Finite Group Databasebeta

← #18080429

Subgroups — #18080429

Order 4864.

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

normal subgroups only

This group has 458 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#14572273C211yesmaximal, characteristic
2#14562082C212yesmaximal, complemented
3#14561969C211yesmaximal, characteristic
4#14561499C212yesmaximal, complemented
5C19×#2599C211yesmaximal, characteristic
6#11926605—24no—
7#11926601C2212yes—
8#11926568—21no—
9#11926508—21no—
10C4×#64520C2212yes—
11Q8⋊(C19⋊C8)—24no—
12#11926270—21no—
13#11926268—21no—
14C2×C4×Q8×C19C2211yescharacteristic
15C2×C19×#117C2211yescharacteristic
16C19×#398C411yescharacteristic
17C19×#397C411yescharacteristic
18C19×#395C411yescharacteristic
19C19×#393C411yescharacteristic
20C19×#388—21no—
21C19×#387—21no—
22C19×#387—21no—
23C19×#385—21no—
24C19×#383C2211yescharacteristic
25C22×Q8×C19C2×C411yescharacteristic
26C23×C4×C19D411yescharacteristic
27C4×Q8×C19—22no—
28C4×Q8×C19—22no—
29C19×#117—22no—
30C19×#117—22no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19C2×C411yescharacteristic
40C2×C22⋊C4×C19D411yescharacteristic
41C2×C42×C19—21no—
42C2×C42×C19D411yescharacteristic
43C2×C42×C19C2311yescharacteristic
44C2×#64520—22no—
45C19×#95—21no—
46C19×#95—21no—
47C19×#95—21no—
48C19×#95—21no—
49C19×#95—21no—
50C19×#95—21no—
51C19×#95C2×C411yescharacteristic
52C19×#95C2×C411yescharacteristic
53C22⋊(C19⋊C8)—24no—
54C22⋊(C19⋊C8)—22no—
55C4⋊(C19⋊C8)—24no—
56C4⋊(C19⋊C8)—22no—
57#10597260—22no—
58#10597260—22no—
59C4×C19⋊C8D414yes—
60C24×C19C22⋊C411yescharacteristic
61C2×Q8×C19—22no—
62C2×Q8×C19—42no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—41no—
70C22×C4×C19—41no—
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C22⋊C411yescharacteristic
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22×C411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C4⋊C4×C19—22no—
78C4⋊C4×C19—22no—
79C4⋊C4×C19—22no—
80C4⋊C4×C19—42no—
81C4⋊C4×C19—42no—
82C4⋊C4×C19—41no—
83C4⋊C4×C19—41no—
84C22⋊C4×C19—22no—
85C22⋊C4×C19—22no—
86C22⋊C4×C19—42no—
87C22⋊C4×C19—42no—
88C42×C19—21no—
89C42×C19—21no—
90C42×C19—42no—
91C42×C19C2×D412yes—
92C42×C19#4112yes—
93#64520—42no—
94#64520—42no—
95C2×C19⋊C8—24no—
96C2×C19⋊C8—42no—
97#9493—191nomaximal, Sylow
98C23×C19—21no—
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—41no—
102C23×C19—41no—
103C23×C19C2×C22⋊C411yescharacteristic
104Q8×C19—24no—
105Q8×C19—42no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—22no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19—42no—
117C2×C4×C19—42no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19C4×D412yes—
132C2×C4×C19#12011yescharacteristic
133C2×C4×C19#12112yes—
134C2×C4×C19#12311yescharacteristic
135C19⋊C8—44no—
136C19⋊C8—82no—
137#2921—191no—
138#2599D1911yescharacteristic
139#1491—192no—
140#1464—191no—
141#1288—192no—
142C22×C19—21no—
143C22×C19—21no—
144C22×C19—42no—
145C22×C19—41no—
146C22×C19—41no—
147C22×C19—41no—
148C22×C19—81no—
149C22×C19#38611yescharacteristic
150C22×C19#42111yescharacteristic
151C22×C19#42111yescharacteristic
152C4×C19—22no—
153C4×C19—21no—
154C4×C19—21no—
155C4×C19—22no—
156C4×C19—41no—
157C4×C19—42no—
158C4×C19—41no—
159C4×C19—41no—
160C4×C19—81no—
161C4×C19—81no—
162C4×C19—81no—
163C2×C4×Q8C2×D1911yescharacteristic
164C2×#117C2×D1911yescharacteristic
165#433—384no—
166#432—192no—
167#423—381no—
168#407—381no—
169C4×M16—192no—
170#398Dic1911yescharacteristic
171#397Dic1911yescharacteristic
172#395Dic1911yescharacteristic
173#393Dic1911yescharacteristic
174#388—21no—
175#387—21no—
176#387—21no—
177#385—21no—
178#383C2×D1911yescharacteristic
179Q8⋊C8—384no—
180#324—381no—
181#323—381no—
182C2×C19—21no—
183C2×C19—21no—
184C2×C19—81no—
185C2×C19#189111yescharacteristic
186C2×C19#189711yescharacteristic
187C2×C19#190911yescharacteristic
188C22×Q8C2×Dic1911yescharacteristic
189C23×C4C22⋊D1911yescharacteristic
190C2×M16—382no—
191C4×Q8—22no—
192C4×Q8—22no—
193#117—22no—
194#117—22no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C2×Dic1911yescharacteristic
199C2×C4⋊C4C2×Dic1911yescharacteristic
200C2×C4⋊C4C22⋊D1911yescharacteristic
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4C2×Dic1911yescharacteristic
204C2×C22⋊C4C22⋊D1911yescharacteristic
205C2×C42—21no—
206C2×C42C22⋊D1911yescharacteristic
207C2×C42C22×D1911yescharacteristic
208C4⋊C8—384no—
209C4⋊C8—382no—
210C22⋊C8—384no—
211C22⋊C8—382no—
212#97—382no—
213#97—382no—
214C4×C8—194no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95C2×Dic1911yescharacteristic
222#95C2×Dic1911yescharacteristic
223C19#949311yescharacteristic, complemented, Sylow
224C24C22⋊Dic1911yescharacteristic
225C2×Q8—22no—
226C2×Q8—42no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4C22⋊Dic1911yescharacteristic
236C22×C4C22⋊Dic1911yescharacteristic
237C22×C4C22⋊Dic1911yescharacteristic
238C22×C4C22×Dic1911yescharacteristic
239C22×C4C2×C22⋊D1911yescharacteristic
240C22×C4C2×C22⋊D1911yescharacteristic
241M16—762no—
242M16—762no—
243C2×C8—384no—
244C2×C8—762no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C42—21no—
257C42—21no—
258C42—42no—
259C42D4×D1912yes—
260C42#6454312yes—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23C2×C22⋊Dic1911yescharacteristic
267Q8—24no—
268Q8—42no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4D4×Dic1912yes—
295C2×C4#1059738111yescharacteristic
296C2×C4#1059738311yescharacteristic
297C2×C4#1059738512yes—
298C8—764no—
299C8—1522no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—81no—
307C22#1192642411yescharacteristic
308C22#1192656111yescharacteristic
309C22#1192656111yescharacteristic
310C4—22no—
311C4—22no—
312C4—21no—
313C4—21no—
314C4—41no—
315C4—42no—
316C4—41no—
317C4—41no—
318C4—81no—
319C4—81no—
320C4—81no—
321C2—21no—
322C2—21no—
323C2—81no—
324C2#1456405411yescharacteristic
325C2#1456408411yescharacteristic
326C2#1456415811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2599C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2599D19
hypocenterC19#9493
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2599

Complements

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

NH ≅ G/Ntype
2. #14562082C2semidirect
4. #14561499C2semidirect
223. C19#9493semidirect

Maximal subgroups

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

subgroupindex
#145722732
#145620822
#145619692
#145614992
C19×#25992
#949319