Finite Group Databasebeta

← SD16×D68 #14540481

Subgroups — SD16×D68 #14540481

Order 2176.

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×D17C212yesmaximal, complemented
2Q8×D68C211yesmaximal, characteristic, complemented
3D4×D68C211yesmaximal, characteristic
4#11763182C211yesmaximal, characteristic, complemented
5#11763039C212yesmaximal, complemented
6#11763014C211yesmaximal, characteristic, complemented
7#11763009C211yesmaximal, characteristic, complemented
8#11762961C212yesmaximal, complemented
9#11762949C212yesmaximal, complemented
10C8×D68C211yesmaximal, characteristic, complemented
11C4×SD16×C17C211yesmaximal, characteristic, complemented
12C2×Q8×D17C2212yescomplemented
13C2×D4×D17C2212yes—
14C22×D68—21no—
15C2×SD16×C17C2211yescharacteristic
16C4×Q8×C17C2211yescharacteristic, complemented
17C4×D4×C17C2211yescharacteristic
18C2×#63230C2212yescomplemented
19C2×#63229C2212yes—
20#10587616—21no—
21SD16×D17—28no—
22C2×#63219C2212yescomplemented
23C2×#63219C2212yescomplemented
24C2×C8×D17C2212yescomplemented
25#10587583—22no—
26#10587583C2212yescomplemented
27#10587581C2212yes—
28#10587568—22no—
29#10587560C2211yescharacteristic
30C4×D68—21no—
31C4×D68C2211yescharacteristic
32#10587555—21no—
33#10587555C2211yescharacteristic, complemented
34C17×#106C2211yescharacteristic, complemented
35C17×#103C2211yescharacteristic, complemented
36C17×#102C2211yescharacteristic
37C4×C8×C17C2211yescharacteristic, complemented
38#10587491C2212yescomplemented
39#10587481C2212yescomplemented
40#10587480C2212yescomplemented
41C4⋊#3622C2211yescharacteristic, complemented
42C23×D17—22no—
43C2×Q8×C17C2311yescharacteristic
44C2×D4×C17C2311yescharacteristic
45C22×C4×C17—21no—
46C2×C22⋊D17—22no—
47Q8×D17—24no—
48Q8×D17—42no—
49D4×D17—24no—
50D4×D17—42no—
51C2×D68—22no—
52C2×D68—21no—
53C2×D68—21no—
54C2×D68—44no—
55C2×D68D411yescharacteristic
56C2×D68C2312yes—
57C2×C4×D17—22no—
58C2×C4×D17C2312yes—
59C2×Dic34—22no—
60C2×Dic34C2312yes—
61SD16×C17D414yescomplemented
62C2×C8×C17C2311yescharacteristic
63C2×C8×C17C2311yescharacteristic
64C4⋊C4×C17—21no—
65C4⋊C4×C17C2311yescharacteristic
66C4⋊C4×C17C2311yescharacteristic
67C22⋊C4×C17—21no—
68C42×C17—21no—
69C42×C17C2311yescharacteristic
70#63230—24no—
71#63229—24no—
72#63227—22no—
73#63227—22no—
74#63227D412yes—
75C4⋊Dic17—21no—
76C4⋊Dic17—21no—
77C4⋊Dic17—22no—
78C4⋊Dic17D411yescharacteristic
79C2×#3622C2312yes—
80#63219—24no—
81#63219—42no—
82C8×D17—24no—
83C23×C17—21no—
84C22×D17—22no—
85C22×D17—44no—
86C22×D17—44no—
87C22×D17—82no—
88C22×D17C2×D412yes—
89Q8×C17—21no—
90Q8×C17C2×D412yescomplemented
91D4×C17—21no—
92D4×C17C2×D412yes—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—42no—
97C2×C4×C17C2×D411yescharacteristic
98C2×C4×C17C2×D411yescharacteristic
99C2×C4×C17C2411yescharacteristic
100C22⋊D17—44no—
101C2×Dic17—22no—
102C2×Dic17C2×D412yes—
103D68—22no—
104D68—22no—
105D68—44no—
106D68—42no—
107D68—81no—
108D68SD1614yesdirect product factor
109C4×D17—22no—
110C4×D17—22no—
111C4×D17—44no—
112Dic34—22no—
113Dic34—22no—
114Dic34—44no—
115C8×C17—21no—
116C8×C17C2×D412yescomplemented
117#3622—22no—
118D4×SD16—171nomaximal, Sylow
119C22×C17—22no—
120C22×C17—41no—
121C22×C17—41no—
122C22×C17C22×D411yescharacteristic
123C2×D17—22no—
124C2×D17—22no—
125C2×D17—42no—
126C2×D17—42no—
127C2×D17—42no—
128C2×D17—88no—
129C2×D17C2×SD1614yescomplemented
130C4×C17—22no—
131C4×C17—21no—
132C4×C17—41no—
133C4×C17—41no—
134C4×C17C2×SD1612yescomplemented
135C4×C17C22×D411yescharacteristic
136C4×C17H(5,𝔽2)11yescharacteristic
137Dic17—22no—
138Dic17—42no—
139C22×SD16—172no—
140D4×Q8—171no—
141D42—171no—
142#492—171no—
143#465—172no—
144#461—171no—
145#460—171no—
146#450—172no—
147#448—172no—
148C4×SD16D1711yescharacteristic, complemented
149C8×D4—171no—
150C2×C17—42no—
151C2×C17D4211yescharacteristic
152C2×C17C22×SD1611yescharacteristic
153C2×C17#57711yescharacteristic
154D17—24no—
155D17—82no—
156C22×Q8—172no—
157C22×D4—172no—
158C22×D4—341no—
159C2×SD16—172no—
160C2×SD16—172no—
161C2×SD16—172no—
162C2×SD16—172no—
163C2×SD16—348no—
164C2×SD16C2×D1711yescharacteristic
165C22×C8—172no—
166C4⋊Q8—171no—
167C4⋊Q8—341no—
168#127—171no—
169C22⋊Q8—172no—
170C22⋊Q8—342no—
171#121—172no—
172#121—341no—
173#120—342no—
174C4×Q8C2×D1711yescharacteristic, complemented
175C4×D4—171no—
176C4×D4—341no—
177C4×D4C2×D1711yescharacteristic
178#106C2×D1711yescharacteristic, complemented
179C4⋊C8—171no—
180#103—172no—
181#103C2×D1711yescharacteristic, complemented
182#102—172no—
183#102C2×D1711yescharacteristic
184C22⋊C8—172no—
185C4×C8C2×D1711yescharacteristic, complemented
186C17D4×SD1611yescharacteristic, complemented, Sylow
187C24—342no—
188C2×Q8—172no—
189C2×Q8—342no—
190C2×Q8—344no—
191C2×Q8—682no—
192C2×Q8C22×D1711yescharacteristic
193C2×D4—171no—
194C2×D4—172no—
195C2×D4—342no—
196C2×D4—342no—
197C2×D4—344no—
198C2×D4—341no—
199C2×D4—341no—
200C2×D4—684no—
201C2×D4—682no—
202C2×D4C22×D1711yescharacteristic
203C22×C4—21no—
204C22×C4—172no—
205C22×C4—342no—
206SD16—344no—
207SD16—344no—
208SD16—344no—
209SD16—682no—
210SD16D6814yesdirect product factor
211C2×C8—172no—
212C2×C8—344no—
213C2×C8C22×D1711yescharacteristic
214C2×C8C22×D1711yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—171no—
217C4⋊C4—342no—
218C4⋊C4—341no—
219C4⋊C4—341no—
220C4⋊C4C22×D1711yescharacteristic
221C4⋊C4C22×D1711yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—172no—
224C22⋊C4—342no—
225C22⋊C4—342no—
226C42—21no—
227C42C22×D1711yescharacteristic
228C23—21no—
229C23—172no—
230C23—342no—
231C23—684no—
232C23—684no—
233C23—1362no—
234Q8—21no—
235Q8—342no—
236Q8—342no—
237Q8—684no—
238Q8C2×D6812yescomplemented
239D4—21no—
240D4—174no—
241D4—342no—
242D4—342no—
243D4—684no—
244D4—684no—
245D4—682no—
246D4—1361no—
247D4C2×D6812yes—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—172no—
253C2×C4—342no—
254C2×C4—342no—
255C2×C4—342no—
256C2×C4—684no—
257C2×C4D4×D1711yescharacteristic
258C2×C4D4×D1711yescharacteristic
259C2×C4C23×D1711yescharacteristic
260C8—21no—
261C8—342no—
262C8C2×D6812yescomplemented
263C22—22no—
264C22—41no—
265C22—41no—
266C22—174no—
267C22—342no—
268C22—342no—
269C22—682no—
270C22—682no—
271C22—682no—
272C22—1368no—
273C22C2×D4×D1711yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—41no—
278C4—342no—
279C4—682no—
280C4SD16×D1712yescomplemented
281C4C22×D6811yescharacteristic
282C4#1058769611yescharacteristic
283C2—42no—
284C2—344no—
285C2—1362no—
286C2D4×D6811yescharacteristic
287C2C2×SD16×D1711yescharacteristic
288C2#1176361611yescharacteristic
subgroupG/H
centerC22C2×D4×D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC4×SD16×C17C2
socleC22×C17C22×D4
prime radicalD4×D68C2
hypercenterC4×SD16D17
hypocenterC17D4×SD16
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D17C2semidirect
2. Q8×D68C2semidirect
4. #11763182C2semidirect
5. #11763039C2semidirect
6. #11763014C2semidirect
7. #11763009C2semidirect
8. #11762961C2semidirect
9. #11762949C2semidirect
10. C8×D68C2semidirect
11. C4×SD16×C17C2semidirect
12. C2×Q8×D17C22semidirect
16. C4×Q8×C17C22semidirect
18. C2×#63230C22semidirect
22. C2×#63219C22semidirect
23. C2×#63219C22semidirect
24. C2×C8×D17C22semidirect
26. #10587583C22semidirect
33. #10587555C22semidirect
34. C17×#106C22semidirect
35. C17×#103C22semidirect
37. C4×C8×C17C22semidirect
38. #10587491C22semidirect
39. #10587481C22semidirect
40. #10587480C22semidirect
41. C4⋊#3622C22semidirect
61. SD16×C17D4semidirect
90. Q8×C17C2×D4semidirect
108. D68SD16direct (N × H)
116. C8×C17C2×D4semidirect
129. C2×D17C2×SD16semidirect
134. C4×C17C2×SD16semidirect
148. C4×SD16D17semidirect
174. C4×Q8C2×D17semidirect
178. #106C2×D17semidirect
181. #103C2×D17semidirect
185. C4×C8C2×D17semidirect
186. C17D4×SD16semidirect
210. SD16D68direct (N × H)
238. Q8C2×D68semidirect
262. C8C2×D68semidirect
280. C4SD16×D17semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D172
Q8×D682
D4×D682
#117631822
#117630392
#117630142
#117630092
#117629612
#117629492
C8×D682
C4×SD16×C172
D4×SD1617