Finite Group Databasebeta

← #18080509

Subgroups — #18080509

Order 4864.

524 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 111 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#14572664C211yesmaximal, characteristic
2#14563715C212yesmaximal, complemented
3#14561973C211yesmaximal, characteristic
4#14561541C212yesmaximal, complemented
5C19×#2487C211yesmaximal, characteristic
6#11926616—24no—
7#11926601—21no—
8#11926508C2212yes—
9#11926508C2212yes—
10C2×C22⋊(C19⋊C8)—21no—
11#11926313—24no—
12#11926270—21no—
13#11926268—21no—
14C2×C4×D4×C19C2211yescharacteristic
15C22×C4⋊C4×C19C2211yescharacteristic
16C19×#400—21no—
17C19×#399—21no—
18C19×#389—21no—
19C19×#386C412yes—
20C19×#385C412yes—
21C19×#380—21no—
22C19×#380C2211yescharacteristic
23C22×D4×C19C2×C411yescharacteristic
24C23×C4×C19C2×C412yes—
25C23×C4×C19D411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C4×D4×C19—22no—
28C4×D4×C19—22no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—22no—
34C2×C4⋊C4×C19—22no—
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C22⋊C4×C19—22no—
37C2×C22⋊C4×C19C2×C411yescharacteristic
38C2×C22⋊C4×C19C2×C412yes—
39C2×C22⋊C4×C19D411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×#64520—22no—
42C2×#64520D414yes—
43C22×C19⋊C8—22no—
44C19×#95—22no—
45C19×#95—22no—
46C19×#95—21no—
47C22⋊(C19⋊C8)—22no—
48C22⋊(C19⋊C8)—22no—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)—22no—
51C22⋊(C19⋊C8)—22no—
52C4⋊(C19⋊C8)—22no—
53#10597260—22no—
54C24×C19C22⋊C411yescharacteristic
55C24×C19C22×C411yescharacteristic
56C2×D4×C19—22no—
57C2×D4×C19—22no—
58C2×D4×C19—41no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—22no—
62C22×C4×C19—22no—
63C22×C4×C19—24no—
64C22×C4×C19—42no—
65C22×C4×C19—42no—
66C22×C4×C19—82no—
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C2×D412yes—
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19#4112yes—
74C4⋊C4×C19—22no—
75C4⋊C4×C19—42no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19—42no—
78C4⋊C4×C19—41no—
79C4⋊C4×C19—82no—
80C22⋊C4×C19—22no—
81C22⋊C4×C19—22no—
82C22⋊C4×C19—42no—
83C22⋊C4×C19—82no—
84C42×C19—21no—
85C42×C19—21no—
86#64520—44no—
87#64520—44no—
88C2×C19⋊C8—24no—
89C2×C19⋊C8—42no—
90C2×C19⋊C8—82no—
91#9509—191nomaximal, Sylow
92C23×C19—21no—
93C23×C19—21no—
94C23×C19—21no—
95C23×C19—21no—
96C23×C19—41no—
97C23×C19—41no—
98C23×C19—41no—
99C23×C19—41no—
100C23×C19#10112yes—
101C23×C19C2×C22⋊C411yescharacteristic
102C23×C19C4×D412yes—
103D4×C19—44no—
104C2×C4×C19—24no—
105C2×C4×C19—22no—
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—42no—
113C2×C4×C19—42no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19—42no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19—81no—
123C2×C4×C19—84no—
124C2×C4×C19#12011yescharacteristic
125C2×C4×C19#12112yes—
126C2×C4×C19#12311yescharacteristic
127C19⋊C8—44no—
128C19⋊C8—82no—
129#2973—191no—
130#2487D1911yescharacteristic
131#1821—192no—
132#1465—191no—
133#1305—192no—
134C22×C19—21no—
135C22×C19—21no—
136C22×C19—22no—
137C22×C19—22no—
138C22×C19—22no—
139C22×C19—22no—
140C22×C19—42no—
141C22×C19—42no—
142C22×C19—42no—
143C22×C19—41no—
144C22×C19—41no—
145C22×C19—81no—
146C22×C19#38611yescharacteristic
147C22×C19C2×#10111yescharacteristic
148C22×C19#41311yescharacteristic
149C4×C19—22no—
150C4×C19—21no—
151C4×C19—41no—
152C4×C19—41no—
153C4×C19—41no—
154C4×C19—82no—
155C4×C19—82no—
156C4×C19#45812yes—
157C2×C4×D4C2×D1911yescharacteristic
158C22×C4⋊C4C2×D1911yescharacteristic
159#435—384no—
160#432—381no—
161#407—192no—
162#407—192no—
163C2×C22⋊C8—381no—
164#400—21no—
165#399—21no—
166#389—21no—
167#386Dic1912yes—
168#385Dic1912yes—
169#380—21no—
170#380C2×D1911yescharacteristic
171#343—384no—
172#324—381no—
173#323—381no—
174C2×C19—21no—
175C2×C19—21no—
176C2×C19—42no—
177C2×C19—42no—
178C2×C19#189011yescharacteristic
179C2×C19#190111yescharacteristic
180C2×C19#191411yescharacteristic
181C22×D4C2×Dic1911yescharacteristic
182C23×C4C2×Dic1912yes—
183C23×C4C22⋊D1911yescharacteristic
184C23×C4C22×D1911yescharacteristic
185C2×M16—194no—
186C2×M16—382no—
187C22×C8—382no—
188C4×D4—22no—
189C4×D4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4C22⋊D1911yescharacteristic
197C2×C22⋊C4—22no—
198C2×C22⋊C4C2×Dic1911yescharacteristic
199C2×C22⋊C4C2×Dic1912yes—
200C2×C22⋊C4C22⋊D1911yescharacteristic
201C2×C42C22⋊D1911yescharacteristic
202C4⋊C8—382no—
203C22⋊C8—382no—
204C22⋊C8—382no—
205C22⋊C8—382no—
206C22⋊C8—382no—
207C22⋊C8—382no—
208#97—382no—
209#95—22no—
210#95—22no—
211#95—21no—
212C19#950911yescharacteristic, complemented, Sylow
213C24C22⋊Dic1911yescharacteristic
214C24C22×Dic1911yescharacteristic
215C2×D4—22no—
216C2×D4—22no—
217C2×D4—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—82no—
226C22×C4C22⋊Dic1911yescharacteristic
227C22×C4C22⋊Dic1911yescharacteristic
228C22×C4C22⋊Dic1911yescharacteristic
229C22×C4D4×D1912yes—
230C22×C4#6454312yes—
231C22×C4C2×C22⋊D1911yescharacteristic
232C22×C4C2×C22⋊D1911yescharacteristic
233M16—764no—
234M16—764no—
235C2×C8—384no—
236C2×C8—762no—
237C2×C8—1522no—
238C4⋊C4—22no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—82no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C22⋊C4—42no—
247C22⋊C4—82no—
248C42—21no—
249C42—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23#1059729312yes—
259C23D4×Dic1912yes—
260C23C2×C22⋊Dic1911yescharacteristic
261D4—44no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—84no—
282C2×C4#1059738111yescharacteristic
283C2×C4#1059738311yescharacteristic
284C2×C4#1059738512yes—
285C8—764no—
286C8—1522no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—42no—
294C22—42no—
295C22—42no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22#1192642411yescharacteristic
300C22C2×#1059729311yescharacteristic
301C22#1192652811yescharacteristic
302C4—22no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—82no—
308C4—82no—
309C4#1192673312yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—42no—
314C2#1456404911yescharacteristic
315C2#1456410411yescharacteristic
316C2#1456418311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2487C2
socleC22×C19#386
prime radicalC22×D4×C19C2×C4
cosocleC23×C4×C19C23
hypercenter#2487D19
hypocenterC19#9509
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2487

Complements

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

NH ≅ G/Ntype
2. #14563715C2semidirect
4. #14561541C2semidirect
212. C19#9509semidirect

Maximal subgroups

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

subgroupindex
#145726642
#145637152
#145619732
#145615412
C19×#24872
#950919