Finite Group Databasebeta

← #18070050

Subgroups — #18070050

Order 4864.

282 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 41 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#14564717C211yesmaximal, characteristic
2#14561760C211yesmaximal, characteristic
3C19×#1318C211yesmaximal, characteristic
4C22×#64526—21no—
5C2×#10597315C411yescharacteristic, complemented
6C2×#10597267—21no—
7C2×#10597291—21no—
8#11926299C411yescharacteristic, complemented
9C19×#390C2211yescharacteristic
10C19×#324—21no—
11C22×D4×C19D411yescharacteristic
12C22×Dic38—21no—
13C2×C4⋊C4×C19D411yescharacteristic
14C2×C22⋊C4×C19—41no—
15C2×C42×C19C2×C411yescharacteristic
16C2×C22⋊Dic19—41no—
17C2×#64526—42no—
18C2×#64526—42no—
19C2×#64526—41no—
20C2×#64526—41no—
21C2×C4⋊Dic19—41no—
22C22×C19⋊C8—21no—
23#10597315—42no—
24C19×C22⋊C8—41no—
25#10597291—22no—
26#10597291—41no—
27#10597267—42no—
28C24×C19—21no—
29C2×D4×C19—21no—
30C2×D4×C19—41no—
31C2×D4×C19—41no—
32C2×D4×C19D811yescharacteristic
33C2×D4×C19SD1611yescharacteristic
34C22×C4×C19—21no—
35C22×C4×C19—21no—
36C22×C4×C19C22⋊C411yescharacteristic
37C22×Dic19—41no—
38C22×Dic19—81no—
39C2×Dic38—22no—
40C2×Dic38—41no—
41C2×Dic38—41no—
42C2×Dic38—41no—
43C2×Dic38—41no—
44C2×Dic38—41no—
45C2×C8×C19—81no—
46C4⋊C4×C19—41no—
47C22⋊C4×C19—82no—
48C42×C19—41no—
49C22⋊Dic19—42no—
50C22⋊Dic19—81no—
51#64526—44no—
52#64526—44no—
53C4⋊Dic19—42no—
54C4⋊Dic19—42no—
55C2×C19⋊C8—22no—
56C2×C19⋊C8—41no—
57C2×C19⋊C8—41no—
58#7403—191nomaximal, Sylow
59C23×C19—21no—
60C23×C19—21no—
61C23×C19—41no—
62C23×C19—41no—
63C23×C19—81no—
64C23×C19—81no—
65C23×C19#9911yescharacteristic
66D4×C19—41no—
67D4×C19—41no—
68D4×C19—81no—
69C2×C4×C19—21no—
70C2×C4×C19—21no—
71C2×C4×C19—22no—
72C2×C4×C19—41no—
73C2×C4×C19—41no—
74C2×C4×C19—41no—
75C2×C4×C19—81no—
76C2×C4×C19#10211yescharacteristic
77C2×C4×C19#10411yescharacteristic
78C2×Dic19—42no—
79C2×Dic19—81no—
80C2×Dic19—81no—
81C2×Dic19—82no—
82C2×Dic19—161no—
83C2×Dic19—161no—
84Dic38—42no—
85Dic38—42no—
86Dic38—81no—
87Dic38—81no—
88C8×C19—161no—
89C19⋊C8—42no—
90#2013—191no—
91#1393—191no—
92#1318D1911yescharacteristic
93C22×C19—21no—
94C22×C19—21no—
95C22×C19—41no—
96C22×C19—41no—
97C22×C19—81no—
98C22×C19—81no—
99C22×C19—81no—
100C22×C19—81no—
101C22×C19—161no—
102C22×C19#32711yescharacteristic
103C22×C19AΣL(1,𝔽16)11yescharacteristic
104C22×C19#35311yescharacteristic
105C4×C19—21no—
106C4×C19—21no—
107C4×C19—42no—
108C4×C19—81no—
109Dic19—82no—
110Dic19—162no—
111C22×SD16—381no—
112C2×C4⋊Q8—191no—
113C2×#103—381no—
114C2×#99—381no—
115#390C2×D1911yescharacteristic
116#336—191no—
117#324—21no—
118C2×C19—21no—
119C2×C19—21no—
120C2×C19—81no—
121C2×C19—81no—
122C2×C19#134311yescharacteristic
123C2×C19#140711yescharacteristic
124C2×C19#140911yescharacteristic
125C22×Q8—381no—
126C22×D4D7611yescharacteristic
127C2×SD16—762no—
128C2×SD16—762no—
129C2×SD16—761no—
130C2×SD16—761no—
131C22×C8—381no—
132C4⋊Q8—762no—
133C2×C4⋊C4—761no—
134C2×C4⋊C4C22⋊D1911yescharacteristic
135C2×C22⋊C4—41no—
136C2×C22⋊C4—761no—
137C2×C42C4×D1911yescharacteristic
138#103—762no—
139#99—382no—
140#99—761no—
141C22⋊C8—41no—
142C19#740311yescharacteristic, complemented, Sylow
143C24—21no—
144C2×Q8—382no—
145C2×Q8—761no—
146C2×Q8—761no—
147C2×Q8—761no—
148C2×Q8—761no—
149C2×Q8—761no—
150C2×D4—21no—
151C2×D4—41no—
152C2×D4—41no—
153C2×D4#6451611yescharacteristic
154C2×D4D15211yescharacteristic
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—761no—
158C22×C4—1521no—
159C22×C4(C2×D19)⋊C411yescharacteristic
160SD16—764no—
161SD16—764no—
162C2×C8—81no—
163C2×C8—382no—
164C2×C8—761no—
165C2×C8—761no—
166C4⋊C4—41no—
167C4⋊C4—762no—
168C4⋊C4—762no—
169C22⋊C4—82no—
170C22⋊C4—762no—
171C22⋊C4—1521no—
172C42—41no—
173C23—21no—
174C23—21no—
175C23—41no—
176C23—41no—
177C23—81no—
178C23—81no—
179C23#1059726311yescharacteristic
180Q8—762no—
181Q8—762no—
182Q8—1521no—
183Q8—1521no—
184D4—41no—
185D4—41no—
186D4—81no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—81no—
194C2×C4—3041no—
195C2×C4—3041no—
196C2×C4—762no—
197C2×C4—1522no—
198C2×C4—1521no—
199C2×C4—1521no—
200C2×C4#1059727811yescharacteristic
201C2×C4#1059728211yescharacteristic
202C8—161no—
203C8—762no—
204C22—21no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—81no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—161no—
213C22#1192627911yescharacteristic
214C22#1192633211yescharacteristic
215C22#1192633611yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—81no—
220C4—3042no—
221C4—1522no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—81no—
226C2#1456163311yescharacteristic
227C2#1456179611yescharacteristic
228C2#1456179911yescharacteristic
subgroupG/H
centerC22#11926336
commutatorC2×C42×C19C2×C4
Frattini#390C2×D19
FittingC19×#1318C2
socleC22×C19#353
prime radicalC22×D4×C19D4
cosocleC19×#390C22
hypercenter#1318D19
hypocenterC19#7403
LCSG ▷ C2×C42×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1318

Complements

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

NH ≅ G/Ntype
5. C2×#10597315C4semidirect
8. #11926299C4semidirect
142. C19#7403semidirect

Maximal subgroups

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

subgroupindex
#145647172
#145617602
C19×#13182
#740319