Finite Group Databasebeta

← #14271721

Subgroups — #14271721

Order 1856.

346 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 103 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×D29C212yesmaximal, complemented
2C29×#121C211yesmaximal, characteristic, complemented
3#11745301C212yesmaximal, complemented
4#11745299C212yesmaximal, complemented
5#11745292C211yesmaximal, characteristic, complemented
6C2×#90781C211yesmaximal, characteristic, complemented
7#11745256C212yesmaximal, complemented
8#11745245C212yesmaximal, complemented
9#11745244C212yesmaximal, complemented
10C23×D29C2211yescharacteristic
11C23×D29C2212yescomplemented
12C2×D4×C29C2212yescomplemented
13C2×D4×C29C2211yescharacteristic, complemented
14C22×C4×C29C2211yescharacteristic, complemented
15C2×C22⋊D29C2212yes—
16C2×C22⋊D29C2212yescomplemented
17C2×C22⋊D29C2212yescomplemented
18C22×Dic29C2211yescharacteristic, complemented
19D4×D29—28no—
20C2×D116C2212yes—
21C2×D116C2211yescharacteristic, complemented
22C2×C4×D29C2212yescomplemented
23C4⋊C4×C29C2211yescharacteristic, complemented
24C22⋊C4×C29C2212yescomplemented
25C22⋊Dic29C2212yescomplemented
26#90781C2212yescomplemented
27#90781C2212yescomplemented
28#90781C2212yescomplemented
29#90781C2212yescomplemented
30C4⋊Dic29C2211yescharacteristic, complemented
31#90779C2212yescomplemented
32C23×C29C2312yes—
33C23×C29C2311yescharacteristic
34C22×D29—24no—
35C22×D29—41no—
36C22×D29—41no—
37C22×D29—42no—
38C22×D29—42no—
39C22×D29D414yescomplemented
40C22×D29C2312yes—
41C22×D29C2312yes—
42D4×C29—24no—
43D4×C29—41no—
44C2×C4×C29—41no—
45C2×C4×C29C2312yes—
46C2×C4×C29C2311yescharacteristic
47C2×C4×C29C2311yescharacteristic
48C22⋊D29—24no—
49C22⋊D29—24no—
50C22⋊D29—42no—
51C2×Dic29—41no—
52C2×Dic29C2312yes—
53C2×Dic29C2312yes—
54D116—24no—
55D116—41no—
56C4×D29—24no—
57C22×C29—21no—
58C22×C29—21no—
59C22×C29—22no—
60C22×C29—22no—
61C22×C29—22no—
62C22×C29C2×D412yes—
63C22×C29C2411yescharacteristic
64C2×D29—22no—
65C2×D29—22no—
66C2×D29—22no—
67C2×D29—22no—
68C2×D29—22no—
69C2×D29—44no—
70C2×D29—48no—
71C2×D29C2×D414yes—
72C4×C29—22no—
73C4×C29—21no—
74C4×C29—21no—
75Dic29—22no—
76Dic29—22no—
77#534—291nomaximal, Sylow
78C2×C29—22no—
79C2×C29—42no—
80C2×C29C22×D411yescharacteristic
81C2×C29H(5,𝔽2)11yescharacteristic
82C2×C29H(5,𝔽2)11yescharacteristic
83D29—24no—
84D29—42no—
85C22×D4—292no—
86#123—292no—
87#123—292no—
88#121—292no—
89#121—291no—
90#121D2911yescharacteristic, complemented
91#120—292no—
92#120—292no—
93C2×C22⋊C4—291no—
94C29#53411yescharacteristic, complemented, Sylow
95C24—291no—
96C24—292no—
97C2×D4—292no—
98C2×D4—292no—
99C2×D4—292no—
100C2×D4—292no—
101C2×D4—291no—
102C2×D4—588no—
103C2×D4C2×D2912yescomplemented
104C2×D4C2×D2911yescharacteristic, complemented
105C22×C4—291no—
106C22×C4—292no—
107C22×C4C2×D2911yescharacteristic, complemented
108C4⋊C4—292no—
109C4⋊C4—291no—
110C4⋊C4C2×D2911yescharacteristic, complemented
111C22⋊C4—292no—
112C22⋊C4—292no—
113C22⋊C4—292no—
114C22⋊C4—292no—
115C22⋊C4—292no—
116C22⋊C4C2×D2912yescomplemented
117C23—292no—
118C23—294no—
119C23—292no—
120C23—584no—
121C23—1161no—
122C23—1161no—
123C23—1162no—
124C23—1162no—
125C23C22×D2912yes—
126C23C22×D2911yescharacteristic
127D4—24no—
128D4—41no—
129D4—584no—
130D4—584no—
131D4—584no—
132D4—1161no—
133D4—1162no—
134C2×C4—41no—
135C2×C4—292no—
136C2×C4—292no—
137C2×C4—584no—
138C2×C4—1161no—
139C2×C4C22×D2911yescharacteristic
140C2×C4C22×D2911yescharacteristic
141C2×C4C22×D2912yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—294no—
148C22—582no—
149C22—582no—
150C22—582no—
151C22—582no—
152C22—582no—
153C22—1164no—
154C22—1168no—
155C22D4×D2912yes—
156C22C23×D2911yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—582no—
161C4—582no—
162C2—22no—
163C2—42no—
164C2—584no—
165C2—1162no—
166C2C2×D4×D2911yescharacteristic
167C2#1174535911yescharacteristic
168C2#1174536411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×#121C2
hypercenter#121D29
hypocenterC29#534
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D29C2semidirect
2. C29×#121C2semidirect
3. #11745301C2semidirect
4. #11745299C2semidirect
5. #11745292C2semidirect
6. C2×#90781C2semidirect
7. #11745256C2semidirect
8. #11745245C2semidirect
9. #11745244C2semidirect
11. C23×D29C22semidirect
12. C2×D4×C29C22semidirect
13. C2×D4×C29C22semidirect
14. C22×C4×C29C22semidirect
16. C2×C22⋊D29C22semidirect
17. C2×C22⋊D29C22semidirect
18. C22×Dic29C22semidirect
21. C2×D116C22semidirect
22. C2×C4×D29C22semidirect
23. C4⋊C4×C29C22semidirect
24. C22⋊C4×C29C22semidirect
25. C22⋊Dic29C22semidirect
26. #90781C22semidirect
27. #90781C22semidirect
28. #90781C22semidirect
29. #90781C22semidirect
30. C4⋊Dic29C22semidirect
31. #90779C22semidirect
39. C22×D29D4semidirect
90. #121D29semidirect
94. C29#534semidirect
103. C2×D4C2×D29semidirect
104. C2×D4C2×D29semidirect
107. C22×C4C2×D29semidirect
110. C4⋊C4C2×D29semidirect
116. 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
C29×#1212
#117453012
#117452992
#117452922
C2×#907812
#117452562
#117452452
#117452442
#53429