Finite Group Databasebeta

← SD16×D1076 #46822582

Subgroups — SD16×D1076 #46822582

Order 34432.

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×D269C212yesmaximal, complemented
2Q8×D1076C211yesmaximal, characteristic, complemented
3D4×D1076C211yesmaximal, characteristic
4#31770978C211yesmaximal, characteristic, complemented
5#31770835C212yesmaximal, complemented
6#31770810C211yesmaximal, characteristic, complemented
7#31770805C211yesmaximal, characteristic, complemented
8#31770757C212yesmaximal, complemented
9#31770745C212yesmaximal, complemented
10C8×D1076C211yesmaximal, characteristic, complemented
11C4×SD16×C269C211yesmaximal, characteristic, complemented
12C2×Q8×D269C2212yescomplemented
13C22×D1076—21no—
14C2×D4×D269C2212yes—
15C2×#16864391C2212yescomplemented
16C2×#16864391C2212yescomplemented
17C2×#16864390C2212yes—
18C2×#16864389C2212yescomplemented
19SD16×D269—28no—
20C2×C8×D269C2212yescomplemented
21#22575453—21no—
22#22575453C2211yescharacteristic, complemented
23#22575450C2211yescharacteristic
24#22575433—22no—
25#22575433C2212yescomplemented
26#22575428C2212yes—
27#22575427—21no—
28#22575423—22no—
29C4×D1076—21no—
30C4×D1076C2211yescharacteristic
31C4⋊#14524130C2211yescharacteristic, complemented
32#22575376C2212yescomplemented
33#22575373C2212yescomplemented
34#22575365C2212yescomplemented
35C2×SD16×C269C2211yescharacteristic
36C4×Q8×C269C2211yescharacteristic, complemented
37C4×D4×C269C2211yescharacteristic
38#106×C269C2211yescharacteristic, complemented
39#103×C269C2211yescharacteristic, complemented
40#102×C269C2211yescharacteristic
41C4×C8×C269C2211yescharacteristic, complemented
42C23×D269—22no—
43C2×Dic538—22no—
44C2×Dic538C2312yes—
45Q8×D269—24no—
46Q8×D269—42no—
47C2×D1076—22no—
48C2×D1076—21no—
49C2×D1076—21no—
50C2×D1076—44no—
51C2×D1076D411yescharacteristic
52C2×D1076C2312yes—
53C2×C22⋊D269—22no—
54D4×D269—24no—
55D4×D269—42no—
56C2×C4×D269—22no—
57C2×C4×D269C2312yes—
58#16864391—24no—
59#16864391—42no—
60#16864390—24no—
61#16864389—24no—
62C2×#14524130C2312yes—
63C8×D269—24no—
64C4⋊Dic269—22no—
65C4⋊Dic269—21no—
66C4⋊Dic269—21no—
67C4⋊Dic269D411yescharacteristic
68#16864379—22no—
69#16864379—22no—
70#16864379D412yes—
71C2×Q8×C269C2311yescharacteristic
72C2×D4×C269C2311yescharacteristic
73C22×C4×C269—21no—
74SD16×C269D414yescomplemented
75C2×C8×C269C2311yescharacteristic
76C2×C8×C269C2311yescharacteristic
77C4⋊C4×C269—21no—
78C4⋊C4×C269C2311yescharacteristic
79C4⋊C4×C269C2311yescharacteristic
80C22⋊C4×C269—21no—
81C42×C269—21no—
82C42×C269C2311yescharacteristic
83C22×D269—22no—
84C22×D269—44no—
85C22×D269—44no—
86C22×D269—82no—
87C22×D269C2×D412yes—
88Dic538—22no—
89Dic538—22no—
90Dic538—44no—
91D1076—22no—
92D1076—22no—
93D1076—44no—
94D1076—42no—
95D1076—81no—
96D1076SD1614yesdirect product factor
97C22⋊D269—44no—
98C2×Dic269—22no—
99C2×Dic269C2×D412yes—
100C4×D269—22no—
101C4×D269—22no—
102C4×D269—44no—
103#14524130—22no—
104C23×C269—21no—
105Q8×C269—21no—
106Q8×C269C2×D412yescomplemented
107D4×C269—21no—
108D4×C269C2×D412yes—
109C2×C4×C269—21no—
110C2×C4×C269—21no—
111C2×C4×C269—21no—
112C2×C4×C269—42no—
113C2×C4×C269C2×D411yescharacteristic
114C2×C4×C269C2×D411yescharacteristic
115C2×C4×C269C2411yescharacteristic
116C8×C269—21no—
117C8×C269C2×D412yescomplemented
118C22×C269—22no—
119C22×C269—41no—
120C22×C269—41no—
121C22×C269C22×D411yescharacteristic
122C2×D269—22no—
123C2×D269—22no—
124C2×D269—42no—
125C2×D269—42no—
126C2×D269—42no—
127C2×D269—88no—
128C2×D269C2×SD1614yescomplemented
129C4×C269—22no—
130C4×C269—21no—
131C4×C269—41no—
132C4×C269—41no—
133C4×C269C2×SD1612yescomplemented
134C4×C269C22×D411yescharacteristic
135C4×C269H(5,𝔽2)11yescharacteristic
136Dic269—22no—
137Dic269—42no—
138C2×C269—42no—
139C2×C269D4211yescharacteristic
140C2×C269C22×SD1611yescharacteristic
141C2×C269#57711yescharacteristic
142D269—24no—
143D269—82no—
144C269D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—2691nomaximal, Sylow
146C22×SD16—2692no—
147D4×Q8—2691no—
148D42—2691no—
149#492—2691no—
150#465—2692no—
151#461—2691no—
152#460—2691no—
153#450—2692no—
154#448—2692no—
155C4×SD16D26911yescharacteristic, complemented
156C8×D4—2691no—
157C22×Q8—2692no—
158C22×D4—2692no—
159C22×D4—5381no—
160C2×SD16—2692no—
161C2×SD16—2692no—
162C2×SD16—2692no—
163C2×SD16—2692no—
164C2×SD16—5388no—
165C2×SD16C2×D26911yescharacteristic
166C22×C8—2692no—
167C4⋊Q8—2691no—
168C4⋊Q8—5381no—
169#127—2691no—
170C22⋊Q8—2692no—
171C22⋊Q8—5382no—
172#121—2692no—
173#121—5381no—
174#120—5382no—
175C4×Q8C2×D26911yescharacteristic, complemented
176C4×D4—2691no—
177C4×D4—5381no—
178C4×D4C2×D26911yescharacteristic
179#106C2×D26911yescharacteristic, complemented
180C4⋊C8—2691no—
181#103—2692no—
182#103C2×D26911yescharacteristic, complemented
183#102—2692no—
184#102C2×D26911yescharacteristic
185C22⋊C8—2692no—
186C4×C8C2×D26911yescharacteristic, complemented
187C24—5382no—
188C2×Q8—2692no—
189C2×Q8—5382no—
190C2×Q8—5384no—
191C2×Q8—10762no—
192C2×Q8C22×D26911yescharacteristic
193C2×D4—2691no—
194C2×D4—2692no—
195C2×D4—5382no—
196C2×D4—5382no—
197C2×D4—5384no—
198C2×D4—5381no—
199C2×D4—5381no—
200C2×D4—10764no—
201C2×D4—10762no—
202C2×D4C22×D26911yescharacteristic
203C22×C4—21no—
204C22×C4—2692no—
205C22×C4—5382no—
206SD16—5384no—
207SD16—5384no—
208SD16—5384no—
209SD16—10762no—
210SD16D107614yesdirect product factor
211C2×C8—2692no—
212C2×C8—5384no—
213C2×C8C22×D26911yescharacteristic
214C2×C8C22×D26911yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—2691no—
217C4⋊C4—5382no—
218C4⋊C4—5381no—
219C4⋊C4—5381no—
220C4⋊C4C22×D26911yescharacteristic
221C4⋊C4C22×D26911yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—2692no—
224C22⋊C4—5382no—
225C22⋊C4—5382no—
226C42—21no—
227C42C22×D26911yescharacteristic
228C23—21no—
229C23—2692no—
230C23—5382no—
231C23—10764no—
232C23—10764no—
233C23—21522no—
234Q8—21no—
235Q8—5382no—
236Q8—5382no—
237Q8—10764no—
238Q8C2×D107612yescomplemented
239D4—21no—
240D4—2694no—
241D4—5382no—
242D4—5382no—
243D4—10764no—
244D4—10764no—
245D4—10762no—
246D4—21521no—
247D4C2×D107612yes—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—2692no—
253C2×C4—5382no—
254C2×C4—5382no—
255C2×C4—5382no—
256C2×C4—10764no—
257C2×C4D4×D26911yescharacteristic
258C2×C4D4×D26911yescharacteristic
259C2×C4C23×D26911yescharacteristic
260C8—21no—
261C8—5382no—
262C8C2×D107612yescomplemented
263C22—22no—
264C22—41no—
265C22—41no—
266C22—2694no—
267C22—5382no—
268C22—5382no—
269C22—10762no—
270C22—10762no—
271C22—10762no—
272C22—21528no—
273C22C2×D4×D26911yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—41no—
278C4—5382no—
279C4—10762no—
280C4SD16×D26912yescomplemented
281C4C22×D107611yescharacteristic
282C4#2257549911yescharacteristic
283C2—42no—
284C2—5384no—
285C2—21522no—
286C2D4×D107611yescharacteristic
287C2C2×SD16×D26911yescharacteristic
288C2#3177141211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC4×SD16×C269C2
socleC22×C269C22×D4
prime radicalD4×D1076C2
hypercenterC4×SD16D269
hypocenterC269D4×SD16
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D269C2semidirect
2. Q8×D1076C2semidirect
4. #31770978C2semidirect
5. #31770835C2semidirect
6. #31770810C2semidirect
7. #31770805C2semidirect
8. #31770757C2semidirect
9. #31770745C2semidirect
10. C8×D1076C2semidirect
11. C4×SD16×C269C2semidirect
12. C2×Q8×D269C22semidirect
15. C2×#16864391C22semidirect
16. C2×#16864391C22semidirect
18. C2×#16864389C22semidirect
20. C2×C8×D269C22semidirect
22. #22575453C22semidirect
25. #22575433C22semidirect
31. C4⋊#14524130C22semidirect
32. #22575376C22semidirect
33. #22575373C22semidirect
34. #22575365C22semidirect
36. C4×Q8×C269C22semidirect
38. #106×C269C22semidirect
39. #103×C269C22semidirect
41. C4×C8×C269C22semidirect
74. SD16×C269D4semidirect
96. D1076SD16direct (N × H)
106. Q8×C269C2×D4semidirect
117. C8×C269C2×D4semidirect
128. C2×D269C2×SD16semidirect
133. C4×C269C2×SD16semidirect
144. C269D4×SD16semidirect
155. C4×SD16D269semidirect
175. C4×Q8C2×D269semidirect
179. #106C2×D269semidirect
182. #103C2×D269semidirect
186. C4×C8C2×D269semidirect
210. SD16D1076direct (N × H)
238. Q8C2×D1076semidirect
262. C8C2×D1076semidirect
280. C4SD16×D269semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D2692
Q8×D10762
D4×D10762
#317709782
#317708352
#317708102
#317708052
#317707572
#317707452
C8×D10762
C4×SD16×C2692
D4×SD16269