Finite Group Databasebeta

← #28389513

Subgroups — #28389513

Order 14464.

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

normal subgroups only

This group has 266 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#20299229C211yesmaximal, characteristic, complemented
2#20298749C212yesmaximal
3#20298334C212yesmaximal, complemented
4#20298324C211yesmaximal, characteristic, complemented
5#394×C113C211yesmaximal, characteristic
6C2×#14268635—22no—
7#16813621—22no—
8#16813613—22no—
9#16813601—21no—
10#16813601C2212yes—
11#16813581—21no—
12#16813543—22no—
13C22⋊#11744751C2212yes—
14C22×D4×C113C2211yescharacteristic
15C2×C4⋊C4×C113C2211yescharacteristic
16C2×C22⋊C4×C113—21no—
17C2×C22⋊C4×C113—21no—
18#95×C113C2211yescharacteristic
19C2×Dic226—21no—
20C2×Dic226D412yes—
21#14268635—44no—
22C2×#11744751—22no—
23C4⋊Dic113—21no—
24C4⋊Dic113—21no—
25C4⋊Dic113—21no—
26C4⋊Dic113D412yes—
27#14268626—22no—
28#14268626—22no—
29C22⋊Dic113—22no—
30C4×Dic113—22no—
31C24×C113—21no—
32C2×D4×C113—22no—
33C2×D4×C113—42no—
34C22×C4×C113—21no—
35C22×C4×C113D411yescharacteristic
36C22×C4×C113D411yescharacteristic
37C22×C4×C113C2311yescharacteristic
38C4⋊C4×C113—22no—
39C22⋊C4×C113—42no—
40C22⋊C4×C113—42no—
41C23×C113—22no—
42C23×C113—41no—
43C23×C113—41no—
44C23×C113—41no—
45C23×C113—41no—
46C23×C113—41no—
47C23×C113—41no—
48C23×C113C2×D411yescharacteristic
49D4×C113—24no—
50D4×C113—42no—
51C2×C4×C113—21no—
52C2×C4×C113—21no—
53C2×C4×C113—21no—
54C2×C4×C113—41no—
55C2×C4×C113—41no—
56C2×C4×C113—41no—
57C2×C4×C113—41no—
58C2×C4×C113—41no—
59C2×C4×C113SD1612yescomplemented
60C2×C4×C113C2×D412yes—
61C2×Dic113—22no—
62C2×Dic113—22no—
63Dic226—42no—
64Dic226—81no—
65#11744751—42no—
66C22×C113—21no—
67C22×C113—21no—
68C22×C113—42no—
69C22×C113—42no—
70C22×C113—42no—
71C22×C113—81no—
72C22×C113—81no—
73C22×C113—81no—
74C22×C113—81no—
75C22×C113#12011yescharacteristic
76C22×C113C2×SD1611yescharacteristic
77C22×C113#13711yescharacteristic
78C4×C113—22no—
79C4×C113—22no—
80C4×C113—41no—
81C4×C113—81no—
82Dic113—42no—
83Dic113—42no—
84C2×C113—21no—
85C2×C113—21no—
86C2×C113—82no—
87C2×C113#44811yescharacteristic
88C2×C113#45411yescharacteristic
89C2×C113B(4,𝔽2)11yescharacteristic
90#1599—1131nomaximal, Sylow
91C113#159911yescharacteristic, complemented, Sylow
92#544—1131no—
93#450—1132no—
94#394D11311yescharacteristic
95#328—1132no—
96#324—1131no—
97C22×D4C2×D11311yescharacteristic
98C2×SD16—2262no—
99C4⋊Q8—2262no—
100#125—2262no—
101C22⋊Q8—1132no—
102C22⋊Q8—2261no—
103#117—2261no—
104C2×C4⋊C4C2×D11311yescharacteristic
105C2×C22⋊C4—21no—
106C2×C22⋊C4—21no—
107#102—2262no—
108C22⋊C8—1132no—
109#95C2×D11311yescharacteristic
110C24—21no—
111C2×Q8—1132no—
112C2×Q8—2261no—
113C2×D4—22no—
114C2×D4—42no—
115C22×C4—21no—
116C22×C4C22⋊D11311yescharacteristic
117C22×C4C22⋊D11311yescharacteristic
118C22×C4C22×D11311yescharacteristic
119SD16—4524no—
120C2×C8—2262no—
121C4⋊C4—22no—
122C4⋊C4—1132no—
123C4⋊C4—2261no—
124C4⋊C4—2261no—
125C4⋊C4—2261no—
126C4⋊C4—2262no—
127C4⋊C4—2262no—
128C22⋊C4—42no—
129C22⋊C4—42no—
130C22⋊C4—2262no—
131C42—2262no—
132C23—22no—
133C23—41no—
134C23—41no—
135C23—41no—
136C23—41no—
137C23—41no—
138C23—41no—
139C23C2×C22⋊D11311yescharacteristic
140Q8—9041no—
141Q8—4522no—
142D4—24no—
143D4—42no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—2262no—
153C2×C4—2262no—
154C2×C4#1426863512yescomplemented
155C2×C4D4×D11312yes—
156C8—4522no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22—81no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22#1681359011yescharacteristic
167C22C2×#1426863511yescharacteristic
168C22#1681365211yescharacteristic
169C4—22no—
170C4—22no—
171C4—41no—
172C4—81no—
173C4—4522no—
174C4—4522no—
175C2—21no—
176C2—21no—
177C2—82no—
178C2#2029873611yescharacteristic
179C2#2029877011yescharacteristic
180C2#2029878411yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#394×C113C2
socleC22×C113#120
prime radicalC22×D4×C113C22
hypercenter#394D113
hypocenterC113#1599
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #20299229C2semidirect
3. #20298334C2semidirect
4. #20298324C2semidirect
59. C2×C4×C113SD16semidirect
91. C113#1599semidirect
154. C2×C4#14268635semidirect

Maximal subgroups

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

subgroupindex
#202992292
#202987492
#202983342
#202983242
#394×C1132
#1599113