Finite Group Databasebeta

← #28401038

Subgroups — #28401038

Order 14464.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16813653C212yesmaximal, complemented
2C2×#16813648C212yesmaximal, complemented
3#20299148C211yesmaximal, characteristic, complemented
4#20298993C212yesmaximal, complemented
5#20298988C212yesmaximal, complemented
6#20298980C214yesmaximal, complemented
7C4×#14268631C211yesmaximal, characteristic, complemented
8C2×#124×C113C211yesmaximal, characteristic, complemented
9C2×#14268647C2212yes—
10#16813653—28no—
11#16813648—28no—
12C2×#14268637C2214yescomplemented
13C2×#14268635C2214yes—
14C2×#14268634C2214yescomplemented
15C2×#14268632C2214yes—
16C2×#14268631C2212yes—
17#16813622C2211yescharacteristic, complemented
18#16813619C2211yescharacteristic, complemented
19#16813610C2212yescomplemented
20#16813596—22no—
21C4×D452—22no—
22#16813533C2212yescomplemented
23C4×#11744751C2212yescomplemented
24C22×Q8×C113C2211yescharacteristic
25C22×D4×C113C2211yescharacteristic
26#124×C113—22no—
27#124×C113C2212yes—
28#124×C113C2212yes—
29C2×C22⋊C4×C113—22no—
30C2×C42×C113C2211yescharacteristic
31#14268647—24no—
32#14268647—24no—
33C2×Dic226C2312yes—
34C2×D452—22no—
35C2×D452C2312yes—
36C2×C22⋊D113—22no—
37C2×C4×D113—22no—
38#14268637—28no—
39#14268635—28no—
40#14268634—28no—
41#14268632—28no—
42#14268631D418yescomplemented
43C2×#11744751C2314yes—
44C4⋊Dic113—22no—
45#14268624—24no—
46C24×C113—21no—
47C2×Q8×C113—21no—
48C2×Q8×C113—24no—
49C2×Q8×C113C2312yes—
50C2×D4×C113—24no—
51C2×D4×C113—21no—
52C2×D4×C113C2312yes—
53C22×C4×C113—21no—
54C22×C4×C113D412yes—
55C22×C4×C113C2311yescharacteristic
56C22⋊C4×C113—24no—
57C22⋊C4×C113—24no—
58C42×C113D412yes—
59C42×C113C2311yescharacteristic
60C42×C113C2311yescharacteristic
61C23×C113—22no—
62C23×C113—44no—
63C23×C113—42no—
64C23×C113C2×D411yescharacteristic
65C22×D113—22no—
66Q8×C113—24no—
67Q8×C113—42no—
68D4×C113—24no—
69D4×C113—42no—
70C2×C4×C113—22no—
71C2×C4×C113—42no—
72C2×C4×C113—42no—
73C2×C4×C113C2×D414yes—
74C2×C4×C113C2×D412yes—
75C2×C4×C113C2×D412yes—
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2411yescharacteristic
78C22⋊D113—44no—
79C2×Dic113—22no—
80D452—22no—
81D452—22no—
82D452—44no—
83C4×D113—44no—
84Dic226—22no—
85Dic226—22no—
86#11744751C2×D418yes—
87C22×C113—22no—
88C22×C113—42no—
89C22×C113—44no—
90C22×C113—84no—
91C22×C113#12712yes—
92C22×C113C22×D411yescharacteristic
93C2×D113—42no—
94C2×D113—44no—
95C4×C113—22no—
96C4×C113—22no—
97C4×C113—42no—
98C4×C113#12712yes—
99C4×C113C22×D412yes—
100Dic113—42no—
101C2×C113—22no—
102C2×C113—82no—
103C2×C113C2×#12711yescharacteristic
104C2×C113#57512yes—
105D113—82no—
106#3153—1131nomaximal, Sylow
107C113#315311yescharacteristic, complemented, Sylow
108C2×#137—1132no—
109C2×AGL(1,ℤ/8)—1132no—
110#532—1131no—
111C2×#124D11311yescharacteristic, complemented
112#497—1132no—
113#496—1132no—
114#495—1134no—
115C4×M16—1131no—
116C2×#41—1132no—
117C22×Q8C2×D11311yescharacteristic
118C22×D4C2×D11311yescharacteristic
119#137—2268no—
120AGL(1,ℤ/8)—2268no—
121C2×Q16—1134no—
122C2×SD16—1134no—
123C2×SD16—1134no—
124C2×D8—1134no—
125C2×M16—1132no—
126C4⋊Q8—1131no—
127#127—1131no—
128#124—22no—
129#124—1132no—
130#124C2×D11312yes—
131#124C2×D11312yes—
132#121—2262no—
133C4×D4—2262no—
134C2×C22⋊C4—22no—
135C2×C42C2×D11311yescharacteristic
136#97—1132no—
137C4×C8—1132no—
138C24—21no—
139#41—2264no—
140#41—2264no—
141C2×Q8—21no—
142C2×Q8—24no—
143C2×Q8—1132no—
144C2×Q8C22×D11312yes—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—1132no—
148C2×D4—2262no—
149C2×D4—2262no—
150C2×D4C22×D11312yes—
151C22×C4—21no—
152C22×C4—2262no—
153C22×C4C22⋊D11312yes—
154C22×C4C22×D11311yescharacteristic
155Q16—2268no—
156SD16—2268no—
157SD16—2268no—
158D8—2268no—
159M16—1138no—
160C2×C8—1134no—
161C4⋊C4—2262no—
162C22⋊C4—24no—
163C22⋊C4—24no—
164C22⋊C4—2264no—
165C42C22⋊D11312yes—
166C42C22×D11311yescharacteristic
167C42C22×D11311yescharacteristic
168C23—22no—
169C23—44no—
170C23—42no—
171C23—2262no—
172C23C2×C22⋊D11311yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—2262no—
176Q8—2262no—
177D4—24no—
178D4—42no—
179D4—4524no—
180D4—4524no—
181D4—2262no—
182D4—2262no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—4524no—
187C2×C4—2262no—
188C2×C4D4×D11314yes—
189C2×C4C2×C22⋊D11312yes—
190C2×C4C2×C22⋊D11312yes—
191C2×C4C2×C22⋊D11311yescharacteristic
192C2×C4C23×D11311yescharacteristic
193C8—1138no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—4522no—
199C22—4524no—
200C22#1681361812yes—
201C22C22×C22⋊D11311yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—4522no—
206C4#1681361812yes—
207C4C2×D4×D11312yes—
208C2—22no—
209C2—82no—
210C2—9042no—
211C2C2×#1681361811yescharacteristic
212C2#2029939612yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#124×C113C2
socleC22×C113C22×D4
hypercenterC2×#124D113
hypocenterC113#3153
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#16813653C2semidirect
2. C2×#16813648C2semidirect
3. #20299148C2semidirect
4. #20298993C2semidirect
5. #20298988C2semidirect
6. #20298980C2semidirect
7. C4×#14268631C2semidirect
8. C2×#124×C113C2semidirect
12. C2×#14268637C22semidirect
14. C2×#14268634C22semidirect
17. #16813622C22semidirect
18. #16813619C22semidirect
19. #16813610C22semidirect
22. #16813533C22semidirect
23. C4×#11744751C22semidirect
42. #14268631D4semidirect
107. C113#3153semidirect
111. C2×#124D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136532
C2×#168136482
#202991482
#202989932
#202989882
#202989802
C4×#142686312
C2×#124×C1132
#3153113