Finite Group Databasebeta

← #28400064

Subgroups — #28400064

Order 14464.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16813653C211yesmaximal, characteristic, complemented
2C2×#16813648C211yesmaximal, characteristic
3C4×#14268647C211yesmaximal, characteristic, complemented
4#20298817C214yesmaximal, complemented
5#20298810C214yesmaximal, complemented
6#20298622C211yesmaximal, characteristic, complemented
7#20298607C211yesmaximal, characteristic, complemented
8#20298603C211yesmaximal, characteristic, complemented
9C2×#124×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11#16813653—24no—
12#16813648—24no—
13C2×#14268637C2212yescomplemented
14C2×#14268635C2212yes—
15C2×#14268634C2212yescomplemented
16C2×#14268632C2212yes—
17C2×#14268631C2211yescharacteristic
18C2×#14268631C2211yescharacteristic
19C4×Dic226C2212yescomplemented
20C4×D452C2212yescomplemented
21C4×C22⋊D113—22no—
22#16813581C2211yescharacteristic
23#16813579—21no—
24C42×D113—21no—
25C4⋊#11744751C2214yescomplemented
26#16813546C2214yescomplemented
27#16813543C2214yes—
28C22×Q8×C113C2211yescharacteristic
29C22×D4×C113C2211yescharacteristic
30#124×C113—21no—
31#124×C113—21no—
32#124×C113C2214yes—
33C2×C22⋊C4×C113—22no—
34C2×C42×C113C2211yescharacteristic
35#14268647—22no—
36#14268647D414yes—
37C2×Dic226C2311yescharacteristic
38C2×D452C2311yescharacteristic
39C2×C22⋊D113—21no—
40C2×C4×D113—21no—
41C2×C4×D113—22no—
42#14268637—24no—
43#14268635—24no—
44#14268634—24no—
45#14268632—24no—
46#14268631—22no—
47#14268631—22no—
48C2×#11744751C2312yes—
49C2×#11744751C2312yes—
50C4⋊Dic113C2312yes—
51#14268626—22no—
52C22⋊Dic113—21no—
53#14268624—22no—
54C4×Dic113—21no—
55C4×Dic113—22no—
56C24×C113—21no—
57C2×Q8×C113—21no—
58C2×Q8×C113—22no—
59C2×Q8×C113—22no—
60C2×Q8×C113C2312yes—
61C2×D4×C113—22no—
62C2×D4×C113—21no—
63C2×D4×C113—22no—
64C2×D4×C113C2312yes—
65C22×C4×C113—21no—
66C22×C4×C113D412yes—
67C22×C4×C113C2311yescharacteristic
68C22⋊C4×C113—24no—
69C22⋊C4×C113—24no—
70C42×C113D411yescharacteristic
71C42×C113D411yescharacteristic
72C42×C113C2312yes—
73C23×C113—22no—
74C23×C113—44no—
75C23×C113—42no—
76C23×C113C2×D411yescharacteristic
77C22×D113—21no—
78Q8×C113—22no—
79Q8×C113—22no—
80Q8×C113—42no—
81D4×C113—22no—
82D4×C113—22no—
83D4×C113—42no—
84C2×C4×C113—22no—
85C2×C4×C113—42no—
86C2×C4×C113—42no—
87C2×C4×C113C2×D412yes—
88C2×C4×C113C2×D412yes—
89C2×C4×C113C2×D412yes—
90C2×C4×C113C2×D411yescharacteristic
91C2×C4×C113#4112yes—
92C2×C4×C113C2411yescharacteristic
93C22⋊D113—24no—
94C2×Dic113—21no—
95C2×Dic113—22no—
96D452—21no—
97D452C2×D412yes—
98C4×D113—24no—
99C4×D113—44no—
100Dic226—21no—
101Dic226C2×D412yes—
102#11744751—22no—
103#11744751—22no—
104C22×C113—22no—
105C22×C113—42no—
106C22×C113—44no—
107C22×C113—84no—
108C22×C113#12112yes—
109C22×C113C22×D411yescharacteristic
110C2×D113—22no—
111C2×D113—42no—
112C4×C113—22no—
113C4×C113—22no—
114C4×C113—42no—
115C4×C113#12112yes—
116C4×C113C22×D411yescharacteristic
117C4×C113C2×#4111yescharacteristic
118Dic113—22no—
119Dic113—42no—
120C2×C113—22no—
121C2×C113—82no—
122C2×C113C2×#12111yescharacteristic
123C2×C113#57512yes—
124D113—42no—
125#3040—1131nomaximal, Sylow
126C113#304011yescharacteristic, complemented, Sylow
127C2×#137—1131no—
128C2×AGL(1,ℤ/8)—1131no—
129C2×#124D11311yescharacteristic, complemented
130C4×#41—1131no—
131#464—1134no—
132#463—1134no—
133#423—1131no—
134#419—1131no—
135#418—1131no—
136C2×#41—1131no—
137C22×Q8C2×D11311yescharacteristic
138C22×D4C2×D11311yescharacteristic
139#137—2264no—
140AGL(1,ℤ/8)—2264no—
141C2×Q16—1132no—
142C2×SD16—1132no—
143C2×SD16—1132no—
144C2×D8—1132no—
145C2×M16—1131no—
146C2×M16—1131no—
147#124—21no—
148#124—21no—
149#124C2×D11314yes—
150C4×Q8—1132no—
151C4×D4—1132no—
152C4×D4—2262no—
153#117—1131no—
154#117—2261no—
155C2×C22⋊C4—22no—
156C2×C42—2261no—
157C2×C42C2×D11311yescharacteristic
158C4⋊C8—1134no—
159#103—1134no—
160#102—1134no—
161C24—21no—
162#41—1134no—
163#41—2262no—
164C2×Q8—21no—
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8—1131no—
168C2×Q8C22×D11312yes—
169C2×D4—22no—
170C2×D4—21no—
171C2×D4—22no—
172C2×D4—1131no—
173C2×D4—2261no—
174C2×D4C22×D11312yes—
175C22×C4—21no—
176C22×C4—2262no—
177C22×C4—2261no—
178C22×C4C22⋊D11312yes—
179C22×C4C22×D11311yescharacteristic
180Q16—2264no—
181SD16—2264no—
182SD16—2264no—
183D8—2264no—
184M16—2262no—
185M16—2262no—
186C2×C8—1132no—
187C2×C8—1132no—
188C4⋊C4—1132no—
189C4⋊C4—2262no—
190C22⋊C4—24no—
191C22⋊C4—24no—
192C22⋊C4—2261no—
193C22⋊C4—2262no—
194C42—2261no—
195C42—2262no—
196C42C22⋊D11311yescharacteristic
197C42C22⋊D11311yescharacteristic
198C42C22×D11312yes—
199C23—22no—
200C23—44no—
201C23—42no—
202C23—2261no—
203C23C2×C22⋊D11311yescharacteristic
204Q8—22no—
205Q8—22no—
206Q8—42no—
207Q8—1132no—
208Q8—2261no—
209D4—22no—
210D4—22no—
211D4—42no—
212D4—1132no—
213D4—2264no—
214D4—2261no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—4524no—
219C2×C4—2262no—
220C2×C4—2261no—
221C2×C4—2264no—
222C2×C4D4×D11312yes—
223C2×C4C2×C22⋊D11312yes—
224C2×C4C2×C22⋊D11312yes—
225C2×C4C2×C22⋊D11311yescharacteristic
226C2×C4#1426864612yes—
227C2×C4C23×D11311yescharacteristic
228C8—2262no—
229C8—2262no—
230C22—22no—
231C22—42no—
232C22—44no—
233C22—84no—
234C22—4522no—
235C22—2262no—
236C22#1681359312yes—
237C22C22×C22⋊D11311yescharacteristic
238C4—22no—
239C4—22no—
240C4—42no—
241C4—4522no—
242C4—2262no—
243C4#1681359312yes—
244C4C2×D4×D11311yescharacteristic
245C4C2×#1426864611yescharacteristic
246C2—22no—
247C2—82no—
248C2—4522no—
249C2C2×#1681359311yescharacteristic
250C2#2029939612yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#124×C113C2
socleC22×C113C22×D4
prime radicalC2×#16813648C2
hypercenterC2×#124D113
hypocenterC113#3040
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
3. C4×#14268647C2semidirect
4. #20298817C2semidirect
5. #20298810C2semidirect
6. #20298622C2semidirect
7. #20298607C2semidirect
8. #20298603C2semidirect
9. C2×#124×C113C2semidirect
13. C2×#14268637C22semidirect
15. C2×#14268634C22semidirect
19. C4×Dic226C22semidirect
20. C4×D452C22semidirect
25. C4⋊#11744751C22semidirect
26. #16813546C22semidirect
126. C113#3040semidirect
129. 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
C4×#142686472
#202988172
#202988102
#202986222
#202986072
#202986032
C2×#124×C1132
#3040113