Finite Group Databasebeta

← #28401436

Subgroups — #28401436

Order 14464.

442 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 109 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#20299164C212yesmaximal, complemented
2#20298924C212yesmaximal, complemented
3#20298921C212yesmaximal, complemented
4#20298851C211yesmaximal, characteristic, complemented
5#20298832C212yesmaximal, complemented
6#20298733C212yesmaximal, complemented
7#20298730C212yesmaximal, complemented
8#20298566C211yesmaximal, characteristic, complemented
9#469×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11C2×D4×D113C2212yescomplemented
12C2×D904C2211yescharacteristic
13C2×#14268632C2212yes—
14C22×#11744751C2211yescharacteristic, complemented
15#16813618—22no—
16#16813608—22no—
17#16813597C2212yes—
18#16813596C2212yescomplemented
19#16813593C2212yes—
20#16813592—22no—
21#16813590—22no—
22#16813580C2212yescomplemented
23#16813555C2212yescomplemented
24#16813554C2211yescharacteristic, complemented
25#16813544C2212yescomplemented
26#16813543C2212yescomplemented
27#16813542C2212yescomplemented
28#16813534C2212yescomplemented
29#16813534C2212yescomplemented
30C2×D8×C113C2211yescharacteristic
31C2×M16×C113C2211yescharacteristic, complemented
32#121×C113C2212yescomplemented
33#106×C113C2211yescharacteristic, complemented
34#102×C113C2212yescomplemented
35C23×D113—22no—
36#14268647—41no—
37#14268647—41no—
38C2×Dic226D411yescharacteristic
39C2×D452—22no—
40C2×D452D411yescharacteristic
41C2×D452C2312yes—
42C2×C22⋊D113—22no—
43C2×C22⋊D113—22no—
44C2×C22⋊D113—22no—
45C2×C22⋊D113D412yes—
46D4×D113—42no—
47D4×D113—42no—
48C2×C4×D113C2312yes—
49D904—41no—
50#14268632—42no—
51C2×#11744751—41no—
52C2×#11744751C2312yes—
53C4⋊Dic113C2312yes—
54C22⋊Dic113—22no—
55#14268624—22no—
56#14268624—22no—
57#14268624—22no—
58C4×Dic113—22no—
59C2×D4×C113—22no—
60C2×D4×C113C2312yes—
61C22×C4×C113C2311yescharacteristic
62D8×C113—41no—
63M16×C113—41no—
64C2×C8×C113C2311yescharacteristic
65C2×C8×C113C2311yescharacteristic
66C4⋊C4×C113C2312yes—
67C22⋊C4×C113—22no—
68C23×C113—22no—
69C23×C113C2×D411yescharacteristic
70C22×D113—22no—
71C22×D113—44no—
72C22×D113—82no—
73C22×D113—82no—
74C22×D113C2×D412yes—
75D4×C113—22no—
76D4×C113—22no—
77D4×C113—82no—
78C2×C4×C113—21no—
79C2×C4×C113—21no—
80C2×C4×C113—22no—
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2411yescharacteristic
83C22⋊D113—42no—
84C22⋊D113—44no—
85C22⋊D113—82no—
86C22⋊D113—82no—
87C2×Dic113—22no—
88C2×Dic113C2×D412yes—
89D452—22no—
90D452—22no—
91D452—41no—
92D452—82no—
93C4×D113—22no—
94C4×D113—22no—
95Dic226—41no—
96C8×C113—21no—
97C8×C113—21no—
98#11744751—22no—
99C22×C113—21no—
100C22×C113—22no—
101C22×C113—42no—
102C22×C113—42no—
103C22×C113—42no—
104C22×C113C22×D411yescharacteristic
105C2×D113—22no—
106C2×D113—22no—
107C2×D113—22no—
108C2×D113—42no—
109C2×D113—42no—
110C2×D113—42no—
111C2×D113—88no—
112C4×C113—21no—
113C4×C113—42no—
114C4×C113H(5,𝔽2)11yescharacteristic
115C4×C113H(5,𝔽2)11yescharacteristic
116Dic113—22no—
117Dic113—42no—
118C2×C113—41no—
119C2×C113—82no—
120C2×C113#53411yescharacteristic
121C2×C113#57612yes—
122D113—42no—
123D113—82no—
124#3199—1131nomaximal, Sylow
125C113#319911yescharacteristic, complemented, Sylow
126#535—1132no—
127#482—1132no—
128#482—1132no—
129#469—1131no—
130#469D11311yescharacteristic, complemented
131#466—1132no—
132#447—1132no—
133#447—1132no—
134#408—1131no—
135C2×#41—1131no—
136C22×D4—1132no—
137C2×D8—1132no—
138C2×D8—1131no—
139C2×D8C2×D11311yescharacteristic
140C2×M16C2×D11311yescharacteristic, complemented
141C22×C8—1131no—
142#127—2262no—
143#124—2262no—
144#121—1132no—
145#121—1132no—
146#121—1132no—
147#121C2×D11312yescomplemented
148#120—2262no—
149#120—2262no—
150#117—1132no—
151#107—1132no—
152#106—1131no—
153#106C2×D11311yescharacteristic, complemented
154#102—1132no—
155#102—1132no—
156#102—1132no—
157#102C2×D11312yescomplemented
158C22⋊C8—1132no—
159C22⋊C8—1132no—
160C24—2262no—
161#41—4521no—
162#41—4521no—
163C2×Q8—1131no—
164C2×D4—22no—
165C2×D4—1132no—
166C2×D4—1131no—
167C2×D4—1132no—
168C2×D4—4522no—
169C2×D4—4522no—
170C2×D4—2262no—
171C2×D4—2262no—
172C2×D4—2262no—
173C2×D4—2262no—
174C2×D4C22×D11312yes—
175C22×C4—1132no—
176C22×C4C22×D11311yescharacteristic
177D8—41no—
178D8—4521no—
179D8—4522no—
180M16—41no—
181C2×C8—1132no—
182C2×C8—4521no—
183C2×C8C22×D11311yescharacteristic
184C2×C8C22×D11311yescharacteristic
185C4⋊C4—1132no—
186C4⋊C4C22×D11312yes—
187C22⋊C4—22no—
188C22⋊C4—2262no—
189C22⋊C4—2262no—
190C22⋊C4—2262no—
191C22⋊C4—2262no—
192C42—2262no—
193C23—22no—
194C23—1132no—
195C23—9042no—
196C23—9042no—
197C23—4524no—
198C23—2262no—
199C23D4×D11311yescharacteristic
200Q8—4521no—
201D4—22no—
202D4—22no—
203D4—82no—
204D4—9042no—
205D4—9042no—
206D4—9042no—
207D4—4521no—
208D4—4522no—
209D4—4524no—
210D4—2262no—
211D4—2262no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—1132no—
216C2×C4—2262no—
217C2×C4—2262no—
218C2×C4—2262no—
219C2×C4D4×D11311yescharacteristic
220C2×C4C23×D11311yescharacteristic
221C8—21no—
222C8—21no—
223C8—2262no—
224C22—22no—
225C22—21no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—9048no—
230C22—4522no—
231C22—4522no—
232C22—4522no—
233C22—2262no—
234C22—2262no—
235C22—2262no—
236C22C2×D4×D11311yescharacteristic
237C4—21no—
238C4—42no—
239C4—4522no—
240C4—2262no—
241C4#1681366711yescharacteristic
242C4#1681366811yescharacteristic
243C2—41no—
244C2—82no—
245C2—9042no—
246C2—4522no—
247C2#2029915611yescharacteristic
248C2#2029940212yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#469×C113C2
socleC22×C113C22×D4
hypercenter#469D113
hypocenterC113#3199
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. #20299164C2semidirect
2. #20298924C2semidirect
3. #20298921C2semidirect
4. #20298851C2semidirect
5. #20298832C2semidirect
6. #20298733C2semidirect
7. #20298730C2semidirect
8. #20298566C2semidirect
9. #469×C113C2semidirect
11. C2×D4×D113C22semidirect
14. C22×#11744751C22semidirect
18. #16813596C22semidirect
22. #16813580C22semidirect
23. #16813555C22semidirect
24. #16813554C22semidirect
25. #16813544C22semidirect
26. #16813543C22semidirect
27. #16813542C22semidirect
28. #16813534C22semidirect
29. #16813534C22semidirect
31. C2×M16×C113C22semidirect
32. #121×C113C22semidirect
33. #106×C113C22semidirect
34. #102×C113C22semidirect
125. C113#3199semidirect
130. #469D113semidirect
140. C2×M16C2×D113semidirect
147. #121C2×D113semidirect
153. #106C2×D113semidirect
157. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991642
#202989242
#202989212
#202988512
#202988322
#202987332
#202987302
#202985662
#469×C1132
#3199113