Finite Group Databasebeta

← #28402273

Subgroups — #28402273

Order 14464.

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

normal subgroups only

This group has 546 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×SD16×D113C212yesmaximal, complemented
2#20299263C211yesmaximal, characteristic, complemented
3D4×D452C211yesmaximal, characteristic
4#20298972C211yesmaximal, characteristic, complemented
5#20298830C212yesmaximal, complemented
6#20298799C211yesmaximal, characteristic, complemented
7#20298747C212yesmaximal, complemented
8#20298738C212yesmaximal, complemented
9C4×#14268635C211yesmaximal, characteristic, complemented
10#20298663C211yesmaximal, characteristic, complemented
11#461×C113C211yesmaximal, characteristic, complemented
12C2×Q8×D113C2212yescomplemented
13C22×D452—21no—
14C2×D4×D113C2212yes—
15C2×#14268636C2212yescomplemented
16C2×#14268635C2211yescharacteristic
17C2×#14268634C2212yescomplemented
18C2×#14268634C2212yescomplemented
19SD16×D113—28no—
20C2×C8×D113C2212yescomplemented
21#16813621—21no—
22#16813619C2211yescharacteristic
23#16813600—22no—
24#16813598C2212yescomplemented
25#16813597C2212yes—
26#16813596—21no—
27#16813592—22no—
28C4×Dic226C2211yescharacteristic, complemented
29C4×D452C2211yescharacteristic
30#16813584—21no—
31#16813553C2211yescharacteristic, complemented
32#16813545C2211yescharacteristic, complemented
33#16813544C2212yescomplemented
34#16813543C2211yescharacteristic
35#16813534C2212yescomplemented
36C4×#11744751C2211yescharacteristic, complemented
37C2×SD16×C113C2212yes—
38C4⋊Q8×C113C2211yescharacteristic, complemented
39C4×D4×C113C2211yescharacteristic
40C4⋊C8×C113C2211yescharacteristic, complemented
41#103×C113C2212yescomplemented
42C23×D113—22no—
43C2×Dic226—22no—
44C2×Dic226C2311yescharacteristic
45Q8×D113—24no—
46Q8×D113—42no—
47C2×D452—22no—
48C2×D452—21no—
49C2×D452—21no—
50C2×D452—44no—
51C2×D452D411yescharacteristic
52C2×D452C2312yes—
53C2×C22⋊D113—22no—
54D4×D113—24no—
55D4×D113—42no—
56C2×C4×D113—22no—
57C2×C4×D113C2312yes—
58#14268636—24no—
59#14268635D414yescomplemented
60#14268634—24no—
61#14268634—42no—
62C2×#11744751C2311yescharacteristic
63C2×#11744751C2311yescharacteristic
64C8×D113—24no—
65C4⋊Dic113D411yescharacteristic
66C4⋊Dic113C2311yescharacteristic
67#14268626—21no—
68#14268626—22no—
69#14268624—22no—
70#14268624—22no—
71#14268624D412yes—
72C4×Dic113—21no—
73C2×Q8×C113C2312yes—
74C2×D4×C113C2311yescharacteristic
75C22×C4×C113—21no—
76SD16×C113—24no—
77C2×C8×C113C2312yes—
78C4⋊C4×C113—21no—
79C4⋊C4×C113—21no—
80C4⋊C4×C113C2311yescharacteristic
81C22⋊C4×C113—21no—
82C42×C113C2311yescharacteristic
83C23×C113—21no—
84C22×D113—22no—
85C22×D113—44no—
86C22×D113—44no—
87C22×D113—82no—
88C22×D113C2×D412yes—
89Q8×C113—22no—
90Q8×C113—22no—
91D4×C113—21no—
92D4×C113C2×D412yes—
93C2×C4×C113—21no—
94C2×C4×C113—22no—
95C2×C4×C113—42no—
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2411yescharacteristic
99C22⋊D113—44no—
100C2×Dic113—21no—
101C2×Dic113—21no—
102C2×Dic113C2×D412yes—
103D452—22no—
104D452—22no—
105D452—44no—
106D452—42no—
107D452—81no—
108D452SD1614yescomplemented
109C4×D113—22no—
110C4×D113—22no—
111C4×D113—44no—
112Dic226—21no—
113Dic226—44no—
114Dic226C2×D412yescomplemented
115C8×C113—22no—
116#11744751—21no—
117#11744751C2×D412yescomplemented
118C22×C113—22no—
119C22×C113—41no—
120C22×C113—41no—
121C22×C113C22×D411yescharacteristic
122C2×D113—22no—
123C2×D113—22no—
124C2×D113—42no—
125C2×D113—42no—
126C2×D113—42no—
127C2×D113—88no—
128C2×D113C2×SD1614yescomplemented
129C4×C113—21no—
130C4×C113—42no—
131C4×C113—41no—
132C4×C113C2×SD1612yescomplemented
133C4×C113C22×D411yescharacteristic
134C4×C113H(5,𝔽2)11yescharacteristic
135Dic113—22no—
136Dic113—22no—
137Dic113—41no—
138C2×C113—42no—
139C2×C113D4211yescharacteristic
140C2×C113C22×SD1611yescharacteristic
141C2×C113#57711yescharacteristic
142D113—24no—
143D113—82no—
144D4×SD16—1131nomaximal, Sylow
145C113D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—1132no—
147D4×Q8—1131no—
148D42—1131no—
149#492—1131no—
150#465—1132no—
151#461D11311yescharacteristic, complemented
152#460—1131no—
153#450—1132no—
154#448—1132no—
155C4×SD16—1131no—
156C8×D4—1131no—
157C22×Q8—1132no—
158C22×D4—1132no—
159C22×D4—2261no—
160C2×SD16—1131no—
161C2×SD16—1132no—
162C2×SD16—1132no—
163C2×SD16—1132no—
164C2×SD16—2268no—
165C2×SD16C2×D11312yes—
166C22×C8—1132no—
167C4⋊Q8—2261no—
168C4⋊Q8C2×D11311yescharacteristic, complemented
169#127—1131no—
170C22⋊Q8—1132no—
171C22⋊Q8—2262no—
172#121—1132no—
173#121—2261no—
174#120—2262no—
175C4×Q8—1131no—
176C4×D4—1131no—
177C4×D4—2261no—
178C4×D4C2×D11311yescharacteristic
179#106—1131no—
180C4⋊C8C2×D11311yescharacteristic, complemented
181#103—1131no—
182#103C2×D11312yescomplemented
183#102—1131no—
184#102—1132no—
185C22⋊C8—1132no—
186C4×C8—1131no—
187C24—2262no—
188C2×Q8—1131no—
189C2×Q8—4522no—
190C2×Q8—2262no—
191C2×Q8—2264no—
192C2×Q8C22×D11312yes—
193C2×D4—1131no—
194C2×D4—1132no—
195C2×D4—4524no—
196C2×D4—4522no—
197C2×D4—2262no—
198C2×D4—2262no—
199C2×D4—2264no—
200C2×D4—2261no—
201C2×D4—2261no—
202C2×D4C22×D11311yescharacteristic
203C22×C4—21no—
204C22×C4—1132no—
205C22×C4—2262no—
206SD16—24no—
207SD16—1134no—
208SD16—4522no—
209SD16—2264no—
210SD16—2264no—
211C2×C8—1131no—
212C2×C8—1131no—
213C2×C8—2264no—
214C2×C8C22×D11312yes—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—1131no—
218C4⋊C4—1131no—
219C4⋊C4—2262no—
220C4⋊C4—2261no—
221C4⋊C4C22×D11311yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—1132no—
224C22⋊C4—2262no—
225C22⋊C4—2262no—
226C42—2261no—
227C42C22×D11311yescharacteristic
228C23—21no—
229C23—1132no—
230C23—9042no—
231C23—4524no—
232C23—4524no—
233C23—2262no—
234Q8—22no—
235Q8—22no—
236Q8—1132no—
237Q8—4524no—
238Q8—2261no—
239D4—21no—
240D4—1134no—
241D4—9041no—
242D4—4524no—
243D4—4524no—
244D4—4522no—
245D4—2262no—
246D4—2262no—
247D4D4×D11312yes—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—1132no—
252C2×C4—4524no—
253C2×C4—2261no—
254C2×C4—2261no—
255C2×C4—2262no—
256C2×C4—2262no—
257C2×C4D4×D11311yescharacteristic
258C2×C4D4×D11311yescharacteristic
259C2×C4C23×D11311yescharacteristic
260C8—22no—
261C8—1132no—
262C8—2261no—
263C22—22no—
264C22—41no—
265C22—41no—
266C22—1134no—
267C22—9048no—
268C22—4522no—
269C22—4522no—
270C22—4522no—
271C22—2262no—
272C22—2262no—
273C22C2×D4×D11311yescharacteristic
274C4—21no—
275C4—41no—
276C4—42no—
277C4—4521no—
278C4—2262no—
279C4—2262no—
280C4SD16×D11312yescomplemented
281C4C2×D4×D11311yescharacteristic
282C4#1681366811yescharacteristic
283C2—42no—
284C2—9042no—
285C2—2264no—
286C2#2029923211yescharacteristic
287C2C2×SD16×D11311yescharacteristic
288C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#461×C113C2
socleC22×C113C22×D4
prime radicalD4×D452C2
hypercenter#461D113
hypocenterC113D4×SD16
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D113C2semidirect
2. #20299263C2semidirect
4. #20298972C2semidirect
5. #20298830C2semidirect
6. #20298799C2semidirect
7. #20298747C2semidirect
8. #20298738C2semidirect
9. C4×#14268635C2semidirect
10. #20298663C2semidirect
11. #461×C113C2semidirect
12. C2×Q8×D113C22semidirect
15. C2×#14268636C22semidirect
17. C2×#14268634C22semidirect
18. C2×#14268634C22semidirect
20. C2×C8×D113C22semidirect
24. #16813598C22semidirect
28. C4×Dic226C22semidirect
31. #16813553C22semidirect
32. #16813545C22semidirect
33. #16813544C22semidirect
35. #16813534C22semidirect
36. C4×#11744751C22semidirect
38. C4⋊Q8×C113C22semidirect
40. C4⋊C8×C113C22semidirect
41. #103×C113C22semidirect
59. #14268635D4semidirect
108. D452SD16semidirect
114. Dic226C2×D4semidirect
117. #11744751C2×D4semidirect
128. C2×D113C2×SD16semidirect
132. C4×C113C2×SD16semidirect
145. C113D4×SD16semidirect
151. #461D113semidirect
168. C4⋊Q8C2×D113semidirect
180. C4⋊C8C2×D113semidirect
182. #103C2×D113semidirect
280. C4SD16×D113semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1132
#202992632
D4×D4522
#202989722
#202988302
#202987992
#202987472
#202987382
C4×#142686352
#202986632
#461×C1132
D4×SD16113