Finite Group Databasebeta

← D4×#64526 #14575327

Subgroups — D4×#64526 #14575327

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×#64526C212yesmaximal, complemented
2D4×Dic38C211yesmaximal, characteristic, complemented
3#11926916C211yesmaximal, characteristic, complemented
4#11926771C212yesmaximal, complemented
5#11926749C211yesmaximal, characteristic, complemented
6#11926741C211yesmaximal, characteristic, complemented
7#11926695C212yesmaximal, complemented
8#11926682C212yesmaximal, complemented
9C4×#64526C211yesmaximal, characteristic, complemented
10D4×C19⋊C8C211yesmaximal, characteristic, complemented
11D42×C19C211yesmaximal, characteristic
12C22×D4×C19—21no—
13C22×D4×C19C2212yes—
14C22×Dic38C2212yescomplemented
15C19×#127C2211yescharacteristic
16C19×#121—21no—
17C19×#121C2212yes—
18C19×#120—22no—
19C4×D4×C19C2211yescharacteristic
20C4×D4×C19C2211yescharacteristic
21D4×Dic19—21no—
22C2×#64526—28no—
23C2×#64526C2212yes—
24C2×#64526C2211yescharacteristic
25C2×#64526C2212yescomplemented
26C2×#64526C2212yescomplemented
27C2×#64526C2212yescomplemented
28#10597370C2212yescomplemented
29C22×C19⋊C8C2212yescomplemented
30#10597334—21no—
31#10597324—22no—
32#10597315C2211yescharacteristic, complemented
33C4×Dic38C2211yescharacteristic, complemented
34#10597289C2211yescharacteristic
35#10597289C2212yescomplemented
36C22⋊(C19⋊C8)C2212yescomplemented
37#10597267C2211yescharacteristic, complemented
38#10597267C2212yescomplemented
39#10597265C2211yescharacteristic, complemented
40C4⋊(C19⋊C8)C2211yescharacteristic, complemented
41C4×C19⋊C8C2211yescharacteristic, complemented
42C24×C19—22no—
43C2×D4×C19—24no—
44C2×D4×C19—22no—
45C2×D4×C19—22no—
46C2×D4×C19—21no—
47C2×D4×C19—21no—
48C2×D4×C19—42no—
49C2×D4×C19—44no—
50C2×D4×C19D411yescharacteristic
51C2×D4×C19C2312yes—
52C2×D4×C19C2311yescharacteristic
53C22×C4×C19—21no—
54C22×C4×C19C2312yes—
55C22×Dic19—22no—
56C2×Dic38—24no—
57C2×Dic38—22no—
58C2×Dic38—42no—
59C2×Dic38C2312yes—
60C2×Dic38C2311yescharacteristic
61C4⋊C4×C19D411yescharacteristic
62C4⋊C4×C19C2311yescharacteristic
63C22⋊C4×C19—21no—
64C22⋊C4×C19—22no—
65C22⋊C4×C19D412yes—
66C42×C19C2311yescharacteristic
67C22⋊Dic19—22no—
68#64526—24no—
69#64526—24no—
70#64526—24no—
71#64526—42no—
72#64526D414yesdirect product factor
73C4⋊Dic19—21no—
74C4⋊Dic19—21no—
75C4⋊Dic19C2311yescharacteristic
76Dic19⋊C4—21no—
77Dic19⋊C4—22no—
78C4×Dic19—21no—
79C2×C19⋊C8—24no—
80C2×C19⋊C8C2312yes—
81C2×C19⋊C8C2311yescharacteristic
82C2×C19⋊C8C2311yescharacteristic
83C23×C19—21no—
84C23×C19—22no—
85C23×C19—44no—
86C23×C19—44no—
87C23×C19—82no—
88C23×C19C2×D412yes—
89D4×C19—22no—
90D4×C19—21no—
91D4×C19—22no—
92D4×C19—44no—
93D4×C19—44no—
94D4×C19—42no—
95D4×C19—81no—
96D4×C19SD1614yescomplemented
97D4×C19C2×D412yes—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—21no—
101C2×C4×C19—42no—
102C2×C4×C19C2×D411yescharacteristic
103C2×C4×C19C2×D412yes—
104C2×C4×C19C2×D411yescharacteristic
105C2×C4×C19C2411yescharacteristic
106C2×Dic19—21no—
107C2×Dic19—21no—
108C2×Dic19—22no—
109C2×Dic19—44no—
110Dic38—21no—
111Dic38—22no—
112Dic38—22no—
113Dic38—44no—
114Dic38C2×D412yescomplemented
115C19⋊C8—22no—
116C19⋊C8—21no—
117C19⋊C8C2×D412yescomplemented
118D4×SD16—191nomaximal, Sylow
119C22×C19—22no—
120C22×C19—22no—
121C22×C19—22no—
122C22×C19—41no—
123C22×C19—41no—
124C22×C19—42no—
125C22×C19—42no—
126C22×C19—42no—
127C22×C19—88no—
128C22×C19C2×SD1614yescomplemented
129C22×C19C22×D411yescharacteristic
130C4×C19—22no—
131C4×C19—21no—
132C4×C19—41no—
133C4×C19C2×SD1612yescomplemented
134C4×C19C22×D411yescharacteristic
135C4×C19H(5,𝔽2)11yescharacteristic
136Dic19—22no—
137Dic19—42no—
138Dic19—41no—
139C22×SD16—192no—
140D4×Q8—191no—
141D42D1911yescharacteristic
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×C19—42no—
152C2×C19—82no—
153C2×C19D4211yescharacteristic
154C2×C19C22×SD1611yescharacteristic
155C2×C19#57711yescharacteristic
156C22×Q8—192no—
157C22×D4—21no—
158C22×D4C2×D1912yes—
159C2×SD16—191no—
160C2×SD16—192no—
161C2×SD16—192no—
162C2×SD16—192no—
163C2×SD16—192no—
164C2×SD16—388no—
165C22×C8—192no—
166C4⋊Q8—191no—
167C4⋊Q8—381no—
168#127C2×D1911yescharacteristic
169C22⋊Q8—192no—
170C22⋊Q8—382no—
171#121—21no—
172#121C2×D1912yes—
173#120—22no—
174C4×Q8—191no—
175C4×D4—381no—
176C4×D4C2×D1911yescharacteristic
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—22no—
188C2×Q8—191no—
189C2×Q8—192no—
190C2×Q8—384no—
191C2×Q8—382no—
192C2×Q8—762no—
193C2×D4—24no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—42no—
199C2×D4—44no—
200C2×D4C22⋊D1911yescharacteristic
201C2×D4C22×D1912yes—
202C2×D4C22×D1911yescharacteristic
203C22×C4—21no—
204C22×C4—382no—
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—191no—
216C4⋊C4—381no—
217C4⋊C4—382no—
218C4⋊C4—381no—
219C4⋊C4—381no—
220C4⋊C4C22⋊D1911yescharacteristic
221C4⋊C4C22×D1911yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—22no—
224C22⋊C4—382no—
225C22⋊C4C22⋊D1912yes—
226C42—381no—
227C42C22×D1911yescharacteristic
228C23—21no—
229C23—22no—
230C23—44no—
231C23—44no—
232C23—82no—
233C23C2×C22⋊D1912yes—
234Q8—192no—
235Q8—381no—
236Q8—382no—
237Q8—382no—
238Q8—764no—
239D4—22no—
240D4—21no—
241D4—22no—
242D4—44no—
243D4—44no—
244D4—42no—
245D4—81no—
246D4#6452614yesdirect product factor
247D4D4×D1912yes—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—381no—
253C2×C4—381no—
254C2×C4—382no—
255C2×C4—764no—
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—22no—
266C22—41no—
267C22—41no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—88no—
272C22C2×#6452614yescomplemented
273C22C22×C22⋊D1911yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—382no—
278C4—761no—
279C4—762no—
280C4C2×#6452612yescomplemented
281C4C2×D4×D1911yescharacteristic
282C4#1059743011yescharacteristic
283C2—24no—
284C2—42no—
285C2—82no—
286C2D4×C22⋊D1911yescharacteristic
287C2C22×#6452611yescharacteristic
288C2#1192735511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
Fitting, prime radicalD42×C19C2
socleC22×C19C22×D4
hypercenterD42D19
hypocenterC19D4×SD16
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C22×#64526C2semidirect
2. D4×Dic38C2semidirect
3. #11926916C2semidirect
4. #11926771C2semidirect
5. #11926749C2semidirect
6. #11926741C2semidirect
7. #11926695C2semidirect
8. #11926682C2semidirect
9. C4×#64526C2semidirect
10. D4×C19⋊C8C2semidirect
14. C22×Dic38C22semidirect
25. C2×#64526C22semidirect
26. C2×#64526C22semidirect
27. C2×#64526C22semidirect
28. #10597370C22semidirect
29. C22×C19⋊C8C22semidirect
32. #10597315C22semidirect
33. C4×Dic38C22semidirect
35. #10597289C22semidirect
36. C22⋊(C19⋊C8)C22semidirect
37. #10597267C22semidirect
38. #10597267C22semidirect
39. #10597265C22semidirect
40. C4⋊(C19⋊C8)C22semidirect
41. C4×C19⋊C8C22semidirect
72. #64526D4direct (N × H)
96. D4×C19SD16semidirect
114. Dic38C2×D4semidirect
117. C19⋊C8C2×D4semidirect
128. C22×C19C2×SD16semidirect
133. C4×C19C2×SD16semidirect
186. C19D4×SD16semidirect
246. D4#64526direct (N × H)
272. C22C2×#64526semidirect
280. C4C2×#64526semidirect

Maximal subgroups

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

subgroupindex
C22×#645262
D4×Dic382
#119269162
#119267712
#119267492
#119267412
#119266952
#119266822
C4×#645262
D4×C19⋊C82
D42×C192
D4×SD1619