Finite Group Databasebeta

← #18071809

Subgroups — #18071809

Order 4864.

418 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 83 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#14570565C211yesmaximal, characteristic
2#14565199C212yesmaximal, complemented
3#14565168C211yesmaximal, characteristic
4#14561457C212yesmaximal, complemented
5C19×#1270C211yesmaximal, characteristic
6C2×#10597381—21no—
7C2×#10597265—21no—
8C2×#10597289—21no—
9#11926474—21no—
10#11926469—22no—
11#11926442C2212yes—
12#11926419—22no—
13#11926414C2211yescharacteristic
14#11926307—22no—
15#11926307—22no—
16#11926299C2211yescharacteristic
17C19×#390C2211yescharacteristic
18C19×#336C2212yes—
19C22×D4×C19D411yescharacteristic
20C23×Dic19—21no—
21C22×C8×C19—22no—
22C2×C4⋊C4×C19D411yescharacteristic
23C2×C22⋊C4×C19—22no—
24C2×C42×C19C2311yescharacteristic
25C2×C22⋊Dic19—22no—
26C2×C22⋊Dic19—21no—
27#10597381—42no—
28#10597381—42no—
29C2×C4⋊Dic19—21no—
30C2×C4⋊Dic19—22no—
31C2×C4⋊Dic19—21no—
32C2×C4⋊Dic19D412yes—
33C2×C4⋊Dic19D412yes—
34C2×Dic19⋊C4—22no—
35C22×C19⋊C8—21no—
36#10597289—42no—
37C19⋊#95—22no—
38C19⋊#95—21no—
39C19⋊#95—22no—
40#10597265—42no—
41C24×C19—21no—
42C2×D4×C19—21no—
43C2×D4×C19—41no—
44C2×D4×C19—41no—
45C2×D4×C19SD1612yes—
46C22×C4×C19—21no—
47C22×C4×C19C2×D411yescharacteristic
48C22×C4×C19C2×D412yes—
49C22×Dic19—22no—
50C22×Dic19—22no—
51C22×Dic19—42no—
52C22×Dic19—41no—
53C22×Dic19—81no—
54C22×Dic19—81no—
55C2×C8×C19—42no—
56C2×C8×C19—42no—
57C2×C8×C19—42no—
58C4⋊C4×C19—41no—
59C22⋊C4×C19—42no—
60C22⋊C4×C19—42no—
61C42×C19—41no—
62C22⋊Dic19—42no—
63C22⋊Dic19—44no—
64C4⋊Dic19—22no—
65C4⋊Dic19—22no—
66C4⋊Dic19—42no—
67C4⋊Dic19—41no—
68C4⋊Dic19—41no—
69C4⋊Dic19—44no—
70C4⋊Dic19—81no—
71Dic19⋊C4—42no—
72Dic19⋊C4—42no—
73C2×C19⋊C8—22no—
74C2×C19⋊C8—41no—
75C2×C19⋊C8—41no—
76#7824—191nomaximal, Sylow
77C23×C19—22no—
78C23×C19—42no—
79C23×C19—41no—
80C23×C19—42no—
81C23×C19—41no—
82C23×C19#12011yescharacteristic
83D4×C19—42no—
84D4×C19—81no—
85C2×C4×C19—21no—
86C2×C4×C19—22no—
87C2×C4×C19—21no—
88C2×C4×C19—22no—
89C2×C4×C19—42no—
90C2×C4×C19—41no—
91C2×C4×C19C2×SD1611yescharacteristic
92C2×C4×C19#13512yes—
93C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
94C2×C4×C19#13712yes—
95C2×Dic19—42no—
96C2×Dic19—42no—
97C2×Dic19—42no—
98C2×Dic19—42no—
99C2×Dic19—42no—
100C2×Dic19—42no—
101C2×Dic19—84no—
102C2×Dic19—81no—
103C2×Dic19—82no—
104C8×C19—82no—
105C19⋊C8—42no—
106#2724—191no—
107#2100—192no—
108#2094—191no—
109#1271—192no—
110#1270D1911yescharacteristic
111C22×C19—42no—
112C22×C19—44no—
113C22×C19—82no—
114C22×C19—81no—
115C22×C19—81no—
116C22×C19#45011yescharacteristic
117C22×C19#45212yes—
118C22×C19#45311yescharacteristic
119C22×C19#45412yes—
120C22×C19#45811yescharacteristic
121C4×C19—21no—
122C4×C19—21no—
123C4×C19—22no—
124C4×C19—22no—
125C4×C19—81no—
126Dic19—82no—
127Dic19—82no—
128Dic19—161no—
129C2×#123—381no—
130C2×#106—381no—
131C2×#102—381no—
132#398—381no—
133#397—382no—
134#390C2×D1911yescharacteristic
135#389—192no—
136#385—382no—
137#384—191no—
138#340—382no—
139#340—382no—
140#336—191no—
141#336C2×D1912yes—
142C2×C19—82no—
143C2×C19#161311yescharacteristic
144C2×C19#161512yes—
145C2×C19#163011yescharacteristic
146C2×C19#163512yes—
147C2×C19#165711yescharacteristic
148C22×D4D7611yescharacteristic
149C23×C4—381no—
150C22×C8—22no—
151C22×C8—381no—
152#123—762no—
153#123—762no—
154C2×C4⋊C4—192no—
155C2×C4⋊C4—192no—
156C2×C4⋊C4—382no—
157C2×C4⋊C4—381no—
158C2×C4⋊C4—382no—
159C2×C4⋊C4—381no—
160C2×C4⋊C4D7611yescharacteristic
161C2×C22⋊C4—22no—
162C2×C22⋊C4—382no—
163C2×C22⋊C4—381no—
164C2×C42C22×D1911yescharacteristic
165#106—762no—
166#102—762no—
167#95—382no—
168#95—381no—
169#95—382no—
170C19#782411yescharacteristic, complemented, Sylow
171C24—21no—
172C2×D4—21no—
173C2×D4—41no—
174C2×D4—41no—
175C2×D4#6451612yes—
176C22×C4—21no—
177C22×C4—382no—
178C22×C4—382no—
179C22×C4—762no—
180C22×C4—761no—
181C22×C4—1521no—
182C22×C4—1521no—
183C22×C4C2×D7611yescharacteristic
184C22×C4D4×D1912yes—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—382no—
189C2×C8—761no—
190C2×C8—761no—
191C4⋊C4—41no—
192C4⋊C4—382no—
193C4⋊C4—382no—
194C4⋊C4—762no—
195C4⋊C4—761no—
196C4⋊C4—761no—
197C4⋊C4—764no—
198C4⋊C4—762no—
199C4⋊C4—762no—
200C4⋊C4—1521no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C22⋊C4—762no—
204C22⋊C4—764no—
205C42—41no—
206C23—22no—
207C23—42no—
208C23—41no—
209C23—42no—
210C23—41no—
211C23#1059732811yescharacteristic
212D4—42no—
213D4—81no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—762no—
221C2×C4—762no—
222C2×C4—762no—
223C2×C4—762no—
224C2×C4—762no—
225C2×C4—762no—
226C2×C4—1521no—
227C2×C4—1522no—
228C2×C4—1524no—
229C2×C4C2×#6451611yescharacteristic
230C2×C4#1059735411yescharacteristic
231C2×C4#1059735812yes—
232C2×C4#1059736112yes—
233C8—82no—
234C8—762no—
235C22—42no—
236C22—44no—
237C22—82no—
238C22—81no—
239C22—81no—
240C22#1192669711yescharacteristic
241C22#1192670712yes—
242C22#1192671411yescharacteristic
243C22#1192671812yes—
244C22#1192673511yescharacteristic
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—81no—
250C4—3041no—
251C4—1522no—
252C4—1522no—
253C2—82no—
254C2#1456265711yescharacteristic
255C2#1456266712yes—
256C2#1456275711yescharacteristic
257C2#1456278812yes—
258C2#1456293411yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#1270D19
hypocenterC19#7824
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #14565199C2semidirect
4. #14561457C2semidirect
170. C19#7824semidirect

Maximal subgroups

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

subgroupindex
#145705652
#145651992
#145651682
#145614572
C19×#12702
#782419