Finite Group Databasebeta

← #28391641

Subgroups — #28391641

Order 14464.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#20299398C211yesmaximal, characteristic, complemented
2#20299109C212yesmaximal, complemented
3#20298614C212yesmaximal, complemented
4#20298355C211yesmaximal, characteristic, complemented
5#407×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C2212yes—
7#16813655—22no—
8#16813650—22no—
9#16813644—22no—
10#16813605—22no—
11#16813601—22no—
12#16813596—22no—
13#16813591—22no—
14C4×C22⋊D113—24no—
15#16813581C2212yes—
16#16813548—24no—
17C23×C4×C113C2211yescharacteristic
18C2×M16×C113C2211yescharacteristic
19C2×M16×C113C2211yescharacteristic
20C22⋊C8×C113—22no—
21#14268647—22no—
22#14268647—22no—
23#14268647—22no—
24#14268647—22no—
25C2×Dic226D412yescomplemented
26C2×D452D412yescomplemented
27C2×C22⋊D113—24no—
28C2×C22⋊D113—22no—
29C2×C4×D113—22no—
30Dic452—22no—
31#14268636—24no—
32D904—22no—
33C4⋊Dic113—22no—
34#14268626—24no—
35C22⋊Dic113—24no—
36C22⋊Dic113—22no—
37#14268624—24no—
38C4×Dic113D414yescomplemented
39C24×C113D411yescharacteristic
40C22×C4×C113—22no—
41C22×C4×C113—22no—
42C22×C4×C113—21no—
43C22×C4×C113—21no—
44C22×C4×C113D411yescharacteristic
45C22×C4×C113C2311yescharacteristic
46M16×C113—22no—
47M16×C113—22no—
48C2×C8×C113—21no—
49C2×C8×C113D412yescomplemented
50C23×C113—22no—
51C23×C113—21no—
52C23×C113—42no—
53C23×C113C2×D411yescharacteristic
54C22×D113—22no—
55C2×C4×C113—22no—
56C2×C4×C113—21no—
57C2×C4×C113—41no—
58C2×C4×C113—42no—
59C2×C4×C113—41no—
60C2×C4×C113C2×D412yes—
61C2×C4×C113C2×D412yes—
62C2×C4×C113C2×D411yescharacteristic
63C2×C4×C113#4111yescharacteristic
64C22⋊D113—48no—
65C22⋊D113—42no—
66C22⋊D113—42no—
67C2×Dic113—24no—
68C2×Dic113—22no—
69D452—22no—
70D452—22no—
71C4×D113—42no—
72C4×D113—42no—
73Dic226—22no—
74Dic226—22no—
75C8×C113—22no—
76C8×C113—41no—
77C22×C113—24no—
78C22×C113—22no—
79C22×C113—41no—
80C22×C113—42no—
81C22×C113—41no—
82C22×C113—41no—
83C22×C113#12012yes—
84C22×C113#12111yescharacteristic
85C2×D113—44no—
86C2×D113—42no—
87C4×C113—41no—
88C4×C113#12011yescharacteristic
89C4×C113#12112yes—
90C4×C113#12711yescharacteristic
91Dic113—44no—
92Dic113—42no—
93C2×C113—22no—
94C2×C113—21no—
95C2×C113—42no—
96C2×C113#39211yescharacteristic
97D113—82no—
98#2010—1131nomaximal, Sylow
99C113#201011yescharacteristic, complemented, Sylow
100#575—1131no—
101#525—1132no—
102#421—1132no—
103#407D11311yescharacteristic, complemented
104H(3,ℤ/4)—1131no—
105C2×#41—1132no—
106C23×C4C2×D11311yescharacteristic
107#137—2262no—
108AGL(1,ℤ/8)—2262no—
109#135—2262no—
110C2×M16C2×D11311yescharacteristic
111C2×M16C2×D11311yescharacteristic
112#123—2262no—
113C22⋊Q8—2262no—
114#121—2262no—
115#120—2262no—
116C4×D4—2264no—
117#117—1132no—
118#104—2264no—
119C22⋊C8—22no—
120C24D45211yescharacteristic
121#41—2262no—
122#41—2262no—
123#41—2262no—
124#41—2262no—
125C2×Q8—1132no—
126C2×D4—1132no—
127C2×D4—2264no—
128C2×D4—2262no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—2262no—
134C22×C4D45211yescharacteristic
135C22×C4C22×D11311yescharacteristic
136Q16—2262no—
137SD16—2264no—
138D8—2262no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D11312yescomplemented
143C4⋊C4—2264no—
144C4⋊C4—2262no—
145C22⋊C4—2264no—
146C22⋊C4—2264no—
147C22⋊C4—2262no—
148C42—1134no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—2262no—
153C23C2×D45211yescharacteristic
154Q8—2262no—
155Q8—2262no—
156D4—4528no—
157D4—4522no—
158D4—4522no—
159D4—2262no—
160D4—2262no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—4522no—
167C2×C4—4522no—
168C2×C4—2264no—
169C2×C4—2262no—
170C2×C4D4×D11312yes—
171C2×C4D4×D11312yes—
172C2×C4C2×C22⋊D11311yescharacteristic
173C2×C4#1426864711yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—4524no—
183C22—4522no—
184C22#1681359212yes—
185C22#1681359611yescharacteristic
186C4—41no—
187C4—4524no—
188C4—4522no—
189C4#1681359011yescharacteristic
190C4#1681359512yes—
191C4#1681361811yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—9042no—
196C2#2029850711yescharacteristic
subgroupG/H
centerC4#16813618
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#407×C113C2
socleC2×C113#392
hypercenter#407D113
hypocenterC113#2010
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #20299398C2semidirect
2. #20299109C2semidirect
3. #20298614C2semidirect
4. #20298355C2semidirect
5. #407×C113C2semidirect
25. C2×Dic226D4semidirect
26. C2×D452D4semidirect
38. C4×Dic113D4semidirect
49. C2×C8×C113D4semidirect
99. C113#2010semidirect
103. #407D113semidirect
142. C2×C8C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202993982
#202991092
#202986142
#202983552
#407×C1132
#2010113