Finite Group Databasebeta

← #18080499

Subgroups — #18080499

Order 4864.

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

normal subgroups only

This group has 544 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×#2486C211yesmaximal, 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×C19×#123C412yes—
15C2×C4×D4×C19C2211yescharacteristic
16C22×C4⋊C4×C19C2211yescharacteristic
17C19×#398—21no—
18C19×#397—21no—
19C19×#389—21no—
20C19×#381C412yes—
21C19×#380—21no—
22C19×#380C2211yescharacteristic
23C22×D4×C19C2×C411yescharacteristic
24C23×C4×C19C2×C412yes—
25C23×C4×C19D411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C19×#123—44no—
28C4×D4×C19—22no—
29C4×D4×C19—22no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—22no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—22no—
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C22⋊C4×C19—22no—
38C2×C22⋊C4×C19C2×C411yescharacteristic
39C2×C22⋊C4×C19C2×C412yes—
40C2×C22⋊C4×C19D411yescharacteristic
41C2×C42×C19D411yescharacteristic
42C2×#64520—22no—
43C2×#64520D414yes—
44C22×C19⋊C8—22no—
45C19×#95—22no—
46C19×#95—22no—
47C19×#95—21no—
48C22⋊(C19⋊C8)—22no—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)—22no—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—22no—
53C4⋊(C19⋊C8)—22no—
54#10597260—22no—
55C24×C19C22⋊C411yescharacteristic
56C24×C19C22×C411yescharacteristic
57C2×D4×C19—22no—
58C2×D4×C19—22no—
59C2×D4×C19—41no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—22no—
63C22×C4×C19—22no—
64C22×C4×C19—24no—
65C22×C4×C19—42no—
66C22×C4×C19—42no—
67C22×C4×C19—42no—
68C22×C4×C19—42no—
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C2×D412yes—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19#4112yes—
76C4⋊C4×C19—22no—
77C4⋊C4×C19—42no—
78C4⋊C4×C19—44no—
79C4⋊C4×C19—41no—
80C4⋊C4×C19—42no—
81C4⋊C4×C19—41no—
82C22⋊C4×C19—22no—
83C22⋊C4×C19—22no—
84C22⋊C4×C19—44no—
85C22⋊C4×C19—42no—
86C42×C19—21no—
87C42×C19—21no—
88#64520—44no—
89#64520—44no—
90C2×C19⋊C8—24no—
91C2×C19⋊C8—42no—
92C2×C19⋊C8—82no—
93#9507—191nomaximal, Sylow
94C23×C19—21no—
95C23×C19—21no—
96C23×C19—21no—
97C23×C19—21no—
98C23×C19—41no—
99C23×C19—41no—
100C23×C19—41no—
101C23×C19—41no—
102C23×C19#10012yes—
103C23×C19C2×C22⋊C411yescharacteristic
104C23×C19C4×D412yes—
105D4×C19—44no—
106C2×C4×C19—24no—
107C2×C4×C19—22no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—41no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—41no—
117C2×C4×C19—41no—
118C2×C4×C19—42no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19—42no—
124C2×C4×C19—81no—
125C2×C4×C19—84no—
126C2×C4×C19#12011yescharacteristic
127C2×C4×C19#12112yes—
128C2×C4×C19#12311yescharacteristic
129C19⋊C8—44no—
130C19⋊C8—82no—
131#2973—191no—
132#2486D1911yescharacteristic
133#1821—192no—
134#1465—191no—
135#1305—192no—
136C22×C19—21no—
137C22×C19—21no—
138C22×C19—22no—
139C22×C19—22no—
140C22×C19—22no—
141C22×C19—22no—
142C22×C19—42no—
143C22×C19—42no—
144C22×C19—42no—
145C22×C19—41no—
146C22×C19—41no—
147C22×C19—81no—
148C22×C19#38611yescharacteristic
149C22×C19C2×#10011yescharacteristic
150C22×C19#41311yescharacteristic
151C4×C19—22no—
152C4×C19—21no—
153C4×C19—41no—
154C4×C19—41no—
155C4×C19—41no—
156C4×C19—82no—
157C4×C19—82no—
158C4×C19#45812yes—
159C2×#123Dic1912yes—
160C2×C4×D4C2×D1911yescharacteristic
161C22×C4⋊C4C2×D1911yescharacteristic
162#435—384no—
163#432—381no—
164#407—192no—
165#407—192no—
166C2×C22⋊C8—381no—
167#398—21no—
168#397—21no—
169#389—21no—
170#381Dic1912yes—
171#380—21no—
172#380C2×D1911yescharacteristic
173#343—384no—
174#324—381no—
175#323—381no—
176C2×C19—21no—
177C2×C19—21no—
178C2×C19—42no—
179C2×C19—42no—
180C2×C19#189011yescharacteristic
181C2×C19#190011yescharacteristic
182C2×C19#191511yescharacteristic
183C22×D4C2×Dic1911yescharacteristic
184C23×C4C2×Dic1912yes—
185C23×C4C22⋊D1911yescharacteristic
186C23×C4C22×D1911yescharacteristic
187C2×M16—194no—
188C2×M16—382no—
189C22×C8—382no—
190#123—44no—
191C4×D4—22no—
192C4×D4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4C22⋊D1911yescharacteristic
200C2×C22⋊C4—22no—
201C2×C22⋊C4C2×Dic1911yescharacteristic
202C2×C22⋊C4C2×Dic1912yes—
203C2×C22⋊C4C22⋊D1911yescharacteristic
204C2×C42C22⋊D1911yescharacteristic
205C4⋊C8—382no—
206C22⋊C8—382no—
207C22⋊C8—382no—
208C22⋊C8—382no—
209C22⋊C8—382no—
210C22⋊C8—382no—
211#97—382no—
212#95—22no—
213#95—22no—
214#95—21no—
215C19#950711yescharacteristic, complemented, Sylow
216C24C22⋊Dic1911yescharacteristic
217C24C22×Dic1911yescharacteristic
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—41no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4C22⋊Dic1911yescharacteristic
231C22×C4C22⋊Dic1911yescharacteristic
232C22×C4C22⋊Dic1911yescharacteristic
233C22×C4D4×D1912yes—
234C22×C4#6454312yes—
235C22×C4C2×C22⋊D1911yescharacteristic
236C22×C4C2×C22⋊D1911yescharacteristic
237M16—764no—
238M16—764no—
239C2×C8—384no—
240C2×C8—762no—
241C2×C8—1522no—
242C4⋊C4—22no—
243C4⋊C4—42no—
244C4⋊C4—44no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—42no—
248C22⋊C4—22no—
249C22⋊C4—22no—
250C22⋊C4—44no—
251C22⋊C4—42no—
252C42—21no—
253C42—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23#1059729012yes—
263C23D4×Dic1912yes—
264C23C2×C22⋊Dic1911yescharacteristic
265D4—44no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—81no—
285C2×C4—84no—
286C2×C4#1059738111yescharacteristic
287C2×C4#1059738311yescharacteristic
288C2×C4#1059738512yes—
289C8—764no—
290C8—1522no—
291C22—21no—
292C22—21no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22#1192642411yescharacteristic
304C22C2×#1059729011yescharacteristic
305C22#1192652811yescharacteristic
306C4—22no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—82no—
312C4—82no—
313C4#1192673312yes—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—42no—
318C2#1456404911yescharacteristic
319C2#1456409911yescharacteristic
320C2#1456418811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2486C2
socleC22×C19#386
prime radicalC22×D4×C19C2×C4
cosocleC23×C4×C19C23
hypercenter#2486D19
hypocenterC19#9507
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2486

Complements

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

NH ≅ G/Ntype
2. #14563715C2semidirect
4. #14561541C2semidirect
215. C19#9507semidirect

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×#24862
#950719