Finite Group Databasebeta

← #18080498

Subgroups — #18080498

Order 4864.

544 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 107 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#14567943C211yesmaximal, characteristic
2#14563713C212yesmaximal, complemented
3#14561973C211yesmaximal, characteristic
4#14561540C212yesmaximal, complemented
5C19×#2973C211yesmaximal, characteristic
6C2×#10597381C412yes—
7C22×C4⋊Dic19C2211yescharacteristic
8#11926508C2212yes—
9#11926474—21no—
10#11926469—21no—
11#11926442—21no—
12#11926405C412yes—
13#11926404—21no—
14#11926404C2211yescharacteristic
15#11926312—24no—
16#11926270—21no—
17#11926268—21no—
18C2×C4×D4×C19C2211yescharacteristic
19C19×#435—24no—
20C19×#432—21no—
21C19×#407C2212yes—
22C2×C19×C22⋊C8—21no—
23C22×D4×C19C2×C411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19C2×C412yes—
27C2×M16×C19D414yes—
28C22×C8×C19—22no—
29C4×D4×C19—22no—
30C4×D4×C19—22no—
31C2×C4⋊C4×C19D411yescharacteristic
32C2×C22⋊C4×C19C2×C411yescharacteristic
33C2×C22⋊C4×C19D411yescharacteristic
34C2×C42×C19D411yescharacteristic
35C2×C22⋊Dic19—22no—
36C2×C22⋊Dic19C2×C412yes—
37#10597381—44no—
38C2×C4⋊Dic19—22no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19—21no—
42C2×C4⋊Dic19—22no—
43C2×Dic19⋊C4—22no—
44C2×#64520—22no—
45C19×C4⋊C8—22no—
46C19×C22⋊C8—22no—
47C19×C22⋊C8—22no—
48C19×C22⋊C8—22no—
49C19×#97—22no—
50C19⋊#95—22no—
51C19⋊#95—22no—
52C19⋊#95—21no—
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—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—42no—
63C22×C4×C19—42no—
64C22×C4×C19C22⋊C411yescharacteristic
65C22×C4×C19C22⋊C411yescharacteristic
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19C2×D412yes—
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19#4112yes—
71C22×Dic19—22no—
72C22×Dic19—22no—
73C22×Dic19—24no—
74C22×Dic19—42no—
75C22×Dic19—42no—
76M16×C19—44no—
77C2×C8×C19—24no—
78C2×C8×C19—82no—
79C4⋊C4×C19—22no—
80C22⋊C4×C19—22no—
81C22⋊C4×C19—22no—
82C42×C19—21no—
83C42×C19—21no—
84C22⋊Dic19—44no—
85C22⋊Dic19—42no—
86C4⋊Dic19—42no—
87C4⋊Dic19—41no—
88C4⋊Dic19—42no—
89C4⋊Dic19—41no—
90Dic19⋊C4—44no—
91#64520—44no—
92C2×C19⋊C8—42no—
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—81no—
119C2×C4×C19#12011yescharacteristic
120C2×C4×C19#12112yes—
121C2×C4×C19#12311yescharacteristic
122C2×Dic19—42no—
123C2×Dic19—42no—
124C2×Dic19—42no—
125C2×Dic19—42no—
126C2×Dic19—42no—
127C2×Dic19—42no—
128C2×Dic19—84no—
129C8×C19—44no—
130C19⋊C8—82no—
131#2973D1911yescharacteristic
132#2486—191no—
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#45812yes—
157Dic19—82no—
158Dic19—82no—
159C2×#123—192no—
160C2×C4×D4C2×D1911yescharacteristic
161C22×C4⋊C4—191no—
162#435—24no—
163#432—21no—
164#407—192no—
165#407C2×D1912yes—
166C2×C22⋊C8—21no—
167#398—381no—
168#397—381no—
169#389—381no—
170#381—192no—
171#380—191no—
172#380—381no—
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×D4C4×D1911yescharacteristic
184C23×C4—192no—
185C23×C4C22⋊D1911yescharacteristic
186C23×C4C22×D1911yescharacteristic
187C2×M16—382no—
188C2×M16C22⋊D1914yes—
189C22×C8—22no—
190#123—764no—
191C4×D4—22no—
192C4×D4—22no—
193C2×C4⋊C4—382no—
194C2×C4⋊C4—381no—
195C2×C4⋊C4—382no—
196C2×C4⋊C4—382no—
197C2×C4⋊C4—381no—
198C2×C4⋊C4—381no—
199C2×C4⋊C4D7611yescharacteristic
200C2×C22⋊C4—192no—
201C2×C22⋊C4—382no—
202C2×C22⋊C4C4×D1911yescharacteristic
203C2×C22⋊C4D7611yescharacteristic
204C2×C42C22⋊D1911yescharacteristic
205C4⋊C8—22no—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209C22⋊C8—382no—
210C22⋊C8—382no—
211#97—22no—
212#95—382no—
213#95—382no—
214#95—381no—
215C19#950711yescharacteristic, complemented, Sylow
216C24(C2×D19)⋊C411yescharacteristic
217C24C2×C4×D1911yescharacteristic
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—41no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—382no—
226C22×C4—382no—
227C22×C4—384no—
228C22×C4—762no—
229C22×C4—762no—
230C22×C4(C2×D19)⋊C411yescharacteristic
231C22×C4(C2×D19)⋊C411yescharacteristic
232C22×C4(C2×D19)⋊C411yescharacteristic
233C22×C4C2×D7611yescharacteristic
234C22×C4#6454112yes—
235C22×C4C2×C22⋊D1912yes—
236C22×C4C2×C22⋊D1911yescharacteristic
237M16—44no—
238M16—764no—
239C2×C8—24no—
240C2×C8—82no—
241C2×C8—762no—
242C4⋊C4—22no—
243C4⋊C4—764no—
244C4⋊C4—762no—
245C4⋊C4—762no—
246C4⋊C4—761no—
247C4⋊C4—761no—
248C22⋊C4—22no—
249C22⋊C4—22no—
250C22⋊C4—764no—
251C22⋊C4—762no—
252C42—21no—
253C42—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23#1059728012yes—
263C23C2×(C2×D19)⋊C411yescharacteristic
264C23C4×C22⋊D1912yes—
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—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—81no—
279C2×C4—762no—
280C2×C4—762no—
281C2×C4—762no—
282C2×C4—762no—
283C2×C4—762no—
284C2×C4—762no—
285C2×C4—1524no—
286C2×C4#1059737511yescharacteristic
287C2×C4#1059737612yes—
288C2×C4#1059739911yescharacteristic
289C8—44no—
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#1192642311yescharacteristic
304C22C2×#1059728011yescharacteristic
305C22#1192652611yescharacteristic
306C4—22no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—1522no—
312C4—1522no—
313C4#1192673412yes—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—42no—
318C2#1456404811yescharacteristic
319C2#1456409811yescharacteristic
320C2#1456418711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2973C2
socleC22×C19#386
prime radicalC22×D4×C19C2×C4
cosocleC23×C4×C19C23
hypercenter#2973D19
hypocenterC19#9507
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #14563713C2semidirect
4. #14561540C2semidirect
215. C19#9507semidirect

Maximal subgroups

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

subgroupindex
#145679432
#145637132
#145619732
#145615402
C19×#29732
#950719