Finite Group Databasebeta

← #18069218

Subgroups — #18069218

Order 4864.

286 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 51 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#14561559C211yesmaximal, characteristic
2#14561503C211yesmaximal, characteristic
3C19×#2001C211yesmaximal, characteristic
4#11926404—21no—
5C22⋊(C19⋊C16)—21no—
6C22×Q16×C19C411yescharacteristic, complemented
7C2×C19×C22⋊Q8—21no—
8C2×C19×#103—21no—
9C2×C19×C22⋊C8C2211yescharacteristic
10C19×#340C411yescharacteristic, complemented
11C22×Q8×C19—21no—
12C23×C4×C19D411yescharacteristic
13C2×Q16×C19—41no—
14C2×Q16×C19—42no—
15C22×C8×C19C2×C411yescharacteristic
16C22×C8×C19D411yescharacteristic
17C19×C22⋊Q8—42no—
18C19×C22⋊Q8—42no—
19C2×C4⋊C4×C19—21no—
20C2×C4⋊C4×C19—41no—
21C2×C22⋊C4×C19—41no—
22C2×C22⋊Dic19—41no—
23C2×C4⋊Dic19—41no—
24C19×#103—42no—
25C19×C22⋊C8—41no—
26C19⋊#95—22no—
27C2×C19⋊C16—41no—
28C24×C19D811yescharacteristic
29C2×Q8×C19—22no—
30C2×Q8×C19—41no—
31C2×Q8×C19—41no—
32C2×Q8×C19—41no—
33C2×Q8×C19—41no—
34C2×Q8×C19—41no—
35C22×C4×C19—21no—
36C22×C4×C19—21no—
37C22×C4×C19—41no—
38C22×C4×C19—41no—
39C22×C4×C19—41no—
40C22×C4×C19—41no—
41C22×C4×C19C22⋊C411yescharacteristic
42C22×C4×C19SD1611yescharacteristic
43C22×Dic19—42no—
44Q16×C19—42no—
45Q16×C19—42no—
46C2×C8×C19—21no—
47C2×C8×C19—21no—
48C2×C8×C19—41no—
49C2×C8×C19—41no—
50C4⋊C4×C19—22no—
51C4⋊C4×C19—41no—
52C4⋊C4×C19—44no—
53C22⋊C4×C19—44no—
54C22⋊Dic19—81no—
55C22⋊Dic19—81no—
56C4⋊Dic19—81no—
57C4⋊Dic19—81no—
58C19⋊C16—81no—
59#7078—191nomaximal, Sylow
60C23×C19—21no—
61C23×C19—21no—
62C23×C19—41no—
63C23×C19—41no—
64C23×C19#10211yescharacteristic
65C23×C19SD3211yescharacteristic
66C23×C19Q3211yescharacteristic
67Q8×C19—42no—
68Q8×C19—42no—
69Q8×C19—81no—
70Q8×C19—81no—
71C2×C4×C19—21no—
72C2×C4×C19—21no—
73C2×C4×C19—21no—
74C2×C4×C19—41no—
75C2×C4×C19—41no—
76C2×C4×C19—41no—
77C2×C4×C19—42no—
78C2×C4×C19—42no—
79C2×C4×C19—81no—
80C2×C4×C19—81no—
81C2×C4×C19—81no—
82C2×C4×C19—81no—
83C2×C4×C19—81no—
84C2×C4×C19#9911yescharacteristic
85C2×C4×C19#10411yescharacteristic
86C2×Dic19—82no—
87C2×Dic19—82no—
88C2×Dic19—82no—
89C8×C19—41no—
90C8×C19—41no—
91#2001D1911yescharacteristic
92#1314—191no—
93#1289—191no—
94C22×C19—21no—
95C22×C19—21no—
96C22×C19—21no—
97C22×C19—21no—
98C22×C19—41no—
99C22×C19—41no—
100C22×C19—41no—
101C22×C19—41no—
102C22×C19—81no—
103C22×C19#32711yescharacteristic
104C22×C19#35811yescharacteristic
105C22×C19#36011yescharacteristic
106C4×C19—21no—
107C4×C19—41no—
108C4×C19—82no—
109C4×C19—82no—
110C4×C19AΣL(1,𝔽16)11yescharacteristic
111C4×C19#35311yescharacteristic
112Dic19—162no—
113C22×Q16Dic1911yescharacteristic, complemented
114C2×C22⋊Q8—21no—
115C2×#103—21no—
116C2×C22⋊C8C2×D1911yescharacteristic
117#380—381no—
118C22⋊C16—381no—
119#340Dic1911yescharacteristic, complemented
120C2×C19—21no—
121C2×C19—21no—
122C2×C19—41no—
123C2×C19—41no—
124C2×C19#134011yescharacteristic
125C2×C19#134311yescharacteristic
126C2×C19#134811yescharacteristic
127C22×Q8—21no—
128C23×C4C22⋊D1911yescharacteristic
129C2×Q16—41no—
130C2×Q16—42no—
131C22×C8C2×Dic1911yescharacteristic
132C22×C8C22⋊D1911yescharacteristic
133C22⋊Q8—42no—
134C22⋊Q8—42no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—761no—
138C2×C22⋊C4—41no—
139C2×C22⋊C4—761no—
140C2×C16—761no—
141#103—42no—
142C22⋊C8—41no—
143#95—382no—
144C19#707811yescharacteristic, complemented, Sylow
145C24#6452511yescharacteristic
146C2×Q8—22no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—41no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—762no—
159C22×C4#6452611yescharacteristic
160C22×C4C22⋊Dic1911yescharacteristic
161Q16—42no—
162Q16—42no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—41no—
166C2×C8—41no—
167C4⋊C4—22no—
168C4⋊C4—41no—
169C4⋊C4—44no—
170C4⋊C4—1521no—
171C4⋊C4—1521no—
172C22⋊C4—44no—
173C22⋊C4—1521no—
174C22⋊C4—1521no—
175C16—1521no—
176C23—21no—
177C23—21no—
178C23—41no—
179C23—41no—
180C23#1059728511yescharacteristic
181C23#1059728611yescharacteristic
182C23#1059728911yescharacteristic
183Q8—42no—
184Q8—42no—
185Q8—81no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—1522no—
201C2×C4—1522no—
202C2×C4—1522no—
203C2×C4#1059729111yescharacteristic
204C2×C4#1059729411yescharacteristic
205C8—41no—
206C8—41no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22—81no—
216C22#1192627811yescharacteristic
217C22#1192634811yescharacteristic
218C22#1192635411yescharacteristic
219C4—21no—
220C4—41no—
221C4—82no—
222C4—82no—
223C4—3042no—
224C4#1192633111yescharacteristic
225C4#1192633711yescharacteristic
226C2—21no—
227C2—21no—
228C2—41no—
229C2—41no—
230C2#1456162311yescharacteristic
231C2#1456163211yescharacteristic
232C2#1456164711yescharacteristic
subgroupG/H
centerC22#11926278
commutatorC22×C8×C19C2×C4
FrattiniC2×C22⋊C8C2×D19
FittingC19×#2001C2
socleC22×C19#327
prime radicalC24×C19D8
cosocleC2×C19×C22⋊C8C22
hypercenter#2001D19
hypocenterC19#7078
LCSG ▷ C22×C8×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #2001

Complements

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

NH ≅ G/Ntype
6. C22×Q16×C19C4semidirect
10. C19×#340C4semidirect
113. C22×Q16Dic19semidirect
119. #340Dic19semidirect
144. C19#7078semidirect

Maximal subgroups

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

subgroupindex
#145615592
#145615032
C19×#20012
#707819