Finite Group Databasebeta

← #18080428

Subgroups — #18080428

Order 4864.

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

normal subgroups only

This group has 458 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#14569212C211yesmaximal, characteristic
2#14562083C212yesmaximal, complemented
3#14561969C211yesmaximal, characteristic
4#14561500C212yesmaximal, complemented
5C19×#2921C211yesmaximal, characteristic
6C2×C4×Dic38C2211yescharacteristic
7#11926601C2212yes—
8#11926474C411yescharacteristic
9#11926469C411yescharacteristic
10#11926464C411yescharacteristic
11#11926456C411yescharacteristic
12#11926432—21no—
13#11926428—21no—
14#11926425—21no—
15#11926417—21no—
16#11926412C2211yescharacteristic
17#11926276—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
26C22×Dic38C2×C411yescharacteristic
27C2×M16×C19—22no—
28C19×#117—22no—
29C19×#117—22no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19D411yescharacteristic
32C2×C22⋊C4×C19C2×C411yescharacteristic
33C2×C22⋊C4×C19D411yescharacteristic
34C2×C42×C19D411yescharacteristic
35C2×C42×C19C2311yescharacteristic
36C2×C22⋊Dic19—21no—
37C2×C22⋊Dic19—21no—
38C2×C4⋊Dic19C2×C411yescharacteristic
39C2×Dic19⋊C4—21no—
40C2×Dic19⋊C4—21no—
41C2×Dic19⋊C4—21no—
42C2×C4×Dic19—21no—
43C4×Dic38—22no—
44C4×Dic38—22no—
45C19×C4⋊C8—24no—
46C19×C22⋊C8—24no—
47C19×#97—22no—
48C4×C8×C19D414yes—
49C19⋊#95—21no—
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—
75C2×Dic38—22no—
76C2×Dic38—42no—
77M16×C19—42no—
78M16×C19—42no—
79C2×C8×C19—24no—
80C4⋊C4×C19—22no—
81C4⋊C4×C19—22no—
82C22⋊C4×C19—22no—
83C22⋊C4×C19—22no—
84C42×C19—21no—
85C42×C19—21no—
86C42×C19C2×D412yes—
87C42×C19#4112yes—
88C22⋊Dic19—42no—
89C22⋊Dic19—42no—
90C4⋊Dic19—22no—
91Dic19⋊C4—42no—
92Dic19⋊C4—42no—
93Dic19⋊C4—41no—
94Dic19⋊C4—41no—
95C4×Dic19—42no—
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
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—
133Dic38—24no—
134Dic38—42no—
135C8×C19—44no—
136C19⋊C8—82no—
137#2921D1911yescharacteristic
138#2599—191no—
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—41no—
158C4×C19—41no—
159Dic19—42no—
160Dic19—81no—
161Dic19—81no—
162Dic19—81no—
163C2×C4×Q8—191no—
164C2×#117C2×D1911yescharacteristic
165#433—24no—
166#432—192no—
167#423—21no—
168#407—21no—
169C4×M16C2×D1912yes—
170#398—191no—
171#397—191no—
172#395—191no—
173#393—191no—
174#388—381no—
175#387—381no—
176#387—381no—
177#385—381no—
178#383—191no—
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×Q8—191no—
189C23×C4C22⋊D1911yescharacteristic
190C2×M16—22no—
191C4×Q8—382no—
192C4×Q8—382no—
193#117—22no—
194#117—22no—
195C2×C4⋊C4—191no—
196C2×C4⋊C4—381no—
197C2×C4⋊C4—381no—
198C2×C4⋊C4—381no—
199C2×C4⋊C4C4×D1911yescharacteristic
200C2×C4⋊C4D7611yescharacteristic
201C2×C22⋊C4—381no—
202C2×C22⋊C4—381no—
203C2×C22⋊C4C4×D1911yescharacteristic
204C2×C22⋊C4D7611yescharacteristic
205C2×C42—381no—
206C2×C42C22⋊D1911yescharacteristic
207C2×C42C22×D1911yescharacteristic
208C4⋊C8—24no—
209C4⋊C8—382no—
210C22⋊C8—24no—
211C22⋊C8—382no—
212#97—22no—
213#97—382no—
214C4×C8C22⋊D1914yes—
215#95—191no—
216#95—191no—
217#95—381no—
218#95—381no—
219#95—381no—
220#95—381no—
221#95—381no—
222#95—381no—
223C19#949311yescharacteristic, complemented, Sylow
224C24(C2×D19)⋊C411yescharacteristic
225C2×Q8—382no—
226C2×Q8—762no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—381no—
232C22×C4—381no—
233C22×C4—381no—
234C22×C4—381no—
235C22×C4(C2×D19)⋊C411yescharacteristic
236C22×C4(C2×D19)⋊C411yescharacteristic
237C22×C4(C2×D19)⋊C411yescharacteristic
238C22×C4C2×C4×D1911yescharacteristic
239C22×C4C2×D7611yescharacteristic
240C22×C4C2×C22⋊D1911yescharacteristic
241M16—42no—
242M16—42no—
243C2×C8—24no—
244C2×C8—762no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—382no—
248C4⋊C4—762no—
249C4⋊C4—762no—
250C4⋊C4—761no—
251C4⋊C4—761no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—762no—
255C22⋊C4—762no—
256C42—21no—
257C42—21no—
258C42—762no—
259C42#6454112yes—
260C42C2×C22⋊D1912yes—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23C2×(C2×D19)⋊C411yescharacteristic
267Q8—384no—
268Q8—762no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—382no—
283C2×C4—761no—
284C2×C4—761no—
285C2×C4—761no—
286C2×C4—761no—
287C2×C4—761no—
288C2×C4—761no—
289C2×C4—761no—
290C2×C4—761no—
291C2×C4—761no—
292C2×C4—761no—
293C2×C4—761no—
294C2×C4C4×C22⋊D1912yes—
295C2×C4#1059737511yescharacteristic
296C2×C4#1059737612yes—
297C2×C4#1059739911yescharacteristic
298C8—44no—
299C8—1522no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—81no—
307C22#1192642311yescharacteristic
308C22#1192656211yescharacteristic
309C22#1192656211yescharacteristic
310C4—22no—
311C4—22no—
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—762no—
318C4—1521no—
319C4—1521no—
320C4—1521no—
321C2—21no—
322C2—21no—
323C2—81no—
324C2#1456405311yescharacteristic
325C2#1456408311yescharacteristic
326C2#1456415711yescharacteristic
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#9493
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. #14562083C2semidirect
4. #14561500C2semidirect
223. C19#9493semidirect

Maximal subgroups

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

subgroupindex
#145692122
#145620832
#145619692
#145615002
C19×#29212
#949319