Finite Group Databasebeta

← #16832632

Subgroups — #16832632

Order 3712.

370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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#14271965C211yesmaximal, characteristic, complemented
2#14271964C211yesmaximal, characteristic, complemented
3#14271601C211yesmaximal, characteristic, complemented
4#14271600C212yesmaximal, complemented
5#14271597C212yesmaximal, complemented
6#14271594C212yesmaximal, complemented
7#14271593C211yesmaximal, characteristic, complemented
8C2×#11745174C211yesmaximal, characteristic, complemented
9D16×D29C212yesmaximal, complemented
10#14271581C211yesmaximal, characteristic, complemented
11C29×#509C211yesmaximal, characteristic, complemented
12#11745364—21no—
13#11745359—21no—
14C29×#135C2211yescharacteristic, complemented
15C2×D8×C29C2211yescharacteristic, complemented
16#11745311—21no—
17#11745294—21no—
18#11745281C2212yescomplemented
19#11745276—22no—
20#11745274C2212yescomplemented
21#11745273—22no—
22D8×D29C2212yescomplemented
23D8×D29C2212yescomplemented
24#11745266C2211yescharacteristic, complemented
25C2×D232C2211yescharacteristic, complemented
26#11745263C2211yescharacteristic
27C29×SD32C2212yescomplemented
28C29×D16C2212yescomplemented
29C29×M32C2211yescharacteristic, complemented
30#11745177C2211yescharacteristic, complemented
31#11745176C2211yescharacteristic, complemented
32#11745175C2211yescharacteristic, complemented
33#11745174C2211yescharacteristic, complemented
34#11745174C2212yescomplemented
35#11745174C2212yescomplemented
36C2×#90768C2211yescharacteristic, complemented
37#11745148C2212yescomplemented
38D464C2212yescomplemented
39#11745146C2212yescomplemented
40C16×D29C2212yescomplemented
41#41×C29—21no—
42C2×D4×C29—21no—
43C2×C22⋊D29—42no—
44#90809—22no—
45#90807—22no—
46#90807—41no—
47D4×D29—22no—
48D4×D29—22no—
49D4×D29—42no—
50D4×D29—41no—
51#90805—21no—
52#90805—41no—
53#90805D411yescharacteristic
54C2×D116—21no—
55C2×D116—41no—
56Q16×C29C2311yescharacteristic
57SD16×C29—21no—
58D8×C29—21no—
59D8×C29C2312yes—
60D8×C29C2311yescharacteristic
61C2×C8×C29C2311yescharacteristic
62#90784—22no—
63#90783—22no—
64#90782—22no—
65#90782—22no—
66#90777D411yescharacteristic
67Dic116C2311yescharacteristic
68D232—21no—
69D232C2312yes—
70D232C2311yescharacteristic
71#90773—21no—
72#90772D412yes—
73C8×D29C2312yes—
74C16×C29C2312yes—
75#90768C2311yescharacteristic
76#90768C2311yescharacteristic
77C23×C29—41no—
78C22×D29—41no—
79C22×D29—42no—
80C22×D29—42no—
81Q8×C29—21no—
82D4×C29—21no—
83D4×C29—22no—
84D4×C29—41no—
85D4×C29—41no—
86C2×C4×C29—41no—
87C2×C4×C29C2×D411yescharacteristic
88C22⋊D29—41no—
89C22⋊D29—42no—
90C22⋊D29—42no—
91C22⋊D29—42no—
92C22⋊D29D812yes—
93C2×Dic29—42no—
94D116—21no—
95D116—22no—
96D116—42no—
97D116—41no—
98D116D811yescharacteristic
99C4×D29—41no—
100C4×D29—42no—
101C4×D29C2×D412yes—
102Dic58—21no—
103Dic58D811yescharacteristic
104C8×C29C2×D411yescharacteristic
105C8×C29C2411yescharacteristic
106#6597C2×D412yes—
107#3415—291nomaximal, Sylow
108C22×C29—42no—
109C22×C29—41no—
110C22×C29—161no—
111C22×C29C2×D811yescharacteristic
112C2×D29—42no—
113C2×D29—41no—
114C2×D29—162no—
115C2×D29—162no—
116C2×D29—161no—
117C2×D29C2×D812yes—
118C4×C29—41no—
119C4×C29C2×D811yescharacteristic
120C4×C29C22×D411yescharacteristic
121Dic29—41no—
122Dic29C2×D812yes—
123#576—291no—
124#576—291no—
125#509—292no—
126#509—292no—
127#509—291no—
128#509D2911yescharacteristic, complemented
129#508—291no—
130#508—292no—
131C2×D16—291no—
132C2×D16—292no—
133#504—291no—
134C2×C29—21no—
135C2×C29—81no—
136C2×C29—82no—
137C2×C29C22×D811yescharacteristic
138D29—22no—
139D29—82no—
140D29—81no—
141H(5,𝔽2)—581no—
142H(5,𝔽2)—581no—
143AGL(1,ℤ/8)—582no—
144AGL(1,ℤ/8)—582no—
145AGL(1,ℤ/8)—581no—
146AGL(1,ℤ/8)—581no—
147#135—292no—
148#135—292no—
149#135—291no—
150#135C2×D2911yescharacteristic, complemented
151C2×D8—292no—
152C2×D8—292no—
153C2×D8—291no—
154C2×D8C2×D2911yescharacteristic, complemented
155#131—291no—
156Q32—291no—
157SD32—291no—
158SD32—291no—
159SD32—292no—
160SD32C2×D2912yescomplemented
161D16—292no—
162D16—291no—
163D16—292no—
164D16—292no—
165D16C2×D2912yescomplemented
166M32—292no—
167M32C2×D2911yescharacteristic, complemented
168C2×C16—291no—
169C2×C16—292no—
170C29#341511yescharacteristic, complemented, Sylow
171#41—21no—
172#41—291no—
173#41—582no—
174#41—582no—
175#41—581no—
176#41—1161no—
177#41—1161no—
178C2×D4—21no—
179C2×D4—582no—
180C2×D4—582no—
181C2×D4—581no—
182C2×D4—1161no—
183C2×D4—1162no—
184C2×D4—1161no—
185C2×D4—1162no—
186Q16—291no—
187Q16C22×D2911yescharacteristic
188SD16—21no—
189SD16—582no—
190SD16—582no—
191SD16—581no—
192D8—21no—
193D8—292no—
194D8—291no—
195D8—582no—
196D8—582no—
197D8—581no—
198D8C22×D2912yes—
199D8C22×D2911yescharacteristic
200M16—291no—
201M16—292no—
202C2×C8—292no—
203C2×C8C22×D2911yescharacteristic
204C16—291no—
205C16—291no—
206C16C22×D2912yes—
207C23—41no—
208C23—1162no—
209C23—1162no—
210C23—1161no—
211Q8—21no—
212Q8—291no—
213Q8—581no—
214D4—22no—
215D4—21no—
216D4—41no—
217D4—41no—
218D4—292no—
219D4—291no—
220D4—581no—
221D4—582no—
222D4—1162no—
223D4—1162no—
224D4—1162no—
225D4—1162no—
226D4—1161no—
227D4—1161no—
228C2×C4—41no—
229C2×C4—292no—
230C2×C4—1162no—
231C2×C4—1162no—
232C2×C4—1161no—
233C2×C4D4×D2911yescharacteristic
234C8—292no—
235C8D4×D2911yescharacteristic
236C8C23×D2911yescharacteristic
237C22—41no—
238C22—42no—
239C22—161no—
240C22—292no—
241C22—1162no—
242C22—1161no—
243C22—4641no—
244C22—4642no—
245C22—4642no—
246C22D8×D2911yescharacteristic
247C4—41no—
248C4—292no—
249C4—1161no—
250C4D8×D2911yescharacteristic
251C4C2×D4×D2911yescharacteristic
252C2—21no—
253C2—82no—
254C2—81no—
255C2—582no—
256C2—2322no—
257C2—2321no—
258C2C2×D8×D2911yescharacteristic
subgroupG/H
centerC2C2×D8×D29
commutator, cosocleC8×C29C24
FrattiniC8C23×D29
FittingC29×#509C2
socleC2×C29C22×D8
hypercenter#509D29
hypocenterC29#3415
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. #14271965C2semidirect
2. #14271964C2semidirect
3. #14271601C2semidirect
4. #14271600C2semidirect
5. #14271597C2semidirect
6. #14271594C2semidirect
7. #14271593C2semidirect
8. C2×#11745174C2semidirect
9. D16×D29C2semidirect
10. #14271581C2semidirect
11. C29×#509C2semidirect
14. C29×#135C22semidirect
15. C2×D8×C29C22semidirect
18. #11745281C22semidirect
20. #11745274C22semidirect
22. D8×D29C22semidirect
23. D8×D29C22semidirect
24. #11745266C22semidirect
25. C2×D232C22semidirect
27. C29×SD32C22semidirect
28. C29×D16C22semidirect
29. C29×M32C22semidirect
30. #11745177C22semidirect
31. #11745176C22semidirect
32. #11745175C22semidirect
33. #11745174C22semidirect
34. #11745174C22semidirect
35. #11745174C22semidirect
36. C2×#90768C22semidirect
37. #11745148C22semidirect
38. D464C22semidirect
39. #11745146C22semidirect
40. C16×D29C22semidirect
128. #509D29semidirect
150. #135C2×D29semidirect
154. C2×D8C2×D29semidirect
160. SD32C2×D29semidirect
165. D16C2×D29semidirect
167. M32C2×D29semidirect
170. C29#3415semidirect

Maximal subgroups

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

subgroupindex
#142719652
#142719642
#142716012
#142716002
#142715972
#142715942
#142715932
C2×#117451742
D16×D292
#142715812
C29×#5092
#341529