Finite Group Databasebeta

← #18080009

Subgroups — #18080009

Order 4864.

552 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 103 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#14569115C211yesmaximal, characteristic
2#14562150C212yesmaximal
3#14561965C211yesmaximal, characteristic, complemented
4#14561521C212yesmaximal, complemented
5C19×#2313C211yesmaximal, characteristic, complemented
6C2×#10597376C2211yescharacteristic
7#11926508C2212yes—
8#11926483C412yescomplemented
9#11926461C412yescomplemented
10#11926434—22no—
11#11926423—21no—
12#11926423—21no—
13C4×C22⋊Dic19C2211yescharacteristic
14#11926277—24no—
15#11926270—22no—
16C22×C4⋊C4×C19C2211yescharacteristic
17C19×#387—24no—
18C19×#381—21no—
19C19×#380—21no—
20C4×C22⋊C4×C19C2212yes—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—21no—
25C22×D76C2×C411yescharacteristic
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19C2×C412yes—
30C2×C4⋊C4×C19D412yes—
31C2×C22⋊C4×C19—22no—
32C2×C42×C19—22no—
33C2×C22⋊Dic19—21no—
34#10597376—22no—
35#10597376—22no—
36C2×(C2×D19)⋊C4—22no—
37C2×(C2×D19)⋊C4—21no—
38C2×(C2×D19)⋊C4—22no—
39C2×C4⋊Dic19C2×C411yescharacteristic
40C2×C4×Dic19—21no—
41C2×#64520—22no—
42C19×#95—22no—
43C19×#95—24no—
44C19×#95D414yes—
45C19⋊#95—22no—
46C19⋊#95—22no—
47C19⋊#95C2×C412yes—
48C22⋊(C19⋊C8)—22no—
49C22⋊(C19⋊C8)—22no—
50C24×C19C2×D411yescharacteristic
51C23×D19—21no—
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—24no—
57C22×C4×C19—42no—
58C22×C4×C19—81no—
59C22×C4×C19—81no—
60C22×C4×C19C22⋊C412yes—
61C22×C4×C19C22⋊C412yes—
62C22×C4×C19C22×C411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D412yes—
65C22×C4×C19#4112yes—
66C2×C22⋊D19—44no—
67C2×C22⋊D19—41no—
68C2×C22⋊D19—41no—
69C22×Dic19—22no—
70C22×Dic19—21no—
71C2×D76—22no—
72C2×D76—81no—
73C4⋊C4×C19—24no—
74C4⋊C4×C19—24no—
75C4⋊C4×C19—82no—
76C22⋊C4×C19—44no—
77C42×C19—82no—
78C22⋊Dic19—42no—
79(C2×D19)⋊C4—44no—
80(C2×D19)⋊C4—42no—
81(C2×D19)⋊C4—82no—
82C4⋊Dic19—22no—
83C4×Dic19—81no—
84#64520—82no—
85C2×C19⋊C8—42no—
86#9414—191nomaximal, Sylow
87C23×C19—22no—
88C23×C19—22no—
89C23×C19—41no—
90C23×C19C2×C22⋊C411yescharacteristic
91C23×C19#12011yescharacteristic
92C23×C19#12311yescharacteristic
93C22×D19—42no—
94C22×D19—42no—
95C22×D19—41no—
96C22×D19—42no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—42no—
102C2×C4×C19—41no—
103C2×C4×C19—42no—
104C2×C4×C19—41no—
105C2×C4×C19—42no—
106C2×C4×C19—42no—
107C2×C4×C19—42no—
108C2×C4×C19—42no—
109C2×C4×C19—44no—
110C2×C4×C19—44no—
111C2×C4×C19—44no—
112C2×C4×C19—81no—
113C2×C4×C19C4×D412yes—
114C2×C4×C19#12112yes—
115C22⋊D19—82no—
116C22⋊D19—82no—
117C2×Dic19—42no—
118C2×Dic19—42no—
119C2×Dic19—42no—
120C2×Dic19—41no—
121C2×Dic19—42no—
122D76—82no—
123C19⋊C8—82no—
124#2591—191no—
125#2313D1911yescharacteristic, complemented
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#38611yescharacteristic
138C22×C19#42112yes—
139C22×C19#45412yes—
140C2×D19—84no—
141C2×D19—81no—
142C2×D19—81no—
143C2×D19—81no—
144C4×C19—22no—
145C4×C19—22no—
146C4×C19—42no—
147C4×C19—42no—
148C4×C19—84no—
149Dic19—82no—
150Dic19—81no—
151C2×#121—191no—
152C22×C4⋊C4C2×D1911yescharacteristic
153#407—192no—
154#400—192no—
155#394—192no—
156#388—382no—
157#387—24no—
158#386—381no—
159#386—381no—
160#381—21no—
161#380—21no—
162C4×C22⋊C4—191no—
163C4×C22⋊C4C2×D1912yes—
164#327—384no—
165#324—382no—
166C2×C19—22no—
167C2×C19—22no—
168C2×C19—41no—
169C2×C19#188811yescharacteristic
170C2×C19#189711yescharacteristic
171C2×C19#191311yescharacteristic
172D19—161no—
173C22×D4—191no—
174C22×D4—381no—
175C23×C4C22⋊D1911yescharacteristic
176C23×C4C22⋊D1911yescharacteristic
177C23×C4C22×D1911yescharacteristic
178C2×M16—382no—
179#121—382no—
180#121—382no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—191no—
185C2×C4⋊C4C4×D1912yes—
186C2×C4⋊C4D7612yes—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—381no—
189C2×C22⋊C4—382no—
190C2×C22⋊C4—381no—
191C2×C22⋊C4—382no—
192C2×C42—22no—
193C2×C42—381no—
194C22⋊C8—382no—
195C22⋊C8—382no—
196#95—22no—
197#95—24no—
198#95—192no—
199#95—382no—
200#95—382no—
201#95C22⋊D1914yes—
202C19#941411yescharacteristic, complemented, Sylow
203C24—381no—
204C24C2×C22⋊D1911yescharacteristic
205C2×D4—382no—
206C2×D4—764no—
207C2×D4—761no—
208C2×D4—761no—
209C2×D4—1521no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—24no—
215C22×C4—42no—
216C22×C4—81no—
217C22×C4—81no—
218C22×C4—382no—
219C22×C4—381no—
220C22×C4(C2×D19)⋊C412yes—
221C22×C4(C2×D19)⋊C412yes—
222C22×C4C2×C4×D1911yescharacteristic
223C22×C4C2×D7611yescharacteristic
224C22×C4#6454112yes—
225C22×C4C2×C22⋊D1912yes—
226M16—1522no—
227C2×C8—762no—
228C4⋊C4—24no—
229C4⋊C4—24no—
230C4⋊C4—82no—
231C4⋊C4—382no—
232C22⋊C4—44no—
233C22⋊C4—764no—
234C22⋊C4—762no—
235C22⋊C4—762no—
236C22⋊C4—1522no—
237C42—82no—
238C42—1521no—
239C23—22no—
240C23—22no—
241C23—41no—
242C23—762no—
243C23—762no—
244C23—762no—
245C23—761no—
246C23C2×(C2×D19)⋊C411yescharacteristic
247C23#1059737511yescharacteristic
248C23#1059739911yescharacteristic
249D4—1522no—
250D4—1522no—
251D4—1522no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—44no—
267C2×C4—81no—
268C2×C4—762no—
269C2×C4—762no—
270C2×C4—762no—
271C2×C4—762no—
272C2×C4—761no—
273C2×C4C4×C22⋊D1912yes—
274C2×C4#1059737612yes—
275C8—1522no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—44no—
284C22—1524no—
285C22—1521no—
286C22—1521no—
287C22—1521no—
288C22#1192642311yescharacteristic
289C22#1192656212yes—
290C22#1192671712yes—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—42no—
295C4—84no—
296C4—1522no—
297C4—1521no—
298C2—22no—
299C2—22no—
300C2—41no—
301C2—3041no—
302C2#1456403811yescharacteristic
303C2#1456408311yescharacteristic
304C2#1456417711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2313C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#2313D19
hypocenterC19#9414
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
3. #14561965C2semidirect
4. #14561521C2semidirect
5. C19×#2313C2semidirect
8. #11926483C4semidirect
9. #11926461C4semidirect
125. #2313D19semidirect
202. C19#9414semidirect

Maximal subgroups

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

subgroupindex
#145691152
#145621502
#145619652
#145615212
C19×#23132
#941419