Finite Group Databasebeta

← #28399948

Subgroups — #28399948

Order 14464.

736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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#20299434C211yesmaximal, characteristic, complemented
2C2×#16813650C212yesmaximal, complemented
3#20299162C211yesmaximal, characteristic, complemented
4#20298773C214yesmaximal, complemented
5#20298768C214yesmaximal, complemented
6#20298614C212yesmaximal, complemented
7#413×C113C211yesmaximal, characteristic, complemented
8#16813670C2212yescomplemented
9#16813669—22no—
10#16813668—22no—
11#16813667—22no—
12#16813667C2212yescomplemented
13C2×#14268647—22no—
14C2×#14268647C2212yes—
15#41×D113—24no—
16C22×D452C2211yescharacteristic, complemented
17#16813650—24no—
18#16813650C2218yescomplemented
19C2×#14268636—22no—
20C2×D904—22no—
21#16813618C2212yescomplemented
22#16813611C2212yescomplemented
23#16813596—22no—
24#16813590—22no—
25#16813581C2211yescharacteristic, complemented
26#16813548C2218yescomplemented
27C2×#41×C113C2211yescharacteristic
28C2×M16×C113C2212yescomplemented
29#101×C113C2212yescomplemented
30#100×C113C2212yescomplemented
31C23×D113—21no—
32#14268648—24no—
33#14268647—24no—
34#14268647—24no—
35#14268647—22no—
36#14268647—24no—
37#14268647—22no—
38#14268647D414yescomplemented
39#14268647C2314yes—
40#14268646—28no—
41#14268646—24no—
42C2×Dic226—22no—
43C2×Dic226D412yescomplemented
44Q8×D113—24no—
45C2×D452—22no—
46C2×D452—22no—
47C2×D452—22no—
48C2×D452—21no—
49C2×D452D412yescomplemented
50C2×D452C2312yes—
51C2×C22⋊D113—24no—
52C2×C22⋊D113—22no—
53C2×C22⋊D113—24no—
54D4×D113—28no—
55D4×D113—24no—
56C2×C4×D113—24no—
57C2×C4×D113—22no—
58#14268636—28no—
59D904—28no—
60C4⋊Dic113—21no—
61C22⋊Dic113—21no—
62#14268624—24no—
63C4×Dic113C2312yes—
64#41×C113—22no—
65#41×C113—22no—
66C2×Q8×C113C2311yescharacteristic
67C2×D4×C113D412yes—
68C2×D4×C113C2311yescharacteristic
69C22×C4×C113D412yes—
70C22×C4×C113C2311yescharacteristic
71M16×C113—22no—
72M16×C113C2314yes—
73C2×C8×C113—22no—
74C23×C113C2×D412yes—
75C23×C113C2×D411yescharacteristic
76C22×D113—24no—
77C22×D113—22no—
78C22×D113—22no—
79C22×D113—42no—
80C22×D113—82no—
81Q8×C113—22no—
82D4×C113—24no—
83D4×C113—22no—
84C2×C4×C113—22no—
85C2×C4×C113—22no—
86C2×C4×C113C2×D412yes—
87C2×C4×C113C2×D412yes—
88C2×C4×C113C2×D412yes—
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113C2411yescharacteristic
91C22⋊D113—28no—
92C22⋊D113—24no—
93C22⋊D113—24no—
94C22⋊D113—84no—
95C2×Dic113—24no—
96C2×Dic113—22no—
97C2×Dic113—22no—
98D452—24no—
99D452—22no—
100D452—24no—
101D452—41no—
102D452—41no—
103D452C2×D414yes—
104C4×D113—28no—
105C4×D113—24no—
106C4×D113—24no—
107Dic226—24no—
108Dic226—22no—
109Dic226C2×D414yes—
110C8×C113—24no—
111C22×C113—22no—
112C22×C113—41no—
113C22×C113—42no—
114C22×C113#12012yes—
115C22×C113C22×D411yescharacteristic
116C2×D113—24no—
117C2×D113—44no—
118C2×D113—42no—
119C2×D113—82no—
120C2×D113—84no—
121C2×D113—84no—
122C4×C113—22no—
123C4×C113#12011yescharacteristic
124C4×C113#12011yescharacteristic
125C4×C113C22×D412yes—
126Dic113—24no—
127Dic113—42no—
128C2×C113—21no—
129C2×C113—22no—
130C2×C113—42no—
131C2×C113C2×#12011yescharacteristic
132D113—44no—
133D113—82no—
134#3021—1131nomaximal, Sylow
135C113#302111yescharacteristic, complemented, Sylow
136#585—1131no—
137C2×AGL(1,ℤ/8)—1132no—
138#535—1131no—
139#454—1134no—
140#453—1134no—
141#421—1132no—
142#413D11311yescharacteristic, complemented
1432−1+4—1132no—
1442−1+4—2262no—
145H(5,𝔽2)—1132no—
146H(5,𝔽2)—2262no—
147H(5,𝔽2)—2262no—
148C2×#41—1132no—
149C2×#41—2264no—
150C2×#41—2262no—
151C2×#41C2×D11311yescharacteristic
152C22×D4—1131no—
153AGL(1,ℤ/8)—1138no—
154AGL(1,ℤ/8)—2264no—
155C2×SD16—2262no—
156C2×D8—2262no—
157C2×M16C2×D11312yescomplemented
158#127—1132no—
159#124—1132no—
160#121—2262no—
161#120—2262no—
162#117—1131no—
163#104—1138no—
164#101C2×D11312yescomplemented
165#100C2×D11312yescomplemented
166C24—2261no—
167#41—22no—
168#41—22no—
169#41—1134no—
170#41—1134no—
171#41—2264no—
172#41—2264no—
173#41—2264no—
174#41—2268no—
175#41—2264no—
176#41—2262no—
177#41—2262no—
178#41—2264no—
179C2×Q8—1132no—
180C2×Q8—2262no—
181C2×Q8—2264no—
182C2×Q8C22×D11311yescharacteristic
183C2×D4—1132no—
184C2×D4—1132no—
185C2×D4—2262no—
186C2×D4—2264no—
187C2×D4—2268no—
188C2×D4—2264no—
189C2×D4—2262no—
190C2×D4—2264no—
191C2×D4—2262no—
192C2×D4—2262no—
193C2×D4—2261no—
194C2×D4D45212yes—
195C2×D4C22×D11311yescharacteristic
196C22×C4—2264no—
197C22×C4—2262no—
198C22×C4D45212yes—
199C22×C4C22×D11311yescharacteristic
200SD16—2268no—
201D8—2268no—
202M16—22no—
203M16C22×D11314yes—
204C2×C8—22no—
205C4⋊C4—2261no—
206C22⋊C4—2261no—
207C22⋊C4—2264no—
208C42—1132no—
209C23—9042no—
210C23—4522no—
211C23—2264no—
212C23—2262no—
213C23—2262no—
214C23C2×D45212yes—
215C23C2×D45211yescharacteristic
216Q8—22no—
217Q8—1134no—
218Q8—2264no—
219Q8—2262no—
220D4—24no—
221D4—22no—
222D4—1134no—
223D4—9044no—
224D4—4521no—
225D4—4521no—
226D4—2264no—
227D4—2268no—
228D4—2264no—
229D4—2264no—
230D4—2262no—
231D4—2264no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—2268no—
235C2×C4—2262no—
236C2×C4—2264no—
237C2×C4—2262no—
238C2×C4—2264no—
239C2×C4—2264no—
240C2×C4D4×D11312yes—
241C2×C4D4×D11312yes—
242C2×C4C2×D45212yes—
243C2×C4C2×D45211yescharacteristic
244C2×C4C23×D11311yescharacteristic
245C8—24no—
246C22—22no—
247C22—41no—
248C22—42no—
249C22—9044no—
250C22—9042no—
251C22—9044no—
252C22—4524no—
253C22—4522no—
254C22—2264no—
255C22#1681359212yes—
256C22C22×D45211yescharacteristic
257C4—22no—
258C4—4522no—
259C4—2264no—
260C4#1681359211yescharacteristic
261C4#1681359211yescharacteristic
262C4C2×D4×D11312yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—9042no—
267C2—4524no—
268C2C2×#1681359211yescharacteristic
subgroupG/H
centerC2C2×#16813592
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#413×C113C2
socleC2×C113C2×#120
hypercenter#413D113
hypocenterC113#3021
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #20299434C2semidirect
2. C2×#16813650C2semidirect
3. #20299162C2semidirect
4. #20298773C2semidirect
5. #20298768C2semidirect
6. #20298614C2semidirect
7. #413×C113C2semidirect
8. #16813670C22semidirect
12. #16813667C22semidirect
16. C22×D452C22semidirect
18. #16813650C22semidirect
21. #16813618C22semidirect
22. #16813611C22semidirect
25. #16813581C22semidirect
26. #16813548C22semidirect
28. C2×M16×C113C22semidirect
29. #101×C113C22semidirect
30. #100×C113C22semidirect
38. #14268647D4semidirect
43. C2×Dic226D4semidirect
49. C2×D452D4semidirect
135. C113#3021semidirect
142. #413D113semidirect
157. C2×M16C2×D113semidirect
164. #101C2×D113semidirect
165. #100C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994342
C2×#168136502
#202991622
#202987732
#202987682
#202986142
#413×C1132
#3021113