Finite Group Databasebeta

← #18086679

Subgroups — #18086679

Order 4864.

370 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 77 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#14563775C211yesmaximal, characteristic, complemented
2#14562357C212yesmaximal, complemented
3#14562246C212yesmaximal, complemented
4#14561546C211yesmaximal, characteristic, complemented
5C19×#3253C211yesmaximal, characteristic
6#11926601C2212yes—
7#11926568C2211yescharacteristic
8C2×#10597260C2211yescharacteristic
9#11926308—22no—
10#11926290—22no—
11#11926288—22no—
12#11926284—24no—
13C19×#532C2212yes—
14C19×#476—22no—
15C19×#469—22no—
16C19×#459—22no—
17C19×#423C2211yescharacteristic
18C2×#41×C19—22no—
19C2×D8×C19—22no—
20C2×M16×C19D412yes—
21C19×C4⋊Q8D412yes—
22C19×#127D412yes—
23C19×#124—22no—
24C19×#121—22no—
25C19×#121—22no—
26C4×D4×C19—22no—
27C4×D4×C19—22no—
28C2×C42×C19C2311yescharacteristic
29C2×#64520—21no—
30C22×C19⋊C8—21no—
31C19×#106—22no—
32C19×C4⋊C8—22no—
33C19×#102—24no—
34C22⋊(C19⋊C8)—22no—
35C4⋊(C19⋊C8)—22no—
36C4⋊(C19⋊C8)—22no—
37#10597260—21no—
38#10597260—22no—
39#10597260D412yes—
40#41×C19—84no—
41C2×Q8×C19—22no—
42C2×D4×C19—22no—
43C2×D4×C19—22no—
44C2×D4×C19—22no—
45C2×D4×C19—42no—
46C22×C4×C19—42no—
47C22×C4×C19C2×D411yescharacteristic
48C22×C4×C19#4112yes—
49D8×C19—82no—
50M16×C19—42no—
51C2×C8×C19—22no—
52C4⋊C4×C19—22no—
53C4⋊C4×C19—22no—
54C22⋊C4×C19—42no—
55C22⋊C4×C19—42no—
56C42×C19C2×D411yescharacteristic
57C42×C19C2×D412yes—
58C42×C19#4111yescharacteristic
59#64520—42no—
60C2×C19⋊C8—22no—
61C2×C19⋊C8—41no—
62C2×C19⋊C8—41no—
63C2×C19⋊C8—41no—
64C2×C19⋊C8—42no—
65#10525—191nomaximal, Sylow
66C23×C19—42no—
67C23×C19#12411yescharacteristic
68Q8×C19—82no—
69D4×C19—42no—
70D4×C19—42no—
71D4×C19—82no—
72D4×C19—82no—
73D4×C19—84no—
74C2×C4×C19—21no—
75C2×C4×C19—21no—
76C2×C4×C19—42no—
77C2×C4×C19—42no—
78C2×C4×C19—84no—
79C2×C4×C19#12011yescharacteristic
80C2×C4×C19#12111yescharacteristic
81C2×C4×C19#12112yes—
82C2×C4×C19#12312yes—
83C8×C19—42no—
84C19⋊C8—42no—
85C19⋊C8—82no—
86C19⋊C8—81no—
87#3253D1911yescharacteristic
88#1838—191no—
89#1557—192no—
90#1530—192no—
91#1307—191no—
92C22×C19—22no—
93C22×C19—21no—
94C22×C19—82no—
95C22×C19—82no—
96C22×C19—82no—
97C22×C19#39411yescharacteristic
98C4×C19—22no—
99C4×C19—22no—
100C4×C19—21no—
101C4×C19—82no—
102C4×C19#45411yescharacteristic
103C4×C19#45511yescharacteristic
104#532C2×D1912yes—
105#476—22no—
106#469—22no—
107#459—22no—
108#432—192no—
109#423—191no—
110#423C2×D1911yescharacteristic
111C2×#97—191no—
112#341—382no—
113#332—382no—
114#331—382no—
115#329—384no—
116C2×C19—41no—
117C2×C19—162no—
118C2×C19#204011yescharacteristic
119C2×C19#204812yes—
120C2×#41—22no—
121C2×D8—22no—
122C2×M16—381no—
123C2×M16C22⋊D1912yes—
124C22×C8—381no—
125C4⋊Q8C22⋊D1912yes—
126#127C22⋊D1912yes—
127#124—22no—
128#121—22no—
129#121—22no—
130C4×D4—22no—
131C4×D4—22no—
132C2×C42C22×D1911yescharacteristic
133#106—22no—
134C4⋊C8—22no—
135C4⋊C8—382no—
136C4⋊C8—382no—
137#102—24no—
138C22⋊C8—382no—
139#97—192no—
140#97—382no—
141#97—381no—
142C19#1052511yescharacteristic, complemented, Sylow
143#41—84no—
144C2×Q8—22no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—22no—
148C2×D4—42no—
149C22×C4—42no—
150C22×C4#6454312yes—
151C22×C4C2×C22⋊D1911yescharacteristic
152D8—82no—
153M16—42no—
154M16—762no—
155C2×C8—22no—
156C2×C8—382no—
157C2×C8—761no—
158C2×C8—761no—
159C2×C8—762no—
160C2×C8—761no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C22⋊C4—42no—
164C22⋊C4—42no—
165C42D4×D1911yescharacteristic
166C42#6454311yescharacteristic
167C42C2×C22⋊D1912yes—
168C23—42no—
169C23#1059738211yescharacteristic
170Q8—82no—
171D4—42no—
172D4—42no—
173D4—82no—
174D4—82no—
175D4—84no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—84no—
181C2×C4#1059738112yes—
182C2×C4#1059738411yescharacteristic
183C2×C4#1059738512yes—
184C2×C4#1059739911yescharacteristic
185C8—42no—
186C8—762no—
187C8—1522no—
188C8—1521no—
189C22—22no—
190C22—21no—
191C22—82no—
192C22—82no—
193C22—82no—
194C22#1192645811yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—82no—
199C4#1192671711yescharacteristic
200C4#1192672211yescharacteristic
201C2—41no—
202C2—162no—
203C2#1456486111yescharacteristic
204C2#1456490512yes—
subgroupG/H
centerC22#11926458
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3253C2
socleC22×C19#394
hypercenter#3253D19
hypocenterC19#10525
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #14563775C2semidirect
2. #14562357C2semidirect
3. #14562246C2semidirect
4. #14561546C2semidirect
142. C19#10525semidirect

Maximal subgroups

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

subgroupindex
#145637752
#145623572
#145622462
#145615462
C19×#32532
#1052519