Finite Group Databasebeta

← #18070123

Subgroups — #18070123

Order 4864.

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

normal subgroups only

This group has 226 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#14564781C211yesmaximal, characteristic
2#14561567C211yesmaximal, characteristic
3C19×#1393C211yesmaximal, characteristic
4C2×#10597316C411yescharacteristic, complemented
5C2×#10597289—21no—
6#11926306—21no—
7#11926299C411yescharacteristic, complemented
8#11926270—21no—
9C2×C19×#99—21no—
10C19×#390C2211yescharacteristic
11C22×D4×C19D411yescharacteristic
12C2×C4⋊C4×C19D411yescharacteristic
13C2×C22⋊C4×C19—41no—
14C2×C22⋊C4×C19—41no—
15C2×C42×C19C2×C411yescharacteristic
16C2×C4⋊Dic19—21no—
17C2×Dic19⋊C4—41no—
18C22×C19⋊C8—21no—
19#10597316—42no—
20C19×#99—22no—
21C19×#99—41no—
22#10597289—42no—
23C22⋊(C19⋊C8)—41no—
24C24×C19—21no—
25C2×D4×C19—21no—
26C2×D4×C19—41no—
27C2×D4×C19—41no—
28C2×D4×C19SD1611yescharacteristic
29C2×D4×C19Q1611yescharacteristic
30C22×C4×C19—21no—
31C22×C4×C19—21no—
32C22×C4×C19—81no—
33C22×C4×C19C22⋊C411yescharacteristic
34C22×Dic19—41no—
35C4⋊C4×C19—41no—
36C22⋊C4×C19—42no—
37C22⋊C4×C19—82no—
38C22⋊C4×C19—81no—
39C42×C19—41no—
40C4⋊Dic19—22no—
41C4⋊Dic19—41no—
42Dic19⋊C4—42no—
43Dic19⋊C4—42no—
44C2×C19⋊C8—41no—
45C2×C19⋊C8—41no—
46C2×C19⋊C8—41no—
47C2×C19⋊C8—81no—
48#7428—191nomaximal, Sylow
49C23×C19—21no—
50C23×C19—21no—
51C23×C19—41no—
52C23×C19—41no—
53C23×C19—81no—
54C23×C19—81no—
55C23×C19#9911yescharacteristic
56D4×C19—41no—
57D4×C19—41no—
58D4×C19—81no—
59C2×C4×C19—21no—
60C2×C4×C19—21no—
61C2×C4×C19—41no—
62C2×C4×C19—41no—
63C2×C4×C19—41no—
64C2×C4×C19—41no—
65C2×C4×C19—81no—
66C2×C4×C19—82no—
67C2×C4×C19—161no—
68C2×C4×C19—161no—
69C2×C4×C19#10311yescharacteristic
70C2×C4×C19#10411yescharacteristic
71C2×Dic19—42no—
72C2×Dic19—81no—
73C2×Dic19—81no—
74C19⋊C8—81no—
75C19⋊C8—161no—
76#2025—191no—
77#1393D1911yescharacteristic
78#1318—191no—
79C22×C19—21no—
80C22×C19—21no—
81C22×C19—41no—
82C22×C19—41no—
83C22×C19—81no—
84C22×C19—81no—
85C22×C19—81no—
86C22×C19—81no—
87C22×C19—161no—
88C22×C19#32811yescharacteristic
89C22×C19AΣL(1,𝔽16)11yescharacteristic
90C22×C19#35411yescharacteristic
91C4×C19—21no—
92C4×C19—21no—
93C4×C19—81no—
94C4×C19—81no—
95C4×C19—162no—
96Dic19—82no—
97C2×#125—191no—
98C2×#102—381no—
99C2×#99—21no—
100#390C2×D1911yescharacteristic
101#340—381no—
102#336—191no—
103#324—381no—
104C2×C19—21no—
105C2×C19—21no—
106C2×C19—81no—
107C2×C19—81no—
108C2×C19#135111yescharacteristic
109C2×C19#141211yescharacteristic
110C2×C19#141411yescharacteristic
111C22×D4C22⋊D1911yescharacteristic
112C22×C8—381no—
113#125—762no—
114C2×C4⋊C4—381no—
115C2×C4⋊C4—761no—
116C2×C4⋊C4D7611yescharacteristic
117C2×C22⋊C4—41no—
118C2×C22⋊C4—41no—
119C2×C42C4×D1911yescharacteristic
120#102—762no—
121#99—22no—
122#99—41no—
123C22⋊C8—761no—
124C19#742811yescharacteristic, complemented, Sylow
125C24—21no—
126C2×D4—21no—
127C2×D4—41no—
128C2×D4—41no—
129C2×D4#6452611yescharacteristic
130C2×D4#6452811yescharacteristic
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—81no—
134C22×C4—761no—
135C22×C4(C2×D19)⋊C411yescharacteristic
136C2×C8—761no—
137C2×C8—761no—
138C2×C8—761no—
139C2×C8—1521no—
140C4⋊C4—41no—
141C4⋊C4—382no—
142C4⋊C4—761no—
143C4⋊C4—762no—
144C4⋊C4—762no—
145C22⋊C4—42no—
146C22⋊C4—82no—
147C22⋊C4—81no—
148C42—41no—
149C23—21no—
150C23—21no—
151C23—41no—
152C23—41no—
153C23—81no—
154C23—81no—
155C23#1059726311yescharacteristic
156D4—41no—
157D4—41no—
158D4—81no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—81no—
166C2×C4—82no—
167C2×C4—161no—
168C2×C4—161no—
169C2×C4—762no—
170C2×C4—1521no—
171C2×C4—1521no—
172C2×C4#1059726211yescharacteristic
173C2×C4#1059726711yescharacteristic
174C8—3041no—
175C8—1521no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22—161no—
185C22#1192628011yescharacteristic
186C22#1192633011yescharacteristic
187C22#1192633811yescharacteristic
188C4—21no—
189C4—21no—
190C4—81no—
191C4—81no—
192C4—162no—
193C4—1522no—
194C2—21no—
195C2—21no—
196C2—81no—
197C2—81no—
198C2#1456165511yescharacteristic
199C2#1456180511yescharacteristic
200C2#1456180911yescharacteristic
subgroupG/H
centerC22#11926338
commutatorC2×C42×C19C2×C4
Frattini#390C2×D19
FittingC19×#1393C2
socleC22×C19#354
prime radicalC22×D4×C19D4
cosocleC19×#390C22
hypercenter#1393D19
hypocenterC19#7428
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
4. C2×#10597316C4semidirect
7. #11926299C4semidirect
124. C19#7428semidirect

Maximal subgroups

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

subgroupindex
#145647812
#145615672
C19×#13932
#742819