Finite Group Databasebeta

← #18079889

Subgroups — #18079889

Order 4864.

446 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 99 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#14569333C211yesmaximal, characteristic
2#14562236C212yesmaximal, complemented
3#14561969C211yesmaximal, characteristic
4#14561529C212yesmaximal, complemented
5C19×#2921C211yesmaximal, characteristic
6C2×#10597316C2211yescharacteristic
7#11926601C2212yes—
8#11926483C411yescharacteristic
9#11926480C411yescharacteristic
10#11926474C411yescharacteristic
11#11926469C411yescharacteristic
12#11926439—21no—
13#11926438—21no—
14#11926428—21no—
15#11926417—21no—
16#11926390C2211yescharacteristic
17#11926285—24no—
18#11926270—21no—
19#11926268—21no—
20C2×C19×#117C2211yescharacteristic
21C19×#433—24no—
22C19×#423—21no—
23C19×#407—21no—
24C4×M16×C19C2212yes—
25C23×C4×C19D411yescharacteristic
26C2×M16×C19—22no—
27C19×#117—22no—
28C19×#117—22no—
29C2×C4⋊C4×C19C2×C411yescharacteristic
30C2×C4⋊C4×C19D411yescharacteristic
31C2×C22⋊C4×C19C2×C411yescharacteristic
32C2×C22⋊C4×C19D411yescharacteristic
33C2×C42×C19D411yescharacteristic
34C2×C42×C19C2311yescharacteristic
35C2×C22⋊Dic19—21no—
36C2×C22⋊Dic19—21no—
37C2×C4⋊Dic19C2×C411yescharacteristic
38C2×C4⋊Dic19C2×C411yescharacteristic
39C2×Dic19⋊C4—21no—
40C2×Dic19⋊C4—21no—
41C2×Dic19⋊C4—21no—
42C2×Dic19⋊C4—21no—
43C2×C4×Dic19—21no—
44#10597316—22no—
45#10597316—22no—
46C19×C4⋊C8—24no—
47C19×C22⋊C8—24no—
48C19×#97D414yes—
49C4×C8×C19—22no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C19⋊#95C2×C411yescharacteristic
56C19⋊#95C2×C411yescharacteristic
57C22⋊(C19⋊C8)—22no—
58C4⋊(C19⋊C8)—22no—
59#10597260—22no—
60C24×C19C22⋊C411yescharacteristic
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—41no—
64C22×C4×C19—41no—
65C22×C4×C19C22⋊C411yescharacteristic
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×Dic19—21no—
72C22×Dic19—21no—
73C22×Dic19—21no—
74C22×Dic19—21no—
75M16×C19—42no—
76M16×C19—42no—
77C2×C8×C19—24no—
78C4⋊C4×C19—22no—
79C4⋊C4×C19—22no—
80C22⋊C4×C19—22no—
81C22⋊C4×C19—22no—
82C42×C19—21no—
83C42×C19—21no—
84C42×C19C2×D412yes—
85C42×C19#4112yes—
86C22⋊Dic19—42no—
87C22⋊Dic19—42no—
88C4⋊Dic19—22no—
89C4⋊Dic19—22no—
90Dic19⋊C4—42no—
91Dic19⋊C4—42no—
92Dic19⋊C4—41no—
93Dic19⋊C4—42no—
94Dic19⋊C4—41no—
95C4×Dic19—42no—
96C2×C19⋊C8—42no—
97#9390—191nomaximal, Sylow
98C23×C19—21no—
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—41no—
102C23×C19—41no—
103C23×C19C2×C22⋊C411yescharacteristic
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19—42no—
114C2×C4×C19—42no—
115C2×C4×C19—41no—
116C2×C4×C19—41no—
117C2×C4×C19C4×D412yes—
118C2×C4×C19#12011yescharacteristic
119C2×C4×C19#12112yes—
120C2×C4×C19#12311yescharacteristic
121C2×Dic19—22no—
122C2×Dic19—41no—
123C2×Dic19—41no—
124C2×Dic19—41no—
125C2×Dic19—41no—
126C2×Dic19—41no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C8×C19—44no—
134C19⋊C8—82no—
135#2921D1911yescharacteristic
136#2611—191no—
137#1528—192no—
138#1464—191no—
139#1300—192no—
140C22×C19—21no—
141C22×C19—21no—
142C22×C19—42no—
143C22×C19—41no—
144C22×C19—41no—
145C22×C19—41no—
146C22×C19—81no—
147C22×C19#38611yescharacteristic
148C22×C19#42111yescharacteristic
149C22×C19#42111yescharacteristic
150C4×C19—22no—
151C4×C19—21no—
152C4×C19—21no—
153C4×C19—22no—
154C4×C19—41no—
155C4×C19—41no—
156C4×C19—41no—
157Dic19—42no—
158Dic19—81no—
159Dic19—81no—
160Dic19—81no—
161C2×#125—191no—
162C2×#117C2×D1911yescharacteristic
163#433—24no—
164#432—192no—
165#423—21no—
166#407—21no—
167C4×M16C2×D1912yes—
168#400—191no—
169#399—191no—
170#398—191no—
171#397—191no—
172#389—381no—
173#388—381no—
174#387—381no—
175#385—381no—
176#376—191no—
177#330—384no—
178#324—381no—
179#323—381no—
180C2×C19—21no—
181C2×C19—21no—
182C2×C19—81no—
183C2×C19#188411yescharacteristic
184C2×C19#189711yescharacteristic
185C2×C19#191511yescharacteristic
186C23×C4C22⋊D1911yescharacteristic
187C2×M16—22no—
188#125—382no—
189#125—382no—
190#117—22no—
191#117—22no—
192C2×C4⋊C4—191no—
193C2×C4⋊C4—191no—
194C2×C4⋊C4—381no—
195C2×C4⋊C4—381no—
196C2×C4⋊C4—381no—
197C2×C4⋊C4—381no—
198C2×C4⋊C4C4×D1911yescharacteristic
199C2×C4⋊C4D7611yescharacteristic
200C2×C22⋊C4—381no—
201C2×C22⋊C4—381no—
202C2×C22⋊C4C4×D1911yescharacteristic
203C2×C22⋊C4D7611yescharacteristic
204C2×C42—381no—
205C2×C42C22⋊D1911yescharacteristic
206C2×C42C22×D1911yescharacteristic
207C4⋊C8—24no—
208C4⋊C8—382no—
209C22⋊C8—24no—
210C22⋊C8—382no—
211#97—382no—
212#97C22⋊D1914yes—
213C4×C8—22no—
214#95—191no—
215#95—191no—
216#95—381no—
217#95—381no—
218#95—381no—
219#95—381no—
220#95—381no—
221C19#939011yescharacteristic, complemented, Sylow
222C24(C2×D19)⋊C411yescharacteristic
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—381no—
228C22×C4—381no—
229C22×C4—381no—
230C22×C4—381no—
231C22×C4(C2×D19)⋊C411yescharacteristic
232C22×C4(C2×D19)⋊C411yescharacteristic
233C22×C4(C2×D19)⋊C411yescharacteristic
234C22×C4C2×C4×D1911yescharacteristic
235C22×C4C2×D7611yescharacteristic
236C22×C4C2×C22⋊D1911yescharacteristic
237M16—42no—
238M16—42no—
239C2×C8—24no—
240C2×C8—762no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—382no—
244C4⋊C4—382no—
245C4⋊C4—762no—
246C4⋊C4—762no—
247C4⋊C4—762no—
248C4⋊C4—761no—
249C4⋊C4—761no—
250C22⋊C4—22no—
251C22⋊C4—22no—
252C22⋊C4—762no—
253C22⋊C4—762no—
254C42—21no—
255C42—21no—
256C42—762no—
257C42#6454112yes—
258C42C2×C22⋊D1912yes—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23C2×(C2×D19)⋊C411yescharacteristic
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—382no—
279C2×C4—761no—
280C2×C4—761no—
281C2×C4—761no—
282C2×C4—761no—
283C2×C4—761no—
284C2×C4—761no—
285C2×C4—761no—
286C2×C4—761no—
287C2×C4—761no—
288C2×C4—761no—
289C2×C4—761no—
290C2×C4C4×C22⋊D1912yes—
291C2×C4#1059737511yescharacteristic
292C2×C4#1059737612yes—
293C2×C4#1059739911yescharacteristic
294C8—44no—
295C8—1522no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22#1192642311yescharacteristic
304C22#1192656211yescharacteristic
305C22#1192656211yescharacteristic
306C4—22no—
307C4—22no—
308C4—21no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—762no—
314C4—1521no—
315C4—1521no—
316C4—1521no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2#1456401811yescharacteristic
321C2#1456408311yescharacteristic
322C2#1456418711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2921C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2921D19
hypocenterC19#9390
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2921

Complements

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

NH ≅ G/Ntype
2. #14562236C2semidirect
4. #14561529C2semidirect
221. C19#9390semidirect

Maximal subgroups

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

subgroupindex
#145693332
#145622362
#145619692
#145615292
C19×#29212
#939019