Finite Group Databasebeta

← #28402369

Subgroups — #28402369

Order 14464.

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

normal subgroups only

This group has 460 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#20299409C212yesmaximal, complemented
2#20299408C212yesmaximal, complemented
3#20298970C211yesmaximal, characteristic, complemented
4#20298860C212yesmaximal, complemented
5#20298859C212yesmaximal, complemented
6#20298782C212yesmaximal, complemented
7#20298765C211yesmaximal, characteristic, complemented
8#20298712C212yesmaximal, complemented
9#453×C113C211yesmaximal, characteristic, complemented
10#16813669C2212yes—
11#16813667C2211yescharacteristic, complemented
12#16813655C2212yescomplemented
13#16813652—22no—
14#16813652C2212yescomplemented
15#16813651—22no—
16#16813648—22no—
17#16813648C2212yes—
18#16813646—22no—
19#16813642—22no—
20#16813642C2212yes—
21#16813641—22no—
22C2×#14268635—22no—
23C2×#14268635C2212yescomplemented
24C2×#14268635C2212yescomplemented
25SD16×D113—22no—
26#16813630C2212yescomplemented
27#16813629C2212yescomplemented
28#16813622C2211yescharacteristic, complemented
29#16813557C2212yescomplemented
30#16813550C2212yescomplemented
31#16813540C2212yescomplemented
32#16813539C2211yescharacteristic, complemented
33C4×#11744751C2211yescharacteristic, complemented
34H(5,𝔽2)×C113C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C113C2212yes—
36#127×C113C2211yescharacteristic
37#104×C113C2212yescomplemented
38#100×C113C2211yescharacteristic, complemented
39#14268647—22no—
40#14268647C2312yes—
41#14268646—22no—
42#14268646—22no—
43#14268646—42no—
44C2×Dic226—22no—
45C2×Dic226C2312yes—
46Q8×D113—22no—
47C2×C22⋊D113—41no—
48D4×D113—22no—
49Dic452—22no—
50#14268637—22no—
51#14268637D412yescomplemented
52#14268636—22no—
53#14268635—22no—
54#14268635—22no—
55#14268635—22no—
56#14268635—22no—
57#14268635—22no—
58#14268635—22no—
59#14268635D412yescomplemented
60#14268634D412yescomplemented
61#14268632—22no—
62#14268632D412yescomplemented
63#14268631—22no—
64#14268631C2312yes—
65#14268630—22no—
66C2×#11744751—22no—
67C2×#11744751C2312yes—
68C8×D113—22no—
69C4⋊Dic113—41no—
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—41no—
85Q8×C113C2×D412yes—
86D4×C113—22no—
87D4×C113—22no—
88D4×C113—22no—
89D4×C113—42no—
90D4×C113—82no—
91D4×C113C2×D412yes—
92C2×C4×C113—21no—
93C2×C4×C113—22no—
94C2×C4×C113—41no—
95C2×C4×C113C2411yescharacteristic
96C22⋊D113—22no—
97C22⋊D113—42no—
98C22⋊D113—42no—
99C2×Dic113—22no—
100C2×Dic113—41no—
101C2×Dic113—42no—
102D452C2×D412yes—
103C4×D113—22no—
104C4×D113—42no—
105Dic226—22no—
106Dic226—22no—
107Dic226—42no—
108Dic226C2×D412yes—
109C8×C113—22no—
110#11744751—22no—
111#11744751C2×D412yes—
112#11744751C2×D412yes—
113C22×C113—22no—
114C22×C113—41no—
115C22×C113—41no—
116C22×C113—81no—
117C22×C113—81no—
118C22×C113—161no—
119C22×C113H(5,𝔽2)11yescharacteristic
120C2×D113—22no—
121C2×D113—161no—
122C4×C113—22no—
123C4×C113—22no—
124C4×C113C22×D412yes—
125Dic113—22no—
126Dic113—42no—
127C2×C113—21no—
128C2×C113—42no—
129C2×C113—81no—
130C2×C113—81no—
131C2×C113D4211yescharacteristic
132D113—42no—
133#3291—1131nomaximal, Sylow
134C113#329111yescharacteristic, complemented, Sylow
135#577—1132no—
136#577—1132no—
137#492—1131no—
138#471—1132no—
139#471—1132no—
140#456—1132no—
141#453—1131no—
142#453D11311yescharacteristic, complemented
143#443—1132no—
1442−1+4—1132no—
145H(5,𝔽2)—1131no—
146H(5,𝔽2)C2×D11311yescharacteristic, complemented
147#137—1132no—
148#137—1132no—
149#137—2262no—
150#137—2262no—
151AGL(1,ℤ/8)—1132no—
152AGL(1,ℤ/8)—2262no—
153AGL(1,ℤ/8)—2262no—
154AGL(1,ℤ/8)C2×D11312yes—
155#135—1132no—
156#135—2262no—
157#135—2262no—
158C2×SD16—1132no—
159C2×SD16—1132no—
160C2×SD16—2262no—
161C2×SD16—2262no—
162#131—1132no—
163#131—1132no—
164C4⋊Q8—1131no—
165#127C2×D11311yescharacteristic
166#108—1132no—
167#104—1132no—
168#104C2×D11312yescomplemented
169#101—1132no—
170#100—1131no—
171#100C2×D11311yescharacteristic, complemented
172C4×C8—1131no—
173#41—22no—
174#41—1132no—
175#41—4522no—
176#41—2262no—
177#41—2262no—
178#41—2262no—
179#41C22×D11312yes—
180C2×Q8—1132no—
181C2×Q8—2262no—
182C2×Q8—2262no—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—4521no—
187C2×D4—2262no—
188C2×D4C22×D11311yescharacteristic
189C2×D4C22×D11311yescharacteristic
190Q16—1132no—
191Q16—2262no—
192Q16—2262no—
193SD16—22no—
194SD16—1132no—
195SD16—1132no—
196SD16—2262no—
197SD16—2262no—
198SD16—2262no—
199SD16—2262no—
200SD16—2262no—
201SD16—2262no—
202SD16—2262no—
203D8—22no—
204D8—1132no—
205D8—2262no—
206M16—1132no—
207M16—2262no—
208M16—2262no—
209M16C22×D11312yes—
210C2×C8—1132no—
211C2×C8—2262no—
212C2×C8—2262no—
213C4⋊C4—4521no—
214C42C22×D11311yescharacteristic
215C23—21no—
216C23—21no—
217C23—41no—
218C23—4521no—
219Q8—1132no—
220Q8—4522no—
221Q8—2262no—
222Q8—2262no—
223Q8D4×D11312yes—
224D4—22no—
225D4—22no—
226D4—22no—
227D4—42no—
228D4—82no—
229D4—1132no—
230D4—4522no—
231D4—4522no—
232D4—2262no—
233D4D4×D11312yes—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—4522no—
238C2×C4—4522no—
239C2×C4—4521no—
240C2×C4—2262no—
241C2×C4—2262no—
242C2×C4C23×D11311yescharacteristic
243C8—22no—
244C8—1132no—
245C8—1132no—
246C8—2262no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—161no—
253C22—18081no—
254C22—2262no—
255C22#1681366711yescharacteristic
256C4—22no—
257C4—22no—
258C4—4522no—
259C4—2262no—
260C4C2×D4×D11312yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—81no—
265C2—4522no—
266C2#2029923011yescharacteristic
subgroupG/H
centerC2#20299230
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#453×C113C2
socleC2×C113D42
hypercenter#453D113
hypocenterC113#3291
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. #20299409C2semidirect
2. #20299408C2semidirect
3. #20298970C2semidirect
4. #20298860C2semidirect
5. #20298859C2semidirect
6. #20298782C2semidirect
7. #20298765C2semidirect
8. #20298712C2semidirect
9. #453×C113C2semidirect
11. #16813667C22semidirect
12. #16813655C22semidirect
14. #16813652C22semidirect
23. C2×#14268635C22semidirect
24. C2×#14268635C22semidirect
26. #16813630C22semidirect
27. #16813629C22semidirect
28. #16813622C22semidirect
29. #16813557C22semidirect
30. #16813550C22semidirect
31. #16813540C22semidirect
32. #16813539C22semidirect
33. C4×#11744751C22semidirect
34. H(5,𝔽2)×C113C22semidirect
37. #104×C113C22semidirect
38. #100×C113C22semidirect
51. #14268637D4semidirect
59. #14268635D4semidirect
60. #14268634D4semidirect
62. #14268632D4semidirect
134. C113#3291semidirect
142. #453D113semidirect
146. H(5,𝔽2)C2×D113semidirect
168. #104C2×D113semidirect
171. #100C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994092
#202994082
#202989702
#202988602
#202988592
#202987822
#202987652
#202987122
#453×C1132
#3291113