Finite Group Databasebeta

← #18069221

Subgroups — #18069221

Order 4864.

218 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 51 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#14561559C211yesmaximal, characteristic
2#14561503C211yesmaximal, characteristic
3C19×#2075C211yesmaximal, characteristic
4#11926404—21no—
5C22⋊(C19⋊C16)—21no—
6C2×C19×#107C411yescharacteristic, complemented
7C2×C19×C22⋊C8C2211yescharacteristic
8C19×#380—21no—
9C19×#340—21no—
10C19×#340C411yescharacteristic, complemented
11C23×C4×C19D411yescharacteristic
12C22×C8×C19C2×C411yescharacteristic
13C22×C8×C19D411yescharacteristic
14C2×C4⋊C4×C19—21no—
15C2×C4⋊C4×C19—21no—
16C2×C22⋊C4×C19—41no—
17C2×C22⋊Dic19—41no—
18C2×C4⋊Dic19—41no—
19C19×#107—41no—
20C19×C22⋊C8—41no—
21C19×#95—41no—
22C19⋊#95—22no—
23C2×C19⋊C16—41no—
24C24×C19D811yescharacteristic
25C22×C4×C19—21no—
26C22×C4×C19—21no—
27C22×C4×C19—41no—
28C22×C4×C19—41no—
29C22×C4×C19—41no—
30C22×C4×C19—41no—
31C22×C4×C19C22⋊C411yescharacteristic
32C22×C4×C19SD1611yescharacteristic
33C22×Dic19—42no—
34C2×C8×C19—21no—
35C2×C8×C19—21no—
36C2×C8×C19—41no—
37C2×C8×C19—41no—
38C4⋊C4×C19—41no—
39C4⋊C4×C19—41no—
40C4⋊C4×C19—41no—
41C4⋊C4×C19—41no—
42C22⋊C4×C19—81no—
43C22⋊C4×C19—81no—
44C22⋊Dic19—81no—
45C22⋊Dic19—81no—
46C4⋊Dic19—81no—
47C4⋊Dic19—81no—
48C19⋊C16—81no—
49#7079—191nomaximal, Sylow
50C23×C19—21no—
51C23×C19—21no—
52C23×C19—41no—
53C23×C19—41no—
54C23×C19#10211yescharacteristic
55C23×C19D1611yescharacteristic
56C23×C19SD3211yescharacteristic
57C2×C4×C19—21no—
58C2×C4×C19—21no—
59C2×C4×C19—21no—
60C2×C4×C19—41no—
61C2×C4×C19—41no—
62C2×C4×C19—41no—
63C2×C4×C19—81no—
64C2×C4×C19—81no—
65C2×C4×C19—81no—
66C2×C4×C19—81no—
67C2×C4×C19—81no—
68C2×C4×C19—81no—
69C2×C4×C19—81no—
70C2×C4×C19#9911yescharacteristic
71C2×C4×C19#10411yescharacteristic
72C2×Dic19—82no—
73C2×Dic19—82no—
74C2×Dic19—82no—
75C8×C19—41no—
76C8×C19—41no—
77#2075D1911yescharacteristic
78#1314—191no—
79#1289—191no—
80C22×C19—21no—
81C22×C19—21no—
82C22×C19—21no—
83C22×C19—21no—
84C22×C19—41no—
85C22×C19—41no—
86C22×C19—41no—
87C22×C19—41no—
88C22×C19—81no—
89C22×C19#32711yescharacteristic
90C22×C19#35711yescharacteristic
91C22×C19#36011yescharacteristic
92C4×C19—21no—
93C4×C19—41no—
94C4×C19—161no—
95C4×C19—161no—
96C4×C19#35211yescharacteristic
97C4×C19#35411yescharacteristic
98Dic19—162no—
99C2×#107Dic1911yescharacteristic, complemented
100C2×C22⋊C8C2×D1911yescharacteristic
101#380—21no—
102#380—381no—
103C22⋊C16—381no—
104#340—21no—
105#340Dic1911yescharacteristic, complemented
106C2×C19—21no—
107C2×C19—21no—
108C2×C19—41no—
109C2×C19—41no—
110C2×C19#134011yescharacteristic
111C2×C19#134411yescharacteristic
112C2×C19#134711yescharacteristic
113C23×C4C22⋊D1911yescharacteristic
114C22×C8C2×Dic1911yescharacteristic
115C22×C8C22⋊D1911yescharacteristic
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—761no—
119C2×C22⋊C4—41no—
120C2×C22⋊C4—761no—
121C2×C16—761no—
122#107—41no—
123C22⋊C8—41no—
124#95—41no—
125#95—382no—
126C19#707911yescharacteristic, complemented, Sylow
127C24#6452511yescharacteristic
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—41no—
131C22×C4—41no—
132C22×C4—41no—
133C22×C4—41no—
134C22×C4—762no—
135C22×C4#6452611yescharacteristic
136C22×C4C22⋊Dic1911yescharacteristic
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—41no—
140C2×C8—41no—
141C4⋊C4—41no—
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—41no—
145C4⋊C4—1521no—
146C4⋊C4—1521no—
147C22⋊C4—81no—
148C22⋊C4—81no—
149C22⋊C4—1521no—
150C22⋊C4—1521no—
151C16—1521no—
152C23—21no—
153C23—21no—
154C23—41no—
155C23—41no—
156C23#1059728311yescharacteristic
157C23#1059728411yescharacteristic
158C23#1059728911yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4—81no—
170C2×C4—81no—
171C2×C4—81no—
172C2×C4—1522no—
173C2×C4—1522no—
174C2×C4—1522no—
175C2×C4#1059729111yescharacteristic
176C2×C4#1059729411yescharacteristic
177C8—41no—
178C8—41no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—81no—
188C22#1192627811yescharacteristic
189C22#1192634511yescharacteristic
190C22#1192635411yescharacteristic
191C4—21no—
192C4—41no—
193C4—161no—
194C4—161no—
195C4—3042no—
196C4#1192633411yescharacteristic
197C4#1192633911yescharacteristic
198C2—21no—
199C2—21no—
200C2—41no—
201C2—41no—
202C2#1456162311yescharacteristic
203C2#1456163511yescharacteristic
204C2#1456164411yescharacteristic
subgroupG/H
centerC22#11926278
commutatorC22×C8×C19C2×C4
FrattiniC2×C22⋊C8C2×D19
FittingC19×#2075C2
socleC22×C19#327
prime radicalC24×C19D8
cosocleC2×C19×C22⋊C8C22
hypercenter#2075D19
hypocenterC19#7079
LCSG ▷ C22×C8×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #2075

Complements

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

NH ≅ G/Ntype
6. C2×C19×#107C4semidirect
10. C19×#340C4semidirect
99. C2×#107Dic19semidirect
105. #340Dic19semidirect
126. C19#7079semidirect

Maximal subgroups

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

subgroupindex
#145615592
#145615032
C19×#20752
#707919