Finite Group Databasebeta

← #28401370

Subgroups — #28401370

Order 14464.

514 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 113 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#121×D113C212yesmaximal, complemented
2#20298918C212yesmaximal, complemented
3#20298915C212yesmaximal, complemented
4#20298851C211yesmaximal, characteristic, complemented
5#20298849C212yesmaximal, complemented
6#20298733C212yesmaximal, complemented
7#20298730C212yesmaximal, complemented
8#20298561C211yesmaximal, characteristic, complemented
9#469×C113C211yesmaximal, characteristic, complemented
10C2×D4×D113—22no—
11C2×D4×D113C2212yescomplemented
12C22×C4×D113C2211yescharacteristic
13C2×D904C2211yescharacteristic, complemented
14C2×#14268632C2212yescomplemented
15C2×#14268631C2211yescharacteristic, complemented
16#16813597C2212yes—
17#16813596C2212yescomplemented
18#16813595—22no—
19#16813594—22no—
20#16813593C2212yes—
21C4⋊C4×D113C2212yescomplemented
22C22⋊C4×D113—22no—
23#16813554C2211yescharacteristic, complemented
24#16813553C2212yescomplemented
25#16813544C2212yescomplemented
26#16813543C2212yescomplemented
27#16813542C2212yescomplemented
28#16813534C2212yescomplemented
29#16813534C2212yescomplemented
30C2×D8×C113C2211yescharacteristic, complemented
31C2×M16×C113C2211yescharacteristic, complemented
32#121×C113C2212yescomplemented
33#106×C113C2211yescharacteristic, complemented
34#102×C113C2212yescomplemented
35C23×D113—22no—
36C23×D113D411yescharacteristic
37C2×D452—22no—
38C2×D452C2312yes—
39C2×C22⋊D113—22no—
40C2×C22⋊D113—22no—
41C2×C22⋊D113—22no—
42D4×D113—42no—
43D4×D113—42no—
44D4×D113—48no—
45C22×Dic113D411yescharacteristic
46C2×C4×D113—22no—
47C2×C4×D113—41no—
48C2×C4×D113—41no—
49C2×C4×D113D412yes—
50C2×C4×D113C2312yes—
51D904—41no—
52#14268632—42no—
53#14268631—41no—
54C2×#11744751C2312yes—
55C4⋊Dic113C2312yes—
56#14268626—22no—
57C22⋊Dic113—22no—
58#14268624—22no—
59#14268624—22no—
60C2×D4×C113—22no—
61C2×D4×C113C2312yes—
62C22×C4×C113C2311yescharacteristic
63D8×C113—41no—
64M16×C113—41no—
65C2×C8×C113C2311yescharacteristic
66C2×C8×C113C2311yescharacteristic
67C4⋊C4×C113C2312yes—
68C22⋊C4×C113—22no—
69C23×C113—22no—
70C23×C113C2×D411yescharacteristic
71C22×D113—24no—
72C22×D113—22no—
73C22×D113—41no—
74C22×D113—44no—
75C22×D113—44no—
76C22×D113—44no—
77C22×D113C2×D412yes—
78D4×C113—22no—
79D4×C113—22no—
80D4×C113—44no—
81C2×C4×C113—21no—
82C2×C4×C113—21no—
83C2×C4×C113—22no—
84C2×C4×C113C2×D411yescharacteristic
85C2×C4×C113C2411yescharacteristic
86C22⋊D113—44no—
87C22⋊D113—44no—
88C22⋊D113—44no—
89C2×Dic113—22no—
90C2×Dic113—41no—
91C2×Dic113C2×D412yes—
92D452—22no—
93D452—22no—
94D452—44no—
95C4×D113—22no—
96C4×D113—22no—
97C4×D113—42no—
98C4×D113—44no—
99C8×C113—21no—
100C8×C113—21no—
101#11744751—22no—
102C22×C113—21no—
103C22×C113—22no—
104C22×C113—42no—
105C22×C113—42no—
106C22×C113—42no—
107C22×C113C22×D411yescharacteristic
108C2×D113—22no—
109C2×D113—22no—
110C2×D113—44no—
111C2×D113—42no—
112C2×D113—42no—
113C2×D113—42no—
114C2×D113—88no—
115C2×D113AGL(1,ℤ/8)14yes—
116C4×C113—21no—
117C4×C113—42no—
118C4×C113H(5,𝔽2)11yescharacteristic
119C4×C113H(5,𝔽2)11yescharacteristic
120Dic113—22no—
121Dic113—42no—
122C2×C113—41no—
123C2×C113—82no—
124C2×C113#53411yescharacteristic
125C2×C113C2×AGL(1,ℤ/8)12yes—
126D113—24no—
127D113—82no—
128#3192—1131nomaximal, Sylow
129C113#319211yescharacteristic, complemented, Sylow
130C2×#121—1132no—
131#481—1132no—
132#481—1132no—
133#469—1131no—
134#469—1132no—
135#469D11311yescharacteristic, complemented
136#447—1132no—
137#447—1132no—
138#407—1131no—
139C22×D4—1132no—
140C22×D4—2262no—
141C23×C4—1131no—
142C2×D8—1132no—
143C2×D8—1131no—
144C2×D8C2×D11311yescharacteristic, complemented
145C2×M16—1131no—
146C2×M16C2×D11311yescharacteristic, complemented
147#121—1132no—
148#121—1132no—
149#121—1132no—
150#121—2262no—
151#121—2262no—
152#121C2×D11312yescomplemented
153C2×C4⋊C4—1132no—
154C2×C22⋊C4—2262no—
155#106—1131no—
156#106—1132no—
157#106C2×D11311yescharacteristic, complemented
158#102—1132no—
159#102—1132no—
160#102—1132no—
161#102C2×D11312yescomplemented
162C22⋊C8—1132no—
163C22⋊C8—1132no—
164C24—1131no—
165C24—2262no—
166C2×D4—22no—
167C2×D4—1132no—
168C2×D4—4528no—
169C2×D4—4522no—
170C2×D4—4522no—
171C2×D4—2262no—
172C2×D4—2262no—
173C2×D4—2262no—
174C2×D4—2262no—
175C2×D4C22×D11312yes—
176C22×C4—1131no—
177C22×C4—1132no—
178C22×C4—1132no—
179C22×C4—4521no—
180C22×C4—4521no—
181C22×C4—2262no—
182C22×C4C22×D11311yescharacteristic
183D8—41no—
184D8—4521no—
185D8—4522no—
186M16—41no—
187M16—4521no—
188C2×C8—1132no—
189C2×C8C22×D11311yescharacteristic
190C2×C8C22×D11311yescharacteristic
191C4⋊C4—1132no—
192C4⋊C4—2262no—
193C4⋊C4C22×D11312yes—
194C22⋊C4—22no—
195C22⋊C4—2262no—
196C22⋊C4—2262no—
197C22⋊C4—2262no—
198C23—22no—
199C23—1132no—
200C23—4521no—
201C23—4524no—
202C23—4524no—
203C23—4524no—
204C23—2264no—
205C23—2262no—
206C23D4×D11311yescharacteristic
207D4—22no—
208D4—22no—
209D4—44no—
210D4—4524no—
211D4—4524no—
212D4—4524no—
213D4—4524no—
214D4—2262no—
215D4—2262no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—1132no—
220C2×C4—4522no—
221C2×C4—4524no—
222C2×C4—4521no—
223C2×C4—2262no—
224C2×C4—2262no—
225C2×C4—2262no—
226C2×C4D4×D11311yescharacteristic
227C2×C4C23×D11311yescharacteristic
228C8—21no—
229C8—21no—
230C8—2262no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—1134no—
237C22—9048no—
238C22—4524no—
239C22—4522no—
240C22—4522no—
241C22—4522no—
242C22—2262no—
243C22—2262no—
244C22C2×D4×D11311yescharacteristic
245C4—21no—
246C4—42no—
247C4—4522no—
248C4—2262no—
249C4#1681366711yescharacteristic
250C4#1681366811yescharacteristic
251C2—41no—
252C2—82no—
253C2—9042no—
254C2—2264no—
255C2#2029915611yescharacteristic
256C2AGL(1,ℤ/8)×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#469×C113C2
socleC22×C113C22×D4
hypercenter#469D113
hypocenterC113#3192
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #121×D113C2semidirect
2. #20298918C2semidirect
3. #20298915C2semidirect
4. #20298851C2semidirect
5. #20298849C2semidirect
6. #20298733C2semidirect
7. #20298730C2semidirect
8. #20298561C2semidirect
9. #469×C113C2semidirect
11. C2×D4×D113C22semidirect
13. C2×D904C22semidirect
14. C2×#14268632C22semidirect
15. C2×#14268631C22semidirect
17. #16813596C22semidirect
21. C4⋊C4×D113C22semidirect
23. #16813554C22semidirect
24. #16813553C22semidirect
25. #16813544C22semidirect
26. #16813543C22semidirect
27. #16813542C22semidirect
28. #16813534C22semidirect
29. #16813534C22semidirect
30. C2×D8×C113C22semidirect
31. C2×M16×C113C22semidirect
32. #121×C113C22semidirect
33. #106×C113C22semidirect
34. #102×C113C22semidirect
129. C113#3192semidirect
135. #469D113semidirect
144. C2×D8C2×D113semidirect
146. C2×M16C2×D113semidirect
152. #121C2×D113semidirect
157. #106C2×D113semidirect
161. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#121×D1132
#202989182
#202989152
#202988512
#202988492
#202987332
#202987302
#202985612
#469×C1132
#3192113