Finite Group Databasebeta

← #18070063

Subgroups — #18070063

Order 4864.

298 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 41 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#14564676C211yesmaximal, characteristic
2#14561456C211yesmaximal, characteristic, complemented
3C19×#1393C211yesmaximal, characteristic, complemented
4C2×#10597378—21no—
5#11927125C411yescharacteristic, complemented
6C2×#10597262—21no—
7#11926313C411yescharacteristic, complemented
8#11926299—21no—
9C2×C19×#99—21no—
10C19×#390C2211yescharacteristic
11C22×D4×C19D411yescharacteristic
12C2×#64541—21no—
13C2×C4⋊C4×C19C2×C411yescharacteristic
14C2×C22⋊C4×C19—41no—
15C2×C22⋊C4×C19—41no—
16C2×C42×C19D411yescharacteristic
17C2×#64526—41no—
18#10597378—42no—
19#10597378—41no—
20#10597378—41no—
21C2×#64525—41no—
22#10597376—41no—
23C2×#64520—21no—
24C22×C19⋊C8—41no—
25#10597343—41no—
26#10597341—41no—
27C19×#99—22no—
28C19×#99—41no—
29#10597262—42no—
30C24×C19—21no—
31C2×D4×C19—21no—
32C2×D4×C19—41no—
33C2×D4×C19—41no—
34C2×D4×C19D811yescharacteristic
35C2×D4×C19SD1611yescharacteristic
36C22×C4×C19—21no—
37C22×C4×C19—21no—
38C22×C4×C19—81no—
39C22×C4×C19C22⋊C411yescharacteristic
40C2×C22⋊D19—41no—
41#64541—41no—
42#64541—41no—
43#64541—41no—
44#64541—41no—
45C2×D76—21no—
46C2×D76—41no—
47C2×C4×D19—41no—
48C2×Dic38—21no—
49C4⋊C4×C19—41no—
50C22⋊C4×C19—42no—
51C22⋊C4×C19—81no—
52C22⋊C4×C19—81no—
53C22⋊C4×C19—81no—
54C42×C19—41no—
55#64526—42no—
56#64526—42no—
57#64525—42no—
58#64525—42no—
59(C2×D19)⋊C4—42no—
60C4⋊Dic19—41no—
61#64520—22no—
62#64520—41no—
63C2×C19⋊C8—41no—
64C2×C19⋊C8—42no—
65C2×C19⋊C8—81no—
66C2×C19⋊C8—81no—
67#7408—191nomaximal, Sylow
68C23×C19—21no—
69C23×C19—21no—
70C23×C19—41no—
71C23×C19—41no—
72C23×C19—81no—
73C23×C19—81no—
74C23×C19#9911yescharacteristic
75C22×D19—41no—
76D4×C19—41no—
77D4×C19—41no—
78D4×C19—81no—
79C2×C4×C19—21no—
80C2×C4×C19—21no—
81C2×C4×C19—21no—
82C2×C4×C19—21no—
83C2×C4×C19—41no—
84C2×C4×C19—41no—
85C2×C4×C19—41no—
86C2×C4×C19—81no—
87C2×C4×C19—82no—
88C2×C4×C19—161no—
89C2×C4×C19—161no—
90C2×C4×C19#10211yescharacteristic
91C2×C4×C19#10411yescharacteristic
92C22⋊D19—81no—
93C22⋊D19—81no—
94C2×Dic19—41no—
95D76—41no—
96D76—41no—
97D76—161no—
98C4×D19—81no—
99C4×D19—81no—
100Dic38—41no—
101Dic38—41no—
102C19⋊C8—42no—
103C19⋊C8—82no—
104#2006—191no—
105#1393D1911yescharacteristic, complemented
106#1270—191no—
107C22×C19—21no—
108C22×C19—21no—
109C22×C19—41no—
110C22×C19—41no—
111C22×C19—81no—
112C22×C19—81no—
113C22×C19—81no—
114C22×C19—81no—
115C22×C19—161no—
116C22×C19#32711yescharacteristic
117C22×C19AΣL(1,𝔽16)11yescharacteristic
118C22×C19#35311yescharacteristic
119C2×D19—81no—
120C2×D19—81no—
121C2×D19—81no—
122C4×C19—21no—
123C4×C19—21no—
124C4×C19—41no—
125C4×C19—41no—
126C4×C19—81no—
127C4×C19—162no—
128Dic19—81no—
129C2×AGL(1,ℤ/8)—381no—
130#537—191no—
131C2×#104—381no—
132C2×#99—21no—
133#390C2×D1911yescharacteristic
134#343—191no—
135#336—381no—
136C2×C19—21no—
137C2×C19—21no—
138C2×C19—81no—
139C2×C19—81no—
140C2×C19#134311yescharacteristic
141C2×C19#140211yescharacteristic
142C2×C19#140411yescharacteristic
143D19—161no—
144C2×#41—381no—
145C22×D4C22⋊D1911yescharacteristic
146AGL(1,ℤ/8)—762no—
147AGL(1,ℤ/8)—761no—
148AGL(1,ℤ/8)—761no—
149C2×SD16—761no—
150C2×D8—761no—
151C2×M16—381no—
152C22×C8—761no—
153C22⋊Q8—761no—
154#121—761no—
155#121—761no—
156C2×C4⋊C4C4×D1911yescharacteristic
157C2×C22⋊C4—41no—
158C2×C22⋊C4—41no—
159C2×C42D7611yescharacteristic
160#104—762no—
161#99—22no—
162#99—41no—
163C19#740811yescharacteristic, complemented, Sylow
164C24—21no—
165#41—761no—
166#41—761no—
167#41—761no—
168#41—761no—
169C2×Q8—381no—
170C2×D4—21no—
171C2×D4—41no—
172C2×D4—41no—
173C2×D4—381no—
174C2×D4—761no—
175C2×D4—761no—
176C2×D4#6452511yescharacteristic
177C2×D4#6452711yescharacteristic
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—81no—
181C22×C4—761no—
182C22×C4(C2×D19)⋊C411yescharacteristic
183SD16—762no—
184SD16—762no—
185D8—762no—
186D8—762no—
187M16—382no—
188M16—761no—
189C2×C8—761no—
190C2×C8—762no—
191C2×C8—1521no—
192C2×C8—1521no—
193C4⋊C4—41no—
194C4⋊C4—761no—
195C22⋊C4—42no—
196C22⋊C4—81no—
197C22⋊C4—81no—
198C22⋊C4—81no—
199C22⋊C4—762no—
200C42—41no—
201C23—21no—
202C23—21no—
203C23—41no—
204C23—41no—
205C23—81no—
206C23—81no—
207C23—761no—
208C23#1059726311yescharacteristic
209Q8—761no—
210Q8—761no—
211D4—41no—
212D4—41no—
213D4—81no—
214D4—3041no—
215D4—761no—
216D4—761no—
217D4—1521no—
218D4—1521no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—81no—
227C2×C4—82no—
228C2×C4—161no—
229C2×C4—161no—
230C2×C4—761no—
231C2×C4—1521no—
232C2×C4—1521no—
233C2×C4#1059726211yescharacteristic
234C2×C4#1059726611yescharacteristic
235C8—762no—
236C8—1522no—
237C22—21no—
238C22—21no—
239C22—41no—
240C22—41no—
241C22—81no—
242C22—81no—
243C22—81no—
244C22—81no—
245C22—161no—
246C22—1521no—
247C22—1521no—
248C22—1521no—
249C22#1192627711yescharacteristic
250C22#1192633011yescharacteristic
251C22#1192633611yescharacteristic
252C4—21no—
253C4—21no—
254C4—41no—
255C4—41no—
256C4—81no—
257C4—162no—
258C4—1521no—
259C2—21no—
260C2—21no—
261C2—81no—
262C2—81no—
263C2—3041no—
264C2#1456163111yescharacteristic
265C2#1456177911yescharacteristic
266C2#1456178511yescharacteristic
subgroupG/H
centerC22#11926330
commutatorC2×C4⋊C4×C19C2×C4
Frattini#390C2×D19
FittingC19×#1393C2
socleC22×C19AΣL(1,𝔽16)
prime radical#14564676C2
cosocleC19×#390C22
hypercenter#1393D19
hypocenterC19#7408
LCSG ▷ C2×C4⋊C4×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1393

Complements

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

NH ≅ G/Ntype
2. #14561456C2semidirect
3. C19×#1393C2semidirect
5. #11927125C4semidirect
7. #11926313C4semidirect
105. #1393D19semidirect
163. C19#7408semidirect

Maximal subgroups

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

subgroupindex
#145646762
#145614562
C19×#13932
#740819