Finite Group Databasebeta

← #18070307

Subgroups — #18070307

Order 4864.

280 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 59 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#14564024C211yesmaximal, characteristic
2#14562259C211yesmaximal, characteristic
3C2×C19×#355C211yesmaximal, characteristic
4#11927019C411yescharacteristic
5#11926601—21no—
6#11926553—21no—
7C2×#10597290C411yescharacteristic
8#11926304—21no—
9#11926284—21no—
10#11926284C412yescomplemented
11C2×C19×#124C2211yescharacteristic
12C2×C19×#101—21no—
13C19×#355—21no—
14C19×#355C412yescomplemented
15C22×Q8×C19D411yescharacteristic
16C22×D4×C19C2×C411yescharacteristic
17C2×M16×C19—41no—
18C19×#124—41no—
19C19×#124C2×C411yescharacteristic
20C19×#124C2×C411yescharacteristic
21C19×#124D411yescharacteristic
22C19×#124Q811yescharacteristic
23C2×C22⋊C4×C19—41no—
24C2×C42×C19D411yescharacteristic
25C2×C22⋊Dic19—41no—
26D4×Dic19—42no—
27#10597372—21no—
28C2×#64520—21no—
29C19×#101—22no—
30C19×#101—41no—
31#10597292—42no—
32#10597290—41no—
33C22⋊(C19⋊C8)—41no—
34C4⋊(C19⋊C8)—41no—
35#10597260—22no—
36C24×C19—21no—
37C2×Q8×C19—21no—
38C2×Q8×C19—41no—
39C2×Q8×C19—41no—
40C2×Q8×C19C22⋊C411yescharacteristic
41C2×Q8×C19C4⋊C411yescharacteristic
42C2×D4×C19—21no—
43C2×D4×C19—41no—
44C2×D4×C19—41no—
45C2×D4×C19C4211yescharacteristic
46C2×D4×C19C4⋊C411yescharacteristic
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19C22⋊C411yescharacteristic
50C22×Dic19—42no—
51M16×C19—42no—
52M16×C19—81no—
53C2×C8×C19—81no—
54C22⋊C4×C19—41no—
55C22⋊C4×C19—41no—
56C22⋊C4×C19—41no—
57C22⋊C4×C19—41no—
58C42×C19—21no—
59C42×C19C22⋊C411yescharacteristic
60C42×C19C4⋊C411yescharacteristic
61C22⋊Dic19—41no—
62C22⋊Dic19—42no—
63C4⋊Dic19—22no—
64C4×Dic19—41no—
65#64520—41no—
66#64520—41no—
67C2×C19⋊C8—42no—
68C2×C19⋊C8—41no—
69#7495—191nomaximal, Sylow
70C23×C19—21no—
71C23×C19—21no—
72C23×C19—41no—
73C23×C19—41no—
74C23×C19—82no—
75C23×C19#9911yescharacteristic
76Q8×C19—41no—
77Q8×C19—41no—
78Q8×C19—81no—
79D4×C19—41no—
80D4×C19—41no—
81D4×C19—42no—
82C2×C4×C19—21no—
83C2×C4×C19—21no—
84C2×C4×C19—21no—
85C2×C4×C19—21no—
86C2×C4×C19—21no—
87C2×C4×C19—21no—
88C2×C4×C19—41no—
89C2×C4×C19—41no—
90C2×C4×C19—81no—
91C2×C4×C19#9511yescharacteristic
92C2×C4×C19#9911yescharacteristic
93C2×Dic19—42no—
94C2×Dic19—162no—
95C8×C19—82no—
96C19⋊C8—81no—
97C19⋊C8—82no—
98C2×#355D1911yescharacteristic
99#1885—191no—
100#1533—191no—
101C22×C19—41no—
102C22×C19—41no—
103C22×C19—41no—
104C22×C19—81no—
105C22×C19—81no—
106C22×C19—82no—
107C22×C19—161no—
108C22×C19#34211yescharacteristic
109C22×C19AΣL(1,𝔽16)11yescharacteristic
110C22×C19#35211yescharacteristic
111C4×C19—21no—
112C4×C19—21no—
113C4×C19—41no—
114C4×C19—41no—
115C4×C19—41no—
116C4×C19—41no—
117Dic19—82no—
118C2×#124C2×D1911yescharacteristic
119#518—191no—
120#432—381no—
121#419—381no—
122C2×#101—21no—
123C2×#100—191no—
124#355—21no—
125#355Dic1912yescomplemented
126#339—381no—
127#329—192no—
128#329—381no—
129C2×C19—21no—
130C2×C19—21no—
131C2×C19—21no—
132C2×C19—81no—
133C2×C19—81no—
134C2×C19#139011yescharacteristic
135C22×Q8C22⋊D1911yescharacteristic
136C22×D4C4×D1911yescharacteristic
137C2×M16—41no—
138C2×M16—381no—
139#124—41no—
140#124Dic3811yescharacteristic
141#124C4×D1911yescharacteristic
142#124C2×Dic1911yescharacteristic
143#124C22⋊D1911yescharacteristic
144C4×D4—762no—
145#117—381no—
146C2×C22⋊C4—41no—
147C2×C22⋊C4—761no—
148C2×C42D7611yescharacteristic
149C4⋊C8—761no—
150#103—762no—
151#101—22no—
152#101—41no—
153#100—761no—
154C22⋊C8—761no—
155#97—382no—
156C19#749511yescharacteristic, complemented, Sylow
157C24—21no—
158C2×Q8—21no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8Dic19⋊C411yescharacteristic
162C2×Q8C22⋊Dic1911yescharacteristic
163C2×D4—21no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4C4×Dic1911yescharacteristic
167C2×D4Dic19⋊C411yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—762no—
171C22×C4(C2×D19)⋊C411yescharacteristic
172M16—42no—
173M16—81no—
174M16—761no—
175M16—761no—
176C2×C8—81no—
177C2×C8—762no—
178C2×C8—761no—
179C4⋊C4—382no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C22⋊C4—41no—
183C22⋊C4—41no—
184C22⋊C4—761no—
185C22⋊C4—762no—
186C42—21no—
187C42—761no—
188C42C4⋊Dic1911yescharacteristic
189C42(C2×D19)⋊C411yescharacteristic
190C23—21no—
191C23—21no—
192C23—41no—
193C23—41no—
194C23—82no—
195C23#1059726311yescharacteristic
196Q8—41no—
197Q8—41no—
198Q8—81no—
199D4—41no—
200D4—41no—
201D4—42no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—81no—
211C2×C4—3042no—
212C2×C4—762no—
213C2×C4#1059726311yescharacteristic
214C2×C4C19⋊#9511yescharacteristic
215C8—82no—
216C8—1521no—
217C8—1522no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—81no—
222C22—81no—
223C22—82no—
224C22—161no—
225C22#1192631011yescharacteristic
226C22#1192633011yescharacteristic
227C22#1192633311yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—1522no—
235C2—21no—
236C2—21no—
237C2—21no—
238C2—81no—
239C2—81no—
240C2#1456175211yescharacteristic
subgroupG/H
centerC2#14561752
commutatorC2×D4×C19C42
FrattiniC2×#124C2×D19
FittingC2×C19×#355C2
socleC2×C19#1390
prime radicalC22×D4×C19C2×C4
cosocleC2×C19×#124C22
hypercenterC2×#355D19
hypocenterC19#7495
LCSG ▷ C2×D4×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×#124 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
10. #11926284C4semidirect
14. C19×#355C4semidirect
125. #355Dic19semidirect
156. C19#7495semidirect

Maximal subgroups

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

subgroupindex
#145640242
#145622592
C2×C19×#3552
#749519