Finite Group Databasebeta

← #18070032

Subgroups — #18070032

Order 4864.

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

normal subgroups only

This group has 268 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#14561522C211yesmaximal, characteristic, complemented
3C19×#1320C211yesmaximal, characteristic, complemented
4#11927344C411yescharacteristic
5#11927055—21no—
6#11926560—21no—
7C2×C22⋊(C19⋊C8)—21no—
8#11926301C411yescharacteristic
9C19×#407C2211yescharacteristic
10C19×#349—21no—
11C23×C4×C19D411yescharacteristic
12C2×#64541—21no—
13C2×M16×C19C2×C411yescharacteristic
14C2×M16×C19D411yescharacteristic
15#10597399—41no—
16#10597376—41no—
17#10597375—41no—
18C4×C22⋊D19—42no—
19#10597372—21no—
20#10597370—41no—
21C22×C19⋊C8—41no—
22#10597355—41no—
23#10597354—41no—
24#10597350—41no—
25C19×M32—41no—
26C19×C22⋊C8—41no—
27C22⋊(C19⋊C8)—22no—
28C22⋊(C19⋊C8)—41no—
29#10597282—42no—
30C24×C19SD1611yescharacteristic
31C22×C4×C19—21no—
32C22×C4×C19—21no—
33C22×C4×C19—41no—
34C22×C4×C19—41no—
35C22×C4×C19C22⋊C411yescharacteristic
36C22×C4×C19D811yescharacteristic
37C2×C22⋊D19—42no—
38C2×C22⋊D19—41no—
39#64541—41no—
40#64541—41no—
41#64541—41no—
42#64541—41no—
43C2×D76—21no—
44C2×C4×D19—41no—
45C2×Dic38—21no—
46M16×C19—41no—
47M16×C19—41no—
48C2×C8×C19—21no—
49C2×C8×C19—21no—
50C22⋊Dic19—42no—
51C22⋊Dic19—41no—
52(C2×D19)⋊C4—42no—
53C4⋊Dic19—41no—
54Dic19⋊C4—42no—
55C4×Dic19—22no—
56C2×C19⋊C8—42no—
57C2×C19⋊C8—81no—
58C2×C19⋊C8—81no—
59Dic76—41no—
60D152—41no—
61#64516—42no—
62C16×C19—81no—
63#7397—191nomaximal, Sylow
64C23×C19—21no—
65C23×C19—41no—
66C23×C19—42no—
67C23×C19#10211yescharacteristic
68C22×D19—41no—
69C2×C4×C19—21no—
70C2×C4×C19—21no—
71C2×C4×C19—21no—
72C2×C4×C19—41no—
73C2×C4×C19—41no—
74C2×C4×C19—41no—
75C2×C4×C19—81no—
76C2×C4×C19#9911yescharacteristic
77C2×C4×C19#10411yescharacteristic
78C22⋊D19—81no—
79C22⋊D19—84no—
80C22⋊D19—81no—
81C2×Dic19—42no—
82C2×Dic19—41no—
83D76—41no—
84D76—41no—
85C4×D19—81no—
86C4×D19—81no—
87Dic38—41no—
88Dic38—41no—
89C8×C19—41no—
90C8×C19—41no—
91C19⋊C8—82no—
92#2010—191no—
93#1320D1911yescharacteristic, complemented
94#1298—191no—
95C22×C19—22no—
96C22×C19—21no—
97C22×C19—41no—
98C22×C19—41no—
99C22×C19—42no—
100C22×C19—41no—
101C22×C19—81no—
102C22×C19#32711yescharacteristic
103C2×D19—82no—
104C2×D19—81no—
105C4×C19—21no—
106C4×C19—41no—
107C4×C19AΣL(1,𝔽16)11yescharacteristic
108C4×C19#35311yescharacteristic
109Dic19—82no—
110Dic19—81no—
111#575—191no—
112#525—381no—
113#421—381no—
114#407C2×D1911yescharacteristic
115C2×C22⋊C8—381no—
116#349—21no—
117H(3,ℤ/4)—191no—
118C2×C19—21no—
119C2×C19—41no—
120C2×C19—42no—
121C2×C19#134311yescharacteristic
122D19—161no—
123C2×#41—381no—
124C23×C4D7611yescharacteristic
125#137—761no—
126AGL(1,ℤ/8)—761no—
127#135—761no—
128C2×M16C4×D1911yescharacteristic
129C2×M16C22⋊D1911yescharacteristic
130C22×C8—761no—
131#123—761no—
132C22⋊Q8—761no—
133#121—761no—
134#120—761no—
135C4×D4—762no—
136#117—381no—
137M32—41no—
138#104—762no—
139C22⋊C8—41no—
140C22⋊C8—382no—
141C22⋊C8—761no—
142C19#739711yescharacteristic, complemented, Sylow
143C24#6451611yescharacteristic
144#41—761no—
145#41—761no—
146#41—761no—
147#41—761no—
148C2×Q8—381no—
149C2×D4—381no—
150C2×D4—762no—
151C2×D4—761no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—761no—
157C22×C4D15211yescharacteristic
158C22×C4(C2×D19)⋊C411yescharacteristic
159Q16—761no—
160SD16—762no—
161D8—761no—
162M16—41no—
163M16—41no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—762no—
167C2×C8—1521no—
168C2×C8—1521no—
169C4⋊C4—761no—
170C4⋊C4—762no—
171C22⋊C4—762no—
172C22⋊C4—762no—
173C22⋊C4—761no—
174C42—382no—
175C16—81no—
176C23—21no—
177C23—41no—
178C23—42no—
179C23—761no—
180C23#1059727811yescharacteristic
181Q8—761no—
182Q8—761no—
183D4—761no—
184D4—761no—
185D4—1521no—
186D4—1524no—
187D4—1521no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—762no—
196C2×C4—761no—
197C2×C4—1521no—
198C2×C4—1521no—
199C2×C4#1059726311yescharacteristic
200C2×C4#1059728211yescharacteristic
201C8—41no—
202C8—41no—
203C8—1522no—
204C22—22no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—41no—
210C22—81no—
211C22—1522no—
212C22—1521no—
213C22#1192627911yescharacteristic
214C4—21no—
215C4—41no—
216C4—1522no—
217C4—1521no—
218C4#1192633211yescharacteristic
219C4#1192633611yescharacteristic
220C2—21no—
221C2—41no—
222C2—42no—
223C2—3041no—
224C2#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#7397
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. #14561522C2semidirect
3. C19×#1320C2semidirect
93. #1320D19semidirect
142. C19#7397semidirect

Maximal subgroups

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

subgroupindex
#145647022
#145615222
C19×#13202
#739719