Finite Group Databasebeta

← #28402370

Subgroups — #28402370

Order 14464.

476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299402C212yesmaximal, complemented
2#20299401C212yesmaximal, complemented
3#20298974C211yesmaximal, characteristic, complemented
4#20298867C212yesmaximal, complemented
5#20298866C212yesmaximal, complemented
6#20298767C212yesmaximal, complemented
7#20298765C211yesmaximal, characteristic, complemented
8#20298712C212yesmaximal, complemented
9#453×C113C211yesmaximal, characteristic, complemented
10#16813668C2212yescomplemented
11#16813667C2211yescharacteristic, complemented
12#16813650C2212yescomplemented
13#16813649—22no—
14#16813648—22no—
15#16813648C2212yescomplemented
16#16813647—22no—
17#16813647C2212yescomplemented
18#16813646—22no—
19#16813643—22no—
20#16813642—22no—
21#16813642C2212yes—
22C2×#14268632—22no—
23C2×#14268632C2212yescomplemented
24C2×#14268632C2212yescomplemented
25D8×D113—22no—
26#16813630C2212yescomplemented
27#16813629C2212yescomplemented
28#16813619C2211yescharacteristic, complemented
29#16813557C2212yescomplemented
30#16813550C2212yescomplemented
31#16813539C2211yescharacteristic, complemented
32#16813538C2212yescomplemented
33C4×#11744751C2211yescharacteristic, complemented
34H(5,𝔽2)×C113C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C113C2212yescomplemented
36#127×C113C2211yescharacteristic, complemented
37#104×C113C2212yescomplemented
38#100×C113C2211yescharacteristic, complemented
39#14268648—22no—
40#14268647—22no—
41#14268647C2312yes—
42#14268646—22no—
43C2×D452—22no—
44C2×D452—41no—
45C2×D452C2312yes—
46C2×C22⋊D113—41no—
47D4×D113—22no—
48D4×D113—22no—
49D4×D113—42no—
50#14268637D412yescomplemented
51#14268636—22no—
52#14268635—22no—
53#14268635D412yescomplemented
54#14268634—22no—
55#14268634D412yescomplemented
56D904—22no—
57#14268632—22no—
58#14268632—22no—
59#14268632—22no—
60#14268632—22no—
61#14268632—22no—
62#14268632—22no—
63#14268632D412yescomplemented
64#14268631—22no—
65#14268631C2312yes—
66#14268630—22no—
67C2×#11744751—22no—
68C2×#11744751C2312yes—
69C8×D113—22no—
70#41×C113—22no—
71#41×C113C2312yes—
72C2×D4×C113—22no—
73C2×D4×C113—41no—
74C2×D4×C113—41no—
75C2×D4×C113C2311yescharacteristic
76C2×D4×C113C2311yescharacteristic
77SD16×C113—22no—
78D8×C113—22no—
79M16×C113C2312yes—
80C42×C113C2311yescharacteristic
81C23×C113—21no—
82C23×C113—21no—
83C23×C113—41no—
84C22×D113—22no—
85C22×D113—41no—
86C22×D113—42no—
87Q8×C113C2×D412yes—
88D4×C113—22no—
89D4×C113—22no—
90D4×C113—22no—
91D4×C113—42no—
92D4×C113—82no—
93D4×C113C2×D412yes—
94C2×C4×C113—21no—
95C2×C4×C113—22no—
96C2×C4×C113—41no—
97C2×C4×C113C2411yescharacteristic
98C22⋊D113—22no—
99C22⋊D113—42no—
100C22⋊D113—42no—
101C2×Dic113—41no—
102D452—22no—
103D452—22no—
104D452—42no—
105D452—82no—
106D452C2×D412yes—
107C4×D113—22no—
108C4×D113—42no—
109Dic226C2×D412yes—
110C8×C113—22no—
111#11744751—22no—
112#11744751C2×D412yes—
113#11744751C2×D412yes—
114C22×C113—22no—
115C22×C113—41no—
116C22×C113—41no—
117C22×C113—81no—
118C22×C113—81no—
119C22×C113—161no—
120C22×C113H(5,𝔽2)11yescharacteristic
121C2×D113—22no—
122C2×D113—42no—
123C2×D113—82no—
124C2×D113—161no—
125C2×D113—162no—
126C4×C113—22no—
127C4×C113—22no—
128C4×C113C22×D412yes—
129Dic113—22no—
130C2×C113—21no—
131C2×C113—42no—
132C2×C113—81no—
133C2×C113—81no—
134C2×C113D4211yescharacteristic
135D113—42no—
136D113—82no—
137#3292—1131nomaximal, Sylow
138C113#329211yescharacteristic, complemented, Sylow
139#576—1132no—
140#576—1132no—
141#493—1131no—
142#472—1132no—
143#472—1132no—
144#453—1131no—
145#453—1132no—
146#453D11311yescharacteristic, complemented
147#443—1132no—
148H(5,𝔽2)—1132no—
149H(5,𝔽2)—1131no—
150H(5,𝔽2)C2×D11311yescharacteristic, complemented
151AGL(1,ℤ/8)—1132no—
152AGL(1,ℤ/8)—1132no—
153AGL(1,ℤ/8)—1132no—
154AGL(1,ℤ/8)—2262no—
155AGL(1,ℤ/8)—2262no—
156AGL(1,ℤ/8)—2262no—
157AGL(1,ℤ/8)—2262no—
158AGL(1,ℤ/8)C2×D11312yescomplemented
159#135—1132no—
160#135—2262no—
161#135—2262no—
162C2×D8—1132no—
163C2×D8—1132no—
164C2×D8—2262no—
165C2×D8—2262no—
166#131—1132no—
167#131—1132no—
168#127—1131no—
169#127C2×D11311yescharacteristic, complemented
170#108—1132no—
171#104—1132no—
172#104C2×D11312yescomplemented
173#100—1131no—
174#100—1132no—
175#100C2×D11311yescharacteristic, complemented
176C4×C8—1131no—
177#41—22no—
178#41—1132no—
179#41—2262no—
180#41—2262no—
181#41—2262no—
182#41C22×D11312yes—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—1132no—
187C2×D4—4521no—
188C2×D4—4522no—
189C2×D4—4521no—
190C2×D4—2262no—
191C2×D4—2262no—
192C2×D4—2262no—
193C2×D4C22×D11311yescharacteristic
194C2×D4C22×D11311yescharacteristic
195Q16—1132no—
196SD16—22no—
197SD16—1132no—
198SD16—1132no—
199SD16—2262no—
200SD16—2262no—
201SD16—2262no—
202D8—22no—
203D8—1132no—
204D8—2262no—
205D8—2262no—
206D8—2262no—
207D8—2262no—
208D8—2262no—
209D8—2262no—
210D8—2262no—
211M16—1132no—
212M16—2262no—
213M16—2262no—
214M16C22×D11312yes—
215C2×C8—1132no—
216C2×C8—2262no—
217C2×C8—2262no—
218C42C22×D11311yescharacteristic
219C23—21no—
220C23—21no—
221C23—41no—
222C23—4522no—
223C23—4521no—
224C23—2262no—
225Q8—1132no—
226Q8D4×D11312yes—
227D4—22no—
228D4—22no—
229D4—22no—
230D4—42no—
231D4—82no—
232D4—1132no—
233D4—9042no—
234D4—4522no—
235D4—4522no—
236D4—4522no—
237D4—2262no—
238D4—2262no—
239D4—2262no—
240D4D4×D11312yes—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—4522no—
245C2×C4—4521no—
246C2×C4—2262no—
247C2×C4C23×D11311yescharacteristic
248C8—22no—
249C8—1132no—
250C8—1132no—
251C8—2262no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—81no—
256C22—81no—
257C22—161no—
258C22—18082no—
259C22—18081no—
260C22—9042no—
261C22—4522no—
262C22—2262no—
263C22#1681366711yescharacteristic
264C4—22no—
265C4—22no—
266C4—2262no—
267C4C2×D4×D11312yes—
268C2—21no—
269C2—42no—
270C2—81no—
271C2—81no—
272C2—9042no—
273C2—4522no—
274C2#2029923011yescharacteristic
subgroupG/H
centerC2#20299230
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#453×C113C2
socleC2×C113D42
hypercenter#453D113
hypocenterC113#3292
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #20299402C2semidirect
2. #20299401C2semidirect
3. #20298974C2semidirect
4. #20298867C2semidirect
5. #20298866C2semidirect
6. #20298767C2semidirect
7. #20298765C2semidirect
8. #20298712C2semidirect
9. #453×C113C2semidirect
10. #16813668C22semidirect
11. #16813667C22semidirect
12. #16813650C22semidirect
15. #16813648C22semidirect
17. #16813647C22semidirect
23. C2×#14268632C22semidirect
24. C2×#14268632C22semidirect
26. #16813630C22semidirect
27. #16813629C22semidirect
28. #16813619C22semidirect
29. #16813557C22semidirect
30. #16813550C22semidirect
31. #16813539C22semidirect
32. #16813538C22semidirect
33. C4×#11744751C22semidirect
34. H(5,𝔽2)×C113C22semidirect
35. AGL(1,ℤ/8)×C113C22semidirect
36. #127×C113C22semidirect
37. #104×C113C22semidirect
38. #100×C113C22semidirect
50. #14268637D4semidirect
53. #14268635D4semidirect
55. #14268634D4semidirect
63. #14268632D4semidirect
138. C113#3292semidirect
146. #453D113semidirect
150. H(5,𝔽2)C2×D113semidirect
158. AGL(1,ℤ/8)C2×D113semidirect
169. #127C2×D113semidirect
172. #104C2×D113semidirect
175. #100C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994022
#202994012
#202989742
#202988672
#202988662
#202987672
#202987652
#202987122
#453×C1132
#3292113