Finite Group Databasebeta

← #49132864

Subgroups — #49132864

Order 36224.

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

normal subgroups only

This group has 546 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
1C2×#22583637C212yesmaximal, complemented
2#31827118C211yesmaximal, characteristic, complemented
3D4×D1132C211yesmaximal, characteristic, complemented
4#31826839C211yesmaximal, characteristic, complemented
5#31826714C212yesmaximal, complemented
6#31826661C211yesmaximal, characteristic, complemented
7#31826614C212yesmaximal, complemented
8#31826613C212yesmaximal, complemented
9C4×#17985377C211yesmaximal, characteristic, complemented
10#31826542C211yesmaximal, characteristic, complemented
11#461×C283C211yesmaximal, characteristic, complemented
12C2×#17985393C2212yescomplemented
13C22×D1132—21no—
14C2×D4×D283C2212yes—
15#22583637—28no—
16C2×#17985379C2212yescomplemented
17C2×#17985379C2212yescomplemented
18C2×D2264C2212yescomplemented
19C2×#17985377C2211yescharacteristic
20C2×#17985375C2212yescomplemented
21#22583607C2211yescharacteristic
22#22583595—22no—
23#22583586C2212yescomplemented
24#22583585—21no—
25#22583585C2212yes—
26#22583584—21no—
27#22583580—22no—
28C4×D1132C2211yescharacteristic
29C4×D1132C2211yescharacteristic, complemented
30C4⋊C4×D283—21no—
31#22583543C2211yescharacteristic, complemented
32#22583532C2212yescomplemented
33#22583531C2211yescharacteristic
34#22583530C2211yescharacteristic, complemented
35(C2×D283)⋊C8C2212yescomplemented
36C4×C283⋊C8C2211yescharacteristic, complemented
37C2×SD16×C283C2212yes—
38C4⋊Q8×C283C2211yescharacteristic, complemented
39C4×D4×C283C2211yescharacteristic
40C4⋊C8×C283C2211yescharacteristic, complemented
41#103×C283C2212yescomplemented
42C23×D283—22no—
43#17985393—24no—
44#17985393—42no—
45C2×D1132—22no—
46C2×D1132—22no—
47C2×D1132—21no—
48C2×D1132—21no—
49C2×D1132—44no—
50C2×D1132D411yescharacteristic
51C2×D1132C2312yes—
52C2×D1132C2311yescharacteristic
53C2×C22⋊D283—22no—
54D4×D283—24no—
55D4×D283—42no—
56C2×C4×D283—22no—
57C2×C4×D283—21no—
58C2×C4×D283C2312yes—
59#17985379—24no—
60#17985379—42no—
61D2264—24no—
62#17985377D414yescomplemented
63#17985375—24no—
64C2×C283⋊C8C2311yescharacteristic
65C2×C283⋊C8C2311yescharacteristic
66C4⋊Dic283D411yescharacteristic
67C4⋊Dic283C2311yescharacteristic
68Dic283⋊C4—22no—
69(C2×D283)⋊C4—22no—
70(C2×D283)⋊C4—22no—
71(C2×D283)⋊C4—21no—
72(C2×D283)⋊C4D412yes—
73C2×Q8×C283C2312yes—
74C2×D4×C283C2311yescharacteristic
75C22×C4×C283—21no—
76SD16×C283—24no—
77C2×C8×C283C2312yes—
78C4⋊C4×C283—21no—
79C4⋊C4×C283—21no—
80C4⋊C4×C283C2311yescharacteristic
81C22⋊C4×C283—21no—
82C42×C283C2311yescharacteristic
83C22×D283—21no—
84C22×D283—22no—
85C22×D283—44no—
86C22×D283—44no—
87C22×D283—82no—
88C22×D283C2×D412yes—
89D1132—22no—
90D1132—22no—
91D1132—21no—
92D1132—22no—
93D1132—44no—
94D1132—44no—
95D1132—42no—
96D1132—81no—
97D1132C2×D412yescomplemented
98C22⋊D283—44no—
99C2×Dic283—21no—
100C2×Dic283C2×D412yes—
101C4×D283—22no—
102C4×D283—22no—
103C4×D283—44no—
104C4×D283—42no—
105C283⋊C8—21no—
106C283⋊C8C2×D412yescomplemented
107C23×C283—21no—
108Q8×C283—22no—
109Q8×C283—22no—
110D4×C283—21no—
111D4×C283C2×D412yes—
112C2×C4×C283—21no—
113C2×C4×C283—22no—
114C2×C4×C283—42no—
115C2×C4×C283C2×D411yescharacteristic
116C2×C4×C283C2×D411yescharacteristic
117C2×C4×C283C2411yescharacteristic
118C8×C283—22no—
119C22×C283—22no—
120C22×C283—41no—
121C22×C283—41no—
122C22×C283C22×D411yescharacteristic
123C2×D283—22no—
124C2×D283—22no—
125C2×D283—22no—
126C2×D283—22no—
127C2×D283—41no—
128C2×D283—41no—
129C2×D283—42no—
130C2×D283—42no—
131C2×D283—42no—
132C2×D283—88no—
133C4×C283—21no—
134C4×C283—42no—
135C4×C283—41no—
136C4×C283AGL(1,ℤ/8)12yescomplemented
137C4×C283C22×D411yescharacteristic
138C4×C283H(5,𝔽2)11yescharacteristic
139Dic283—22no—
140Dic283—41no—
141C2×C283—42no—
142C2×C283D4211yescharacteristic
143C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C283#57711yescharacteristic
145D283—42no—
146D283—42no—
147D283—82no—
148C283#327211yescharacteristic, complemented, Sylow
149#3272—2831nomaximal, Sylow
150C2×AGL(1,ℤ/8)—2832no—
151#547—2831no—
152D42—2831no—
153#492—2831no—
154#468—2832no—
155#461D28311yescharacteristic, complemented
156#459—2831no—
157#450—2832no—
158#449—2832no—
159C4×D8—2831no—
160#436—2831no—
161C2×#41—2832no—
162C22×D4—2832no—
163C22×D4—5661no—
164AGL(1,ℤ/8)—5668no—
165C2×SD16—2832no—
166C2×SD16—2832no—
167C2×SD16C2×D28312yes—
168C2×D8—2831no—
169C2×D8—2832no—
170C2×M16—2832no—
171C4⋊Q8C2×D28311yescharacteristic, complemented
172#127—2831no—
173#123—5662no—
174C22⋊Q8—2832no—
175#121—2832no—
176#121—5661no—
177#121—5661no—
178#120—5662no—
179C4×D4—2831no—
180C4×D4—2831no—
181C4×D4C2×D28311yescharacteristic
182C2×C4⋊C4—5661no—
183#107—2831no—
184C4⋊C8C2×D28311yescharacteristic, complemented
185#103C2×D28312yescomplemented
186#102—2831no—
187#102—2832no—
188#102—2831no—
189C22⋊C8—2832no—
190C4×C8—2831no—
191C24—5662no—
192#41—5664no—
193#41—11322no—
194C2×Q8C22×D28312yes—
195C2×D4—2831no—
196C2×D4—2831no—
197C2×D4—2832no—
198C2×D4—5662no—
199C2×D4—5662no—
200C2×D4—5662no—
201C2×D4—5664no—
202C2×D4—5661no—
203C2×D4—5661no—
204C2×D4—11324no—
205C2×D4—11322no—
206C2×D4C22×D28311yescharacteristic
207C22×C4—21no—
208C22×C4—2832no—
209C22×C4—5662no—
210C22×C4—5661no—
211SD16—24no—
212SD16—5664no—
213SD16—11322no—
214D8—2834no—
215D8—5664no—
216M16—5664no—
217C2×C8—2831no—
218C2×C8—2831no—
219C2×C8C22×D28312yes—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—2831no—
223C4⋊C4—2831no—
224C4⋊C4—5662no—
225C4⋊C4C22×D28311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2832no—
228C22⋊C4—5662no—
229C22⋊C4—5662no—
230C22⋊C4—5661no—
231C42C22×D28311yescharacteristic
232C23—21no—
233C23—2832no—
234C23—5661no—
235C23—5662no—
236C23—11324no—
237C23—11324no—
238C23—22642no—
239Q8—22no—
240Q8—22no—
241D4—21no—
242D4—2832no—
243D4—5662no—
244D4—5662no—
245D4—5661no—
246D4—5662no—
247D4—11324no—
248D4—11324no—
249D4—11324no—
250D4—11322no—
251D4—22641no—
252D4D4×D28312yes—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—2832no—
257C2×C4—5662no—
258C2×C4—5662no—
259C2×C4—5661no—
260C2×C4—11324no—
261C2×C4—11322no—
262C2×C4D4×D28311yescharacteristic
263C2×C4D4×D28311yescharacteristic
264C2×C4C23×D28311yescharacteristic
265C8—22no—
266C8—2832no—
267C8—5661no—
268C22—22no—
269C22—41no—
270C22—41no—
271C22—5662no—
272C22—5662no—
273C22—5662no—
274C22—5662no—
275C22—11321no—
276C22—11321no—
277C22—11322no—
278C22—11322no—
279C22—11322no—
280C22—22648no—
281C22C2×D4×D28311yescharacteristic
282C4—21no—
283C4—41no—
284C4—42no—
285C4—5662no—
286C4—11321no—
287C4#2258363712yescomplemented
288C4C2×D4×D28311yescharacteristic
289C4#2258365611yescharacteristic
290C2—42no—
291C2—11322no—
292C2—11322no—
293C2—22642no—
294C2#3182709911yescharacteristic
295C2C2×#2258363711yescharacteristic
296C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#461×C283C2
socleC22×C283C22×D4
hypercenter#461D283
hypocenterC283#3272
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#22583637C2semidirect
2. #31827118C2semidirect
3. D4×D1132C2semidirect
4. #31826839C2semidirect
5. #31826714C2semidirect
6. #31826661C2semidirect
7. #31826614C2semidirect
8. #31826613C2semidirect
9. C4×#17985377C2semidirect
10. #31826542C2semidirect
11. #461×C283C2semidirect
12. C2×#17985393C22semidirect
16. C2×#17985379C22semidirect
17. C2×#17985379C22semidirect
18. C2×D2264C22semidirect
20. C2×#17985375C22semidirect
23. #22583586C22semidirect
29. C4×D1132C22semidirect
31. #22583543C22semidirect
32. #22583532C22semidirect
34. #22583530C22semidirect
35. (C2×D283)⋊C8C22semidirect
36. C4×C283⋊C8C22semidirect
38. C4⋊Q8×C283C22semidirect
40. C4⋊C8×C283C22semidirect
41. #103×C283C22semidirect
62. #17985377D4semidirect
97. D1132C2×D4semidirect
106. C283⋊C8C2×D4semidirect
136. C4×C283AGL(1,ℤ/8)semidirect
148. C283#3272semidirect
155. #461D283semidirect
171. C4⋊Q8C2×D283semidirect
184. C4⋊C8C2×D283semidirect
185. #103C2×D283semidirect
287. C4#22583637semidirect

Maximal subgroups

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

subgroupindex
C2×#225836372
#318271182
D4×D11322
#318268392
#318267142
#318266612
#318266142
#318266132
C4×#179853772
#318265422
#461×C2832
#3272283