Finite Group Databasebeta

← #14575326

Subgroups — #14575326

Order 2432.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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
3#11927179C211yesmaximal, characteristic
4#11926916C211yesmaximal, characteristic, complemented
5#11926772C212yesmaximal, complemented
6#11926750C211yesmaximal, characteristic, complemented
7#11926696C212yesmaximal, complemented
8#11926681C212yesmaximal, complemented
9C4×#64527C211yesmaximal, characteristic, complemented
10#11926609C211yesmaximal, characteristic, complemented
11C19×#460C211yesmaximal, characteristic, complemented
12C2×Q8×D19C2212yescomplemented
13C2×D4×D19—21no—
14C2×D4×D19C2212yes—
15C2×SD16×C19C2212yescomplemented
16C19×#127C2211yescharacteristic
17C4×Q8×C19C2211yescharacteristic, complemented
18C2×#64527C2211yescharacteristic
19#10597384—21no—
20#10597384C2212yes—
21#10597383—22no—
22C2×#64526C2212yescomplemented
23C2×#64526C2212yescomplemented
24SD16×D19—28no—
25C2×#64516C2212yes—
26C2×C8×D19C2212yescomplemented
27#10597343—22no—
28#10597343C2212yescomplemented
29C4×D76—21no—
30C4×D76C2211yescharacteristic
31C4×D76C2211yescharacteristic
32#10597315—21no—
33#10597315C2211yescharacteristic, complemented
34C19×C4⋊C8C2211yescharacteristic, complemented
35C19×#102C2212yescomplemented
36#10597292C2211yescharacteristic, complemented
37(C2×D19)⋊C8C2212yescomplemented
38#10597273C2212yescomplemented
39#10597266C2211yescharacteristic
40#10597265C2211yescharacteristic, complemented
41C4×C19⋊C8C2211yescharacteristic, complemented
42C23×D19—22no—
43C2×Q8×C19C2311yescharacteristic
44C2×D4×C19—21no—
45C2×D4×C19—21no—
46C2×D4×C19C2312yes—
47C2×C22⋊D19—22no—
48C2×C22⋊D19—22no—
49Q8×D19—24no—
50Q8×D19—42no—
51D4×D19—24no—
52D4×D19—42no—
53D4×D19—44no—
54C2×D76D411yescharacteristic
55C2×D76C2311yescharacteristic
56C2×C4×D19—22no—
57C2×C4×D19—21no—
58C2×C4×D19C2312yes—
59C2×Dic38—22no—
60C2×Dic38C2312yes—
61SD16×C19—24no—
62C2×C8×C19C2312yes—
63C4⋊C4×C19—21no—
64C4⋊C4×C19C2311yescharacteristic
65C42×C19—21no—
66C42×C19C2311yescharacteristic
67C22⋊Dic19—22no—
68#64527D414yescomplemented
69#64526—24no—
70#64526—42no—
71(C2×D19)⋊C4—22no—
72(C2×D19)⋊C4—21no—
73(C2×D19)⋊C4D412yes—
74C4⋊Dic19—21no—
75C4⋊Dic19—21no—
76C4⋊Dic19—22no—
77C4⋊Dic19D411yescharacteristic
78C4⋊Dic19C2311yescharacteristic
79C2×C19⋊C8C2311yescharacteristic
80C2×C19⋊C8C2311yescharacteristic
81#64516—24no—
82C8×D19—24no—
83C23×C19—22no—
84C22×D19—21no—
85C22×D19—44no—
86C22×D19—44no—
87C22×D19—82no—
88C22×D19C2×D412yes—
89Q8×C19—21no—
90Q8×C19C2×D412yescomplemented
91D4×C19—22no—
92D4×C19—22no—
93D4×C19—42no—
94D4×C19—81no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19C2×D411yescharacteristic
98C2×C4×C19C2×D411yescharacteristic
99C2×C4×C19C2411yescharacteristic
100C22⋊D19—44no—
101C22⋊D19—44no—
102C2×Dic19—22no—
103C2×Dic19—21no—
104C2×Dic19C2×D412yes—
105D76—21no—
106D76SD1614yescomplemented
107D76C2×D412yes—
108C4×D19—22no—
109C4×D19—22no—
110C4×D19—44no—
111C4×D19—42no—
112Dic38—22no—
113Dic38—22no—
114Dic38—44no—
115C8×C19—22no—
116C19⋊C8—21no—
117C19⋊C8C2×D412yescomplemented
118D4×SD16—191nomaximal, Sylow
119C22×C19—42no—
120C22×C19—42no—
121C22×C19—42no—
122C22×C19C22×D411yescharacteristic
123C2×D19—22no—
124C2×D19—22no—
125C2×D19—22no—
126C2×D19—41no—
127C2×D19—41no—
128C2×D19—88no—
129C2×D19C2×SD1614yescomplemented
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—
141D42—191no—
142#492—191no—
143#465—192no—
144#461—191no—
145#460D1911yescharacteristic, complemented
146#450—192no—
147#448—192no—
148C4×SD16—191no—
149C8×D4—191no—
150C2×C19—82no—
151C2×C19D4211yescharacteristic
152C2×C19C22×SD1611yescharacteristic
153C2×C19#57711yescharacteristic
154D19—24no—
155D19—42no—
156C22×Q8—192no—
157C22×D4—192no—
158C22×D4—381no—
159C2×SD16—191no—
160C2×SD16—192no—
161C2×SD16—192no—
162C2×SD16—192no—
163C2×SD16—388no—
164C2×SD16C2×D1912yescomplemented
165C22×C8—192no—
166C4⋊Q8—191no—
167C4⋊Q8—381no—
168#127C2×D1911yescharacteristic
169C22⋊Q8—192no—
170C22⋊Q8—382no—
171#121—192no—
172#121—381no—
173#120—382no—
174C4×Q8C2×D1911yescharacteristic, complemented
175C4×D4—191no—
176C4×D4—191no—
177C4×D4—381no—
178#106—191no—
179C4⋊C8C2×D1911yescharacteristic, complemented
180#103—191no—
181#103—192no—
182#102—191no—
183#102C2×D1912yescomplemented
184C22⋊C8—192no—
185C4×C8—191no—
186C19D4×SD1611yescharacteristic, complemented, Sylow
187C24—382no—
188C2×Q8—192no—
189C2×Q8—382no—
190C2×Q8—384no—
191C2×Q8—762no—
192C2×Q8C22×D1911yescharacteristic
193C2×D4—21no—
194C2×D4—21no—
195C2×D4—191no—
196C2×D4—191no—
197C2×D4—382no—
198C2×D4—384no—
199C2×D4—382no—
200C2×D4—762no—
201C2×D4—764no—
202C2×D4C22×D1912yes—
203C22×C4—192no—
204C22×C4—382no—
205C22×C4—381no—
206SD16—24no—
207SD16—194no—
208SD16—384no—
209SD16—384no—
210SD16—762no—
211C2×C8—191no—
212C2×C8—191no—
213C2×C8—384no—
214C2×C8C22×D1912yes—
215C4⋊C4—21no—
216C4⋊C4—191no—
217C4⋊C4—191no—
218C4⋊C4—382no—
219C4⋊C4—381no—
220C4⋊C4—381no—
221C4⋊C4C22×D1911yescharacteristic
222C22⋊C4—192no—
223C22⋊C4—382no—
224C22⋊C4—382no—
225C22⋊C4—381no—
226C42—21no—
227C42C22×D1911yescharacteristic
228C23—22no—
229C23—192no—
230C23—381no—
231C23—764no—
232C23—764no—
233C23—1522no—
234Q8—21no—
235Q8—382no—
236Q8—382no—
237Q8—764no—
238Q8D4×D1912yescomplemented
239D4—22no—
240D4—22no—
241D4—42no—
242D4—81no—
243D4—192no—
244D4—194no—
245D4—381no—
246D4—764no—
247D4—764no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—192no—
251C2×C4—382no—
252C2×C4—382no—
253C2×C4—381no—
254C2×C4—382no—
255C2×C4—764no—
256C2×C4—762no—
257C2×C4D4×D1911yescharacteristic
258C2×C4D4×D1911yescharacteristic
259C2×C4C23×D1911yescharacteristic
260C8—22no—
261C8—192no—
262C8—381no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—194no—
267C22—382no—
268C22—382no—
269C22—382no—
270C22—761no—
271C22—761no—
272C22—1528no—
273C22C2×D4×D1911yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—382no—
278C4—761no—
279C4—762no—
280C4SD16×D1912yescomplemented
281C4C2×D4×D1911yescharacteristic
282C4#1059743511yescharacteristic
283C2—82no—
284C2—384no—
285C2—762no—
286C2#1192717811yescharacteristic
287C2C2×SD16×D1911yescharacteristic
288C2#1192735411yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#460C2
socleC22×C19C22×D4
prime radical#11927179C2
hypercenter#460D19
hypocenterC19D4×SD16
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D19C2semidirect
2. Q8×D76C2semidirect
4. #11926916C2semidirect
5. #11926772C2semidirect
6. #11926750C2semidirect
7. #11926696C2semidirect
8. #11926681C2semidirect
9. C4×#64527C2semidirect
10. #11926609C2semidirect
11. C19×#460C2semidirect
12. C2×Q8×D19C22semidirect
15. C2×SD16×C19C22semidirect
17. C4×Q8×C19C22semidirect
22. C2×#64526C22semidirect
23. C2×#64526C22semidirect
26. C2×C8×D19C22semidirect
28. #10597343C22semidirect
33. #10597315C22semidirect
34. C19×C4⋊C8C22semidirect
35. C19×#102C22semidirect
36. #10597292C22semidirect
37. (C2×D19)⋊C8C22semidirect
38. #10597273C22semidirect
40. #10597265C22semidirect
41. C4×C19⋊C8C22semidirect
68. #64527D4semidirect
90. Q8×C19C2×D4semidirect
106. D76SD16semidirect
117. C19⋊C8C2×D4semidirect
129. C2×D19C2×SD16semidirect
133. C4×C19C2×SD16semidirect
145. #460D19semidirect
164. C2×SD16C2×D19semidirect
174. C4×Q8C2×D19semidirect
179. C4⋊C8C2×D19semidirect
183. #102C2×D19semidirect
186. C19D4×SD16semidirect
238. Q8D4×D19semidirect
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
#119271792
#119269162
#119267722
#119267502
#119266962
#119266812
C4×#645272
#119266092
C19×#4602
D4×SD1619