Finite Group Databasebeta

← #18069237

Subgroups — #18069237

Order 4864.

316 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 45 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#14564633C211yesmaximal, characteristic
2#14561512C211yesmaximal, characteristic, complemented
3C19×#1314C211yesmaximal, characteristic, complemented
4C22×D152C411yescharacteristic
5C2×#10597376—21no—
6C2×#10597278—21no—
7#11926508—21no—
8#11926307C411yescharacteristic
9C2×C19×C22⋊C8C2211yescharacteristic
10C19×C22⋊C16—21no—
11C23×C4×C19D411yescharacteristic
12C22×C22⋊D19—41no—
13C22×D76—21no—
14C22×C8×C19C2×C411yescharacteristic
15C22×C8×C19D411yescharacteristic
16#10597376—42no—
17#10597376—42no—
18C2×(C2×D19)⋊C4—41no—
19C2×C4⋊Dic19—21no—
20C2×#64520—41no—
21C2×D152—41no—
22C2×D152—42no—
23C2×C16×C19—41no—
24C19×C22⋊C8—41no—
25C22⋊(C19⋊C8)—22no—
26C22⋊(C19⋊C8)—41no—
27#10597278—42no—
28C24×C19SD1611yescharacteristic
29C23×D19—41no—
30C22×C4×C19—21no—
31C22×C4×C19—21no—
32C22×C4×C19—41no—
33C22×C4×C19—41no—
34C22×C4×C19C22⋊C411yescharacteristic
35C22×C4×C19D811yescharacteristic
36C2×C22⋊D19—44no—
37C2×C22⋊D19—82no—
38C2×C22⋊D19—82no—
39C22×Dic19—41no—
40C2×D76—22no—
41C2×D76—41no—
42C2×D76—41no—
43C2×D76—41no—
44C2×D76—41no—
45C2×D76—41no—
46C2×C8×C19—21no—
47C2×C8×C19—21no—
48C2×C8×C19—41no—
49C2×C8×C19—41no—
50(C2×D19)⋊C4—44no—
51C4⋊Dic19—22no—
52C4⋊Dic19—41no—
53#64520—81no—
54#64520—81no—
55C2×C19⋊C8—42no—
56D152—42no—
57D152—42no—
58C16×C19—81no—
59#7084—191nomaximal, Sylow
60C23×C19—21no—
61C23×C19—21no—
62C23×C19—21no—
63C23×C19—41no—
64C23×C19—41no—
65C23×C19#10211yescharacteristic
66C22×D19—42no—
67C22×D19—81no—
68C22×D19—81no—
69C22×D19—81no—
70C22×D19—81no—
71C22×D19—81no—
72C22×D19—81no—
73C2×C4×C19—21no—
74C2×C4×C19—21no—
75C2×C4×C19—21no—
76C2×C4×C19—41no—
77C2×C4×C19—41no—
78C2×C4×C19—41no—
79C2×C4×C19—81no—
80C2×C4×C19#9911yescharacteristic
81C2×C4×C19#10411yescharacteristic
82C22⋊D19—88no—
83C2×Dic19—42no—
84C2×Dic19—81no—
85C2×Dic19—81no—
86D76—42no—
87D76—42no—
88D76—81no—
89D76—81no—
90C8×C19—41no—
91C8×C19—41no—
92C19⋊C8—82no—
93#1999—191no—
94#1314D1911yescharacteristic, complemented
95#1293—191no—
96C22×C19—21no—
97C22×C19—21no—
98C22×C19—42no—
99C22×C19—41no—
100C22×C19—41no—
101C22×C19—41no—
102C22×C19—81no—
103C22×C19#32711yescharacteristic
104C22×C19#35911yescharacteristic
105C22×C19#36111yescharacteristic
106C2×D19—82no—
107C2×D19—82no—
108C2×D19—82no—
109C2×D19—161no—
110C2×D19—161no—
111C2×D19—161no—
112C2×D19—161no—
113C4×C19—21no—
114C4×C19—41no—
115C4×C19AΣL(1,𝔽16)11yescharacteristic
116C4×C19#35311yescharacteristic
117Dic19—82no—
118C22×D8—191no—
119C2×#121—381no—
120C2×#102—381no—
121#407—381no—
122C2×C22⋊C8C2×D1911yescharacteristic
123C22⋊C16—21no—
124#340—191no—
125C2×C19—21no—
126C2×C19—21no—
127C2×C19—81no—
128C2×C19#134111yescharacteristic
129C2×C19#134311yescharacteristic
130C2×C19#134911yescharacteristic
131D19—162no—
132C22×D4—381no—
133C22×D4—761no—
134C23×C4D7611yescharacteristic
135C2×D8—761no—
136C2×D8—762no—
137C2×M16—761no—
138C22×C8C4×D1911yescharacteristic
139C22×C8C22⋊D1911yescharacteristic
140#121—762no—
141#121—762no—
142C2×C4⋊C4—381no—
143C2×C22⋊C4—761no—
144C2×C16—41no—
145#102—762no—
146C22⋊C8—41no—
147C22⋊C8—382no—
148C22⋊C8—761no—
149C19#708411yescharacteristic, complemented, Sylow
150C24—761no—
151C24#6451611yescharacteristic
152C2×D4—382no—
153C2×D4—761no—
154C2×D4—761no—
155C2×D4—761no—
156C2×D4—764no—
157C2×D4—761no—
158C2×D4—761no—
159C2×D4—1522no—
160C2×D4—1522no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—761no—
166C22×C4D15211yescharacteristic
167C22×C4(C2×D19)⋊C411yescharacteristic
168D8—762no—
169D8—762no—
170M16—1521no—
171M16—1521no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—762no—
177C4⋊C4—382no—
178C4⋊C4—761no—
179C22⋊C4—764no—
180C16—81no—
181C23—21no—
182C23—21no—
183C23—21no—
184C23—41no—
185C23—41no—
186C23—762no—
187C23—1521no—
188C23—1521no—
189C23—1521no—
190C23—1521no—
191C23—1521no—
192C23—1521no—
193C23#1059727811yescharacteristic
194D4—762no—
195D4—762no—
196D4—1521no—
197D4—1528no—
198D4—1521no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—81no—
206C2×C4—762no—
207C2×C4—1521no—
208C2×C4—1521no—
209C2×C4#1059726311yescharacteristic
210C2×C4#1059728211yescharacteristic
211C8—41no—
212C8—41no—
213C8—1522no—
214C22—21no—
215C22—21no—
216C22—42no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—81no—
221C22—3041no—
222C22—3041no—
223C22—3041no—
224C22—3041no—
225C22—1522no—
226C22—1522no—
227C22—1522no—
228C22#1192627911yescharacteristic
229C22#1192635211yescharacteristic
230C22#1192635811yescharacteristic
231C4—21no—
232C4—41no—
233C4—1522no—
234C4#1192633211yescharacteristic
235C4#1192633611yescharacteristic
236C2—21no—
237C2—21no—
238C2—81no—
239C2—3042no—
240C2#1456162711yescharacteristic
241C2#1456163311yescharacteristic
242C2#1456165111yescharacteristic
subgroupG/H
centerC22#11926279
commutatorC22×C8×C19C2×C4
FrattiniC2×C22⋊C8C2×D19
FittingC19×#1314C2
socleC22×C19#327
prime radical#14564633C2
cosocleC2×C19×C22⋊C8C22
hypercenter#1314D19
hypocenterC19#7084
LCSG ▷ C22×C8×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #14561512C2semidirect
3. C19×#1314C2semidirect
94. #1314D19semidirect
149. C19#7084semidirect

Maximal subgroups

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

subgroupindex
#145646332
#145615122
C19×#13142
#708419