Finite Group Databasebeta

← #14271807

Subgroups — #14271807

Order 1856.

334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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
2C2×#90807C211yesmaximal, characteristic, complemented
3#11745315C212yesmaximal, complemented
4C2×C22⋊Dic29C212yesmaximal, complemented
5#11745301C212yesmaximal, complemented
6#11745300C211yesmaximal, characteristic, complemented
7#11745298C211yesmaximal, characteristic, complemented
8#11745297C212yesmaximal, complemented
9D4×Dic29C211yesmaximal, characteristic, complemented
10C4×C22⋊D29C211yesmaximal, characteristic, complemented
11#11745286C211yesmaximal, characteristic, complemented
12C24×C29C2212yes—
13C2×D4×C29—24no—
14C2×D4×C29C2212yes—
15C2×D4×C29C2211yescharacteristic
16C2×D4×C29C2211yescharacteristic
17C22×C4×C29C2211yescharacteristic
18C2×C22⋊D29C2211yescharacteristic
19C2×C22⋊D29C2212yescomplemented
20C2×C22⋊D29C2212yescomplemented
21C22×Dic29C2212yescomplemented
22C22×Dic29C2212yescomplemented
23#90807—24no—
24C2×C4×D29C2211yescharacteristic, complemented
25C2×Dic58C2211yescharacteristic, complemented
26C22⋊Dic29C2212yes—
27C22⋊Dic29C2211yescharacteristic
28C22⋊Dic29C2212yescomplemented
29C22⋊Dic29C2212yescomplemented
30C22⋊Dic29C2212yescomplemented
31C22⋊Dic29C2212yescomplemented
32#90781C2211yescharacteristic, complemented
33C4⋊Dic29C2211yescharacteristic, complemented
34#90779C2212yescomplemented
35#90779C2211yescharacteristic, complemented
36C4×Dic29C2211yescharacteristic, complemented
37C23×C29—24no—
38C23×C29—24no—
39C23×C29—42no—
40C23×C29C2312yes—
41C23×C29C2312yes—
42C23×C29C2311yescharacteristic
43C22×D29C2311yescharacteristic
44D4×C29—24no—
45D4×C29—22no—
46D4×C29D414yescomplemented
47C2×C4×C29—22no—
48C2×C4×C29C2311yescharacteristic
49C2×C4×C29C2311yescharacteristic
50C22⋊D29—24no—
51C22⋊D29—22no—
52C22⋊D29—42no—
53C2×Dic29—24no—
54C2×Dic29—42no—
55C2×Dic29C2311yescharacteristic
56C2×Dic29C2311yescharacteristic
57C2×Dic29C2312yes—
58C2×Dic29C2312yes—
59C2×Dic29C2311yescharacteristic
60C4×D29—22no—
61Dic58—22no—
62C22×C29—21no—
63C22×C29—22no—
64C22×C29—22no—
65C22×C29—21no—
66C22×C29—22no—
67C22×C29—22no—
68C22×C29—22no—
69C22×C29—48no—
70C22×C29C2×D414yes—
71C22×C29#4112yescomplemented
72C22×C29C2411yescharacteristic
73C2×D29—21no—
74C2×D29—21no—
75C2×D29—21no—
76C4×C29—21no—
77C4×C29C2×D412yes—
78Dic29—22no—
79Dic29—21no—
80Dic29—21no—
81Dic29—21no—
82Dic29—22no—
83#546—291nomaximal, Sylow
84C2×C29—22no—
85C2×C29—24no—
86C2×C29—42no—
87C2×C29C22×D411yescharacteristic
88C2×C29C2×#4111yescharacteristic
89C2×C29H(5,𝔽2)11yescharacteristic
90D29—41no—
91C2×#41—291no—
92C22×D4D2911yescharacteristic, complemented
93#124—291no—
94#123—292no—
95C22⋊Q8—291no—
96#121—291no—
97#121—292no—
98#120—292no—
99C4×D4—291no—
100C4×D4—291no—
101C2×C22⋊C4—292no—
102C29#54611yescharacteristic, complemented, Sylow
103C24C2×D2912yes—
104#41—584no—
105C2×Q8—291no—
106C2×D4—24no—
107C2×D4—291no—
108C2×D4—292no—
109C2×D4—292no—
110C2×D4C2×D2912yes—
111C2×D4C2×D2911yescharacteristic
112C2×D4C2×D2911yescharacteristic
113C22×C4—292no—
114C22×C4—292no—
115C22×C4—291no—
116C22×C4C2×D2911yescharacteristic
117C4⋊C4—291no—
118C4⋊C4—291no—
119C4⋊C4—292no—
120C22⋊C4—291no—
121C22⋊C4—292no—
122C22⋊C4—292no—
123C22⋊C4—292no—
124C22⋊C4—292no—
125C22⋊C4—292no—
126C22⋊C4—291no—
127C42—291no—
128C23—24no—
129C23—24no—
130C23—42no—
131C23—291no—
132C23C22×D2912yes—
133C23C22×D2911yescharacteristic
134C23C22×D2912yes—
135Q8—582no—
136D4—24no—
137D4—22no—
138D4—582no—
139D4—584no—
140D4—1162no—
141D4C22⋊D2914yescomplemented
142C2×C4—22no—
143C2×C4—291no—
144C2×C4—291no—
145C2×C4—292no—
146C2×C4—291no—
147C2×C4—292no—
148C2×C4—584no—
149C2×C4—582no—
150C2×C4—1162no—
151C2×C4C22×D2911yescharacteristic
152C2×C4C22×D2911yescharacteristic
153C22—22no—
154C22—22no—
155C22—21no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—48no—
161C22—581no—
162C22—581no—
163C22—581no—
164C22#9080712yescomplemented
165C22C2×C22⋊D2914yes—
166C22C23×D2911yescharacteristic
167C4—21no—
168C4—581no—
169C4—581no—
170C4—582no—
171C4—581no—
172C4—582no—
173C4C2×C22⋊D2912yes—
174C2—22no—
175C2—24no—
176C2—42no—
177C2—1161no—
178C2C2×#9080711yescharacteristic
179C2#1174535911yescharacteristic
180C2C22×C22⋊D2911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC22×D4×C29C2
hypercenterC22×D4D29
hypocenterC29#546
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. C2×#90807C2semidirect
3. #11745315C2semidirect
4. C2×C22⋊Dic29C2semidirect
5. #11745301C2semidirect
6. #11745300C2semidirect
7. #11745298C2semidirect
8. #11745297C2semidirect
9. D4×Dic29C2semidirect
10. C4×C22⋊D29C2semidirect
11. #11745286C2semidirect
19. C2×C22⋊D29C22semidirect
20. C2×C22⋊D29C22semidirect
21. C22×Dic29C22semidirect
22. C22×Dic29C22semidirect
24. C2×C4×D29C22semidirect
25. C2×Dic58C22semidirect
28. C22⋊Dic29C22semidirect
29. C22⋊Dic29C22semidirect
30. C22⋊Dic29C22semidirect
31. C22⋊Dic29C22semidirect
32. #90781C22semidirect
33. C4⋊Dic29C22semidirect
34. #90779C22semidirect
35. #90779C22semidirect
36. C4×Dic29C22semidirect
46. D4×C29D4semidirect
71. C22×C29#41semidirect
92. C22×D4D29semidirect
102. C29#546semidirect
141. D4C22⋊D29semidirect
164. C22#90807semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C292
C2×#908072
#117453152
C2×C22⋊Dic292
#117453012
#117453002
#117452982
#117452972
D4×Dic292
C4×C22⋊D292
#117452862
#54629