Finite Group Databasebeta

← #14271801

Subgroups — #14271801

Order 1856.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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×#41×C29C211yesmaximal, characteristic, complemented
2C2×D4×D29C211yesmaximal, characteristic, complemented
3#11745309C211yesmaximal, characteristic, complemented
4#11745308C211yesmaximal, characteristic, complemented
5#11745301C212yesmaximal, complemented
6#11745299C212yesmaximal, complemented
7D4×Dic29C211yesmaximal, characteristic, complemented
8#11745292C211yesmaximal, characteristic, complemented
9#11745291C212yesmaximal, complemented
10C4×C22⋊D29C211yesmaximal, characteristic, complemented
11C2×#90781C212yesmaximal, complemented
12C23×D29C2212yes—
13#41×C29—24no—
14C2×Q8×C29C2211yescharacteristic, complemented
15C2×D4×C29C2211yescharacteristic
16C2×D4×C29C2212yescomplemented
17C22×C4×C29C2212yescomplemented
18C22×C4×C29C2211yescharacteristic, complemented
19C2×C22⋊D29C2211yescharacteristic
20C2×C22⋊D29C2212yes—
21C2×C22⋊D29C2212yescomplemented
22C22×Dic29C2212yescomplemented
23D4×D29—24no—
24C2×D116C2211yescharacteristic
25C2×C4×D29C2211yescharacteristic
26C22⋊Dic29C2211yescharacteristic, complemented
27C22⋊Dic29C2212yescomplemented
28#90781C2211yescharacteristic
29#90781C2212yes—
30#90781C2212yescomplemented
31#90781C2212yescomplemented
32#90781C2212yescomplemented
33C4⋊Dic29C2211yescharacteristic, complemented
34#90779C2211yescharacteristic, complemented
35#90779C2212yescomplemented
36C4×Dic29C2211yescharacteristic, complemented
37C23×C29C2311yescharacteristic
38C23×C29C2312yes—
39C22×D29—24no—
40C22×D29—24no—
41C22×D29—42no—
42C22×D29C2312yes—
43C22×D29C2311yescharacteristic
44Q8×C29—22no—
45D4×C29—24no—
46D4×C29D414yescomplemented
47C2×C4×C29—24no—
48C2×C4×C29—22no—
49C2×C4×C29C2311yescharacteristic
50C2×C4×C29C2312yes—
51C2×C4×C29C2311yescharacteristic
52C22⋊D29—24no—
53C22⋊D29—22no—
54C22⋊D29—42no—
55C2×Dic29—42no—
56C2×Dic29C2311yescharacteristic
57C2×Dic29C2311yescharacteristic
58C2×Dic29C2311yescharacteristic
59C2×Dic29C2312yes—
60D116—22no—
61C4×D29—22no—
62C22×C29—22no—
63C22×C29—22no—
64C22×C29—21no—
65C22×C29—21no—
66C22×C29—21no—
67C22×C29C2×D414yes—
68C22×C29C2411yescharacteristic
69C2×D29—21no—
70C2×D29—21no—
71C2×D29—22no—
72C2×D29—22no—
73C2×D29—22no—
74C2×D29—48no—
75C2×D29#4112yescomplemented
76C4×C29—21no—
77C4×C29—22no—
78C4×C29C2×D412yes—
79Dic29—21no—
80Dic29—21no—
81Dic29—21no—
82Dic29—22no—
83#546—291nomaximal, Sylow
84C2×C29—24no—
85C2×C29—41no—
86C2×C29C22×D411yescharacteristic
87C2×C29C2×#4111yescharacteristic
88C2×C29H(5,𝔽2)11yescharacteristic
89D29—22no—
90D29—42no—
91C2×#41D2911yescharacteristic, complemented
92C22×D4—291no—
93#124—291no—
94#123—292no—
95C22⋊Q8—291no—
96#121—292no—
97#121—291no—
98#120—292no—
99C4×D4—291no—
100C4×D4—291no—
101C2×C22⋊C4—292no—
102C29#54611yescharacteristic, complemented, Sylow
103C24—292no—
104#41—24no—
105C2×Q8C2×D2911yescharacteristic, complemented
106C2×D4—291no—
107C2×D4—292no—
108C2×D4—292no—
109C2×D4—291no—
110C2×D4—584no—
111C2×D4C2×D2911yescharacteristic
112C2×D4C2×D2912yescomplemented
113C22×C4—292no—
114C22×C4—291no—
115C22×C4C2×D2912yescomplemented
116C22×C4C2×D2911yescharacteristic, complemented
117C4⋊C4—291no—
118C4⋊C4—291no—
119C4⋊C4—292no—
120C22⋊C4—292no—
121C22⋊C4—291no—
122C22⋊C4—291no—
123C22⋊C4—292no—
124C22⋊C4—292no—
125C22⋊C4—292no—
126C22⋊C4—292no—
127C42—291no—
128C23—291no—
129C23—292no—
130C23—584no—
131C23—584no—
132C23—1162no—
133C23C22×D2911yescharacteristic
134C23C22×D2912yes—
135Q8—22no—
136D4—24no—
137D4—582no—
138D4—584no—
139D4—582no—
140D4—1162no—
141D4C22⋊D2914yescomplemented
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—291no—
145C2×C4—291no—
146C2×C4—292no—
147C2×C4—291no—
148C2×C4—582no—
149C2×C4—1162no—
150C2×C4C22×D2911yescharacteristic
151C2×C4C22×D2912yes—
152C2×C4C22×D2911yescharacteristic
153C22—22no—
154C22—22no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—292no—
159C22—581no—
160C22—581no—
161C22—582no—
162C22—582no—
163C22—582no—
164C22—1168no—
165C22C2×C22⋊D2914yes—
166C22C23×D2911yescharacteristic
167C4—21no—
168C4—22no—
169C4—581no—
170C4—581no—
171C4—582no—
172C4—581no—
173C4C2×C22⋊D2912yes—
174C2—24no—
175C2—41no—
176C2—582no—
177C2—1162no—
178C2#41×D2911yescharacteristic
179C2#1174536411yescharacteristic
180C2C22×C22⋊D2911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC2×#41×C29C2
hypercenterC2×#41D29
hypocenterC29#546
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×C29C2semidirect
2. C2×D4×D29C2semidirect
3. #11745309C2semidirect
4. #11745308C2semidirect
5. #11745301C2semidirect
6. #11745299C2semidirect
7. D4×Dic29C2semidirect
8. #11745292C2semidirect
9. #11745291C2semidirect
10. C4×C22⋊D29C2semidirect
11. C2×#90781C2semidirect
14. C2×Q8×C29C22semidirect
16. C2×D4×C29C22semidirect
17. C22×C4×C29C22semidirect
18. C22×C4×C29C22semidirect
21. C2×C22⋊D29C22semidirect
22. C22×Dic29C22semidirect
26. C22⋊Dic29C22semidirect
27. C22⋊Dic29C22semidirect
30. #90781C22semidirect
31. #90781C22semidirect
32. #90781C22semidirect
33. C4⋊Dic29C22semidirect
34. #90779C22semidirect
35. #90779C22semidirect
36. C4×Dic29C22semidirect
46. D4×C29D4semidirect
75. C2×D29#41semidirect
91. C2×#41D29semidirect
102. C29#546semidirect
105. C2×Q8C2×D29semidirect
112. C2×D4C2×D29semidirect
115. C22×C4C2×D29semidirect
116. C22×C4C2×D29semidirect
141. D4C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C292
C2×D4×D292
#117453092
#117453082
#117453012
#117452992
D4×Dic292
#117452922
#117452912
C4×C22⋊D292
C2×#907812
#54629