Finite Group Databasebeta

← #28402372

Subgroups — #28402372

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#20299403C211yesmaximal, characteristic, complemented
2#20299402C212yesmaximal, complemented
3#20299399C211yesmaximal, characteristic, complemented
4#20298973C211yesmaximal, characteristic, complemented
5#20298869C211yesmaximal, characteristic, complemented
6#20298867C212yesmaximal, complemented
7#20298768C212yesmaximal, complemented
8#20298764C212yesmaximal, complemented
9#20298714C211yesmaximal, characteristic, complemented
10#20298713C211yesmaximal, characteristic, complemented
11#472×C113C211yesmaximal, characteristic, complemented
12#16813668C2212yescomplemented
13#16813667C2212yescomplemented
14#16813650—22no—
15#16813650C2212yescomplemented
16#16813650C2212yescomplemented
17#16813649—22no—
18#16813648C2212yescomplemented
19#16813646—22no—
20#16813646—22no—
21#16813644—21no—
22#16813644C2211yescharacteristic
23#16813643—22no—
24#16813642C2211yescharacteristic
25#16813641—21no—
26C2×D904—21no—
27C2×D904C2211yescharacteristic, complemented
28C2×#14268632C2212yescomplemented
29D8×D113—21no—
30D8×D113—22no—
31#16813630C2212yescomplemented
32#16813628C2211yescharacteristic, complemented
33#16813618C2212yescomplemented
34#16813557C2211yescharacteristic, complemented
35#16813549C2211yescharacteristic, complemented
36#16813548C2212yescomplemented
37#16813548C2211yescharacteristic, complemented
38#16813538C2212yescomplemented
39C8×Dic113C2211yescharacteristic, complemented
40AGL(1,ℤ/8)×C113C2212yescomplemented
41C2×D8×C113C2211yescharacteristic, complemented
42#131×C113C2211yescharacteristic, complemented
43#108×C113C2211yescharacteristic, complemented
44#100×C113C2212yescomplemented
45#14268648—22no—
46#14268647—22no—
47#14268647C2311yescharacteristic
48#14268647C2312yes—
49#14268646—22no—
50#14268646—22no—
51C2×D452—22no—
52C2×D452C2312yes—
53C2×C22⋊D113—42no—
54C2×C22⋊D113—42no—
55D4×D113—22no—
56D4×D113—22no—
57D4×D113—22no—
58D4×D113—42no—
59Dic452D411yescharacteristic, complemented
60#14268637D411yescharacteristic, complemented
61#14268636—22no—
62#14268636—22no—
63#14268636D412yescomplemented
64#14268635—22no—
65#14268635D411yescharacteristic, complemented
66#14268634D411yescharacteristic, complemented
67D904—22no—
68D904—22no—
69D904—21no—
70D904—21no—
71D904D411yescharacteristic, complemented
72#14268632—22no—
73#14268632—22no—
74#14268632—22no—
75#14268632D411yescharacteristic, complemented
76#14268631C2311yescharacteristic
77#14268630—21no—
78#14268630—22no—
79C2×#11744751C2311yescharacteristic
80C8×D113—21no—
81C8×D113—22no—
82C4×Dic113C2311yescharacteristic
83#41×C113C2311yescharacteristic
84C2×D4×C113C2312yes—
85SD16×C113—22no—
86D8×C113—22no—
87D8×C113—21no—
88D8×C113—21no—
89M16×C113—21no—
90M16×C113C2312yes—
91M16×C113C2311yescharacteristic
92C2×C8×C113—21no—
93C2×C8×C113C2311yescharacteristic
94C23×C113—22no—
95C22×D113—22no—
96C22×D113—42no—
97C22×D113—42no—
98Q8×C113C2×D411yescharacteristic
99D4×C113—21no—
100D4×C113—22no—
101D4×C113—22no—
102D4×C113C2×D411yescharacteristic
103C2×C4×C113—21no—
104C2×C4×C113C2411yescharacteristic
105C22⋊D113—22no—
106C22⋊D113—21no—
107C22⋊D113—42no—
108C22⋊D113—42no—
109C22⋊D113—42no—
110C22⋊D113—84no—
111C2×Dic113—21no—
112C2×Dic113—42no—
113D452—22no—
114D452—22no—
115D452—42no—
116D452C2×D412yes—
117D452C2×D411yescharacteristic
118C4×D113—21no—
119C4×D113—22no—
120C4×D113—42no—
121Dic226C2×D412yes—
122Dic226C2×D411yescharacteristic
123C8×C113—21no—
124C8×C113—22no—
125C8×C113C2×D411yescharacteristic
126C8×C113C2×D411yescharacteristic
127#11744751—21no—
128#11744751C2×D411yescharacteristic
129#11744751C2×D411yescharacteristic
130C22×C113—21no—
131C22×C113—42no—
132C22×C113—82no—
133C22×C113H(5,𝔽2)11yescharacteristic
134C2×D113—22no—
135C2×D113—21no—
136C2×D113—42no—
137C2×D113—82no—
138C2×D113—162no—
139C2×D113—162no—
140C4×C113—21no—
141C4×C113C22×D411yescharacteristic
142C4×C113C22×D411yescharacteristic
143Dic113—22no—
144Dic113—22no—
145Dic113—21no—
146C2×C113—21no—
147C2×C113—41no—
148C2×C113—82no—
149C2×C113D4211yescharacteristic
150D113—42no—
151D113—41no—
152D113—82no—
153#3292—1131nomaximal, Sylow
154C113#329211yescharacteristic, complemented, Sylow
155#576—1132no—
156#576—1131no—
157#576—1131no—
158#493—1131no—
159#472—1131no—
160#472—1132no—
161#472D11311yescharacteristic, complemented
162#453—1132no—
163#453—1132no—
164#443—1131no—
165#443—1131no—
166H(5,𝔽2)—1132no—
167H(5,𝔽2)—1132no—
168AGL(1,ℤ/8)—1132no—
169AGL(1,ℤ/8)—1132no—
170AGL(1,ℤ/8)—1132no—
171AGL(1,ℤ/8)—2262no—
172AGL(1,ℤ/8)—2262no—
173AGL(1,ℤ/8)—2262no—
174AGL(1,ℤ/8)—2262no—
175AGL(1,ℤ/8)C2×D11312yescomplemented
176#135—1131no—
177#135—1131no—
178#135—2261no—
179#135—2261no—
180#135—2262no—
181C2×D8—1132no—
182C2×D8—1131no—
183C2×D8—2261no—
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#108C2×D11311yescharacteristic, complemented
193#104—1131no—
194#104—1132no—
195#104—1131no—
196#100—1132no—
197#100C2×D11312yescomplemented
198C4×C8—1131no—
199#41—1132no—
200#41—1131no—
201#41—2262no—
202#41—2262no—
203#41—2262no—
204#41—2262no—
205#41C22×D11311yescharacteristic
206C2×D4—1132no—
207C2×D4—4522no—
208C2×D4—4522no—
209C2×D4—4522no—
210C2×D4—2262no—
211C2×D4—2262no—
212C2×D4—2262no—
213C2×D4—2262no—
214C2×D4C22×D11312yes—
215Q16—1131no—
216Q16—1131no—
217SD16—22no—
218SD16—1131no—
219SD16—1131no—
220SD16—1132no—
221SD16—2262no—
222SD16—2262no—
223SD16—2262no—
224D8—22no—
225D8—21no—
226D8—21no—
227D8—1131no—
228D8—1131no—
229D8—2262no—
230D8—2262no—
231D8—2262no—
232D8—2262no—
233D8—2262no—
234D8—2261no—
235D8—2261no—
236M16—21no—
237M16—1131no—
238M16—2262no—
239M16—2261no—
240M16C22×D11312yes—
241M16C22×D11311yescharacteristic
242C2×C8—21no—
243C2×C8—1131no—
244C2×C8—2262no—
245C2×C8—2261no—
246C2×C8C22×D11311yescharacteristic
247C42—1131no—
248C23—22no—
249C23—4522no—
250C23—4522no—
251C23—2262no—
252Q8—1131no—
253Q8—1132no—
254Q8D4×D11311yescharacteristic
255D4—21no—
256D4—22no—
257D4—22no—
258D4—1131no—
259D4—1132no—
260D4—9044no—
261D4—4522no—
262D4—4522no—
263D4—4522no—
264D4—4522no—
265D4—2262no—
266D4—2261no—
267D4—2262no—
268D4—2262no—
269D4D4×D11311yescharacteristic
270C2×C4—21no—
271C2×C4—4522no—
272C2×C4—4522no—
273C2×C4—2261no—
274C2×C4—2262no—
275C2×C4—2261no—
276C2×C4C23×D11311yescharacteristic
277C8—21no—
278C8—22no—
279C8—1131no—
280C8—1131no—
281C8—2261no—
282C8D4×D11311yescharacteristic
283C8D4×D11311yescharacteristic
284C22—21no—
285C22—42no—
286C22—82no—
287C22—18082no—
288C22—18082no—
289C22—9042no—
290C22—4522no—
291C22—2262no—
292C22—2261no—
293C22#1681366811yescharacteristic
294C4—21no—
295C4—2262no—
296C4—2262no—
297C4—2261no—
298C4C2×D4×D11311yescharacteristic
299C4C2×D4×D11311yescharacteristic
300C2—21no—
301C2—41no—
302C2—82no—
303C2—9042no—
304C2—4522no—
305C2—4521no—
306C2#2029923211yescharacteristic
subgroupG/H
centerC2#20299232
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#472×C113C2
socleC2×C113D42
hypercenter#472D113
hypocenterC113#3292
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #20299403C2semidirect
2. #20299402C2semidirect
3. #20299399C2semidirect
4. #20298973C2semidirect
5. #20298869C2semidirect
6. #20298867C2semidirect
7. #20298768C2semidirect
8. #20298764C2semidirect
9. #20298714C2semidirect
10. #20298713C2semidirect
11. #472×C113C2semidirect
12. #16813668C22semidirect
13. #16813667C22semidirect
15. #16813650C22semidirect
16. #16813650C22semidirect
18. #16813648C22semidirect
27. C2×D904C22semidirect
28. C2×#14268632C22semidirect
31. #16813630C22semidirect
32. #16813628C22semidirect
33. #16813618C22semidirect
34. #16813557C22semidirect
35. #16813549C22semidirect
36. #16813548C22semidirect
37. #16813548C22semidirect
38. #16813538C22semidirect
39. C8×Dic113C22semidirect
40. AGL(1,ℤ/8)×C113C22semidirect
41. C2×D8×C113C22semidirect
42. #131×C113C22semidirect
43. #108×C113C22semidirect
44. #100×C113C22semidirect
59. Dic452D4semidirect
60. #14268637D4semidirect
63. #14268636D4semidirect
65. #14268635D4semidirect
66. #14268634D4semidirect
71. D904D4semidirect
75. #14268632D4semidirect
154. C113#3292semidirect
161. #472D113semidirect
175. AGL(1,ℤ/8)C2×D113semidirect
186. C2×D8C2×D113semidirect
189. #131C2×D113semidirect
192. #108C2×D113semidirect
197. #100C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994032
#202994022
#202993992
#202989732
#202988692
#202988672
#202987682
#202987642
#202987142
#202987132
#472×C1132
#3292113