Finite Group Databasebeta

← #14271809

Subgroups — #14271809

Order 1856.

334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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×#90805C211yesmaximal, characteristic, complemented
2C22×D116C211yesmaximal, characteristic, complemented
3C4×D4×C29C211yesmaximal, characteristic, complemented
4#11745299C212yesmaximal, complemented
5#11745292C211yesmaximal, characteristic, complemented
6#11745286C211yesmaximal, characteristic, complemented
7#11745256C212yesmaximal, complemented
8#11745246C212yesmaximal, complemented
9C22⋊C4×D29C212yesmaximal, complemented
10#11745237C211yesmaximal, characteristic, complemented
11C4×D116C211yesmaximal, characteristic, complemented
12C23×D29C2212yes—
13C2×D4×C29C2211yescharacteristic
14C22×C4×C29C2211yescharacteristic
15C22×C4×C29C2211yescharacteristic, complemented
16C2×C22⋊D29C2212yescomplemented
17C2×C22⋊D29C2212yescomplemented
18#90805—24no—
19C2×D116—24no—
20C2×D116C2211yescharacteristic
21C2×D116C2212yes—
22C2×D116C2211yescharacteristic
23C2×C4×D29C2212yescomplemented
24C2×C4×D29C2212yescomplemented
25C2×Dic58C2211yescharacteristic, complemented
26C4⋊C4×C29C2211yescharacteristic, complemented
27C22⋊C4×C29C2211yescharacteristic
28C22⋊C4×C29C2211yescharacteristic, complemented
29C42×C29C2211yescharacteristic, complemented
30C22⋊Dic29C2212yes—
31#90781C2212yescomplemented
32#90781C2212yescomplemented
33#90781C2212yescomplemented
34#90781C2212yescomplemented
35C4⋊Dic29C2211yescharacteristic, complemented
36#90779C2212yescomplemented
37C23×C29C2311yescharacteristic
38C23×C29C2311yescharacteristic
39C22×D29—24no—
40C22×D29—24no—
41C22×D29—42no—
42C22×D29C2312yes—
43C22×D29C2312yes—
44D4×C29—22no—
45C2×C4×C29—22no—
46C2×C4×C29—22no—
47C2×C4×C29C2311yescharacteristic
48C2×C4×C29C2311yescharacteristic
49C2×C4×C29C2311yescharacteristic
50C2×C4×C29C2311yescharacteristic
51C2×C4×C29C2311yescharacteristic
52C22⋊D29—24no—
53C22⋊D29—42no—
54C2×Dic29C2312yes—
55C2×Dic29C2312yes—
56D116—24no—
57D116—22no—
58D116D414yescomplemented
59C4×D29—24no—
60C4×D29—42no—
61Dic58—22no—
62C22×C29—21no—
63C22×C29—21no—
64C22×C29—21no—
65C22×C29—21no—
66C22×C29—21no—
67C22×C29#4112yescomplemented
68C22×C29C2411yescharacteristic
69C2×D29—22no—
70C2×D29—22no—
71C2×D29—22no—
72C2×D29—22no—
73C2×D29—22no—
74C2×D29—48no—
75C2×D29C2×D414yes—
76C4×C29—21no—
77C4×C29—21no—
78C4×C29—21no—
79C4×C29—21no—
80C4×C29C2×D412yes—
81Dic29—22no—
82Dic29—22no—
83#546—291nomaximal, Sylow
84C2×C29—22no—
85C2×C29—41no—
86C2×C29C22×D411yescharacteristic
87C2×C29C2×#4111yescharacteristic
88C2×C29H(5,𝔽2)11yescharacteristic
89D29—24no—
90D29—42no—
91C2×#41—291no—
92C22×D4—291no—
93#124—291no—
94#123—292no—
95C22⋊Q8—291no—
96#121—291no—
97#121—292no—
98#120—292no—
99C4×D4—291no—
100C4×D4D2911yescharacteristic, complemented
101C2×C22⋊C4—292no—
102C29#54611yescharacteristic, complemented, Sylow
103C24—292no—
104#41—584no—
105C2×Q8—291no—
106C2×D4—292no—
107C2×D4—292no—
108C2×D4—291no—
109C2×D4—292no—
110C2×D4—291no—
111C2×D4—584no—
112C2×D4C2×D2911yescharacteristic
113C22×C4—292no—
114C22×C4—292no—
115C22×C4C2×D2911yescharacteristic
116C22×C4C2×D2911yescharacteristic, complemented
117C4⋊C4—291no—
118C4⋊C4—292no—
119C4⋊C4C2×D2911yescharacteristic, complemented
120C22⋊C4—292no—
121C22⋊C4—292no—
122C22⋊C4—292no—
123C22⋊C4—292no—
124C22⋊C4—292no—
125C22⋊C4C2×D2911yescharacteristic
126C22⋊C4C2×D2911yescharacteristic, complemented
127C42C2×D2911yescharacteristic, complemented
128C23—292no—
129C23—292no—
130C23—584no—
131C23—584no—
132C23—1162no—
133C23C22×D2911yescharacteristic
134C23C22×D2911yescharacteristic
135Q8—582no—
136D4—22no—
137D4—294no—
138D4—584no—
139D4—584no—
140D4—582no—
141D4—1162no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—292no—
145C2×C4—292no—
146C2×C4—584no—
147C2×C4—1162no—
148C2×C4C22×D2911yescharacteristic
149C2×C4C22×D2911yescharacteristic
150C2×C4C22×D2911yescharacteristic
151C2×C4C22×D2911yescharacteristic
152C2×C4C22×D2911yescharacteristic
153C22—21no—
154C22—21no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—294no—
159C22—582no—
160C22—582no—
161C22—582no—
162C22—582no—
163C22—582no—
164C22—1168no—
165C22#9080512yescomplemented
166C22C23×D2911yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—582no—
172C4—582no—
173C4D4×D2912yes—
174C2—22no—
175C2—41no—
176C2—584no—
177C2—1162no—
178C2C2×#9080511yescharacteristic
179C2C2×D4×D2911yescharacteristic
180C2#1174536411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC4×D4×C29C2
hypercenterC4×D4D29
hypocenterC29#546
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#90805C2semidirect
2. C22×D116C2semidirect
3. C4×D4×C29C2semidirect
4. #11745299C2semidirect
5. #11745292C2semidirect
6. #11745286C2semidirect
7. #11745256C2semidirect
8. #11745246C2semidirect
9. C22⋊C4×D29C2semidirect
10. #11745237C2semidirect
11. C4×D116C2semidirect
15. C22×C4×C29C22semidirect
16. C2×C22⋊D29C22semidirect
17. C2×C22⋊D29C22semidirect
23. C2×C4×D29C22semidirect
24. C2×C4×D29C22semidirect
25. C2×Dic58C22semidirect
26. C4⋊C4×C29C22semidirect
28. C22⋊C4×C29C22semidirect
29. C42×C29C22semidirect
31. #90781C22semidirect
32. #90781C22semidirect
33. #90781C22semidirect
34. #90781C22semidirect
35. C4⋊Dic29C22semidirect
36. #90779C22semidirect
58. D116D4semidirect
67. C22×C29#41semidirect
100. C4×D4D29semidirect
102. C29#546semidirect
116. C22×C4C2×D29semidirect
119. C4⋊C4C2×D29semidirect
126. C22⋊C4C2×D29semidirect
127. C42C2×D29semidirect
165. C22#90805semidirect

Maximal subgroups

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

subgroupindex
C2×#908052
C22×D1162
C4×D4×C292
#117452992
#117452922
#117452862
#117452562
#117452462
C22⋊C4×D292
#117452372
C4×D1162
#54629