Finite Group Databasebeta

← #18078067

Subgroups — #18078067

Order 4864.

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

normal subgroups only

This group has 522 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#14572720C211yesmaximal, characteristic, complemented
2#14566342C211yesmaximal, characteristic
3#14562025C212yesmaximal
4#14561463C212yesmaximal, complemented
5C19×#1461C211yesmaximal, characteristic, complemented
6C2×#10597393C411yescharacteristic
7C2×C4×D76C2211yescharacteristic
8#11926675—24no—
9#11926601—22no—
10#11926597C2212yes—
11#11926451C411yescharacteristic
12#11926445C411yescharacteristic
13#11926435—22no—
14#11926415—22no—
15#11926413C411yescharacteristic
16#11926390C2211yescharacteristic
17#11926271—24no—
18C2×C4×Q8×C19C2211yescharacteristic
19C19×#431C2212yes—
20C19×#324—22no—
21C22×Q8×C19C2×C411yescharacteristic
22C22×D76C2×C411yescharacteristic
23C22×C4×D19—21no—
24C4×Q8×C19—22no—
25C4×Q8×C19—22no—
26C2×C4⋊C4×C19C2×C411yescharacteristic
27C2×C4⋊C4×C19D412yes—
28C2×C42×C19D412yes—
29C2×C42×C19C2311yescharacteristic
30#10597393—22no—
31#10597393—22no—
32C2×(C2×D19)⋊C4—22no—
33C2×(C2×D19)⋊C4—21no—
34C2×(C2×D19)⋊C4—22no—
35C2×C4⋊Dic19C2×C411yescharacteristic
36C2×Dic19⋊C4—22no—
37C2×C4×Dic19C2×C411yescharacteristic
38C2×C4×Dic19C2×C411yescharacteristic
39C4×D76—22no—
40C4×D76—22no—
41C19×C4⋊C8—22no—
42C19×C22⋊C8—22no—
43C4×C8×C19—22no—
44C19⋊#95—22no—
45C19⋊#95—21no—
46C19⋊#95—21no—
47C22⋊(C19⋊C8)—22no—
48C4⋊(C19⋊C8)—24no—
49C4⋊(C19⋊C8)—22no—
50#10597260—24no—
51C4×C19⋊C8D414yes—
52C23×D19—21no—
53C2×Q8×C19—22no—
54C2×Q8×C19—21no—
55C2×Q8×C19—21no—
56C2×Q8×C19—22no—
57C22×C4×C19C22⋊C412yes—
58C22×C4×C19C22⋊C412yes—
59C22×C4×C19C22×C411yescharacteristic
60C22×C4×C19C2×D411yescharacteristic
61C22×C4×C19C2×D411yescharacteristic
62C22×Dic19—21no—
63C22×Dic19—21no—
64C22×Dic19—21no—
65C2×D76—22no—
66C2×D76—22no—
67C2×D76—21no—
68C2×D76M1612yes—
69C2×C4×D19—42no—
70C2×C4×D19—82no—
71C2×C8×C19—42no—
72C4⋊C4×C19—22no—
73C4⋊C4×C19—24no—
74C42×C19—22no—
75C42×C19—22no—
76C42×C19C2×D412yes—
77C42×C19#4112yes—
78(C2×D19)⋊C4—28no—
79(C2×D19)⋊C4—41no—
80(C2×D19)⋊C4—41no—
81(C2×D19)⋊C4—82no—
82C4⋊Dic19—22no—
83Dic19⋊C4—82no—
84C4×Dic19—21no—
85C4×Dic19—22no—
86C4×Dic19M1612yes—
87C2×C19⋊C8—24no—
88#9106—191nomaximal, Sylow
89C23×C19C2×C22⋊C411yescharacteristic
90C22×D19—22no—
91C22×D19—42no—
92C22×D19—42no—
93C22×D19—41no—
94C22×D19—41no—
95Q8×C19—42no—
96Q8×C19—42no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—41no—
102C2×C4×C19—41no—
103C2×C4×C19—42no—
104C2×C4×C19C4×D412yes—
105C2×C4×C19#12011yescharacteristic
106C2×C4×C19#12112yes—
107C2×C4×C19#12311yescharacteristic
108C2×C4×C19C2×M1611yescharacteristic
109C2×C4×C19C2×M1611yescharacteristic
110C2×C4×C19#13112yes—
111C2×Dic19—22no—
112C2×Dic19—41no—
113C2×Dic19—41no—
114C2×Dic19—42no—
115C2×Dic19—41no—
116C2×Dic19—41no—
117C2×Dic19—41no—
118C2×Dic19—41no—
119D76—24no—
120D76—42no—
121C4×D19—84no—
122C8×C19—82no—
123C19⋊C8—44no—
124#2983—191no—
125#2326—191no—
126#1478—192no—
127#1461D1911yescharacteristic, complemented
128#1274—192no—
129C22×C19—21no—
130C22×C19—21no—
131C22×C19#38611yescharacteristic
132C22×C19#40711yescharacteristic
133C22×C19#40811yescharacteristic
134C2×D19—44no—
135C2×D19—42no—
136C2×D19—82no—
137C2×D19—81no—
138C2×D19—81no—
139C4×C19—22no—
140C4×C19—21no—
141C4×C19—21no—
142C4×C19—42no—
143C4×C19—42no—
144C4×C19#43512yes—
145C4×C19#43612yes—
146Dic19—42no—
147Dic19—81no—
148Dic19—81no—
149C2×#124—191no—
150C2×C4×Q8C2×D1911yescharacteristic
151C2×C4×D4—191no—
152#446—384no—
153#432—382no—
154#431—192no—
155#431C2×D1912yes—
156#391—191no—
157#390—191no—
158#388—382no—
159#385—382no—
160#384—191no—
161#376—191no—
162D4⋊C8—384no—
163#324—22no—
164C2×C19—21no—
165C2×C19—21no—
166C2×C19#187011yescharacteristic
167C2×C19#191011yescharacteristic
168C2×C19#191211yescharacteristic
169D19—82no—
170C22×Q8C4×D1911yescharacteristic
171C22×D4—191no—
172C23×C4—381no—
173#124—382no—
174#124—382no—
175C4×Q8—22no—
176C4×Q8—22no—
177C4×D4—382no—
178C4×D4—382no—
179C2×C4⋊C4—191no—
180C2×C4⋊C4—382no—
181C2×C4⋊C4C4×D1911yescharacteristic
182C2×C4⋊C4C22⋊D1912yes—
183C2×C22⋊C4—382no—
184C2×C22⋊C4—381no—
185C2×C22⋊C4—382no—
186C2×C42—191no—
187C2×C42—191no—
188C2×C42D7612yes—
189C2×C42C22×D1911yescharacteristic
190C4⋊C8—22no—
191C4⋊C8—384no—
192C4⋊C8—382no—
193C22⋊C8—22no—
194C22⋊C8—382no—
195#97—384no—
196C4×C8—22no—
197C4×C8—194no—
198#95—382no—
199#95—381no—
200#95—381no—
201C19#910611yescharacteristic, complemented, Sylow
202C24—381no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—21no—
206C2×Q8—21no—
207C2×D4—192no—
208C2×D4—382no—
209C2×D4—382no—
210C2×D4—381no—
211C22×C4—381no—
212C22×C4—381no—
213C22×C4—381no—
214C22×C4—762no—
215C22×C4—1522no—
216C22×C4(C2×D19)⋊C412yes—
217C22×C4(C2×D19)⋊C412yes—
218C22×C4C2×C4×D1911yescharacteristic
219C22×C4C2×D7611yescharacteristic
220C22×C4C2×C22⋊D1911yescharacteristic
221C2×C8—42no—
222C2×C8—384no—
223C4⋊C4—24no—
224C4⋊C4—22no—
225C4⋊C4—382no—
226C4⋊C4—1522no—
227C22⋊C4—388no—
228C22⋊C4—761no—
229C22⋊C4—761no—
230C22⋊C4—1522no—
231C42—22no—
232C42—22no—
233C42—192no—
234C42—381no—
235C42—382no—
236C42D4×D1912yes—
237C42#6454312yes—
238C23—382no—
239C23—762no—
240C23—762no—
241C23—761no—
242C23—761no—
243C23C2×(C2×D19)⋊C411yescharacteristic
244Q8—42no—
245Q8—42no—
246D4—384no—
247D4—762no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—382no—
256C2×C4—761no—
257C2×C4—761no—
258C2×C4—761no—
259C2×C4—762no—
260C2×C4—761no—
261C2×C4—761no—
262C2×C4—761no—
263C2×C4—1524no—
264C2×C4(C22⋊D19)⋊C412yes—
265C2×C4#1059732811yescharacteristic
266C2×C4#1059733211yescharacteristic
267C2×C4#1059734712yes—
268C2×C4M16×D1911yescharacteristic
269C2×C4M16×D1911yescharacteristic
270C2×C4#1059738512yes—
271C8—82no—
272C8—764no—
273C22—21no—
274C22—21no—
275C22—764no—
276C22—762no—
277C22—1522no—
278C22—1521no—
279C22—1521no—
280C22#1192642111yescharacteristic
281C22#1192650711yescharacteristic
282C22#1192651011yescharacteristic
283C4—22no—
284C4—21no—
285C4—21no—
286C4—42no—
287C4—42no—
288C4—762no—
289C4—1521no—
290C4—1521no—
291C4#1192661812yes—
292C4#1192661912yes—
293C2—21no—
294C2—21no—
295C2—1522no—
296C2#1456393011yescharacteristic
297C2#1456416011yescharacteristic
298C2#1456417011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1461C2
socleC22×C19#386
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1461D19
hypocenterC19#9106
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
1. #14572720C2semidirect
4. #14561463C2semidirect
5. C19×#1461C2semidirect
127. #1461D19semidirect
201. C19#9106semidirect

Maximal subgroups

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

subgroupindex
#145727202
#145663422
#145620252
#145614632
C19×#14612
#910619