Finite Group Databasebeta

← SD16×D16 #492574

Subgroups — SD16×D16 #492574

Order 512.

525 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 525 conjugacy classes of subgroups — too many to draw. Only its 134 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
1Q8×D16C211yesmaximal, characteristic, complemented
2D4×D16C211yesmaximal, characteristic
3D8×SD16C212yesmaximal, complemented
4#12503C211yesmaximal, characteristic, complemented
5#12451C211yesmaximal, characteristic, complemented
6#12439C211yesmaximal, characteristic, complemented
7#12416C212yesmaximal, complemented
8#12368C212yesmaximal, complemented
9#12352C212yesmaximal, complemented
10C16×SD16C211yesmaximal, characteristic, complemented
11C8×D16C211yesmaximal, characteristic, complemented
12C22×D16—21no—
13Q8×D8C2212yescomplemented
14D4×SD16—22no—
15D4×D8C2212yes—
16#2252—21no—
17#2252C2211yescharacteristic, complemented
18#2246C2211yescharacteristic
19#2240C2212yescomplemented
20#2224—22no—
21#2224C2212yescomplemented
22#2215—21no—
23#2206C2212yes—
24#2184—22no—
25Q8×C16C2211yescharacteristic, complemented
26C4×D16—21no—
27C4×D16C2211yescharacteristic
28D4×C16C2211yescharacteristic
29#1706C2212yescomplemented
30#1673C2212yes—
31#1668C2212yescomplemented
32#1665—22no—
33#1639—22no—
34#1627—22no—
35C8×SD16C2211yescharacteristic
36C8×D8C2212yescomplemented
37#1371C2211yescharacteristic, complemented
38#1367C2211yescharacteristic, complemented
39#1364C2212yescomplemented
40#1361C2212yescomplemented
41Q8⋊C16C2211yescharacteristic, complemented
42#1331C2212yescomplemented
43D4⋊C16C2211yescharacteristic
44C8×C16C2211yescharacteristic, complemented
45C22×SD16—42no—
46C22×D8—22no—
47D4×Q8—22no—
48D42—22no—
49C2×D16—22no—
50C2×D16—21no—
51C2×D16—21no—
52C2×D16—44no—
53C2×D16D411yescharacteristic
54C22×C16—21no—
55#500—22no—
56#500C2312yes—
57#493C2312yes—
58#492—22no—
59#486—22no—
60#474—22no—
61#474—42no—
62#466—22no—
63#465—42no—
64#461—22no—
65#460—22no—
66#459—22no—
67#450—42no—
68#448—42no—
69#447—42no—
70C8×Q8C2311yescharacteristic
71C4×SD16D411yescharacteristic
72C4×D8—22no—
73C4×D8C2312yes—
74C8×D4—22no—
75C8×D4C2311yescharacteristic
76#366—21no—
77#366—21no—
78#366—22no—
79#366D411yescharacteristic
80C4⋊C16—21no—
81C4⋊C16C2311yescharacteristic
82C4⋊C16C2311yescharacteristic
83#357—22no—
84#357—22no—
85#357—42no—
86#357D412yes—
87C22⋊C16—21no—
88C4×C16—21no—
89C4×C16C2311yescharacteristic
90C4×C16C2311yescharacteristic
91#335C2312yes—
92#334D411yescharacteristic
93#332—22no—
94#331—22no—
95Q8⋊C8D411yescharacteristic
96D4⋊C8—22no—
97D4⋊C8D411yescharacteristic
98C82C2311yescharacteristic
99C22×Q8—42no—
100C22×D4—42no—
101C22×D4—42no—
102C2×SD16—42no—
103C2×SD16—42no—
104C2×SD16—42no—
105C2×SD16—42no—
106C2×SD16—88no—
107C2×SD16D811yescharacteristic
108C2×D8—22no—
109C2×D8—22no—
110C2×D8—42no—
111C2×D8—44no—
112C2×D8—82no—
113C2×D8C2×D412yes—
114C22×C8—21no—
115C22×C8—42no—
116C4⋊Q8—22no—
117C4⋊Q8—42no—
118#127—22no—
119C22⋊Q8—42no—
120C22⋊Q8—82no—
121#121—42no—
122#121—42no—
123#120—82no—
124C4×Q8C2×D411yescharacteristic
125C4×D4—22no—
126C4×D4—42no—
127C4×D4C2×D411yescharacteristic
128D16—44no—
129D16—42no—
130D16—81no—
131D16SD1614yesdirect product factor
132C2×C16—21no—
133C2×C16—21no—
134C2×C16—21no—
135C2×C16—42no—
136C2×C16C2×D411yescharacteristic
137C2×C16C2×D411yescharacteristic
138#107—22no—
139#107—22no—
140#107—42no—
141#107C2×D412yes—
142#106D811yescharacteristic
143C4⋊C8—21no—
144C4⋊C8—22no—
145C4⋊C8C2×D411yescharacteristic
146C4⋊C8C2×D411yescharacteristic
147#103—42no—
148#103D811yescharacteristic
149#102—22no—
150#102—42no—
151#102—42no—
152#102—42no—
153#102—82no—
154#102D811yescharacteristic
155C22⋊C8—21no—
156C22⋊C8—42no—
157C4×C8—21no—
158C4×C8C2×D411yescharacteristic
159C4×C8C2×D411yescharacteristic
160C4×C8C2411yescharacteristic
161C24—82no—
162C2×Q8—42no—
163C2×Q8—82no—
164C2×Q8—84no—
165C2×Q8—162no—
166C2×Q8C2×D811yescharacteristic
167C2×D4—22no—
168C2×D4—42no—
169C2×D4—42no—
170C2×D4—42no—
171C2×D4—82no—
172C2×D4—84no—
173C2×D4—82no—
174C2×D4—84no—
175C2×D4—162no—
176C2×D4—162no—
177C2×D4C2×D811yescharacteristic
178C22×C4—21no—
179C22×C4—42no—
180C22×C4—82no—
181SD16—84no—
182SD16—84no—
183SD16—84no—
184SD16—162no—
185SD16D1614yesdirect product factor
186D8—22no—
187D8—42no—
188D8—42no—
189D8—82no—
190D8—84no—
191D8C2×SD1614yescomplemented
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—42no—
198C2×C8—84no—
199C2×C8C2×D811yescharacteristic
200C2×C8C2×D811yescharacteristic
201C2×C8C22×D411yescharacteristic
202C2×C8H(5,𝔽2)11yescharacteristic
203C4⋊C4—21no—
204C4⋊C4—22no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—82no—
208C4⋊C4C2×D811yescharacteristic
209C4⋊C4C2×D811yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—42no—
212C22⋊C4—82no—
213C22⋊C4—82no—
214C42—21no—
215C42C22×D411yescharacteristic
216C16—21no—
217C16—41no—
218C16—41no—
219C16—41no—
220C16C2×SD1612yescomplemented
221C23—21no—
222C23—42no—
223C23—82no—
224C23—164no—
225C23—164no—
226C23—322no—
227Q8—21no—
228Q8—82no—
229Q8—82no—
230Q8—164no—
231Q8C2×D1612yescomplemented
232D4—21no—
233D4—24no—
234D4—42no—
235D4—82no—
236D4—82no—
237D4—82no—
238D4—82no—
239D4—162no—
240D4—164no—
241D4—164no—
242D4C2×D1612yes—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—82no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4—164no—
253C2×C4D4211yescharacteristic
254C2×C4C22×D811yescharacteristic
255C2×C4#57611yescharacteristic
256C8—21no—
257C8—21no—
258C8—41no—
259C8—41no—
260C8—41no—
261C8—82no—
262C8C2×D1612yescomplemented
263C8C22×SD1611yescharacteristic
264C8#57711yescharacteristic
265C22—22no—
266C22—41no—
267C22—41no—
268C22—44no—
269C22—82no—
270C22—82no—
271C22—162no—
272C22—162no—
273C22—162no—
274C22—328no—
275C22D4×D811yescharacteristic
276C4—22no—
277C4—21no—
278C4—41no—
279C4—41no—
280C4—82no—
281C4—162no—
282C4D4×SD1611yescharacteristic
283C4#329011yescharacteristic
284C4C22×D1611yescharacteristic
285C4#341511yescharacteristic
286C2—42no—
287C2—84no—
288C2—322no—
289C2D8×SD1611yescharacteristic
290C2D4×D1611yescharacteristic
291C2#3385911yescharacteristic
subgroupG/H
center, socleC22D4×D8
commutator, Frattini, cosocleC4×C8C24
prime radicalD4×D16C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C42 ◁ C8×SD16 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. Q8×D16C2semidirect
3. D8×SD16C2semidirect
4. #12503C2semidirect
5. #12451C2semidirect
6. #12439C2semidirect
7. #12416C2semidirect
8. #12368C2semidirect
9. #12352C2semidirect
10. C16×SD16C2semidirect
11. C8×D16C2semidirect
13. Q8×D8C22semidirect
17. #2252C22semidirect
19. #2240C22semidirect
21. #2224C22semidirect
25. Q8×C16C22semidirect
29. #1706C22semidirect
31. #1668C22semidirect
36. C8×D8C22semidirect
37. #1371C22semidirect
38. #1367C22semidirect
39. #1364C22semidirect
40. #1361C22semidirect
41. Q8⋊C16C22semidirect
42. #1331C22semidirect
44. C8×C16C22semidirect
131. D16SD16direct (N × H)
185. SD16D16direct (N × H)
191. D8C2×SD16semidirect
220. C16C2×SD16semidirect
231. Q8C2×D16semidirect
262. C8C2×D16semidirect

Maximal subgroups

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

subgroupindex
Q8×D162
D4×D162
D8×SD162
#125032
#124512
#124392
#124162
#123682
#123522
C16×SD162
C8×D162