Finite Group Databasebeta

← #18079890

Subgroups — #18079890

Order 4864.

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

normal subgroups only

This group has 446 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#14562237C212yesmaximal, complemented
3#14561969C211yesmaximal, characteristic
4#14561528C212yesmaximal, complemented
5C19×#2611C211yesmaximal, characteristic
6#11926605—24no—
7#11926601C2212yes—
8#11926568—21no—
9#11926508—21no—
10C4×#64520C2212yes—
11#11926286—24no—
12#11926270—21no—
13#11926268—21no—
14C2×C19×#125C2211yescharacteristic
15C2×C19×#117C2211yescharacteristic
16C19×#400C411yescharacteristic
17C19×#399C411yescharacteristic
18C19×#398C411yescharacteristic
19C19×#397C411yescharacteristic
20C19×#389—21no—
21C19×#388—21no—
22C19×#387—21no—
23C19×#385—21no—
24C19×#376C2211yescharacteristic
25C23×C4×C19D411yescharacteristic
26C19×#125—22no—
27C19×#125—22no—
28C19×#117—22no—
29C19×#117—22no—
30C2×C4⋊C4×C19—21no—
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×C19C2×C411yescharacteristic
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19C2×C411yescharacteristic
41C2×C22⋊C4×C19D411yescharacteristic
42C2×C42×C19—21no—
43C2×C42×C19D411yescharacteristic
44C2×C42×C19C2311yescharacteristic
45C2×#64520—22no—
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#10597260D414yes—
59C4×C19⋊C8—22no—
60C24×C19C22⋊C411yescharacteristic
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—41no—
68C22×C4×C19—41no—
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C4⋊C4×C19—22no—
76C4⋊C4×C19—22no—
77C4⋊C4×C19—22no—
78C4⋊C4×C19—22no—
79C4⋊C4×C19—42no—
80C4⋊C4×C19—42no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19—42no—
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#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—22no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—41no—
113C2×C4×C19—41no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—41no—
117C2×C4×C19—41no—
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×C19C4×D412yes—
130C2×C4×C19#12011yescharacteristic
131C2×C4×C19#12112yes—
132C2×C4×C19#12311yescharacteristic
133C19⋊C8—44no—
134C19⋊C8—82no—
135#2921—191no—
136#2611D1911yescharacteristic
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—42no—
155C4×C19—41no—
156C4×C19—41no—
157C4×C19—41no—
158C4×C19—81no—
159C4×C19—81no—
160C4×C19—81no—
161C2×#125C2×D1911yescharacteristic
162C2×#117C2×D1911yescharacteristic
163#433—384no—
164#432—192no—
165#423—381no—
166#407—381no—
167C4×M16—192no—
168#400Dic1911yescharacteristic
169#399Dic1911yescharacteristic
170#398Dic1911yescharacteristic
171#397Dic1911yescharacteristic
172#389—21no—
173#388—21no—
174#387—21no—
175#385—21no—
176#376C2×D1911yescharacteristic
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—382no—
188#125—22no—
189#125—22no—
190#117—22no—
191#117—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4C2×Dic1911yescharacteristic
197C2×C4⋊C4C2×Dic1911yescharacteristic
198C2×C4⋊C4C2×Dic1911yescharacteristic
199C2×C4⋊C4C22⋊D1911yescharacteristic
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4C2×Dic1911yescharacteristic
203C2×C22⋊C4C22⋊D1911yescharacteristic
204C2×C42—21no—
205C2×C42C22⋊D1911yescharacteristic
206C2×C42C22×D1911yescharacteristic
207C4⋊C8—384no—
208C4⋊C8—382no—
209C22⋊C8—384no—
210C22⋊C8—382no—
211#97—194no—
212#97—382no—
213C4×C8—382no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95C2×Dic1911yescharacteristic
220#95C2×Dic1911yescharacteristic
221C19#939011yescharacteristic, complemented, Sylow
222C24C22⋊Dic1911yescharacteristic
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4C22⋊Dic1911yescharacteristic
232C22×C4C22⋊Dic1911yescharacteristic
233C22×C4C22⋊Dic1911yescharacteristic
234C22×C4C22×Dic1911yescharacteristic
235C22×C4C2×C22⋊D1911yescharacteristic
236C22×C4C2×C22⋊D1911yescharacteristic
237M16—762no—
238M16—762no—
239C2×C8—384no—
240C2×C8—762no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C22⋊C4—22no—
251C22⋊C4—22no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C42—21no—
255C42—21no—
256C42—42no—
257C42D4×D1912yes—
258C42#6454312yes—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23C2×C22⋊Dic1911yescharacteristic
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
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×C4D4×Dic1912yes—
291C2×C4#1059738111yescharacteristic
292C2×C4#1059738311yescharacteristic
293C2×C4#1059738512yes—
294C8—764no—
295C8—1522no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22#1192642411yescharacteristic
304C22#1192656111yescharacteristic
305C22#1192656111yescharacteristic
306C4—22no—
307C4—22no—
308C4—21no—
309C4—21no—
310C4—42no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—81no—
315C4—81no—
316C4—81no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2#1456401911yescharacteristic
321C2#1456408411yescharacteristic
322C2#1456418811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2611C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2611D19
hypocenterC19#9390
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2611

Complements

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

NH ≅ G/Ntype
2. #14562237C2semidirect
4. #14561528C2semidirect
221. C19#9390semidirect

Maximal subgroups

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

subgroupindex
#145722732
#145622372
#145619692
#145615282
C19×#26112
#939019