Finite Group Databasebeta

← #28389543

Subgroups — #28389543

Order 14464.

282 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 57 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#20298736C212yesmaximal, complemented
2#20298518C211yesmaximal, characteristic, complemented
3#20298332C212yesmaximal, complemented
4#20298324C211yesmaximal, characteristic, complemented
5#537×C113C211yesmaximal, characteristic
6C22×Dic226C2211yescharacteristic
7C2×#14268635—22no—
8C2×#14268626—21no—
9#16813545—22no—
10C22⋊#11744751C2212yes—
11#16813529—21no—
12#16813529C2211yescharacteristic
13C2×#41×C113—21no—
14C22⋊Q8×C113—22no—
15#121×C113—22no—
16#121×C113—21no—
17#121×C113C2212yes—
18C2×C4⋊C4×C113C2211yescharacteristic
19C2×Dic226—22no—
20C2×Dic226—42no—
21C22×Dic113—21no—
22C22×Dic113—21no—
23#14268635—44no—
24C2×#11744751—22no—
25#14268626—42no—
26#41×C113—42no—
27#41×C113—42no—
28C2×Q8×C113—21no—
29C2×D4×C113—21no—
30C2×D4×C113—22no—
31C2×D4×C113—21no—
32C2×D4×C113D412yes—
33C22×C4×C113—22no—
34C22×C4×C113D411yescharacteristic
35C22×C4×C113D411yescharacteristic
36C22×C4×C113C2311yescharacteristic
37C4⋊C4×C113—21no—
38C4⋊C4×C113—22no—
39C4⋊C4×C113D412yes—
40C22⋊C4×C113—22no—
41C22⋊C4×C113—22no—
42C23×C113—22no—
43C23×C113C2×D411yescharacteristic
44Q8×C113—42no—
45D4×C113—42no—
46D4×C113—42no—
47D4×C113—42no—
48D4×C113—42no—
49D4×C113—81no—
50C2×C4×C113—21no—
51C2×C4×C113—21no—
52C2×C4×C113—21no—
53C2×C4×C113—22no—
54C2×C4×C113—41no—
55C2×C4×C113—44no—
56C2×C4×C113—41no—
57C2×C4×C113SD1612yescomplemented
58C2×C4×C113C2×D412yes—
59C2×Dic113—22no—
60C2×Dic113—22no—
61C2×Dic113—41no—
62C2×Dic113—41no—
63C2×Dic113—41no—
64C2×Dic113—41no—
65Dic226—24no—
66Dic226—42no—
67#11744751—42no—
68C22×C113—21no—
69C22×C113—21no—
70C22×C113—42no—
71C22×C113—42no—
72C22×C113—42no—
73C22×C113#12011yescharacteristic
74C22×C113C2×SD1611yescharacteristic
75C22×C113AGL(1,ℤ/8)11yescharacteristic
76C4×C113—22no—
77C4×C113—22no—
78C4×C113—42no—
79C4×C113—41no—
80Dic113—42no—
81Dic113—42no—
82C2×C113—21no—
83C2×C113—21no—
84C2×C113—82no—
85C2×C113#45011yescharacteristic
86C2×C113#45611yescharacteristic
87C2×C113B(4,𝔽2)11yescharacteristic
88#1604—1131nomaximal, Sylow
89C113#160411yescharacteristic, complemented, Sylow
90#537D11311yescharacteristic
91#448—1132no—
92#395—1131no—
93#327—1132no—
94#324—1131no—
95C2×#41—21no—
96C22×Q8—1131no—
97C2×SD16—2262no—
98C22⋊Q8—22no—
99#121—22no—
100#121—21no—
101#121C2×D11312yes—
102C2×C4⋊C4—2261no—
103C2×C4⋊C4C2×D11311yescharacteristic
104#103—2262no—
105C22⋊C8—1132no—
106#95—1131no—
107#95—2261no—
108#41—42no—
109#41—42no—
110C2×Q8—21no—
111C2×Q8—4522no—
112C2×Q8—2262no—
113C2×D4—21no—
114C2×D4—22no—
115C2×D4—21no—
116C2×D4C22⋊D11312yes—
117C22×C4—22no—
118C22×C4—2261no—
119C22×C4—2261no—
120C22×C4C22⋊D11311yescharacteristic
121C22×C4C22⋊D11311yescharacteristic
122C22×C4C22×D11311yescharacteristic
123SD16—4524no—
124C2×C8—2262no—
125C4⋊C4—21no—
126C4⋊C4—22no—
127C4⋊C4—4522no—
128C4⋊C4C22⋊D11312yes—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C23—22no—
132C23C2×C22⋊D11311yescharacteristic
133Q8—42no—
134Q8—4522no—
135Q8—2264no—
136D4—42no—
137D4—42no—
138D4—42no—
139D4—42no—
140D4—81no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—44no—
147C2×C4—41no—
148C2×C4—4521no—
149C2×C4—4521no—
150C2×C4—4521no—
151C2×C4—4521no—
152C2×C4—2262no—
153C2×C4—2262no—
154C2×C4#1426863512yescomplemented
155C2×C4C2×C22⋊D11312yes—
156C8—4522no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22#1681359111yescharacteristic
163C22C2×#1426863511yescharacteristic
164C22#1681364811yescharacteristic
165C4—22no—
166C4—22no—
167C4—41no—
168C4—42no—
169C4—4522no—
170C4—4522no—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#2029874911yescharacteristic
175C2#2029878111yescharacteristic
176C2#2029878511yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting, prime radical#537×C113C2
socleC22×C113#120
hypercenter#537D113
hypocenterC113#1604
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #20298736C2semidirect
2. #20298518C2semidirect
3. #20298332C2semidirect
4. #20298324C2semidirect
57. C2×C4×C113SD16semidirect
89. C113#1604semidirect
154. C2×C4#14268635semidirect

Maximal subgroups

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

subgroupindex
#202987362
#202985182
#202983322
#202983242
#537×C1132
#1604113