Finite Group Databasebeta

← #18077503

Subgroups — #18077503

Order 4864.

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

normal subgroups only

This group has 398 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#14573983C211yesmaximal, characteristic
2#14562300C211yesmaximal, characteristic, complemented
3#14562103C212yesmaximal
4#14561533C212yesmaximal, complemented
5C19×#2987C211yesmaximal, characteristic, complemented
6#11927094C2211yescharacteristic
7#11926914C412yes—
8#11926910C412yes—
9#11926906—22no—
10#11926597C2212yes—
11#11926538—22no—
12C2×#10597260C2211yescharacteristic
13#11926290—22no—
14#11926271—24no—
15C19×#533C2211yescharacteristic
16C19×#446—24no—
17C19×#433—22no—
18C19×#432C2212yes—
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—24no—
33C19×C4⋊C8D414yes—
34C19×C22⋊C8—22no—
35C19×#97—22no—
36C19×#97—22no—
37C4×C8×C19—22no—
38C22⋊(C19⋊C8)—22no—
39#10597267—24no—
40#10597266—24no—
41C4⋊(C19⋊C8)—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—24no—
55C4⋊C4×C19—24no—
56C4⋊C4×C19—22no—
57C4⋊C4×C19C22⋊C414yes—
58C22⋊C4×C19—22no—
59C42×C19—22no—
60C42×C19C22×C411yescharacteristic
61C42×C19C2×D411yescharacteristic
62C42×C19C2×D412yes—
63(C2×D19)⋊C4—42no—
64C4⋊Dic19—22no—
65C2×C19⋊C8—22no—
66C2×C19⋊C8—42no—
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—44no—
86C19⋊C8—42no—
87C19⋊C8—82no—
88#3135—191no—
89#2987D1911yescharacteristic, complemented
90#1544—191no—
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—24no—
110#433—22no—
111#432C2×D1912yes—
112#431—192no—
113#416—382no—
114C2×#97—191no—
115#332—382no—
116D4⋊C8—384no—
117C2×C19—41no—
118C2×C19#188112yes—
119C2×C19#188811yescharacteristic
120D19—161no—
121C2×#41—381no—
122C22×C8—381no—
123C4⋊Q8—191no—
124C4⋊Q8D7612yes—
125#127—191no—
126#125C4×D1912yes—
127#124—381no—
128C22⋊Q8—22no—
129#121—382no—
130C4×Q8—22no—
131C4×D4—382no—
132#117C22⋊D1912yes—
133C2×C42C22×D1911yescharacteristic
134C4⋊C8—24no—
135C4⋊C8—382no—
136C4⋊C8C22⋊D1914yes—
137#103—384no—
138#102—384no—
139C22⋊C8—22no—
140C22⋊C8—382no—
141#97—22no—
142#97—22no—
143#97—192no—
144#97—381no—
145C4×C8—22no—
146C4×C8—382no—
147C19#900811yescharacteristic, complemented, Sylow
148#41—764no—
149C2×Q8—22no—
150C2×Q8—381no—
151C2×D4—381no—
152C2×D4—382no—
153C2×D4—761no—
154C22×C4—761no—
155C22×C4#6454112yes—
156C22×C4C2×C22⋊D1911yescharacteristic
157C2×C8—24no—
158C2×C8—382no—
159C2×C8—762no—
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
169C42C2×D7611yescharacteristic
170C42C2×C22⋊D1912yes—
171C23—761no—
172C23#1059737511yescharacteristic
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×C4C2×(C2×D19)⋊C411yescharacteristic
184C2×C4C4×C22⋊D1912yes—
185C2×C4#1059737612yes—
186C2×C4#1059739911yescharacteristic
187C8—44no—
188C8—762no—
189C8—1522no—
190C22—22no—
191C22—21no—
192C22—1522no—
193C22—1521no—
194C22#1192642311yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—44no—
199C4—1521no—
200C4#1192671712yes—
201C2—41no—
202C2—3041no—
203C2#1456399712yes—
204C2#1456403811yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2987C2
socleC22×C19#386
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#2987D19
hypocenterC19#9008
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2987

Complements

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

NH ≅ G/Ntype
2. #14562300C2semidirect
4. #14561533C2semidirect
5. C19×#2987C2semidirect
89. #2987D19semidirect
147. C19#9008semidirect

Maximal subgroups

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

subgroupindex
#145739832
#145623002
#145621032
#145615332
C19×#29872
#900819