Finite Group Databasebeta

← #18069891

Subgroups — #18069891

Order 4864.

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

normal subgroups only

This group has 324 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#14563558C211yesmaximal, characteristic
2#14561571C211yesmaximal, characteristic
3C19×#1320C211yesmaximal, characteristic
4C23×Dic38C411yescharacteristic
5C2×#10597281—21no—
6C2×#10597281—21no—
7#11926508C411yescharacteristic
8#11926326—21no—
9C19×#407C2211yescharacteristic
10C19×#349—21no—
11C23×C4×C19C2×C411yescharacteristic
12C23×Dic19C812yes—
13C22×Dic38—21no—
14C22×Dic38—21no—
15C22×Dic38—42no—
16C22×Dic38—42no—
17C22×Dic38—41no—
18C22×Dic38—41no—
19C2×M16×C19D411yescharacteristic
20C2×M16×C19D411yescharacteristic
21C2×#64520—21no—
22C19×M32—41no—
23C19×C22⋊C8—41no—
24C22⋊(C19⋊C8)—41no—
25#10597281—42no—
26#10597281—42no—
27#10597269—41no—
28C24×C19C2×C811yescharacteristic
29C22×C4×C19—21no—
30C22×C4×C19—21no—
31C22×C4×C19—41no—
32C22×C4×C19—41no—
33C22×C4×C19C22⋊C411yescharacteristic
34C22×C4×C19M1611yescharacteristic
35C22×Dic19—22no—
36C22×Dic19—44no—
37C22×Dic19—42no—
38C2×Dic38—22no—
39C2×Dic38—22no—
40C2×Dic38—44no—
41C2×Dic38—41no—
42C2×Dic38—41no—
43C2×Dic38—42no—
44C2×Dic38—48no—
45C2×Dic38—42no—
46C2×Dic38—42no—
47C2×Dic38—41no—
48C2×Dic38—41no—
49C2×Dic38—42no—
50C2×Dic38—42no—
51M16×C19—41no—
52M16×C19—41no—
53C2×C8×C19—21no—
54C2×C8×C19—21no—
55#64520—41no—
56#64520—41no—
57C2×C19⋊C8—41no—
58C16×C19—81no—
59C19⋊C16—81no—
60#7341—191nomaximal, Sylow
61C23×C19—21no—
62C23×C19—41no—
63C23×C19—42no—
64C23×C19C22⋊C811yescharacteristic
65C2×C4×C19—21no—
66C2×C4×C19—21no—
67C2×C4×C19—21no—
68C2×C4×C19—42no—
69C2×C4×C19—41no—
70C2×C4×C19—41no—
71C2×C4×C19—41no—
72C2×C4×C19#9911yescharacteristic
73C2×C4×C19#10011yescharacteristic
74C2×Dic19—24no—
75C2×Dic19—42no—
76C2×Dic19—44no—
77C2×Dic19—42no—
78C2×Dic19—44no—
79Dic38—42no—
80Dic38—42no—
81Dic38—44no—
82Dic38—44no—
83Dic38—42no—
84Dic38—42no—
85C8×C19—41no—
86C8×C19—41no—
87C19⋊C8—81no—
88#1784—191no—
89#1320—191no—
90#1320D1911yescharacteristic
91C22×C19—22no—
92C22×C19—21no—
93C22×C19—41no—
94C22×C19—41no—
95C22×C19—42no—
96C22×C19—42no—
97C22×C19—41no—
98C22×C19#32311yescharacteristic
99C4×C19—21no—
100C4×C19—41no—
101C4×C19AΣL(1,𝔽16)11yescharacteristic
102C4×C19AΣL(1,𝔽16)11yescharacteristic
103Dic19—44no—
104C23×Q8—191no—
105C2×#101—381no—
106C2×#101—381no—
107#407—191no—
108#407C2×D1911yescharacteristic
109#349—21no—
110#349—381no—
111C2×C19—21no—
112C2×C19—42no—
113C2×C19—41no—
114C2×C19#131611yescharacteristic
115C22×Q8—381no—
116C22×Q8—381no—
117C22×Q8—761no—
118C22×Q8—761no—
119C22×Q8—762no—
120C22×Q8—762no—
121C23×C4—192no—
122C23×C4C4×D1911yescharacteristic
123C2×M16—381no—
124C2×M16D7611yescharacteristic
125C2×M16C22⋊D1911yescharacteristic
126M32—41no—
127M32—761no—
128#101—762no—
129#101—762no—
130C22⋊C8—41no—
131C22⋊C8—761no—
132C19#734111yescharacteristic, complemented, Sylow
133C24C8×D1911yescharacteristic
134C2×Q8—382no—
135C2×Q8—382no—
136C2×Q8—761no—
137C2×Q8—761no—
138C2×Q8—762no—
139C2×Q8—764no—
140C2×Q8—762no—
141C2×Q8—762no—
142C2×Q8—768no—
143C2×Q8—762no—
144C2×Q8—762no—
145C2×Q8—761no—
146C2×Q8—761no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—382no—
152C22×C4—764no—
153C22×C4—762no—
154C22×C4#6451511yescharacteristic
155C22×C4(C2×D19)⋊C411yescharacteristic
156M16—41no—
157M16—41no—
158M16—761no—
159M16—761no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—761no—
163C16—81no—
164C16—1521no—
165C23—21no—
166C23—41no—
167C23—42no—
168C23(C2×D19)⋊C811yescharacteristic
169Q8—762no—
170Q8—762no—
171Q8—764no—
172Q8—764no—
173Q8—762no—
174Q8—762no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—384no—
183C2×C4—762no—
184C2×C4—764no—
185C2×C4—762no—
186C2×C4—764no—
187C2×C4#1059726311yescharacteristic
188C2×C4#1059728011yescharacteristic
189C8—41no—
190C8—41no—
191C8—1521no—
192C22—22no—
193C22—21no—
194C22—41no—
195C22—41no—
196C22—42no—
197C22—42no—
198C22—41no—
199C22#1192626711yescharacteristic
200C4—21no—
201C4—41no—
202C4—764no—
203C4#1192633011yescharacteristic
204C4#1192633211yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2#1456156211yescharacteristic
subgroupG/H
centerC2#14561562
commutator, prime radicalC24×C19C2×C8
Frattini#407C2×D19
FittingC19×#1320C2
socleC2×C19#1316
cosocleC19×#407C22
hypercenter#1320D19
hypocenterC19#7341
LCSG ▷ C24×C19 ▷ C23×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #407 ◁ #1320

Complements

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

NH ≅ G/Ntype
132. C19#7341semidirect

Maximal subgroups

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

subgroupindex
#145635582
#145615712
C19×#13202
#734119