Finite Group Databasebeta

← #14271810

Subgroups — #14271810

Order 1856.

334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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, complemented
2C2×#90805C211yesmaximal, characteristic, complemented
3C29×#121C211yesmaximal, characteristic, complemented
4#11745300C212yesmaximal, complemented
5#11745299C212yesmaximal, complemented
6#11745298C211yesmaximal, characteristic, complemented
7C4×C22⋊D29C211yesmaximal, characteristic, complemented
8#11745259C211yesmaximal, characteristic, complemented
9#11745255C211yesmaximal, characteristic, complemented
10#11745245C212yesmaximal, complemented
11C22⋊C4×D29C212yesmaximal, complemented
12C23×D29C2212yes—
13C2×D4×C29C2211yescharacteristic
14C2×D4×C29C2212yescomplemented
15C22×C4×C29C2211yescharacteristic, complemented
16C2×C22⋊D29C2211yescharacteristic
17C2×C22⋊D29C2212yes—
18C2×C22⋊D29C2212yescomplemented
19D4×D29—24no—
20#90805—24no—
21C2×D116C2211yescharacteristic
22C2×C4×D29C2211yescharacteristic
23C2×C4×D29C2212yescomplemented
24C2×C4×D29C2212yescomplemented
25C2×Dic58C2211yescharacteristic, complemented
26C4⋊C4×C29C2211yescharacteristic, complemented
27C22⋊C4×C29C2212yescomplemented
28C22⋊Dic29C2211yescharacteristic, complemented
29C22⋊Dic29C2212yescomplemented
30C22⋊Dic29C2212yescomplemented
31#90781C2211yescharacteristic
32#90781C2212yes—
33#90781C2212yescomplemented
34C4⋊Dic29C2212yescomplemented
35#90779C2211yescharacteristic, complemented
36C4×Dic29C2211yescharacteristic, complemented
37C23×C29C2312yes—
38C23×C29C2311yescharacteristic
39C22×D29—24no—
40C22×D29—24no—
41C22×D29—42no—
42C22×D29C2312yes—
43C22×D29C2311yescharacteristic
44D4×C29—22no—
45D4×C29—42no—
46C2×C4×C29—22no—
47C2×C4×C29C2311yescharacteristic
48C2×C4×C29C2312yes—
49C2×C4×C29C2311yescharacteristic
50C22⋊D29—24no—
51C22⋊D29—24no—
52C22⋊D29—22no—
53C2×Dic29C2311yescharacteristic
54C2×Dic29C2311yescharacteristic
55C2×Dic29C2311yescharacteristic
56C2×Dic29C2312yes—
57D116D414yescomplemented
58C4×D29—24no—
59C4×D29—22no—
60C4×D29—42no—
61Dic58—22no—
62C22×C29—21no—
63C22×C29—22no—
64C22×C29—21no—
65C22×C29—22no—
66C22×C29—21no—
67C22×C29—22no—
68C22×C29C2411yescharacteristic
69C2×D29—21no—
70C2×D29—22no—
71C2×D29—22no—
72C2×D29—21no—
73C2×D29—48no—
74C2×D29C2×D414yes—
75C2×D29#4112yescomplemented
76C4×C29—21no—
77C4×C29—22no—
78C4×C29C2×D412yes—
79Dic29—22no—
80Dic29—21no—
81Dic29—21no—
82Dic29—21no—
83#546—291nomaximal, Sylow
84C2×C29—42no—
85C2×C29—41no—
86C2×C29C22×D411yescharacteristic
87C2×C29C2×#4111yescharacteristic
88C2×C29H(5,𝔽2)11yescharacteristic
89D29—22no—
90D29—24no—
91C2×#41—291no—
92C22×D4—291no—
93#124—291no—
94#123—292no—
95C22⋊Q8—291no—
96#121—292no—
97#121D2911yescharacteristic, complemented
98#120—292no—
99C4×D4—291no—
100C4×D4—291no—
101C2×C22⋊C4—292no—
102C29#54611yescharacteristic, complemented, Sylow
103C24—292no—
104#41—584no—
105C2×Q8—291no—
106C2×D4—291no—
107C2×D4—292no—
108C2×D4—292no—
109C2×D4—291no—
110C2×D4—584no—
111C2×D4C2×D2911yescharacteristic
112C2×D4C2×D2912yescomplemented
113C22×C4—292no—
114C22×C4—291no—
115C22×C4—292no—
116C22×C4C2×D2911yescharacteristic, complemented
117C4⋊C4—291no—
118C4⋊C4—292no—
119C4⋊C4C2×D2911yescharacteristic, complemented
120C22⋊C4—292no—
121C22⋊C4—291no—
122C22⋊C4—292no—
123C22⋊C4—291no—
124C22⋊C4—292no—
125C22⋊C4—292no—
126C22⋊C4C2×D2912yescomplemented
127C42—291no—
128C23—291no—
129C23—292no—
130C23—584no—
131C23—584no—
132C23—1162no—
133C23C22×D2912yes—
134C23C22×D2911yescharacteristic
135Q8—582no—
136D4—22no—
137D4—42no—
138D4—294no—
139D4—584no—
140D4—584no—
141D4—582no—
142C2×C4—22no—
143C2×C4—291no—
144C2×C4—291no—
145C2×C4—292no—
146C2×C4—291no—
147C2×C4—584no—
148C2×C4—582no—
149C2×C4—1162no—
150C2×C4C22×D2912yes—
151C2×C4C22×D2911yescharacteristic
152C2×C4C22×D2911yescharacteristic
153C22—21no—
154C22—22no—
155C22—21no—
156C22—22no—
157C22—21no—
158C22—22no—
159C22—294no—
160C22—292no—
161C22—581no—
162C22—582no—
163C22—581no—
164C22—582no—
165C22—1168no—
166C22C23×D2911yescharacteristic
167C4—21no—
168C4—22no—
169C4—581no—
170C4—582no—
171C4—581no—
172C4—581no—
173C4D4×D2912yes—
174C2—42no—
175C2—41no—
176C2—582no—
177C2—584no—
178C2C2×D4×D2911yescharacteristic
179C2#1174535911yescharacteristic
180C2#41×D2911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×#121C2
hypercenter#121D29
hypocenterC29#546
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. C2×#90805C2semidirect
3. C29×#121C2semidirect
4. #11745300C2semidirect
5. #11745299C2semidirect
6. #11745298C2semidirect
7. C4×C22⋊D29C2semidirect
8. #11745259C2semidirect
9. #11745255C2semidirect
10. #11745245C2semidirect
11. C22⋊C4×D29C2semidirect
14. C2×D4×C29C22semidirect
15. C22×C4×C29C22semidirect
18. C2×C22⋊D29C22semidirect
23. C2×C4×D29C22semidirect
24. C2×C4×D29C22semidirect
25. C2×Dic58C22semidirect
26. C4⋊C4×C29C22semidirect
27. C22⋊C4×C29C22semidirect
28. C22⋊Dic29C22semidirect
29. C22⋊Dic29C22semidirect
30. C22⋊Dic29C22semidirect
33. #90781C22semidirect
34. C4⋊Dic29C22semidirect
35. #90779C22semidirect
36. C4×Dic29C22semidirect
57. D116D4semidirect
75. C2×D29#41semidirect
97. #121D29semidirect
102. C29#546semidirect
112. C2×D4C2×D29semidirect
116. C22×C4C2×D29semidirect
119. C4⋊C4C2×D29semidirect
126. 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
C2×#908052
C29×#1212
#117453002
#117452992
#117452982
C4×C22⋊D292
#117452592
#117452552
#117452452
C22⋊C4×D292
#54629