Finite Group Databasebeta

← #18080264

Subgroups — #18080264

Order 4864.

512 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 107 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#14566238C211yesmaximal, characteristic
2#14563715C211yesmaximal, characteristic
3#14562168C212yesmaximal
4#14561488C212yesmaximal
5C19×#2503C211yesmaximal, characteristic
6#11926508C2212yes—
7#11926430—24no—
8#11926407C2212yes—
9#11926404—21no—
10C4×C22⋊Dic19—21no—
11#11926313—22no—
12#11926281—24no—
13C2×C19×C22⋊Q8C2211yescharacteristic
14C22×C4⋊C4×C19C2211yescharacteristic
15C19×#400—22no—
16C19×#391C412yescomplemented
17C19×#382C412yescomplemented
18C19×#381—21no—
19C19×#381—21no—
20C4×C22⋊C4×C19C2211yescharacteristic
21C22×Q8×C19C2×C411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C19×C22⋊Q8—22no—
26C19×C22⋊Q8—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19C2×C412yes—
32C2×C4⋊C4×C19D412yes—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—21no—
35C2×C42×C19C2×C412yes—
36C2×C22⋊Dic19—22no—
37C2×C4⋊Dic19—22no—
38C2×C4×Dic19—22no—
39C2×#64520—22no—
40C19×#95—22no—
41C19×#95—22no—
42C19×#95—22no—
43C19×#95—22no—
44C19×#95—21no—
45C19⋊#95—22no—
46C19⋊#95—22no—
47C19⋊#95—22no—
48C19⋊#95D414yes—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)—22no—
51C24×C19C2×D411yescharacteristic
52C2×Q8×C19—22no—
53C2×Q8×C19—42no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—22no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—42no—
62C22×C4×C19—42no—
63C22×C4×C19—42no—
64C22×C4×C19C22⋊C412yes—
65C22×C4×C19C22⋊C412yes—
66C22×C4×C19C22×C411yescharacteristic
67C22×C4×C19C2×D412yes—
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19#4112yes—
70C22×Dic19—24no—
71C4⋊C4×C19—24no—
72C4⋊C4×C19—24no—
73C4⋊C4×C19—22no—
74C4⋊C4×C19—42no—
75C22⋊C4×C19—42no—
76C22⋊C4×C19—41no—
77C22⋊C4×C19—41no—
78C42×C19—42no—
79C22⋊Dic19—44no—
80C4⋊Dic19—82no—
81C4×Dic19—82no—
82#64520—44no—
83C2×C19⋊C8—42no—
84#9460—191nomaximal, Sylow
85C23×C19—22no—
86C23×C19—22no—
87C23×C19—41no—
88C23×C19C2×C22⋊C411yescharacteristic
89C23×C19#12011yescharacteristic
90C23×C19#12311yescharacteristic
91Q8×C19—82no—
92C2×C4×C19—22no—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—42no—
97C2×C4×C19—42no—
98C2×C4×C19—42no—
99C2×C4×C19—42no—
100C2×C4×C19—42no—
101C2×C4×C19—42no—
102C2×C4×C19—42no—
103C2×C4×C19—42no—
104C2×C4×C19—42no—
105C2×C4×C19—41no—
106C2×C4×C19—41no—
107C2×C4×C19—42no—
108C2×C4×C19—42no—
109C2×C4×C19—81no—
110C2×C4×C19—81no—
111C2×C4×C19C4×D412yes—
112C2×C4×C19#12112yes—
113C2×Dic19—44no—
114C2×Dic19—44no—
115C2×Dic19—44no—
116C19⋊C8—82no—
117#2503D1911yescharacteristic
118#2313—191no—
119#1821—191no—
120#1511—192no—
121#1284—192no—
122C22×C19—21no—
123C22×C19—21no—
124C22×C19—21no—
125C22×C19—21no—
126C22×C19—21no—
127C22×C19—21no—
128C22×C19—21no—
129C22×C19—44no—
130C22×C19#38611yescharacteristic
131C22×C19#41012yes—
132C22×C19#45512yes—
133C4×C19—22no—
134C4×C19—22no—
135C4×C19—42no—
136C4×C19—42no—
137C4×C19—82no—
138C4×C19—81no—
139C4×C19—81no—
140Dic19—84no—
141C2×C22⋊Q8C2×D1911yescharacteristic
142C22×C4⋊C4C2×D1911yescharacteristic
143#407—192no—
144#400—22no—
145#391Dic1912yescomplemented
146#387—384no—
147#382Dic1912yescomplemented
148#381—21no—
149#381—21no—
150#381—192no—
151#380—381no—
152C4×C22⋊C4—381no—
153C4×C22⋊C4C2×D1911yescharacteristic
154#343—382no—
155#328—384no—
156C2×C19—22no—
157C2×C19—22no—
158C2×C19—41no—
159C2×C19#188511yescharacteristic
160C2×C19#189911yescharacteristic
161C2×C19#191211yescharacteristic
162C22×Q8C2×Dic1911yescharacteristic
163C23×C4C22⋊D1911yescharacteristic
164C23×C4C22⋊D1911yescharacteristic
165C23×C4C22×D1911yescharacteristic
166C2×M16—382no—
167C22⋊Q8—22no—
168C22⋊Q8—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—382no—
173C2×C4⋊C4C2×Dic1911yescharacteristic
174C2×C4⋊C4C2×Dic1912yes—
175C2×C4⋊C4C22⋊D1912yes—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—21no—
178C2×C22⋊C4—382no—
179C2×C42—382no—
180C2×C42C2×Dic1912yes—
181C22⋊C8—382no—
182C22⋊C8—382no—
183#95—22no—
184#95—22no—
185#95—22no—
186#95—22no—
187#95—21no—
188#95—194no—
189#95—382no—
190#95—382no—
191#95—382no—
192C19#946011yescharacteristic, complemented, Sylow
193C24C2×C22⋊D1911yescharacteristic
194C2×Q8—22no—
195C2×Q8—42no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—384no—
207C22×C4C22⋊Dic1912yes—
208C22×C4C22⋊Dic1912yes—
209C22×C4D4×D1912yes—
210C22×C4#6454312yes—
211C22×C4C22×Dic1911yescharacteristic
212C22×C4C2×C22⋊D1911yescharacteristic
213M16—764no—
214C2×C8—762no—
215C4⋊C4—24no—
216C4⋊C4—24no—
217C4⋊C4—22no—
218C4⋊C4—42no—
219C4⋊C4—1522no—
220C22⋊C4—42no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C22⋊C4—764no—
224C42—42no—
225C42—1522no—
226C23—22no—
227C23—22no—
228C23—41no—
229C23#1059738111yescharacteristic
230C23#1059738311yescharacteristic
231C23C2×C22⋊Dic1911yescharacteristic
232Q8—82no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—764no—
253C2×C4—764no—
254C2×C4—764no—
255C2×C4D4×Dic1912yes—
256C2×C4#1059738512yes—
257C8—1522no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—44no—
266C22#1192642411yescharacteristic
267C22#1192651812yes—
268C22#1192672112yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—82no—
274C4—81no—
275C4—81no—
276C4—1524no—
277C2—22no—
278C2—22no—
279C2—41no—
280C2#1456402411yescharacteristic
281C2#1456409411yescharacteristic
282C2#1456417311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2503C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2503D19
hypocenterC19#9460
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2503

Complements

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

NH ≅ G/Ntype
16. C19×#391C4semidirect
17. C19×#382C4semidirect
145. #391Dic19semidirect
147. #382Dic19semidirect
192. C19#9460semidirect

Maximal subgroups

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

subgroupindex
#145662382
#145637152
#145621682
#145614882
C19×#25032
#946019