Finite Group Databasebeta

← #509×D283 #49134381

Subgroups — #509×D283 #49134381

Order 36224.

400 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 115 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#135×D283C211yesmaximal, characteristic, complemented
2C2×D8×D283C211yesmaximal, characteristic, complemented
3#31826903C211yesmaximal, characteristic, complemented
4#31826902C212yesmaximal, complemented
5#31826901C211yesmaximal, characteristic, complemented
6#31826900C211yesmaximal, characteristic, complemented
7#31826899C212yesmaximal, complemented
8SD32×D283C212yesmaximal, complemented
9D16×D283C212yesmaximal, complemented
10M32×D283C211yesmaximal, characteristic, complemented
11#509×C283C211yesmaximal, characteristic, complemented
12#41×D283—21no—
13C2×D4×D283—21no—
14#22583633C2211yescharacteristic, complemented
15#22583632C2211yescharacteristic, complemented
16#22583631—21no—
17#22583630—21no—
18#22583629C2211yescharacteristic, complemented
19Q16×D283C2211yescharacteristic, complemented
20SD16×D283—21no—
21C2×D2264C2211yescharacteristic, complemented
22C2×#17985377—21no—
23D8×D283—21no—
24D8×D283—21no—
25D8×D283C2212yes—
26D8×D283C2212yescomplemented
27D8×D283C2211yescharacteristic, complemented
28C2×C8×D283C2211yescharacteristic
29#22583555C2212yescomplemented
30#22583554C2212yescomplemented
31#22583553C2212yescomplemented
32D4528C2212yescomplemented
33#22583551C2212yescomplemented
34#22583551C2212yescomplemented
35#22583550C2211yescharacteristic, complemented
36#22583549C2212yescomplemented
37C16×D283C2212yescomplemented
38#135×C283C2211yescharacteristic, complemented
39C2×D8×C283C2211yescharacteristic, complemented
40SD32×C283C2212yescomplemented
41D16×C283C2212yescomplemented
42M32×C283C2211yescharacteristic, complemented
43C23×D283—41no—
44#17985393—21no—
45#17985392—21no—
46#17985392—41no—
47#17985391—21no—
48#17985391—41no—
49Q8×D283—21no—
50C2×D1132—21no—
51C2×C22⋊D283—41no—
52D4×D283—22no—
53D4×D283—22no—
54D4×D283—21no—
55D4×D283—41no—
56D4×D283—41no—
57D4×D283—41no—
58C2×C4×D283—41no—
59C2×C4×D283D411yescharacteristic
60Dic1132C2311yescharacteristic, complemented
61#17985382—21no—
62#17985381—21no—
63#17985380—21no—
64#17985379—21no—
65D2264—21no—
66D2264C2312yes—
67D2264C2311yescharacteristic, complemented
68#17985377—22no—
69#17985377—22no—
70#17985377—21no—
71C2×C283⋊C8D411yescharacteristic
72C8×D283D411yescharacteristic
73C8×D283D411yescharacteristic
74C8×D283C2311yescharacteristic
75C8×D283C2311yescharacteristic
76C283⋊C16C2312yescomplemented
77#41×C283—21no—
78C2×D4×C283—21no—
79Q16×C283C2311yescharacteristic, complemented
80SD16×C283—21no—
81D8×C283—21no—
82D8×C283C2312yes—
83D8×C283C2311yescharacteristic, complemented
84C2×C8×C283C2311yescharacteristic
85C16×C283C2312yescomplemented
86C22×D283—41no—
87C22×D283—41no—
88C22×D283—42no—
89C22×D283—42no—
90C22×D283—84no—
91C22×D283D811yescharacteristic
92Dic566—21no—
93Dic566—41no—
94D1132—22no—
95D1132—21no—
96D1132—41no—
97D1132—41no—
98C22⋊D283—41no—
99C22⋊D283—41no—
100C22⋊D283—42no—
101C22⋊D283—42no—
102C22⋊D283—41no—
103C2×Dic283—41no—
104C2×Dic283D811yescharacteristic
105C4×D283—41no—
106C4×D283—41no—
107C4×D283—41no—
108C4×D283D811yescharacteristic
109C4×D283D811yescharacteristic
110C4×D283C2×D411yescharacteristic
111C4×D283C2×D411yescharacteristic
112C283⋊C8C2×D411yescharacteristic
113C283⋊C8C2×D411yescharacteristic
114C23×C283—41no—
115Q8×C283—21no—
116D4×C283—22no—
117D4×C283—21no—
118D4×C283—41no—
119D4×C283—41no—
120C2×C4×C283—41no—
121C2×C4×C283C2×D411yescharacteristic
122C8×C283C2×D411yescharacteristic
123C8×C283C2411yescharacteristic
124C22×C283—41no—
125C22×C283—42no—
126C22×C283—82no—
127C22×C283C2×D811yescharacteristic
128C2×D283—22no—
129C2×D283—41no—
130C2×D283—42no—
131C2×D283—84no—
132C2×D283—82no—
133C2×D283—82no—
134C2×D283—84no—
135C2×D283C2×D811yescharacteristic
136C2×D283C2×D811yescharacteristic
137C4×C283—41no—
138C4×C283C2×D811yescharacteristic
139C4×C283C22×D411yescharacteristic
140Dic283—41no—
141Dic283C2×D811yescharacteristic
142Dic283C2×D811yescharacteristic
143C2×C283—21no—
144C2×C283—82no—
145C2×C283—81no—
146C2×C283C22×D811yescharacteristic
147D283—21no—
148D283—81no—
149D283—82no—
150D283#50912yesdirect product factor
151C283C2×#50911yescharacteristic, complemented, Sylow
152C2×#509—2831nomaximal, Sylow
153C2×#135—2831no—
154C22×D8—2831no—
155#509—2831no—
156#509—2831no—
157#509—2832no—
158#509—2832no—
159#509—2831no—
160#509D28311yescharacteristic, direct product factor
161C2×SD32—2832no—
162C2×D16—2832no—
163C2×M32—2831no—
164C2×#41—5661no—
165C22×D4—5661no—
166#135—2831no—
167#135—2831no—
168#135—2831no—
169#135—5661no—
170#135—5661no—
171#135C2×D28311yescharacteristic, complemented
172C2×Q16—2831no—
173C2×SD16—5661no—
174C2×D8—2832no—
175C2×D8—2832no—
176C2×D8—2831no—
177C2×D8—2831no—
178C2×D8—5661no—
179C2×D8—5661no—
180C2×D8—5661no—
181C2×D8C2×D28311yescharacteristic, complemented
182C22×C8—2831no—
183SD32—2832no—
184SD32—2832no—
185SD32—2832no—
186SD32C2×D28312yescomplemented
187D16—2832no—
188D16—2832no—
189D16—2832no—
190D16C2×D28312yescomplemented
191M32—2831no—
192M32—2832no—
193M32C2×D28311yescharacteristic, complemented
194C2×C16—2832no—
195C24—11321no—
196#41—21no—
197#41—5661no—
198#41—5661no—
199#41—5661no—
200#41—11321no—
201#41—11321no—
202C2×Q8—5661no—
203C2×D4—21no—
204C2×D4—5662no—
205C2×D4—5662no—
206C2×D4—5661no—
207C2×D4—5661no—
208C2×D4—11321no—
209C2×D4—11321no—
210C2×D4—11321no—
211C2×D4—11321no—
212C22×C4—2831no—
213C22×C4—11321no—
214Q16—2831no—
215Q16—5661no—
216Q16C22×D28311yescharacteristic, complemented
217SD16—21no—
218SD16—5661no—
219SD16—5661no—
220SD16—5661no—
221D8—21no—
222D8—2832no—
223D8—2831no—
224D8—5662no—
225D8—5662no—
226D8—5661no—
227D8—5661no—
228D8C22×D28312yes—
229D8C22×D28311yescharacteristic, complemented
230C2×C8—2831no—
231C2×C8—2831no—
232C2×C8—2831no—
233C2×C8—2831no—
234C2×C8—2831no—
235C2×C8C22×D28311yescharacteristic
236C16—2832no—
237C16C22×D28312yescomplemented
238C23—41no—
239C23—2831no—
240C23—11321no—
241C23—11322no—
242C23—11322no—
243C23—11321no—
244C23—22644no—
245Q8—21no—
246Q8—5661no—
247Q8—11321no—
248D4—22no—
249D4—21no—
250D4—41no—
251D4—41no—
252D4—5662no—
253D4—5661no—
254D4—11321no—
255D4—11322no—
256D4—11322no—
257D4—11321no—
258D4—11321no—
259D4—11321no—
260D4—11321no—
261C2×C4—41no—
262C2×C4—2831no—
263C2×C4—2831no—
264C2×C4—2831no—
265C2×C4—2831no—
266C2×C4—2831no—
267C2×C4—11321no—
268C2×C4—11321no—
269C2×C4—11321no—
270C2×C4—11321no—
271C2×C4D4×D28311yescharacteristic
272C8—2831no—
273C8—2831no—
274C8D4×D28311yescharacteristic
275C8C23×D28311yescharacteristic
276C22—41no—
277C22—42no—
278C22—82no—
279C22—2831no—
280C22—2831no—
281C22—5662no—
282C22—11321no—
283C22—11322no—
284C22—22642no—
285C22—22644no—
286C22—22642no—
287C22—22644no—
288C22D8×D28311yescharacteristic
289C4—41no—
290C4—2831no—
291C4—2831no—
292C4—11321no—
293C4D8×D28311yescharacteristic
294C4C2×D4×D28311yescharacteristic
295C2—21no—
296C2—82no—
297C2—81no—
298C2—2832no—
299C2—5661no—
300C2—22642no—
301C2—22641no—
302C2C2×D8×D28311yescharacteristic
subgroupG/H
centerC2C2×D8×D283
commutator, cosocleC8×C283C24
FrattiniC8C23×D283
Fitting#509×C283C2
socleC2×C283C22×D8
hypercenter#509D283
hypocenterC283C2×#509
LCSG ▷ C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #135×D283C2semidirect
2. C2×D8×D283C2semidirect
3. #31826903C2semidirect
4. #31826902C2semidirect
5. #31826901C2semidirect
6. #31826900C2semidirect
7. #31826899C2semidirect
8. SD32×D283C2semidirect
9. D16×D283C2semidirect
10. M32×D283C2semidirect
11. #509×C283C2semidirect
14. #22583633C22semidirect
15. #22583632C22semidirect
18. #22583629C22semidirect
19. Q16×D283C22semidirect
21. C2×D2264C22semidirect
26. D8×D283C22semidirect
27. D8×D283C22semidirect
29. #22583555C22semidirect
30. #22583554C22semidirect
31. #22583553C22semidirect
32. D4528C22semidirect
33. #22583551C22semidirect
34. #22583551C22semidirect
35. #22583550C22semidirect
36. #22583549C22semidirect
37. C16×D283C22semidirect
38. #135×C283C22semidirect
39. C2×D8×C283C22semidirect
40. SD32×C283C22semidirect
41. D16×C283C22semidirect
42. M32×C283C22semidirect
60. Dic1132C23semidirect
67. D2264C23semidirect
76. C283⋊C16C23semidirect
79. Q16×C283C23semidirect
83. D8×C283C23semidirect
85. C16×C283C23semidirect
150. D283#509direct (N × H)
151. C283C2×#509semidirect
160. #509D283direct (N × H)
171. #135C2×D283semidirect
181. C2×D8C2×D283semidirect
186. SD32C2×D283semidirect
190. D16C2×D283semidirect
193. M32C2×D283semidirect
216. Q16C22×D283semidirect
229. D8C22×D283semidirect
237. C16C22×D283semidirect

Maximal subgroups

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

subgroupindex
#135×D2832
C2×D8×D2832
#318269032
#318269022
#318269012
#318269002
#318268992
SD32×D2832
D16×D2832
M32×D2832
#509×C2832
C2×#509283