Finite Group Databasebeta

← #14271806

Subgroups — #14271806

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×#90809C211yesmaximal, characteristic, complemented
2C2×D4×D29C211yesmaximal, characteristic, complemented
3C29×#124C211yesmaximal, characteristic, complemented
4#11745308C211yesmaximal, characteristic, complemented
5#11745300C211yesmaximal, characteristic, complemented
6#11745246C212yesmaximal, complemented
7#11745245C212yesmaximal, complemented
8#11745244C212yesmaximal, complemented
9C22⋊C4×D29C212yesmaximal, complemented
10C4×D116C211yesmaximal, characteristic, complemented
11C4×D116C211yesmaximal, characteristic, complemented
12C23×D29C2212yes—
13C2×Q8×C29C2211yescharacteristic, complemented
14C2×D4×C29C2211yescharacteristic
15C2×C22⋊D29C2212yes—
16C2×C22⋊D29C2212yescomplemented
17#90809—24no—
18D4×D29—24no—
19C2×D116C2211yescharacteristic
20C2×D116C2211yescharacteristic
21C2×D116C2212yescomplemented
22C2×C4×D29C2211yescharacteristic
23C2×C4×D29C2211yescharacteristic, complemented
24C2×C4×D29C2212yescomplemented
25C2×C4×D29C2212yescomplemented
26C22⋊C4×C29C2212yescomplemented
27C22⋊C4×C29C2212yescomplemented
28C42×C29C2211yescharacteristic, complemented
29C22⋊Dic29C2212yescomplemented
30#90781C2212yes—
31#90781C2211yescharacteristic
32#90781C2212yescomplemented
33#90781C2211yescharacteristic, complemented
34C4⋊Dic29C2211yescharacteristic, complemented
35C4⋊Dic29C2211yescharacteristic, complemented
36#90779C2212yescomplemented
37C23×C29C2312yes—
38C22×D29—24no—
39C22×D29—24no—
40C22×D29—42no—
41C22×D29C2311yescharacteristic
42C22×D29C2312yes—
43C22×D29C2311yescharacteristic
44Q8×C29—22no—
45D4×C29—22no—
46C2×C4×C29C2312yes—
47C2×C4×C29C2311yescharacteristic
48C2×C4×C29C2311yescharacteristic
49C2×C4×C29C2311yescharacteristic
50C22⋊D29—24no—
51C22⋊D29—42no—
52C2×Dic29C2311yescharacteristic
53C2×Dic29C2312yes—
54C2×Dic29C2311yescharacteristic
55D116—24no—
56D116—22no—
57D116D414yescomplemented
58C4×D29—24no—
59C4×D29—22no—
60C4×D29—22no—
61C4×D29—42no—
62C22×C29—22no—
63C22×C29—22no—
64C22×C29—22no—
65C22×C29C2411yescharacteristic
66C2×D29—21no—
67C2×D29—22no—
68C2×D29—22no—
69C2×D29—21no—
70C2×D29—21no—
71C2×D29—21no—
72C2×D29—21no—
73C2×D29—48no—
74C2×D29C2×D414yes—
75C2×D29#4112yescomplemented
76C4×C29—22no—
77C4×C29—21no—
78C4×C29—21no—
79C4×C29C2×D412yes—
80Dic29—21no—
81Dic29—21no—
82Dic29—22no—
83#546—291nomaximal, Sylow
84C2×C29—42no—
85C2×C29C22×D411yescharacteristic
86C2×C29C2×#4111yescharacteristic
87C2×C29H(5,𝔽2)11yescharacteristic
88D29—22no—
89D29—24no—
90D29—41no—
91C2×#41—291no—
92C22×D4—291no—
93#124D2911yescharacteristic, complemented
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
103C24—292no—
104#41—584no—
105C2×Q8C2×D2911yescharacteristic, complemented
106C2×D4—292no—
107C2×D4—292no—
108C2×D4—291no—
109C2×D4—291no—
110C2×D4—292no—
111C2×D4—584no—
112C2×D4C2×D2911yescharacteristic
113C22×C4—292no—
114C22×C4—291no—
115C22×C4—291no—
116C22×C4—292no—
117C4⋊C4—291no—
118C4⋊C4—291no—
119C4⋊C4—292no—
120C22⋊C4—292no—
121C22⋊C4—291no—
122C22⋊C4—292no—
123C22⋊C4—292no—
124C22⋊C4—291no—
125C22⋊C4C2×D2912yescomplemented
126C22⋊C4C2×D2912yescomplemented
127C42C2×D2911yescharacteristic, complemented
128C23—291no—
129C23—292no—
130C23—291no—
131C23—584no—
132C23—584no—
133C23—1162no—
134C23C22×D2912yes—
135Q8—22no—
136D4—22no—
137D4—294no—
138D4—584no—
139D4—582no—
140D4—584no—
141D4—1162no—
142C2×C4—292no—
143C2×C4—291no—
144C2×C4—291no—
145C2×C4—584no—
146C2×C4—582no—
147C2×C4—582no—
148C2×C4—1162no—
149C2×C4C22×D2911yescharacteristic
150C2×C4C22×D2911yescharacteristic
151C2×C4C22×D2912yes—
152C2×C4C22×D2911yescharacteristic
153C22—22no—
154C22—22no—
155C22—22no—
156C22—294no—
157C22—292no—
158C22—581no—
159C22—582no—
160C22—582no—
161C22—581no—
162C22—581no—
163C22—581no—
164C22—581no—
165C22—1168no—
166C22C23×D2911yescharacteristic
167C4—22no—
168C4—21no—
169C4—21no—
170C4—581no—
171C4—581no—
172C4—582no—
173C4D4×D2912yes—
174C2—42no—
175C2—582no—
176C2—584no—
177C2—1161no—
178C2C2×D4×D2911yescharacteristic
179C2#41×D2911yescharacteristic
180C2#1174536411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×#124C2
hypercenter#124D29
hypocenterC29#546
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#90809C2semidirect
2. C2×D4×D29C2semidirect
3. C29×#124C2semidirect
4. #11745308C2semidirect
5. #11745300C2semidirect
6. #11745246C2semidirect
7. #11745245C2semidirect
8. #11745244C2semidirect
9. C22⋊C4×D29C2semidirect
10. C4×D116C2semidirect
11. C4×D116C2semidirect
13. C2×Q8×C29C22semidirect
16. C2×C22⋊D29C22semidirect
21. C2×D116C22semidirect
23. C2×C4×D29C22semidirect
24. C2×C4×D29C22semidirect
25. C2×C4×D29C22semidirect
26. C22⋊C4×C29C22semidirect
27. C22⋊C4×C29C22semidirect
28. C42×C29C22semidirect
29. C22⋊Dic29C22semidirect
32. #90781C22semidirect
33. #90781C22semidirect
34. C4⋊Dic29C22semidirect
35. C4⋊Dic29C22semidirect
36. #90779C22semidirect
57. D116D4semidirect
75. C2×D29#41semidirect
93. #124D29semidirect
102. C29#546semidirect
105. C2×Q8C2×D29semidirect
125. C22⋊C4C2×D29semidirect
126. C22⋊C4C2×D29semidirect
127. C42C2×D29semidirect

Maximal subgroups

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

subgroupindex
C2×#908092
C2×D4×D292
C29×#1242
#117453082
#117453002
#117452462
#117452452
#117452442
C22⋊C4×D292
C4×D1162
#54629