Finite Group Databasebeta

← #18070068

Subgroups — #18070068

Order 4864.

268 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 41 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#14564681C211yesmaximal, characteristic
2#14561762C211yesmaximal, characteristic, complemented
3C19×#1272C211yesmaximal, characteristic, complemented
4C2×#10597388—21no—
5#11927125C411yescharacteristic
6C2×#10597262—21no—
7C2×#10597293—21no—
8#11926313C411yescharacteristic
9C19×#391C2211yescharacteristic
10C19×#336—21no—
11C22×Q8×C19D411yescharacteristic
12C2×#64541—21no—
13C22×C8×C19—41no—
14C2×C4⋊C4×C19C2×C411yescharacteristic
15C2×C42×C19D411yescharacteristic
16C2×#64528—41no—
17#10597388—42no—
18#10597388—41no—
19#10597388—41no—
20C2×#64527—41no—
21#10597376—41no—
22C2×#64520—21no—
23C2×#64520—41no—
24#10597343—41no—
25#10597341—41no—
26C19×#95—41no—
27#10597293—22no—
28#10597293—41no—
29#10597262—42no—
30C2×Q8×C19—21no—
31C2×Q8×C19—41no—
32C2×Q8×C19—41no—
33C2×Q8×C19D811yescharacteristic
34C2×Q8×C19SD1611yescharacteristic
35C22×C4×C19—21no—
36C22×C4×C19—21no—
37C22×C4×C19—21no—
38C22×C4×C19C22⋊C411yescharacteristic
39C2×C22⋊D19—41no—
40#64541—41no—
41#64541—41no—
42#64541—41no—
43#64541—41no—
44C2×D76—21no—
45C2×D76—41no—
46C2×C4×D19—41no—
47C2×Dic38—21no—
48C2×C8×C19—42no—
49C2×C8×C19—81no—
50C2×C8×C19—81no—
51C4⋊C4×C19—41no—
52C42×C19—41no—
53#64528—42no—
54#64528—42no—
55#64527—42no—
56#64527—42no—
57(C2×D19)⋊C4—42no—
58C4⋊Dic19—41no—
59#64520—22no—
60#64520—41no—
61#64520—42no—
62#64520—81no—
63C2×C19⋊C8—41no—
64C2×C19⋊C8—81no—
65#7409—191nomaximal, Sylow
66C23×C19#9911yescharacteristic
67C22×D19—41no—
68Q8×C19—41no—
69Q8×C19—41no—
70Q8×C19—81no—
71C2×C4×C19—21no—
72C2×C4×C19—21no—
73C2×C4×C19—21no—
74C2×C4×C19—21no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—41no—
78C2×C4×C19—41no—
79C2×C4×C19—41no—
80C2×C4×C19—41no—
81C2×C4×C19—41no—
82C2×C4×C19—81no—
83C2×C4×C19#10211yescharacteristic
84C2×C4×C19#10411yescharacteristic
85C22⋊D19—81no—
86C22⋊D19—81no—
87C2×Dic19—41no—
88D76—41no—
89D76—41no—
90D76—161no—
91C4×D19—81no—
92C4×D19—81no—
93Dic38—41no—
94Dic38—41no—
95C8×C19—82no—
96C19⋊C8—42no—
97C19⋊C8—82no—
98#2007—191no—
99#1394—191no—
100#1272D1911yescharacteristic, complemented
101C22×C19—21no—
102C22×C19—21no—
103C22×C19#32711yescharacteristic
104C22×C19AΣL(1,𝔽16)11yescharacteristic
105C22×C19#35311yescharacteristic
106C2×D19—81no—
107C2×D19—81no—
108C2×D19—81no—
109C4×C19—21no—
110C4×C19—21no—
111C4×C19—41no—
112C4×C19—41no—
113C4×C19—41no—
114C4×C19—41no—
115C4×C19—81no—
116Dic19—81no—
117C2×#137—381no—
118#537—191no—
119C2×#104—381no—
120C2×#101—381no—
121#391C2×D1911yescharacteristic
122#343—191no—
123#336—21no—
124C2×C19—21no—
125C2×C19—21no—
126C2×C19#134311yescharacteristic
127C2×C19#140311yescharacteristic
128C2×C19#140511yescharacteristic
129D19—161no—
130C2×#41—381no—
131C22×Q8D7611yescharacteristic
132#137—762no—
133#137—761no—
134#137—761no—
135C2×Q16—761no—
136C2×SD16—761no—
137C2×M16—381no—
138C2×M16—761no—
139C22×C8—41no—
140C22⋊Q8—761no—
141#121—761no—
142#121—761no—
143C2×C4⋊C4C4×D1911yescharacteristic
144C2×C42C22⋊D1911yescharacteristic
145#104—762no—
146#101—382no—
147#101—761no—
148#95—41no—
149C19#740911yescharacteristic, complemented, Sylow
150#41—761no—
151#41—761no—
152#41—761no—
153#41—761no—
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—381no—
158C2×Q8#6451611yescharacteristic
159C2×Q8D15211yescharacteristic
160C2×D4—381no—
161C2×D4—761no—
162C2×D4—761no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—761no—
167C22×C4(C2×D19)⋊C411yescharacteristic
168Q16—762no—
169Q16—762no—
170SD16—762no—
171SD16—762no—
172M16—382no—
173M16—761no—
174M16—762no—
175M16—1521no—
176C2×C8—42no—
177C2×C8—81no—
178C2×C8—81no—
179C2×C8—761no—
180C2×C8—1521no—
181C4⋊C4—41no—
182C4⋊C4—761no—
183C22⋊C4—762no—
184C42—41no—
185C23—761no—
186C23#1059726311yescharacteristic
187Q8—41no—
188Q8—41no—
189Q8—81no—
190Q8—761no—
191Q8—761no—
192D4—3041no—
193D4—761no—
194D4—761no—
195D4—1521no—
196D4—1521no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—81no—
209C2×C4—761no—
210C2×C4—1521no—
211C2×C4—1521no—
212C2×C4#1059727811yescharacteristic
213C2×C4#1059728211yescharacteristic
214C8—82no—
215C8—762no—
216C8—1522no—
217C22—21no—
218C22—21no—
219C22—1521no—
220C22—1521no—
221C22—1521no—
222C22#1192627911yescharacteristic
223C22#1192633211yescharacteristic
224C22#1192633611yescharacteristic
225C4—21no—
226C4—21no—
227C4—41no—
228C4—41no—
229C4—41no—
230C4—41no—
231C4—81no—
232C4—1521no—
233C2—21no—
234C2—21no—
235C2—3041no—
236C2#1456163311yescharacteristic
237C2#1456178411yescharacteristic
238C2#1456179011yescharacteristic
subgroupG/H
centerC22#11926332
commutatorC2×C4⋊C4×C19C2×C4
Frattini#391C2×D19
FittingC19×#1272C2
socleC22×C19AΣL(1,𝔽16)
prime radical#11927125C4
cosocleC19×#391C22
hypercenter#1272D19
hypocenterC19#7409
LCSG ▷ C2×C4⋊C4×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #14561762C2semidirect
3. C19×#1272C2semidirect
100. #1272D19semidirect
149. C19#7409semidirect

Maximal subgroups

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

subgroupindex
#145646812
#145617622
C19×#12722
#740919