Finite Group Databasebeta

← #18078567

Subgroups — #18078567

Order 4864.

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

normal subgroups only

This group has 478 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#14569401C211yesmaximal, characteristic
2#14562308C212yesmaximal, complemented
3#14561949C211yesmaximal, characteristic
4#14561495C212yesmaximal, complemented
5C19×#2921C211yesmaximal, characteristic
6C2×#10597315C2211yescharacteristic
7C2×#10597370—21no—
8#11926597C2212yes—
9#11926474—21no—
10#11926474C412yes—
11#11926469—21no—
12#11926469C412yes—
13#11926450—21no—
14#11926410C2211yescharacteristic
15#11926291—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×Dic38—21no—
25C2×M16×C19—22no—
26C19×#117—22no—
27C19×#117—22no—
28C2×C4⋊C4×C19C2×C411yescharacteristic
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C22⋊C4×C19C2×C411yescharacteristic
31C2×C22⋊C4×C19D411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19C2311yescharacteristic
34C2×C22⋊Dic19—22no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19C2×C412yes—
38#10597370—44no—
39C2×Dic19⋊C4—22no—
40#10597315—22no—
41#10597315—22no—
42C19×C4⋊C8—22no—
43C19×C4⋊C8D414yes—
44C19×C22⋊C8—24no—
45C19×#97—22no—
46C4×C8×C19—22no—
47C19⋊#95—22no—
48C19⋊#95—22no—
49C19⋊#95—21no—
50C19⋊#95C2×C412yes—
51C22⋊(C19⋊C8)—22no—
52C4⋊(C19⋊C8)—22no—
53C4×C19⋊C8—22no—
54C24×C19C22⋊C411yescharacteristic
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—22no—
58C22×C4×C19—22no—
59C22×C4×C19C22⋊C411yescharacteristic
60C22×C4×C19C22⋊C411yescharacteristic
61C22×C4×C19C22⋊C411yescharacteristic
62C22×C4×C19C22×C411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×Dic19—22no—
66C22×Dic19—22no—
67C2×Dic38—41no—
68C2×Dic38—41no—
69C2×Dic38—42no—
70C2×Dic38—42no—
71M16×C19—42no—
72M16×C19—42no—
73C2×C8×C19—24no—
74C4⋊C4×C19—22no—
75C4⋊C4×C19—22no—
76C22⋊C4×C19—22no—
77C22⋊C4×C19—22no—
78C42×C19—21no—
79C42×C19—21no—
80C42×C19C2×D412yes—
81C42×C19#4112yes—
82C22⋊Dic19—44no—
83C4⋊Dic19—24no—
84C4⋊Dic19—42no—
85C4⋊Dic19—42no—
86Dic19⋊C4—44no—
87C2×C19⋊C8—42no—
88#9196—191nomaximal, Sylow
89C23×C19—21no—
90C23×C19—21no—
91C23×C19—21no—
92C23×C19—41no—
93C23×C19—41no—
94C23×C19C2×C22⋊C411yescharacteristic
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—21no—
98C2×C4×C19—21no—
99C2×C4×C19—21no—
100C2×C4×C19—41no—
101C2×C4×C19—41no—
102C2×C4×C19—42no—
103C2×C4×C19—42no—
104C2×C4×C19—41no—
105C2×C4×C19—41no—
106C2×C4×C19C4×D412yes—
107C2×C4×C19#12011yescharacteristic
108C2×C4×C19#12112yes—
109C2×C4×C19#12311yescharacteristic
110C2×C4×C19#13512yes—
111C2×C4×C19AGL(1,ℤ/8)12yes—
112C2×Dic19—42no—
113C2×Dic19—42no—
114C2×Dic19—42no—
115C2×Dic19—42no—
116C2×Dic19—42no—
117C2×Dic19—42no—
118Dic38—82no—
119Dic38—82no—
120C8×C19—44no—
121C19⋊C8—82no—
122#2921D1911yescharacteristic
123#2621—191no—
124#1546—192no—
125#1458—191no—
126#1286—192no—
127C22×C19—21no—
128C22×C19—21no—
129C22×C19—42no—
130C22×C19—41no—
131C22×C19—41no—
132C22×C19—41no—
133C22×C19—81no—
134C22×C19#38611yescharacteristic
135C22×C19#41611yescharacteristic
136C22×C19#41811yescharacteristic
137C4×C19—22no—
138C4×C19—22no—
139C4×C19—41no—
140C4×C19—41no—
141C4×C19—41no—
142C4×C19#44912yes—
143C4×C19#48212yes—
144Dic19—82no—
145Dic19—82no—
146C2×C4⋊Q8—191no—
147C2×C22⋊Q8—381no—
148C2×#117C2×D1911yescharacteristic
149#433—24no—
150#431—192no—
151#423C2×D1912yes—
152#407—21no—
153C4×M16—21no—
154#398—192no—
155#398—381no—
156#397—192no—
157#397—381no—
158#391—381no—
159#382—191no—
160#332—384no—
161#324—381no—
162#323—381no—
163C2×C19—21no—
164C2×C19—21no—
165C2×C19—81no—
166C2×C19#187511yescharacteristic
167C2×C19#190911yescharacteristic
168C2×C19#191511yescharacteristic
169C22×Q8—381no—
170C23×C4C22⋊D1911yescharacteristic
171C2×M16—22no—
172C4⋊Q8—382no—
173C4⋊Q8—382no—
174C22⋊Q8—764no—
175#117—22no—
176#117—22no—
177C2×C4⋊C4—192no—
178C2×C4⋊C4—382no—
179C2×C4⋊C4—381no—
180C2×C4⋊C4—381no—
181C2×C4⋊C4C4×D1911yescharacteristic
182C2×C4⋊C4D7611yescharacteristic
183C2×C22⋊C4—382no—
184C2×C22⋊C4C4×D1911yescharacteristic
185C2×C22⋊C4D7611yescharacteristic
186C2×C42C22⋊D1911yescharacteristic
187C2×C42C22×D1911yescharacteristic
188C4⋊C8—22no—
189C4⋊C8—382no—
190C4⋊C8C22⋊D1914yes—
191C22⋊C8—24no—
192C22⋊C8—382no—
193#97—22no—
194C4×C8—22no—
195C4×C8—382no—
196#95—192no—
197#95—382no—
198#95—382no—
199#95—381no—
200C19#919611yescharacteristic, complemented, Sylow
201C24(C2×D19)⋊C411yescharacteristic
202C2×Q8—762no—
203C2×Q8—762no—
204C2×Q8—761no—
205C2×Q8—761no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—382no—
211C22×C4—382no—
212C22×C4(C2×D19)⋊C411yescharacteristic
213C22×C4(C2×D19)⋊C411yescharacteristic
214C22×C4(C2×D19)⋊C411yescharacteristic
215C22×C4C2×C4×D1911yescharacteristic
216C22×C4C2×D7611yescharacteristic
217C22×C4C2×C22⋊D1911yescharacteristic
218M16—42no—
219M16—42no—
220C2×C8—24no—
221C2×C8—762no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—384no—
225C4⋊C4—764no—
226C4⋊C4—762no—
227C4⋊C4—762no—
228C22⋊C4—22no—
229C22⋊C4—22no—
230C22⋊C4—764no—
231C42—21no—
232C42—21no—
233C42#6454112yes—
234C42C2×C22⋊D1912yes—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—41no—
239C23—41no—
240C23C2×(C2×D19)⋊C411yescharacteristic
241Q8—1522no—
242Q8—1522no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—762no—
255C2×C4—762no—
256C2×C4—762no—
257C2×C4—762no—
258C2×C4—762no—
259C2×C4—762no—
260C2×C4C4×C22⋊D1912yes—
261C2×C4#1059737511yescharacteristic
262C2×C4#1059737612yes—
263C2×C4#1059739512yes—
264C2×C4#1059739612yes—
265C2×C4#1059739911yescharacteristic
266C8—44no—
267C8—1522no—
268C22—21no—
269C22—21no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—81no—
275C22#1192642311yescharacteristic
276C22#1192653811yescharacteristic
277C22#1192654811yescharacteristic
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—1522no—
284C4—1522no—
285C4#1192668912yes—
286C4#1192686812yes—
287C2—21no—
288C2—21no—
289C2—81no—
290C2#1456395711yescharacteristic
291C2#1456415711yescharacteristic
292C2#1456418711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2921C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2921D19
hypocenterC19#9196
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. #14562308C2semidirect
4. #14561495C2semidirect
200. C19#9196semidirect

Maximal subgroups

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

subgroupindex
#145694012
#145623082
#145619492
#145614952
C19×#29212
#919619