Finite Group Databasebeta

← #18069911

Subgroups — #18069911

Order 4864.

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

normal subgroups only

This group has 302 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#14563707C211yesmaximal, characteristic
2#14561563C211yesmaximal, characteristic
3C19×#1316C211yesmaximal, characteristic
4C22×C22⋊Dic19C411yescharacteristic
5#11926400C411yescharacteristic
6#11926310—21no—
7#11926310—21no—
8#11926268—21no—
9C19×#379C2211yescharacteristic
10C19×#323—21no—
11C25×C19C2×C411yescharacteristic
12C23×Dic19—21no—
13C2×C22⋊C4×C19—41no—
14C2×C22⋊C4×C19D411yescharacteristic
15C2×C22⋊C4×C19D411yescharacteristic
16C2×C22⋊Dic19—21no—
17C2×C22⋊Dic19—21no—
18C2×C22⋊Dic19—41no—
19C2×C22⋊Dic19—41no—
20C2×C22⋊Dic19—41no—
21C2×C22⋊Dic19C812yescomplemented
22C19×C22⋊C8—41no—
23C22⋊(C19⋊C8)—41no—
24C24×C19—21no—
25C24×C19—21no—
26C24×C19—41no—
27C24×C19—41no—
28C24×C19—82no—
29C24×C19C22⋊C411yescharacteristic
30C24×C19C2×C811yescharacteristic
31C24×C19M1611yescharacteristic
32C22×C4×C19—21no—
33C22×C4×C19—21no—
34C22×Dic19—22no—
35C22×Dic19—41no—
36C22×Dic19—41no—
37C22×Dic19—41no—
38C22×Dic19—82no—
39C2×C8×C19—81no—
40C22⋊C4×C19—41no—
41C22⋊C4×C19—41no—
42C22⋊C4×C19—82no—
43C22⋊Dic19—41no—
44C22⋊Dic19—41no—
45C22⋊Dic19—42no—
46C22⋊Dic19—41no—
47C22⋊Dic19—41no—
48C22⋊Dic19—82no—
49C2×C19⋊C8—81no—
50#7349—191nomaximal, Sylow
51C23×C19—21no—
52C23×C19—21no—
53C23×C19—21no—
54C23×C19—21no—
55C23×C19—42no—
56C23×C19—41no—
57C23×C19—42no—
58C23×C19—42no—
59C23×C19—42no—
60C23×C19—41no—
61C23×C19—41no—
62C23×C19—41no—
63C23×C19—81no—
64C23×C19—81no—
65C23×C19—81no—
66C23×C19—81no—
67C23×C19—82no—
68C23×C19—82no—
69C23×C19—82no—
70C23×C19—82no—
71C23×C19C22⋊C811yescharacteristic
72C23×C19#9911yescharacteristic
73C23×C19#10011yescharacteristic
74C2×C4×C19—41no—
75C2×C4×C19—41no—
76C2×C4×C19—81no—
77C2×C4×C19—81no—
78C2×Dic19—42no—
79C2×Dic19—82no—
80C2×Dic19—82no—
81C2×Dic19—82no—
82C2×Dic19—81no—
83C2×Dic19—82no—
84C8×C19—161no—
85C19⋊C8—161no—
86#1819—191no—
87#1316—191no—
88#1316D1911yescharacteristic
89C22×C19—22no—
90C22×C19—21no—
91C22×C19—21no—
92C22×C19—41no—
93C22×C19—41no—
94C22×C19—41no—
95C22×C19—41no—
96C22×C19—41no—
97C22×C19—41no—
98C22×C19—42no—
99C22×C19—42no—
100C22×C19—41no—
101C22×C19—41no—
102C22×C19—81no—
103C22×C19—81no—
104C22×C19—82no—
105C22×C19—82no—
106C22×C19—84no—
107C22×C19—81no—
108C22×C19—81no—
109C22×C19#32311yescharacteristic
110C22×C19#35211yescharacteristic
111C22×C19#35211yescharacteristic
112C4×C19—81no—
113C4×C19—81no—
114Dic19—82no—
115Dic19—161no—
116C22×C22⋊C4—191no—
117#379—191no—
118#379C2×D1911yescharacteristic
119#342—381no—
120#342—381no—
121#323—21no—
122#323—381no—
123C2×C19—21no—
124C2×C19—21no—
125C2×C19—21no—
126C2×C19—41no—
127C2×C19—42no—
128C2×C19—41no—
129C2×C19—81no—
130C2×C19#131711yescharacteristic
131C25C4×D1911yescharacteristic
132C23×C4—381no—
133C2×C22⋊C4—41no—
134C2×C22⋊C4—192no—
135C2×C22⋊C4—381no—
136C2×C22⋊C4—381no—
137C2×C22⋊C4—761no—
138C2×C22⋊C4—761no—
139C2×C22⋊C4—761no—
140C2×C22⋊C4D7611yescharacteristic
141C2×C22⋊C4C22⋊D1911yescharacteristic
142C22⋊C8—41no—
143C22⋊C8—761no—
144C19#734911yescharacteristic, complemented, Sylow
145C24—21no—
146C24—21no—
147C24—41no—
148C24—41no—
149C24—82no—
150C24C8×D1911yescharacteristic
151C24#6451511yescharacteristic
152C24(C2×D19)⋊C411yescharacteristic
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—382no—
156C22×C4—761no—
157C22×C4—761no—
158C22×C4—761no—
159C22×C4—1522no—
160C2×C8—81no—
161C2×C8—1521no—
162C22⋊C4—41no—
163C22⋊C4—41no—
164C22⋊C4—82no—
165C22⋊C4—761no—
166C22⋊C4—761no—
167C22⋊C4—762no—
168C22⋊C4—761no—
169C22⋊C4—761no—
170C22⋊C4—1522no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23—21no—
175C23—42no—
176C23—41no—
177C23—42no—
178C23—42no—
179C23—42no—
180C23—41no—
181C23—41no—
182C23—41no—
183C23—81no—
184C23—81no—
185C23—81no—
186C23—81no—
187C23—82no—
188C23—82no—
189C23—82no—
190C23—82no—
191C23#1059726311yescharacteristic
192C23(C2×D19)⋊C811yescharacteristic
193C23#1059728011yescharacteristic
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—762no—
199C2×C4—1521no—
200C2×C4—1522no—
201C2×C4—1522no—
202C2×C4—1522no—
203C2×C4—1522no—
204C8—161no—
205C8—3041no—
206C22—22no—
207C22—21no—
208C22—21no—
209C22—41no—
210C22—41no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22—42no—
216C22—42no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—81no—
221C22—82no—
222C22—82no—
223C22—84no—
224C22—81no—
225C22—81no—
226C22#1192626711yescharacteristic
227C22#1192633311yescharacteristic
228C22#1192633511yescharacteristic
229C4—81no—
230C4—81no—
231C4—3041no—
232C4—1522no—
233C2—21no—
234C2—21no—
235C2—21no—
236C2—41no—
237C2—42no—
238C2—41no—
239C2—81no—
240C2#1456156411yescharacteristic
subgroupG/H
centerC2#14561564
commutatorC24×C19C2×C8
Frattini#379C2×D19
FittingC19×#1316C2
socleC2×C19#1317
prime radicalC25×C19C2×C4
cosocleC19×#379C22
hypercenter#1316D19
hypocenterC19#7349
LCSG ▷ C24×C19 ▷ C23×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #379 ◁ #1316

Complements

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

NH ≅ G/Ntype
21. C2×C22⋊Dic19C8semidirect
144. C19#7349semidirect

Maximal subgroups

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

subgroupindex
#145637072
#145615632
C19×#13162
#734919