Finite Group Databasebeta

← SD16×D452 #28402271

Subgroups — SD16×D452 #28402271

Order 14464.

546 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 141 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
3D4×D452C211yesmaximal, characteristic
4#20298971C211yesmaximal, characteristic, complemented
5#20298828C212yesmaximal, complemented
6#20298803C211yesmaximal, characteristic, complemented
7#20298798C211yesmaximal, characteristic, complemented
8#20298750C212yesmaximal, complemented
9#20298738C212yesmaximal, complemented
10C8×D452C211yesmaximal, characteristic, complemented
11C4×SD16×C113C211yesmaximal, characteristic, complemented
12C2×Q8×D113C2212yescomplemented
13C22×D452—21no—
14C2×D4×D113C2212yes—
15C2×#14268636C2212yescomplemented
16C2×#14268636C2212yescomplemented
17C2×#14268635C2212yes—
18C2×#14268634C2212yescomplemented
19SD16×D113—28no—
20C2×C8×D113C2212yescomplemented
21#16813622—21no—
22#16813622C2211yescharacteristic, complemented
23#16813619C2211yescharacteristic
24#16813602—22no—
25#16813602C2212yescomplemented
26#16813597C2212yes—
27#16813596—21no—
28#16813592—22no—
29C4×D452—21no—
30C4×D452C2211yescharacteristic
31C4⋊#11744751C2211yescharacteristic, complemented
32#16813545C2212yescomplemented
33#16813542C2212yescomplemented
34#16813534C2212yescomplemented
35C2×SD16×C113C2211yescharacteristic
36C4×Q8×C113C2211yescharacteristic, complemented
37C4×D4×C113C2211yescharacteristic
38#106×C113C2211yescharacteristic, complemented
39#103×C113C2211yescharacteristic, complemented
40#102×C113C2211yescharacteristic
41C4×C8×C113C2211yescharacteristic, complemented
42C23×D113—22no—
43C2×Dic226—22no—
44C2×Dic226C2312yes—
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#14268636—42no—
60#14268635—24no—
61#14268634—24no—
62C2×#11744751C2312yes—
63C8×D113—24no—
64C4⋊Dic113—21no—
65C4⋊Dic113—21no—
66C4⋊Dic113—22no—
67C4⋊Dic113D411yescharacteristic
68#14268624—22no—
69#14268624—22no—
70#14268624D412yes—
71C2×Q8×C113C2311yescharacteristic
72C2×D4×C113C2311yescharacteristic
73C22×C4×C113—21no—
74SD16×C113D414yescomplemented
75C2×C8×C113C2311yescharacteristic
76C2×C8×C113C2311yescharacteristic
77C4⋊C4×C113—21no—
78C4⋊C4×C113C2311yescharacteristic
79C4⋊C4×C113C2311yescharacteristic
80C22⋊C4×C113—21no—
81C42×C113—21no—
82C42×C113C2311yescharacteristic
83C23×C113—21no—
84C22×D113—22no—
85C22×D113—44no—
86C22×D113—44no—
87C22×D113—82no—
88C22×D113C2×D412yes—
89Q8×C113—21no—
90Q8×C113C2×D412yescomplemented
91D4×C113—21no—
92D4×C113C2×D412yes—
93C2×C4×C113—21no—
94C2×C4×C113—21no—
95C2×C4×C113—21no—
96C2×C4×C113—42no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2411yescharacteristic
100C22⋊D113—44no—
101C2×Dic113—22no—
102C2×Dic113C2×D412yes—
103D452—22no—
104D452—22no—
105D452—44no—
106D452—42no—
107D452—81no—
108D452SD1614yesdirect product factor
109C4×D113—22no—
110C4×D113—22no—
111C4×D113—44no—
112Dic226—22no—
113Dic226—22no—
114Dic226—44no—
115C8×C113—21no—
116C8×C113C2×D412yescomplemented
117#11744751—22no—
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—22no—
130C4×C113—21no—
131C4×C113—41no—
132C4×C113—41no—
133C4×C113C2×SD1612yescomplemented
134C4×C113C22×D411yescharacteristic
135C4×C113H(5,𝔽2)11yescharacteristic
136Dic113—22no—
137Dic113—42no—
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#461—1131no—
152#460—1131no—
153#450—1132no—
154#448—1132no—
155C4×SD16D11311yescharacteristic, complemented
156C8×D4—1131no—
157C22×Q8—1132no—
158C22×D4—1132no—
159C22×D4—2261no—
160C2×SD16—1132no—
161C2×SD16—1132no—
162C2×SD16—1132no—
163C2×SD16—1132no—
164C2×SD16—2268no—
165C2×SD16C2×D11311yescharacteristic
166C22×C8—1132no—
167C4⋊Q8—1131no—
168C4⋊Q8—2261no—
169#127—1131no—
170C22⋊Q8—1132no—
171C22⋊Q8—2262no—
172#121—1132no—
173#121—2261no—
174#120—2262no—
175C4×Q8C2×D11311yescharacteristic, complemented
176C4×D4—1131no—
177C4×D4—2261no—
178C4×D4C2×D11311yescharacteristic
179#106C2×D11311yescharacteristic, complemented
180C4⋊C8—1131no—
181#103—1132no—
182#103C2×D11311yescharacteristic, complemented
183#102—1132no—
184#102C2×D11311yescharacteristic
185C22⋊C8—1132no—
186C4×C8C2×D11311yescharacteristic, complemented
187C24—2262no—
188C2×Q8—1132no—
189C2×Q8—4522no—
190C2×Q8—2262no—
191C2×Q8—2264no—
192C2×Q8C22×D11311yescharacteristic
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—4522no—
207SD16—2264no—
208SD16—2264no—
209SD16—2264no—
210SD16D45214yesdirect product factor
211C2×C8—1132no—
212C2×C8—2264no—
213C2×C8C22×D11311yescharacteristic
214C2×C8C22×D11311yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—1131no—
217C4⋊C4—2262no—
218C4⋊C4—2261no—
219C4⋊C4—2261no—
220C4⋊C4C22×D11311yescharacteristic
221C4⋊C4C22×D11311yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—1132no—
224C22⋊C4—2262no—
225C22⋊C4—2262no—
226C42—21no—
227C42C22×D11311yescharacteristic
228C23—21no—
229C23—1132no—
230C23—9042no—
231C23—4524no—
232C23—4524no—
233C23—2262no—
234Q8—21no—
235Q8—4524no—
236Q8—2262no—
237Q8—2262no—
238Q8C2×D45212yescomplemented
239D4—21no—
240D4—1134no—
241D4—9041no—
242D4—4524no—
243D4—4524no—
244D4—4522no—
245D4—2262no—
246D4—2262no—
247D4C2×D45212yes—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—1132no—
253C2×C4—4524no—
254C2×C4—2262no—
255C2×C4—2262no—
256C2×C4—2262no—
257C2×C4D4×D11311yescharacteristic
258C2×C4D4×D11311yescharacteristic
259C2×C4C23×D11311yescharacteristic
260C8—21no—
261C8—2262no—
262C8C2×D45212yescomplemented
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—22no—
276C4—41no—
277C4—41no—
278C4—4522no—
279C4—2262no—
280C4SD16×D11312yescomplemented
281C4C22×D45211yescharacteristic
282C4#1681366811yescharacteristic
283C2—42no—
284C2—9042no—
285C2—2264no—
286C2D4×D45211yescharacteristic
287C2C2×SD16×D11311yescharacteristic
288C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×SD16×C113C2
socleC22×C113C22×D4
prime radicalD4×D452C2
hypercenterC4×SD16D113
hypocenterC113D4×SD16
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D113C2semidirect
2. Q8×D452C2semidirect
4. #20298971C2semidirect
5. #20298828C2semidirect
6. #20298803C2semidirect
7. #20298798C2semidirect
8. #20298750C2semidirect
9. #20298738C2semidirect
10. C8×D452C2semidirect
11. C4×SD16×C113C2semidirect
12. C2×Q8×D113C22semidirect
15. C2×#14268636C22semidirect
16. C2×#14268636C22semidirect
18. C2×#14268634C22semidirect
20. C2×C8×D113C22semidirect
22. #16813622C22semidirect
25. #16813602C22semidirect
31. C4⋊#11744751C22semidirect
32. #16813545C22semidirect
33. #16813542C22semidirect
34. #16813534C22semidirect
36. C4×Q8×C113C22semidirect
38. #106×C113C22semidirect
39. #103×C113C22semidirect
41. C4×C8×C113C22semidirect
74. SD16×C113D4semidirect
90. Q8×C113C2×D4semidirect
108. D452SD16direct (N × H)
116. C8×C113C2×D4semidirect
128. C2×D113C2×SD16semidirect
133. C4×C113C2×SD16semidirect
145. C113D4×SD16semidirect
155. C4×SD16D113semidirect
175. C4×Q8C2×D113semidirect
179. #106C2×D113semidirect
182. #103C2×D113semidirect
186. C4×C8C2×D113semidirect
210. SD16D452direct (N × H)
238. Q8C2×D452semidirect
262. C8C2×D452semidirect
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
D4×D4522
#202989712
#202988282
#202988032
#202987982
#202987502
#202987382
C8×D4522
C4×SD16×C1132
D4×SD16113