Finite Group Databasebeta

← #18080269

Subgroups — #18080269

Order 4864.

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

normal subgroups only

This group has 528 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×#2502C211yesmaximal, 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×#398—22no—
16C19×#391C412yescomplemented
17C19×#385—21no—
18C19×#385—21no—
19C19×#384C412yescomplemented
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×C19—22no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19C2×C411yescharacteristic
33C2×C4⋊C4×C19C2×C412yes—
34C2×C4⋊C4×C19D412yes—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C42×C19C2×C412yes—
38C2×C22⋊Dic19—22no—
39C2×C4⋊Dic19—22no—
40C2×C4×Dic19—22no—
41C2×#64520—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—22no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—42no—
62C22×C4×C19—81no—
63C22×C4×C19—81no—
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—
75C4⋊C4×C19—82no—
76C4⋊C4×C19—82no—
77C22⋊C4×C19—24no—
78C22⋊C4×C19—41no—
79C22⋊C4×C19—41no—
80C42×C19—42no—
81C22⋊Dic19—44no—
82C4⋊Dic19—82no—
83C4×Dic19—82no—
84#64520—44no—
85C2×C19⋊C8—42no—
86#9461—191nomaximal, Sylow
87C23×C19—22no—
88C23×C19—22no—
89C23×C19—41no—
90C23×C19C2×C22⋊C411yescharacteristic
91C23×C19#12011yescharacteristic
92C23×C19#12311yescharacteristic
93Q8×C19—82no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—24no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
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—42no—
106C2×C4×C19—42no—
107C2×C4×C19—42no—
108C2×C4×C19—41no—
109C2×C4×C19—41no—
110C2×C4×C19—42no—
111C2×C4×C19—81no—
112C2×C4×C19—81no—
113C2×C4×C19C4×D412yes—
114C2×C4×C19#12112yes—
115C2×Dic19—44no—
116C2×Dic19—44no—
117C2×Dic19—44no—
118C19⋊C8—82no—
119#2502D1911yescharacteristic
120#2313—191no—
121#1821—191no—
122#1511—192no—
123#1284—192no—
124C22×C19—21no—
125C22×C19—21no—
126C22×C19—21no—
127C22×C19—21no—
128C22×C19—21no—
129C22×C19—21no—
130C22×C19—21no—
131C22×C19—44no—
132C22×C19#38611yescharacteristic
133C22×C19#41012yes—
134C22×C19#45612yes—
135C4×C19—22no—
136C4×C19—22no—
137C4×C19—44no—
138C4×C19—42no—
139C4×C19—42no—
140C4×C19—81no—
141C4×C19—81no—
142Dic19—84no—
143C2×C22⋊Q8C2×D1911yescharacteristic
144C22×C4⋊C4C2×D1911yescharacteristic
145#407—192no—
146#398—22no—
147#391Dic1912yescomplemented
148#387—384no—
149#385—21no—
150#385—21no—
151#384Dic1912yescomplemented
152#381—192no—
153#380—381no—
154C4×C22⋊C4—381no—
155C4×C22⋊C4C2×D1911yescharacteristic
156#343—382no—
157#328—384no—
158C2×C19—22no—
159C2×C19—22no—
160C2×C19—41no—
161C2×C19#188611yescharacteristic
162C2×C19#189911yescharacteristic
163C2×C19#191111yescharacteristic
164C22×Q8C2×Dic1911yescharacteristic
165C23×C4C22⋊D1911yescharacteristic
166C23×C4C22⋊D1911yescharacteristic
167C23×C4C22×D1911yescharacteristic
168C2×M16—382no—
169C22⋊Q8—22no—
170C22⋊Q8—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—382no—
177C2×C4⋊C4C2×Dic1911yescharacteristic
178C2×C4⋊C4C2×Dic1912yes—
179C2×C4⋊C4C22⋊D1912yes—
180C2×C22⋊C4—21no—
181C2×C22⋊C4—21no—
182C2×C22⋊C4—382no—
183C2×C42—382no—
184C2×C42C2×Dic1912yes—
185C22⋊C8—382no—
186C22⋊C8—382no—
187#95—22no—
188#95—22no—
189#95—21no—
190#95—194no—
191#95—382no—
192#95—382no—
193#95—382no—
194C19#946111yescharacteristic, complemented, Sylow
195C24C2×C22⋊D1911yescharacteristic
196C2×Q8—22no—
197C2×Q8—42no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—42no—
206C22×C4—81no—
207C22×C4—81no—
208C22×C4—384no—
209C22×C4C22⋊Dic1912yes—
210C22×C4C22⋊Dic1912yes—
211C22×C4D4×D1912yes—
212C22×C4#6454312yes—
213C22×C4C22×Dic1911yescharacteristic
214C22×C4C2×C22⋊D1911yescharacteristic
215M16—764no—
216C2×C8—762no—
217C4⋊C4—24no—
218C4⋊C4—24no—
219C4⋊C4—22no—
220C4⋊C4—42no—
221C4⋊C4—82no—
222C4⋊C4—82no—
223C4⋊C4—1522no—
224C22⋊C4—24no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—764no—
228C42—42no—
229C42—1522no—
230C23—22no—
231C23—22no—
232C23—41no—
233C23#1059738111yescharacteristic
234C23#1059738311yescharacteristic
235C23C2×C22⋊Dic1911yescharacteristic
236Q8—82no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—24no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—764no—
257C2×C4—764no—
258C2×C4—764no—
259C2×C4D4×Dic1912yes—
260C2×C4#1059738512yes—
261C8—1522no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—44no—
270C22#1192642411yescharacteristic
271C22#1192651812yes—
272C22#1192672612yes—
273C4—22no—
274C4—22no—
275C4—44no—
276C4—42no—
277C4—42no—
278C4—81no—
279C4—81no—
280C4—1524no—
281C2—22no—
282C2—22no—
283C2—41no—
284C2#1456402911yescharacteristic
285C2#1456409411yescharacteristic
286C2#1456416811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2502C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2502D19
hypocenterC19#9461
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2502

Complements

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

NH ≅ G/Ntype
16. C19×#391C4semidirect
19. C19×#384C4semidirect
147. #391Dic19semidirect
151. #384Dic19semidirect
194. C19#9461semidirect

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×#25022
#946119