Finite Group Databasebeta

← #509×D43 #19147715

Subgroups — #509×D43 #19147715

Order 5504.

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×D43C211yesmaximal, characteristic, complemented
2C2×D8×D43C211yesmaximal, characteristic, complemented
3#14583337C211yesmaximal, characteristic, complemented
4#14583336C212yesmaximal, complemented
5#14583335C211yesmaximal, characteristic, complemented
6#14583334C211yesmaximal, characteristic, complemented
7#14583333C212yesmaximal, complemented
8SD32×D43C212yesmaximal, complemented
9D16×D43C212yesmaximal, complemented
10M32×D43C211yesmaximal, characteristic, complemented
11C43×#509C211yesmaximal, characteristic, complemented
12#41×D43—21no—
13C2×D4×D43—21no—
14#13063348C2211yescharacteristic, complemented
15#13063347C2211yescharacteristic, complemented
16#13063346—21no—
17#13063345—21no—
18#13063344C2211yescharacteristic, complemented
19Q16×D43C2211yescharacteristic, complemented
20SD16×D43—21no—
21C2×D344C2211yescharacteristic, complemented
22C2×#10621882—21no—
23D8×D43—21no—
24D8×D43—21no—
25D8×D43C2212yes—
26D8×D43C2212yescomplemented
27D8×D43C2211yescharacteristic, complemented
28C2×C8×D43C2211yescharacteristic
29#13063270C2212yescomplemented
30#13063269C2212yescomplemented
31#13063268C2212yescomplemented
32D688C2212yescomplemented
33#13063266C2212yescomplemented
34#13063266C2212yescomplemented
35#13063265C2211yescharacteristic, complemented
36#13063264C2212yescomplemented
37C16×D43C2212yescomplemented
38#135×C43C2211yescharacteristic, complemented
39C2×D8×C43C2211yescharacteristic, complemented
40SD32×C43C2212yescomplemented
41D16×C43C2212yescomplemented
42M32×C43C2211yescharacteristic, complemented
43C23×D43—41no—
44#41×C43—21no—
45C2×D4×C43—21no—
46C2×C22⋊D43—41no—
47#10621902—21no—
48Q8×D43—21no—
49#10621900—21no—
50#10621900—41no—
51D4×D43—22no—
52D4×D43—22no—
53D4×D43—21no—
54D4×D43—41no—
55D4×D43—41no—
56D4×D43—41no—
57#10621898—21no—
58#10621898—41no—
59C2×D172—21no—
60C2×C4×D43—41no—
61C2×C4×D43D411yescharacteristic
62Q16×C43C2311yescharacteristic, complemented
63SD16×C43—21no—
64D8×C43—21no—
65D8×C43C2312yes—
66D8×C43C2311yescharacteristic, complemented
67C2×C8×C43C2311yescharacteristic
68#10621885—21no—
69#10621884—21no—
70#10621883—21no—
71#10621882—22no—
72#10621882—22no—
73#10621882—21no—
74C2×C43⋊C8D411yescharacteristic
75Dic172C2311yescharacteristic, complemented
76D344—21no—
77D344C2312yes—
78D344C2311yescharacteristic, complemented
79#10621873—21no—
80C8×D43D411yescharacteristic
81C8×D43D411yescharacteristic
82C8×D43C2311yescharacteristic
83C8×D43C2311yescharacteristic
84C16×C43C2312yescomplemented
85C43⋊C16C2312yescomplemented
86C23×C43—41no—
87C22×D43—41no—
88C22×D43—41no—
89C22×D43—42no—
90C22×D43—42no—
91C22×D43—84no—
92C22×D43D811yescharacteristic
93Q8×C43—21no—
94D4×C43—22no—
95D4×C43—21no—
96D4×C43—41no—
97D4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43C2×D411yescharacteristic
100C22⋊D43—41no—
101C22⋊D43—41no—
102C22⋊D43—41no—
103C22⋊D43—42no—
104C22⋊D43—42no—
105C2×Dic43—41no—
106C2×Dic43D811yescharacteristic
107D172—21no—
108D172—22no—
109D172—41no—
110D172—41no—
111C4×D43—41no—
112C4×D43—41no—
113C4×D43—41no—
114C4×D43D811yescharacteristic
115C4×D43D811yescharacteristic
116C4×D43C2×D411yescharacteristic
117C4×D43C2×D411yescharacteristic
118Dic86—21no—
119Dic86—41no—
120C8×C43C2×D411yescharacteristic
121C8×C43C2411yescharacteristic
122C43⋊C8C2×D411yescharacteristic
123C43⋊C8C2×D411yescharacteristic
124C22×C43—42no—
125C22×C43—41no—
126C22×C43—82no—
127C22×C43C2×D811yescharacteristic
128C2×D43—22no—
129C2×D43—42no—
130C2×D43—41no—
131C2×D43—84no—
132C2×D43—82no—
133C2×D43—82no—
134C2×D43—84no—
135C2×D43C2×D811yescharacteristic
136C2×D43C2×D811yescharacteristic
137C4×C43—41no—
138C4×C43C2×D811yescharacteristic
139C4×C43C22×D411yescharacteristic
140Dic43—41no—
141Dic43C2×D811yescharacteristic
142Dic43C2×D811yescharacteristic
143C2×#509—431nomaximal, Sylow
144C2×C43—21no—
145C2×C43—82no—
146C2×C43—81no—
147C2×C43C22×D811yescharacteristic
148D43—21no—
149D43—81no—
150D43—82no—
151D43#50912yesdirect product factor
152C2×#135—431no—
153C22×D8—431no—
154#509—431no—
155#509—431no—
156#509—432no—
157#509—432no—
158#509—431no—
159#509D4311yescharacteristic, direct product factor
160C2×SD32—432no—
161C2×D16—432no—
162C2×M32—431no—
163C43C2×#50911yescharacteristic, complemented, Sylow
164C2×#41—861no—
165C22×D4—861no—
166#135—431no—
167#135—431no—
168#135—431no—
169#135—861no—
170#135—861no—
171#135C2×D4311yescharacteristic, complemented
172C2×Q16—431no—
173C2×SD16—861no—
174C2×D8—432no—
175C2×D8—432no—
176C2×D8—431no—
177C2×D8—431no—
178C2×D8—861no—
179C2×D8—861no—
180C2×D8—861no—
181C2×D8C2×D4311yescharacteristic, complemented
182C22×C8—431no—
183SD32—432no—
184SD32—432no—
185SD32—432no—
186SD32C2×D4312yescomplemented
187D16—432no—
188D16—432no—
189D16—432no—
190D16C2×D4312yescomplemented
191M32—431no—
192M32—432no—
193M32C2×D4311yescharacteristic, complemented
194C2×C16—432no—
195C24—1721no—
196#41—21no—
197#41—861no—
198#41—861no—
199#41—861no—
200#41—1721no—
201#41—1721no—
202C2×Q8—861no—
203C2×D4—21no—
204C2×D4—862no—
205C2×D4—862no—
206C2×D4—861no—
207C2×D4—861no—
208C2×D4—1721no—
209C2×D4—1721no—
210C2×D4—1721no—
211C2×D4—1721no—
212C22×C4—431no—
213C22×C4—1721no—
214Q16—431no—
215Q16—861no—
216Q16C22×D4311yescharacteristic, complemented
217SD16—21no—
218SD16—861no—
219SD16—861no—
220SD16—861no—
221D8—21no—
222D8—431no—
223D8—432no—
224D8—862no—
225D8—862no—
226D8—861no—
227D8—861no—
228D8C22×D4312yes—
229D8C22×D4311yescharacteristic, complemented
230C2×C8—431no—
231C2×C8—431no—
232C2×C8—431no—
233C2×C8—431no—
234C2×C8—431no—
235C2×C8C22×D4311yescharacteristic
236C16—432no—
237C16C22×D4312yescomplemented
238C23—41no—
239C23—431no—
240C23—3444no—
241C23—1721no—
242C23—1722no—
243C23—1722no—
244C23—1721no—
245Q8—21no—
246Q8—861no—
247Q8—1721no—
248D4—22no—
249D4—21no—
250D4—41no—
251D4—41no—
252D4—862no—
253D4—861no—
254D4—1721no—
255D4—1722no—
256D4—1722no—
257D4—1721no—
258D4—1721no—
259D4—1721no—
260D4—1721no—
261C2×C4—41no—
262C2×C4—431no—
263C2×C4—431no—
264C2×C4—431no—
265C2×C4—431no—
266C2×C4—431no—
267C2×C4—1721no—
268C2×C4—1721no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4D4×D4311yescharacteristic
272C8—431no—
273C8—431no—
274C8D4×D4311yescharacteristic
275C8C23×D4311yescharacteristic
276C22—41no—
277C22—42no—
278C22—82no—
279C22—431no—
280C22—431no—
281C22—862no—
282C22—3442no—
283C22—3444no—
284C22—3442no—
285C22—3444no—
286C22—1721no—
287C22—1722no—
288C22D8×D4311yescharacteristic
289C4—41no—
290C4—431no—
291C4—431no—
292C4—1721no—
293C4D8×D4311yescharacteristic
294C4C2×D4×D4311yescharacteristic
295C2—21no—
296C2—82no—
297C2—81no—
298C2—432no—
299C2—861no—
300C2—3442no—
301C2—3441no—
302C2C2×D8×D4311yescharacteristic
subgroupG/H
centerC2C2×D8×D43
commutatorC8×C43C24
FrattiniC8C23×D43
FittingC43×#509C2
socleC2×C43C22×D8
hypercenter#509D43
hypocenterC43C2×#509
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #135×D43C2semidirect
2. C2×D8×D43C2semidirect
3. #14583337C2semidirect
4. #14583336C2semidirect
5. #14583335C2semidirect
6. #14583334C2semidirect
7. #14583333C2semidirect
8. SD32×D43C2semidirect
9. D16×D43C2semidirect
10. M32×D43C2semidirect
11. C43×#509C2semidirect
14. #13063348C22semidirect
15. #13063347C22semidirect
18. #13063344C22semidirect
19. Q16×D43C22semidirect
21. C2×D344C22semidirect
26. D8×D43C22semidirect
27. D8×D43C22semidirect
29. #13063270C22semidirect
30. #13063269C22semidirect
31. #13063268C22semidirect
32. D688C22semidirect
33. #13063266C22semidirect
34. #13063266C22semidirect
35. #13063265C22semidirect
36. #13063264C22semidirect
37. C16×D43C22semidirect
38. #135×C43C22semidirect
39. C2×D8×C43C22semidirect
40. SD32×C43C22semidirect
41. D16×C43C22semidirect
42. M32×C43C22semidirect
62. Q16×C43C23semidirect
66. D8×C43C23semidirect
75. Dic172C23semidirect
78. D344C23semidirect
84. C16×C43C23semidirect
85. C43⋊C16C23semidirect
151. D43#509direct (N × H)
159. #509D43direct (N × H)
163. C43C2×#509semidirect
171. #135C2×D43semidirect
181. C2×D8C2×D43semidirect
186. SD32C2×D43semidirect
190. D16C2×D43semidirect
193. M32C2×D43semidirect
216. Q16C22×D43semidirect
229. D8C22×D43semidirect
237. C16C22×D43semidirect