Finite Group Databasebeta

← D4×#64516 #14575333

Subgroups — D4×#64516 #14575333

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×#64516C212yesmaximal, complemented
2D4×Dic38C211yesmaximal, characteristic, complemented
3D4×D76C211yesmaximal, characteristic
4#11926917C211yesmaximal, characteristic, complemented
5#11926773C212yesmaximal, complemented
6#11926750C211yesmaximal, characteristic, complemented
7#11926745C211yesmaximal, characteristic, complemented
8#11926697C212yesmaximal, complemented
9#11926685C212yesmaximal, complemented
10C4×#64516C211yesmaximal, characteristic, complemented
11C8×D4×C19C211yesmaximal, characteristic, complemented
12C2×D4×D19—21no—
13C22×D76C2212yes—
14C22×Dic38C2212yescomplemented
15C22×C8×C19C2212yescomplemented
16C4×D4×C19C2211yescharacteristic
17D4×Dic19—21no—
18#10597376C2212yes—
19#10597370C2212yescomplemented
20C2×#64516—28no—
21C2×#64516C2212yes—
22C2×#64516C2211yescharacteristic
23C2×#64516C2212yescomplemented
24C2×#64516C2212yescomplemented
25C2×#64516C2212yescomplemented
26#10597341—21no—
27#10597334—21no—
28#10597328—22no—
29#10597324—22no—
30#10597320C2211yescharacteristic
31C4×D76C2211yescharacteristic
32#10597315C2211yescharacteristic, complemented
33C4×Dic38C2211yescharacteristic, complemented
34C19×C4⋊C8C2211yescharacteristic, complemented
35C19×C22⋊C8C2212yescomplemented
36C4×C8×C19C2211yescharacteristic, complemented
37#10597278C2211yescharacteristic
38#10597278C2212yescomplemented
39#10597274C2211yescharacteristic, complemented
40#10597273C2211yescharacteristic, complemented
41#10597273C2212yescomplemented
42C23×D19—22no—
43C2×D4×C19D411yescharacteristic
44C22×C4×C19C2312yes—
45C2×C22⋊D19—22no—
46C22×Dic19—22no—
47D4×D19—44no—
48C2×D76—24no—
49C2×D76—22no—
50C2×D76—21no—
51C2×D76—21no—
52C2×D76—42no—
53C2×D76C2312yes—
54C2×D76C2311yescharacteristic
55C2×C4×D19—21no—
56C2×Dic38—24no—
57C2×Dic38—22no—
58C2×Dic38—42no—
59C2×Dic38C2312yes—
60C2×Dic38C2311yescharacteristic
61C2×C8×C19—24no—
62C2×C8×C19C2312yes—
63C2×C8×C19C2311yescharacteristic
64C2×C8×C19C2311yescharacteristic
65C4⋊C4×C19D411yescharacteristic
66C22⋊C4×C19D412yes—
67C42×C19C2311yescharacteristic
68C22⋊Dic19—22no—
69(C2×D19)⋊C4—22no—
70(C2×D19)⋊C4—21no—
71C4⋊Dic19—21no—
72C4⋊Dic19—21no—
73C4⋊Dic19C2311yescharacteristic
74C4⋊Dic19C2311yescharacteristic
75Dic19⋊C4—21no—
76Dic19⋊C4—22no—
77C4×Dic19—21no—
78#64516—24no—
79#64516—24no—
80#64516—24no—
81#64516—42no—
82#64516D414yesdirect product factor
83C23×C19C2×D412yes—
84C22×D19—21no—
85C22×D19—22no—
86C22×D19—44no—
87C22×D19—44no—
88C22×D19—82no—
89D4×C19SD1614yescomplemented
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19C2×D411yescharacteristic
93C2×C4×C19C2×D412yes—
94C2×C4×C19C2×D411yescharacteristic
95C2×C4×C19C2411yescharacteristic
96C22⋊D19—44no—
97C2×Dic19—21no—
98C2×Dic19—21no—
99C2×Dic19—22no—
100C2×Dic19—21no—
101C2×Dic19—44no—
102D76—22no—
103D76—21no—
104D76—22no—
105D76—44no—
106D76—42no—
107D76—81no—
108D76C2×D412yes—
109C4×D19—42no—
110Dic38—21no—
111Dic38—22no—
112Dic38—22no—
113Dic38—44no—
114Dic38C2×D412yescomplemented
115C8×C19—22no—
116C8×C19—21no—
117C8×C19C2×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—21no—
132C4×C19C2×SD1612yescomplemented
133C4×C19C22×D411yescharacteristic
134C4×C19H(5,𝔽2)11yescharacteristic
135Dic19—22no—
136Dic19—42no—
137Dic19—41no—
138Dic19—41no—
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×SD16—191no—
149C8×D4D1911yescharacteristic, complemented
150C2×C19—24no—
151C2×C19D4211yescharacteristic
152C2×C19C22×SD1611yescharacteristic
153C2×C19#57711yescharacteristic
154D19—42no—
155D19—82no—
156C22×Q8—192no—
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×C8C2×D1912yescomplemented
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×Q8—191no—
175C4×D4—191no—
176C4×D4—381no—
177C4×D4C2×D1911yescharacteristic
178#106—191no—
179C4⋊C8C2×D1911yescharacteristic, complemented
180#103—191no—
181#103—192no—
182#102—191no—
183#102—192no—
184C22⋊C8C2×D1912yescomplemented
185C4×C8C2×D1911yescharacteristic, complemented
186C19D4×SD1611yescharacteristic, complemented, Sylow
187C24—382no—
188C2×Q8—191no—
189C2×Q8—192no—
190C2×Q8—384no—
191C2×Q8—382no—
192C2×Q8—762no—
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×D4D7611yescharacteristic
203C22×C4—382no—
204C22×C4—381no—
205C22×C4C22×D1912yes—
206SD16—194no—
207SD16—384no—
208SD16—384no—
209SD16—384no—
210SD16—762no—
211C2×C8—24no—
212C2×C8C22×D1911yescharacteristic
213C2×C8C22×D1912yes—
214C2×C8C22×D1911yescharacteristic
215C4⋊C4—191no—
216C4⋊C4—191no—
217C4⋊C4—381no—
218C4⋊C4—382no—
219C4⋊C4—381no—
220C4⋊C4—381no—
221C4⋊C4D7611yescharacteristic
222C22⋊C4—382no—
223C22⋊C4—381no—
224C22⋊C4—382no—
225C22⋊C4D7612yes—
226C42—381no—
227C42C22×D1911yescharacteristic
228C23—381no—
229C23—382no—
230C23—764no—
231C23—764no—
232C23—1522no—
233C23C2×D7612yes—
234Q8—192no—
235Q8—381no—
236Q8—382no—
237Q8—382no—
238Q8—764no—
239D4—192no—
240D4—382no—
241D4—381no—
242D4—382no—
243D4—764no—
244D4—764no—
245D4—762no—
246D4—1521no—
247D4#6451614yesdirect product factor
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—381no—
251C2×C4—381no—
252C2×C4—381no—
253C2×C4—382no—
254C2×C4—764no—
255C2×C4—762no—
256C2×C4C2×D7611yescharacteristic
257C2×C4C2×D7612yes—
258C2×C4C2×D7611yescharacteristic
259C2×C4C23×D1911yescharacteristic
260C8—22no—
261C8—21no—
262C8D4×D1912yescomplemented
263C22—22no—
264C22—22no—
265C22—382no—
266C22—761no—
267C22—761no—
268C22—762no—
269C22—762no—
270C22—762no—
271C22—1528no—
272C22C2×#6451614yescomplemented
273C22C22×D7611yescharacteristic
274C4—21no—
275C4—22no—
276C4—382no—
277C4—761no—
278C4—761no—
279C4—762no—
280C4C2×#6451612yescomplemented
281C4C2×D4×D1911yescharacteristic
282C4#1059743511yescharacteristic
283C2—24no—
284C2—762no—
285C2—1522no—
286C2D4×D7611yescharacteristic
287C2C22×#6451611yescharacteristic
288C2#1192735611yescharacteristic
subgroupG/H
centerC22C22×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC8×D4×C19C2
socleC22×C19C22×D4
prime radicalD4×D76C2
hypercenterC8×D4D19
hypocenterC19D4×SD16
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×#64516C2semidirect
2. D4×Dic38C2semidirect
4. #11926917C2semidirect
5. #11926773C2semidirect
6. #11926750C2semidirect
7. #11926745C2semidirect
8. #11926697C2semidirect
9. #11926685C2semidirect
10. C4×#64516C2semidirect
11. C8×D4×C19C2semidirect
14. C22×Dic38C22semidirect
15. C22×C8×C19C22semidirect
19. #10597370C22semidirect
23. C2×#64516C22semidirect
24. C2×#64516C22semidirect
25. C2×#64516C22semidirect
32. #10597315C22semidirect
33. C4×Dic38C22semidirect
34. C19×C4⋊C8C22semidirect
35. C19×C22⋊C8C22semidirect
36. C4×C8×C19C22semidirect
38. #10597278C22semidirect
39. #10597274C22semidirect
40. #10597273C22semidirect
41. #10597273C22semidirect
82. #64516D4direct (N × H)
89. D4×C19SD16semidirect
114. Dic38C2×D4semidirect
117. C8×C19C2×D4semidirect
121. C22×C19C2×SD16semidirect
132. C4×C19C2×SD16semidirect
149. C8×D4D19semidirect
165. C22×C8C2×D19semidirect
179. C4⋊C8C2×D19semidirect
184. C22⋊C8C2×D19semidirect
185. C4×C8C2×D19semidirect
186. C19D4×SD16semidirect
247. D4#64516direct (N × H)
262. C8D4×D19semidirect
272. C22C2×#64516semidirect
280. C4C2×#64516semidirect

Maximal subgroups

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

subgroupindex
C22×#645162
D4×Dic382
D4×D762
#119269172
#119267732
#119267502
#119267452
#119266972
#119266852
C4×#645162
C8×D4×C192
D4×SD1619