Finite Group Databasebeta

← D29×#509 #16832612

Subgroups — D29×#509 #16832612

Order 3712.

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×D29C211yesmaximal, characteristic, complemented
2C2×D8×D29C211yesmaximal, characteristic, complemented
3#14271601C211yesmaximal, characteristic, complemented
4#14271600C212yesmaximal, complemented
5#14271599C211yesmaximal, characteristic, complemented
6#14271598C211yesmaximal, characteristic, complemented
7#14271597C212yesmaximal, complemented
8SD32×D29C212yesmaximal, complemented
9D16×D29C212yesmaximal, complemented
10M32×D29C211yesmaximal, characteristic, complemented
11C29×#509C211yesmaximal, characteristic, complemented
12#41×D29—21no—
13C2×D4×D29—21no—
14C29×#135C2211yescharacteristic, complemented
15C2×D8×C29C2211yescharacteristic, complemented
16#11745312—21no—
17C2×#90782—21no—
18#11745281C2211yescharacteristic, complemented
19Q16×D29C2211yescharacteristic, complemented
20#11745278—21no—
21SD16×D29—21no—
22#11745274C2211yescharacteristic, complemented
23D8×D29—21no—
24D8×D29—21no—
25D8×D29C2212yes—
26D8×D29C2212yescomplemented
27D8×D29C2211yescharacteristic, complemented
28#11745266C2211yescharacteristic, complemented
29C2×D232C2211yescharacteristic, complemented
30C2×C8×D29C2211yescharacteristic
31C29×SD32C2212yescomplemented
32C29×D16C2212yescomplemented
33C29×M32C2211yescharacteristic, complemented
34#11745176C2212yescomplemented
35#11745175C2212yescomplemented
36#11745174C2212yescomplemented
37#11745174C2212yescomplemented
38#11745160C2211yescharacteristic, complemented
39#11745148C2212yescomplemented
40D464C2212yescomplemented
41#11745146C2212yescomplemented
42C16×D29C2212yescomplemented
43C23×D29—41no—
44#41×C29—21no—
45C2×D4×C29—21no—
46C2×C22⋊D29—41no—
47#90809—21no—
48Q8×D29—21no—
49#90807—21no—
50#90807—41no—
51D4×D29—22no—
52D4×D29—22no—
53D4×D29—21no—
54D4×D29—41no—
55D4×D29—41no—
56D4×D29—41no—
57#90805—21no—
58#90805—41no—
59C2×D116—21no—
60C2×C4×D29—41no—
61C2×C4×D29D411yescharacteristic
62Q16×C29C2311yescharacteristic, complemented
63SD16×C29—21no—
64D8×C29—21no—
65D8×C29C2312yes—
66D8×C29C2311yescharacteristic, complemented
67C2×C8×C29C2311yescharacteristic
68#90785—21no—
69#90784—21no—
70#90783—21no—
71#90782—22no—
72#90782—22no—
73#90782—21no—
74C2×#6597D411yescharacteristic
75Dic116C2311yescharacteristic, complemented
76D232—21no—
77D232C2312yes—
78D232C2311yescharacteristic, complemented
79#90773—21no—
80C8×D29D411yescharacteristic
81C8×D29D411yescharacteristic
82C8×D29C2311yescharacteristic
83C8×D29C2311yescharacteristic
84C16×C29C2312yescomplemented
85#90768C2312yescomplemented
86C23×C29—41no—
87C22×D29—41no—
88C22×D29—41no—
89C22×D29—42no—
90C22×D29—42no—
91C22×D29—84no—
92C22×D29D811yescharacteristic
93Q8×C29—21no—
94D4×C29—22no—
95D4×C29—21no—
96D4×C29—41no—
97D4×C29—41no—
98C2×C4×C29—41no—
99C2×C4×C29C2×D411yescharacteristic
100C22⋊D29—41no—
101C22⋊D29—41no—
102C22⋊D29—41no—
103C22⋊D29—42no—
104C22⋊D29—42no—
105C2×Dic29—41no—
106C2×Dic29D811yescharacteristic
107D116—21no—
108D116—22no—
109D116—41no—
110D116—41no—
111C4×D29—41no—
112C4×D29—41no—
113C4×D29—41no—
114C4×D29D811yescharacteristic
115C4×D29D811yescharacteristic
116C4×D29C2×D411yescharacteristic
117C4×D29C2×D411yescharacteristic
118Dic58—21no—
119Dic58—41no—
120C8×C29C2×D411yescharacteristic
121C8×C29C2411yescharacteristic
122#6597C2×D411yescharacteristic
123#6597C2×D411yescharacteristic
124C2×#509—291nomaximal, Sylow
125C22×C29—41no—
126C22×C29—42no—
127C22×C29—82no—
128C22×C29C2×D811yescharacteristic
129C2×D29—22no—
130C2×D29—41no—
131C2×D29—42no—
132C2×D29—84no—
133C2×D29—82no—
134C2×D29—82no—
135C2×D29—84no—
136C2×D29C2×D811yescharacteristic
137C2×D29C2×D811yescharacteristic
138C4×C29—41no—
139C4×C29C2×D811yescharacteristic
140C4×C29C22×D411yescharacteristic
141Dic29—41no—
142Dic29C2×D811yescharacteristic
143Dic29C2×D811yescharacteristic
144C2×#135—291no—
145C22×D8—291no—
146#509—291no—
147#509—291no—
148#509—292no—
149#509—292no—
150#509—291no—
151#509D2911yescharacteristic, direct product factor
152C2×SD32—292no—
153C2×D16—292no—
154C2×M32—291no—
155C2×C29—21no—
156C2×C29—82no—
157C2×C29—81no—
158C2×C29C22×D811yescharacteristic
159D29—21no—
160D29—81no—
161D29—82no—
162D29#50912yesdirect product factor
163C2×#41—581no—
164C22×D4—581no—
165#135—291no—
166#135—291no—
167#135—291no—
168#135—581no—
169#135—581no—
170#135C2×D2911yescharacteristic, complemented
171C2×Q16—291no—
172C2×SD16—581no—
173C2×D8—292no—
174C2×D8—292no—
175C2×D8—291no—
176C2×D8—291no—
177C2×D8—581no—
178C2×D8—581no—
179C2×D8—581no—
180C2×D8C2×D2911yescharacteristic, complemented
181C22×C8—291no—
182SD32—292no—
183SD32—292no—
184SD32—292no—
185SD32C2×D2912yescomplemented
186D16—292no—
187D16—292no—
188D16—292no—
189D16C2×D2912yescomplemented
190M32—291no—
191M32—292no—
192M32C2×D2911yescharacteristic, complemented
193C2×C16—292no—
194C29C2×#50911yescharacteristic, complemented, Sylow
195C24—1161no—
196#41—21no—
197#41—581no—
198#41—581no—
199#41—581no—
200#41—1161no—
201#41—1161no—
202C2×Q8—581no—
203C2×D4—21no—
204C2×D4—582no—
205C2×D4—582no—
206C2×D4—581no—
207C2×D4—581no—
208C2×D4—1161no—
209C2×D4—1161no—
210C2×D4—1161no—
211C2×D4—1161no—
212C22×C4—291no—
213C22×C4—1161no—
214Q16—291no—
215Q16—581no—
216Q16C22×D2911yescharacteristic, complemented
217SD16—21no—
218SD16—581no—
219SD16—581no—
220SD16—581no—
221D8—21no—
222D8—291no—
223D8—292no—
224D8—582no—
225D8—582no—
226D8—581no—
227D8—581no—
228D8C22×D2912yes—
229D8C22×D2911yescharacteristic, complemented
230C2×C8—291no—
231C2×C8—291no—
232C2×C8—291no—
233C2×C8—291no—
234C2×C8—291no—
235C2×C8C22×D2911yescharacteristic
236C16—292no—
237C16C22×D2912yescomplemented
238C23—41no—
239C23—291no—
240C23—1161no—
241C23—1162no—
242C23—1162no—
243C23—1161no—
244C23—2324no—
245Q8—21no—
246Q8—581no—
247Q8—1161no—
248D4—22no—
249D4—21no—
250D4—41no—
251D4—41no—
252D4—582no—
253D4—581no—
254D4—1161no—
255D4—1162no—
256D4—1162no—
257D4—1161no—
258D4—1161no—
259D4—1161no—
260D4—1161no—
261C2×C4—41no—
262C2×C4—291no—
263C2×C4—291no—
264C2×C4—291no—
265C2×C4—291no—
266C2×C4—291no—
267C2×C4—1161no—
268C2×C4—1161no—
269C2×C4—1161no—
270C2×C4—1161no—
271C2×C4D4×D2911yescharacteristic
272C8—291no—
273C8—291no—
274C8D4×D2911yescharacteristic
275C8C23×D2911yescharacteristic
276C22—41no—
277C22—42no—
278C22—82no—
279C22—291no—
280C22—291no—
281C22—582no—
282C22—1161no—
283C22—1162no—
284C22—2322no—
285C22—2324no—
286C22—2322no—
287C22—2324no—
288C22D8×D2911yescharacteristic
289C4—41no—
290C4—291no—
291C4—291no—
292C4—1161no—
293C4D8×D2911yescharacteristic
294C4C2×D4×D2911yescharacteristic
295C2—21no—
296C2—82no—
297C2—81no—
298C2—292no—
299C2—581no—
300C2—2322no—
301C2—2321no—
302C2C2×D8×D2911yescharacteristic
subgroupG/H
centerC2C2×D8×D29
commutator, cosocleC8×C29C24
FrattiniC8C23×D29
FittingC29×#509C2
socleC2×C29C22×D8
hypercenter#509D29
hypocenterC29C2×#509
LCSG ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #135×D29C2semidirect
2. C2×D8×D29C2semidirect
3. #14271601C2semidirect
4. #14271600C2semidirect
5. #14271599C2semidirect
6. #14271598C2semidirect
7. #14271597C2semidirect
8. SD32×D29C2semidirect
9. D16×D29C2semidirect
10. M32×D29C2semidirect
11. C29×#509C2semidirect
14. C29×#135C22semidirect
15. C2×D8×C29C22semidirect
18. #11745281C22semidirect
19. Q16×D29C22semidirect
22. #11745274C22semidirect
26. D8×D29C22semidirect
27. D8×D29C22semidirect
28. #11745266C22semidirect
29. C2×D232C22semidirect
31. C29×SD32C22semidirect
32. C29×D16C22semidirect
33. C29×M32C22semidirect
34. #11745176C22semidirect
35. #11745175C22semidirect
36. #11745174C22semidirect
37. #11745174C22semidirect
38. #11745160C22semidirect
39. #11745148C22semidirect
40. D464C22semidirect
41. #11745146C22semidirect
42. C16×D29C22semidirect
62. Q16×C29C23semidirect
66. D8×C29C23semidirect
75. Dic116C23semidirect
78. D232C23semidirect
84. C16×C29C23semidirect
85. #90768C23semidirect
151. #509D29direct (N × H)
162. D29#509direct (N × H)
170. #135C2×D29semidirect
180. C2×D8C2×D29semidirect
185. SD32C2×D29semidirect
189. D16C2×D29semidirect
192. M32C2×D29semidirect
194. C29C2×#509semidirect
216. Q16C22×D29semidirect
229. D8C22×D29semidirect
237. C16C22×D29semidirect

Maximal subgroups

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

subgroupindex
#135×D292
C2×D8×D292
#142716012
#142716002
#142715992
#142715982
#142715972
SD32×D292
D16×D292
M32×D292
C29×#5092
C2×#50929