Finite Group Databasebeta

← #14271669

Subgroups — #14271669

Order 1856.

330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C23×Dic29C211yesmaximal, characteristic, complemented
2C2×#90807C211yesmaximal, characteristic, complemented
3C29×#120C211yesmaximal, characteristic, complemented
4#11745315C211yesmaximal, characteristic, complemented
5#11745301C212yesmaximal, complemented
6#11745297C211yesmaximal, characteristic, complemented
7D4×Dic29C212yesmaximal, complemented
8#11745248C211yesmaximal, characteristic, complemented
9#11745243C212yesmaximal, complemented
10#11745240C212yesmaximal, complemented
11#11745239C211yesmaximal, characteristic, complemented
12C24×C29C2211yescharacteristic
13C2×D4×C29C2212yes—
14C2×D4×C29C2211yescharacteristic
15C2×C22⋊D29C2212yes—
16C2×C22⋊D29C2211yescharacteristic
17C2×C22⋊D29C2211yescharacteristic, complemented
18C22×Dic29—24no—
19C22×Dic29C2212yes—
20C22×Dic29C2211yescharacteristic
21C22×Dic29C2212yes—
22C22×Dic29C2211yescharacteristic
23C22×Dic29C2211yescharacteristic, complemented
24#90807—24no—
25C2×C4×D29C2211yescharacteristic, complemented
26C2×Dic58C2211yescharacteristic, complemented
27C22⋊C4×C29C2211yescharacteristic
28C22⋊C4×C29C2212yes—
29C22⋊Dic29C2212yes—
30C22⋊Dic29C2211yescharacteristic
31C22⋊Dic29C2212yescomplemented
32#90781C2212yescomplemented
33C4⋊Dic29C2212yescomplemented
34#90779C2212yescomplemented
35#90779C2212yescomplemented
36C4×Dic29C2212yescomplemented
37C23×C29—22no—
38C23×C29—24no—
39C23×C29C2311yescharacteristic
40C23×C29C2311yescharacteristic
41C23×C29C2312yes—
42C22×D29C2311yescharacteristic
43D4×C29—22no—
44D4×C29—24no—
45C2×C4×C29C2312yes—
46C2×C4×C29C2311yescharacteristic
47C22⋊D29—22no—
48C22⋊D29—24no—
49C22⋊D29—22no—
50C2×Dic29—22no—
51C2×Dic29—22no—
52C2×Dic29—24no—
53C2×Dic29—24no—
54C2×Dic29D414yescomplemented
55C2×Dic29C2312yes—
56C2×Dic29C2312yes—
57C2×Dic29C2311yescharacteristic
58C2×Dic29C2311yescharacteristic
59C2×Dic29C2311yescharacteristic
60C4×D29—22no—
61Dic58—22no—
62C22×C29—28no—
63C22×C29—22no—
64C22×C29—22no—
65C22×C29—22no—
66C22×C29—21no—
67C22×C29—22no—
68C22×C29C2×D412yes—
69C22×C29#4114yescomplemented
70C22×C29C2411yescharacteristic
71C2×D29—21no—
72C2×D29—22no—
73C4×C29—21no—
74C4×C29—22no—
75Dic29—21no—
76Dic29—22no—
77Dic29—22no—
78Dic29C2×D412yes—
79Dic29C2×D412yes—
80#525—291nomaximal, Sylow
81C2×C29—22no—
82C2×C29—24no—
83C2×C29—41no—
84C2×C29C22×D411yescharacteristic
85C2×C29C2×#4112yes—
86D29—41no—
87C2×#41—291no—
88C23×C4—291no—
89#123—291no—
90#123—291no—
91C22⋊Q8—292no—
92#121—292no—
93#120—291no—
94#120D2911yescharacteristic, complemented
95C4×D4—292no—
96C4×D4—292no—
97#117—291no—
98C29#52511yescharacteristic, complemented, Sylow
99C24C2×D2911yescharacteristic
100#41—584no—
101C2×Q8—291no—
102C2×D4—292no—
103C2×D4—291no—
104C2×D4—291no—
105C2×D4C2×D2912yes—
106C2×D4C2×D2911yescharacteristic
107C22×C4—291no—
108C22×C4—292no—
109C22×C4—291no—
110C22×C4—292no—
111C22×C4—291no—
112C22×C4—291no—
113C22×C4—584no—
114C4⋊C4—292no—
115C4⋊C4—292no—
116C4⋊C4—292no—
117C22⋊C4—291no—
118C22⋊C4—292no—
119C22⋊C4—292no—
120C22⋊C4—292no—
121C22⋊C4C2×D2911yescharacteristic
122C22⋊C4C2×D2912yes—
123C42—292no—
124C23—22no—
125C23—24no—
126C23—291no—
127C23C22×D2911yescharacteristic
128C23C22×D2911yescharacteristic
129C23C22×D2912yes—
130Q8—582no—
131D4—22no—
132D4—24no—
133D4—582no—
134D4—582no—
135D4—584no—
136C2×C4—294no—
137C2×C4—291no—
138C2×C4—291no—
139C2×C4—292no—
140C2×C4—292no—
141C2×C4—291no—
142C2×C4—582no—
143C2×C4—584no—
144C2×C4—584no—
145C2×C4—582no—
146C2×C4—582no—
147C2×C4C22×D2912yes—
148C2×C4C22×D2911yescharacteristic
149C22—28no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—21no—
154C22—22no—
155C22—581no—
156C22—582no—
157C22D4×D2912yes—
158C22#9080714yescomplemented
159C22C23×D2911yescharacteristic
160C4—21no—
161C4—22no—
162C4—292no—
163C4—292no—
164C4—582no—
165C4—581no—
166C4—582no—
167C2—22no—
168C2—24no—
169C2—41no—
170C2—1161no—
171C2C2×D4×D2911yescharacteristic
172C2C2×#9080712yes—
subgroupG/H
center, FrattiniC22C23×D29
commutator, socle, cosocleC22×C29C24
FittingC29×#120C2
hypercenter#120D29
hypocenterC29#525
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C23×Dic29C2semidirect
2. C2×#90807C2semidirect
3. C29×#120C2semidirect
4. #11745315C2semidirect
5. #11745301C2semidirect
6. #11745297C2semidirect
7. D4×Dic29C2semidirect
8. #11745248C2semidirect
9. #11745243C2semidirect
10. #11745240C2semidirect
11. #11745239C2semidirect
17. C2×C22⋊D29C22semidirect
23. C22×Dic29C22semidirect
25. C2×C4×D29C22semidirect
26. C2×Dic58C22semidirect
31. C22⋊Dic29C22semidirect
32. #90781C22semidirect
33. C4⋊Dic29C22semidirect
34. #90779C22semidirect
35. #90779C22semidirect
36. C4×Dic29C22semidirect
54. C2×Dic29D4semidirect
69. C22×C29#41semidirect
94. #120D29semidirect
98. C29#525semidirect
158. C22#90807semidirect

Maximal subgroups

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

subgroupindex
C23×Dic292
C2×#908072
C29×#1202
#117453152
#117453012
#117452972
D4×Dic292
#117452482
#117452432
#117452402
#117452392
#52529