Finite Group Databasebeta

← #18077501

Subgroups — #18077501

Order 4864.

398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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#14573983C211yesmaximal, characteristic
2#14572741C211yesmaximal, characteristic, complemented
3#14562105C212yesmaximal
4#14561535C212yesmaximal, complemented
5C19×#1544C211yesmaximal, characteristic, complemented
6#11927094C2211yescharacteristic
7#11926914C412yes—
8#11926910C412yes—
9#11926906—22no—
10#11926675—24no—
11#11926605—22no—
12#11926601C2212yes—
13#11926538—22no—
14C2×#10597260C2211yescharacteristic
15#11926273—24no—
16C19×#533C2211yescharacteristic
17C19×#431C2212yes—
18C19×#332—22no—
19C2×#64541—21no—
20C19×C4⋊Q8D412yes—
21C19×#125C2×C412yes—
22C19×C22⋊Q8—22no—
23C4×Q8×C19—22no—
24C19×#117D412yes—
25C2×C42×C19C2311yescharacteristic
26#10597376—22no—
27C22×C19⋊C8—21no—
28#10597321—21no—
29#10597320C2×C411yescharacteristic
30C4×D76—22no—
31#10597315C2×C411yescharacteristic
32C19×C4⋊C8—22no—
33C19×C22⋊C8—22no—
34C4×C8×C19—22no—
35C22⋊(C19⋊C8)—22no—
36#10597267—24no—
37#10597266—24no—
38C4⋊(C19⋊C8)—24no—
39C4⋊(C19⋊C8)D414yes—
40#10597260—22no—
41#10597260—22no—
42#10597260—21no—
43#10597260C2×C412yes—
44C4×C19⋊C8—22no—
45C2×Q8×C19—22no—
46C22×C4×C19C2×D411yescharacteristic
47C22×C4×C19#4112yes—
48C2×C22⋊D19—41no—
49#64541—44no—
50C2×D76—21no—
51C2×D76—22no—
52C2×C4×D19—41no—
53C2×Dic38—21no—
54C2×C8×C19—42no—
55C4⋊C4×C19—24no—
56C4⋊C4×C19—22no—
57C4⋊C4×C19C22⋊C414yes—
58C22⋊C4×C19—22no—
59C42×C19—22no—
60C42×C19C22×C411yescharacteristic
61C42×C19C2×D412yes—
62C42×C19C2×D411yescharacteristic
63(C2×D19)⋊C4—42no—
64C4⋊Dic19—22no—
65C2×C19⋊C8—22no—
66C2×C19⋊C8—24no—
67C2×C19⋊C8—42no—
68#9008—191nomaximal, Sylow
69C23×C19#12311yescharacteristic
70C22×D19—41no—
71Q8×C19—82no—
72C2×C4×C19—22no—
73C2×C4×C19—24no—
74C2×C4×C19—42no—
75C2×C4×C19C2×C22⋊C411yescharacteristic
76C2×C4×C19C4×D412yes—
77C2×C4×C19#12011yescharacteristic
78C2×C4×C19#12112yes—
79C22⋊D19—82no—
80C2×Dic19—41no—
81D76—44no—
82D76—42no—
83C4×D19—82no—
84Dic38—42no—
85C8×C19—82no—
86C19⋊C8—42no—
87C19⋊C8—44no—
88#3135—191no—
89#2987—191no—
90#1544D1911yescharacteristic, complemented
91#1496—192no—
92#1302—192no—
93C22×C19—22no—
94C22×C19—21no—
95C22×C19#38611yescharacteristic
96C2×D19—82no—
97C2×D19—81no—
98C4×C19—22no—
99C4×C19—22no—
100C4×C19—21no—
101C4×C19—44no—
102C4×C19#45412yes—
103Dic19—81no—
104#533C2×D1911yescharacteristic
105#532—191no—
106#491—192no—
107#490—192no—
108#489—382no—
109#446—384no—
110#433—382no—
111#432—192no—
112#431C2×D1912yes—
113#416—382no—
114C2×#97—191no—
115#332—22no—
116D4⋊C8—384no—
117C2×C19—41no—
118C2×C19#188112yes—
119C2×C19#188811yescharacteristic
120D19—161no—
121C2×#41—381no—
122C22×C8—381no—
123C4⋊Q8—191no—
124C4⋊Q8C22⋊D1912yes—
125#127—191no—
126#125C4×D1912yes—
127#124—381no—
128C22⋊Q8—22no—
129#121—382no—
130C4×Q8—22no—
131C4×D4—382no—
132#117D7612yes—
133C2×C42C22×D1911yescharacteristic
134C4⋊C8—22no—
135C4⋊C8—194no—
136C4⋊C8—384no—
137#103—384no—
138#102—384no—
139C22⋊C8—22no—
140C22⋊C8—382no—
141#97—192no—
142#97—382no—
143#97—382no—
144#97—381no—
145C4×C8—22no—
146C4×C8—382no—
147C19#900811yescharacteristic, complemented, Sylow
148#41—764no—
149C2×Q8—22no—
150C2×Q8—381no—
151C2×D4—382no—
152C2×D4—381no—
153C2×D4—761no—
154C22×C4—761no—
155C22×C4C2×D7611yescharacteristic
156C22×C4#6454312yes—
157C2×C8—42no—
158C2×C8—384no—
159C2×C8—382no—
160C2×C8—762no—
161C4⋊C4—22no—
162C4⋊C4—24no—
163C4⋊C4—382no—
164C4⋊C4(C2×D19)⋊C414yes—
165C22⋊C4—22no—
166C22⋊C4—762no—
167C42—22no—
168C42C2×C4×D1911yescharacteristic
169C42D4×D1912yes—
170C42C2×C22⋊D1911yescharacteristic
171C23—761no—
172C23#1059733211yescharacteristic
173Q8—82no—
174Q8—762no—
175D4—762no—
176D4—764no—
177D4—1522no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—42no—
181C2×C4—761no—
182C2×C4—1522no—
183C2×C4(C22⋊D19)⋊C412yes—
184C2×C4#1059732811yescharacteristic
185C2×C4C2×(C2×D19)⋊C411yescharacteristic
186C2×C4#1059738512yes—
187C8—82no—
188C8—762no—
189C8—764no—
190C22—22no—
191C22—21no—
192C22—1522no—
193C22—1521no—
194C22#1192642111yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—44no—
199C4—1521no—
200C4#1192671912yes—
201C2—41no—
202C2—3041no—
203C2#1456399512yes—
204C2#1456403611yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1544C2
socleC22×C19#386
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#1544D19
hypocenterC19#9008
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1544

Complements

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

NH ≅ G/Ntype
2. #14572741C2semidirect
4. #14561535C2semidirect
5. C19×#1544C2semidirect
90. #1544D19semidirect
147. C19#9008semidirect

Maximal subgroups

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

subgroupindex
#145739832
#145727412
#145621052
#145615352
C19×#15442
#900819