Finite Group Databasebeta

← #18070029

Subgroups — #18070029

Order 4864.

296 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 37 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#14564702C211yesmaximal, characteristic
2#14561520C211yesmaximal, characteristic, complemented
3C19×#1320C211yesmaximal, characteristic, complemented
4#11927344C411yescharacteristic, complemented
5#11927055—21no—
6#11926560—21no—
7C4×C22⋊Dic19—21no—
8#11926301C411yescharacteristic, complemented
9C19×#407C2211yescharacteristic
10C19×#349—21no—
11C23×C4×C19D411yescharacteristic
12C2×#64541—21no—
13C2×M16×C19C2×C411yescharacteristic
14C2×M16×C19D411yescharacteristic
15#10597399—41no—
16C2×C22⋊Dic19—41no—
17#10597376—41no—
18#10597375—41no—
19C4×C22⋊D19—42no—
20#10597372—21no—
21#10597370—41no—
22C2×C4×Dic19—41no—
23#10597355—41no—
24#10597354—41no—
25#10597350—41no—
26C19×M32—41no—
27C19×C22⋊C8—41no—
28C19⋊#95—22no—
29#10597282—42no—
30C24×C19D811yescharacteristic
31C22×C4×C19—21no—
32C22×C4×C19—21no—
33C22×C4×C19—41no—
34C22×C4×C19—41no—
35C22×C4×C19C22⋊C411yescharacteristic
36C22×C4×C19SD1611yescharacteristic
37C2×C22⋊D19—42no—
38C2×C22⋊D19—41no—
39C22×Dic19—42no—
40#64541—41no—
41#64541—41no—
42#64541—41no—
43#64541—41no—
44C2×D76—21no—
45C2×C4×D19—41no—
46C2×Dic38—21no—
47M16×C19—41no—
48M16×C19—41no—
49C2×C8×C19—21no—
50C2×C8×C19—21no—
51C22⋊Dic19—44no—
52C22⋊Dic19—42no—
53C22⋊Dic19—41no—
54(C2×D19)⋊C4—42no—
55C4⋊Dic19—41no—
56Dic19⋊C4—42no—
57C4×Dic19—22no—
58C4×Dic19—81no—
59C4×Dic19—81no—
60Dic76—41no—
61D152—41no—
62#64516—42no—
63C16×C19—81no—
64#7396—191nomaximal, Sylow
65C23×C19—21no—
66C23×C19—41no—
67C23×C19—42no—
68C23×C19#10211yescharacteristic
69C22×D19—41no—
70C2×C4×C19—21no—
71C2×C4×C19—21no—
72C2×C4×C19—21no—
73C2×C4×C19—41no—
74C2×C4×C19—41no—
75C2×C4×C19—41no—
76C2×C4×C19—81no—
77C2×C4×C19#9911yescharacteristic
78C2×C4×C19#10411yescharacteristic
79C22⋊D19—81no—
80C22⋊D19—84no—
81C22⋊D19—81no—
82C2×Dic19—42no—
83C2×Dic19—41no—
84C2×Dic19—44no—
85C2×Dic19—82no—
86C2×Dic19—82no—
87D76—41no—
88D76—41no—
89C4×D19—81no—
90C4×D19—81no—
91Dic38—41no—
92Dic38—41no—
93C8×C19—41no—
94C8×C19—41no—
95#2010—191no—
96#1320D1911yescharacteristic, complemented
97#1297—191no—
98C22×C19—22no—
99C22×C19—21no—
100C22×C19—41no—
101C22×C19—41no—
102C22×C19—42no—
103C22×C19—41no—
104C22×C19—81no—
105C22×C19#32711yescharacteristic
106C2×D19—82no—
107C2×D19—81no—
108C4×C19—21no—
109C4×C19—41no—
110C4×C19AΣL(1,𝔽16)11yescharacteristic
111C4×C19#35311yescharacteristic
112Dic19—84no—
113Dic19—82no—
114Dic19—81no—
115#575—191no—
116#525—381no—
117#421—381no—
118#407C2×D1911yescharacteristic
119C4×C22⋊C4—381no—
120#349—21no—
121H(3,ℤ/4)—191no—
122C2×C19—21no—
123C2×C19—41no—
124C2×C19—42no—
125C2×C19#134311yescharacteristic
126D19—161no—
127C2×#41—381no—
128C23×C4D7611yescharacteristic
129#137—761no—
130AGL(1,ℤ/8)—761no—
131#135—761no—
132C2×M16C4×D1911yescharacteristic
133C2×M16C22⋊D1911yescharacteristic
134#123—761no—
135C22⋊Q8—761no—
136#121—761no—
137#120—761no—
138C4×D4—762no—
139#117—381no—
140C2×C22⋊C4—761no—
141C2×C42—761no—
142M32—41no—
143#104—762no—
144C22⋊C8—41no—
145#95—382no—
146C19#739611yescharacteristic, complemented, Sylow
147C24D15211yescharacteristic
148#41—761no—
149#41—761no—
150#41—761no—
151#41—761no—
152C2×Q8—381no—
153C2×D4—381no—
154C2×D4—762no—
155C2×D4—761no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—761no—
161C22×C4—762no—
162C22×C4#6451611yescharacteristic
163C22×C4(C2×D19)⋊C411yescharacteristic
164Q16—761no—
165SD16—762no—
166D8—761no—
167M16—41no—
168M16—41no—
169C2×C8—21no—
170C2×C8—21no—
171C4⋊C4—761no—
172C4⋊C4—762no—
173C22⋊C4—762no—
174C22⋊C4—764no—
175C22⋊C4—762no—
176C22⋊C4—761no—
177C42—382no—
178C42—1521no—
179C42—1521no—
180C16—81no—
181C23—21no—
182C23—41no—
183C23—42no—
184C23—761no—
185C23#1059727811yescharacteristic
186Q8—761no—
187Q8—761no—
188D4—761no—
189D4—761no—
190D4—1521no—
191D4—1524no—
192D4—1521no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—81no—
200C2×C4—762no—
201C2×C4—761no—
202C2×C4—764no—
203C2×C4—1521no—
204C2×C4—1522no—
205C2×C4—1522no—
206C2×C4—1521no—
207C2×C4#1059726311yescharacteristic
208C2×C4#1059728211yescharacteristic
209C8—41no—
210C8—41no—
211C22—22no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—42no—
216C22—41no—
217C22—81no—
218C22—1522no—
219C22—1521no—
220C22#1192627911yescharacteristic
221C4—21no—
222C4—41no—
223C4—1524no—
224C4—1522no—
225C4—1521no—
226C4#1192633211yescharacteristic
227C4#1192633611yescharacteristic
228C2—21no—
229C2—41no—
230C2—42no—
231C2—3041no—
232C2#1456163311yescharacteristic
subgroupG/H
centerC4#11926336
commutatorC2×M16×C19C2×C4
Frattini#407C2×D19
FittingC19×#1320C2
socleC2×C19#1343
prime radical#14564702C2
cosocleC19×#407C22
hypercenter#1320D19
hypocenterC19#7396
LCSG ▷ C2×M16×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #407 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #14561520C2semidirect
3. C19×#1320C2semidirect
4. #11927344C4semidirect
8. #11926301C4semidirect
96. #1320D19semidirect
146. C19#7396semidirect

Maximal subgroups

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

subgroupindex
#145647022
#145615202
C19×#13202
#739619