Finite Group Databasebeta

← #28400038

Subgroups — #28400038

Order 14464.

548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#16813648C212yesmaximal, complemented
2#20299148C211yesmaximal, characteristic, complemented
3#20298813C214yesmaximal, complemented
4#20298803C212yesmaximal, complemented
5#20298793C212yesmaximal, complemented
6#20298622C211yesmaximal, characteristic, complemented
7#20298597C212yesmaximal, complemented
8C2×C4×D4×C113C211yesmaximal, characteristic, complemented
9C2×#14268647C2212yes—
10#16813648—28no—
11C2×#14268635C2214yes—
12C2×#14268632C2214yes—
13C2×#14268631C2212yes—
14#16813622C2211yescharacteristic, complemented
15#16813619C2211yescharacteristic, complemented
16#16813610C2212yescomplemented
17#16813596—21no—
18#16813596—21no—
19C4×D452—21no—
20C4×D452—21no—
21C4⋊#11744751C2212yescomplemented
22C4⋊#11744751C2212yescomplemented
23#16813545C2214yescomplemented
24#16813542C2214yescomplemented
25C22×D4×C113C2211yescharacteristic
26C23×C4×C113—21no—
27C4×D4×C113—21no—
28C4×D4×C113—21no—
29C4×D4×C113C2212yes—
30C4×D4×C113C2212yes—
31C2×C4⋊C4×C113C2211yescharacteristic
32C2×C22⋊C4×C113—21no—
33C2×C42×C113C2211yescharacteristic
34#14268647—24no—
35#14268647—24no—
36C2×Dic226C2312yes—
37C2×D452—21no—
38C2×D452—21no—
39C2×D452C2312yes—
40C2×C22⋊D113—22no—
41C2×C4×D113—22no—
42#14268635—28no—
43#14268632—28no—
44#14268631—24no—
45C2×#11744751C2314yes—
46C4⋊Dic113—21no—
47C4⋊Dic113—21no—
48#14268624—22no—
49#14268624—22no—
50C24×C113—21no—
51C2×D4×C113—21no—
52C2×D4×C113—22no—
53C2×D4×C113D414yescomplemented
54C2×D4×C113C2312yes—
55C22×C4×C113—21no—
56C22×C4×C113—22no—
57C22×C4×C113—22no—
58C22×C4×C113—44no—
59C22×C4×C113D411yescharacteristic
60C22×C4×C113D411yescharacteristic
61C22×C4×C113C2311yescharacteristic
62C4⋊C4×C113—21no—
63C4⋊C4×C113C2312yes—
64C22⋊C4×C113—22no—
65C22⋊C4×C113—22no—
66C42×C113D411yescharacteristic
67C42×C113D411yescharacteristic
68C42×C113C2311yescharacteristic
69C42×C113C2311yescharacteristic
70C23×C113—24no—
71C23×C113—22no—
72C23×C113—42no—
73C23×C113—42no—
74C23×C113C2×D411yescharacteristic
75C22×D113—22no—
76D4×C113—24no—
77D4×C113—22no—
78D4×C113C2×D414yes—
79C2×C4×C113—22no—
80C2×C4×C113—22no—
81C2×C4×C113—41no—
82C2×C4×C113—44no—
83C2×C4×C113—42no—
84C2×C4×C113—44no—
85C2×C4×C113C2×D411yescharacteristic
86C2×C4×C113C2×D411yescharacteristic
87C2×C4×C113C2×D411yescharacteristic
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113C2×D412yes—
91C2×C4×C113#4112yes—
92C2×C4×C113C2411yescharacteristic
93C22⋊D113—44no—
94C2×Dic113—22no—
95D452—22no—
96D452—22no—
97D452—42no—
98D452—42no—
99C4×D113—44no—
100Dic226—22no—
101Dic226—22no—
102#11744751—24no—
103C22×C113—21no—
104C22×C113—21no—
105C22×C113—24no—
106C22×C113—48no—
107C22×C113—42no—
108C22×C113—42no—
109C22×C113#12112yes—
110C22×C113C22×D411yescharacteristic
111C2×D113—42no—
112C2×D113—42no—
113C2×D113—42no—
114C4×C113—21no—
115C4×C113—21no—
116C4×C113—21no—
117C4×C113—42no—
118C4×C113#12112yes—
119C4×C113AGL(1,ℤ/8)12yescomplemented
120C4×C113C22×D411yescharacteristic
121C4×C113C2×#4111yescharacteristic
122Dic113—42no—
123C2×C113—22no—
124C2×C113—44no—
125C2×C113C2×#12111yescharacteristic
126C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
127C2×C113#57511yescharacteristic
128D113—82no—
129#3036—1131nomaximal, Sylow
130C113#303611yescharacteristic, complemented, Sylow
131C2×AGL(1,ℤ/8)—1132no—
132#532—1131no—
133C2×C4×D4D11311yescharacteristic, complemented
134#463—1134no—
135#461—1132no—
136#459—1132no—
137#423—1131no—
138#417—1132no—
139C2×#41—1132no—
140C22×D4C2×D11311yescharacteristic
141C23×C4—21no—
142AGL(1,ℤ/8)—2268no—
143C2×SD16—1134no—
144C2×D8—1134no—
145C2×M16—1132no—
146C4⋊Q8—1131no—
147#127—1131no—
148#124—1132no—
149#121—2261no—
150#121—2261no—
151C4×D4—21no—
152C4×D4—21no—
153C4×D4—2261no—
154C4×D4—2261no—
155C4×D4C2×D11312yes—
156C4×D4C2×D11312yes—
157C2×C4⋊C4C2×D11311yescharacteristic
158C2×C22⋊C4—21no—
159C2×C42C2×D11311yescharacteristic
160C4⋊C8—1132no—
161C4⋊C8—1132no—
162#103—1134no—
163#102—1134no—
164C24—21no—
165#41—2264no—
166#41—2264no—
167C2×Q8—1132no—
168C2×D4—21no—
169C2×D4—22no—
170C2×D4—1132no—
171C2×D4—2262no—
172C2×D4—2261no—
173C2×D4—2261no—
174C2×D4D45214yescomplemented
175C2×D4C22×D11312yes—
176C22×C4—21no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—44no—
180C22×C4—2262no—
181C22×C4C22⋊D11311yescharacteristic
182C22×C4C22⋊D11311yescharacteristic
183C22×C4C22×D11311yescharacteristic
184SD16—2268no—
185D8—2268no—
186M16—2264no—
187C2×C8—1134no—
188C4⋊C4—21no—
189C4⋊C4—2261no—
190C4⋊C4—2261no—
191C4⋊C4C22×D11312yes—
192C22⋊C4—22no—
193C22⋊C4—22no—
194C22⋊C4—2262no—
195C22⋊C4—2262no—
196C42C22⋊D11311yescharacteristic
197C42C22⋊D11311yescharacteristic
198C42C22×D11311yescharacteristic
199C42C22×D11311yescharacteristic
200C23—24no—
201C23—22no—
202C23—42no—
203C23—42no—
204C23—2262no—
205C23C2×C22⋊D11311yescharacteristic
206Q8—2262no—
207Q8—2262no—
208D4—24no—
209D4—22no—
210D4—4522no—
211D4—4524no—
212D4—4522no—
213D4—2262no—
214D4—2262no—
215D4C2×D45214yes—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—44no—
222C2×C4—4524no—
223C2×C4—2262no—
224C2×C4C2×C22⋊D11311yescharacteristic
225C2×C4C2×C22⋊D11311yescharacteristic
226C2×C4C2×C22⋊D11311yescharacteristic
227C2×C4C2×C22⋊D11311yescharacteristic
228C2×C4C2×C22⋊D11311yescharacteristic
229C2×C4C2×D45212yes—
230C2×C4#1426864712yes—
231C2×C4C23×D11311yescharacteristic
232C8—2264no—
233C22—21no—
234C22—21no—
235C22—24no—
236C22—48no—
237C22—42no—
238C22—42no—
239C22—4522no—
240C22—4522no—
241C22—4522no—
242C22#1681359612yes—
243C22C22×C22⋊D11311yescharacteristic
244C4—21no—
245C4—21no—
246C4—21no—
247C4—42no—
248C4—4522no—
249C4#1681359612yes—
250C4#1681364812yescomplemented
251C4C22×D45211yescharacteristic
252C4C2×#1426864711yescharacteristic
253C2—22no—
254C2—44no—
255C2—9042no—
256C2C2×#1681359611yescharacteristic
257C2C2×#1681364811yescharacteristic
258C2#2029939611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×C4×D4×C113C2
socleC22×C113C22×D4
hypercenterC2×C4×D4D113
hypocenterC113#3036
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. #20299148C2semidirect
3. #20298813C2semidirect
4. #20298803C2semidirect
5. #20298793C2semidirect
6. #20298622C2semidirect
7. #20298597C2semidirect
8. C2×C4×D4×C113C2semidirect
14. #16813622C22semidirect
15. #16813619C22semidirect
16. #16813610C22semidirect
21. C4⋊#11744751C22semidirect
22. C4⋊#11744751C22semidirect
23. #16813545C22semidirect
24. #16813542C22semidirect
53. C2×D4×C113D4semidirect
119. C4×C113AGL(1,ℤ/8)semidirect
130. C113#3036semidirect
133. C2×C4×D4D113semidirect
174. C2×D4D452semidirect
250. C4#16813648semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
#202991482
#202988132
#202988032
#202987932
#202986222
#202985972
C2×C4×D4×C1132
#3036113