Finite Group Databasebeta

← #14271723

Subgroups — #14271723

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
1C22×C22⋊D29C211yesmaximal, characteristic, complemented
2C2×D4×D29C211yesmaximal, characteristic, complemented
3C29×#120C211yesmaximal, characteristic, complemented
4#11745315C211yesmaximal, characteristic, complemented
5#11745300C212yesmaximal, complemented
6#11745299C212yesmaximal, complemented
7#11745297C211yesmaximal, characteristic, complemented
8#11745248C211yesmaximal, characteristic, complemented
9#11745246C212yesmaximal, complemented
10#11745245C212yesmaximal, complemented
11C22⋊C4×D29C211yesmaximal, characteristic, complemented
12C24×C29C2211yescharacteristic, complemented
13C23×D29C2211yescharacteristic
14C23×D29C2211yescharacteristic, complemented
15C2×D4×C29C2211yescharacteristic
16C2×D4×C29C2212yescomplemented
17C2×C22⋊D29—24no—
18C2×C22⋊D29C2212yes—
19C2×C22⋊D29C2211yescharacteristic
20C2×C22⋊D29C2211yescharacteristic, complemented
21C2×C22⋊D29C2212yescomplemented
22C2×C22⋊D29C2212yescomplemented
23C22×Dic29C2211yescharacteristic, complemented
24D4×D29—24no—
25C2×D116C2211yescharacteristic, complemented
26C2×C4×D29C2211yescharacteristic, complemented
27C2×C4×D29C2212yescomplemented
28C22⋊C4×C29C2211yescharacteristic, complemented
29C22⋊C4×C29C2212yescomplemented
30C22⋊Dic29C2212yescomplemented
31C22⋊Dic29C2211yescharacteristic, complemented
32C22⋊Dic29C2212yescomplemented
33#90781C2212yescomplemented
34#90781C2212yescomplemented
35C4⋊Dic29C2212yescomplemented
36#90779C2212yescomplemented
37C23×C29—22no—
38C23×C29—42no—
39C23×C29C2311yescharacteristic
40C23×C29C2312yes—
41C23×C29C2311yescharacteristic
42C22×D29—22no—
43C22×D29—42no—
44C22×D29—42no—
45C22×D29D414yescomplemented
46C22×D29C2311yescharacteristic
47C22×D29C2311yescharacteristic
48C22×D29C2311yescharacteristic
49D4×C29—22no—
50D4×C29—42no—
51C2×C4×C29C2311yescharacteristic
52C2×C4×C29C2312yes—
53C22⋊D29—22no—
54C22⋊D29—22no—
55C22⋊D29—24no—
56C22⋊D29—24no—
57C22⋊D29—42no—
58C2×Dic29—22no—
59C2×Dic29C2312yes—
60C2×Dic29C2312yes—
61C2×Dic29C2311yescharacteristic
62D116—22no—
63C4×D29—22no—
64C4×D29—42no—
65C22×C29—22no—
66C22×C29—22no—
67C22×C29—21no—
68C22×C29—22no—
69C22×C29—22no—
70C22×C29—22no—
71C22×C29—44no—
72C22×C29C2×D412yes—
73C22×C29C2411yescharacteristic
74C2×D29—22no—
75C2×D29—22no—
76C2×D29—21no—
77C2×D29—22no—
78C2×D29—44no—
79C2×D29—44no—
80C2×D29C2×D412yes—
81C2×D29C2×D412yes—
82C4×C29—21no—
83C4×C29—22no—
84Dic29—21no—
85Dic29—22no—
86Dic29—22no—
87#534—291nomaximal, Sylow
88C2×C29—22no—
89C2×C29—41no—
90C2×C29—42no—
91C2×C29C22×D411yescharacteristic
92C2×C29H(5,𝔽2)12yes—
93D29—22no—
94D29—22no—
95D29—41no—
96C22×D4—291no—
97C22×D4—291no—
98#123—291no—
99#123—292no—
100#123—291no—
101#121—292no—
102#121—292no—
103#120—291no—
104#120—292no—
105#120D2911yescharacteristic, complemented
106C2×C22⋊C4—291no—
107C29#53411yescharacteristic, complemented, Sylow
108C24—291no—
109C24—291no—
110C24C2×D2911yescharacteristic, complemented
111C2×D4—292no—
112C2×D4—291no—
113C2×D4—291no—
114C2×D4—292no—
115C2×D4—292no—
116C2×D4—291no—
117C2×D4—584no—
118C2×D4—584no—
119C2×D4C2×D2911yescharacteristic
120C2×D4C2×D2912yescomplemented
121C22×C4—291no—
122C22×C4—291no—
123C22×C4—292no—
124C4⋊C4—292no—
125C4⋊C4—292no—
126C22⋊C4—291no—
127C22⋊C4—292no—
128C22⋊C4—292no—
129C22⋊C4—292no—
130C22⋊C4—292no—
131C22⋊C4C2×D2911yescharacteristic, complemented
132C22⋊C4C2×D2912yescomplemented
133C23—22no—
134C23—42no—
135C23—291no—
136C23—291no—
137C23—294no—
138C23—291no—
139C23—582no—
140C23—1162no—
141C23—1162no—
142C23C22×D2911yescharacteristic
143C23C22×D2912yes—
144C23C22×D2911yescharacteristic
145D4—22no—
146D4—42no—
147D4—582no—
148D4—582no—
149D4—584no—
150D4—584no—
151D4—582no—
152D4—1162no—
153C2×C4—292no—
154C2×C4—291no—
155C2×C4—292no—
156C2×C4—582no—
157C2×C4—582no—
158C2×C4—1162no—
159C2×C4C22×D2912yes—
160C2×C4C22×D2911yescharacteristic
161C22—22no—
162C22—21no—
163C22—22no—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—44no—
168C22—292no—
169C22—292no—
170C22—582no—
171C22—582no—
172C22—581no—
173C22—582no—
174C22—1164no—
175C22—1164no—
176C22D4×D2912yes—
177C22C23×D2911yescharacteristic
178C4—21no—
179C4—22no—
180C4—581no—
181C4—582no—
182C4—582no—
183C2—22no—
184C2—42no—
185C2—41no—
186C2—582no—
187C2—582no—
188C2—1161no—
189C2C2×D4×D2911yescharacteristic
190C2#1174535912yes—
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×#120C2
hypercenter#120D29
hypocenterC29#534
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D29C2semidirect
2. C2×D4×D29C2semidirect
3. C29×#120C2semidirect
4. #11745315C2semidirect
5. #11745300C2semidirect
6. #11745299C2semidirect
7. #11745297C2semidirect
8. #11745248C2semidirect
9. #11745246C2semidirect
10. #11745245C2semidirect
11. C22⋊C4×D29C2semidirect
12. C24×C29C22semidirect
14. C23×D29C22semidirect
16. C2×D4×C29C22semidirect
20. C2×C22⋊D29C22semidirect
21. C2×C22⋊D29C22semidirect
22. C2×C22⋊D29C22semidirect
23. C22×Dic29C22semidirect
25. C2×D116C22semidirect
26. C2×C4×D29C22semidirect
27. C2×C4×D29C22semidirect
28. C22⋊C4×C29C22semidirect
29. C22⋊C4×C29C22semidirect
30. C22⋊Dic29C22semidirect
31. C22⋊Dic29C22semidirect
32. C22⋊Dic29C22semidirect
33. #90781C22semidirect
34. #90781C22semidirect
35. C4⋊Dic29C22semidirect
36. #90779C22semidirect
45. C22×D29D4semidirect
105. #120D29semidirect
107. C29#534semidirect
110. C24C2×D29semidirect
120. C2×D4C2×D29semidirect
131. C22⋊C4C2×D29semidirect
132. C22⋊C4C2×D29semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D292
C2×D4×D292
C29×#1202
#117453152
#117453002
#117452992
#117452972
#117452482
#117452462
#117452452
C22⋊C4×D292
#53429