Finite Group Databasebeta

← #18070045

Subgroups — #18070045

Order 4864.

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

normal subgroups only

This group has 334 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#14564705C211yesmaximal, characteristic
2#14561567C211yesmaximal, characteristic, complemented
3C19×#1393C211yesmaximal, characteristic, complemented
4C22×#64525—21no—
5C2×#10597320C411yescharacteristic, complemented
6C2×#10597266—21no—
7#11926299C411yescharacteristic, complemented
8#11926270—21no—
9C2×C19×#99—21no—
10C19×#390C2211yescharacteristic
11C22×D4×C19D411yescharacteristic
12C22×D76—21no—
13C22×D76—41no—
14C2×C4⋊C4×C19D411yescharacteristic
15C2×C22⋊C4×C19—41no—
16C2×C22⋊C4×C19—41no—
17C2×C42×C19C2×C411yescharacteristic
18C2×#64525—42no—
19C2×#64525—42no—
20C2×#64525—41no—
21C2×#64525—41no—
22C22×C19⋊C8—21no—
23#10597320—42no—
24C19×#99—22no—
25C19×#99—41no—
26C22⋊(C19⋊C8)—41no—
27#10597266—42no—
28C24×C19—21no—
29C23×D19—41no—
30C2×D4×C19—21no—
31C2×D4×C19—41no—
32C2×D4×C19—41no—
33C2×D4×C19D811yescharacteristic
34C2×D4×C19SD1611yescharacteristic
35C22×C4×C19—21no—
36C22×C4×C19—21no—
37C22×C4×C19—81no—
38C22×C4×C19C22⋊C411yescharacteristic
39C2×D76—22no—
40C2×D76—41no—
41C2×D76—41no—
42C2×D76—41no—
43C2×D76—41no—
44C2×D76—41no—
45C2×D76—42no—
46C2×D76—42no—
47C2×D76—82no—
48C2×D76—82no—
49C4⋊C4×C19—41no—
50C22⋊C4×C19—42no—
51C22⋊C4×C19—82no—
52C22⋊C4×C19—81no—
53C42×C19—41no—
54#64525—44no—
55#64525—44no—
56C2×C19⋊C8—22no—
57C2×C19⋊C8—41no—
58C2×C19⋊C8—41no—
59C2×C19⋊C8—81no—
60#7402—191nomaximal, Sylow
61C23×C19—21no—
62C23×C19—21no—
63C23×C19—41no—
64C23×C19—41no—
65C23×C19—81no—
66C23×C19—81no—
67C23×C19#9911yescharacteristic
68C22×D19—42no—
69C22×D19—82no—
70C22×D19—82no—
71C22×D19—81no—
72C22×D19—81no—
73D4×C19—41no—
74D4×C19—41no—
75D4×C19—81no—
76C2×C4×C19—21no—
77C2×C4×C19—21no—
78C2×C4×C19—22no—
79C2×C4×C19—41no—
80C2×C4×C19—41no—
81C2×C4×C19—41no—
82C2×C4×C19—81no—
83C2×C4×C19—82no—
84C2×C4×C19—161no—
85C2×C4×C19—161no—
86C2×C4×C19#10211yescharacteristic
87C2×C4×C19#10411yescharacteristic
88D76—42no—
89D76—42no—
90D76—81no—
91D76—81no—
92D76—84no—
93D76—84no—
94C19⋊C8—42no—
95C19⋊C8—161no—
96#2011—191no—
97#1393D1911yescharacteristic, complemented
98#1318—191no—
99C22×C19—21no—
100C22×C19—21no—
101C22×C19—41no—
102C22×C19—41no—
103C22×C19—81no—
104C22×C19—81no—
105C22×C19—81no—
106C22×C19—81no—
107C22×C19—161no—
108C22×C19#32711yescharacteristic
109C22×C19AΣL(1,𝔽16)11yescharacteristic
110C22×C19#35311yescharacteristic
111C2×D19—84no—
112C2×D19—82no—
113C2×D19—162no—
114C2×D19—161no—
115C2×D19—161no—
116C4×C19—21no—
117C4×C19—21no—
118C4×C19—42no—
119C4×C19—81no—
120C4×C19—162no—
121C22×D8—381no—
122C2×#127—191no—
123C2×#102—381no—
124C2×#99—21no—
125#390C2×D1911yescharacteristic
126#336—191no—
127#324—381no—
128C2×C19—21no—
129C2×C19—21no—
130C2×C19—81no—
131C2×C19—81no—
132C2×C19#134311yescharacteristic
133C2×C19#140611yescharacteristic
134C2×C19#140811yescharacteristic
135D19—162no—
136C22×D4—381no—
137C22×D4—761no—
138C22×D4C22⋊D1911yescharacteristic
139C2×D8—762no—
140C2×D8—762no—
141C2×D8—761no—
142C2×D8—761no—
143C22×C8—381no—
144#127—762no—
145C2×C4⋊C4D7611yescharacteristic
146C2×C22⋊C4—41no—
147C2×C22⋊C4—41no—
148C2×C42C4×D1911yescharacteristic
149#102—762no—
150#99—22no—
151#99—41no—
152C22⋊C8—761no—
153C19#740211yescharacteristic, complemented, Sylow
154C24—21no—
155C24—761no—
156C2×D4—21no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—382no—
160C2×D4—761no—
161C2×D4—761no—
162C2×D4—761no—
163C2×D4—762no—
164C2×D4—762no—
165C2×D4—761no—
166C2×D4—761no—
167C2×D4—1522no—
168C2×D4—1522no—
169C2×D4#6452511yescharacteristic
170C2×D4#6452711yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—81no—
174C22×C4(C2×D19)⋊C411yescharacteristic
175D8—764no—
176D8—764no—
177C2×C8—382no—
178C2×C8—761no—
179C2×C8—761no—
180C2×C8—1521no—
181C4⋊C4—41no—
182C22⋊C4—42no—
183C22⋊C4—82no—
184C22⋊C4—81no—
185C42—41no—
186C23—21no—
187C23—21no—
188C23—41no—
189C23—41no—
190C23—81no—
191C23—81no—
192C23—762no—
193C23—1522no—
194C23—1522no—
195C23—1521no—
196C23—1521no—
197C23#1059726311yescharacteristic
198D4—41no—
199D4—41no—
200D4—81no—
201D4—762no—
202D4—762no—
203D4—1521no—
204D4—1521no—
205D4—1524no—
206D4—1524no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—81no—
214C2×C4—82no—
215C2×C4—161no—
216C2×C4—161no—
217C2×C4#1059726211yescharacteristic
218C2×C4#1059726611yescharacteristic
219C8—3041no—
220C8—762no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—81no—
227C22—81no—
228C22—81no—
229C22—161no—
230C22—3042no—
231C22—3041no—
232C22—3041no—
233C22—1524no—
234C22—1522no—
235C22#1192627711yescharacteristic
236C22#1192633011yescharacteristic
237C22#1192633611yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—81no—
242C4—162no—
243C2—21no—
244C2—21no—
245C2—81no—
246C2—81no—
247C2—3042no—
248C2#1456163111yescharacteristic
249C2#1456179111yescharacteristic
250C2#1456179711yescharacteristic
subgroupG/H
centerC22#11926336
commutatorC2×C42×C19C2×C4
Frattini#390C2×D19
FittingC19×#1393C2
socleC22×C19#353
prime radical#14564705C2
cosocleC19×#390C22
hypercenter#1393D19
hypocenterC19#7402
LCSG ▷ C2×C42×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. #14561567C2semidirect
3. C19×#1393C2semidirect
5. C2×#10597320C4semidirect
7. #11926299C4semidirect
97. #1393D19semidirect
153. C19#7402semidirect

Maximal subgroups

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

subgroupindex
#145647052
#145615672
C19×#13932
#740219