Finite Group Databasebeta

← #14572867

Subgroups — #14572867

Order 2432.

738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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×Q8×D19C211yesmaximal, characteristic, complemented
2C2×#10597397C211yesmaximal, characteristic, complemented
3#11927051C211yesmaximal, characteristic
4#11926698C214yesmaximal, complemented
5#11926681C214yesmaximal, complemented
6#11926554C211yesmaximal, characteristic, complemented
7#11926553C211yesmaximal, characteristic, complemented
8#11926507C211yesmaximal, characteristic, complemented
9C2×C19×#137C211yesmaximal, characteristic, complemented
10C2×#41×C19C2211yescharacteristic
11C22×Q8×C19C2211yescharacteristic
12C2×Q8×D19—24no—
13C2×Q8×D19—22no—
14C2×Q8×D19—24no—
15C2×Q8×D19C2214yes—
16C22×C4×D19—21no—
17C22×C4×D19C2211yescharacteristic
18C22×Dic38—21no—
19C22×Dic38C2211yescharacteristic
20C19×#137—24no—
21C2×Q16×C19C2212yescomplemented
22C2×SD16×C19C2212yescomplemented
23C2×M16×C19C2211yescharacteristic
24#10597397—24no—
25#10597392C2212yes—
26C2×#64528C2212yescomplemented
27#10597384C2212yes—
28#10597383—21no—
29#10597381—21no—
30C2×#64526C2212yescomplemented
31C4×C22⋊D19—22no—
32#10597372C2211yescharacteristic
33C2×#64520C2211yescharacteristic
34#10597292C2214yescomplemented
35(C2×D19)⋊C8C2214yes—
36#10597273C2214yescomplemented
37C23×D19D411yescharacteristic
38#41×C19—22no—
39#41×C19—22no—
40C2×Q8×C19—22no—
41C2×Q8×C19—21no—
42C2×Q8×C19D414yescomplemented
43C2×Q8×C19C2311yescharacteristic
44C2×Q8×C19C2312yes—
45C2×D4×C19—21no—
46C2×D4×C19C2311yescharacteristic
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19C2311yescharacteristic
50C2×C22⋊D19—22no—
51C22×Dic19—21no—
52C22×Dic19D411yescharacteristic
53Q8×D19—216no—
54Q8×D19—28no—
55Q8×D19—28no—
56C2×C4×D19—28no—
57C2×C4×D19—24no—
58C2×C4×D19—22no—
59C2×C4×D19—22no—
60C2×C4×D19D412yes—
61C2×C4×D19C2312yes—
62C2×Dic38—28no—
63C2×Dic38—21no—
64C2×Dic38—22no—
65C2×Dic38—24no—
66C2×Dic38D414yescomplemented
67C2×Dic38C2312yes—
68Q16×C19—24no—
69SD16×C19—24no—
70M16×C19—22no—
71C2×C8×C19C2312yes—
72C22⋊Dic19—21no—
73C22⋊Dic19—22no—
74#64528—24no—
75#64526—24no—
76(C2×D19)⋊C4—22no—
77C4⋊Dic19C2312yes—
78Dic19⋊C4—22no—
79C4×Dic19—21no—
80#64520—22no—
81C2×C19⋊C8C2312yes—
82C23×C19—21no—
83C23×C19C2×D411yescharacteristic
84C22×D19—22no—
85C22×D19—24no—
86C22×D19C2×D412yes—
87Q8×C19—24no—
88Q8×C19—22no—
89Q8×C19—21no—
90Q8×C19—21no—
91Q8×C19C2×D414yes—
92D4×C19—21no—
93D4×C19—21no—
94D4×C19—42no—
95C2×C4×C19—24no—
96C2×C4×C19—22no—
97C2×C4×C19—21no—
98C2×C4×C19—42no—
99C2×C4×C19C2×D411yescharacteristic
100C2×C4×C19C2×D412yes—
101C2×C4×C19C2×D412yes—
102C2×C4×C19C2411yescharacteristic
103C22⋊D19—44no—
104C2×Dic19—22no—
105C2×Dic19—24no—
106C2×Dic19—22no—
107C2×Dic19—22no—
108C2×Dic19C2×D412yes—
109C4×D19—216no—
110C4×D19—24no—
111C4×D19—22no—
112C4×D19—22no—
113Dic38—216no—
114Dic38—24no—
115Dic38—22no—
116Dic38C2×D414yes—
117C8×C19—22no—
118C19⋊C8—22no—
119#3004—191nomaximal, Sylow
120C22×C19—22no—
121C22×C19—41no—
122C22×C19—42no—
123C22×C19#12012yes—
124C22×C19C22×D411yescharacteristic
125C2×D19—28no—
126C2×D19—22no—
127C2×D19—22no—
128C2×D19#13714yescomplemented
129C4×C19—24no—
130C4×C19—41no—
131C4×C19#12012yes—
132C4×C19C22×D411yescharacteristic
133C4×C19C22×D411yescharacteristic
134Dic19—22no—
135Dic19—24no—
136Dic19—42no—
137C23×Q8—191no—
138C2×#137—191no—
139C2×#137D1911yescharacteristic, complemented
140#525—191no—
141#451—194no—
142#448—194no—
143#419—191no—
144#419—191no—
145#407—191no—
146C2×C19—22no—
147C2×C19—81no—
148C2×C19C2×#12011yescharacteristic
149C2×C19C2×#13712yes—
150D19—24no—
151C2×#41C2×D1911yescharacteristic
152C22×Q8—194no—
153C22×Q8—191no—
154C22×Q8—381no—
155C22×Q8—382no—
156C22×Q8—384no—
157C22×Q8—384no—
158C22×Q8C2×D1911yescharacteristic
159C23×C4—191no—
160C23×C4—381no—
161#137—24no—
162#137—384no—
163C2×Q16—192no—
164C2×Q16C2×D1912yescomplemented
165C2×SD16—192no—
166C2×SD16C2×D1912yescomplemented
167C2×M16—191no—
168C2×M16C2×D1911yescharacteristic
169#123—381no—
170C22⋊Q8—192no—
171#121—192no—
172#120—381no—
173C4×D4—382no—
174#117—191no—
175#103—194no—
176#103—194no—
177C22⋊C8—194no—
178C19#300411yescharacteristic, complemented, Sylow
179C24—191no—
180#41—22no—
181#41—22no—
182C2×Q8—22no—
183C2×Q8—21no—
184C2×Q8—194no—
185C2×Q8—192no—
186C2×Q8—384no—
187C2×Q8—388no—
188C2×Q8—388no—
189C2×Q8—3816no—
190C2×Q8—388no—
191C2×Q8—381no—
192C2×Q8—382no—
193C2×Q8C22⋊D1914yescomplemented
194C2×Q8C22×D1911yescharacteristic
195C2×Q8C22×D1912yes—
196C2×D4—21no—
197C2×D4—382no—
198C2×D4C22×D1911yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—191no—
202C22×C4—192no—
203C22×C4—192no—
204C22×C4—384no—
205C22×C4—388no—
206C22×C4—381no—
207C22×C4—382no—
208C22×C4—382no—
209C22×C4C22×D1911yescharacteristic
210Q16—24no—
211Q16—384no—
212SD16—24no—
213SD16—384no—
214M16—22no—
215M16—382no—
216C2×C8—192no—
217C2×C8C22×D1912yes—
218C4⋊C4—192no—
219C4⋊C4—382no—
220C22⋊C4—382no—
221C22⋊C4—382no—
222C22⋊C4—381no—
223C42—381no—
224C23—21no—
225C23—192no—
226C23—384no—
227C23—382no—
228C23D4×D1911yescharacteristic
229Q8—24no—
230Q8—22no—
231Q8—21no—
232Q8—21no—
233Q8—194no—
234Q8—3816no—
235Q8—384no—
236Q8—382no—
237Q8C2×C22⋊D1914yes—
238D4—21no—
239D4—21no—
240D4—42no—
241D4—764no—
242C2×C4—24no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—192no—
247C2×C4—3816no—
248C2×C4—382no—
249C2×C4—384no—
250C2×C4—382no—
251C2×C4—384no—
252C2×C4—382no—
253C2×C4—382no—
254C2×C4—382no—
255C2×C4D4×D1911yescharacteristic
256C2×C4D4×D1912yes—
257C2×C4C2×C22⋊D1912yes—
258C2×C4C23×D1911yescharacteristic
259C8—22no—
260C8—382no—
261C22—22no—
262C22—42no—
263C22—41no—
264C22—194no—
265C22—388no—
266C22—382no—
267C22—382no—
268C22#1059738312yes—
269C22C2×D4×D1911yescharacteristic
270C4—24no—
271C4—41no—
272C4—382no—
273C4—384no—
274C4—762no—
275C4#1059738312yes—
276C4C2×D4×D1911yescharacteristic
277C4C22×C22⋊D1911yescharacteristic
278C2—22no—
279C2—81no—
280C2—384no—
281C2C2×#1059738311yescharacteristic
282C2#137×D1912yes—
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×#137C2
socleC22×C19C22×D4
prime radical#11927051C2
hypercenterC2×#137D19
hypocenterC19#3004
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D19C2semidirect
2. C2×#10597397C2semidirect
4. #11926698C2semidirect
5. #11926681C2semidirect
6. #11926554C2semidirect
7. #11926553C2semidirect
8. #11926507C2semidirect
9. C2×C19×#137C2semidirect
21. C2×Q16×C19C22semidirect
22. C2×SD16×C19C22semidirect
26. C2×#64528C22semidirect
30. C2×#64526C22semidirect
34. #10597292C22semidirect
36. #10597273C22semidirect
42. C2×Q8×C19D4semidirect
66. C2×Dic38D4semidirect
128. C2×D19#137semidirect
139. C2×#137D19semidirect
164. C2×Q16C2×D19semidirect
166. C2×SD16C2×D19semidirect
178. C19#3004semidirect
193. C2×Q8C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D192
C2×#105973972
#119270512
#119266982
#119266812
#119265542
#119265532
#119265072
C2×C19×#1372
#300419