Finite Group Databasebeta

← D29×#490 #16829824

Subgroups — D29×#490 #16829824

Order 3712.

488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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#127×D29C211yesmaximal, characteristic
2#125×D29C211yesmaximal, characteristic, complemented
3#14271529C211yesmaximal, characteristic, complemented
4#14271528C211yesmaximal, characteristic, complemented
5#14271527C211yesmaximal, characteristic, complemented
6#14271526C214yesmaximal, complemented
7#102×D29C214yesmaximal, complemented
8#97×D29C211yesmaximal, characteristic, complemented
9C29×#490C211yesmaximal, characteristic, complemented
10C2×D4×D29—22no—
11C2×D4×D29C2212yes—
12C29×#127C2211yescharacteristic
13C29×#125C2211yescharacteristic, complemented
14#11745302—22no—
15#11745302C2212yes—
16C2×C8×D29C2212yes—
17C4⋊C4×D29—22no—
18C4⋊C4×D29C2212yes—
19#11745252C2212yescomplemented
20#11745251—22no—
21#11745236C2211yescharacteristic
22C42×D29C2211yescharacteristic
23#11745232C2211yescharacteristic, complemented
24C29×#102C2214yescomplemented
25C29×#97C2211yescharacteristic, complemented
26#11745180C2214yescomplemented
27#11745169C2214yescomplemented
28#11745163C2212yescomplemented
29#11745157C2214yescomplemented
30#11745151C2211yescharacteristic, complemented
31C23×D29—22no—
32C2×D4×C29—22no—
33C2×D4×C29C2312yes—
34C2×C22⋊D29—22no—
35C2×C22⋊D29—24no—
36D4×D29—28no—
37D4×D29—48no—
38C2×D116—22no—
39C2×D116C2312yes—
40C2×C4×D29—22no—
41C2×C4×D29D412yes—
42C2×C4×D29C2311yescharacteristic
43C2×C8×C29C2312yes—
44C4⋊C4×C29—22no—
45C4⋊C4×C29C2312yes—
46C42×C29C2311yescharacteristic
47C4⋊Dic29—22no—
48C4⋊Dic29C2312yes—
49#90779—22no—
50#90779—22no—
51#90779—22no—
52C4×Dic29D412yes—
53C4×Dic29C2311yescharacteristic
54C2×#6597C2312yes—
55C8×D29—24no—
56C23×C29—22no—
57C22×D29—22no—
58C22×D29—44no—
59C22×D29—48no—
60C22×D29C2×D411yescharacteristic
61D4×C29—24no—
62D4×C29—44no—
63C2×C4×C29—22no—
64C2×C4×C29C2×D412yes—
65C2×C4×C29C2411yescharacteristic
66C22⋊D29—48no—
67C22⋊D29—44no—
68C2×Dic29—22no—
69C2×Dic29C2×D412yes—
70C2×Dic29C2×D411yescharacteristic
71D116—24no—
72D116—44no—
73C4×D29—24no—
74C4×D29—44no—
75C4×D29#4114yes—
76C8×C29—22no—
77#6597—22no—
78C2×#490—291nomaximal, Sylow
79C22×C29—42no—
80C22×C29—44no—
81C22×C29C22×D411yescharacteristic
82C2×D29—42no—
83C2×D29—44no—
84C2×D29—88no—
85C2×D29#12412yes—
86C2×D29AGL(1,ℤ/8)14yes—
87C4×C29—22no—
88C4×C29—42no—
89C4×C29C2×#4112yes—
90Dic29—22no—
91Dic29—42no—
92Dic29#12412yes—
93C2×#127—291no—
94C2×#125—291no—
95#490—291no—
96#490—291no—
97#490—294no—
98#490—291no—
99#490D2911yescharacteristic, direct product factor
100C2×#102—294no—
101C2×#97—291no—
102C2×C29—82no—
103C2×C29C2×#12411yescharacteristic
104C2×C29C2×AGL(1,ℤ/8)12yes—
105D29—82no—
106D29#49014yesdirect product factor
107C22×D4—292no—
108C22×D4—582no—
109C22×C8—292no—
110#127—292no—
111#127—291no—
112#127—582no—
113#127C2×D2911yescharacteristic
114#125—292no—
115#125—291no—
116#125—582no—
117#125C2×D2911yescharacteristic, complemented
118C2×C4⋊C4—292no—
119C2×C4⋊C4—582no—
120C2×C42—291no—
121#102—294no—
122#102—294no—
123#102—294no—
124#102C2×D2914yescomplemented
125#97—292no—
126#97—291no—
127#97C2×D2911yescharacteristic, complemented
128C29C2×#49011yescharacteristic, complemented, Sylow
129C24—582no—
130C2×D4—22no—
131C2×D4—292no—
132C2×D4—588no—
133C2×D4—584no—
134C2×D4—582no—
135C2×D4—582no—
136C2×D4—1168no—
137C2×D4C22×D2912yes—
138C22×C4—291no—
139C22×C4—292no—
140C22×C4—582no—
141C2×C8—292no—
142C2×C8—584no—
143C2×C8C22×D2912yes—
144C4⋊C4—22no—
145C4⋊C4—292no—
146C4⋊C4—582no—
147C4⋊C4—582no—
148C4⋊C4—582no—
149C4⋊C4—582no—
150C4⋊C4C22×D2912yes—
151C42—292no—
152C42—291no—
153C42C22×D2911yescharacteristic
154C23—22no—
155C23—291no—
156C23—582no—
157C23—1164no—
158C23—1168no—
159D4—24no—
160D4—44no—
161D4—584no—
162D4—1164no—
163D4—1164no—
164D4—1168no—
165C2×C4—22no—
166C2×C4—291no—
167C2×C4—294no—
168C2×C4—292no—
169C2×C4—584no—
170C2×C4—582no—
171C2×C4—1164no—
172C2×C4D4×D2912yes—
173C2×C4C23×D2911yescharacteristic
174C8—22no—
175C8—582no—
176C22—42no—
177C22—44no—
178C22—292no—
179C22—294no—
180C22—1162no—
181C22—1164no—
182C22—2328no—
183C22C2×D4×D2911yescharacteristic
184C4—22no—
185C4—42no—
186C4—292no—
187C4—582no—
188C4—1162no—
189C4#41×D2912yes—
190C2—82no—
191C2—294no—
192C2—2322no—
193C2#124×D2911yescharacteristic
194C2AGL(1,ℤ/8)×D2912yes—
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#490C2
socleC22×C29C22×D4
prime radical#127×D29C2
hypercenter#490D29
hypocenterC29C2×#490
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #125×D29C2semidirect
3. #14271529C2semidirect
4. #14271528C2semidirect
5. #14271527C2semidirect
6. #14271526C2semidirect
7. #102×D29C2semidirect
8. #97×D29C2semidirect
9. C29×#490C2semidirect
13. C29×#125C22semidirect
19. #11745252C22semidirect
23. #11745232C22semidirect
24. C29×#102C22semidirect
25. C29×#97C22semidirect
26. #11745180C22semidirect
27. #11745169C22semidirect
28. #11745163C22semidirect
29. #11745157C22semidirect
30. #11745151C22semidirect
99. #490D29direct (N × H)
106. D29#490direct (N × H)
117. #125C2×D29semidirect
124. #102C2×D29semidirect
127. #97C2×D29semidirect
128. C29C2×#490semidirect

Maximal subgroups

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

subgroupindex
#127×D292
#125×D292
#142715292
#142715282
#142715272
#142715262
#102×D292
#97×D292
C29×#4902
C2×#49029