Finite Group Databasebeta

← #18076018

Subgroups — #18076018

Order 4864.

418 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 99 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#14563718C211yesmaximal, characteristic
2#14563712C211yesmaximal, characteristic
3#14561488C214yesmaximal
4C19×#2298C211yesmaximal, characteristic
5#11926508C2212yes—
6#11926407C2212yes—
7#11926313—22no—
8#11926311—22no—
9C2×C19×#117C2211yescharacteristic
10C19×#388—22no—
11C19×#387—22no—
12C4×C4⋊C4×C19C412yescomplemented
13C4×C22⋊C4×C19C2212yes—
14C19×#376C411yescharacteristic, complemented
15C43×C19C411yescharacteristic, complemented
16C23×C4×C19C2311yescharacteristic
17C19×#117—24no—
18C2×C4⋊C4×C19—22no—
19C2×C4⋊C4×C19D412yes—
20C2×C22⋊C4×C19—22no—
21C2×C22⋊C4×C19D412yes—
22C2×C42×C19—22no—
23C2×C42×C19C2×C411yescharacteristic
24C2×C42×C19C2×C411yescharacteristic
25C2×C42×C19C2×C412yes—
26C2×C42×C19C2×C412yes—
27C2×C22⋊Dic19—22no—
28C2×#64520—22no—
29C19×#95—22no—
30C19×#95—22no—
31C19×#95—22no—
32C19⋊#95—24no—
33C22⋊(C19⋊C8)—24no—
34C24×C19C2×D411yescharacteristic
35C22×C4×C19—22no—
36C22×C4×C19—22no—
37C22×C4×C19—42no—
38C22×C4×C19C22⋊C412yes—
39C22×C4×C19C22⋊C412yes—
40C22×C4×C19C22×C411yescharacteristic
41C22×C4×C19C2×D411yescharacteristic
42C22×C4×C19#4114yes—
43C22×Dic19—42no—
44C4⋊C4×C19—24no—
45C4⋊C4×C19—44no—
46C22⋊C4×C19—24no—
47C22⋊C4×C19—44no—
48C42×C19—22no—
49C42×C19—22no—
50C42×C19—42no—
51C42×C19—42no—
52C42×C19—44no—
53C22⋊Dic19—44no—
54#64520—44no—
55C2×C19⋊C8—42no—
56#8740—191nomaximal, Sylow
57C23×C19—22no—
58C23×C19—42no—
59C23×C19C2×C22⋊C411yescharacteristic
60C23×C19#12312yes—
61C2×C4×C19—22no—
62C2×C4×C19—22no—
63C2×C4×C19—24no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—44no—
67C2×C4×C19—42no—
68C2×C4×C19—42no—
69C2×C4×C19—42no—
70C2×C4×C19—42no—
71C2×C4×C19—42no—
72C2×C4×C19—42no—
73C2×C4×C19—42no—
74C2×C4×C19#11712yes—
75C2×C4×C19#12312yes—
76C2×Dic19—82no—
77C2×Dic19—84no—
78C19⋊C8—82no—
79#2298D1911yescharacteristic
80#1822—191no—
81#1820—191no—
82#1284—194no—
83C22×C19—22no—
84C22×C19—22no—
85C22×C19—24no—
86C22×C19—82no—
87C22×C19#38111yescharacteristic
88C22×C19#41012yes—
89C4×C19—22no—
90C4×C19—22no—
91C4×C19—44no—
92C4×C19—42no—
93C4×C19—42no—
94C4×C19—82no—
95Dic19—162no—
96C2×#117C2×D1911yescharacteristic
97#407—192no—
98#388—22no—
99#387—22no—
100#381—192no—
101C4×C4⋊C4Dic1912yescomplemented
102C4×C22⋊C4C2×D1912yes—
103#376Dic1911yescharacteristic, complemented
104C43Dic1911yescharacteristic, complemented
105#343—382no—
106#342—382no—
107C2×C19—22no—
108C2×C19—42no—
109C2×C19#182011yescharacteristic
110C2×C19#182712yes—
111C23×C4C22×D1911yescharacteristic
112C2×M16—382no—
113#117—24no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4C22⋊D1912yes—
116C2×C22⋊C4—22no—
117C2×C22⋊C4—382no—
118C2×C22⋊C4C22⋊D1912yes—
119C2×C42—22no—
120C2×C42C2×Dic1911yescharacteristic
121C2×C42C2×Dic1911yescharacteristic
122C2×C42C2×Dic1912yes—
123C2×C42C2×Dic1912yes—
124C22⋊C8—384no—
125#95—22no—
126#95—22no—
127#95—22no—
128#95—384no—
129C19#874011yescharacteristic, complemented, Sylow
130C24C2×C22⋊D1911yescharacteristic
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—42no—
134C22×C4—762no—
135C22×C4C22⋊Dic1912yes—
136C22×C4C22⋊Dic1912yes—
137C22×C4#6454114yes—
138C22×C4C22×Dic1911yescharacteristic
139C22×C4C2×C22⋊D1911yescharacteristic
140M16—764no—
141C2×C8—762no—
142C4⋊C4—24no—
143C4⋊C4—44no—
144C22⋊C4—24no—
145C22⋊C4—44no—
146C22⋊C4—764no—
147C42—22no—
148C42—22no—
149C42—42no—
150C42—42no—
151C42—44no—
152C23—22no—
153C23—42no—
154C23#1059737512yes—
155C23C2×C22⋊Dic1911yescharacteristic
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—1522no—
170C2×C4—1524no—
171C2×C4#1059737212yes—
172C2×C4#1059737512yes—
173C8—1522no—
174C22—22no—
175C22—22no—
176C22—24no—
177C22—82no—
178C22#1192640711yescharacteristic
179C22#1192651812yes—
180C4—22no—
181C4—22no—
182C4—44no—
183C4—42no—
184C4—42no—
185C4—82no—
186C4—3042no—
187C2—22no—
188C2—42no—
189C2#1456371211yescharacteristic
190C2#1456373912yes—
subgroupG/H
centerC22#11926407
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2298C2
socleC22×C19#381
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2298D19
hypocenterC19#8740
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2298

Complements

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

NH ≅ G/Ntype
12. C4×C4⋊C4×C19C4semidirect
14. C19×#376C4semidirect
15. C43×C19C4semidirect
101. C4×C4⋊C4Dic19semidirect
103. #376Dic19semidirect
104. C43Dic19semidirect
129. C19#8740semidirect

Maximal subgroups

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

subgroupindex
#145637182
#145637122
#145614882
C19×#22982
#874019