Finite Group Databasebeta

← SD16×D76 #14575332

Subgroups — SD16×D76 #14575332

Order 2432.

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×D19C212yesmaximal, complemented
2Q8×D76C211yesmaximal, characteristic, complemented
3D4×D76C211yesmaximal, characteristic
4#11926917C211yesmaximal, characteristic, complemented
5#11926774C212yesmaximal, complemented
6#11926749C211yesmaximal, characteristic, complemented
7#11926744C211yesmaximal, characteristic, complemented
8#11926696C212yesmaximal, complemented
9#11926684C212yesmaximal, complemented
10C8×D76C211yesmaximal, characteristic, complemented
11C4×SD16×C19C211yesmaximal, characteristic, complemented
12C2×Q8×D19C2212yescomplemented
13C2×D4×D19C2212yes—
14C22×D76—21no—
15C2×SD16×C19C2211yescharacteristic
16C4×Q8×C19C2211yescharacteristic, complemented
17C4×D4×C19C2211yescharacteristic
18C2×#64527C2212yescomplemented
19C2×#64526C2212yes—
20#10597376—21no—
21SD16×D19—28no—
22C2×#64516C2212yescomplemented
23C2×#64516C2212yescomplemented
24C2×C8×D19C2212yescomplemented
25#10597343—22no—
26#10597343C2212yescomplemented
27#10597341C2212yes—
28#10597328—22no—
29#10597320C2211yescharacteristic
30C4×D76—21no—
31C4×D76C2211yescharacteristic
32#10597315—21no—
33#10597315C2211yescharacteristic, complemented
34C19×#106C2211yescharacteristic, complemented
35C19×#103C2211yescharacteristic, complemented
36C19×#102C2211yescharacteristic
37C4×C8×C19C2211yescharacteristic, complemented
38(C2×D19)⋊C8C2212yescomplemented
39#10597267C2212yescomplemented
40#10597266C2212yescomplemented
41C4⋊(C19⋊C8)C2211yescharacteristic, complemented
42C23×D19—22no—
43C2×Q8×C19C2311yescharacteristic
44C2×D4×C19C2311yescharacteristic
45C22×C4×C19—21no—
46C2×C22⋊D19—22no—
47Q8×D19—24no—
48Q8×D19—42no—
49D4×D19—24no—
50D4×D19—42no—
51C2×D76—22no—
52C2×D76—21no—
53C2×D76—21no—
54C2×D76—44no—
55C2×D76D411yescharacteristic
56C2×D76C2312yes—
57C2×C4×D19—22no—
58C2×C4×D19C2312yes—
59C2×Dic38—22no—
60C2×Dic38C2312yes—
61SD16×C19D414yescomplemented
62C2×C8×C19C2311yescharacteristic
63C2×C8×C19C2311yescharacteristic
64C4⋊C4×C19—21no—
65C4⋊C4×C19C2311yescharacteristic
66C4⋊C4×C19C2311yescharacteristic
67C22⋊C4×C19—21no—
68C42×C19—21no—
69C42×C19C2311yescharacteristic
70#64527—24no—
71#64526—24no—
72(C2×D19)⋊C4—22no—
73(C2×D19)⋊C4—22no—
74(C2×D19)⋊C4D412yes—
75C4⋊Dic19—21no—
76C4⋊Dic19—21no—
77C4⋊Dic19—22no—
78C4⋊Dic19D411yescharacteristic
79C2×C19⋊C8C2312yes—
80#64516—24no—
81#64516—42no—
82C8×D19—24no—
83C23×C19—21no—
84C22×D19—22no—
85C22×D19—44no—
86C22×D19—44no—
87C22×D19—82no—
88C22×D19C2×D412yes—
89Q8×C19—21no—
90Q8×C19C2×D412yescomplemented
91D4×C19—21no—
92D4×C19C2×D412yes—
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—42no—
97C2×C4×C19C2×D411yescharacteristic
98C2×C4×C19C2×D411yescharacteristic
99C2×C4×C19C2411yescharacteristic
100C22⋊D19—44no—
101C2×Dic19—22no—
102C2×Dic19C2×D412yes—
103D76—22no—
104D76—22no—
105D76—44no—
106D76—42no—
107D76—81no—
108D76SD1614yesdirect product factor
109C4×D19—22no—
110C4×D19—22no—
111C4×D19—44no—
112Dic38—22no—
113Dic38—22no—
114Dic38—44no—
115C8×C19—21no—
116C8×C19C2×D412yescomplemented
117C19⋊C8—22no—
118D4×SD16—191nomaximal, Sylow
119C22×C19—22no—
120C22×C19—41no—
121C22×C19—41no—
122C22×C19C22×D411yescharacteristic
123C2×D19—22no—
124C2×D19—22no—
125C2×D19—42no—
126C2×D19—42no—
127C2×D19—42no—
128C2×D19—88no—
129C2×D19C2×SD1614yescomplemented
130C4×C19—22no—
131C4×C19—21no—
132C4×C19—41no—
133C4×C19—41no—
134C4×C19C2×SD1612yescomplemented
135C4×C19C22×D411yescharacteristic
136C4×C19H(5,𝔽2)11yescharacteristic
137Dic19—22no—
138Dic19—42no—
139C22×SD16—192no—
140D4×Q8—191no—
141D42—191no—
142#492—191no—
143#465—192no—
144#461—191no—
145#460—191no—
146#450—192no—
147#448—192no—
148C4×SD16D1911yescharacteristic, complemented
149C8×D4—191no—
150C2×C19—42no—
151C2×C19D4211yescharacteristic
152C2×C19C22×SD1611yescharacteristic
153C2×C19#57711yescharacteristic
154D19—24no—
155D19—82no—
156C22×Q8—192no—
157C22×D4—192no—
158C22×D4—381no—
159C2×SD16—192no—
160C2×SD16—192no—
161C2×SD16—192no—
162C2×SD16—192no—
163C2×SD16—388no—
164C2×SD16C2×D1911yescharacteristic
165C22×C8—192no—
166C4⋊Q8—191no—
167C4⋊Q8—381no—
168#127—191no—
169C22⋊Q8—192no—
170C22⋊Q8—382no—
171#121—192no—
172#121—381no—
173#120—382no—
174C4×Q8C2×D1911yescharacteristic, complemented
175C4×D4—191no—
176C4×D4—381no—
177C4×D4C2×D1911yescharacteristic
178#106C2×D1911yescharacteristic, complemented
179C4⋊C8—191no—
180#103—192no—
181#103C2×D1911yescharacteristic, complemented
182#102—192no—
183#102C2×D1911yescharacteristic
184C22⋊C8—192no—
185C4×C8C2×D1911yescharacteristic, complemented
186C19D4×SD1611yescharacteristic, complemented, Sylow
187C24—382no—
188C2×Q8—192no—
189C2×Q8—382no—
190C2×Q8—384no—
191C2×Q8—762no—
192C2×Q8C22×D1911yescharacteristic
193C2×D4—191no—
194C2×D4—192no—
195C2×D4—382no—
196C2×D4—382no—
197C2×D4—384no—
198C2×D4—381no—
199C2×D4—381no—
200C2×D4—764no—
201C2×D4—762no—
202C2×D4C22×D1911yescharacteristic
203C22×C4—21no—
204C22×C4—192no—
205C22×C4—382no—
206SD16—384no—
207SD16—384no—
208SD16—384no—
209SD16—762no—
210SD16D7614yesdirect product factor
211C2×C8—192no—
212C2×C8—384no—
213C2×C8C22×D1911yescharacteristic
214C2×C8C22×D1911yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—191no—
217C4⋊C4—382no—
218C4⋊C4—381no—
219C4⋊C4—381no—
220C4⋊C4C22×D1911yescharacteristic
221C4⋊C4C22×D1911yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—192no—
224C22⋊C4—382no—
225C22⋊C4—382no—
226C42—21no—
227C42C22×D1911yescharacteristic
228C23—21no—
229C23—192no—
230C23—382no—
231C23—764no—
232C23—764no—
233C23—1522no—
234Q8—21no—
235Q8—382no—
236Q8—382no—
237Q8—764no—
238Q8C2×D7612yescomplemented
239D4—21no—
240D4—194no—
241D4—382no—
242D4—382no—
243D4—764no—
244D4—764no—
245D4—762no—
246D4—1521no—
247D4C2×D7612yes—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—192no—
253C2×C4—382no—
254C2×C4—382no—
255C2×C4—382no—
256C2×C4—764no—
257C2×C4D4×D1911yescharacteristic
258C2×C4D4×D1911yescharacteristic
259C2×C4C23×D1911yescharacteristic
260C8—21no—
261C8—382no—
262C8C2×D7612yescomplemented
263C22—22no—
264C22—41no—
265C22—41no—
266C22—194no—
267C22—382no—
268C22—382no—
269C22—762no—
270C22—762no—
271C22—762no—
272C22—1528no—
273C22C2×D4×D1911yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—41no—
278C4—382no—
279C4—762no—
280C4SD16×D1912yescomplemented
281C4C22×D7611yescharacteristic
282C4#1059743511yescharacteristic
283C2—42no—
284C2—384no—
285C2—1522no—
286C2D4×D7611yescharacteristic
287C2C2×SD16×D1911yescharacteristic
288C2#1192735111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC4×SD16×C19C2
socleC22×C19C22×D4
prime radicalD4×D76C2
hypercenterC4×SD16D19
hypocenterC19D4×SD16
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D19C2semidirect
2. Q8×D76C2semidirect
4. #11926917C2semidirect
5. #11926774C2semidirect
6. #11926749C2semidirect
7. #11926744C2semidirect
8. #11926696C2semidirect
9. #11926684C2semidirect
10. C8×D76C2semidirect
11. C4×SD16×C19C2semidirect
12. C2×Q8×D19C22semidirect
16. C4×Q8×C19C22semidirect
18. C2×#64527C22semidirect
22. C2×#64516C22semidirect
23. C2×#64516C22semidirect
24. C2×C8×D19C22semidirect
26. #10597343C22semidirect
33. #10597315C22semidirect
34. C19×#106C22semidirect
35. C19×#103C22semidirect
37. C4×C8×C19C22semidirect
38. (C2×D19)⋊C8C22semidirect
39. #10597267C22semidirect
40. #10597266C22semidirect
41. C4⋊(C19⋊C8)C22semidirect
61. SD16×C19D4semidirect
90. Q8×C19C2×D4semidirect
108. D76SD16direct (N × H)
116. C8×C19C2×D4semidirect
129. C2×D19C2×SD16semidirect
134. C4×C19C2×SD16semidirect
148. C4×SD16D19semidirect
174. C4×Q8C2×D19semidirect
178. #106C2×D19semidirect
181. #103C2×D19semidirect
185. C4×C8C2×D19semidirect
186. C19D4×SD16semidirect
210. SD16D76direct (N × H)
238. Q8C2×D76semidirect
262. C8C2×D76semidirect
280. C4SD16×D19semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D192
Q8×D762
D4×D762
#119269172
#119267742
#119267492
#119267442
#119266962
#119266842
C8×D762
C4×SD16×C192
D4×SD1619