Finite Group Databasebeta

← #28402371

Subgroups — #28402371

Order 14464.

476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299401C212yesmaximal, complemented
2#20299400C211yesmaximal, characteristic, complemented
3#20298973C211yesmaximal, characteristic, complemented
4#20298868C211yesmaximal, characteristic, complemented
5#20298866C212yesmaximal, complemented
6#20298865C211yesmaximal, characteristic, complemented
7#20298766C212yesmaximal, complemented
8#20298764C212yesmaximal, complemented
9#20298715C211yesmaximal, characteristic, complemented
10#20298713C211yesmaximal, characteristic, complemented
11#576×C113C211yesmaximal, characteristic, complemented
12#16813668C2212yescomplemented
13#16813649—22no—
14#16813648—22no—
15#16813648C2212yescomplemented
16#16813647—22no—
17#16813647C2212yescomplemented
18#16813647C2212yescomplemented
19#16813645—21no—
20#16813642—22no—
21#16813642C2211yescharacteristic
22C2×D904C2211yescharacteristic, complemented
23C2×#14268632—22no—
24C2×#14268632C2212yescomplemented
25D8×D113—21no—
26#16813629C2212yescomplemented
27#16813628C2211yescharacteristic, complemented
28#16813618C2212yescomplemented
29#16813558C2211yescharacteristic, complemented
30#16813557C2211yescharacteristic, complemented
31#16813549C2212yescomplemented
32#16813549C2211yescharacteristic, complemented
33#16813548C2211yescharacteristic, complemented
34#16813539C2212yescomplemented
35#16813538C2212yescomplemented
36C8×Dic113C2211yescharacteristic, complemented
37H(5,𝔽2)×C113C2212yescomplemented
38AGL(1,ℤ/8)×C113—22no—
39AGL(1,ℤ/8)×C113C2212yescomplemented
40#135×C113—21no—
41#135×C113C2211yescharacteristic
42C2×D8×C113—21no—
43C2×D8×C113C2211yescharacteristic, complemented
44#131×C113C2211yescharacteristic, complemented
45#14268648—22no—
46#14268647—22no—
47#14268647C2311yescharacteristic
48C2×D452—22no—
49C2×D452C2312yes—
50C2×C22⋊D113—42no—
51D4×D113—22no—
52D4×D113—42no—
53#14268637D411yescharacteristic, complemented
54#14268635—22no—
55#14268635D411yescharacteristic, complemented
56#14268634—22no—
57#14268634—22no—
58#14268634D411yescharacteristic, complemented
59D904—21no—
60D904—21no—
61#14268632—22no—
62#14268632—22no—
63#14268632—22no—
64#14268632—22no—
65#14268632—22no—
66#14268632D411yescharacteristic, complemented
67#14268631—22no—
68#14268631C2311yescharacteristic
69#14268631C2312yes—
70#14268630—21no—
71C2×#11744751—22no—
72C2×#11744751C2311yescharacteristic
73C8×D113—21no—
74C4×Dic113C2311yescharacteristic
75#41×C113—22no—
76#41×C113—22no—
77#41×C113C2312yes—
78#41×C113C2311yescharacteristic
79C2×D4×C113—22no—
80C2×D4×C113—22no—
81C2×D4×C113—42no—
82C2×D4×C113C2312yes—
83Q16×C113D411yescharacteristic, complemented
84SD16×C113—22no—
85SD16×C113D412yescomplemented
86D8×C113—22no—
87D8×C113—21no—
88D8×C113—21no—
89D8×C113D411yescharacteristic, complemented
90M16×C113—21no—
91M16×C113C2311yescharacteristic
92C2×C8×C113—21no—
93C2×C8×C113C2311yescharacteristic
94C23×C113—22no—
95C23×C113—42no—
96C22×D113—22no—
97C22×D113—42no—
98Q8×C113C2×D411yescharacteristic
99Q8×C113C2×D412yes—
100D4×C113—21no—
101D4×C113—22no—
102D4×C113—22no—
103D4×C113—22no—
104D4×C113—42no—
105D4×C113—42no—
106D4×C113C2×D411yescharacteristic
107D4×C113C2×D412yes—
108C2×C4×C113—21no—
109C2×C4×C113—22no—
110C2×C4×C113—42no—
111C2×C4×C113C2411yescharacteristic
112C22⋊D113—21no—
113C22⋊D113—42no—
114C22⋊D113—84no—
115C2×Dic113—21no—
116D452—22no—
117D452—22no—
118D452—42no—
119D452C2×D411yescharacteristic
120C4×D113—21no—
121C4×D113—42no—
122Dic226C2×D411yescharacteristic
123C8×C113—21no—
124C8×C113C2×D411yescharacteristic
125C8×C113C2×D411yescharacteristic
126#11744751—21no—
127#11744751—22no—
128#11744751C2×D411yescharacteristic
129#11744751C2×D411yescharacteristic
130C22×C113—22no—
131C22×C113—21no—
132C22×C113—42no—
133C22×C113—82no—
134C22×C113—162no—
135C22×C113H(5,𝔽2)11yescharacteristic
136C2×D113—21no—
137C2×D113—42no—
138C2×D113—82no—
139C2×D113—162no—
140C4×C113—22no—
141C4×C113—21no—
142C4×C113C22×D411yescharacteristic
143C4×C113C22×D411yescharacteristic
144Dic113—22no—
145Dic113—21no—
146C2×C113—21no—
147C2×C113—42no—
148C2×C113—41no—
149C2×C113—82no—
150C2×C113D4211yescharacteristic
151D113—41no—
152D113—82no—
153#3292—1131nomaximal, Sylow
154C113#329211yescharacteristic, complemented, Sylow
155#576—1132no—
156#576—1131no—
157#576D11311yescharacteristic, complemented
158#493—1131no—
159#472—1132no—
160#472—1131no—
161#472—1131no—
162#453—1132no—
163#453—1132no—
164#443—1131no—
165#443—1131no—
166H(5,𝔽2)—1132no—
167H(5,𝔽2)C2×D11312yescomplemented
168AGL(1,ℤ/8)—22no—
169AGL(1,ℤ/8)—1132no—
170AGL(1,ℤ/8)—1132no—
171AGL(1,ℤ/8)—1132no—
172AGL(1,ℤ/8)—2262no—
173AGL(1,ℤ/8)—2262no—
174AGL(1,ℤ/8)—2262no—
175AGL(1,ℤ/8)C2×D11312yescomplemented
176#135—21no—
177#135—1131no—
178#135—2262no—
179#135—2261no—
180#135C2×D11311yescharacteristic
181C2×D8—21no—
182C2×D8—1132no—
183C2×D8—1131no—
184C2×D8—2262no—
185C2×D8—2261no—
186C2×D8C2×D11311yescharacteristic, complemented
187#131—1132no—
188#131—1131no—
189#131C2×D11311yescharacteristic, complemented
190#127—1132no—
191#108—1131no—
192#108—1131no—
193#104—1131no—
194#104—1132no—
195#104—1131no—
196#100—1132no—
197#100—1132no—
198C4×C8—1131no—
199#41—22no—
200#41—22no—
201#41—1131no—
202#41—2262no—
203#41—2262no—
204#41C22×D11311yescharacteristic
205#41C22×D11312yes—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4—1132no—
210C2×D4—4522no—
211C2×D4—4522no—
212C2×D4—2262no—
213C2×D4—2262no—
214C2×D4C22×D11312yes—
215Q16—1131no—
216Q16C22⋊D11311yescharacteristic, complemented
217SD16—22no—
218SD16—1131no—
219SD16—1131no—
220SD16—2262no—
221SD16—2262no—
222SD16—2262no—
223SD16C22⋊D11312yescomplemented
224D8—22no—
225D8—21no—
226D8—21no—
227D8—1131no—
228D8—2262no—
229D8—2262no—
230D8—2262no—
231D8—2262no—
232D8—2262no—
233D8—2261no—
234D8—2261no—
235D8C22⋊D11311yescharacteristic, complemented
236M16—21no—
237M16—1132no—
238M16—1131no—
239M16—2262no—
240M16—2261no—
241M16C22×D11311yescharacteristic
242C2×C8—21no—
243C2×C8—1131no—
244C2×C8—2262no—
245C2×C8—2261no—
246C2×C8C22×D11311yescharacteristic
247C42—1131no—
248C23—22no—
249C23—42no—
250C23—4522no—
251C23—2262no—
252Q8—1131no—
253Q8D4×D11311yescharacteristic
254Q8C2×C22⋊D11312yes—
255D4—21no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—1131no—
262D4—9044no—
263D4—4522no—
264D4—4522no—
265D4—2261no—
266D4—2262no—
267D4—2262no—
268D4D4×D11311yescharacteristic
269D4C2×C22⋊D11312yes—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—4522no—
274C2×C4—2261no—
275C2×C4—2261no—
276C2×C4C23×D11311yescharacteristic
277C8—21no—
278C8—1131no—
279C8—1131no—
280C8—2262no—
281C8—2261no—
282C8C2×C22⋊D11311yescharacteristic
283C8C2×C22⋊D11311yescharacteristic
284C22—21no—
285C22—22no—
286C22—42no—
287C22—82no—
288C22—162no—
289C22—18082no—
290C22—9042no—
291C22—4522no—
292C22—2261no—
293C22#1681366711yescharacteristic
294C4—21no—
295C4—22no—
296C4—2262no—
297C4—2261no—
298C4C2×D4×D11311yescharacteristic
299C4C22×C22⋊D11311yescharacteristic
300C2—21no—
301C2—41no—
302C2—42no—
303C2—82no—
304C2—9042no—
305C2—4521no—
306C2D4×C22⋊D11311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#576×C113C2
socleC2×C113D42
hypercenter#576D113
hypocenterC113#3292
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #20299401C2semidirect
2. #20299400C2semidirect
3. #20298973C2semidirect
4. #20298868C2semidirect
5. #20298866C2semidirect
6. #20298865C2semidirect
7. #20298766C2semidirect
8. #20298764C2semidirect
9. #20298715C2semidirect
10. #20298713C2semidirect
11. #576×C113C2semidirect
12. #16813668C22semidirect
15. #16813648C22semidirect
17. #16813647C22semidirect
18. #16813647C22semidirect
22. C2×D904C22semidirect
24. C2×#14268632C22semidirect
26. #16813629C22semidirect
27. #16813628C22semidirect
28. #16813618C22semidirect
29. #16813558C22semidirect
30. #16813557C22semidirect
31. #16813549C22semidirect
32. #16813549C22semidirect
33. #16813548C22semidirect
34. #16813539C22semidirect
35. #16813538C22semidirect
36. C8×Dic113C22semidirect
37. H(5,𝔽2)×C113C22semidirect
39. AGL(1,ℤ/8)×C113C22semidirect
43. C2×D8×C113C22semidirect
44. #131×C113C22semidirect
53. #14268637D4semidirect
55. #14268635D4semidirect
58. #14268634D4semidirect
66. #14268632D4semidirect
83. Q16×C113D4semidirect
85. SD16×C113D4semidirect
89. D8×C113D4semidirect
154. C113#3292semidirect
157. #576D113semidirect
167. H(5,𝔽2)C2×D113semidirect
175. AGL(1,ℤ/8)C2×D113semidirect
186. C2×D8C2×D113semidirect
189. #131C2×D113semidirect
216. Q16C22⋊D113semidirect
223. SD16C22⋊D113semidirect
235. D8C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202994012
#202994002
#202989732
#202988682
#202988662
#202988652
#202987662
#202987642
#202987152
#202987132
#576×C1132
#3292113