Finite Group Databasebeta

← #18070169

Subgroups — #18070169

Order 4864.

198 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 43 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#14561581C211yesmaximal, characteristic
2#14561518C211yesmaximal, characteristic
3C19×#2060C211yesmaximal, characteristic
4C2×C4⋊(C19⋊C8)—21no—
5#11926270—21no—
6C19×#544C411yescharacteristic
7C19×#428—21no—
8C19×#384C2211yescharacteristic
9C19×#343C411yescharacteristic
10C19×#339—21no—
11C2×M16×C19—21no—
12C19×C4⋊Q8—41no—
13C19×#125—41no—
14C19×C22⋊Q8—41no—
15C19×#117—21no—
16C2×C4⋊C4×C19—41no—
17C2×C4⋊C4×C19C2×C411yescharacteristic
18C2×C4⋊C4×C19D411yescharacteristic
19C2×C42×C19D411yescharacteristic
20C22×C19⋊C8—41no—
21C19×#107—41no—
22C19×#106—41no—
23C22⋊(C19⋊C8)—41no—
24C4⋊(C19⋊C8)—22no—
25C4⋊(C19⋊C8)—41no—
26C2×Q8×C19—41no—
27C22×C4×C19—21no—
28C22×C4×C19—21no—
29C22×C4×C19—21no—
30C22×C4×C19C22⋊C411yescharacteristic
31M16×C19—22no—
32M16×C19—41no—
33C2×C8×C19—41no—
34C4⋊C4×C19—21no—
35C4⋊C4×C19—21no—
36C4⋊C4×C19—41no—
37C4⋊C4×C19—41no—
38C4⋊C4×C19—41no—
39C4⋊C4×C19—42no—
40C4⋊C4×C19—81no—
41C4⋊C4×C19—81no—
42C22⋊C4×C19—41no—
43C42×C19—21no—
44C42×C19—41no—
45C42×C19SD1611yescharacteristic
46C42×C19Q1611yescharacteristic
47C2×C19⋊C8—42no—
48C2×C19⋊C8—81no—
49C2×C19⋊C8—81no—
50C2×C19⋊C8—81no—
51#7443—191nomaximal, Sylow
52C23×C19#9911yescharacteristic
53Q8×C19—161no—
54C2×C4×C19—21no—
55C2×C4×C19—21no—
56C2×C4×C19—21no—
57C2×C4×C19—21no—
58C2×C4×C19—21no—
59C2×C4×C19—21no—
60C2×C4×C19—21no—
61C2×C4×C19—21no—
62C2×C4×C19—41no—
63C2×C4×C19—41no—
64C2×C4×C19—41no—
65C2×C4×C19—41no—
66C2×C4×C19—81no—
67C2×C4×C19—81no—
68C2×C4×C19#10311yescharacteristic
69C2×C4×C19#10411yescharacteristic
70C8×C19—42no—
71C19⋊C8—82no—
72C19⋊C8—161no—
73#2060D1911yescharacteristic
74#1325—191no—
75#1296—191no—
76C22×C19—21no—
77C22×C19—21no—
78C22×C19#32811yescharacteristic
79C22×C19AΣL(1,𝔽16)11yescharacteristic
80C22×C19#35611yescharacteristic
81C4×C19—21no—
82C4×C19—21no—
83C4×C19—21no—
84C4×C19—21no—
85C4×C19—21no—
86C4×C19—21no—
87C4×C19—81no—
88C4×C19—81no—
89C4×C19—81no—
90C4×C19—81no—
91#544Dic1911yescharacteristic
92#428—21no—
93C2×C4⋊C8—381no—
94#384C2×D1911yescharacteristic
95#343Dic1911yescharacteristic
96#339—21no—
97#324—381no—
98C2×C19—21no—
99C2×C19—21no—
100C2×C19#135411yescharacteristic
101C2×C19#140211yescharacteristic
102C2×C19#140511yescharacteristic
103C2×M16—21no—
104C22×C8—761no—
105C4⋊Q8—41no—
106#125—41no—
107C22⋊Q8—41no—
108#117—21no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4C2×Dic1911yescharacteristic
111C2×C4⋊C4C22⋊D1911yescharacteristic
112C2×C42C22⋊D1911yescharacteristic
113#107—41no—
114#106—41no—
115C4⋊C8—382no—
116C4⋊C8—761no—
117C22⋊C8—761no—
118C19#744311yescharacteristic, complemented, Sylow
119C2×Q8—41no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4C22⋊Dic1911yescharacteristic
124M16—22no—
125M16—41no—
126C2×C8—41no—
127C2×C8—762no—
128C2×C8—1521no—
129C2×C8—1521no—
130C2×C8—1521no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—41no—
134C4⋊C4—41no—
135C4⋊C4—41no—
136C4⋊C4—42no—
137C4⋊C4—81no—
138C4⋊C4—81no—
139C22⋊C4—41no—
140C42—21no—
141C42—41no—
142C42#6452711yescharacteristic
143C42#6452811yescharacteristic
144C23#1059729111yescharacteristic
145Q8—161no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4#1059729211yescharacteristic
161C2×C4#1059729411yescharacteristic
162C8—42no—
163C8—3041no—
164C8—1522no—
165C22—21no—
166C22—21no—
167C22#1192628111yescharacteristic
168C22#1192633111yescharacteristic
169C22#1192634311yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—81no—
177C4—81no—
178C4—81no—
179C4—81no—
180C2—21no—
181C2—21no—
182C2#1456166511yescharacteristic
183C2#1456178011yescharacteristic
184C2#1456178911yescharacteristic
subgroupG/H
centerC22#11926331
commutatorC2×C4⋊C4×C19C2×C4
Frattini#384C2×D19
FittingC19×#2060C2
socleC22×C19AΣL(1,𝔽16)
prime radicalC23×C19#99
cosocleC19×#384C22
hypercenter#2060D19
hypocenterC19#7443
LCSG ▷ C2×C4⋊C4×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #2060

Complements

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

NH ≅ G/Ntype
118. C19#7443semidirect

Maximal subgroups

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

subgroupindex
#145615812
#145615182
C19×#20602
#744319