Finite Group Databasebeta

← #28402184

Subgroups — #28402184

Order 14464.

520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#16813646C212yesmaximal, complemented
2#20299243C212yesmaximal, complemented
3#20298982C211yesmaximal, characteristic, complemented
4#20298845C212yesmaximal, complemented
5#20298813C212yesmaximal, complemented
6#20298761C212yesmaximal, complemented
7#20298733C212yesmaximal, complemented
8#20298677C211yesmaximal, characteristic, complemented
9C4×D8×C113C211yesmaximal, characteristic, complemented
10C2×#14268646C2212yes—
11C2×D4×D113C2212yescomplemented
12#16813646—28no—
13C2×Dic452C2211yescharacteristic, complemented
14C2×#14268636C2212yescomplemented
15C2×#14268635C2212yescomplemented
16C2×D904C2211yescharacteristic
17C2×#14268632C2212yes—
18C2×#14268630C2212yescomplemented
19#16813610C2212yescomplemented
20#16813606—22no—
21#16813602C2212yescomplemented
22#16813597C2212yes—
23#16813596—22no—
24#16813592—22no—
25C4×D452C2211yescharacteristic
26C2×#14268624—22no—
27C4⋊#11744751C2211yescharacteristic, complemented
28#16813545C2212yescomplemented
29#16813542C2212yescomplemented
30#16813534C2212yescomplemented
31C2×D8×C113C2211yescharacteristic
32C4×D4×C113C2212yescomplemented
33#107×C113C2211yescharacteristic, complemented
34#102×C113C2212yescomplemented
35C4×C8×C113C2211yescharacteristic, complemented
36C23×D113—22no—
37#14268646—24no—
38#14268646—42no—
39C2×Dic226C2312yes—
40C2×D452—22no—
41C2×D452D411yescharacteristic
42C2×D452C2312yes—
43C2×C22⋊D113—22no—
44C2×C22⋊D113—22no—
45D4×D113—24no—
46D4×D113—42no—
47C22×Dic113—22no—
48C2×C4×D113C2312yes—
49Dic452—41no—
50#14268636—24no—
51#14268635—24no—
52D904—41no—
53#14268632—24no—
54#14268630—24no—
55C2×#11744751C2312yes—
56C4⋊Dic113—22no—
57C4⋊Dic113D411yescharacteristic
58#14268624—22no—
59#14268624—22no—
60#14268624—22no—
61#14268624—22no—
62#14268624D412yes—
63C2×D4×C113C2312yes—
64C22×C4×C113—22no—
65D8×C113D414yescomplemented
66C2×C8×C113C2311yescharacteristic
67C2×C8×C113C2311yescharacteristic
68C4⋊C4×C113C2312yes—
69C22⋊C4×C113—22no—
70C42×C113C2311yescharacteristic
71C23×C113—22no—
72C22×D113—22no—
73C22×D113—44no—
74C22×D113—44no—
75C22×D113—82no—
76C22×D113C2×D412yes—
77D4×C113—22no—
78D4×C113C2×D414yes—
79C2×C4×C113—22no—
80C2×C4×C113—82no—
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2×D411yescharacteristic
83C2×C4×C113C2411yescharacteristic
84C22⋊D113—44no—
85C22⋊D113—44no—
86C2×Dic113—22no—
87C2×Dic113—44no—
88C2×Dic113C2×D412yes—
89D452—22no—
90D452—22no—
91D452—41no—
92D452—82no—
93C4×D113—22no—
94C4×D113—22no—
95Dic226—22no—
96Dic226—22no—
97C8×C113—21no—
98C8×C113C2×D412yes—
99#11744751—22no—
100C22×C113—24no—
101C22×C113—42no—
102C22×C113—42no—
103C22×C113C22×D411yescharacteristic
104C2×D113—22no—
105C2×D113—22no—
106C2×D113—22no—
107C2×D113—42no—
108C2×D113—42no—
109C2×D113—42no—
110C2×D113—88no—
111C4×C113—21no—
112C4×C113—21no—
113C4×C113—42no—
114C4×C113C22×D411yescharacteristic
115C4×C113H(5,𝔽2)11yescharacteristic
116Dic113—22no—
117Dic113—42no—
118C2×C113—44no—
119C2×C113D4211yescharacteristic
120C2×C113#57511yescharacteristic
121C2×C113#57611yescharacteristic
122D113—42no—
123D113—82no—
124#3273—1131nomaximal, Sylow
125C113#327311yescharacteristic, complemented, Sylow
126C2×AGL(1,ℤ/8)—1132no—
127#546—1132no—
128#495—1131no—
129#468—1132no—
130#463—1132no—
131#452—1132no—
132#447—1132no—
133C4×D8D11311yescharacteristic, complemented
134#436—1131no—
135C2×#41—1132no—
136C22×D4—1132no—
137AGL(1,ℤ/8)—2268no—
138C2×Q16—1131no—
139C2×SD16—1132no—
140C2×SD16—1132no—
141C2×D8—1132no—
142C2×D8—1131no—
143C2×D8C2×D11311yescharacteristic
144C2×M16—1132no—
145#124—1132no—
146#123—2262no—
147C22⋊Q8—1132no—
148#121—1132no—
149#121—2262no—
150#120—2262no—
151C4×D4—1131no—
152C4×D4C2×D11312yescomplemented
153C2×C22⋊C4—2262no—
154#107C2×D11311yescharacteristic, complemented
155C4⋊C8—1131no—
156#103—1132no—
157#102—1132no—
158#102C2×D11312yescomplemented
159C22⋊C8—1132no—
160C4×C8C2×D11311yescharacteristic, complemented
161C24—2262no—
162#41—4522no—
163#41—2264no—
164C2×Q8—1132no—
165C2×D4—1131no—
166C2×D4—1132no—
167C2×D4—4522no—
168C2×D4—2262no—
169C2×D4—2262no—
170C2×D4—2262no—
171C2×D4—2264no—
172C2×D4C22×D11312yes—
173C22×C4—22no—
174C22×C4—1132no—
175C22×C4—2262no—
176Q16—4521no—
177SD16—2264no—
178SD16—2264no—
179D8—4521no—
180D8—2264no—
181D8D45214yescomplemented
182M16—2264no—
183C2×C8—1132no—
184C2×C8C22×D11311yescharacteristic
185C2×C8C22×D11311yescharacteristic
186C4⋊C4—1131no—
187C4⋊C4—2262no—
188C4⋊C4C22×D11312yes—
189C22⋊C4—22no—
190C22⋊C4—1132no—
191C22⋊C4—2262no—
192C22⋊C4—2262no—
193C22⋊C4—2262no—
194C22⋊C4—2262no—
195C42C22×D11311yescharacteristic
196C23—22no—
197C23—1132no—
198C23—9042no—
199C23—4524no—
200C23—4524no—
201C23—2262no—
202Q8—2262no—
203Q8—2262no—
204D4—22no—
205D4—9042no—
206D4—4521no—
207D4—4524no—
208D4—4524no—
209D4—2262no—
210D4—2262no—
211D4C2×D45214yes—
212C2×C4—22no—
213C2×C4—82no—
214C2×C4—1132no—
215C2×C4—4524no—
216C2×C4—2262no—
217C2×C4—2262no—
218C2×C4—2262no—
219C2×C4D4×D11311yescharacteristic
220C2×C4D4×D11311yescharacteristic
221C2×C4C23×D11311yescharacteristic
222C8—21no—
223C8—2262no—
224C8C2×D45212yes—
225C22—24no—
226C22—42no—
227C22—42no—
228C22—9048no—
229C22—4522no—
230C22—4522no—
231C22—4522no—
232C22—2262no—
233C22—2262no—
234C22—2262no—
235C22C2×D4×D11311yescharacteristic
236C4—21no—
237C4—21no—
238C4—42no—
239C4—4522no—
240C4—2262no—
241C4C22×D45211yescharacteristic
242C4#1681366811yescharacteristic
243C2—44no—
244C2—9042no—
245C2—4522no—
246C2D4×D45211yescharacteristic
247C2#2029939511yescharacteristic
248C2#2029939911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×D8×C113C2
socleC22×C113C22×D4
hypercenterC4×D8D113
hypocenterC113#3273
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#16813646C2semidirect
2. #20299243C2semidirect
3. #20298982C2semidirect
4. #20298845C2semidirect
5. #20298813C2semidirect
6. #20298761C2semidirect
7. #20298733C2semidirect
8. #20298677C2semidirect
9. C4×D8×C113C2semidirect
11. C2×D4×D113C22semidirect
13. C2×Dic452C22semidirect
14. C2×#14268636C22semidirect
15. C2×#14268635C22semidirect
18. C2×#14268630C22semidirect
19. #16813610C22semidirect
21. #16813602C22semidirect
27. C4⋊#11744751C22semidirect
28. #16813545C22semidirect
29. #16813542C22semidirect
30. #16813534C22semidirect
32. C4×D4×C113C22semidirect
33. #107×C113C22semidirect
34. #102×C113C22semidirect
35. C4×C8×C113C22semidirect
65. D8×C113D4semidirect
125. C113#3273semidirect
133. C4×D8D113semidirect
152. C4×D4C2×D113semidirect
154. #107C2×D113semidirect
158. #102C2×D113semidirect
160. C4×C8C2×D113semidirect
181. D8D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136462
#202992432
#202989822
#202988452
#202988132
#202987612
#202987332
#202986772
C4×D8×C1132
#3273113