#489
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D283C2semidirect
3. #31826827C2semidirect
4. #31826826C2semidirect
5. #31826825C2semidirect
6. #31826824C2semidirect
7. #31826823C2semidirect
8. #103×D283C2semidirect
10. #97×D283C2semidirect
11. #489×C283C2semidirect
16. #22583610C22semidirect
18. #22583609C22semidirect
30. #22583535C22semidirect
31. #22583534C22semidirect
32. #22583533C22semidirect
36. #22583521C22semidirect
37. #22583520C22semidirect
38. C4⋊Q8×C283C22semidirect
40. #103×C283C22semidirect
42. #97×C283C22semidirect
140. D283#489direct (N × H)
141. C283C2×#489semidirect
150. #489D283direct (N × H)
162. C4⋊Q8C2×D283semidirect
177. #103C2×D283semidirect
184. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D2832
#124×D2832
#318268272
#318268262
#318268252
#318268242
#318268232
#103×D2832
#102×D2832
#97×D2832
#489×C2832
C2×#489283