Finite Group Databasebeta

← #16818463

Subgroups — #16818463

Order 3712.

282 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#14271744C211yesmaximal, characteristic
2#14271304C212yesmaximal, complemented
3#14271083C211yesmaximal, characteristic, complemented
4#14270898C212yesmaximal, complemented
5C29×#324C211yesmaximal, characteristic, complemented
6C2×#90805—21no—
7C22×Dic58C2211yescharacteristic
8C2×C4⋊C4×C29C2211yescharacteristic
9#11745292—21no—
10#11745292C2212yes—
11C2×#90779—21no—
12C2×#90773—22no—
13#11745259—22no—
14#11745257—22no—
15C29×C22⋊C8C2212yes—
16#11745179—21no—
17#11745179C2211yescharacteristic
18#11745164—22no—
19C22×C4×C29D411yescharacteristic
20C22×C4×C29D411yescharacteristic
21C22×C4×C29C2311yescharacteristic
22C2×C22⋊D29—22no—
23C22×Dic29—21no—
24C22×Dic29—21no—
25#90805—42no—
26#90805—42no—
27C2×D116—21no—
28C2×D116—21no—
29C2×D116D412yes—
30C2×C4×D29—22no—
31C2×Dic58—22no—
32C2×Dic58—21no—
33C2×Dic58—42no—
34C2×C8×C29—22no—
35C4⋊C4×C29—22no—
36#90781—22no—
37#90781—22no—
38C4⋊Dic29—21no—
39C4⋊Dic29D412yes—
40#90779—42no—
41#90773—44no—
42C23×C29C2×D411yescharacteristic
43C22×D29—22no—
44C2×C4×C29—21no—
45C2×C4×C29—21no—
46C2×C4×C29—21no—
47C2×C4×C29—41no—
48C2×C4×C29—41no—
49C2×C4×C29SD1612yescomplemented
50C2×C4×C29C2×D412yes—
51C22⋊D29—42no—
52C22⋊D29—42no—
53C2×Dic29—22no—
54C2×Dic29—22no—
55C2×Dic29—22no—
56C2×Dic29—41no—
57C2×Dic29—41no—
58C2×Dic29—41no—
59C2×Dic29—41no—
60D116—42no—
61D116—42no—
62D116—81no—
63C4×D29—44no—
64Dic58—24no—
65Dic58—42no—
66Dic58—42no—
67C8×C29—42no—
68#1604—291nomaximal, Sylow
69C22×C29—21no—
70C22×C29—21no—
71C22×C29#12011yescharacteristic
72C22×C29C2×SD1611yescharacteristic
73C22×C29AGL(1,ℤ/8)11yescharacteristic
74C2×D29—42no—
75C2×D29—42no—
76C2×D29—42no—
77C4×C29—22no—
78C4×C29—22no—
79C4×C29—41no—
80Dic29—42no—
81Dic29—42no—
82Dic29—42no—
83#537—291no—
84#448—292no—
85#395—291no—
86#327—292no—
87#324D2911yescharacteristic, complemented
88C2×C29—21no—
89C2×C29—21no—
90C2×C29#45011yescharacteristic
91C2×C29#45611yescharacteristic
92C2×C29B(4,𝔽2)11yescharacteristic
93D29—82no—
94C2×#41—581no—
95C22×Q8—291no—
96C2×SD16—582no—
97C22⋊Q8—582no—
98#121—292no—
99#121—582no—
100#121—581no—
101C2×C4⋊C4—581no—
102C2×C4⋊C4C2×D2911yescharacteristic
103#103—582no—
104C22⋊C8C2×D2912yes—
105#95—291no—
106#95—581no—
107C29#160411yescharacteristic, complemented, Sylow
108#41—1162no—
109#41—1162no—
110C2×Q8—581no—
111C2×Q8—582no—
112C2×Q8—1162no—
113C2×D4—292no—
114C2×D4—581no—
115C2×D4—581no—
116C2×D4—582no—
117C22×C4—582no—
118C22×C4—581no—
119C22×C4—581no—
120C22×C4D11611yescharacteristic
121C22×C4D11611yescharacteristic
122C22×C4C22×D2911yescharacteristic
123SD16—1164no—
124C2×C8—22no—
125C4⋊C4—22no—
126C4⋊C4—292no—
127C4⋊C4—581no—
128C4⋊C4—1162no—
129C22⋊C4—582no—
130C22⋊C4—582no—
131C23—582no—
132C23C2×D11611yescharacteristic
133Q8—584no—
134Q8—1162no—
135Q8—1162no—
136D4—1162no—
137D4—1162no—
138D4—1162no—
139D4—1162no—
140D4—2321no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—582no—
147C2×C4—582no—
148C2×C4—582no—
149C2×C4—1164no—
150C2×C4—1161no—
151C2×C4—1161no—
152C2×C4—1161no—
153C2×C4—1161no—
154C2×C4#9077312yescomplemented
155C2×C4D4×D2912yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—1162no—
160C22—1162no—
161C22—1162no—
162C22#1174524411yescharacteristic
163C22C2×#9077311yescharacteristic
164C22#1174527011yescharacteristic
165C4—22no—
166C4—22no—
167C4—41no—
168C4—1162no—
169C4—1162no—
170C4—1162no—
171C2—21no—
172C2—21no—
173C2—2322no—
174C2#1427131611yescharacteristic
175C2#1427134811yescharacteristic
176C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#324C2
socleC22×C29#120
prime radical#14271744C2
hypercenter#324D29
hypocenterC29#1604
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #14271304C2semidirect
3. #14271083C2semidirect
4. #14270898C2semidirect
5. C29×#324C2semidirect
49. C2×C4×C29SD16semidirect
87. #324D29semidirect
107. C29#1604semidirect
154. C2×C4#90773semidirect

Maximal subgroups

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

subgroupindex
#142717442
#142713042
#142710832
#142708982
C29×#3242
#160429