Finite Group Databasebeta

← #18078577

Subgroups — #18078577

Order 4864.

578 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 115 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#14569385C211yesmaximal, characteristic
2#14562304C212yesmaximal, complemented
3#14561949C211yesmaximal, characteristic, complemented
4#14561495C212yesmaximal, complemented
5C19×#2921C211yesmaximal, characteristic, complemented
6C2×#10597320C2211yescharacteristic
7C2×#10597376—21no—
8#11926597C2212yes—
9#11926461—21no—
10#11926461C412yes—
11#11926453—21no—
12#11926453C412yes—
13#11926446—21no—
14#11926410C2211yescharacteristic
15#11926287—24no—
16#11926270—21no—
17#11926268—21no—
18C2×C19×#117C2211yescharacteristic
19C19×#433—24no—
20C19×#423C2212yes—
21C19×#407—21no—
22C4×M16×C19—21no—
23C23×C4×C19D411yescharacteristic
24C22×C22⋊D19—22no—
25C22×D76—21no—
26C22×D76—21no—
27C22×D76C2×C412yes—
28C2×M16×C19—22no—
29C19×#117—22no—
30C19×#117—22no—
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C4⋊C4×C19D411yescharacteristic
33C2×C22⋊C4×C19C2×C411yescharacteristic
34C2×C22⋊C4×C19D411yescharacteristic
35C2×C42×C19D411yescharacteristic
36C2×C42×C19C2311yescharacteristic
37#10597376—44no—
38C2×(C2×D19)⋊C4—22no—
39C2×(C2×D19)⋊C4—22no—
40C2×(C2×D19)⋊C4—22no—
41C2×C4⋊Dic19—21no—
42#10597320—22no—
43#10597320—22no—
44C19×C4⋊C8—22no—
45C19×C4⋊C8D414yescomplemented
46C19×C22⋊C8—24no—
47C19×#97—22no—
48C4×C8×C19—22no—
49C19⋊#95—21no—
50C19⋊#95C2×C412yes—
51C22⋊(C19⋊C8)—22no—
52C4⋊(C19⋊C8)—22no—
53C4×C19⋊C8—22no—
54C24×C19C22⋊C411yescharacteristic
55C23×D19—22no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—22no—
59C22×C4×C19—22no—
60C22×C4×C19C22⋊C411yescharacteristic
61C22×C4×C19C22⋊C411yescharacteristic
62C22×C4×C19C22⋊C411yescharacteristic
63C22×C4×C19C22×C411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×C4×C19C2×D411yescharacteristic
66C2×C22⋊D19—44no—
67C2×C22⋊D19—82no—
68C2×C22⋊D19—82no—
69C22×Dic19—22no—
70C2×D76—24no—
71C2×D76—41no—
72C2×D76—42no—
73C2×D76—41no—
74C2×D76—42no—
75C2×D76—42no—
76C2×D76—82no—
77C2×D76—82no—
78M16×C19—42no—
79M16×C19—42no—
80C2×C8×C19—24no—
81C4⋊C4×C19—22no—
82C4⋊C4×C19—22no—
83C22⋊C4×C19—22no—
84C22⋊C4×C19—22no—
85C42×C19—21no—
86C42×C19—21no—
87C42×C19C2×D412yes—
88C42×C19#4112yes—
89(C2×D19)⋊C4—44no—
90(C2×D19)⋊C4—82no—
91(C2×D19)⋊C4—82no—
92C4⋊Dic19—42no—
93C2×C19⋊C8—42no—
94#9198—191nomaximal, Sylow
95C23×C19—21no—
96C23×C19—21no—
97C23×C19—21no—
98C23×C19—41no—
99C23×C19—41no—
100C23×C19C2×C22⋊C411yescharacteristic
101C22×D19—42no—
102C22×D19—42no—
103C22×D19—42no—
104C22×D19—42no—
105C22×D19—42no—
106C22×D19—42no—
107C22×D19—42no—
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—41no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19—41no—
118C2×C4×C19—41no—
119C2×C4×C19C4×D412yes—
120C2×C4×C19#12011yescharacteristic
121C2×C4×C19#12112yes—
122C2×C4×C19#12311yescharacteristic
123C2×C4×C19#13512yes—
124C2×C4×C19AGL(1,ℤ/8)12yes—
125C22⋊D19—88no—
126C2×Dic19—42no—
127C2×Dic19—42no—
128C2×Dic19—42no—
129D76—84no—
130D76—84no—
131D76—82no—
132D76—82no—
133C8×C19—44no—
134C19⋊C8—82no—
135#2921D1911yescharacteristic, complemented
136#2619—191no—
137#1545—192no—
138#1458—191no—
139#1286—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#41611yescharacteristic
149C22×C19#41811yescharacteristic
150C2×D19—82no—
151C2×D19—82no—
152C2×D19—82no—
153C2×D19—82no—
154C2×D19—82no—
155C2×D19—82no—
156C2×D19—82no—
157C4×C19—22no—
158C4×C19—22no—
159C4×C19—41no—
160C4×C19—41no—
161C4×C19—41no—
162C4×C19#44912yes—
163C4×C19#48212yes—
164Dic19—82no—
165C2×#127—191no—
166C2×#121—381no—
167C2×#117C2×D1911yescharacteristic
168#433—24no—
169#431—192no—
170#423C2×D1912yes—
171#407—21no—
172C4×M16—21no—
173#394—192no—
174#394—381no—
175#392—192no—
176#392—381no—
177#390—381no—
178#382—191no—
179#331—384no—
180#324—381no—
181#323—381no—
182C2×C19—21no—
183C2×C19—21no—
184C2×C19—81no—
185C2×C19#187511yescharacteristic
186C2×C19#191011yescharacteristic
187C2×C19#191411yescharacteristic
188D19—162no—
189C22×D4—192no—
190C22×D4—382no—
191C22×D4—381no—
192C22×D4—381no—
193C23×C4C22⋊D1911yescharacteristic
194C2×M16—22no—
195#127—382no—
196#127—382no—
197#121—764no—
198#117—22no—
199#117—22no—
200C2×C4⋊C4—381no—
201C2×C4⋊C4C4×D1911yescharacteristic
202C2×C4⋊C4D7611yescharacteristic
203C2×C22⋊C4—382no—
204C2×C22⋊C4—382no—
205C2×C22⋊C4—382no—
206C2×C22⋊C4C4×D1911yescharacteristic
207C2×C22⋊C4D7611yescharacteristic
208C2×C42C22⋊D1911yescharacteristic
209C2×C42C22×D1911yescharacteristic
210C4⋊C8—22no—
211C4⋊C8—382no—
212C4⋊C8C22⋊D1914yescomplemented
213C22⋊C8—24no—
214C22⋊C8—382no—
215#97—22no—
216C4×C8—22no—
217C4×C8—382no—
218#95—192no—
219#95—381no—
220C19#919811yescharacteristic, complemented, Sylow
221C24—382no—
222C24(C2×D19)⋊C411yescharacteristic
223C2×D4—384no—
224C2×D4—764no—
225C2×D4—762no—
226C2×D4—762no—
227C2×D4—762no—
228C2×D4—761no—
229C2×D4—761no—
230C2×D4—1522no—
231C2×D4—1522no—
232C2×D4—1522no—
233C2×D4—1522no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—382no—
239C22×C4(C2×D19)⋊C411yescharacteristic
240C22×C4(C2×D19)⋊C411yescharacteristic
241C22×C4(C2×D19)⋊C411yescharacteristic
242C22×C4C2×C4×D1911yescharacteristic
243C22×C4C2×D7611yescharacteristic
244C22×C4C2×C22⋊D1911yescharacteristic
245M16—42no—
246M16—42no—
247C2×C8—24no—
248C2×C8—762no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—762no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—764no—
255C22⋊C4—1522no—
256C22⋊C4—1522no—
257C42—21no—
258C42—21no—
259C42#6454112yes—
260C42C2×C22⋊D1912yes—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23—762no—
267C23—762no—
268C23—762no—
269C23—762no—
270C23—762no—
271C23—762no—
272C23—762no—
273C23C2×(C2×D19)⋊C411yescharacteristic
274D4—1524no—
275D4—1524no—
276D4—1528no—
277D4—1522no—
278D4—1522no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—762no—
291C2×C4—762no—
292C2×C4—762no—
293C2×C4C4×C22⋊D1912yes—
294C2×C4#1059737511yescharacteristic
295C2×C4#1059737612yes—
296C2×C4#1059739512yes—
297C2×C4#1059739612yes—
298C2×C4#1059739911yescharacteristic
299C8—44no—
300C8—1522no—
301C22—21no—
302C22—21no—
303C22—42no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22—1522no—
309C22—1522no—
310C22—1522no—
311C22—1522no—
312C22—1522no—
313C22—1522no—
314C22—1522no—
315C22#1192642311yescharacteristic
316C22#1192653811yescharacteristic
317C22#1192654811yescharacteristic
318C4—22no—
319C4—22no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—1522no—
324C4#1192668912yes—
325C4#1192686812yes—
326C2—21no—
327C2—21no—
328C2—81no—
329C2—3042no—
330C2#1456395711yescharacteristic
331C2#1456416211yescharacteristic
332C2#1456418211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2921C2
socleC22×C19#386
prime radical#14569385C2
cosocleC2×C42×C19C23
hypercenter#2921D19
hypocenterC19#9198
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. #14562304C2semidirect
3. #14561949C2semidirect
4. #14561495C2semidirect
5. C19×#2921C2semidirect
45. C19×C4⋊C8D4semidirect
135. #2921D19semidirect
212. C4⋊C8C22⋊D19semidirect
220. C19#9198semidirect

Maximal subgroups

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

subgroupindex
#145693852
#145623042
#145619492
#145614952
C19×#29212
#919819