Finite Group Databasebeta

← #18069965

Subgroups — #18069965

Order 4864.

228 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 47 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#14561567C211yesmaximal, characteristic
2#14561456C211yesmaximal, characteristic
3C19×#1856C211yesmaximal, characteristic
4#11926299—21no—
5#11926270—21no—
6C19×#518C411yescharacteristic
7C19×#428—21no—
8C2×C19×#100C411yescharacteristic
9C19×#390C2211yescharacteristic
10C19×#339—21no—
11C22×D4×C19C2×C411yescharacteristic
12C2×M16×C19—21no—
13C4×D4×C19—41no—
14C4×D4×C19—41no—
15C19×#117—21no—
16C2×C4⋊C4×C19D411yescharacteristic
17C2×C22⋊C4×C19—41no—
18C2×C22⋊C4×C19—41no—
19C2×C42×C19D411yescharacteristic
20C22×C19⋊C8—41no—
21C19×#107—41no—
22C19×#106—41no—
23C19×#100—21no—
24C19×#100C812yescomplemented
25C22⋊(C19⋊C8)—41no—
26C24×C19—21no—
27C2×D4×C19—21no—
28C2×D4×C19—41no—
29C2×D4×C19—41no—
30C2×D4×C19C2×C811yescharacteristic
31C2×D4×C19M1611yescharacteristic
32C22×C4×C19—21no—
33C22×C4×C19—21no—
34C22×C4×C19—41no—
35C22×C4×C19—41no—
36C22×C4×C19C22⋊C411yescharacteristic
37M16×C19—22no—
38M16×C19—41no—
39C2×C8×C19—41no—
40C4⋊C4×C19—21no—
41C4⋊C4×C19—21no—
42C4⋊C4×C19—41no—
43C22⋊C4×C19—42no—
44C22⋊C4×C19—41no—
45C22⋊C4×C19—81no—
46C22⋊C4×C19—81no—
47C42×C19—41no—
48C42×C19—41no—
49C2×C19⋊C8—42no—
50C2×C19⋊C8—81no—
51C2×C19⋊C8—81no—
52C2×C19⋊C8—81no—
53#7375—191nomaximal, Sylow
54C23×C19—21no—
55C23×C19—21no—
56C23×C19—41no—
57C23×C19—41no—
58C23×C19—81no—
59C23×C19—81no—
60C23×C19#9911yescharacteristic
61D4×C19—41no—
62D4×C19—41no—
63D4×C19—42no—
64C2×C4×C19—21no—
65C2×C4×C19—21no—
66C2×C4×C19—21no—
67C2×C4×C19—21no—
68C2×C4×C19—41no—
69C2×C4×C19—41no—
70C2×C4×C19—41no—
71C2×C4×C19—41no—
72C2×C4×C19—41no—
73C2×C4×C19—81no—
74C2×C4×C19—161no—
75C2×C4×C19—161no—
76C2×C4×C19C22⋊C811yescharacteristic
77C2×C4×C19#10111yescharacteristic
78C8×C19—42no—
79C19⋊C8—82no—
80C19⋊C8—161no—
81#1856D1911yescharacteristic
82#1318—191no—
83#1270—191no—
84C22×C19—21no—
85C22×C19—21no—
86C22×C19—41no—
87C22×C19—41no—
88C22×C19—81no—
89C22×C19—81no—
90C22×C19—81no—
91C22×C19—81no—
92C22×C19—161no—
93C22×C19#32411yescharacteristic
94C22×C19AΣL(1,𝔽16)11yescharacteristic
95C22×C19#35211yescharacteristic
96C4×C19—21no—
97C4×C19—21no—
98C4×C19—41no—
99C4×C19—41no—
100C4×C19—81no—
101C4×C19—81no—
102C4×C19—81no—
103#518Dic1911yescharacteristic
104#428—21no—
105C2×#100Dic1911yescharacteristic
106#390C2×D1911yescharacteristic
107#339—21no—
108#336—381no—
109#324—381no—
110C2×C19—21no—
111C2×C19—21no—
112C2×C19—81no—
113C2×C19—81no—
114C2×C19#132611yescharacteristic
115C2×C19#140211yescharacteristic
116C2×C19#140311yescharacteristic
117C22×D4C2×Dic1911yescharacteristic
118C2×M16—21no—
119C22×C8—761no—
120C4×D4—41no—
121C4×D4—41no—
122#117—21no—
123C2×C4⋊C4C22⋊D1911yescharacteristic
124C2×C22⋊C4—41no—
125C2×C22⋊C4—41no—
126C2×C42C22⋊D1911yescharacteristic
127#107—41no—
128#106—41no—
129#100—21no—
130#100C19⋊C812yescomplemented
131C22⋊C8—761no—
132C19#737511yescharacteristic, complemented, Sylow
133C24—21no—
134C2×D4—21no—
135C2×D4—41no—
136C2×D4—41no—
137C2×D4C2×C19⋊C811yescharacteristic
138C2×D4#6452011yescharacteristic
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—41no—
142C22×C4—41no—
143C22×C4C22⋊Dic1911yescharacteristic
144M16—22no—
145M16—41no—
146C2×C8—41no—
147C2×C8—762no—
148C2×C8—1521no—
149C2×C8—1521no—
150C2×C8—1521no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—41no—
154C22⋊C4—42no—
155C22⋊C4—41no—
156C22⋊C4—81no—
157C22⋊C4—81no—
158C42—41no—
159C42—41no—
160C23—21no—
161C23—21no—
162C23—41no—
163C23—41no—
164C23—81no—
165C23—81no—
166C23#1059729111yescharacteristic
167D4—41no—
168D4—41no—
169D4—42no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—81no—
180C2×C4—161no—
181C2×C4—161no—
182C2×C4C22⋊(C19⋊C8)11yescharacteristic
183C2×C4#1059729311yescharacteristic
184C8—42no—
185C8—3041no—
186C8—1522no—
187C22—21no—
188C22—21no—
189C22—41no—
190C22—41no—
191C22—81no—
192C22—81no—
193C22—81no—
194C22—81no—
195C22—161no—
196C22#1192627011yescharacteristic
197C22#1192633111yescharacteristic
198C22#1192633411yescharacteristic
199C4—21no—
200C4—21no—
201C4—41no—
202C4—41no—
203C4—81no—
204C4—81no—
205C4—81no—
206C2—21no—
207C2—21no—
208C2—81no—
209C2—81no—
210C2#1456158311yescharacteristic
211C2#1456178011yescharacteristic
212C2#1456178311yescharacteristic
subgroupG/H
centerC22#11926331
commutatorC2×D4×C19C2×C8
Frattini#390C2×D19
FittingC19×#1856C2
socleC22×C19AΣL(1,𝔽16)
prime radicalC22×D4×C19C2×C4
cosocleC19×#390C22
hypercenter#1856D19
hypocenterC19#7375
LCSG ▷ C2×D4×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1856

Complements

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

NH ≅ G/Ntype
24. C19×#100C8semidirect
130. #100C19⋊C8semidirect
132. C19#7375semidirect

Maximal subgroups

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

subgroupindex
#145615672
#145614562
C19×#18562
#737519