Finite Group Databasebeta

← #123×D29 #14271663

Subgroups — #123×D29 #14271663

Order 1856.

342 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×D4×D29C211yesmaximal, characteristic
2C22×C4×D29C211yesmaximal, characteristic, complemented
3C29×#123C211yesmaximal, characteristic, complemented
4#11745297C211yesmaximal, characteristic, complemented
5#11745291C211yesmaximal, characteristic, complemented
6#11745256C212yesmaximal, complemented
7C4⋊C4×D29C212yesmaximal, complemented
8#11745248C211yesmaximal, characteristic, complemented
9#11745245C212yesmaximal, complemented
10C22⋊C4×D29C212yesmaximal, complemented
11C22⋊C4×D29C211yesmaximal, characteristic, complemented
12C23×D29C2211yescharacteristic
13C23×D29C2211yescharacteristic
14C2×D4×C29C2211yescharacteristic
15C22×C4×C29C2211yescharacteristic, complemented
16C2×C22⋊D29C2211yescharacteristic
17C2×C22⋊D29C2211yescharacteristic
18C22×Dic29C2211yescharacteristic, complemented
19D4×D29—24no—
20C2×D116C2211yescharacteristic
21C2×C4×D29—24no—
22C2×C4×D29C2212yes—
23C2×C4×D29C2211yescharacteristic
24C2×C4×D29C2212yes—
25C2×C4×D29C2212yescomplemented
26C4⋊C4×C29C2212yescomplemented
27C22⋊C4×C29C2212yescomplemented
28C22⋊C4×C29C2211yescharacteristic, complemented
29C22⋊Dic29C2211yescharacteristic, complemented
30C22⋊Dic29C2212yescomplemented
31#90781C2212yescomplemented
32#90781C2212yescomplemented
33#90781C2212yescomplemented
34C4⋊Dic29C2212yescomplemented
35#90779C2212yescomplemented
36#90779C2212yescomplemented
37C23×C29C2311yescharacteristic
38C23×C29C2311yescharacteristic
39C22×D29—24no—
40C22×D29—22no—
41C22×D29—24no—
42C22×D29D414yes—
43C22×D29C2311yescharacteristic
44C22×D29C2311yescharacteristic
45C22×D29C2311yescharacteristic
46D4×C29—22no—
47C2×C4×C29—22no—
48C2×C4×C29C2311yescharacteristic
49C2×C4×C29C2312yes—
50C2×C4×C29C2312yes—
51C22⋊D29—22no—
52C22⋊D29—22no—
53C2×Dic29—22no—
54C2×Dic29C2311yescharacteristic
55C2×Dic29C2312yes—
56C2×Dic29C2312yes—
57D116—22no—
58C4×D29—24no—
59C4×D29—24no—
60C4×D29—22no—
61C4×D29—24no—
62C22×C29—22no—
63C22×C29—21no—
64C22×C29—22no—
65C22×C29C2×D412yes—
66C22×C29C2411yescharacteristic
67C2×D29—22no—
68C2×D29—28no—
69C2×D29—21no—
70C2×D29—22no—
71C2×D29—44no—
72C2×D29C2×D412yes—
73C2×D29C2×D412yes—
74C2×D29#4114yes—
75C4×C29—22no—
76C4×C29—21no—
77C4×C29—22no—
78Dic29—22no—
79Dic29—21no—
80Dic29—22no—
81C2×#123—291nomaximal, Sylow
82C2×C29—22no—
83C2×C29—41no—
84C2×C29C22×D411yescharacteristic
85C2×C29C2×#4112yes—
86D29—22no—
87D29—41no—
88D29#12314yesdirect product factor
89C22×D4—291no—
90C23×C4—291no—
91#123—291no—
92#123—291no—
93#123—292no—
94#123—292no—
95#123—291no—
96#123D2911yescharacteristic, direct product factor
97C2×C4⋊C4—292no—
98C2×C22⋊C4—291no—
99C2×C22⋊C4—292no—
100C29C2×#12311yescharacteristic, complemented, Sylow
101C24—291no—
102C24—291no—
103C2×D4—291no—
104C2×D4—291no—
105C2×D4—291no—
106C2×D4—584no—
107C2×D4C2×D2911yescharacteristic
108C22×C4—291no—
109C22×C4—292no—
110C22×C4—292no—
111C22×C4—291no—
112C22×C4—292no—
113C22×C4—584no—
114C22×C4C2×D2911yescharacteristic, complemented
115C4⋊C4—292no—
116C4⋊C4—292no—
117C4⋊C4—292no—
118C4⋊C4C2×D2912yescomplemented
119C22⋊C4—291no—
120C22⋊C4—292no—
121C22⋊C4—292no—
122C22⋊C4—292no—
123C22⋊C4—292no—
124C22⋊C4C2×D2911yescharacteristic, complemented
125C22⋊C4C2×D2912yescomplemented
126C23—291no—
127C23—294no—
128C23—291no—
129C23—291no—
130C23—584no—
131C23—582no—
132C23—584no—
133C23C22×D2911yescharacteristic
134C23C22×D2911yescharacteristic
135D4—22no—
136D4—582no—
137D4—582no—
138D4—582no—
139C2×C4—22no—
140C2×C4—292no—
141C2×C4—292no—
142C2×C4—291no—
143C2×C4—584no—
144C2×C4—584no—
145C2×C4—582no—
146C2×C4—584no—
147C2×C4—582no—
148C2×C4C22×D2912yes—
149C2×C4C22×D2912yes—
150C2×C4C22×D2911yescharacteristic
151C22—22no—
152C22—21no—
153C22—22no—
154C22—292no—
155C22—294no—
156C22—292no—
157C22—588no—
158C22—582no—
159C22—581no—
160C22—582no—
161C22—1164no—
162C22D4×D2912yes—
163C22C23×D2911yescharacteristic
164C4—22no—
165C4—21no—
166C4—22no—
167C4—582no—
168C4—581no—
169C4—582no—
170C2—22no—
171C2—41no—
172C2—294no—
173C2—582no—
174C2—1161no—
175C2C2×D4×D2911yescharacteristic
176C2#41×D2912yes—
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×#123C2
prime radicalC2×D4×D29C2
hypercenter#123D29
hypocenterC29C2×#123
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. C22×C4×D29C2semidirect
3. C29×#123C2semidirect
4. #11745297C2semidirect
5. #11745291C2semidirect
6. #11745256C2semidirect
7. C4⋊C4×D29C2semidirect
8. #11745248C2semidirect
9. #11745245C2semidirect
10. C22⋊C4×D29C2semidirect
11. C22⋊C4×D29C2semidirect
15. C22×C4×C29C22semidirect
18. C22×Dic29C22semidirect
25. C2×C4×D29C22semidirect
26. C4⋊C4×C29C22semidirect
27. C22⋊C4×C29C22semidirect
28. C22⋊C4×C29C22semidirect
29. C22⋊Dic29C22semidirect
30. C22⋊Dic29C22semidirect
31. #90781C22semidirect
32. #90781C22semidirect
33. #90781C22semidirect
34. C4⋊Dic29C22semidirect
35. #90779C22semidirect
36. #90779C22semidirect
88. D29#123direct (N × H)
96. #123D29direct (N × H)
100. C29C2×#123semidirect
114. C22×C4C2×D29semidirect
118. C4⋊C4C2×D29semidirect
124. C22⋊C4C2×D29semidirect
125. C22⋊C4C2×D29semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D292
C22×C4×D292
C29×#1232
#117452972
#117452912
#117452562
C4⋊C4×D292
#117452482
#117452452
C22⋊C4×D292
C2×#12329