Finite Group Databasebeta

← #18070119

Subgroups — #18070119

Order 4864.

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

normal subgroups only

This group has 332 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#14564799C211yesmaximal, characteristic
2C19⋊#1304C211yesmaximal, characteristic
3C19×#1316C211yesmaximal, characteristic
4#11927170C411yescharacteristic, complemented
5#11926400—21no—
6#11926400—21no—
7#11926311C411yescharacteristic, complemented
8#11926310—21no—
9C19×#379C2211yescharacteristic
10C19×#323—21no—
11C25×C19D411yescharacteristic
12C2×C22⋊C4×C19—41no—
13C2×C22⋊C4×C19C2×C411yescharacteristic
14C2×C22⋊C4×C19D411yescharacteristic
15C2×C22⋊Dic19—21no—
16C2×C22⋊Dic19—21no—
17C2×C22⋊Dic19—22no—
18C2×C22⋊Dic19—42no—
19C2×C22⋊Dic19—41no—
20C2×C22⋊Dic19—41no—
21#10597370—41no—
22#10597324—42no—
23C19×C22⋊C8—41no—
24C24×C19—21no—
25C24×C19—21no—
26C24×C19—41no—
27C24×C19—41no—
28C24×C19—82no—
29C24×C19C22⋊C411yescharacteristic
30C24×C19SD1611yescharacteristic
31C24×C19Q1611yescharacteristic
32C22×C4×C19—21no—
33C22×C4×C19—21no—
34C22×Dic19—22no—
35C22×Dic19—41no—
36C22×Dic19—42no—
37C2×Dic38—41no—
38C2×C8×C19—81no—
39C22⋊C4×C19—41no—
40C22⋊C4×C19—41no—
41C22⋊C4×C19—82no—
42C22⋊Dic19—41no—
43C22⋊Dic19—41no—
44C22⋊Dic19—41no—
45C22⋊Dic19—41no—
46C22⋊Dic19—84no—
47C22⋊Dic19—82no—
48C22⋊Dic19—81no—
49C22⋊Dic19—81no—
50C22⋊Dic19—82no—
51C4⋊Dic19—41no—
52Dic19⋊C4—42no—
53#7426—191nomaximal, Sylow
54C23×C19—21no—
55C23×C19—21no—
56C23×C19—21no—
57C23×C19—21no—
58C23×C19—42no—
59C23×C19—41no—
60C23×C19—41no—
61C23×C19—42no—
62C23×C19—42no—
63C23×C19—44no—
64C23×C19—41no—
65C23×C19—41no—
66C23×C19—81no—
67C23×C19—81no—
68C23×C19—81no—
69C23×C19—81no—
70C23×C19—81no—
71C23×C19—82no—
72C23×C19—82no—
73C23×C19—82no—
74C23×C19#9911yescharacteristic
75C23×C19#10311yescharacteristic
76C23×C19#10411yescharacteristic
77C2×C4×C19—41no—
78C2×C4×C19—41no—
79C2×C4×C19—81no—
80C2×C4×C19—81no—
81C2×Dic19—42no—
82C2×Dic19—82no—
83C2×Dic19—81no—
84C2×Dic19—82no—
85C2×Dic19—82no—
86C2×Dic19—82no—
87C2×Dic19—82no—
88Dic38—161no—
89C8×C19—161no—
90#2029—191no—
91#1316D1911yescharacteristic
92#1304—191no—
93C22×C19—22no—
94C22×C19—21no—
95C22×C19—21no—
96C22×C19—41no—
97C22×C19—41no—
98C22×C19—41no—
99C22×C19—42no—
100C22×C19—41no—
101C22×C19—41no—
102C22×C19—41no—
103C22×C19—42no—
104C22×C19—41no—
105C22×C19—42no—
106C22×C19—41no—
107C22×C19—81no—
108C22×C19—82no—
109C22×C19—82no—
110C22×C19—81no—
111C22×C19—84no—
112C22×C19—81no—
113C22×C19#32811yescharacteristic
114C22×C19AΣL(1,𝔽16)11yescharacteristic
115C22×C19#35411yescharacteristic
116C4×C19—81no—
117C4×C19—81no—
118Dic19—82no—
119Dic19—161no—
120Dic19—162no—
121#543—191no—
122#379—381no—
123#379—381no—
124#379C2×D1911yescharacteristic
125#342—191no—
126#342—381no—
127#323—21no—
128C2×C19—21no—
129C2×C19—21no—
130C2×C19—21no—
131C2×C19—42no—
132C2×C19—41no—
133C2×C19—41no—
134C2×C19—81no—
135C2×C19#135111yescharacteristic
136C25D7611yescharacteristic
137C22⋊Q8—762no—
138C22⋊Q8—761no—
139C2×C22⋊C4—41no—
140C2×C22⋊C4—381no—
141C2×C22⋊C4—381no—
142C2×C22⋊C4—382no—
143C2×C22⋊C4—762no—
144C2×C22⋊C4—761no—
145C2×C22⋊C4—761no—
146C2×C22⋊C4C4×D1911yescharacteristic
147C2×C22⋊C4C22⋊D1911yescharacteristic
148C22⋊C8—41no—
149C19#742611yescharacteristic, complemented, Sylow
150C24—21no—
151C24—21no—
152C24—41no—
153C24—41no—
154C24—82no—
155C24#6451611yescharacteristic
156C24Dic7611yescharacteristic
157C24(C2×D19)⋊C411yescharacteristic
158C2×Q8—761no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—382no—
162C22×C4—761no—
163C22×C4—762no—
164C2×C8—81no—
165C4⋊C4—762no—
166C4⋊C4—761no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C22⋊C4—82no—
170C22⋊C4—761no—
171C22⋊C4—761no—
172C22⋊C4—761no—
173C22⋊C4—761no—
174C22⋊C4—1522no—
175C22⋊C4—1521no—
176C22⋊C4—1521no—
177C22⋊C4—1524no—
178C22⋊C4—1522no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—21no—
183C23—42no—
184C23—41no—
185C23—41no—
186C23—42no—
187C23—42no—
188C23—44no—
189C23—41no—
190C23—41no—
191C23—81no—
192C23—81no—
193C23—81no—
194C23—81no—
195C23—81no—
196C23—82no—
197C23—82no—
198C23—82no—
199C23#1059726311yescharacteristic
200C23#1059727311yescharacteristic
201C23#1059728211yescharacteristic
202Q8—3041no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—81no—
206C2×C4—81no—
207C2×C4—762no—
208C2×C4—1521no—
209C2×C4—1522no—
210C2×C4—1522no—
211C2×C4—1522no—
212C2×C4—1522no—
213C2×C4—1522no—
214C8—161no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—41no—
227C22—42no—
228C22—41no—
229C22—81no—
230C22—82no—
231C22—82no—
232C22—81no—
233C22—84no—
234C22—81no—
235C22#1192628211yescharacteristic
236C22#1192633211yescharacteristic
237C22#1192633811yescharacteristic
238C4—81no—
239C4—81no—
240C4—3041no—
241C4—3042no—
242C4—1522no—
243C2—21no—
244C2—21no—
245C2—21no—
246C2—42no—
247C2—41no—
248C2—41no—
249C2—81no—
250C2#1456165711yescharacteristic
subgroupG/H
centerC2#14561657
commutatorC2×C22⋊C4×C19C2×C4
Frattini#379C2×D19
FittingC19×#1316C2
socleC2×C19#1351
prime radicalC25×C19D4
cosocleC19×#379C22
hypercenter#1316D19
hypocenterC19#7426
LCSG ▷ C2×C22⋊C4×C19 ▷ C24×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #379 ◁ #1316

Complements

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

NH ≅ G/Ntype
4. #11927170C4semidirect
7. #11926311C4semidirect
149. C19#7426semidirect

Maximal subgroups

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

subgroupindex
#145647992
C19⋊#13042
C19×#13162
#742619