Finite Group Databasebeta

← #28401040

Subgroups — #28401040

Order 14464.

572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#16813655C212yesmaximal, complemented
2C2×#16813650C212yesmaximal, complemented
3#20299148C211yesmaximal, characteristic, complemented
4C2×#16813610C211yesmaximal, characteristic, complemented
5#20298992C212yesmaximal, complemented
6#20298987C212yesmaximal, complemented
7#20298982C214yesmaximal, complemented
8C4×M16×C113C211yesmaximal, characteristic, complemented
9C2×#14268647C2212yes—
10C22×Dic226C2211yescharacteristic
11C22×D452C2211yescharacteristic
12#16813655—28no—
13#16813650—28no—
14C2×Dic452C2214yescomplemented
15C2×#14268636C2214yes—
16C2×#14268636C2214yescomplemented
17C2×D904C2214yes—
18#16813622C2211yescharacteristic, complemented
19#16813619C2211yescharacteristic, complemented
20#16813610—22no—
21#16813610C2212yes—
22#16813610C2212yes—
23#16813610C2212yescomplemented
24#16813596—22no—
25C4×D452—22no—
26C2×#14268624—22no—
27C2×M16×C113C2212yes—
28C2×C42×C113C2211yescharacteristic
29#97×C113C2212yescomplemented
30C4×C8×C113C2212yescomplemented
31C23×D113—21no—
32#14268647—24no—
33#14268647—24no—
34C2×Dic226—24no—
35C2×Dic226—21no—
36C2×Dic226C2312yes—
37C2×Dic226C2312yes—
38C2×D452—24no—
39C2×D452—22no—
40C2×D452—21no—
41C2×D452C2312yes—
42C2×D452C2312yes—
43C2×C22⋊D113—22no—
44C22×Dic113—21no—
45C2×C4×D113—22no—
46Dic452—28no—
47#14268636—28no—
48#14268636—28no—
49D904—28no—
50C4⋊Dic113—22no—
51#14268624—24no—
52#14268624—24no—
53#14268624—24no—
54C22×C4×C113D412yes—
55C22×C4×C113C2311yescharacteristic
56M16×C113D418yescomplemented
57C2×C8×C113C2314yes—
58C42×C113D412yes—
59C42×C113C2311yescharacteristic
60C42×C113C2311yescharacteristic
61C23×C113C2×D411yescharacteristic
62C22×D113—22no—
63C22×D113—22no—
64C22×D113—44no—
65C22×D113—42no—
66C2×C4×C113—42no—
67C2×C4×C113C2×D412yes—
68C2×C4×C113C2×D412yes—
69C2×C4×C113C2×D411yescharacteristic
70C2×C4×C113C2×D414yes—
71C2×C4×C113C2411yescharacteristic
72C22⋊D113—44no—
73C2×Dic113—22no—
74C2×Dic113—22no—
75C2×Dic113—42no—
76D452—22no—
77D452—24no—
78D452—22no—
79D452—44no—
80D452—42no—
81C4×D113—44no—
82Dic226—22no—
83Dic226—24no—
84Dic226—22no—
85Dic226—42no—
86C8×C113C2×D418yes—
87C22×C113—22no—
88C22×C113#12712yes—
89C22×C113C22×D411yescharacteristic
90C2×D113—42no—
91C2×D113—42no—
92C2×D113—44no—
93C2×D113—44no—
94C2×D113—84no—
95C4×C113—22no—
96C4×C113—22no—
97C4×C113#12712yes—
98C4×C113C22×D412yes—
99Dic113—42no—
100Dic113—42no—
101C2×C113—22no—
102C2×C113C2×#12711yescharacteristic
103C2×C113#57512yes—
104D113—82no—
105D113—82no—
106#3153—1131nomaximal, Sylow
107C113#315311yescharacteristic, complemented, Sylow
108C2×#137—1132no—
109C2×AGL(1,ℤ/8)—1132no—
110#532—1131no—
111C2×#124—1131no—
112#497—1132no—
113#496—1132no—
114#495—1134no—
115C4×M16D11311yescharacteristic, complemented
116C2×#41—1132no—
117C22×Q8—1131no—
118C22×D4—1131no—
119#137—2268no—
120AGL(1,ℤ/8)—2268no—
121C2×Q16—1134no—
122C2×SD16—1134no—
123C2×SD16—1134no—
124C2×D8—1134no—
125C2×M16C2×D11312yes—
126C4⋊Q8—1131no—
127#127—1131no—
128#124—1132no—
129#124—1132no—
130#124—1132no—
131#124—2262no—
132#121—2262no—
133C4×D4—2262no—
134C2×C22⋊C4—2262no—
135C2×C42C2×D11311yescharacteristic
136#97C2×D11312yescomplemented
137C4×C8C2×D11312yescomplemented
138C24—2261no—
139#41—2264no—
140#41—2264no—
141C2×Q8—1132no—
142C2×Q8—1132no—
143C2×Q8—2264no—
144C2×Q8—2261no—
145C2×D4—1132no—
146C2×D4—1132no—
147C2×D4—2262no—
148C2×D4—2262no—
149C2×D4—2261no—
150C2×D4—2264no—
151C22×C4—2261no—
152C22×C4—2262no—
153C22×C4D45212yes—
154C22×C4C22×D11311yescharacteristic
155Q16—2268no—
156SD16—2268no—
157SD16—2268no—
158D8—2268no—
159M16D45218yescomplemented
160C2×C8C22×D11314yes—
161C4⋊C4—2262no—
162C22⋊C4—2264no—
163C22⋊C4—2264no—
164C22⋊C4—2264no—
165C42D45212yes—
166C42C22×D11311yescharacteristic
167C42C22×D11311yescharacteristic
168C23—4524no—
169C23—4522no—
170C23—2262no—
171C23—2262no—
172C23C2×D45211yescharacteristic
173Q8—4522no—
174Q8—2262no—
175Q8—2264no—
176Q8—2262no—
177D4—4524no—
178D4—4524no—
179D4—4522no—
180D4—2262no—
181D4—2264no—
182D4—2262no—
183C2×C4—42no—
184C2×C4—4522no—
185C2×C4—4524no—
186C2×C4—2262no—
187C2×C4—2262no—
188C2×C4C2×D45212yes—
189C2×C4C2×D45212yes—
190C2×C4C2×D45211yescharacteristic
191C2×C4C2×D45214yes—
192C2×C4C23×D11311yescharacteristic
193C8C2×D45218yes—
194C22—22no—
195C22—9044no—
196C22—4522no—
197C22—4522no—
198C22—4524no—
199C22—4524no—
200C22#1681361912yes—
201C22C22×D45211yescharacteristic
202C4—22no—
203C4—22no—
204C4—4522no—
205C4—4522no—
206C4#1681361912yes—
207C4C22×D45212yes—
208C2—22no—
209C2—9042no—
210C2—9042no—
211C2C2×#1681361911yescharacteristic
212C2#2029939812yes—
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×M16×C113C2
socleC22×C113C22×D4
hypercenterC4×M16D113
hypocenterC113#3153
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#16813655C2semidirect
2. C2×#16813650C2semidirect
3. #20299148C2semidirect
4. C2×#16813610C2semidirect
5. #20298992C2semidirect
6. #20298987C2semidirect
7. #20298982C2semidirect
8. C4×M16×C113C2semidirect
14. C2×Dic452C22semidirect
16. C2×#14268636C22semidirect
18. #16813622C22semidirect
19. #16813619C22semidirect
23. #16813610C22semidirect
29. #97×C113C22semidirect
30. C4×C8×C113C22semidirect
56. M16×C113D4semidirect
107. C113#3153semidirect
115. C4×M16D113semidirect
136. #97C2×D113semidirect
137. C4×C8C2×D113semidirect
159. M16D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136552
C2×#168136502
#202991482
C2×#168136102
#202989922
#202989872
#202989822
C4×M16×C1132
#3153113