Finite Group Databasebeta

← #28392558

Subgroups — #28392558

Order 14464.

354 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 45 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#20298784C212yesmaximal, complemented
2#20298765C211yesmaximal, characteristic, complemented
3#20298391C211yesmaximal, characteristic, complemented
4#20298385C212yesmaximal, complemented
5D42×C113C211yesmaximal, characteristic, complemented
6#16813667C2211yescharacteristic, complemented
7#16813648—21no—
8#16813591—22no—
9#16813550—21no—
10#16813539C2211yescharacteristic, complemented
11#16813537C2212yescomplemented
12#16813536—22no—
13C22×D4×C113—22no—
14#127×C113C2211yescharacteristic
15#121×C113—22no—
16#120×C113—21no—
17#120×C113C2212yes—
18C4×D4×C113—21no—
19#14268647—21no—
20#14268646—41no—
21C2×C22⋊D113—22no—
22C2×C22⋊D113—42no—
23D4×D113—41no—
24#14268635—41no—
25#14268632—41no—
26#14268631—21no—
27C22⋊Dic113—22no—
28C22⋊Dic113—42no—
29C24×C113—21no—
30C24×C113D412yescomplemented
31C2×D4×C113—21no—
32C2×D4×C113—22no—
33C2×D4×C113—22no—
34C2×D4×C113—22no—
35C2×D4×C113—48no—
36C2×D4×C113D411yescharacteristic, complemented
37C2×D4×C113C2311yescharacteristic
38C22×C4×C113—22no—
39C4⋊C4×C113—21no—
40C22⋊C4×C113—21no—
41C22⋊C4×C113—22no—
42C22⋊C4×C113D412yescomplemented
43C42×C113D411yescharacteristic, complemented
44C23×C113—22no—
45C23×C113—21no—
46C23×C113—44no—
47C23×C113—42no—
48C23×C113—44no—
49C23×C113—81no—
50C23×C113C2×D412yes—
51C22×D113—22no—
52D4×C113—24no—
53D4×C113—41no—
54D4×C113—41no—
55D4×C113—44no—
56D4×C113—44no—
57D4×C113—44no—
58C2×C4×C113—21no—
59C2×C4×C113—22no—
60C2×C4×C113—44no—
61C2×C4×C113C2×D411yescharacteristic
62C22⋊D113—42no—
63C22⋊D113—41no—
64C22⋊D113—84no—
65C2×Dic113—22no—
66C2×Dic113—42no—
67D452—21no—
68C4×D113—41no—
69Dic226—21no—
70#11744751—41no—
71C22×C113—24no—
72C22×C113—22no—
73C22×C113—42no—
74C22×C113—42no—
75C22×C113—42no—
76C22×C113—44no—
77C22×C113—42no—
78C22×C113—41no—
79C22×C113—82no—
80C22×C113—84no—
81C22×C113#12011yescharacteristic
82C2×D113—41no—
83C2×D113—82no—
84C4×C113—22no—
85C4×C113—21no—
86C4×C113—42no—
87Dic113—41no—
88Dic113—82no—
89C2×C113—21no—
90C2×C113—42no—
91C2×C113—44no—
92C2×C113—81no—
93C2×C113B(4,𝔽2)11yescharacteristic
94D113—81no—
95#2196—1131nomaximal, Sylow
96C113#219611yescharacteristic, complemented, Sylow
97D42D11311yescharacteristic, complemented
98B(4,𝔽2)—1132no—
99#453—1131no—
100#353—1131no—
101AΣL(1,𝔽16)—1132no—
102H(5,𝔽2)—1131no—
103C22×D4—22no—
104AGL(1,ℤ/8)—2261no—
105#127C2×D11311yescharacteristic
106#121—22no—
107#120—21no—
108#120—2262no—
109#120C2×D11312yes—
110C4×D4—21no—
111#104—2261no—
112#100—1131no—
113#99—1132no—
114#99—2262no—
115C24—21no—
116C24C22⋊D11312yescomplemented
117#41—4521no—
118#41—2261no—
119C2×D4—21no—
120C2×D4—22no—
121C2×D4—22no—
122C2×D4—22no—
123C2×D4—48no—
124C2×D4—4521no—
125C2×D4—4522no—
126C2×D4—2262no—
127C2×D4C22⋊D11311yescharacteristic, complemented
128C2×D4C22×D11311yescharacteristic
129C22×C4—22no—
130SD16—4521no—
131D8—4521no—
132M16—2261no—
133C4⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—22no—
136C22⋊C4—4522no—
137C22⋊C4—2262no—
138C22⋊C4C22⋊D11312yescomplemented
139C42C22⋊D11311yescharacteristic, complemented
140C23—22no—
141C23—21no—
142C23—42no—
143C23—44no—
144C23—44no—
145C23—81no—
146C23—2262no—
147C23C2×C22⋊D11312yes—
148Q8—2261no—
149D4—24no—
150D4—41no—
151D4—41no—
152D4—44no—
153D4—44no—
154D4—44no—
155D4—9044no—
156D4—4522no—
157D4—4521no—
158D4—2261no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—4521no—
163C2×C4—4522no—
164C2×C4—2262no—
165C2×C4C2×C22⋊D11311yescharacteristic
166C8—4521no—
167C22—24no—
168C22—22no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—44no—
173C22—42no—
174C22—41no—
175C22—82no—
176C22—84no—
177C22—9042no—
178C22—4521no—
179C22#1681359111yescharacteristic
180C4—22no—
181C4—21no—
182C4—42no—
183C4—9042no—
184C4—4521no—
185C2—21no—
186C2—42no—
187C2—44no—
188C2—81no—
189C2—9041no—
190C2#2029878511yescharacteristic
subgroupG/H
centerC2#20298785
commutator, cosocleC2×D4×C113C23
FrattiniC2×D4C22×D113
FittingD42×C113C2
socleC2×C113B(4,𝔽2)
hypercenterD42D113
hypocenterC113#2196
LCSG ▷ C2×D4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #20298784C2semidirect
2. #20298765C2semidirect
3. #20298391C2semidirect
4. #20298385C2semidirect
5. D42×C113C2semidirect
6. #16813667C22semidirect
10. #16813539C22semidirect
11. #16813537C22semidirect
30. C24×C113D4semidirect
36. C2×D4×C113D4semidirect
42. C22⋊C4×C113D4semidirect
43. C42×C113D4semidirect
96. C113#2196semidirect
97. D42D113semidirect
116. C24C22⋊D113semidirect
127. C2×D4C22⋊D113semidirect
138. C22⋊C4C22⋊D113semidirect
139. C42C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202987842
#202987652
#202983912
#202983852
D42×C1132
#2196113