Finite Group Databasebeta

← #28400077

Subgroups — #28400077

Order 14464.

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

normal subgroups only

This group has 526 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×#16813648C211yesmaximal, characteristic, complemented
2C22×#14268632C211yesmaximal, characteristic, complemented
3#20299167C211yesmaximal, characteristic, complemented
4#20298813C214yesmaximal, complemented
5#20298793C214yesmaximal, complemented
6#20298625C211yesmaximal, characteristic, complemented
7#20298602C211yesmaximal, characteristic, complemented
8#20298592C211yesmaximal, characteristic, complemented
9#518×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11C22×D452C2211yescharacteristic
12#16813648—24no—
13C2×#14268635C2212yescomplemented
14C2×#14268632—24no—
15C2×#14268632C2214yes—
16C2×#14268632C2212yescomplemented
17C2×#14268631C2211yescharacteristic
18C22×#11744751C2211yescharacteristic
19#16813619C2212yescomplemented
20#16813610C2212yescomplemented
21#16813597—22no—
22#16813592—22no—
23C4⋊#11744751C2214yescomplemented
24#16813545C2212yescomplemented
25#16813542C2212yescomplemented
26#16813542C2214yescomplemented
27C22×D4×C113C2211yescharacteristic
28C4×D4×C113—22no—
29C4×D4×C113C2214yescomplemented
30#117×C113C2211yescharacteristic
31#117×C113C2211yescharacteristic
32C2×C22⋊C4×C113—22no—
33C23×D113—21no—
34#14268647—22no—
35#14268647—22no—
36C2×Dic226C2311yescharacteristic
37C2×D452—22no—
38C2×D452—22no—
39C2×D452—21no—
40C2×D452—24no—
41C2×D452C2312yes—
42C2×D452C2311yescharacteristic
43C2×C22⋊D113—21no—
44C2×C4×D113—21no—
45#14268635—24no—
46#14268632—28no—
47#14268632—24no—
48#14268631—22no—
49C2×#11744751—22no—
50C2×#11744751C2312yes—
51C2×#11744751C2312yes—
52#14268624—24no—
53C24×C113—21no—
54C2×D4×C113—21no—
55C2×D4×C113—22no—
56C2×D4×C113D414yescomplemented
57C2×D4×C113C2312yes—
58C22×C4×C113—24no—
59C22×C4×C113C2311yescharacteristic
60C4⋊C4×C113D412yes—
61C4⋊C4×C113C2312yes—
62C22⋊C4×C113—21no—
63C22⋊C4×C113—24no—
64C22⋊C4×C113D412yes—
65C42×C113—21no—
66C42×C113C2312yes—
67C23×C113—22no—
68C23×C113—24no—
69C23×C113—82no—
70C23×C113C2×D411yescharacteristic
71C22×D113—22no—
72C22×D113—21no—
73C22×D113—42no—
74C22×D113—82no—
75D4×C113—24no—
76D4×C113—22no—
77D4×C113C2×D414yes—
78C2×C4×C113—22no—
79C2×C4×C113—84no—
80C2×C4×C113C2×D414yes—
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2×D412yes—
83C2×C4×C113#4112yes—
84C2×C4×C113C2411yescharacteristic
85C22⋊D113—42no—
86C2×Dic113—21no—
87D452—22no—
88D452—21no—
89D452—22no—
90D452—21no—
91D452—42no—
92D452—84no—
93C4×D113—42no—
94Dic226—21no—
95Dic226—21no—
96#11744751—22no—
97#11744751—22no—
98C22×C113—22no—
99C22×C113—24no—
100C22×C113—44no—
101C22×C113—84no—
102C22×C113#12112yes—
103C22×C113C22×D411yescharacteristic
104C2×D113—41no—
105C2×D113—42no—
106C2×D113—42no—
107C2×D113—44no—
108C2×D113—84no—
109C4×C113—24no—
110C4×C113—42no—
111C4×C113#12112yes—
112C4×C113C22×D411yescharacteristic
113C4×C113C2×#4111yescharacteristic
114Dic113—41no—
115C2×C113—22no—
116C2×C113—44no—
117C2×C113C2×#12111yescharacteristic
118C2×C113#57612yes—
119D113—81no—
120D113—82no—
121#3041—1131nomaximal, Sylow
122C113#304111yescharacteristic, complemented, Sylow
123C2×AGL(1,ℤ/8)—1131no—
124C22×D8—1131no—
125#535—1131no—
126#518D11311yescharacteristic, complemented
127#463—1134no—
128#459—1134no—
129#424—1131no—
130#418—1131no—
131#416—1131no—
132C2×#41—1131no—
133C22×D4—1131no—
134C22×D4C2×D11311yescharacteristic
135AGL(1,ℤ/8)—2264no—
136C2×SD16—1132no—
137C2×D8—1134no—
138C2×D8—1132no—
139C2×D8—2264no—
140C2×M16—1131no—
141C22×C8—1131no—
142#127—1132no—
143#124—1132no—
144#121—2262no—
145#120—2262no—
146C4×D4—22no—
147C4×D4C2×D11314yescomplemented
148#117C2×D11311yescharacteristic
149#117C2×D11311yescharacteristic
150C2×C22⋊C4—22no—
151C4⋊C8—1134no—
152#103—1132no—
153#102—1132no—
154#102—1134no—
155C24—21no—
156C24—2261no—
157#41—2262no—
158#41—2262no—
159C2×Q8—1131no—
160C2×D4—21no—
161C2×D4—22no—
162C2×D4—1132no—
163C2×D4—1131no—
164C2×D4—2261no—
165C2×D4—2264no—
166C2×D4—2261no—
167C2×D4—2262no—
168C2×D4—2262no—
169C2×D4D45214yescomplemented
170C2×D4C22×D11312yes—
171C22×C4—24no—
172C22×C4—2261no—
173C22×C4C22×D11311yescharacteristic
174SD16—2264no—
175D8—2268no—
176D8—2264no—
177M16—2262no—
178C2×C8—1132no—
179C2×C8—1132no—
180C2×C8—2262no—
181C4⋊C4C22⋊D11312yes—
182C4⋊C4C22×D11312yes—
183C22⋊C4—21no—
184C22⋊C4—24no—
185C22⋊C4—2264no—
186C22⋊C4C22⋊D11312yes—
187C42—21no—
188C42C22×D11312yes—
189C23—22no—
190C23—24no—
191C23—82no—
192C23—9042no—
193C23—4522no—
194C23—2262no—
195C23—2261no—
196C23C2×C22⋊D11311yescharacteristic
197Q8—2261no—
198Q8—2261no—
199D4—24no—
200D4—22no—
201D4—9044no—
202D4—4522no—
203D4—4522no—
204D4—2262no—
205D4—2261no—
206D4—2262no—
207D4—2261no—
208D4C2×D45214yes—
209C2×C4—22no—
210C2×C4—84no—
211C2×C4—4522no—
212C2×C4—2261no—
213C2×C4C2×C22⋊D11314yes—
214C2×C4C2×C22⋊D11311yescharacteristic
215C2×C4C2×D45212yes—
216C2×C4#1426864712yes—
217C2×C4C23×D11311yescharacteristic
218C8—2262no—
219C8—2262no—
220C22—22no—
221C22—24no—
222C22—44no—
223C22—84no—
224C22—9044no—
225C22—4521no—
226C22—4522no—
227C22—4522no—
228C22—4524no—
229C22#1681359612yes—
230C22C22×C22⋊D11311yescharacteristic
231C4—24no—
232C4—42no—
233C4—4521no—
234C4#1681359612yes—
235C4C22×D45211yescharacteristic
236C4C2×#1426864711yescharacteristic
237C2—22no—
238C2—44no—
239C2—9042no—
240C2—9041no—
241C2C2×#1681359611yescharacteristic
242C2#2029940112yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#518×C113C2
socleC22×C113C22×D4
hypercenter#518D113
hypocenterC113#3041
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. C22×#14268632C2semidirect
3. #20299167C2semidirect
4. #20298813C2semidirect
5. #20298793C2semidirect
6. #20298625C2semidirect
7. #20298602C2semidirect
8. #20298592C2semidirect
9. #518×C113C2semidirect
13. C2×#14268635C22semidirect
16. C2×#14268632C22semidirect
19. #16813619C22semidirect
20. #16813610C22semidirect
23. C4⋊#11744751C22semidirect
24. #16813545C22semidirect
25. #16813542C22semidirect
26. #16813542C22semidirect
29. C4×D4×C113C22semidirect
56. C2×D4×C113D4semidirect
122. C113#3041semidirect
126. #518D113semidirect
147. C4×D4C2×D113semidirect
169. C2×D4D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
C22×#142686322
#202991672
#202988132
#202987932
#202986252
#202986022
#202985922
#518×C1132
#3041113