Finite Group Databasebeta

← #28400818

Subgroups — #28400818

Order 14464.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#20299203C211yesmaximal, characteristic, complemented
2#20299072C211yesmaximal, characteristic, complemented
3#20298923C212yesmaximal, complemented
4#20298899C212yesmaximal, complemented
5#20298794C212yesmaximal, complemented
6#20298734C212yesmaximal, complemented
7#20298711C212yesmaximal, complemented
8C4×D904C212yesmaximal, complemented
9#433×C113C211yesmaximal, characteristic, complemented
10C22×D452C2211yescharacteristic
11C2×D904C2212yes—
12C2×D904C2212yes—
13#16813619C2211yescharacteristic, complemented
14#16813614C2211yescharacteristic, complemented
15#16813607—22no—
16#16813596C2212yes—
17#16813595—22no—
18C4×D452C2212yes—
19C4×D452C2212yes—
20C4×D452C2212yescomplemented
21#16813584—22no—
22#16813581C2211yescharacteristic
23C22⋊C4×D113—22no—
24#16813556C2212yescomplemented
25#16813554C2212yescomplemented
26#16813544C2212yes—
27#16813544C2212yes—
28#16813544C2212yescomplemented
29#16813544C2212yescomplemented
30#117×C113C2211yescharacteristic
31C4⋊C8×C113C2212yescomplemented
32C22⋊C8×C113C2212yes—
33#97×C113C2211yescharacteristic, complemented
34C4×C8×C113C2211yescharacteristic, complemented
35C23×D113—21no—
36C2×D452—21no—
37C2×D452—24no—
38C2×D452—22no—
39C2×D452C2312yes—
40C2×D452C2312yes—
41C2×C22⋊D113—22no—
42C2×C4×D113—22no—
43C2×C4×D113—22no—
44C2×C4×D113—22no—
45D904—24no—
46D904—24no—
47C4⋊Dic113C2312yes—
48C4⋊Dic113C2312yes—
49#14268626—22no—
50C22⋊Dic113—21no—
51#14268624—22no—
52#14268624—22no—
53#14268624—22no—
54#14268624—22no—
55C4×Dic113—21no—
56C22×C4×C113C2311yescharacteristic
57C2×C8×C113C2312yes—
58C2×C8×C113C2312yes—
59C4⋊C4×C113D412yes—
60C22⋊C4×C113D412yes—
61C42×C113C2311yescharacteristic
62C42×C113C2311yescharacteristic
63C23×C113C2×D411yescharacteristic
64C22×D113—22no—
65C22×D113—24no—
66C22×D113—22no—
67C22×D113—82no—
68C2×C4×C113—22no—
69C2×C4×C113C2×D412yes—
70C2×C4×C113C2×D412yes—
71C2×C4×C113C2×D411yescharacteristic
72C2×C4×C113C2411yescharacteristic
73C22⋊D113—82no—
74C2×Dic113—22no—
75C2×Dic113—22no—
76D452—24no—
77D452—22no—
78D452—22no—
79D452—22no—
80D452—82no—
81D452#4114yes—
82C4×D113—82no—
83C4×D113—82no—
84C4×D113—82no—
85C8×C113—22no—
86C8×C113—22no—
87C22×C113—21no—
88C22×C113—22no—
89C22×C113C22×D411yescharacteristic
90C2×D113—24no—
91C2×D113—42no—
92C2×D113—42no—
93C2×D113—42no—
94C2×D113—42no—
95C2×D113—42no—
96C2×D113—84no—
97C4×C113—21no—
98C4×C113—22no—
99C4×C113—22no—
100C4×C113C2×#4112yes—
101Dic113—42no—
102Dic113—42no—
103C2×C113—41no—
104C2×C113#52511yescharacteristic
105C2×C113#57612yes—
106D113—44no—
107D113—82no—
108#3122—1131nomaximal, Sylow
109C113#312211yescharacteristic, complemented, Sylow
110#540—1131no—
111#518—1131no—
112#482—1132no—
113#478—1132no—
114#459—1132no—
115#447—1132no—
116#442—1132no—
117C4×D8—1132no—
118#433D11311yescharacteristic, complemented
119C22×D4—1131no—
120C2×D8—1132no—
121C2×D8—1132no—
122#127—1131no—
123#125—1131no—
124#123—2262no—
125#121—1132no—
126#121—2262no—
127C4×D4—1132no—
128C4×D4—1132no—
129C4×D4—1132no—
130C4×D4—2262no—
131#117—1131no—
132#117C2×D11311yescharacteristic
133C2×C22⋊C4—2262no—
134#107—1132no—
135#106—1132no—
136C4⋊C8C2×D11312yescomplemented
137#102—1132no—
138#102—1132no—
139#102—1132no—
140#102—1132no—
141C22⋊C8C2×D11312yes—
142#97C2×D11311yescharacteristic, complemented
143C4×C8C2×D11311yescharacteristic, complemented
144C24—2261no—
145C2×D4—1132no—
146C2×D4—1132no—
147C2×D4—2264no—
148C2×D4—2262no—
149C2×D4—2262no—
150C2×D4—2261no—
151C22×C4—2262no—
152C22×C4—2262no—
153C22×C4—2262no—
154C22×C4C22×D11311yescharacteristic
155D8—2264no—
156D8—2264no—
157C2×C8C22×D11312yes—
158C2×C8C22×D11312yes—
159C4⋊C4—1132no—
160C4⋊C4—1132no—
161C4⋊C4—2262no—
162C4⋊C4D45212yes—
163C22⋊C4—2261no—
164C22⋊C4—2262no—
165C22⋊C4—2262no—
166C22⋊C4—2262no—
167C22⋊C4—2262no—
168C22⋊C4D45212yes—
169C42—2261no—
170C42C22×D11311yescharacteristic
171C42C22×D11311yescharacteristic
172C23—9042no—
173C23—2264no—
174C23—2262no—
175C23—2262no—
176C23C2×D45211yescharacteristic
177D4—1134no—
178D4—9042no—
179D4—9042no—
180D4—2264no—
181D4—2262no—
182D4—2262no—
183D4—2262no—
184C2×C4—22no—
185C2×C4—9042no—
186C2×C4—9042no—
187C2×C4—9042no—
188C2×C4—2262no—
189C2×C4—2262no—
190C2×C4C2×D45211yescharacteristic
191C2×C4C2×D45212yes—
192C2×C4C2×D45212yes—
193C2×C4C23×D11311yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—9044no—
199C22—4522no—
200C22—4522no—
201C22—4522no—
202C22—4522no—
203C22—4522no—
204C22—2264no—
205C22C22×D45211yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—4522no—
210C4—4522no—
211C4#41×D11312yes—
212C2—41no—
213C2—9042no—
214C2—4524no—
215C2#2029911011yescharacteristic
216C2#2029940312yes—
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#433×C113C2
socleC22×C113C22×D4
hypercenter#433D113
hypocenterC113#3122
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20299203C2semidirect
2. #20299072C2semidirect
3. #20298923C2semidirect
4. #20298899C2semidirect
5. #20298794C2semidirect
6. #20298734C2semidirect
7. #20298711C2semidirect
8. C4×D904C2semidirect
9. #433×C113C2semidirect
13. #16813619C22semidirect
14. #16813614C22semidirect
20. C4×D452C22semidirect
24. #16813556C22semidirect
25. #16813554C22semidirect
28. #16813544C22semidirect
29. #16813544C22semidirect
31. C4⋊C8×C113C22semidirect
33. #97×C113C22semidirect
34. C4×C8×C113C22semidirect
109. C113#3122semidirect
118. #433D113semidirect
136. C4⋊C8C2×D113semidirect
142. #97C2×D113semidirect
143. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992032
#202990722
#202989232
#202988992
#202987942
#202987342
#202987112
C4×D9042
#433×C1132
#3122113