Finite Group Databasebeta

← D4×#64527 #14575331

Subgroups — D4×#64527 #14575331

Order 2432.

546 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×#64527C212yesmaximal, complemented
2D4×D76C211yesmaximal, characteristic
3#11926918C211yesmaximal, characteristic, complemented
4#11926775C212yesmaximal, complemented
5#11926746C211yesmaximal, characteristic, complemented
6#11926744C211yesmaximal, characteristic, complemented
7#11926694C212yesmaximal, complemented
8#11926683C212yesmaximal, complemented
9C4×#64527C211yesmaximal, characteristic, complemented
10D4×C19⋊C8C211yesmaximal, characteristic, complemented
11D4×Q8×C19C211yesmaximal, characteristic, complemented
12C22×Q8×C19C2212yescomplemented
13C2×D4×D19—21no—
14C22×D76C2212yes—
15C19×C4⋊Q8—21no—
16C19×C4⋊Q8C2211yescharacteristic, complemented
17C19×C22⋊Q8—22no—
18C19×C22⋊Q8C2212yescomplemented
19C4×Q8×C19C2211yescharacteristic, complemented
20C4×D4×C19—21no—
21C4×D4×C19C2211yescharacteristic
22C2×#64527—28no—
23C2×#64527C2212yes—
24C2×#64527C2211yescharacteristic
25C2×#64527C2212yescomplemented
26C2×#64527C2212yescomplemented
27C2×#64527C2212yescomplemented
28#10597376C2212yes—
29C22×C19⋊C8C2212yescomplemented
30#10597341—21no—
31#10597328—22no—
32#10597320C2211yescharacteristic
33C4×D76C2211yescharacteristic
34#10597292C2211yescharacteristic, complemented
35#10597292C2212yescomplemented
36C22⋊(C19⋊C8)C2212yescomplemented
37#10597266C2211yescharacteristic
38#10597266C2212yescomplemented
39#10597265C2211yescharacteristic, complemented
40C4⋊(C19⋊C8)C2211yescharacteristic, complemented
41C4×C19⋊C8C2211yescharacteristic, complemented
42C23×D19—22no—
43C2×Q8×C19—22no—
44C2×Q8×C19—24no—
45C2×Q8×C19—42no—
46C2×Q8×C19C2312yes—
47C2×Q8×C19C2311yescharacteristic
48C2×D4×C19D411yescharacteristic
49C22×C4×C19—22no—
50C22×C4×C19C2312yes—
51C2×C22⋊D19—22no—
52D4×D19—44no—
53C2×D76—24no—
54C2×D76—22no—
55C2×D76—21no—
56C2×D76—21no—
57C2×D76—42no—
58C2×D76C2312yes—
59C2×D76C2311yescharacteristic
60C2×C4×D19—21no—
61C4⋊C4×C19—21no—
62C4⋊C4×C19—21no—
63C4⋊C4×C19—21no—
64C4⋊C4×C19—22no—
65C4⋊C4×C19D411yescharacteristic
66C4⋊C4×C19C2311yescharacteristic
67C22⋊C4×C19—22no—
68C22⋊C4×C19D412yes—
69C42×C19—21no—
70C42×C19C2311yescharacteristic
71#64527—24no—
72#64527—24no—
73#64527—24no—
74#64527—42no—
75#64527D414yesdirect product factor
76(C2×D19)⋊C4—22no—
77(C2×D19)⋊C4—21no—
78C4⋊Dic19C2311yescharacteristic
79C2×C19⋊C8—24no—
80C2×C19⋊C8C2312yes—
81C2×C19⋊C8C2311yescharacteristic
82C2×C19⋊C8C2311yescharacteristic
83C23×C19C2×D412yes—
84C22×D19—21no—
85C22×D19—22no—
86C22×D19—44no—
87C22×D19—44no—
88C22×D19—82no—
89Q8×C19—21no—
90Q8×C19—22no—
91Q8×C19—22no—
92Q8×C19—44no—
93Q8×C19C2×D412yescomplemented
94D4×C19SD1614yescomplemented
95C2×C4×C19—21no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—21no—
99C2×C4×C19—22no—
100C2×C4×C19—44no—
101C2×C4×C19C2×D411yescharacteristic
102C2×C4×C19C2×D412yes—
103C2×C4×C19C2×D411yescharacteristic
104C2×C4×C19C2411yescharacteristic
105C22⋊D19—44no—
106C2×Dic19—21no—
107D76—22no—
108D76—21no—
109D76—22no—
110D76—44no—
111D76—42no—
112D76—81no—
113D76C2×D412yes—
114C4×D19—42no—
115C19⋊C8—22no—
116C19⋊C8—21no—
117C19⋊C8C2×D412yescomplemented
118D4×SD16—191nomaximal, Sylow
119C22×C19—22no—
120C22×C19—22no—
121C22×C19C2×SD1614yescomplemented
122C22×C19C22×D411yescharacteristic
123C2×D19—22no—
124C2×D19—41no—
125C2×D19—41no—
126C2×D19—42no—
127C2×D19—42no—
128C2×D19—42no—
129C2×D19—88no—
130C4×C19—22no—
131C4×C19—22no—
132C4×C19—21no—
133C4×C19—42no—
134C4×C19—41no—
135C4×C19C2×SD1612yescomplemented
136C4×C19C22×D411yescharacteristic
137C4×C19H(5,𝔽2)11yescharacteristic
138Dic19—41no—
139C22×SD16—192no—
140D4×Q8D1911yescharacteristic, complemented
141D42—191no—
142#492—191no—
143#465—192no—
144#461—191no—
145#460—191no—
146#450—192no—
147#448—192no—
148C4×SD16—191no—
149C8×D4—191no—
150C2×C19—24no—
151C2×C19D4211yescharacteristic
152C2×C19C22×SD1611yescharacteristic
153C2×C19#57711yescharacteristic
154D19—42no—
155D19—82no—
156C22×Q8C2×D1912yescomplemented
157C22×D4—192no—
158C22×D4—381no—
159C2×SD16—191no—
160C2×SD16—192no—
161C2×SD16—192no—
162C2×SD16—192no—
163C2×SD16—192no—
164C2×SD16—388no—
165C22×C8—192no—
166C4⋊Q8—21no—
167C4⋊Q8C2×D1911yescharacteristic, complemented
168#127—191no—
169C22⋊Q8—22no—
170C22⋊Q8C2×D1912yescomplemented
171#121—192no—
172#121—381no—
173#120—382no—
174C4×Q8C2×D1911yescharacteristic, complemented
175C4×D4—21no—
176C4×D4—191no—
177C4×D4C2×D1911yescharacteristic
178#106—191no—
179C4⋊C8—191no—
180#103—191no—
181#103—192no—
182#102—191no—
183#102—192no—
184C22⋊C8—192no—
185C4×C8—191no—
186C19D4×SD1611yescharacteristic, complemented, Sylow
187C24—382no—
188C2×Q8—22no—
189C2×Q8—24no—
190C2×Q8—42no—
191C2×Q8C22×D1912yes—
192C2×Q8C22×D1911yescharacteristic
193C2×D4—191no—
194C2×D4—192no—
195C2×D4—384no—
196C2×D4—382no—
197C2×D4—382no—
198C2×D4—381no—
199C2×D4—381no—
200C2×D4—762no—
201C2×D4—764no—
202C2×D4C22⋊D1911yescharacteristic
203C22×C4—22no—
204C22×C4—381no—
205C22×C4C22×D1912yes—
206SD16—194no—
207SD16—384no—
208SD16—384no—
209SD16—384no—
210SD16—762no—
211C2×C8—191no—
212C2×C8—191no—
213C2×C8—192no—
214C2×C8—384no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—22no—
219C4⋊C4—191no—
220C4⋊C4C22⋊D1911yescharacteristic
221C4⋊C4C22×D1911yescharacteristic
222C22⋊C4—22no—
223C22⋊C4—381no—
224C22⋊C4—382no—
225C22⋊C4C22⋊D1912yes—
226C42—21no—
227C42C22×D1911yescharacteristic
228C23—381no—
229C23—382no—
230C23—764no—
231C23—764no—
232C23—1522no—
233C23C2×C22⋊D1912yes—
234Q8—21no—
235Q8—22no—
236Q8—22no—
237Q8—44no—
238Q8D4×D1912yescomplemented
239D4—192no—
240D4—382no—
241D4—381no—
242D4—382no—
243D4—764no—
244D4—764no—
245D4—762no—
246D4—1521no—
247D4#6452714yesdirect product factor
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—44no—
254C2×C4—381no—
255C2×C4—762no—
256C2×C4C2×C22⋊D1911yescharacteristic
257C2×C4C2×C22⋊D1912yes—
258C2×C4C2×C22⋊D1911yescharacteristic
259C2×C4C23×D1911yescharacteristic
260C8—192no—
261C8—382no—
262C8—381no—
263C22—22no—
264C22—22no—
265C22—382no—
266C22—761no—
267C22—761no—
268C22—762no—
269C22—762no—
270C22—762no—
271C22—1528no—
272C22C2×#6452714yescomplemented
273C22C22×C22⋊D1911yescharacteristic
274C4—21no—
275C4—22no—
276C4—22no—
277C4—41no—
278C4—42no—
279C4—761no—
280C4C2×#6452712yescomplemented
281C4C2×D4×D1911yescharacteristic
282C4#1059743011yescharacteristic
283C2—24no—
284C2—762no—
285C2—1522no—
286C2D4×C22⋊D1911yescharacteristic
287C2C22×#6452711yescharacteristic
288C2#1192735211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingD4×Q8×C19C2
socleC22×C19C22×D4
prime radicalD4×D76C2
hypercenterD4×Q8D19
hypocenterC19D4×SD16
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#64527C2semidirect
3. #11926918C2semidirect
4. #11926775C2semidirect
5. #11926746C2semidirect
6. #11926744C2semidirect
7. #11926694C2semidirect
8. #11926683C2semidirect
9. C4×#64527C2semidirect
10. D4×C19⋊C8C2semidirect
11. D4×Q8×C19C2semidirect
12. C22×Q8×C19C22semidirect
16. C19×C4⋊Q8C22semidirect
18. C19×C22⋊Q8C22semidirect
19. C4×Q8×C19C22semidirect
25. C2×#64527C22semidirect
26. C2×#64527C22semidirect
27. C2×#64527C22semidirect
29. C22×C19⋊C8C22semidirect
34. #10597292C22semidirect
35. #10597292C22semidirect
36. C22⋊(C19⋊C8)C22semidirect
38. #10597266C22semidirect
39. #10597265C22semidirect
40. C4⋊(C19⋊C8)C22semidirect
41. C4×C19⋊C8C22semidirect
75. #64527D4direct (N × H)
93. Q8×C19C2×D4semidirect
94. D4×C19SD16semidirect
117. C19⋊C8C2×D4semidirect
121. C22×C19C2×SD16semidirect
135. C4×C19C2×SD16semidirect
140. D4×Q8D19semidirect
156. C22×Q8C2×D19semidirect
167. C4⋊Q8C2×D19semidirect
170. C22⋊Q8C2×D19semidirect
174. C4×Q8C2×D19semidirect
186. C19D4×SD16semidirect
238. Q8D4×D19semidirect
247. D4#64527direct (N × H)
272. C22C2×#64527semidirect
280. C4C2×#64527semidirect

Maximal subgroups

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

subgroupindex
C22×#645272
D4×D762
#119269182
#119267752
#119267462
#119267442
#119266942
#119266832
C4×#645272
D4×C19⋊C82
D4×Q8×C192
D4×SD1619