Finite Group Databasebeta

← #14574020

Subgroups — #14574020

Order 2432.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#11927099C211yesmaximal, characteristic, complemented
2#124×D19C211yesmaximal, characteristic
3#11926906C211yesmaximal, characteristic, complemented
4#11926904C211yesmaximal, characteristic, complemented
5#11926903C211yesmaximal, characteristic, complemented
6#11926900C212yesmaximal, complemented
7#11926897C212yesmaximal, complemented
8#11926551C212yesmaximal, complemented
9#11926547C212yesmaximal
10#11926496C211yesmaximal, characteristic, complemented
11C19×#489C211yesmaximal, characteristic, complemented
12C2×Q8×D19C2211yescharacteristic
13C2×D4×D19C2211yescharacteristic
14C19×C4⋊Q8C2211yescharacteristic, complemented
15C19×#124C2211yescharacteristic
16#10597393C2211yescharacteristic
17#10597392—21no—
18Q8×Dic19—21no—
19#10597382C2211yescharacteristic
20C2×#64515C2212yes—
21#10597343—21no—
22#10597338C2212yes—
23#10597336C2212yescomplemented
24#10597333—21no—
25#10597331—21no—
26#10597331—21no—
27C22⋊C4×D19—21no—
28C22⋊C4×D19—21no—
29#10597321C2211yescharacteristic
30C42×D19C2211yescharacteristic
31#10597315C2211yescharacteristic, complemented
32C19×#103C2212yescomplemented
33C19×#102C2212yes—
34C19×#97C2211yescharacteristic, complemented
35#10597292C2212yescomplemented
36#10597289C2212yes—
37#10597278C2212yes—
38#10597273C2212yescomplemented
39C8×Dic19C2212yescomplemented
40#10597267C2212yescomplemented
41#10597266C2212yes—
42#10597260C2211yescharacteristic, complemented
43C23×D19—21no—
44C2×Q8×C19—21no—
45C2×Q8×C19C2311yescharacteristic
46C2×D4×C19C2311yescharacteristic
47C2×C22⋊D19—21no—
48Q8×D19—24no—
49D4×D19—24no—
50C2×D76C2311yescharacteristic
51C2×C4×D19—21no—
52C2×C4×D19D411yescharacteristic
53C2×C4×D19D411yescharacteristic
54C2×C4×D19C2311yescharacteristic
55C2×Dic38—21no—
56C2×Dic38—21no—
57C2×Dic38C2311yescharacteristic
58C2×C8×C19C2312yes—
59C4⋊C4×C19—21no—
60C4⋊C4×C19C2312yes—
61C22⋊C4×C19—21no—
62C22⋊C4×C19—21no—
63C42×C19C2311yescharacteristic
64C22⋊Dic19—21no—
65C22⋊Dic19—21no—
66(C2×D19)⋊C4—22no—
67(C2×D19)⋊C4—21no—
68(C2×D19)⋊C4—21no—
69(C2×D19)⋊C4—21no—
70(C2×D19)⋊C4—21no—
71C4⋊Dic19—21no—
72C4⋊Dic19—22no—
73C4⋊Dic19C2312yes—
74Dic19⋊C4—22no—
75C4×Dic19—22no—
76C4×Dic19D411yescharacteristic
77C4×Dic19D411yescharacteristic
78C4×Dic19C2311yescharacteristic
79C2×C19⋊C8C2312yes—
80#64515—24no—
81C23×C19—21no—
82C22×D19—21no—
83C22×D19—42no—
84C22×D19—42no—
85C22×D19—42no—
86C22×D19C2×D411yescharacteristic
87Q8×C19—22no—
88Q8×C19—42no—
89D4×C19—22no—
90C2×C4×C19—22no—
91C2×C4×C19—21no—
92C2×C4×C19C2×D411yescharacteristic
93C2×C4×C19C2×D411yescharacteristic
94C2×C4×C19C2411yescharacteristic
95C22⋊D19—42no—
96C2×Dic19—22no—
97C2×Dic19—21no—
98C2×Dic19C2×D411yescharacteristic
99C2×Dic19C2×D411yescharacteristic
100C2×Dic19C2×D411yescharacteristic
101D76—22no—
102C4×D19—41no—
103C4×D19—41no—
104C4×D19—42no—
105C4×D19#4114yes—
106Dic38—22no—
107Dic38—42no—
108Dic38—42no—
109C8×C19—22no—
110C19⋊C8—22no—
111#3140—191nomaximal, Sylow
112C22×C19—41no—
113C22×C19—41no—
114C22×C19—41no—
115C22×C19C22×D411yescharacteristic
116C2×D19—21no—
117C2×D19—21no—
118C2×D19—41no—
119C2×D19—41no—
120C2×D19—41no—
121C2×D19—84no—
122C2×D19#12412yes—
123C4×C19—21no—
124C4×C19—21no—
125C4×C19—41no—
126C4×C19—42no—
127C4×C19C2×#4112yes—
128Dic19—21no—
129Dic19—21no—
130Dic19—41no—
131Dic19—42no—
132Dic19#12412yes—
133#533—191no—
134C2×#124—191no—
135#489—191no—
136#489—191no—
137#489—191no—
138#489D1911yescharacteristic, complemented
139#488—192no—
140#488—192no—
141#419—192no—
142#418—192no—
143C4×M16—191no—
144C2×C19—81no—
145C2×C19C2×#12411yescharacteristic
146C2×C19#57511yescharacteristic
147C2×C19#57511yescharacteristic
148D19—22no—
149D19—81no—
150C22×Q8—191no—
151C22×D4—191no—
152C2×M16—192no—
153C4⋊Q8—191no—
154C4⋊Q8C2×D1911yescharacteristic, complemented
155#125—192no—
156#124—191no—
157#124—191no—
158#124—191no—
159#124—381no—
160#124—381no—
161#124C2×D1911yescharacteristic
162C22⋊Q8—381no—
163C22⋊Q8—381no—
164C4×Q8—381no—
165C4×Q8—381no—
166#117—192no—
167C2×C22⋊C4—381no—
168C2×C22⋊C4—381no—
169C2×C42—191no—
170#103—192no—
171#103—192no—
172#103—192no—
173#103C2×D1912yescomplemented
174#102—192no—
175#102—192no—
176#102—192no—
177#102C2×D1912yes—
178#97—191no—
179#97C2×D1911yescharacteristic, complemented
180C4×C8—192no—
181C19#314011yescharacteristic, complemented, Sylow
182C24—381no—
183C2×Q8—21no—
184C2×Q8—191no—
185C2×Q8—381no—
186C2×Q8—384no—
187C2×Q8—381no—
188C2×Q8C22×D1911yescharacteristic
189C2×D4—191no—
190C2×D4—384no—
191C2×D4—381no—
192C2×D4C22×D1911yescharacteristic
193C22×C4—191no—
194C22×C4—191no—
195C22×C4—191no—
196C22×C4—381no—
197M16—384no—
198C2×C8—192no—
199C2×C8C22×D1912yes—
200C4⋊C4—21no—
201C4⋊C4—192no—
202C4⋊C4—382no—
203C4⋊C4—382no—
204C4⋊C4—381no—
205C4⋊C4C22×D1912yes—
206C22⋊C4—21no—
207C22⋊C4—21no—
208C22⋊C4—381no—
209C22⋊C4—381no—
210C22⋊C4—382no—
211C22⋊C4—381no—
212C22⋊C4—381no—
213C22⋊C4—381no—
214C22⋊C4—381no—
215C42—191no—
216C42—191no—
217C42—191no—
218C42—382no—
219C42C22×D1911yescharacteristic
220C23—21no—
221C23—191no—
222C23—381no—
223C23—762no—
224C23—762no—
225C23—762no—
226Q8—22no—
227Q8—42no—
228Q8—382no—
229Q8—762no—
230Q8—762no—
231D4—22no—
232D4—382no—
233D4—762no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—191no—
237C2×C4—194no—
238C2×C4—191no—
239C2×C4—191no—
240C2×C4—382no—
241C2×C4—381no—
242C2×C4—761no—
243C2×C4—761no—
244C2×C4—762no—
245C2×C4D4×D1911yescharacteristic
246C2×C4D4×D1911yescharacteristic
247C2×C4C23×D1911yescharacteristic
248C8—22no—
249C8—382no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—192no—
254C22—381no—
255C22—381no—
256C22—761no—
257C22—761no—
258C22—761no—
259C22—1524no—
260C22C2×D4×D1911yescharacteristic
261C4—21no—
262C4—21no—
263C4—41no—
264C4—42no—
265C4—192no—
266C4—381no—
267C4—381no—
268C4—761no—
269C4—762no—
270C4#41×D1912yes—
271C2—81no—
272C2—382no—
273C2—1521no—
274C2#124×D1911yescharacteristic
275C2#1192734011yescharacteristic
276C2#1192734311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#489C2
socleC22×C19C22×D4
prime radicalC2×D4×D19C22
hypercenter#489D19
hypocenterC19#3140
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #11927099C2semidirect
3. #11926906C2semidirect
4. #11926904C2semidirect
5. #11926903C2semidirect
6. #11926900C2semidirect
7. #11926897C2semidirect
8. #11926551C2semidirect
10. #11926496C2semidirect
11. C19×#489C2semidirect
14. C19×C4⋊Q8C22semidirect
23. #10597336C22semidirect
31. #10597315C22semidirect
32. C19×#103C22semidirect
34. C19×#97C22semidirect
35. #10597292C22semidirect
38. #10597273C22semidirect
39. C8×Dic19C22semidirect
40. #10597267C22semidirect
42. #10597260C22semidirect
138. #489D19semidirect
154. C4⋊Q8C2×D19semidirect
173. #103C2×D19semidirect
179. #97C2×D19semidirect
181. C19#3140semidirect

Maximal subgroups

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

subgroupindex
#119270992
#124×D192
#119269062
#119269042
#119269032
#119269002
#119268972
#119265512
#119265472
#119264962
C19×#4892
#314019