Finite Group Databasebeta

← #16832634

Subgroups — #16832634

Order 3712.

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

normal subgroups only

This group has 360 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#14271976C211yesmaximal, characteristic, complemented
2#14271964C211yesmaximal, characteristic, complemented
3#14271604C211yesmaximal, characteristic, complemented
4#14271602C212yesmaximal, complemented
5#14271600C212yesmaximal, complemented
6#14271599C211yesmaximal, characteristic, complemented
7#14271595C211yesmaximal, characteristic, complemented
8#14271594C212yesmaximal, complemented
9SD32×D29C212yesmaximal, complemented
10#14271579C211yesmaximal, characteristic, complemented
11C2×C29×SD32C211yesmaximal, characteristic, complemented
12#11745362—21no—
13#11745359—21no—
14C2×Q16×C29C2211yescharacteristic, complemented
15C2×D8×C29C2211yescharacteristic
16#11745304—21no—
17#11745294—21no—
18#11745281C2212yescomplemented
19#11745280—22no—
20Q16×D29C2212yescomplemented
21#11745274C2212yes—
22#11745273—22no—
23D8×D29C2212yes—
24#11745266C2211yescharacteristic
25#11745266C2211yescharacteristic, complemented
26#11745263C2211yescharacteristic
27C29×SD32C2212yescomplemented
28C29×SD32C2212yescomplemented
29C2×C16×C29C2211yescharacteristic, complemented
30#11745177C2212yescomplemented
31#11745176C2212yescomplemented
32#11745175C2212yescomplemented
33#11745174C2212yescomplemented
34#11745160C2211yescharacteristic, complemented
35Dic232C2211yescharacteristic, complemented
36#11745148C2211yescharacteristic, complemented
37#11745148C2211yescharacteristic, complemented
38D464C2211yescharacteristic, complemented
39#11745146C2212yescomplemented
40C16×D29C2212yescomplemented
41C2×Q8×C29—21no—
42C2×D4×C29—21no—
43C2×C22⋊D29—42no—
44#90809—22no—
45#90809—41no—
46Q8×D29—22no—
47Q8×D29—41no—
48#90807—22no—
49#90807—41no—
50D4×D29—22no—
51D4×D29—41no—
52#90805—21no—
53#90805—21no—
54#90805—42no—
55#90805D411yescharacteristic
56Q16×C29—21no—
57Q16×C29C2312yes—
58D8×C29—21no—
59D8×C29C2312yes—
60C2×C8×C29C2311yescharacteristic
61#90785—22no—
62#90784—22no—
63#90783—22no—
64#90782—22no—
65#90777D411yescharacteristic
66Dic116C2311yescharacteristic
67Dic116C2311yescharacteristic
68D232C2311yescharacteristic
69D232C2311yescharacteristic
70#90773—21no—
71#90773—21no—
72#90772D412yes—
73C8×D29C2312yes—
74C16×C29C2311yescharacteristic
75C16×C29C2311yescharacteristic
76#90768C2312yes—
77C23×C29—41no—
78C22×D29—42no—
79Q8×C29—22no—
80Q8×C29—41no—
81D4×C29—22no—
82D4×C29—41no—
83C2×C4×C29—41no—
84C2×C4×C29C2×D411yescharacteristic
85C22⋊D29—41no—
86C22⋊D29—41no—
87C22⋊D29—42no—
88C22⋊D29—42no—
89C22⋊D29D812yes—
90C2×Dic29—42no—
91D116—21no—
92D116—21no—
93D116—42no—
94D116D811yescharacteristic
95C4×D29—42no—
96C4×D29—41no—
97C4×D29—41no—
98C4×D29—42no—
99C4×D29C2×D412yes—
100Dic58—21no—
101Dic58—21no—
102Dic58—42no—
103Dic58D811yescharacteristic
104C8×C29C2×D411yescharacteristic
105C8×C29C2411yescharacteristic
106#6597C2×D412yes—
107#3416—291nomaximal, Sylow
108C22×C29—42no—
109C22×C29—161no—
110C22×C29C2×D811yescharacteristic
111C2×D29—41no—
112C2×D29—41no—
113C2×D29—162no—
114C2×D29C2×D812yes—
115C4×C29—42no—
116C4×C29C2×D811yescharacteristic
117C4×C29C22×D411yescharacteristic
118Dic29—41no—
119Dic29—41no—
120Dic29C2×D812yes—
121#578—291no—
122#576—291no—
123#510—291no—
124#510—292no—
125#509—291no—
126#509—292no—
127#508—292no—
128#508—291no—
129C2×SD32—292no—
130C2×SD32D2911yescharacteristic, complemented
131#504—291no—
132C2×C29—21no—
133C2×C29—82no—
134C2×C29C22×D811yescharacteristic
135D29—22no—
136D29—81no—
137D29—81no—
1382−1+4—581no—
139H(5,𝔽2)—581no—
140#137—582no—
141#137—581no—
142AGL(1,ℤ/8)—582no—
143AGL(1,ℤ/8)—581no—
144#135—292no—
145#135—292no—
146#135—291no—
147#135—291no—
148C2×Q16—292no—
149C2×Q16C2×D2911yescharacteristic, complemented
150C2×D8—292no—
151C2×D8C2×D2911yescharacteristic
152#131—291no—
153Q32—292no—
154Q32—291no—
155SD32—292no—
156SD32—292no—
157SD32—291no—
158SD32—291no—
159SD32C2×D2912yescomplemented
160SD32C2×D2912yescomplemented
161D16—292no—
162D16—291no—
163M32—291no—
164M32—292no—
165C2×C16—292no—
166C2×C16C2×D2911yescharacteristic, complemented
167C29#341611yescharacteristic, complemented, Sylow
168#41—291no—
169#41—582no—
170#41—582no—
171#41—581no—
172#41—581no—
173#41—1162no—
174#41—1161no—
175#41—1161no—
176C2×Q8—21no—
177C2×Q8—582no—
178C2×Q8—1161no—
179C2×D4—21no—
180C2×D4—582no—
181C2×D4—1161no—
182C2×D4—1162no—
183Q16—21no—
184Q16—291no—
185Q16—291no—
186Q16—582no—
187Q16C22×D2912yes—
188SD16—582no—
189SD16—582no—
190SD16—581no—
191SD16—581no—
192D8—21no—
193D8—291no—
194D8—291no—
195D8—582no—
196D8C22×D2912yes—
197M16—291no—
198M16—292no—
199C2×C8—292no—
200C2×C8C22×D2911yescharacteristic
201C16—292no—
202C16C22×D2911yescharacteristic
203C16C22×D2911yescharacteristic
204C23—41no—
205C23—1162no—
206Q8—22no—
207Q8—41no—
208Q8—291no—
209Q8—581no—
210Q8—581no—
211Q8—1162no—
212D4—22no—
213D4—41no—
214D4—292no—
215D4—291no—
216D4—581no—
217D4—581no—
218D4—1162no—
219D4—1162no—
220D4—1162no—
221D4—1161no—
222D4—1161no—
223C2×C4—41no—
224C2×C4—292no—
225C2×C4—1162no—
226C2×C4—1162no—
227C2×C4—1162no—
228C2×C4—1161no—
229C2×C4—1161no—
230C2×C4D4×D2911yescharacteristic
231C8—292no—
232C8D4×D2911yescharacteristic
233C8C23×D2911yescharacteristic
234C22—42no—
235C22—161no—
236C22—292no—
237C22—1161no—
238C22—1161no—
239C22—4642no—
240C22D8×D2911yescharacteristic
241C4—42no—
242C4—292no—
243C4—1161no—
244C4—1161no—
245C4D8×D2911yescharacteristic
246C4C2×D4×D2911yescharacteristic
247C2—21no—
248C2—82no—
249C2—582no—
250C2—2321no—
251C2—2321no—
252C2C2×D8×D2911yescharacteristic
subgroupG/H
centerC2C2×D8×D29
commutator, cosocleC8×C29C24
FrattiniC8C23×D29
FittingC2×C29×SD32C2
socleC2×C29C22×D8
hypercenterC2×SD32D29
hypocenterC29#3416
LCSG ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #14271976C2semidirect
2. #14271964C2semidirect
3. #14271604C2semidirect
4. #14271602C2semidirect
5. #14271600C2semidirect
6. #14271599C2semidirect
7. #14271595C2semidirect
8. #14271594C2semidirect
9. SD32×D29C2semidirect
10. #14271579C2semidirect
11. C2×C29×SD32C2semidirect
14. C2×Q16×C29C22semidirect
18. #11745281C22semidirect
20. Q16×D29C22semidirect
25. #11745266C22semidirect
27. C29×SD32C22semidirect
28. C29×SD32C22semidirect
29. C2×C16×C29C22semidirect
30. #11745177C22semidirect
31. #11745176C22semidirect
32. #11745175C22semidirect
33. #11745174C22semidirect
34. #11745160C22semidirect
35. Dic232C22semidirect
36. #11745148C22semidirect
37. #11745148C22semidirect
38. D464C22semidirect
39. #11745146C22semidirect
40. C16×D29C22semidirect
130. C2×SD32D29semidirect
149. C2×Q16C2×D29semidirect
159. SD32C2×D29semidirect
160. SD32C2×D29semidirect
166. C2×C16C2×D29semidirect
167. C29#3416semidirect

Maximal subgroups

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

subgroupindex
#142719762
#142719642
#142716042
#142716022
#142716002
#142715992
#142715952
#142715942
SD32×D292
#142715792
C2×C29×SD322
#341629