Finite Group Databasebeta

← #18069856

Subgroups — #18069856

Order 4864.

482 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 71 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#14561962C212yesmaximal
2C19×#1440C211yesmaximal, characteristic
3#11926508—22no—
4#11926268—22no—
5#11926268C414yescomplemented
6C22×C22⋊C4×C19C412yes—
7C22×C22⋊C4×C19C2211yescharacteristic
8C2×C19×#95—22no—
9C25×C19C2×C411yescharacteristic
10C23×C4×C19—22no—
11C23×C4×C19D412yes—
12C2×C22⋊C4×C19—42no—
13C2×C22⋊C4×C19—42no—
14C2×C22⋊C4×C19—44no—
15C2×C22⋊C4×C19C2×C412yes—
16C2×C22⋊C4×C19D411yescharacteristic
17C2×C22⋊C4×C19Q811yescharacteristic
18C2×#64520—42no—
19C19×#95—44no—
20C22⋊(C19⋊C8)—24no—
21C22⋊(C19⋊C8)—42no—
22C24×C19—22no—
23C24×C19—42no—
24C24×C19—42no—
25C24×C19—42no—
26C24×C19C4211yescharacteristic
27C24×C19C22⋊C411yescharacteristic
28C24×C19C4⋊C411yescharacteristic
29C22×C4×C19—22no—
30C22×C4×C19—22no—
31C22×C4×C19—24no—
32C22×C4×C19—42no—
33C22×C4×C19—42no—
34C22×C4×C19—42no—
35C22×C4×C19—42no—
36C22×C4×C19—42no—
37C22×C4×C19—42no—
38C22×C4×C19—42no—
39C22×C4×C19—42no—
40C22×C4×C19C22⋊C412yes—
41C22×C4×C19C4⋊C412yes—
42C22⋊C4×C19—42no—
43C22⋊C4×C19—41no—
44C22⋊C4×C19—41no—
45C22⋊C4×C19—44no—
46C22⋊C4×C19—44no—
47#64520—82no—
48#64520—82no—
49C2×C19⋊C8—44no—
50#7324—191nomaximal, Sylow
51C23×C19—22no—
52C23×C19—22no—
53C23×C19—22no—
54C23×C19—21no—
55C23×C19—21no—
56C23×C19—22no—
57C23×C19—22no—
58C23×C19—44no—
59C23×C19—44no—
60C23×C19—42no—
61C23×C19—42no—
62C23×C19—42no—
63C23×C19—42no—
64C23×C19—82no—
65C23×C19—82no—
66C23×C19—82no—
67C23×C19—82no—
68C23×C19#9511yescharacteristic
69C23×C19#9912yes—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—42no—
73C2×C4×C19—42no—
74C2×C4×C19—42no—
75C2×C4×C19—42no—
76C2×C4×C19—44no—
77C2×C4×C19—44no—
78C2×C4×C19—44no—
79C2×C4×C19—82no—
80C2×C4×C19—82no—
81C2×C4×C19—82no—
82C2×C4×C19—82no—
83C2×C4×C19—82no—
84C19⋊C8—84no—
85#1462—192no—
86#1440D1911yescharacteristic
87C22×C19—22no—
88C22×C19—22no—
89C22×C19—22no—
90C22×C19—22no—
91C22×C19—22no—
92C22×C19—22no—
93C22×C19—22no—
94C22×C19—41no—
95C22×C19—41no—
96C22×C19—42no—
97C22×C19—42no—
98C22×C19—82no—
99C22×C19—82no—
100C22×C19—84no—
101C22×C19—84no—
102C22×C19#34211yescharacteristic
103C22×C19#34412yes—
104C22×C19AΣL(1,𝔽16)12yes—
105C22×C19#35212yes—
106C4×C19—42no—
107C4×C19—42no—
108C4×C19—84no—
109C22×C22⋊C4Dic1912yes—
110C22×C22⋊C4C2×D1911yescharacteristic
111#407—382no—
112C2×#95—22no—
113#323—194no—
114#323—382no—
115C2×C19—22no—
116C2×C19—22no—
117C2×C19—22no—
118C2×C19—81no—
119C2×C19—81no—
120C2×C19#130611yescharacteristic
121C2×C19#139012yes—
122C25C2×Dic1911yescharacteristic
123C23×C4—22no—
124C23×C4C22⋊D1912yes—
125C2×M16—762no—
126C2×C22⋊C4—42no—
127C2×C22⋊C4—42no—
128C2×C22⋊C4—44no—
129C2×C22⋊C4Dic3811yescharacteristic
130C2×C22⋊C4C4×D1912yes—
131C2×C22⋊C4D7611yescharacteristic
132C22⋊C8—384no—
133C22⋊C8—762no—
134#95—44no—
135C19#732411yescharacteristic, complemented, Sylow
136C24—22no—
137C24—42no—
138C24—42no—
139C24—42no—
140C24C4×Dic1911yescharacteristic
141C24C4⋊Dic1911yescharacteristic
142C24C22⋊Dic1911yescharacteristic
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—24no—
146C22×C4—42no—
147C22×C4—42no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4Dic19⋊C412yes—
155C22×C4(C2×D19)⋊C412yes—
156M16—1522no—
157M16—1522no—
158C2×C8—764no—
159C22⋊C4—41no—
160C22⋊C4—42no—
161C22⋊C4—41no—
162C22⋊C4—44no—
163C22⋊C4—44no—
164C23—22no—
165C23—22no—
166C23—22no—
167C23—21no—
168C23—21no—
169C23—22no—
170C23—22no—
171C23—44no—
172C23—44no—
173C23—42no—
174C23—42no—
175C23—42no—
176C23—42no—
177C23—82no—
178C23—82no—
179C23—82no—
180C23—82no—
181C23C19⋊#9511yescharacteristic
182C23#1059729112yes—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—44no—
190C2×C4—44no—
191C2×C4—44no—
192C2×C4—82no—
193C2×C4—82no—
194C2×C4—82no—
195C2×C4—82no—
196C2×C4—82no—
197C8—1524no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—41no—
206C22—41no—
207C22—42no—
208C22—42no—
209C22—82no—
210C22—82no—
211C22—84no—
212C22—84no—
213C22#1192631111yescharacteristic
214C22#1192631412yes—
215C22#1192633112yes—
216C22#1192633412yes—
217C4—42no—
218C4—42no—
219C4—84no—
220C2—22no—
221C2—22no—
222C2—22no—
223C2—81no—
224C2—81no—
225C2#1456154311yescharacteristic
226C2#1456175312yes—
subgroupG/H
centerC22#11926311
commutatorC24×C19C42
FrattiniC22×C22⋊C4C2×D19
FittingC19×#1440C2
socleC22×C19#342
prime radicalC25×C19C2×C4
cosocleC22×C22⋊C4×C19C22
hypercenter#1440D19
hypocenterC19#7324
LCSG ▷ C24×C19 ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1440

Complements

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

NH ≅ G/Ntype
5. #11926268C4semidirect
135. C19#7324semidirect

Maximal subgroups

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

subgroupindex
#145619622
C19×#14402
#732419