Finite Group Databasebeta

← #14271729

Subgroups — #14271729

Order 1856.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 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
1C2×D4×D29C211yesmaximal, characteristic, complemented
2C2×#90805C211yesmaximal, characteristic, complemented
3C29×#121C211yesmaximal, characteristic, complemented
4#11745302C212yesmaximal, complemented
5#11745300C211yesmaximal, characteristic, complemented
6#11745299C212yesmaximal, complemented
7#11745292C211yesmaximal, characteristic, complemented
8#11745257C211yesmaximal, characteristic, complemented
9#11745254C211yesmaximal, characteristic, complemented
10#11745247C212yesmaximal, complemented
11#11745244C212yesmaximal, complemented
12C23×D29C2212yes—
13C2×D4×C29C2211yescharacteristic
14C2×D4×C29C2212yescomplemented
15C22×C4×C29C2211yescharacteristic, complemented
16C2×C22⋊D29C2211yescharacteristic
17C2×C22⋊D29C2212yes—
18C2×C22⋊D29C2211yescharacteristic, complemented
19C2×C22⋊D29C2212yescomplemented
20C2×C22⋊D29C2212yescomplemented
21D4×D29—24no—
22#90805—24no—
23C2×D116C2211yescharacteristic
24C2×D116C2211yescharacteristic
25C2×D116C2212yescomplemented
26C2×C4×D29C2211yescharacteristic
27C2×C4×D29C2211yescharacteristic, complemented
28C2×Dic58C2211yescharacteristic, complemented
29C4⋊C4×C29C2211yescharacteristic, complemented
30C22⋊C4×C29C2212yescomplemented
31C22⋊Dic29C2212yescomplemented
32#90781C2212yes—
33#90781C2212yescomplemented
34#90781C2212yescomplemented
35C4⋊Dic29C2211yescharacteristic, complemented
36C4×Dic29C2212yescomplemented
37C23×C29C2312yes—
38C23×C29C2311yescharacteristic
39C22×D29—24no—
40C22×D29—42no—
41C22×D29—42no—
42C22×D29C2312yes—
43C22×D29C2311yescharacteristic
44C22×D29C2311yescharacteristic
45D4×C29—22no—
46D4×C29—42no—
47C2×C4×C29—22no—
48C2×C4×C29C2312yes—
49C2×C4×C29C2311yescharacteristic
50C2×C4×C29C2311yescharacteristic
51C22⋊D29—22no—
52C22⋊D29—22no—
53C22⋊D29—24no—
54C22⋊D29—42no—
55C22⋊D29—42no—
56C2×Dic29C2312yes—
57C2×Dic29C2311yescharacteristic
58C2×Dic29C2311yescharacteristic
59D116—22no—
60D116—22no—
61D116—42no—
62C4×D29—22no—
63C4×D29D414yescomplemented
64Dic58—22no—
65C22×C29—21no—
66C22×C29—22no—
67C22×C29—21no—
68C22×C29—22no—
69C22×C29—21no—
70C22×C29—22no—
71C22×C29C2411yescharacteristic
72C2×D29—21no—
73C2×D29—21no—
74C2×D29—21no—
75C2×D29—22no—
76C2×D29—21no—
77C2×D29—22no—
78C2×D29—21no—
79C2×D29—22no—
80C2×D29—48no—
81C2×D29C2×D412yes—
82C4×C29—21no—
83C4×C29—22no—
84C4×C29C2×D412yes—
85Dic29—21no—
86Dic29—22no—
87Dic29C2×D412yes—
88#535—291nomaximal, Sylow
89C2×C29—42no—
90C2×C29—41no—
91C2×C29C22×D411yescharacteristic
92C2×C29H(5,𝔽2)11yescharacteristic
93C2×C29H(5,𝔽2)11yescharacteristic
94D29—22no—
95D29—41no—
96D29—42no—
97C2×#41—291no—
98C22×D4—291no—
99#127—292no—
100#124—292no—
101#121—291no—
102#121—291no—
103#121—291no—
104#121D2911yescharacteristic, complemented
105#120—292no—
106#120—292no—
107#117—291no—
108C29#53511yescharacteristic, complemented, Sylow
109C24—292no—
110#41—584no—
111C2×Q8—291no—
112C2×D4—291no—
113C2×D4—292no—
114C2×D4—291no—
115C2×D4—292no—
116C2×D4—292no—
117C2×D4—291no—
118C2×D4—291no—
119C2×D4—292no—
120C2×D4—584no—
121C2×D4C2×D2911yescharacteristic
122C2×D4C2×D2912yescomplemented
123C22×C4—291no—
124C22×C4—291no—
125C22×C4C2×D2911yescharacteristic, complemented
126C4⋊C4—291no—
127C4⋊C4C2×D2911yescharacteristic, complemented
128C22⋊C4—292no—
129C22⋊C4—292no—
130C22⋊C4—292no—
131C22⋊C4—292no—
132C22⋊C4C2×D2912yescomplemented
133C42—292no—
134C23—291no—
135C23—292no—
136C23—291no—
137C23—584no—
138C23—1162no—
139C23—1162no—
140C23C22×D2912yes—
141C23C22×D2911yescharacteristic
142Q8—582no—
143D4—22no—
144D4—42no—
145D4—582no—
146D4—584no—
147D4—582no—
148D4—582no—
149D4—582no—
150D4—1162no—
151D4—1162no—
152D4—1162no—
153C2×C4—22no—
154C2×C4—291no—
155C2×C4—294no—
156C2×C4—292no—
157C2×C4—291no—
158C2×C4—582no—
159C2×C4C22×D2912yes—
160C2×C4C22×D2911yescharacteristic
161C2×C4C22×D2911yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—292no—
169C22—581no—
170C22—581no—
171C22—581no—
172C22—582no—
173C22—581no—
174C22—582no—
175C22—581no—
176C22—582no—
177C22—1168no—
178C22C23×D2911yescharacteristic
179C4—21no—
180C4—22no—
181C4—292no—
182C4—581no—
183C4—582no—
184C4D4×D2912yes—
185C2—42no—
186C2—41no—
187C2—582no—
188C2—1162no—
189C2—1161no—
190C2C2×D4×D2911yescharacteristic
191C2#1174535911yescharacteristic
192C2#1174536411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×#121C2
hypercenter#121D29
hypocenterC29#535
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. #11745302C2semidirect
5. #11745300C2semidirect
6. #11745299C2semidirect
7. #11745292C2semidirect
8. #11745257C2semidirect
9. #11745254C2semidirect
10. #11745247C2semidirect
11. #11745244C2semidirect
14. C2×D4×C29C22semidirect
15. C22×C4×C29C22semidirect
18. C2×C22⋊D29C22semidirect
19. C2×C22⋊D29C22semidirect
20. C2×C22⋊D29C22semidirect
25. C2×D116C22semidirect
27. C2×C4×D29C22semidirect
28. C2×Dic58C22semidirect
29. C4⋊C4×C29C22semidirect
30. C22⋊C4×C29C22semidirect
31. C22⋊Dic29C22semidirect
33. #90781C22semidirect
34. #90781C22semidirect
35. C4⋊Dic29C22semidirect
36. C4×Dic29C22semidirect
63. C4×D29D4semidirect
104. #121D29semidirect
108. C29#535semidirect
122. C2×D4C2×D29semidirect
125. C22×C4C2×D29semidirect
127. C4⋊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
C2×D4×D292
C2×#908052
C29×#1212
#117453022
#117453002
#117452992
#117452922
#117452572
#117452542
#117452472
#117452442
#53529