Finite Group Databasebeta

← #14271722

Subgroups — #14271722

Order 1856.

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

normal subgroups only

This group has 346 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
1C22×D4×C29C211yesmaximal, characteristic, complemented
2C22×C22⋊D29C211yesmaximal, characteristic, complemented
3#11745315C212yesmaximal, complemented
4C2×C22⋊Dic29C211yesmaximal, characteristic, complemented
5#11745301C214yesmaximal, complemented
6#11745299C212yesmaximal, complemented
7#11745297C212yesmaximal, complemented
8#11745291C212yesmaximal, complemented
9C24×C29C2211yescharacteristic
10C24×C29C2211yescharacteristic, complemented
11C23×D29C2211yescharacteristic, complemented
12C2×D4×C29—24no—
13C2×D4×C29C2212yes—
14C2×D4×C29C2212yescomplemented
15C22×C4×C29C2211yescharacteristic, complemented
16C2×C22⋊D29—24no—
17C2×C22⋊D29C2212yes—
18C2×C22⋊D29C2212yescomplemented
19C2×C22⋊D29C2214yescomplemented
20C22×Dic29C2211yescharacteristic, complemented
21C22×Dic29C2212yescomplemented
22C22⋊Dic29C2212yescomplemented
23C22⋊Dic29C2212yescomplemented
24C22⋊Dic29C2214yescomplemented
25#90781C2214yescomplemented
26#90779C2214yescomplemented
27C23×C29—22no—
28C23×C29—42no—
29C23×C29—42no—
30C23×C29D414yescomplemented
31C23×C29C2312yes—
32C23×C29C2311yescharacteristic
33C23×C29C2311yescharacteristic
34C23×C29C2311yescharacteristic
35C22×D29—22no—
36C22×D29—42no—
37C22×D29C2312yes—
38D4×C29—24no—
39D4×C29—24no—
40C2×C4×C29—22no—
41C2×C4×C29C2312yes—
42C22⋊D29—24no—
43C22⋊D29—24no—
44C22⋊D29—44no—
45C2×Dic29—22no—
46C2×Dic29—42no—
47C2×Dic29C2312yes—
48C2×Dic29C2314yes—
49C22×C29—22no—
50C22×C29—22no—
51C22×C29—22no—
52C22×C29—22no—
53C22×C29—24no—
54C22×C29—44no—
55C22×C29—44no—
56C22×C29C2×D412yes—
57C22×C29C2×D412yes—
58C22×C29C2×D412yes—
59C22×C29C2411yescharacteristic
60C2×D29—22no—
61C2×D29—24no—
62C2×D29—44no—
63C4×C29—22no—
64Dic29—22no—
65Dic29—24no—
66#534—291nomaximal, Sylow
67C2×C29—22no—
68C2×C29—22no—
69C2×C29—22no—
70C2×C29—42no—
71C2×C29C22×D411yescharacteristic
72C2×C29H(5,𝔽2)12yes—
73D29—42no—
74C22×D4—291no—
75C22×D4D2911yescharacteristic, complemented
76#123—292no—
77#123—292no—
78#121—294no—
79#120—292no—
80#120—292no—
81C2×C22⋊C4—291no—
82C29#53411yescharacteristic, complemented, Sylow
83C24—291no—
84C24C2×D2911yescharacteristic
85C24C2×D2911yescharacteristic, complemented
86C2×D4—24no—
87C2×D4—292no—
88C2×D4—292no—
89C2×D4—294no—
90C2×D4—584no—
91C2×D4C2×D2912yes—
92C2×D4C2×D2912yescomplemented
93C22×C4—291no—
94C22×C4—292no—
95C22×C4C2×D2911yescharacteristic, complemented
96C4⋊C4—294no—
97C22⋊C4—292no—
98C22⋊C4—292no—
99C22⋊C4—294no—
100C22⋊C4—294no—
101C23—22no—
102C23—42no—
103C23—42no—
104C23—292no—
105C23—582no—
106C23—1162no—
107C23C22⋊D2914yescomplemented
108C23C22×D2912yes—
109C23C22×D2911yescharacteristic
110C23C22×D2911yescharacteristic
111C23C22×D2911yescharacteristic
112D4—24no—
113D4—24no—
114D4—584no—
115D4—584no—
116D4—1164no—
117C2×C4—22no—
118C2×C4—294no—
119C2×C4—292no—
120C2×C4—582no—
121C2×C4—1162no—
122C2×C4C22×D2912yes—
123C22—22no—
124C22—22no—
125C22—22no—
126C22—24no—
127C22—22no—
128C22—44no—
129C22—44no—
130C22—584no—
131C22—582no—
132C22—1164no—
133C22C2×C22⋊D2912yes—
134C22C2×C22⋊D2912yes—
135C22C2×C22⋊D2912yes—
136C22C23×D2911yescharacteristic
137C4—22no—
138C4—584no—
139C4—582no—
140C2—22no—
141C2—22no—
142C2—22no—
143C2—42no—
144C2—1162no—
145C2#1174535912yes—
146C2C22×C22⋊D2911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC22×D4×C29C2
hypercenterC22×D4D29
hypocenterC29#534
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D4×C29C2semidirect
2. C22×C22⋊D29C2semidirect
3. #11745315C2semidirect
4. C2×C22⋊Dic29C2semidirect
5. #11745301C2semidirect
6. #11745299C2semidirect
7. #11745297C2semidirect
8. #11745291C2semidirect
10. C24×C29C22semidirect
11. C23×D29C22semidirect
14. C2×D4×C29C22semidirect
15. C22×C4×C29C22semidirect
18. C2×C22⋊D29C22semidirect
19. C2×C22⋊D29C22semidirect
20. C22×Dic29C22semidirect
21. C22×Dic29C22semidirect
22. C22⋊Dic29C22semidirect
23. C22⋊Dic29C22semidirect
24. C22⋊Dic29C22semidirect
25. #90781C22semidirect
26. #90779C22semidirect
30. C23×C29D4semidirect
75. C22×D4D29semidirect
82. C29#534semidirect
85. C24C2×D29semidirect
92. C2×D4C2×D29semidirect
95. C22×C4C2×D29semidirect
107. C23C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C292
C22×C22⋊D292
#117453152
C2×C22⋊Dic292
#117453012
#117452992
#117452972
#117452912
#53429