Finite Group Databasebeta

← SD16×D1084 #46848061

Subgroups — SD16×D1084 #46848061

Order 34688.

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×D271C212yesmaximal, complemented
2Q8×D1084C211yesmaximal, characteristic, complemented
3D4×D1084C211yesmaximal, characteristic
4#31774270C211yesmaximal, characteristic, complemented
5#31774127C212yesmaximal, complemented
6#31774102C211yesmaximal, characteristic, complemented
7#31774097C211yesmaximal, characteristic, complemented
8#31774049C212yesmaximal, complemented
9#31774037C212yesmaximal, complemented
10C8×D1084C211yesmaximal, characteristic, complemented
11C4×SD16×C271C211yesmaximal, characteristic, complemented
12C2×Q8×D271C2212yescomplemented
13C22×D1084—21no—
14C2×D4×D271C2212yes—
15C2×#16864643C2212yescomplemented
16C2×#16864643C2212yescomplemented
17C2×#16864642C2212yes—
18C2×#16864641C2212yescomplemented
19SD16×D271—28no—
20C2×C8×D271C2212yescomplemented
21#22576160—21no—
22#22576160C2211yescharacteristic, complemented
23#22576157C2211yescharacteristic
24#22576140—22no—
25#22576140C2212yescomplemented
26#22576135C2212yes—
27#22576134—21no—
28#22576130—22no—
29C4×D1084—21no—
30C4×D1084C2211yescharacteristic
31C4⋊(C271⋊C8)C2211yescharacteristic, complemented
32#22576083C2212yescomplemented
33#22576080C2212yescomplemented
34(C2×D271)⋊C8C2212yescomplemented
35C2×SD16×C271C2211yescharacteristic
36C4×Q8×C271C2211yescharacteristic, complemented
37C4×D4×C271C2211yescharacteristic
38#106×C271C2211yescharacteristic, complemented
39#103×C271C2211yescharacteristic, complemented
40#102×C271C2211yescharacteristic
41C4×C8×C271C2211yescharacteristic, complemented
42C23×D271—22no—
43C2×Dic542—22no—
44C2×Dic542C2312yes—
45Q8×D271—24no—
46Q8×D271—42no—
47C2×D1084—22no—
48C2×D1084—21no—
49C2×D1084—21no—
50C2×D1084—44no—
51C2×D1084D411yescharacteristic
52C2×D1084C2312yes—
53C2×C22⋊D271—22no—
54D4×D271—24no—
55D4×D271—42no—
56C2×C4×D271—22no—
57C2×C4×D271C2312yes—
58#16864643—24no—
59#16864643—42no—
60#16864642—24no—
61#16864641—24no—
62C2×C271⋊C8C2312yes—
63C8×D271—24no—
64C4⋊Dic271—22no—
65C4⋊Dic271—21no—
66C4⋊Dic271—21no—
67C4⋊Dic271D411yescharacteristic
68(C2×D271)⋊C4—22no—
69(C2×D271)⋊C4—22no—
70(C2×D271)⋊C4D412yes—
71C2×Q8×C271C2311yescharacteristic
72C2×D4×C271C2311yescharacteristic
73C22×C4×C271—21no—
74SD16×C271D414yescomplemented
75C2×C8×C271C2311yescharacteristic
76C2×C8×C271C2311yescharacteristic
77C4⋊C4×C271—21no—
78C4⋊C4×C271C2311yescharacteristic
79C4⋊C4×C271C2311yescharacteristic
80C22⋊C4×C271—21no—
81C42×C271—21no—
82C42×C271C2311yescharacteristic
83C22×D271—22no—
84C22×D271—44no—
85C22×D271—44no—
86C22×D271—82no—
87C22×D271C2×D412yes—
88Dic542—22no—
89Dic542—22no—
90Dic542—44no—
91D1084—22no—
92D1084—22no—
93D1084—44no—
94D1084—42no—
95D1084—81no—
96D1084SD1614yesdirect product factor
97C22⋊D271—44no—
98C2×Dic271—22no—
99C2×Dic271C2×D412yes—
100C4×D271—22no—
101C4×D271—22no—
102C4×D271—44no—
103C271⋊C8—22no—
104C23×C271—21no—
105Q8×C271—21no—
106Q8×C271C2×D412yescomplemented
107D4×C271—21no—
108D4×C271C2×D412yes—
109C2×C4×C271—21no—
110C2×C4×C271—21no—
111C2×C4×C271—21no—
112C2×C4×C271—42no—
113C2×C4×C271C2×D411yescharacteristic
114C2×C4×C271C2×D411yescharacteristic
115C2×C4×C271C2411yescharacteristic
116C8×C271—21no—
117C8×C271C2×D412yescomplemented
118C22×C271—22no—
119C22×C271—41no—
120C22×C271—41no—
121C22×C271C22×D411yescharacteristic
122C2×D271—22no—
123C2×D271—22no—
124C2×D271—42no—
125C2×D271—42no—
126C2×D271—42no—
127C2×D271—88no—
128C2×D271C2×SD1614yescomplemented
129C4×C271—22no—
130C4×C271—21no—
131C4×C271—41no—
132C4×C271—41no—
133C4×C271C2×SD1612yescomplemented
134C4×C271C22×D411yescharacteristic
135C4×C271H(5,𝔽2)11yescharacteristic
136Dic271—22no—
137Dic271—42no—
138C2×C271—42no—
139C2×C271D4211yescharacteristic
140C2×C271C22×SD1611yescharacteristic
141C2×C271#57711yescharacteristic
142D271—24no—
143D271—82no—
144C271D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—2711nomaximal, Sylow
146C22×SD16—2712no—
147D4×Q8—2711no—
148D42—2711no—
149#492—2711no—
150#465—2712no—
151#461—2711no—
152#460—2711no—
153#450—2712no—
154#448—2712no—
155C4×SD16D27111yescharacteristic, complemented
156C8×D4—2711no—
157C22×Q8—2712no—
158C22×D4—2712no—
159C22×D4—5421no—
160C2×SD16—2712no—
161C2×SD16—2712no—
162C2×SD16—2712no—
163C2×SD16—2712no—
164C2×SD16—5428no—
165C2×SD16C2×D27111yescharacteristic
166C22×C8—2712no—
167C4⋊Q8—2711no—
168C4⋊Q8—5421no—
169#127—2711no—
170C22⋊Q8—2712no—
171C22⋊Q8—5422no—
172#121—2712no—
173#121—5421no—
174#120—5422no—
175C4×Q8C2×D27111yescharacteristic, complemented
176C4×D4—2711no—
177C4×D4—5421no—
178C4×D4C2×D27111yescharacteristic
179#106C2×D27111yescharacteristic, complemented
180C4⋊C8—2711no—
181#103—2712no—
182#103C2×D27111yescharacteristic, complemented
183#102—2712no—
184#102C2×D27111yescharacteristic
185C22⋊C8—2712no—
186C4×C8C2×D27111yescharacteristic, complemented
187C24—5422no—
188C2×Q8—2712no—
189C2×Q8—5422no—
190C2×Q8—5424no—
191C2×Q8—10842no—
192C2×Q8C22×D27111yescharacteristic
193C2×D4—2711no—
194C2×D4—2712no—
195C2×D4—5422no—
196C2×D4—5422no—
197C2×D4—5424no—
198C2×D4—5421no—
199C2×D4—5421no—
200C2×D4—10844no—
201C2×D4—10842no—
202C2×D4C22×D27111yescharacteristic
203C22×C4—21no—
204C22×C4—2712no—
205C22×C4—5422no—
206SD16—5424no—
207SD16—5424no—
208SD16—5424no—
209SD16—10842no—
210SD16D108414yesdirect product factor
211C2×C8—2712no—
212C2×C8—5424no—
213C2×C8C22×D27111yescharacteristic
214C2×C8C22×D27111yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—2711no—
217C4⋊C4—5422no—
218C4⋊C4—5421no—
219C4⋊C4—5421no—
220C4⋊C4C22×D27111yescharacteristic
221C4⋊C4C22×D27111yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—2712no—
224C22⋊C4—5422no—
225C22⋊C4—5422no—
226C42—21no—
227C42C22×D27111yescharacteristic
228C23—21no—
229C23—2712no—
230C23—5422no—
231C23—10844no—
232C23—10844no—
233C23—21682no—
234Q8—21no—
235Q8—5422no—
236Q8—5422no—
237Q8—10844no—
238Q8C2×D108412yescomplemented
239D4—21no—
240D4—2714no—
241D4—5422no—
242D4—5422no—
243D4—10844no—
244D4—10844no—
245D4—10842no—
246D4—21681no—
247D4C2×D108412yes—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—2712no—
253C2×C4—5422no—
254C2×C4—5422no—
255C2×C4—5422no—
256C2×C4—10844no—
257C2×C4D4×D27111yescharacteristic
258C2×C4D4×D27111yescharacteristic
259C2×C4C23×D27111yescharacteristic
260C8—21no—
261C8—5422no—
262C8C2×D108412yescomplemented
263C22—22no—
264C22—41no—
265C22—41no—
266C22—2714no—
267C22—5422no—
268C22—5422no—
269C22—10842no—
270C22—10842no—
271C22—10842no—
272C22—21688no—
273C22C2×D4×D27111yescharacteristic
274C4—22no—
275C4—21no—
276C4—41no—
277C4—41no—
278C4—5422no—
279C4—10842no—
280C4SD16×D27112yescomplemented
281C4C22×D108411yescharacteristic
282C4#2257620611yescharacteristic
283C2—42no—
284C2—5424no—
285C2—21682no—
286C2D4×D108411yescharacteristic
287C2C2×SD16×D27111yescharacteristic
288C2#3177470411yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
FittingC4×SD16×C271C2
socleC22×C271C22×D4
prime radicalD4×D1084C2
hypercenterC4×SD16D271
hypocenterC271D4×SD16
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D271C2semidirect
2. Q8×D1084C2semidirect
4. #31774270C2semidirect
5. #31774127C2semidirect
6. #31774102C2semidirect
7. #31774097C2semidirect
8. #31774049C2semidirect
9. #31774037C2semidirect
10. C8×D1084C2semidirect
11. C4×SD16×C271C2semidirect
12. C2×Q8×D271C22semidirect
15. C2×#16864643C22semidirect
16. C2×#16864643C22semidirect
18. C2×#16864641C22semidirect
20. C2×C8×D271C22semidirect
22. #22576160C22semidirect
25. #22576140C22semidirect
31. C4⋊(C271⋊C8)C22semidirect
32. #22576083C22semidirect
33. #22576080C22semidirect
34. (C2×D271)⋊C8C22semidirect
36. C4×Q8×C271C22semidirect
38. #106×C271C22semidirect
39. #103×C271C22semidirect
41. C4×C8×C271C22semidirect
74. SD16×C271D4semidirect
96. D1084SD16direct (N × H)
106. Q8×C271C2×D4semidirect
117. C8×C271C2×D4semidirect
128. C2×D271C2×SD16semidirect
133. C4×C271C2×SD16semidirect
144. C271D4×SD16semidirect
155. C4×SD16D271semidirect
175. C4×Q8C2×D271semidirect
179. #106C2×D271semidirect
182. #103C2×D271semidirect
186. C4×C8C2×D271semidirect
210. SD16D1084direct (N × H)
238. Q8C2×D1084semidirect
262. C8C2×D1084semidirect
280. C4SD16×D271semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D2712
Q8×D10842
D4×D10842
#317742702
#317741272
#317741022
#317740972
#317740492
#317740372
C8×D10842
C4×SD16×C2712
D4×SD16271