Finite Group Databasebeta

← #18070062

Subgroups — #18070062

Order 4864.

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

normal subgroups only

This group has 240 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#14564739C211yesmaximal, characteristic
2#14561758C211yesmaximal, characteristic, complemented
3C19×#1315C211yesmaximal, characteristic, complemented
4#11927344C411yescharacteristic
5#11927342—21no—
6#11926528—21no—
7#11926510—21no—
8C19⋊#338C411yescharacteristic
9C19×#408C2211yescharacteristic
10C19×C22⋊C16—21no—
11C2×#41×C19D411yescharacteristic
12C2×#64541—21no—
13C2×M16×C19C2×C411yescharacteristic
14C22×C8×C19D411yescharacteristic
15#10597397—41no—
16#10597396—42no—
17#10597395—41no—
18#10597388—41no—
19#10597378—41no—
20C2×#64520—21no—
21C2×#64520—41no—
22#10597355—41no—
23#10597354—41no—
24#10597350—41no—
25C2×C16×C19—41no—
26C19×C22⋊C8—41no—
27#10597293—41no—
28#10597290—22no—
29(C2×D19)⋊C8—42no—
30#41×C19—41no—
31#41×C19—41no—
32C2×Q8×C19D811yescharacteristic
33C2×D4×C19—21no—
34C2×D4×C19SD1611yescharacteristic
35C22×C4×C19—21no—
36C22×C4×C19C22⋊C411yescharacteristic
37C2×C22⋊D19—41no—
38#64541—41no—
39#64541—41no—
40#64541—41no—
41#64541—41no—
42C2×D76—21no—
43C2×C4×D19—41no—
44C2×Dic38—21no—
45M16×C19—41no—
46C2×C8×C19—21no—
47C2×C8×C19—21no—
48C2×C8×C19—41no—
49#64528—42no—
50#64527—42no—
51#64526—42no—
52#64525—42no—
53#64520—41no—
54#64520—41no—
55#64520—42no—
56#64520—81no—
57C2×C19⋊C8—22no—
58C2×C19⋊C8—81no—
59Dic76—41no—
60D152—41no—
61#64516—42no—
62C16×C19—81no—
63#7407—191nomaximal, Sylow
64C23×C19—21no—
65C23×C19#10411yescharacteristic
66C22×D19—41no—
67Q8×C19—41no—
68D4×C19—41no—
69D4×C19—81no—
70C2×C4×C19—21no—
71C2×C4×C19—21no—
72C2×C4×C19—21no—
73C2×C4×C19—41no—
74C2×C4×C19—41no—
75C2×C4×C19#9911yescharacteristic
76C2×C4×C19#10211yescharacteristic
77C22⋊D19—81no—
78C22⋊D19—81no—
79C2×Dic19—41no—
80D76—41no—
81D76—41no—
82C4×D19—81no—
83C4×D19—81no—
84Dic38—41no—
85Dic38—41no—
86C8×C19—41no—
87C8×C19—41no—
88C19⋊C8—42no—
89C19⋊C8—82no—
90#2017—191no—
91#1392—191no—
92#1315D1911yescharacteristic, complemented
93C22×C19—21no—
94C22×C19—41no—
95C22×C19—41no—
96C22×C19—81no—
97C22×C19#32711yescharacteristic
98C2×D19—82no—
99C2×D19—81no—
100C4×C19—21no—
101C4×C19—41no—
102C4×C19AΣL(1,𝔽16)11yescharacteristic
103C4×C19#35311yescharacteristic
104Dic19—81no—
105#575—191no—
106#575—381no—
107#413—381no—
108#408—381no—
109#408C2×D1911yescharacteristic
110C22⋊C16—21no—
111#338—191no—
112C2×C19—21no—
113C2×C19—41no—
114C2×C19—81no—
115C2×C19#134311yescharacteristic
116D19—161no—
117C2×#41—381no—
118C2×#41D7611yescharacteristic
119#137—761no—
120#137—761no—
121#137—761no—
122AGL(1,ℤ/8)—761no—
123AGL(1,ℤ/8)—761no—
124AGL(1,ℤ/8)—761no—
125#135—761no—
126#135—762no—
127C2×M16—381no—
128C2×M16—761no—
129C2×M16C4×D1911yescharacteristic
130C22×C8C22⋊D1911yescharacteristic
131C2×C16—41no—
132#101—761no—
133#100—382no—
134C22⋊C8—41no—
135C22⋊C8—762no—
136C19#740711yescharacteristic, complemented, Sylow
137#41—41no—
138#41—41no—
139#41—761no—
140#41—761no—
141#41—761no—
142#41—761no—
143C2×Q8—381no—
144C2×Q8D15211yescharacteristic
145C2×D4—21no—
146C2×D4—381no—
147C2×D4—761no—
148C2×D4#6451611yescharacteristic
149C22×C4—21no—
150C22×C4—761no—
151C22×C4(C2×D19)⋊C411yescharacteristic
152Q16—761no—
153Q16—762no—
154SD16—762no—
155SD16—762no—
156SD16—762no—
157D8—761no—
158D8—762no—
159M16—41no—
160M16—761no—
161M16—761no—
162M16—762no—
163M16—1521no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—41no—
167C2×C8—382no—
168C2×C8—1521no—
169C16—81no—
170C23—21no—
171C23—761no—
172C23#1059728211yescharacteristic
173Q8—41no—
174Q8—761no—
175Q8—761no—
176D4—41no—
177D4—81no—
178D4—761no—
179D4—761no—
180D4—1521no—
181D4—1521no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—761no—
188C2×C4—1521no—
189C2×C4—1521no—
190C2×C4#1059726311yescharacteristic
191C2×C4#1059727811yescharacteristic
192C8—41no—
193C8—41no—
194C8—762no—
195C8—1522no—
196C22—21no—
197C22—41no—
198C22—41no—
199C22—81no—
200C22—1522no—
201C22—1521no—
202C22#1192627911yescharacteristic
203C4—21no—
204C4—41no—
205C4—1521no—
206C4#1192633211yescharacteristic
207C4#1192633611yescharacteristic
208C2—21no—
209C2—41no—
210C2—81no—
211C2—3041no—
212C2#1456163311yescharacteristic
subgroupG/H
centerC4#11926336
commutatorC2×M16×C19C2×C4
Frattini#408C2×D19
FittingC19×#1315C2
socleC2×C19#1343
prime radical#14564739C2
cosocleC19×#408C22
hypercenter#1315D19
hypocenterC19#7407
LCSG ▷ C2×M16×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ #1315

Complements

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

NH ≅ G/Ntype
2. #14561758C2semidirect
3. C19×#1315C2semidirect
92. #1315D19semidirect
136. C19#7407semidirect

Maximal subgroups

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

subgroupindex
#145647392
#145617582
C19×#13152
#740719