Finite Group Databasebeta

← #509×D139 #31819524

Subgroups — #509×D139 #31819524

Order 17792.

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×D139C211yesmaximal, characteristic, complemented
2C2×D8×D139C211yesmaximal, characteristic, complemented
3#22581391C211yesmaximal, characteristic, complemented
4#22581390C212yesmaximal, complemented
5#22581389C211yesmaximal, characteristic, complemented
6#22581388C211yesmaximal, characteristic, complemented
7#22581387C212yesmaximal, complemented
8SD32×D139C212yesmaximal, complemented
9D16×D139C212yesmaximal, complemented
10M32×D139C211yesmaximal, characteristic, complemented
11#509×C139C211yesmaximal, characteristic, complemented
12#41×D139—21no—
13C2×D4×D139—21no—
14#17984865C2211yescharacteristic, complemented
15#17984864C2211yescharacteristic, complemented
16#17984863—21no—
17#17984862—21no—
18#17984861C2211yescharacteristic, complemented
19Q16×D139C2211yescharacteristic, complemented
20SD16×D139—21no—
21C2×D1112C2211yescharacteristic, complemented
22C2×#14555770—21no—
23D8×D139—21no—
24D8×D139—21no—
25D8×D139C2212yes—
26D8×D139C2212yescomplemented
27D8×D139C2211yescharacteristic, complemented
28C2×C8×D139C2211yescharacteristic
29#17984787C2212yescomplemented
30#17984786C2212yescomplemented
31#17984785C2212yescomplemented
32D2224C2212yescomplemented
33#17984783C2212yescomplemented
34#17984783C2212yescomplemented
35#17984782C2211yescharacteristic, complemented
36#17984781C2212yescomplemented
37C16×D139C2212yescomplemented
38#135×C139C2211yescharacteristic, complemented
39C2×D8×C139C2211yescharacteristic, complemented
40SD32×C139C2212yescomplemented
41D16×C139C2212yescomplemented
42M32×C139C2211yescharacteristic, complemented
43C23×D139—41no—
44#14555786—21no—
45#14555785—21no—
46#14555785—41no—
47#14555784—21no—
48#14555784—41no—
49Q8×D139—21no—
50C2×D556—21no—
51C2×C22⋊D139—41no—
52D4×D139—22no—
53D4×D139—22no—
54D4×D139—21no—
55D4×D139—41no—
56D4×D139—41no—
57D4×D139—41no—
58C2×C4×D139—41no—
59C2×C4×D139D411yescharacteristic
60Dic556C2311yescharacteristic, complemented
61#14555775—21no—
62#14555774—21no—
63#14555773—21no—
64#14555772—21no—
65D1112—21no—
66D1112C2312yes—
67D1112C2311yescharacteristic, complemented
68#14555770—22no—
69#14555770—22no—
70#14555770—21no—
71C2×C139⋊C8D411yescharacteristic
72C8×D139D411yescharacteristic
73C8×D139D411yescharacteristic
74C8×D139C2311yescharacteristic
75C8×D139C2311yescharacteristic
76C139⋊C16C2312yescomplemented
77#41×C139—21no—
78C2×D4×C139—21no—
79Q16×C139C2311yescharacteristic, complemented
80SD16×C139—21no—
81D8×C139—21no—
82D8×C139C2312yes—
83D8×C139C2311yescharacteristic, complemented
84C2×C8×C139C2311yescharacteristic
85C16×C139C2312yescomplemented
86C22×D139—41no—
87C22×D139—41no—
88C22×D139—42no—
89C22×D139—42no—
90C22×D139—84no—
91C22×D139D811yescharacteristic
92Dic278—21no—
93Dic278—41no—
94D556—22no—
95D556—21no—
96D556—41no—
97D556—41no—
98C22⋊D139—41no—
99C22⋊D139—41no—
100C22⋊D139—42no—
101C22⋊D139—42no—
102C22⋊D139—41no—
103C2×Dic139—41no—
104C2×Dic139D811yescharacteristic
105C4×D139—41no—
106C4×D139—41no—
107C4×D139—41no—
108C4×D139D811yescharacteristic
109C4×D139D811yescharacteristic
110C4×D139C2×D411yescharacteristic
111C4×D139C2×D411yescharacteristic
112C139⋊C8C2×D411yescharacteristic
113C139⋊C8C2×D411yescharacteristic
114C23×C139—41no—
115Q8×C139—21no—
116D4×C139—22no—
117D4×C139—21no—
118D4×C139—41no—
119D4×C139—41no—
120C2×C4×C139—41no—
121C2×C4×C139C2×D411yescharacteristic
122C8×C139C2×D411yescharacteristic
123C8×C139C2411yescharacteristic
124C22×C139—41no—
125C22×C139—42no—
126C22×C139—82no—
127C22×C139C2×D811yescharacteristic
128C2×D139—22no—
129C2×D139—41no—
130C2×D139—42no—
131C2×D139—84no—
132C2×D139—82no—
133C2×D139—82no—
134C2×D139—84no—
135C2×D139C2×D811yescharacteristic
136C2×D139C2×D811yescharacteristic
137C4×C139—41no—
138C4×C139C2×D811yescharacteristic
139C4×C139C22×D411yescharacteristic
140Dic139—41no—
141Dic139C2×D811yescharacteristic
142Dic139C2×D811yescharacteristic
143C2×C139—21no—
144C2×C139—82no—
145C2×C139—81no—
146C2×C139C22×D811yescharacteristic
147D139—21no—
148D139—81no—
149D139—82no—
150D139#50912yesdirect product factor
151C139C2×#50911yescharacteristic, complemented, Sylow
152C2×#509—1391nomaximal, Sylow
153C2×#135—1391no—
154C22×D8—1391no—
155#509—1391no—
156#509—1391no—
157#509—1392no—
158#509—1392no—
159#509—1391no—
160#509D13911yescharacteristic, direct product factor
161C2×SD32—1392no—
162C2×D16—1392no—
163C2×M32—1391no—
164C2×#41—2781no—
165C22×D4—2781no—
166#135—2781no—
167#135—2781no—
168#135—1391no—
169#135—1391no—
170#135—1391no—
171#135C2×D13911yescharacteristic, complemented
172C2×Q16—1391no—
173C2×SD16—2781no—
174C2×D8—2781no—
175C2×D8—2781no—
176C2×D8—2781no—
177C2×D8—1392no—
178C2×D8—1392no—
179C2×D8—1391no—
180C2×D8—1391no—
181C2×D8C2×D13911yescharacteristic, complemented
182C22×C8—1391no—
183SD32—1392no—
184SD32—1392no—
185SD32—1392no—
186SD32C2×D13912yescomplemented
187D16—1392no—
188D16—1392no—
189D16—1392no—
190D16C2×D13912yescomplemented
191M32—1391no—
192M32—1392no—
193M32C2×D13911yescharacteristic, complemented
194C2×C16—1392no—
195C24—5561no—
196#41—21no—
197#41—2781no—
198#41—2781no—
199#41—2781no—
200#41—5561no—
201#41—5561no—
202C2×Q8—2781no—
203C2×D4—21no—
204C2×D4—2782no—
205C2×D4—2782no—
206C2×D4—2781no—
207C2×D4—2781no—
208C2×D4—5561no—
209C2×D4—5561no—
210C2×D4—5561no—
211C2×D4—5561no—
212C22×C4—5561no—
213C22×C4—1391no—
214Q16—2781no—
215Q16—1391no—
216Q16C22×D13911yescharacteristic, complemented
217SD16—21no—
218SD16—2781no—
219SD16—2781no—
220SD16—2781no—
221D8—21no—
222D8—2782no—
223D8—2782no—
224D8—2781no—
225D8—2781no—
226D8—1391no—
227D8—1392no—
228D8C22×D13912yes—
229D8C22×D13911yescharacteristic, complemented
230C2×C8—1391no—
231C2×C8—1391no—
232C2×C8—1391no—
233C2×C8—1391no—
234C2×C8—1391no—
235C2×C8C22×D13911yescharacteristic
236C16—1392no—
237C16C22×D13912yescomplemented
238C23—41no—
239C23—5561no—
240C23—5562no—
241C23—5562no—
242C23—5561no—
243C23—11124no—
244C23—1391no—
245Q8—21no—
246Q8—2781no—
247Q8—5561no—
248D4—22no—
249D4—21no—
250D4—41no—
251D4—41no—
252D4—2782no—
253D4—2781no—
254D4—5561no—
255D4—5561no—
256D4—5561no—
257D4—5562no—
258D4—5562no—
259D4—5561no—
260D4—5561no—
261C2×C4—41no—
262C2×C4—5561no—
263C2×C4—5561no—
264C2×C4—5561no—
265C2×C4—5561no—
266C2×C4—1391no—
267C2×C4—1391no—
268C2×C4—1391no—
269C2×C4—1391no—
270C2×C4—1391no—
271C2×C4D4×D13911yescharacteristic
272C8—1391no—
273C8—1391no—
274C8D4×D13911yescharacteristic
275C8C23×D13911yescharacteristic
276C22—41no—
277C22—42no—
278C22—82no—
279C22—2782no—
280C22—5561no—
281C22—5562no—
282C22—11122no—
283C22—11124no—
284C22—11124no—
285C22—11122no—
286C22—1391no—
287C22—1391no—
288C22D8×D13911yescharacteristic
289C4—41no—
290C4—5561no—
291C4—1391no—
292C4—1391no—
293C4D8×D13911yescharacteristic
294C4C2×D4×D13911yescharacteristic
295C2—21no—
296C2—82no—
297C2—81no—
298C2—2781no—
299C2—11122no—
300C2—11121no—
301C2—1392no—
302C2C2×D8×D13911yescharacteristic
subgroupG/H
centerC2C2×D8×D139
commutator, cosocleC8×C139C24
FrattiniC8C23×D139
Fitting#509×C139C2
socleC2×C139C22×D8
hypercenter#509D139
hypocenterC139C2×#509
LCSG ▷ C8×C139 ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #135×D139C2semidirect
2. C2×D8×D139C2semidirect
3. #22581391C2semidirect
4. #22581390C2semidirect
5. #22581389C2semidirect
6. #22581388C2semidirect
7. #22581387C2semidirect
8. SD32×D139C2semidirect
9. D16×D139C2semidirect
10. M32×D139C2semidirect
11. #509×C139C2semidirect
14. #17984865C22semidirect
15. #17984864C22semidirect
18. #17984861C22semidirect
19. Q16×D139C22semidirect
21. C2×D1112C22semidirect
26. D8×D139C22semidirect
27. D8×D139C22semidirect
29. #17984787C22semidirect
30. #17984786C22semidirect
31. #17984785C22semidirect
32. D2224C22semidirect
33. #17984783C22semidirect
34. #17984783C22semidirect
35. #17984782C22semidirect
36. #17984781C22semidirect
37. C16×D139C22semidirect
38. #135×C139C22semidirect
39. C2×D8×C139C22semidirect
40. SD32×C139C22semidirect
41. D16×C139C22semidirect
42. M32×C139C22semidirect
60. Dic556C23semidirect
67. D1112C23semidirect
76. C139⋊C16C23semidirect
79. Q16×C139C23semidirect
83. D8×C139C23semidirect
85. C16×C139C23semidirect
150. D139#509direct (N × H)
151. C139C2×#509semidirect
160. #509D139direct (N × H)
171. #135C2×D139semidirect
181. C2×D8C2×D139semidirect
186. SD32C2×D139semidirect
190. D16C2×D139semidirect
193. M32C2×D139semidirect
216. Q16C22×D139semidirect
229. D8C22×D139semidirect
237. C16C22×D139semidirect

Maximal subgroups

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

subgroupindex
#135×D1392
C2×D8×D1392
#225813912
#225813902
#225813892
#225813882
#225813872
SD32×D1392
D16×D1392
M32×D1392
#509×C1392
C2×#509139