Finite Group Databasebeta

← #28389530

Subgroups — #28389530

Order 14464.

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

normal subgroups only

This group has 256 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#20299224C211yesmaximal, characteristic
2#20298754C212yesmaximal, complemented
3#20298334C212yesmaximal, complemented
4#20298322C211yesmaximal, characteristic
5#393×C113C211yesmaximal, characteristic
6C2×#14268637—22no—
7#16813601—21no—
8#16813601C2212yes—
9#16813599—22no—
10#16813599—22no—
11C2×C22⋊Dic113—21no—
12#16813546—22no—
13C22⋊#11744751C2212yes—
14C22×Q8×C113C2211yescharacteristic
15C2×C22⋊C4×C113—21no—
16C2×C22⋊C4×C113C2211yescharacteristic
17#95×C113—21no—
18#95×C113C2211yescharacteristic
19C2×Dic226—21no—
20C2×Dic226D412yes—
21C22×Dic113—21no—
22C22×Dic113—21no—
23#14268637—44no—
24C2×#11744751—22no—
25C4⋊Dic113—21no—
26C4⋊Dic113D412yes—
27#14268626—22no—
28#14268626—22no—
29C22⋊Dic113—22no—
30C22⋊Dic113—22no—
31C24×C113D411yescharacteristic
32C2×Q8×C113—22no—
33C2×Q8×C113—42no—
34C22×C4×C113—21no—
35C22×C4×C113—21no—
36C22×C4×C113D411yescharacteristic
37C22×C4×C113C2311yescharacteristic
38C22⋊C4×C113—22no—
39C22⋊C4×C113—42no—
40C23×C113—21no—
41C23×C113—21no—
42C23×C113—41no—
43C23×C113—41no—
44C23×C113Q1612yescomplemented
45C23×C113C2×D411yescharacteristic
46Q8×C113—24no—
47Q8×C113—42no—
48C2×C4×C113—22no—
49C2×C4×C113—21no—
50C2×C4×C113—41no—
51C2×C4×C113—41no—
52C2×C4×C113—41no—
53C2×C4×C113—41no—
54C2×C4×C113—41no—
55C2×C4×C113—41no—
56C2×C4×C113—41no—
57C2×C4×C113C2×D412yes—
58C2×Dic113—22no—
59C2×Dic113—22no—
60C2×Dic113—81no—
61C2×Dic113—81no—
62Dic226—42no—
63Dic226—81no—
64#11744751—42no—
65C22×C113—21no—
66C22×C113—21no—
67C22×C113—22no—
68C22×C113—42no—
69C22×C113—41no—
70C22×C113—41no—
71C22×C113—81no—
72C22×C113#12011yescharacteristic
73C22×C113C2×Q1611yescharacteristic
74C22×C113#13711yescharacteristic
75C4×C113—22no—
76C4×C113—41no—
77C4×C113—42no—
78C4×C113—81no—
79Dic113—42no—
80Dic113—42no—
81C2×C113—21no—
82C2×C113—21no—
83C2×C113—42no—
84C2×C113#45111yescharacteristic
85C2×C113#45511yescharacteristic
86C2×C113B(4,𝔽2)11yescharacteristic
87#1602—1131nomaximal, Sylow
88C113#160211yescharacteristic, complemented, Sylow
89#543—1131no—
90#451—1132no—
91#393D11311yescharacteristic
92#328—1132no—
93#323—1131no—
94C22×Q8C2×D11311yescharacteristic
95C2×Q16—2262no—
96C22⋊Q8—1132no—
97C22⋊Q8—2262no—
98C22⋊Q8—2262no—
99C22⋊Q8—2261no—
100C2×C22⋊C4—21no—
101C2×C22⋊C4—2261no—
102C2×C22⋊C4C2×D11311yescharacteristic
103#103—2262no—
104C22⋊C8—1132no—
105#95—21no—
106#95C2×D11311yescharacteristic
107C24C22⋊D11311yescharacteristic
108C2×Q8—22no—
109C2×Q8—42no—
110C2×Q8—1132no—
111C2×Q8—2261no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—2261no—
115C22×C4—2261no—
116C22×C4C22⋊D11311yescharacteristic
117C22×C4C22×D11311yescharacteristic
118Q16—4524no—
119C2×C8—2262no—
120C4⋊C4—1132no—
121C4⋊C4—2262no—
122C4⋊C4—2261no—
123C4⋊C4—2262no—
124C22⋊C4—22no—
125C22⋊C4—42no—
126C22⋊C4—2262no—
127C22⋊C4—2262no—
128C23—21no—
129C23—21no—
130C23—41no—
131C23—41no—
132C23#1426863712yescomplemented
133C23C2×C22⋊D11311yescharacteristic
134Q8—24no—
135Q8—42no—
136Q8—9041no—
137Q8—4522no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—9041no—
148C2×C4—9041no—
149C2×C4—2262no—
150C2×C4—2262no—
151C2×C4D4×D11312yes—
152C8—4522no—
153C22—21no—
154C22—21no—
155C22—22no—
156C22—42no—
157C22—41no—
158C22—41no—
159C22—81no—
160C22#1681359011yescharacteristic
161C22C2×#1426863711yescharacteristic
162C22#1681365211yescharacteristic
163C4—22no—
164C4—41no—
165C4—42no—
166C4—81no—
167C4—4522no—
168C4—4522no—
169C2—21no—
170C2—21no—
171C2—42no—
172C2#2029875311yescharacteristic
173C2#2029877511yescharacteristic
174C2#2029878411yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#393×C113C2
socleC22×C113#120
prime radicalC24×C113D4
hypercenter#393D113
hypocenterC113#1602
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #20298754C2semidirect
3. #20298334C2semidirect
44. C23×C113Q16semidirect
88. C113#1602semidirect
132. C23#14268637semidirect

Maximal subgroups

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

subgroupindex
#202992242
#202987542
#202983342
#202983222
#393×C1132
#1602113