Finite Group Databasebeta

← #14271804

Subgroups — #14271804

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×#90809C211yesmaximal, characteristic, complemented
2C22×D116C211yesmaximal, characteristic, complemented
3C29×C22⋊Q8C211yesmaximal, characteristic, complemented
4#11745309C211yesmaximal, characteristic, complemented
5C4×C22⋊D29C211yesmaximal, characteristic, complemented
6#11745257C212yesmaximal, complemented
7#11745257C211yesmaximal, characteristic, complemented
8#11745256C212yesmaximal, complemented
9#11745255C211yesmaximal, characteristic, complemented
10#11745244C212yesmaximal, complemented
11C22⋊C4×D29C212yesmaximal, complemented
12C23×D29C2212yes—
13C2×Q8×C29C2211yescharacteristic, complemented
14C22×C4×C29C2211yescharacteristic
15C2×C22⋊D29C2211yescharacteristic
16#90809—24no—
17C2×D116—24no—
18C2×D116C2211yescharacteristic
19C2×D116C2212yes—
20C2×D116C2211yescharacteristic
21C2×D116C2212yescomplemented
22C2×D116C2212yescomplemented
23C2×C4×D29C2211yescharacteristic, complemented
24C2×C4×D29C2212yescomplemented
25C2×C4×D29C2212yescomplemented
26C4⋊C4×C29C2211yescharacteristic, complemented
27C4⋊C4×C29C2212yescomplemented
28C22⋊C4×C29C2212yes—
29C22⋊Dic29C2211yescharacteristic
30#90781C2211yescharacteristic, complemented
31#90781C2212yescomplemented
32#90781C2212yescomplemented
33#90781C2212yescomplemented
34#90781C2212yescomplemented
35#90779C2211yescharacteristic, complemented
36C4×Dic29C2211yescharacteristic, complemented
37C23×C29C2311yescharacteristic
38C22×D29—24no—
39C22×D29—24no—
40C22×D29—42no—
41C22×D29C2312yes—
42C22×D29C2311yescharacteristic
43C22×D29C2312yes—
44Q8×C29—22no—
45C2×C4×C29—22no—
46C2×C4×C29C2311yescharacteristic
47C2×C4×C29C2312yes—
48C2×C4×C29C2312yes—
49C2×C4×C29C2311yescharacteristic
50C22⋊D29—22no—
51C2×Dic29C2311yescharacteristic
52C2×Dic29C2311yescharacteristic
53C2×Dic29C2311yescharacteristic
54D116—24no—
55D116—24no—
56D116—22no—
57D116—42no—
58D116D414yescomplemented
59C4×D29—24no—
60C4×D29—22no—
61C4×D29—42no—
62C22×C29—21no—
63C22×C29—21no—
64C22×C29#4112yescomplemented
65C22×C29C2411yescharacteristic
66C2×D29—22no—
67C2×D29—22no—
68C2×D29—21no—
69C2×D29—22no—
70C2×D29—21no—
71C2×D29—22no—
72C2×D29—21no—
73C2×D29—22no—
74C2×D29—48no—
75C2×D29C2×D414yes—
76C4×C29—22no—
77C4×C29—21no—
78C4×C29—22no—
79C4×C29C2×D412yes—
80Dic29—21no—
81Dic29—21no—
82Dic29—21no—
83#546—291nomaximal, Sylow
84C2×C29—22no—
85C2×C29C22×D411yescharacteristic
86C2×C29C2×#4111yescharacteristic
87C2×C29H(5,𝔽2)11yescharacteristic
88D29—24no—
89D29—41no—
90D29—42no—
91C2×#41—291no—
92C22×D4—291no—
93#124—291no—
94#123—292no—
95C22⋊Q8D2911yescharacteristic, complemented
96#121—291no—
97#121—292no—
98#120—292no—
99C4×D4—291no—
100C4×D4—291no—
101C2×C22⋊C4—292no—
102C29#54611yescharacteristic, complemented, Sylow
103C24—292no—
104#41—584no—
105C2×Q8C2×D2911yescharacteristic, complemented
106C2×D4—291no—
107C2×D4—291no—
108C2×D4—292no—
109C2×D4—292no—
110C2×D4—291no—
111C2×D4—292no—
112C2×D4—584no—
113C22×C4—292no—
114C22×C4—291no—
115C22×C4—292no—
116C22×C4C2×D2911yescharacteristic
117C4⋊C4—291no—
118C4⋊C4C2×D2911yescharacteristic, complemented
119C4⋊C4C2×D2912yescomplemented
120C22⋊C4—291no—
121C22⋊C4—292no—
122C22⋊C4—292no—
123C22⋊C4—292no—
124C22⋊C4—291no—
125C22⋊C4—292no—
126C22⋊C4C2×D2912yes—
127C42—291no—
128C23—292no—
129C23—292no—
130C23—291no—
131C23—584no—
132C23—584no—
133C23—1162no—
134C23C22×D2911yescharacteristic
135Q8—22no—
136D4—294no—
137D4—584no—
138D4—584no—
139D4—582no—
140D4—582no—
141D4—1162no—
142C2×C4—22no—
143C2×C4—291no—
144C2×C4—291no—
145C2×C4—291no—
146C2×C4—584no—
147C2×C4—582no—
148C2×C4—1162no—
149C2×C4C22×D2912yes—
150C2×C4C22×D2912yes—
151C2×C4C22×D2911yescharacteristic
152C2×C4C22×D2911yescharacteristic
153C22—21no—
154C22—21no—
155C22—294no—
156C22—582no—
157C22—582no—
158C22—581no—
159C22—582no—
160C22—581no—
161C22—582no—
162C22—581no—
163C22—582no—
164C22—1168no—
165C22#9080912yescomplemented
166C22C23×D2911yescharacteristic
167C4—21no—
168C4—22no—
169C4—22no—
170C4—581no—
171C4—581no—
172C4—581no—
173C4D4×D2912yes—
174C2—22no—
175C2—584no—
176C2—1162no—
177C2—1161no—
178C2C2×D4×D2911yescharacteristic
179C2C2×#9080911yescharacteristic
180C2#1174536411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×C22⋊Q8C2
hypercenterC22⋊Q8D29
hypocenterC29#546
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#90809C2semidirect
2. C22×D116C2semidirect
3. C29×C22⋊Q8C2semidirect
4. #11745309C2semidirect
5. C4×C22⋊D29C2semidirect
6. #11745257C2semidirect
7. #11745257C2semidirect
8. #11745256C2semidirect
9. #11745255C2semidirect
10. #11745244C2semidirect
11. C22⋊C4×D29C2semidirect
13. C2×Q8×C29C22semidirect
21. C2×D116C22semidirect
22. C2×D116C22semidirect
23. C2×C4×D29C22semidirect
24. C2×C4×D29C22semidirect
25. C2×C4×D29C22semidirect
26. C4⋊C4×C29C22semidirect
27. C4⋊C4×C29C22semidirect
30. #90781C22semidirect
31. #90781C22semidirect
32. #90781C22semidirect
33. #90781C22semidirect
34. #90781C22semidirect
35. #90779C22semidirect
36. C4×Dic29C22semidirect
58. D116D4semidirect
64. C22×C29#41semidirect
95. C22⋊Q8D29semidirect
102. C29#546semidirect
105. C2×Q8C2×D29semidirect
118. C4⋊C4C2×D29semidirect
119. C4⋊C4C2×D29semidirect
165. C22#90809semidirect

Maximal subgroups

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

subgroupindex
C2×#908092
C22×D1162
C29×C22⋊Q82
#117453092
C4×C22⋊D292
#117452572
#117452562
#117452552
#117452442
C22⋊C4×D292
#54629