Finite Group Databasebeta

← #16832625

Subgroups — #16832625

Order 3712.

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

normal subgroups only

This group has 364 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#135×D29C212yesmaximal, complemented
2#14271605C212yesmaximal, complemented
3#14271602C212yesmaximal, complemented
4#14271600C212yesmaximal, complemented
5#14271597C212yesmaximal, complemented
6#14271595C211yesmaximal, characteristic, complemented
7#14271593C212yesmaximal, complemented
8C2×#11745146C211yesmaximal, characteristic, complemented
9C29×#508C211yesmaximal, characteristic, complemented
10#41×D29—22no—
11C29×#135C2212yescomplemented
12#11745312—22no—
13#11745281C2212yes—
14Q16×D29C2212yescomplemented
15#11745278—22no—
16SD16×D29—22no—
17#11745274C2212yes—
18D8×D29C2212yescomplemented
19#11745266C2212yescomplemented
20C2×C8×D29C2211yescharacteristic
21C29×Q32C2211yescharacteristic, complemented
22C29×SD32C2212yescomplemented
23C29×D16C2211yescharacteristic, complemented
24C2×C16×C29C2211yescharacteristic, complemented
25#11745177C2212yescomplemented
26#11745176C2212yescomplemented
27#11745175C2212yescomplemented
28#11745174C2212yescomplemented
29C2×#90768C2211yescharacteristic, complemented
30Dic232C2211yescharacteristic, complemented
31#11745148C2212yescomplemented
32D464C2211yescharacteristic, complemented
33#11745146C2212yescomplemented
34#11745146C2212yescomplemented
35#41×C29—22no—
36#90809—22no—
37Q8×D29—22no—
38#90807—22no—
39#90807—42no—
40D4×D29—22no—
41D4×D29—42no—
42#90805—22no—
43#90805—42no—
44C2×C4×D29—42no—
45C2×C4×D29D411yescharacteristic
46Q16×C29C2312yes—
47SD16×C29—22no—
48D8×C29C2312yes—
49C2×C8×C29C2311yescharacteristic
50#90785—22no—
51#90784—22no—
52#90783—22no—
53#90782—22no—
54C2×#6597D411yescharacteristic
55Dic116C2312yes—
56D232C2312yes—
57#90773—22no—
58C8×D29D412yes—
59C8×D29C2312yes—
60C16×C29C2311yescharacteristic
61C16×C29C2311yescharacteristic
62#90768C2312yes—
63C22×D29—42no—
64C22×D29D811yescharacteristic
65Q8×C29—22no—
66D4×C29—22no—
67D4×C29—42no—
68C2×C4×C29—42no—
69C2×C4×C29C2×D411yescharacteristic
70C22⋊D29—42no—
71C22⋊D29—42no—
72C22⋊D29—42no—
73C2×Dic29—42no—
74C2×Dic29D811yescharacteristic
75D116—22no—
76D116—42no—
77C4×D29—42no—
78C4×D29—42no—
79C4×D29—42no—
80C4×D29D812yes—
81C4×D29C2×D412yes—
82Dic58—22no—
83Dic58—42no—
84C8×C29C2×D411yescharacteristic
85C8×C29C2411yescharacteristic
86#6597C2×D412yes—
87#3414—291nomaximal, Sylow
88C22×C29—42no—
89C22×C29C2×D811yescharacteristic
90C2×D29—41no—
91C2×D29—42no—
92C2×D29—84no—
93C2×D29C2×D812yes—
94C4×C29—42no—
95C4×C29C2×D811yescharacteristic
96C4×C29C22×D411yescharacteristic
97Dic29—42no—
98Dic29C2×D812yes—
99C2×#135—292no—
100#510—292no—
101#510—292no—
102#509—292no—
103#509—292no—
104#508—292no—
105#508—291no—
106#508D2911yescharacteristic, complemented
107C2×M32—291no—
108C2×C29—21no—
109C2×C29—82no—
110C2×C29C22×D811yescharacteristic
111D29—22no—
112D29—82no—
113C2×#41—582no—
114#135—292no—
115#135—292no—
116#135—292no—
117#135—582no—
118#135—582no—
119#135C2×D2912yescomplemented
120C2×Q16—292no—
121C2×SD16—582no—
122C2×D8—292no—
123C22×C8—291no—
124Q32—292no—
125Q32—291no—
126Q32C2×D2911yescharacteristic, complemented
127SD32—292no—
128SD32—292no—
129SD32—292no—
130SD32C2×D2912yescomplemented
131D16—292no—
132D16—291no—
133D16C2×D2911yescharacteristic, complemented
134M32—292no—
135M32—292no—
136C2×C16—291no—
137C2×C16C2×D2911yescharacteristic, complemented
138C29#341411yescharacteristic, complemented, Sylow
139#41—22no—
140#41—582no—
141#41—582no—
142#41—582no—
143#41—1162no—
144#41—1162no—
145C2×Q8—582no—
146C2×D4—582no—
147C2×D4—1162no—
148C22×C4—291no—
149C22×C4—1162no—
150Q16—292no—
151Q16—582no—
152Q16C22×D2912yes—
153SD16—22no—
154SD16—582no—
155SD16—582no—
156SD16—582no—
157D8—292no—
158D8—582no—
159D8C22×D2912yes—
160C2×C8—291no—
161C2×C8—292no—
162C2×C8—292no—
163C2×C8C22×D2911yescharacteristic
164C16—292no—
165C16C22×D2911yescharacteristic
166C16C22×D2911yescharacteristic
167C23—291no—
168C23—1162no—
169Q8—22no—
170Q8—582no—
171Q8—1162no—
172D4—22no—
173D4—42no—
174D4—582no—
175D4—1162no—
176D4—1162no—
177D4—1162no—
178D4—1162no—
179C2×C4—42no—
180C2×C4—291no—
181C2×C4—292no—
182C2×C4—292no—
183C2×C4—1162no—
184C2×C4—1162no—
185C2×C4—1162no—
186C2×C4—1162no—
187C2×C4D4×D2911yescharacteristic
188C8—292no—
189C8D4×D2911yescharacteristic
190C8C23×D2911yescharacteristic
191C22—42no—
192C22—292no—
193C22—1161no—
194C22—1162no—
195C22—2324no—
196C22D8×D2911yescharacteristic
197C4—42no—
198C4—292no—
199C4—1162no—
200C4D8×D2911yescharacteristic
201C4C2×D4×D2911yescharacteristic
202C2—21no—
203C2—82no—
204C2—582no—
205C2—2322no—
206C2C2×D8×D2911yescharacteristic
subgroupG/H
centerC4D8×D29
commutator, cosocleC8×C29C24
FrattiniC8C23×D29
FittingC29×#508C2
socleC2×C29C22×D8
hypercenter#508D29
hypocenterC29#3414
LCSG ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D29C2semidirect
2. #14271605C2semidirect
3. #14271602C2semidirect
4. #14271600C2semidirect
5. #14271597C2semidirect
6. #14271595C2semidirect
7. #14271593C2semidirect
8. C2×#11745146C2semidirect
9. C29×#508C2semidirect
11. C29×#135C22semidirect
14. Q16×D29C22semidirect
18. D8×D29C22semidirect
19. #11745266C22semidirect
21. C29×Q32C22semidirect
22. C29×SD32C22semidirect
23. C29×D16C22semidirect
24. C2×C16×C29C22semidirect
25. #11745177C22semidirect
26. #11745176C22semidirect
27. #11745175C22semidirect
28. #11745174C22semidirect
29. C2×#90768C22semidirect
30. Dic232C22semidirect
31. #11745148C22semidirect
32. D464C22semidirect
33. #11745146C22semidirect
34. #11745146C22semidirect
106. #508D29semidirect
119. #135C2×D29semidirect
126. Q32C2×D29semidirect
130. SD32C2×D29semidirect
133. D16C2×D29semidirect
137. C2×C16C2×D29semidirect
138. C29#3414semidirect

Maximal subgroups

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

subgroupindex
#135×D292
#142716052
#142716022
#142716002
#142715972
#142715952
#142715932
C2×#117451462
C29×#5082
#341429