Finite Group Databasebeta

← #18069887

Subgroups — #18069887

Order 4864.

356 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 39 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#14563552C211yesmaximal, characteristic
2#14561565C211yesmaximal, characteristic, complemented
3C19×#1317C211yesmaximal, characteristic, complemented
4C22×#64541C411yescharacteristic
5C2×#10597263—21no—
6C2×#10597263—21no—
7#11926407C411yescharacteristic
8#11926268—21no—
9C19×#381C2211yescharacteristic
10C19×#323—21no—
11C23×C4×C19C2×C411yescharacteristic
12C22×C22⋊D19—21no—
13C2×#64541—41no—
14C2×#64541—41no—
15C2×#64541—42no—
16C2×#64541—42no—
17C22×D76C811yescharacteristic, complemented
18C22×C4×D19—21no—
19C22×Dic38C811yescharacteristic, complemented
20C2×C22⋊C4×C19D411yescharacteristic
21C2×C22⋊C4×C19D411yescharacteristic
22C2×C22⋊Dic19—21no—
23C19×C22⋊C8—41no—
24C19×#95—41no—
25C19⋊#95—41no—
26C22⋊(C19⋊C8)—41no—
27#10597263—42no—
28#10597263—42no—
29C24×C19C22⋊C411yescharacteristic
30C23×D19—21no—
31C22×C4×C19—21no—
32C22×C4×C19—21no—
33C22×C4×C19—21no—
34C22×C4×C19—21no—
35C22×C4×C19—41no—
36C22×C4×C19—41no—
37C22×C4×C19C2×C811yescharacteristic
38C22×C4×C19M1611yescharacteristic
39C2×C22⋊D19—22no—
40C2×C22⋊D19—22no—
41C2×C22⋊D19—41no—
42C2×C22⋊D19—41no—
43C2×C22⋊D19—41no—
44C2×C22⋊D19—41no—
45C22×Dic19—21no—
46C22×Dic19—41no—
47#64541—44no—
48#64541—42no—
49#64541—42no—
50#64541—44no—
51#64541—42no—
52#64541—42no—
53C2×D76—41no—
54C2×D76—42no—
55C2×C4×D19—42no—
56C2×C4×D19—42no—
57C2×C4×D19—42no—
58C2×Dic38—41no—
59C2×Dic38—42no—
60C2×C8×C19—81no—
61C22⋊C4×C19—41no—
62C22⋊C4×C19—41no—
63C22⋊Dic19—41no—
64C22⋊Dic19—41no—
65C2×C19⋊C8—81no—
66#7339—191nomaximal, Sylow
67C23×C19—21no—
68C23×C19—21no—
69C23×C19—81no—
70C23×C19C22⋊C811yescharacteristic
71C23×C19#9911yescharacteristic
72C23×C19#10011yescharacteristic
73C22×D19—22no—
74C22×D19—41no—
75C22×D19—41no—
76C22×D19—82no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19—42no—
80C2×C4×C19—41no—
81C2×C4×C19—41no—
82C2×C4×C19—41no—
83C2×C4×C19—41no—
84C2×C4×C19—41no—
85C2×C4×C19—41no—
86C2×C4×C19—81no—
87C2×C4×C19—81no—
88C22⋊D19—42no—
89C22⋊D19—42no—
90C22⋊D19—42no—
91C22⋊D19—42no—
92C2×Dic19—22no—
93C2×Dic19—41no—
94C2×Dic19—41no—
95C2×Dic19—81no—
96C2×Dic19—82no—
97D76—42no—
98D76—42no—
99C4×D19—44no—
100C4×D19—44no—
101Dic38—42no—
102Dic38—42no—
103C8×C19—161no—
104C19⋊C8—161no—
105#1782—191no—
106#1317—191no—
107#1317D1911yescharacteristic, complemented
108C22×C19—21no—
109C22×C19—21no—
110C22×C19—41no—
111C22×C19—41no—
112C22×C19—41no—
113C22×C19—81no—
114C22×C19—81no—
115C22×C19#32311yescharacteristic
116C22×C19AΣL(1,𝔽16)11yescharacteristic
117C22×C19AΣL(1,𝔽16)11yescharacteristic
118C2×D19—42no—
119C2×D19—82no—
120C2×D19—82no—
121C2×D19—82no—
122C4×C19—41no—
123C4×C19—41no—
124C4×C19—81no—
125C4×C19—81no—
126Dic19—42no—
127Dic19—161no—
128C22×#41—191no—
129C2×#99—381no—
130C2×#99—381no—
131#381—191no—
132#381C2×D1911yescharacteristic
133#323—21no—
134#323—381no—
135C2×C19—21no—
136C2×C19—21no—
137C2×C19—21no—
138C2×C19—41no—
139C2×C19—41no—
140C2×C19#131611yescharacteristic
141D19—82no—
142C2×#41—761no—
143C2×#41—761no—
144C2×#41—762no—
145C2×#41—762no—
146C22×Q8—191no—
147C22×D4—191no—
148C22×D4—381no—
149C23×C4—381no—
150C23×C4C4×D1911yescharacteristic
151C2×C22⋊C4—381no—
152C2×C22⋊C4D7611yescharacteristic
153C2×C22⋊C4C22⋊D1911yescharacteristic
154#99—762no—
155#99—762no—
156C22⋊C8—41no—
157C22⋊C8—761no—
158#95—41no—
159#95—761no—
160C19#733911yescharacteristic, complemented, Sylow
161C24—381no—
162C24(C2×D19)⋊C411yescharacteristic
163#41—764no—
164#41—764no—
165#41—762no—
166#41—762no—
167#41—762no—
168#41—762no—
169C2×Q8—761no—
170C2×Q8—762no—
171C2×D4—382no—
172C2×D4—382no—
173C2×D4—761no—
174C2×D4—762no—
175C2×D4—761no—
176C2×D4—761no—
177C2×D4—761no—
178C2×D4—761no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—381no—
186C22×C4—762no—
187C22×C4—762no—
188C22×C4—762no—
189C22×C4—761no—
190C22×C4C8×D1911yescharacteristic
191C22×C4#6451511yescharacteristic
192C2×C8—81no—
193C2×C8—1521no—
194C22⋊C4—41no—
195C22⋊C4—41no—
196C22⋊C4—761no—
197C22⋊C4—761no—
198C23—21no—
199C23—21no—
200C23—81no—
201C23—382no—
202C23—761no—
203C23—761no—
204C23—1522no—
205C23#1059726311yescharacteristic
206C23(C2×D19)⋊C811yescharacteristic
207C23#1059728011yescharacteristic
208Q8—762no—
209Q8—762no—
210D4—762no—
211D4—762no—
212D4—762no—
213D4—762no—
214D4—762no—
215D4—762no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—382no—
228C2×C4—764no—
229C2×C4—764no—
230C2×C4—761no—
231C2×C4—761no—
232C2×C4—1521no—
233C2×C4—1522no—
234C8—161no—
235C8—3041no—
236C22—21no—
237C22—21no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—81no—
242C22—81no—
243C22—762no—
244C22—1522no—
245C22—1522no—
246C22—1522no—
247C22#1192626711yescharacteristic
248C22#1192633011yescharacteristic
249C22#1192633211yescharacteristic
250C4—41no—
251C4—41no—
252C4—81no—
253C4—81no—
254C4—3041no—
255C4—762no—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—41no—
260C2—41no—
261C2—1522no—
262C2#1456156211yescharacteristic
subgroupG/H
centerC2#14561562
commutatorC22×C4×C19C2×C8
Frattini#381C2×D19
FittingC19×#1317C2
socleC2×C19#1316
prime radicalC22×#64541C4
cosocleC19×#381C22
hypercenter#1317D19
hypocenterC19#7339
LCSG ▷ C22×C4×C19 ▷ C23×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #1317

Complements

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

NH ≅ G/Ntype
2. #14561565C2semidirect
3. C19×#1317C2semidirect
17. C22×D76C8semidirect
19. C22×Dic38C8semidirect
107. #1317D19semidirect
160. C19#7339semidirect

Maximal subgroups

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

subgroupindex
#145635522
#145615652
C19×#13172
#733919