Finite Group Databasebeta

← #481×D283 #49131157

Subgroups — #481×D283 #49131157

Order 36224.

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

normal subgroups only

This group has 512 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
1#121×D283C211yesmaximal, characteristic
2C2×C4⋊C4×D283C211yesmaximal, characteristic, complemented
3#31826785C212yesmaximal, complemented
4#31826784C211yesmaximal, characteristic, complemented
5#31826783C211yesmaximal, characteristic, complemented
6#31826782C212yesmaximal, complemented
7#31826781C211yesmaximal, characteristic, complemented
8#106×D283C212yesmaximal, complemented
9#102×D283C212yesmaximal, complemented
10C22⋊C8×D283C211yesmaximal, characteristic, complemented
11#481×C283C211yesmaximal, characteristic, complemented
12C2×D4×D283—21no—
13C2×D4×D283C2211yescharacteristic
14C22×C4×D283—21no—
15C22×C4×D283C2211yescharacteristic
16C2×C8×D283C2212yes—
17#22583585C2211yescharacteristic
18#22583584C2211yescharacteristic
19#22583583—21no—
20#22583582—21no—
21#22583581C2211yescharacteristic
22C2×C4⋊Dic283C2211yescharacteristic, complemented
23C2×Dic283⋊C4—21no—
24C4⋊C4×D283—21no—
25C4⋊C4×D283—21no—
26C4⋊C4×D283C2211yescharacteristic
27C4⋊C4×D283C2212yes—
28C4⋊C4×D283C2212yescomplemented
29C22⋊C4×D283—21no—
30#22583542C2212yescomplemented
31#22583541C2212yescomplemented
32#22583541C2212yescomplemented
33#22583532C2212yescomplemented
34#22583531C2212yescomplemented
35#22583530C2212yescomplemented
36C22⋊(C283⋊C8)C2211yescharacteristic, complemented
37(C2×D283)⋊C8C2212yescomplemented
38#121×C283C2211yescharacteristic
39C2×C4⋊C4×C283C2211yescharacteristic, complemented
40#106×C283C2212yescomplemented
41#102×C283C2212yescomplemented
42C22⋊C8×C283C2211yescharacteristic, complemented
43C23×D283—21no—
44C23×D283D411yescharacteristic
45C2×D1132—21no—
46C2×D1132C2311yescharacteristic
47C2×C22⋊D283—21no—
48C2×C22⋊D283—21no—
49C2×C22⋊D283—21no—
50D4×D283—24no—
51D4×D283—44no—
52C22×Dic283—21no—
53C22×Dic283D411yescharacteristic
54C2×C4×D283—24no—
55C2×C4×D283—21no—
56C2×C4×D283—22no—
57C2×C4×D283—22no—
58C2×C4×D283—44no—
59C2×C4×D283D411yescharacteristic
60C2×C4×D283D411yescharacteristic
61C2×C4×D283C2311yescharacteristic
62C2×C4×D283C2311yescharacteristic
63C2×C283⋊C8C2312yes—
64C8×D283—24no—
65C4⋊Dic283—21no—
66C4⋊Dic283C2312yes—
67C4⋊Dic283C2311yescharacteristic
68Dic283⋊C4—22no—
69Dic283⋊C4—22no—
70Dic283⋊C4—21no—
71C22⋊Dic283—21no—
72(C2×D283)⋊C4—21no—
73(C2×D283)⋊C4—21no—
74C2×D4×C283—21no—
75C2×D4×C283C2311yescharacteristic
76C22×C4×C283—21no—
77C22×C4×C283C2311yescharacteristic
78C2×C8×C283C2312yes—
79C4⋊C4×C283—21no—
80C4⋊C4×C283C2312yes—
81C4⋊C4×C283C2311yescharacteristic
82C22⋊C4×C283—21no—
83C22×D283—22no—
84C22×D283—22no—
85C22×D283—21no—
86C22×D283—42no—
87C22×D283—42no—
88C22×D283—42no—
89C22×D283SD1614yes—
90C22×D283C2×D411yescharacteristic
91C22×D283C2×D411yescharacteristic
92D1132—22no—
93D1132—42no—
94C22⋊D283—42no—
95C22⋊D283—42no—
96C22⋊D283—42no—
97C2×Dic283—22no—
98C2×Dic283—21no—
99C2×Dic283—22no—
100C2×Dic283—42no—
101C2×Dic283C2×D411yescharacteristic
102C2×Dic283C2×D411yescharacteristic
103C4×D283—22no—
104C4×D283—22no—
105C4×D283—22no—
106C4×D283—44no—
107C4×D283—42no—
108C4×D283—44no—
109C4×D283#4114yes—
110C283⋊C8—22no—
111C23×C283—21no—
112C23×C283C2×D411yescharacteristic
113D4×C283—22no—
114D4×C283—42no—
115C2×C4×C283—22no—
116C2×C4×C283—21no—
117C2×C4×C283—22no—
118C2×C4×C283—42no—
119C2×C4×C283C2×D411yescharacteristic
120C2×C4×C283C2411yescharacteristic
121C8×C283—22no—
122C22×C283—21no—
123C22×C283—21no—
124C22×C283—41no—
125C22×C283—41no—
126C22×C283—41no—
127C22×C283C2×SD1612yes—
128C22×C283C22×D411yescharacteristic
129C2×D283—21no—
130C2×D283—21no—
131C2×D283—28no—
132C2×D283—41no—
133C2×D283—41no—
134C2×D283—41no—
135C2×D283—84no—
136C2×D283#12312yes—
137C2×D283C2×SD1612yes—
138C2×D283C2×SD1612yes—
139C2×D283AGL(1,ℤ/8)12yes—
140C4×C283—21no—
141C4×C283—41no—
142C4×C283—42no—
143C4×C283C2×#4112yes—
144Dic283—21no—
145Dic283—41no—
146Dic283—42no—
147Dic283#12312yes—
148C2×C283—22no—
149C2×C283—81no—
150C2×C283C2×#12311yescharacteristic
151C2×C283C22×SD1611yescharacteristic
152C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
153D283—22no—
154D283—81no—
155D283#48114yesdirect product factor
156C283C2×#48111yescharacteristic, complemented, Sylow
157C2×#481—2831nomaximal, Sylow
158C2×#121—2831no—
159C22×C4⋊C4—2831no—
160#481—2831no—
161#481—2831no—
162#481—2832no—
163#481—2832no—
164#481—2831no—
165#481D28311yescharacteristic, direct product factor
166C2×#106—2832no—
167C2×#102—2832no—
168C2×C22⋊C8—2831no—
169C22×D4—2831no—
170C22×D4—5661no—
171C23×C4—2831no—
172C23×C4—5661no—
173C22×C8—2832no—
174#121—2831no—
175#121—2831no—
176#121—2831no—
177#121—5661no—
178#121—5661no—
179#121C2×D28311yescharacteristic
180C2×C4⋊C4—2831no—
181C2×C4⋊C4—2832no—
182C2×C4⋊C4—2832no—
183C2×C4⋊C4—2831no—
184C2×C4⋊C4—5661no—
185C2×C4⋊C4—5661no—
186C2×C4⋊C4—5661no—
187C2×C4⋊C4C2×D28311yescharacteristic, complemented
188C2×C22⋊C4—5661no—
189#106—2832no—
190#106—2832no—
191#106—2832no—
192#106C2×D28312yescomplemented
193#102—2832no—
194#102—2832no—
195#102—2832no—
196#102C2×D28312yescomplemented
197C22⋊C8—2831no—
198C22⋊C8—2832no—
199C22⋊C8C2×D28311yescharacteristic, complemented
200C24—2831no—
201C24—5661no—
202C2×D4—21no—
203C2×D4—2831no—
204C2×D4—5661no—
205C2×D4—5664no—
206C2×D4—5661no—
207C2×D4—5661no—
208C2×D4—5661no—
209C2×D4—11324no—
210C2×D4C22×D28311yescharacteristic
211C22×C4—21no—
212C22×C4—2831no—
213C22×C4—2831no—
214C22×C4—2831no—
215C22×C4—2831no—
216C22×C4—2831no—
217C22×C4—5664no—
218C22×C4—5661no—
219C22×C4—5662no—
220C22×C4—5662no—
221C22×C4—5661no—
222C22×C4—11324no—
223C22×C4C22×D28311yescharacteristic
224C2×C8—2832no—
225C2×C8—5664no—
226C2×C8C22×D28312yes—
227C4⋊C4—21no—
228C4⋊C4—2832no—
229C4⋊C4—2831no—
230C4⋊C4—5662no—
231C4⋊C4—5662no—
232C4⋊C4—5661no—
233C4⋊C4—5661no—
234C4⋊C4C22×D28312yes—
235C4⋊C4C22×D28311yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—5661no—
238C22⋊C4—5661no—
239C22⋊C4—5661no—
240C23—21no—
241C23—2831no—
242C23—2834no—
243C23—2831no—
244C23—5662no—
245C23—5662no—
246C23—5661no—
247C23—11322no—
248C23—11322no—
249C23—11322no—
250C23D4×D28311yescharacteristic
251D4—22no—
252D4—42no—
253D4—5662no—
254D4—11322no—
255D4—11322no—
256D4—11322no—
257D4—11322no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—2831no—
263C2×C4—2834no—
264C2×C4—2831no—
265C2×C4—5662no—
266C2×C4—5662no—
267C2×C4—5662no—
268C2×C4—5662no—
269C2×C4—5661no—
270C2×C4—5662no—
271C2×C4—11324no—
272C2×C4—11322no—
273C2×C4—11324no—
274C2×C4—11322no—
275C2×C4D4×D28311yescharacteristic
276C2×C4C23×D28311yescharacteristic
277C8—22no—
278C8—5662no—
279C22—21no—
280C22—21no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—2832no—
285C22—2832no—
286C22—2832no—
287C22—2832no—
288C22—5668no—
289C22—5661no—
290C22—5661no—
291C22—11321no—
292C22—11321no—
293C22—11321no—
294C22—22644no—
295C22SD16×D28312yes—
296C22C2×D4×D28311yescharacteristic
297C4—21no—
298C4—41no—
299C4—42no—
300C4—2832no—
301C4—5661no—
302C4—11321no—
303C4—11322no—
304C4#41×D28312yes—
305C2—22no—
306C2—81no—
307C2—2834no—
308C2—5662no—
309C2—22641no—
310C2#123×D28311yescharacteristic
311C2C2×SD16×D28311yescharacteristic
312C2AGL(1,ℤ/8)×D28311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#481×C283C2
socleC22×C283C22×D4
prime radical#121×D283C2
hypercenter#481D283
hypocenterC283C2×#481
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D283C2semidirect
3. #31826785C2semidirect
4. #31826784C2semidirect
5. #31826783C2semidirect
6. #31826782C2semidirect
7. #31826781C2semidirect
8. #106×D283C2semidirect
9. #102×D283C2semidirect
10. C22⋊C8×D283C2semidirect
11. #481×C283C2semidirect
22. C2×C4⋊Dic283C22semidirect
28. C4⋊C4×D283C22semidirect
30. #22583542C22semidirect
31. #22583541C22semidirect
32. #22583541C22semidirect
33. #22583532C22semidirect
34. #22583531C22semidirect
35. #22583530C22semidirect
36. C22⋊(C283⋊C8)C22semidirect
37. (C2×D283)⋊C8C22semidirect
39. C2×C4⋊C4×C283C22semidirect
40. #106×C283C22semidirect
41. #102×C283C22semidirect
42. C22⋊C8×C283C22semidirect
155. D283#481direct (N × H)
156. C283C2×#481semidirect
165. #481D283direct (N × H)
187. C2×C4⋊C4C2×D283semidirect
192. #106C2×D283semidirect
196. #102C2×D283semidirect
199. C22⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#121×D2832
C2×C4⋊C4×D2832
#318267852
#318267842
#318267832
#318267822
#318267812
#106×D2832
#102×D2832
C22⋊C8×D2832
#481×C2832
C2×#481283