Finite Group Databasebeta

← #16832635

Subgroups — #16832635

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#14271977C211yesmaximal, characteristic, complemented
2#14271965C211yesmaximal, characteristic, complemented
3#14271605C212yesmaximal, complemented
4#14271603C211yesmaximal, characteristic, complemented
5#14271598C211yesmaximal, characteristic, complemented
6#14271597C212yesmaximal, complemented
7#14271594C212yesmaximal, complemented
8C2×#11745148C211yesmaximal, characteristic, complemented
9SD32×D29C212yesmaximal, complemented
10#14271579C211yesmaximal, characteristic, complemented
11C29×#508C211yesmaximal, characteristic, complemented
12#11745365—21no—
13#11745364—21no—
14C29×#135C2211yescharacteristic
15C29×#135C2211yescharacteristic, complemented
16#11745313—21no—
17#11745311—21no—
18#11745281C2212yes—
19Q16×D29C2212yescomplemented
20#11745277—22no—
21#11745276—22no—
22#11745274C2212yescomplemented
23D8×D29C2212yes—
24C2×Dic116C2211yescharacteristic, complemented
25C2×D232C2211yescharacteristic
26#11745263C2211yescharacteristic
27C29×Q32C2211yescharacteristic, complemented
28C29×SD32C2211yescharacteristic, complemented
29C29×SD32C2211yescharacteristic, complemented
30C29×D16C2211yescharacteristic, complemented
31C2×C16×C29C2211yescharacteristic, complemented
32#11745177C2212yescomplemented
33#11745176C2212yescomplemented
34#11745175C2212yescomplemented
35#11745174C2212yescomplemented
36#11745160C2211yescharacteristic, complemented
37#11745148C2212yescomplemented
38#11745148C2212yescomplemented
39#11745146C2212yescomplemented
40C16×D29C2212yescomplemented
41#41×C29—21no—
42#41×C29—21no—
43#90809—22no—
44Q8×D29—22no—
45#90807—22no—
46#90807—42no—
47D4×D29—22no—
48D4×D29—42no—
49#90805—41no—
50#90805—41no—
51#90805D411yescharacteristic
52C2×D116—21no—
53C2×D116—41no—
54C2×Dic58—21no—
55C2×Dic58—41no—
56Q16×C29C2311yescharacteristic
57Q16×C29C2311yescharacteristic
58SD16×C29—21no—
59SD16×C29—21no—
60D8×C29C2311yescharacteristic
61D8×C29C2311yescharacteristic
62C2×C8×C29C2311yescharacteristic
63#90785—22no—
64#90784—22no—
65#90783—22no—
66#90782—22no—
67#90777D411yescharacteristic
68Dic116—21no—
69Dic116C2312yes—
70D232—21no—
71D232C2312yes—
72#90772D412yes—
73C8×D29C2312yes—
74C16×C29C2311yescharacteristic
75C16×C29C2311yescharacteristic
76#90768C2312yes—
77C22×D29—41no—
78C22×D29—42no—
79Q8×C29—21no—
80Q8×C29—21no—
81D4×C29—21no—
82D4×C29—21no—
83D4×C29—41no—
84D4×C29—41no—
85C2×C4×C29—41no—
86C2×C4×C29—41no—
87C2×C4×C29C2×D411yescharacteristic
88C22⋊D29—42no—
89C22⋊D29—42no—
90C22⋊D29D812yes—
91C2×Dic29—41no—
92C2×Dic29—42no—
93D116—22no—
94D116—42no—
95D116—41no—
96D116D811yescharacteristic
97C4×D29—42no—
98C4×D29—42no—
99C4×D29C2×D412yes—
100Dic58—22no—
101Dic58—41no—
102Dic58—42no—
103Dic58D811yescharacteristic
104C8×C29C2×D411yescharacteristic
105C8×C29C2411yescharacteristic
106#6597C2×D412yes—
107#3416—291nomaximal, Sylow
108C22×C29—41no—
109C22×C29—41no—
110C22×C29C2×D811yescharacteristic
111C2×D29—42no—
112C2×D29—162no—
113C2×D29—161no—
114C2×D29C2×D812yes—
115C4×C29—41no—
116C4×C29—41no—
117C4×C29C2×D811yescharacteristic
118C4×C29C22×D411yescharacteristic
119Dic29—42no—
120Dic29C2×D812yes—
121#578—291no—
122#576—291no—
123#510—291no—
124#510—292no—
125#509—291no—
126#509—292no—
127#508—292no—
128#508D2911yescharacteristic, complemented
129C2×SD32—292no—
130C2×SD32—291no—
131#504—291no—
132C2×C29—21no—
133C2×C29—81no—
134C2×C29—81no—
135C2×C29C22×D811yescharacteristic
136D29—22no—
137D29—82no—
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#135C2×D2911yescharacteristic
147#135C2×D2911yescharacteristic, complemented
148C2×Q16—292no—
149C2×Q16—291no—
150C2×D8—292no—
151C2×D8—291no—
152#131—291no—
153Q32—292no—
154Q32C2×D2911yescharacteristic, complemented
155SD32—292no—
156SD32—292no—
157SD32—292no—
158SD32—292no—
159SD32C2×D2911yescharacteristic, complemented
160SD32C2×D2911yescharacteristic, complemented
161D16—292no—
162D16C2×D2911yescharacteristic, complemented
163M32—291no—
164M32—292no—
165C2×C16—292no—
166C2×C16C2×D2911yescharacteristic, complemented
167C29#341611yescharacteristic, complemented, Sylow
168#41—21no—
169#41—21no—
170#41—291no—
171#41—582no—
172#41—582no—
173#41—1161no—
174#41—1161no—
175#41—1162no—
176C2×Q8—582no—
177C2×Q8—581no—
178C2×Q8—1161no—
179C2×D4—582no—
180C2×D4—581no—
181C2×D4—1161no—
182C2×D4—1162no—
183Q16—292no—
184Q16—582no—
185Q16—581no—
186Q16C22×D2911yescharacteristic
187Q16C22×D2911yescharacteristic
188SD16—21no—
189SD16—21no—
190SD16—582no—
191SD16—582no—
192D8—292no—
193D8—582no—
194D8—581no—
195D8C22×D2911yescharacteristic
196D8C22×D2911yescharacteristic
197M16—291no—
198M16—292no—
199C2×C8—292no—
200C2×C8C22×D2911yescharacteristic
201C16—292no—
202C16C22×D2911yescharacteristic
203C16C22×D2911yescharacteristic
204C23—1162no—
205C23—1161no—
206Q8—21no—
207Q8—21no—
208Q8—291no—
209Q8—582no—
210Q8—1162no—
211Q8—1161no—
212D4—21no—
213D4—21no—
214D4—41no—
215D4—41no—
216D4—292no—
217D4—291no—
218D4—582no—
219D4—1162no—
220D4—1162no—
221D4—1162no—
222D4—1161no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—292no—
226C2×C4—1162no—
227C2×C4—1162no—
228C2×C4—1162no—
229C2×C4—1161no—
230C2×C4D4×D2911yescharacteristic
231C8—292no—
232C8D4×D2911yescharacteristic
233C8C23×D2911yescharacteristic
234C22—41no—
235C22—41no—
236C22—292no—
237C22—1162no—
238C22—4641no—
239C22—4642no—
240C22D8×D2911yescharacteristic
241C4—41no—
242C4—41no—
243C4—292no—
244C4—1162no—
245C4D8×D2911yescharacteristic
246C4C2×D4×D2911yescharacteristic
247C2—21no—
248C2—81no—
249C2—81no—
250C2—582no—
251C2—2322no—
252C2C2×D8×D2911yescharacteristic
subgroupG/H
centerC2C2×D8×D29
commutator, cosocleC8×C29C24
FrattiniC8C23×D29
FittingC29×#508C2
socleC2×C29C22×D8
hypercenter#508D29
hypocenterC29#3416
LCSG ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #14271977C2semidirect
2. #14271965C2semidirect
3. #14271605C2semidirect
4. #14271603C2semidirect
5. #14271598C2semidirect
6. #14271597C2semidirect
7. #14271594C2semidirect
8. C2×#11745148C2semidirect
9. SD32×D29C2semidirect
10. #14271579C2semidirect
11. C29×#508C2semidirect
15. C29×#135C22semidirect
19. Q16×D29C22semidirect
22. #11745274C22semidirect
24. C2×Dic116C22semidirect
27. C29×Q32C22semidirect
28. C29×SD32C22semidirect
29. C29×SD32C22semidirect
30. C29×D16C22semidirect
31. C2×C16×C29C22semidirect
32. #11745177C22semidirect
33. #11745176C22semidirect
34. #11745175C22semidirect
35. #11745174C22semidirect
36. #11745160C22semidirect
37. #11745148C22semidirect
38. #11745148C22semidirect
39. #11745146C22semidirect
40. C16×D29C22semidirect
128. #508D29semidirect
147. #135C2×D29semidirect
154. Q32C2×D29semidirect
159. SD32C2×D29semidirect
160. SD32C2×D29semidirect
162. D16C2×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
#142719772
#142719652
#142716052
#142716032
#142715982
#142715972
#142715942
C2×#117451482
SD32×D292
#142715792
C29×#5082
#341629