Finite Group Databasebeta

← #18069243

Subgroups — #18069243

Order 4864.

264 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 45 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#14564645C211yesmaximal, characteristic
2#14561512C211yesmaximal, characteristic
3C19×#1314C211yesmaximal, characteristic
4C22×Dic76C411yescharacteristic
5C2×#10597370—21no—
6C2×#10597273—21no—
7#11926508—21no—
8#11926307C411yescharacteristic
9C2×C19×C22⋊C8C2211yescharacteristic
10C19×C22⋊C16—21no—
11C23×C4×C19D411yescharacteristic
12C22×Dic38—21no—
13C22×C8×C19C2×C411yescharacteristic
14C22×C8×C19D411yescharacteristic
15C2×C22⋊Dic19—41no—
16C2×C4⋊Dic19—21no—
17#10597370—42no—
18#10597370—42no—
19C2×Dic19⋊C4—41no—
20C2×#64520—41no—
21C2×Dic76—41no—
22C2×Dic76—42no—
23C2×C16×C19—41no—
24C19×C22⋊C8—41no—
25C22⋊(C19⋊C8)—22no—
26C22⋊(C19⋊C8)—41no—
27#10597273—42no—
28C24×C19SD1611yescharacteristic
29C22×C4×C19—21no—
30C22×C4×C19—21no—
31C22×C4×C19—41no—
32C22×C4×C19—41no—
33C22×C4×C19C22⋊C411yescharacteristic
34C22×C4×C19D811yescharacteristic
35C22×Dic19—41no—
36C22×Dic19—41no—
37C2×Dic38—22no—
38C2×Dic38—41no—
39C2×Dic38—41no—
40C2×Dic38—41no—
41C2×Dic38—41no—
42C2×Dic38—41no—
43C2×C8×C19—21no—
44C2×C8×C19—21no—
45C2×C8×C19—41no—
46C2×C8×C19—41no—
47C22⋊Dic19—44no—
48C4⋊Dic19—22no—
49C4⋊Dic19—41no—
50Dic19⋊C4—44no—
51#64520—81no—
52#64520—81no—
53C2×C19⋊C8—42no—
54Dic76—42no—
55Dic76—42no—
56C16×C19—81no—
57#7086—191nomaximal, Sylow
58C23×C19—21no—
59C23×C19—21no—
60C23×C19—21no—
61C23×C19—41no—
62C23×C19—41no—
63C23×C19#10211yescharacteristic
64C2×C4×C19—21no—
65C2×C4×C19—21no—
66C2×C4×C19—21no—
67C2×C4×C19—41no—
68C2×C4×C19—41no—
69C2×C4×C19—41no—
70C2×C4×C19—81no—
71C2×C4×C19#9911yescharacteristic
72C2×C4×C19#10411yescharacteristic
73C2×Dic19—42no—
74C2×Dic19—42no—
75C2×Dic19—81no—
76C2×Dic19—81no—
77C2×Dic19—81no—
78C2×Dic19—81no—
79Dic38—42no—
80Dic38—42no—
81Dic38—81no—
82Dic38—81no—
83C8×C19—41no—
84C8×C19—41no—
85C19⋊C8—82no—
86#2001—191no—
87#1314D1911yescharacteristic
88#1293—191no—
89C22×C19—21no—
90C22×C19—21no—
91C22×C19—42no—
92C22×C19—41no—
93C22×C19—41no—
94C22×C19—41no—
95C22×C19—81no—
96C22×C19#32711yescharacteristic
97C22×C19#35911yescharacteristic
98C22×C19#36211yescharacteristic
99C4×C19—21no—
100C4×C19—41no—
101C4×C19AΣL(1,𝔽16)11yescharacteristic
102C4×C19#35311yescharacteristic
103Dic19—82no—
104Dic19—82no—
105C22×Q16—191no—
106C2×C22⋊Q8—381no—
107C2×#103—381no—
108#407—381no—
109C2×C22⋊C8C2×D1911yescharacteristic
110C22⋊C16—21no—
111#340—191no—
112C2×C19—21no—
113C2×C19—21no—
114C2×C19—81no—
115C2×C19#134211yescharacteristic
116C2×C19#134311yescharacteristic
117C2×C19#135011yescharacteristic
118C22×Q8—381no—
119C23×C4D7611yescharacteristic
120C2×Q16—761no—
121C2×Q16—762no—
122C2×M16—761no—
123C22×C8C4×D1911yescharacteristic
124C22×C8C22⋊D1911yescharacteristic
125C22⋊Q8—762no—
126C22⋊Q8—762no—
127C2×C4⋊C4—381no—
128C2×C4⋊C4—761no—
129C2×C22⋊C4—761no—
130C2×C16—41no—
131#103—762no—
132C22⋊C8—41no—
133C22⋊C8—382no—
134C22⋊C8—761no—
135C19#708611yescharacteristic, complemented, Sylow
136C24#6451611yescharacteristic
137C2×Q8—382no—
138C2×Q8—761no—
139C2×Q8—761no—
140C2×Q8—761no—
141C2×Q8—761no—
142C2×Q8—761no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—761no—
148C22×C4—761no—
149C22×C4D15211yescharacteristic
150C22×C4(C2×D19)⋊C411yescharacteristic
151Q16—762no—
152Q16—762no—
153M16—1521no—
154M16—1521no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—762no—
160C4⋊C4—382no—
161C4⋊C4—761no—
162C4⋊C4—764no—
163C22⋊C4—764no—
164C16—81no—
165C23—21no—
166C23—21no—
167C23—21no—
168C23—41no—
169C23—41no—
170C23#1059727811yescharacteristic
171Q8—762no—
172Q8—762no—
173Q8—1521no—
174Q8—1521no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—81no—
182C2×C4—762no—
183C2×C4—762no—
184C2×C4—1521no—
185C2×C4—1521no—
186C2×C4—1521no—
187C2×C4—1521no—
188C2×C4#1059726311yescharacteristic
189C2×C4#1059728211yescharacteristic
190C8—41no—
191C8—41no—
192C8—1522no—
193C22—21no—
194C22—21no—
195C22—42no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—81no—
200C22#1192627911yescharacteristic
201C22#1192635211yescharacteristic
202C22#1192636111yescharacteristic
203C4—21no—
204C4—41no—
205C4—1522no—
206C4—1522no—
207C4#1192633211yescharacteristic
208C4#1192633611yescharacteristic
209C2—21no—
210C2—21no—
211C2—81no—
212C2#1456163011yescharacteristic
213C2#1456163311yescharacteristic
214C2#1456165411yescharacteristic
subgroupG/H
centerC22#11926279
commutatorC22×C8×C19C2×C4
FrattiniC2×C22⋊C8C2×D19
FittingC19×#1314C2
socleC22×C19#327
prime radicalC24×C19SD16
cosocleC2×C19×C22⋊C8C22
hypercenter#1314D19
hypocenterC19#7086
LCSG ▷ C22×C8×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
135. C19#7086semidirect

Maximal subgroups

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

subgroupindex
#145646452
#145615122
C19×#13142
#708619