Finite Group Databasebeta

← #18070081

Subgroups — #18070081

Order 4864.

198 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 37 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#14564922C211yesmaximal, characteristic
2#14561586C211yesmaximal, characteristic, complemented
3C19×#1309C211yesmaximal, characteristic, complemented
4#11927344C411yescharacteristic
5C2×#10597262—21no—
6#11926526—21no—
7#11926326—21no—
8C19⋊#338C411yescharacteristic
9C19×#423—21no—
10C19×#423C2211yescharacteristic
11C2×#64541—21no—
12C2×M16×C19—22no—
13C2×M16×C19C2×C411yescharacteristic
14C2×M16×C19D411yescharacteristic
15C2×C42×C19D411yescharacteristic
16C2×#64520—21no—
17#10597355—41no—
18#10597354—41no—
19#10597350—41no—
20C19×C4⋊C8—41no—
21C19×C4⋊C8—41no—
22C19×C4⋊C8—41no—
23#10597281—41no—
24#10597280—41no—
25#10597269—41no—
26#10597262—41no—
27#10597262—41no—
28C22×C4×C19—21no—
29C22×C4×C19C22⋊C411yescharacteristic
30C2×C22⋊D19—41no—
31#64541—41no—
32#64541—41no—
33#64541—41no—
34#64541—41no—
35C2×D76—21no—
36C2×C4×D19—41no—
37C2×Dic38—21no—
38M16×C19—41no—
39M16×C19—41no—
40M16×C19—82no—
41C2×C8×C19—21no—
42C2×C8×C19—21no—
43C2×C8×C19—42no—
44C42×C19—21no—
45C42×C19D811yescharacteristic
46C42×C19SD1611yescharacteristic
47#64520—41no—
48#64520—41no—
49C2×C19⋊C8—41no—
50Dic76—41no—
51D152—41no—
52#64516—42no—
53C19⋊C16—81no—
54#7414—191nomaximal, Sylow
55C23×C19#10411yescharacteristic
56C22×D19—41no—
57C2×C4×C19—21no—
58C2×C4×C19—21no—
59C2×C4×C19—21no—
60C2×C4×C19—21no—
61C2×C4×C19—41no—
62C2×C4×C19—41no—
63C2×C4×C19#9911yescharacteristic
64C2×C4×C19#10211yescharacteristic
65C22⋊D19—81no—
66C22⋊D19—81no—
67C2×Dic19—41no—
68D76—41no—
69D76—41no—
70C4×D19—81no—
71C4×D19—81no—
72Dic38—41no—
73Dic38—41no—
74C8×C19—41no—
75C8×C19—41no—
76C8×C19—82no—
77C19⋊C8—81no—
78#2050—191no—
79#1327—191no—
80#1309D1911yescharacteristic, complemented
81C22×C19—21no—
82C22×C19—41no—
83C22×C19#32711yescharacteristic
84C2×D19—81no—
85C2×D19—161no—
86C4×C19—21no—
87C4×C19—21no—
88C4×C19—21no—
89C4×C19—41no—
90C4×C19AΣL(1,𝔽16)11yescharacteristic
91C4×C19#35511yescharacteristic
92Dic19—81no—
93#575—191no—
94#423—21no—
95#423C2×D1911yescharacteristic
96C2×#104—381no—
97#413—381no—
98#349—381no—
99#338—191no—
100C2×C19—21no—
101C2×C19—41no—
102C2×C19#134511yescharacteristic
103D19—161no—
104C2×#41—381no—
105#137—761no—
106AGL(1,ℤ/8)—761no—
107#135—761no—
108C2×M16—22no—
109C2×M16—381no—
110C2×M16C4×D1911yescharacteristic
111C2×M16D7611yescharacteristic
112C2×C42C22⋊D1911yescharacteristic
113M32—761no—
114C4⋊C8—41no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117#104—761no—
118#104—761no—
119#101—761no—
120#100—761no—
121C19#741411yescharacteristic, complemented, Sylow
122#41—761no—
123#41—761no—
124#41—761no—
125#41—761no—
126C2×Q8—381no—
127C2×D4—381no—
128C2×D4—761no—
129C22×C4—21no—
130C22×C4—761no—
131C22×C4(C2×D19)⋊C411yescharacteristic
132Q16—761no—
133SD16—762no—
134D8—761no—
135M16—41no—
136M16—41no—
137M16—82no—
138M16—761no—
139M16—761no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—42no—
143C2×C8—761no—
144C42—21no—
145C42#6452511yescharacteristic
146C42#6452711yescharacteristic
147C16—1521no—
148C23—761no—
149C23#1059726211yescharacteristic
150Q8—761no—
151Q8—761no—
152D4—761no—
153D4—761no—
154D4—1521no—
155D4—1521no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—761no—
163C2×C4—1521no—
164C2×C4—1521no—
165C2×C4#1059726311yescharacteristic
166C2×C4#1059726611yescharacteristic
167C8—41no—
168C8—41no—
169C8—82no—
170C8—1521no—
171C22—21no—
172C22—41no—
173C22—3041no—
174C22—1521no—
175C22#1192627711yescharacteristic
176C4—21no—
177C4—21no—
178C4—21no—
179C4—41no—
180C4—1521no—
181C4#1192633211yescharacteristic
182C4#1192634011yescharacteristic
183C2—21no—
184C2—41no—
185C2—3041no—
186C2#1456163711yescharacteristic
subgroupG/H
centerC2#14561637
commutatorC2×M16×C19C2×C4
Frattini#423C2×D19
FittingC19×#1309C2
socleC2×C19#1345
prime radical#11927344C4
cosocleC19×#423C22
hypercenter#1309D19
hypocenterC19#7414
LCSG ▷ C2×M16×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #1309

Complements

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

NH ≅ G/Ntype
2. #14561586C2semidirect
3. C19×#1309C2semidirect
80. #1309D19semidirect
121. C19#7414semidirect

Maximal subgroups

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

subgroupindex
#145649222
#145615862
C19×#13092
#741419