Finite Group Databasebeta

← #18080010

Subgroups — #18080010

Order 4864.

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

normal subgroups only

This group has 552 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, complemented
2#14562151C212yesmaximal
3#14561965C211yesmaximal, characteristic, complemented
4#14561521C212yesmaximal, complemented
5C19×#2591C211yesmaximal, characteristic
6#11926508C2212yes—
7#11926430—24no—
8#11926407—21no—
9#11926404—21no—
10C4×C22⋊Dic19C2212yes—
11#11926278—24no—
12#11926270—22no—
13C2×C19×#121C2211yescharacteristic
14C22×C4⋊C4×C19C2211yescharacteristic
15C19×#400C412yescomplemented
16C19×#394C412yescomplemented
17C19×#388—22no—
18C19×#386—21no—
19C19×#386—21no—
20C4×C22⋊C4×C19C2211yescharacteristic
21C22×D4×C19—21no—
22C22×D4×C19C2×C411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C19×#121—22no—
27C19×#121—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—22no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19C2×C412yes—
32C2×C4⋊C4×C19D412yes—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—22no—
37C2×C42×C19—21no—
38C2×C22⋊Dic19—22no—
39C2×C4⋊Dic19—22no—
40C2×C4×Dic19—22no—
41C2×#64520—22no—
42C19×#95—22no—
43C19×#95—22no—
44C19×#95C2×C412yes—
45C19⋊#95—22no—
46C19⋊#95—24no—
47C19⋊#95D414yes—
48C22⋊(C19⋊C8)—22no—
49C22⋊(C19⋊C8)—22no—
50C24×C19—21no—
51C24×C19C2×D411yescharacteristic
52C2×D4×C19—22no—
53C2×D4×C19—44no—
54C2×D4×C19—41no—
55C2×D4×C19—41no—
56C2×D4×C19—81no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—22no—
62C22×C4×C19—21no—
63C22×C4×C19—42no—
64C22×C4×C19—81no—
65C22×C4×C19—81no—
66C22×C4×C19C22⋊C412yes—
67C22×C4×C19C22⋊C412yes—
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D412yes—
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19#4112yes—
72C22×Dic19—24no—
73C4⋊C4×C19—24no—
74C4⋊C4×C19—24no—
75C4⋊C4×C19—22no—
76C22⋊C4×C19—44no—
77C22⋊C4×C19—42no—
78C22⋊C4×C19—42no—
79C22⋊C4×C19—82no—
80C42×C19—81no—
81C22⋊Dic19—44no—
82C4⋊Dic19—82no—
83C4×Dic19—82no—
84#64520—82no—
85C2×C19⋊C8—42no—
86#9414—191nomaximal, Sylow
87C23×C19—22no—
88C23×C19—22no—
89C23×C19—41no—
90C23×C19—42no—
91C23×C19—42no—
92C23×C19—41no—
93C23×C19—42no—
94C23×C19C2×C22⋊C411yescharacteristic
95C23×C19#12011yescharacteristic
96C23×C19#12311yescharacteristic
97D4×C19—82no—
98D4×C19—82no—
99D4×C19—82no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—22no—
103C2×C4×C19—22no—
104C2×C4×C19—42no—
105C2×C4×C19—42no—
106C2×C4×C19—41no—
107C2×C4×C19—41no—
108C2×C4×C19—42no—
109C2×C4×C19—42no—
110C2×C4×C19—42no—
111C2×C4×C19—42no—
112C2×C4×C19—42no—
113C2×C4×C19—42no—
114C2×C4×C19—42no—
115C2×C4×C19—41no—
116C2×C4×C19—42no—
117C2×C4×C19—81no—
118C2×C4×C19C4×D412yes—
119C2×C4×C19#12112yes—
120C2×Dic19—44no—
121C2×Dic19—44no—
122C2×Dic19—44no—
123C19⋊C8—82no—
124#2591D1911yescharacteristic
125#2313—191no—
126#1507—192no—
127#1463—191no—
128#1297—192no—
129C22×C19—21no—
130C22×C19—21no—
131C22×C19—21no—
132C22×C19—21no—
133C22×C19—21no—
134C22×C19—21no—
135C22×C19—21no—
136C22×C19—44no—
137C22×C19—84no—
138C22×C19—81no—
139C22×C19—81no—
140C22×C19—81no—
141C22×C19#38611yescharacteristic
142C22×C19#42112yes—
143C22×C19#45412yes—
144C4×C19—22no—
145C4×C19—22no—
146C4×C19—42no—
147C4×C19—42no—
148C4×C19—82no—
149C4×C19—81no—
150Dic19—84no—
151C2×#121C2×D1911yescharacteristic
152C22×C4⋊C4C2×D1911yescharacteristic
153#407—192no—
154#400Dic1912yescomplemented
155#394Dic1912yescomplemented
156#388—22no—
157#387—384no—
158#386—21no—
159#386—21no—
160#381—381no—
161#380—381no—
162C4×C22⋊C4—192no—
163C4×C22⋊C4C2×D1911yescharacteristic
164#327—384no—
165#324—382no—
166C2×C19—22no—
167C2×C19—22no—
168C2×C19—41no—
169C2×C19—161no—
170C2×C19#188811yescharacteristic
171C2×C19#189711yescharacteristic
172C2×C19#191311yescharacteristic
173C22×D4—21no—
174C22×D4C2×Dic1911yescharacteristic
175C23×C4C22⋊D1911yescharacteristic
176C23×C4C22⋊D1911yescharacteristic
177C23×C4C22×D1911yescharacteristic
178C2×M16—382no—
179#121—22no—
180#121—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—382no—
184C2×C4⋊C4C2×Dic1911yescharacteristic
185C2×C4⋊C4C2×Dic1912yes—
186C2×C4⋊C4C22⋊D1912yes—
187C2×C22⋊C4—21no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—21no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—382no—
192C2×C42—21no—
193C2×C42—382no—
194C22⋊C8—382no—
195C22⋊C8—382no—
196#95—22no—
197#95—22no—
198#95—194no—
199#95—382no—
200#95—384no—
201#95C2×Dic1912yes—
202C19#941411yescharacteristic, complemented, Sylow
203C24—21no—
204C24C2×C22⋊D1911yescharacteristic
205C2×D4—22no—
206C2×D4—44no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—81no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—42no—
217C22×C4—81no—
218C22×C4—81no—
219C22×C4—384no—
220C22×C4C22⋊Dic1912yes—
221C22×C4C22⋊Dic1912yes—
222C22×C4D4×D1912yes—
223C22×C4#6454312yes—
224C22×C4C22×Dic1911yescharacteristic
225C22×C4C2×C22⋊D1911yescharacteristic
226M16—1522no—
227C2×C8—762no—
228C4⋊C4—24no—
229C4⋊C4—24no—
230C4⋊C4—22no—
231C4⋊C4—1522no—
232C22⋊C4—44no—
233C22⋊C4—42no—
234C22⋊C4—42no—
235C22⋊C4—82no—
236C22⋊C4—764no—
237C42—81no—
238C42—1522no—
239C23—22no—
240C23—22no—
241C23—41no—
242C23—42no—
243C23—42no—
244C23—42no—
245C23—41no—
246C23#1059738111yescharacteristic
247C23#1059738311yescharacteristic
248C23C2×C22⋊Dic1911yescharacteristic
249D4—82no—
250D4—82no—
251D4—82no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—81no—
270C2×C4—764no—
271C2×C4—764no—
272C2×C4—764no—
273C2×C4D4×Dic1912yes—
274C2×C4#1059738512yes—
275C8—1522no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—44no—
284C22—84no—
285C22—81no—
286C22—81no—
287C22—81no—
288C22#1192642411yescharacteristic
289C22#1192656112yes—
290C22#1192671612yes—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—42no—
295C4—82no—
296C4—81no—
297C4—1524no—
298C2—22no—
299C2—22no—
300C2—41no—
301C2—161no—
302C2#1456403911yescharacteristic
303C2#1456408411yescharacteristic
304C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2591C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#2591D19
hypocenterC19#9414
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2591

Complements

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

NH ≅ G/Ntype
1. #14566238C2semidirect
3. #14561965C2semidirect
4. #14561521C2semidirect
15. C19×#400C4semidirect
16. C19×#394C4semidirect
154. #400Dic19semidirect
155. #394Dic19semidirect
202. C19#9414semidirect

Maximal subgroups

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

subgroupindex
#145662382
#145621512
#145619652
#145615212
C19×#25912
#941419