Finite Group Databasebeta

← #28402190

Subgroups — #28402190

Order 14464.

556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#16813648C212yesmaximal, complemented
2#20299269C211yesmaximal, characteristic, complemented
3#20298974C211yesmaximal, characteristic, complemented
4#20298849C212yesmaximal, complemented
5#20298795C211yesmaximal, characteristic, complemented
6#20298793C211yesmaximal, characteristic, complemented
7#20298741C212yesmaximal, complemented
8#20298732C212yesmaximal, complemented
9C4×#14268635C211yesmaximal, characteristic, complemented
10#20298676C211yesmaximal, characteristic, complemented
11D42×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2212yescomplemented
13#16813648—28no—
14C2×#14268635C2211yescharacteristic
15C2×#14268635C2212yescomplemented
16C2×#14268632C2212yes—
17C2×#14268632C2212yescomplemented
18C2×#14268632C2212yescomplemented
19C2×#14268631C2212yescomplemented
20#16813619C2211yescharacteristic, complemented
21#16813618—21no—
22#16813596C2212yescomplemented
23#16813595—22no—
24C4×Dic226C2211yescharacteristic, complemented
25#16813584—21no—
26#16813553C2211yescharacteristic, complemented
27C4⋊#11744751C2211yescharacteristic, complemented
28#16813545C2211yescharacteristic, complemented
29#16813543C2211yescharacteristic
30#16813543C2212yescomplemented
31#16813542C2212yescomplemented
32C22⋊#11744751C2212yescomplemented
33C4×#11744751C2211yescharacteristic, complemented
34C22×D4×C113—21no—
35C22×D4×C113C2212yes—
36#127×C113C2211yescharacteristic
37#121×C113—21no—
38#121×C113C2212yes—
39#120×C113—22no—
40C4×D4×C113C2211yescharacteristic
41C4×D4×C113C2211yescharacteristic
42#14268647—24no—
43#14268647—42no—
44C2×Dic226C2311yescharacteristic
45C2×D452—21no—
46C2×D452—21no—
47C2×D452C2312yes—
48C2×C22⋊D113—22no—
49C2×C22⋊D113—22no—
50C2×C4×D113—22no—
51#14268635—24no—
52#14268635D414yescomplemented
53#14268632—24no—
54#14268632—24no—
55#14268632—42no—
56#14268631—24no—
57C2×#11744751C2312yes—
58C2×#11744751C2311yescharacteristic
59C2×#11744751C2311yescharacteristic
60C4⋊Dic113C2311yescharacteristic
61#14268626—21no—
62#14268624—22no—
63C4×Dic113—21no—
64C24×C113—22no—
65C2×D4×C113—24no—
66C2×D4×C113—22no—
67C2×D4×C113—22no—
68C2×D4×C113—21no—
69C2×D4×C113—21no—
70C2×D4×C113—42no—
71C2×D4×C113—44no—
72C2×D4×C113D411yescharacteristic
73C2×D4×C113C2312yes—
74C2×D4×C113C2311yescharacteristic
75C22×C4×C113—21no—
76C22×C4×C113C2312yes—
77C4⋊C4×C113D411yescharacteristic
78C4⋊C4×C113C2311yescharacteristic
79C22⋊C4×C113—21no—
80C22⋊C4×C113—22no—
81C22⋊C4×C113D412yes—
82C42×C113C2311yescharacteristic
83C23×C113—21no—
84C23×C113—22no—
85C23×C113—44no—
86C23×C113—44no—
87C23×C113—82no—
88C23×C113C2×D412yes—
89C22×D113—22no—
90D4×C113—22no—
91D4×C113—22no—
92D4×C113—21no—
93D4×C113—22no—
94D4×C113—44no—
95D4×C113—44no—
96D4×C113—42no—
97D4×C113—81no—
98D4×C113C2×D412yes—
99C2×C4×C113—22no—
100C2×C4×C113—22no—
101C2×C4×C113—21no—
102C2×C4×C113—42no—
103C2×C4×C113C2×D411yescharacteristic
104C2×C4×C113C2×D412yes—
105C2×C4×C113C2×D411yescharacteristic
106C2×C4×C113C2411yescharacteristic
107C22⋊D113—44no—
108C22⋊D113—82no—
109C2×Dic113—21no—
110C2×Dic113—21no—
111D452—22no—
112D452—22no—
113D452—42no—
114D452—81no—
115C4×D113—44no—
116Dic226—21no—
117Dic226C2×D412yescomplemented
118#11744751—22no—
119#11744751—21no—
120#11744751C2×D412yescomplemented
121C22×C113—22no—
122C22×C113—22no—
123C22×C113—22no—
124C22×C113—22no—
125C22×C113—41no—
126C22×C113—41no—
127C22×C113—42no—
128C22×C113—42no—
129C22×C113—42no—
130C22×C113—88no—
131C22×C113C22×D411yescharacteristic
132C2×D113—42no—
133C2×D113—42no—
134C2×D113—42no—
135C4×C113—22no—
136C4×C113—21no—
137C4×C113—41no—
138C4×C113AGL(1,ℤ/8)12yescomplemented
139C4×C113C22×D411yescharacteristic
140C4×C113H(5,𝔽2)11yescharacteristic
141Dic113—22no—
142Dic113—41no—
143C2×C113—42no—
144C2×C113—42no—
145C2×C113—82no—
146C2×C113D4211yescharacteristic
147C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C113#57611yescharacteristic
149D113—82no—
150#3274—1131nomaximal, Sylow
151C113#327411yescharacteristic, complemented, Sylow
152C2×AGL(1,ℤ/8)—1132no—
153#550—1131no—
154D42D11311yescharacteristic, complemented
155#493—1131no—
156#469—1132no—
157#460—1131no—
158#459—1131no—
159#449—1132no—
160#447—1132no—
161C4×SD16—1131no—
162#436—1131no—
163C2×#41—1132no—
164C22×D4—21no—
165C22×D4C2×D11312yes—
166AGL(1,ℤ/8)—2268no—
167C2×SD16—1131no—
168C2×SD16—1132no—
169C2×D8—1132no—
170C2×D8—1132no—
171C2×D8—1132no—
172C2×M16—1132no—
173#127—1131no—
174#127—2261no—
175#127C2×D11311yescharacteristic
176#121—21no—
177#121—1132no—
178#121—2262no—
179#121C2×D11312yes—
180#120—22no—
181C4×Q8—1131no—
182C4×D4—2261no—
183C4×D4C2×D11311yescharacteristic
184C4×D4C2×D11311yescharacteristic
185#106—1131no—
186C4⋊C8—1131no—
187#103—1131no—
188#102—1131no—
189#102—1132no—
190#102—1132no—
191C22⋊C8—1132no—
192C4×C8—1131no—
193C24—22no—
194#41—4522no—
195#41—2264no—
196C2×Q8—1131no—
197C2×D4—24no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—21no—
202C2×D4—42no—
203C2×D4—44no—
204C2×D4—1132no—
205C2×D4—2262no—
206C2×D4—2262no—
207C2×D4—2261no—
208C2×D4—2261no—
209C2×D4C22⋊D11311yescharacteristic
210C2×D4C22×D11312yes—
211C2×D4C22×D11311yescharacteristic
212C22×C4—21no—
213C22×C4—2262no—
214C22×C4C22×D11312yes—
215SD16—1134no—
216SD16—2264no—
217D8—4522no—
218D8—2264no—
219D8—2264no—
220M16—2264no—
221C2×C8—1131no—
222C2×C8—1131no—
223C2×C8—1132no—
224C4⋊C4—1131no—
225C4⋊C4—2261no—
226C4⋊C4C22⋊D11311yescharacteristic
227C4⋊C4C22×D11311yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—22no—
230C22⋊C4—2262no—
231C22⋊C4C22⋊D11312yes—
232C42—2261no—
233C42C22×D11311yescharacteristic
234C23—21no—
235C23—22no—
236C23—44no—
237C23—44no—
238C23—82no—
239C23—2262no—
240C23C2×C22⋊D11312yes—
241Q8—1132no—
242Q8—2261no—
243D4—22no—
244D4—22no—
245D4—21no—
246D4—22no—
247D4—44no—
248D4—44no—
249D4—42no—
250D4—81no—
251D4—9041no—
252D4—9042no—
253D4—4524no—
254D4—4522no—
255D4—2262no—
256D4—2262no—
257D4D4×D11312yes—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—4524no—
263C2×C4—2261no—
264C2×C4—2261no—
265C2×C4C2×C22⋊D11311yescharacteristic
266C2×C4C2×C22⋊D11312yes—
267C2×C4C2×C22⋊D11311yescharacteristic
268C2×C4C23×D11311yescharacteristic
269C8—1132no—
270C8—2262no—
271C8—2261no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—88no—
282C22—4522no—
283C22—4522no—
284C22—4522no—
285C22C22×C22⋊D11311yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—4521no—
290C4—2262no—
291C4#1681364812yescomplemented
292C4C2×D4×D11311yescharacteristic
293C4#1681366711yescharacteristic
294C2—42no—
295C2—42no—
296C2—82no—
297C2—9042no—
298C2D4×C22⋊D11311yescharacteristic
299C2C2×#1681364811yescharacteristic
300C2#2029940111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingD42×C113C2
socleC22×C113C22×D4
hypercenterD42D113
hypocenterC113#3274
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. #20299269C2semidirect
3. #20298974C2semidirect
4. #20298849C2semidirect
5. #20298795C2semidirect
6. #20298793C2semidirect
7. #20298741C2semidirect
8. #20298732C2semidirect
9. C4×#14268635C2semidirect
10. #20298676C2semidirect
11. D42×C113C2semidirect
12. C2×#14268647C22semidirect
15. C2×#14268635C22semidirect
17. C2×#14268632C22semidirect
18. C2×#14268632C22semidirect
19. C2×#14268631C22semidirect
20. #16813619C22semidirect
22. #16813596C22semidirect
24. C4×Dic226C22semidirect
26. #16813553C22semidirect
27. C4⋊#11744751C22semidirect
28. #16813545C22semidirect
30. #16813543C22semidirect
31. #16813542C22semidirect
32. C22⋊#11744751C22semidirect
33. C4×#11744751C22semidirect
52. #14268635D4semidirect
117. Dic226C2×D4semidirect
120. #11744751C2×D4semidirect
138. C4×C113AGL(1,ℤ/8)semidirect
151. C113#3274semidirect
154. D42D113semidirect
291. C4#16813648semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
#202992692
#202989742
#202988492
#202987952
#202987932
#202987412
#202987322
C4×#142686352
#202986762
D42×C1132
#3274113