Finite Group Databasebeta

← #28402265

Subgroups — #28402265

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
2Q8×D452C211yesmaximal, characteristic, complemented
3#20299233C211yesmaximal, characteristic
4#20298970C211yesmaximal, characteristic, complemented
5#20298826C212yesmaximal, complemented
6#20298804C211yesmaximal, characteristic, complemented
7#20298750C212yesmaximal, complemented
8#20298735C212yesmaximal, complemented
9C4×#14268634C211yesmaximal, characteristic, complemented
10#20298663C211yesmaximal, characteristic, complemented
11#460×C113C211yesmaximal, characteristic, complemented
12C2×Q8×D113C2212yescomplemented
13C2×D4×D113—21no—
14C2×D4×D113C2212yes—
15C2×#14268636C2212yes—
16C2×#14268635C2212yescomplemented
17C2×#14268635C2212yescomplemented
18C2×#14268634C2211yescharacteristic
19SD16×D113—28no—
20C2×C8×D113C2212yescomplemented
21#16813622—21no—
22#16813622C2211yescharacteristic, complemented
23#16813602—22no—
24#16813602C2212yescomplemented
25#16813593—21no—
26#16813593C2212yes—
27#16813590—22no—
28C4×D452—21no—
29C4×D452C2211yescharacteristic
30C4×D452C2211yescharacteristic
31#16813553C2211yescharacteristic, complemented
32#16813547C2212yescomplemented
33#16813546C2211yescharacteristic, complemented
34#16813542C2211yescharacteristic
35#16813534C2212yescomplemented
36C4×#11744751C2211yescharacteristic, complemented
37C2×SD16×C113C2212yescomplemented
38#127×C113C2211yescharacteristic
39C4×Q8×C113C2211yescharacteristic, complemented
40C4⋊C8×C113C2211yescharacteristic, complemented
41#102×C113C2212yescomplemented
42C23×D113—22no—
43C2×Dic226—22no—
44C2×Dic226C2312yes—
45Q8×D113—24no—
46Q8×D113—42no—
47C2×D452D411yescharacteristic
48C2×D452C2311yescharacteristic
49C2×C22⋊D113—22no—
50C2×C22⋊D113—22no—
51D4×D113—24no—
52D4×D113—42no—
53D4×D113—44no—
54C2×C4×D113—22no—
55C2×C4×D113—21no—
56C2×C4×D113C2312yes—
57#14268636—24no—
58#14268635—24no—
59#14268635—42no—
60#14268634D414yescomplemented
61C2×#11744751C2311yescharacteristic
62C2×#11744751C2311yescharacteristic
63C8×D113—24no—
64C4⋊Dic113—21no—
65C4⋊Dic113—21no—
66C4⋊Dic113—22no—
67C4⋊Dic113D411yescharacteristic
68C4⋊Dic113C2311yescharacteristic
69C22⋊Dic113—22no—
70#14268624—22no—
71#14268624—21no—
72#14268624D412yes—
73C2×Q8×C113C2311yescharacteristic
74C2×D4×C113—21no—
75C2×D4×C113—21no—
76C2×D4×C113C2312yes—
77SD16×C113—24no—
78C2×C8×C113C2312yes—
79C4⋊C4×C113—21no—
80C4⋊C4×C113C2311yescharacteristic
81C42×C113—21no—
82C42×C113C2311yescharacteristic
83C23×C113—22no—
84C22×D113—21no—
85C22×D113—44no—
86C22×D113—44no—
87C22×D113—82no—
88C22×D113C2×D412yes—
89Q8×C113—21no—
90Q8×C113C2×D412yescomplemented
91D4×C113—22no—
92D4×C113—22no—
93D4×C113—42no—
94D4×C113—81no—
95C2×C4×C113—21no—
96C2×C4×C113—21no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2411yescharacteristic
100C22⋊D113—44no—
101C22⋊D113—44no—
102C2×Dic113—21no—
103C2×Dic113—22no—
104C2×Dic113C2×D412yes—
105D452—21no—
106D452SD1614yescomplemented
107D452C2×D412yes—
108C4×D113—22no—
109C4×D113—22no—
110C4×D113—44no—
111C4×D113—42no—
112Dic226—22no—
113Dic226—22no—
114Dic226—44no—
115C8×C113—22no—
116#11744751—21no—
117#11744751C2×D412yescomplemented
118C22×C113—42no—
119C22×C113—42no—
120C22×C113—42no—
121C22×C113C22×D411yescharacteristic
122C2×D113—22no—
123C2×D113—22no—
124C2×D113—22no—
125C2×D113—41no—
126C2×D113—41no—
127C2×D113—88no—
128C2×D113C2×SD1614yescomplemented
129C4×C113—22no—
130C4×C113—21no—
131C4×C113—41no—
132C4×C113C2×SD1612yescomplemented
133C4×C113C22×D411yescharacteristic
134C4×C113H(5,𝔽2)11yescharacteristic
135Dic113—22no—
136Dic113—42no—
137Dic113—41no—
138C2×C113—82no—
139C2×C113D4211yescharacteristic
140C2×C113C22×SD1611yescharacteristic
141C2×C113#57711yescharacteristic
142D113—24no—
143D113—42no—
144D4×SD16—1131nomaximal, Sylow
145C113D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—1132no—
147D4×Q8—1131no—
148D42—1131no—
149#492—1131no—
150#465—1132no—
151#461—1131no—
152#460D11311yescharacteristic, complemented
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×D11312yescomplemented
166C22×C8—1132no—
167C4⋊Q8—1131no—
168C4⋊Q8—2261no—
169#127C2×D11311yescharacteristic
170C22⋊Q8—1132no—
171C22⋊Q8—2262no—
172#121—1132no—
173#121—2261no—
174#120—2262no—
175C4×Q8C2×D11311yescharacteristic, complemented
176C4×D4—1131no—
177C4×D4—1131no—
178C4×D4—2261no—
179#106—1131no—
180C4⋊C8C2×D11311yescharacteristic, complemented
181#103—1131no—
182#103—1132no—
183#102—1131no—
184#102C2×D11312yescomplemented
185C22⋊C8—1132no—
186C4×C8—1131no—
187C24—2262no—
188C2×Q8—1132no—
189C2×Q8—4522no—
190C2×Q8—2262no—
191C2×Q8—2264no—
192C2×Q8C22×D11311yescharacteristic
193C2×D4—21no—
194C2×D4—21no—
195C2×D4—1131no—
196C2×D4—1131no—
197C2×D4—4524no—
198C2×D4—4522no—
199C2×D4—2262no—
200C2×D4—2264no—
201C2×D4—2262no—
202C2×D4C22×D11312yes—
203C22×C4—1132no—
204C22×C4—2262no—
205C22×C4—2261no—
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—1131no—
217C4⋊C4—1131no—
218C4⋊C4—2262no—
219C4⋊C4—2261no—
220C4⋊C4—2261no—
221C4⋊C4C22×D11311yescharacteristic
222C22⋊C4—1132no—
223C22⋊C4—2262no—
224C22⋊C4—2262no—
225C22⋊C4—2261no—
226C42—21no—
227C42C22×D11311yescharacteristic
228C23—22no—
229C23—1132no—
230C23—9042no—
231C23—4524no—
232C23—4524no—
233C23—2261no—
234Q8—21no—
235Q8—4524no—
236Q8—2262no—
237Q8—2262no—
238Q8D4×D11312yescomplemented
239D4—22no—
240D4—22no—
241D4—42no—
242D4—81no—
243D4—1134no—
244D4—1132no—
245D4—4524no—
246D4—4524no—
247D4—2261no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—1132no—
251C2×C4—4524no—
252C2×C4—4522no—
253C2×C4—2261no—
254C2×C4—2262no—
255C2×C4—2262no—
256C2×C4—2262no—
257C2×C4D4×D11311yescharacteristic
258C2×C4D4×D11311yescharacteristic
259C2×C4C23×D11311yescharacteristic
260C8—22no—
261C8—1132no—
262C8—2261no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—1134no—
267C22—9048no—
268C22—4521no—
269C22—4521no—
270C22—2262no—
271C22—2262no—
272C22—2262no—
273C22C2×D4×D11311yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—4521no—
278C4—4522no—
279C4—2262no—
280C4SD16×D11312yescomplemented
281C4C2×D4×D11311yescharacteristic
282C4#1681366811yescharacteristic
283C2—82no—
284C2—4522no—
285C2—2264no—
286C2#2029923211yescharacteristic
287C2C2×SD16×D11311yescharacteristic
288C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#460×C113C2
socleC22×C113C22×D4
prime radical#20299233C2
hypercenter#460D113
hypocenterC113D4×SD16
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D113C2semidirect
2. Q8×D452C2semidirect
4. #20298970C2semidirect
5. #20298826C2semidirect
6. #20298804C2semidirect
7. #20298750C2semidirect
8. #20298735C2semidirect
9. C4×#14268634C2semidirect
10. #20298663C2semidirect
11. #460×C113C2semidirect
12. C2×Q8×D113C22semidirect
16. C2×#14268635C22semidirect
17. C2×#14268635C22semidirect
20. C2×C8×D113C22semidirect
22. #16813622C22semidirect
24. #16813602C22semidirect
31. #16813553C22semidirect
32. #16813547C22semidirect
33. #16813546C22semidirect
35. #16813534C22semidirect
36. C4×#11744751C22semidirect
37. C2×SD16×C113C22semidirect
39. C4×Q8×C113C22semidirect
40. C4⋊C8×C113C22semidirect
41. #102×C113C22semidirect
60. #14268634D4semidirect
90. Q8×C113C2×D4semidirect
106. D452SD16semidirect
117. #11744751C2×D4semidirect
128. C2×D113C2×SD16semidirect
132. C4×C113C2×SD16semidirect
145. C113D4×SD16semidirect
152. #460D113semidirect
165. C2×SD16C2×D113semidirect
175. C4×Q8C2×D113semidirect
180. C4⋊C8C2×D113semidirect
184. #102C2×D113semidirect
238. Q8D4×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
Q8×D4522
#202992332
#202989702
#202988262
#202988042
#202987502
#202987352
C4×#142686342
#202986632
#460×C1132
D4×SD16113