Finite Group Databasebeta

← #18070064

Subgroups — #18070064

Order 4864.

298 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 43 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#14561760C211yesmaximal, characteristic, complemented
2#14561456C211yesmaximal, characteristic, complemented
3C19×#2006C211yesmaximal, characteristic
4C2×#10597291—21no—
5#11926299—21no—
6C2×C19×AGL(1,ℤ/8)—21no—
7C19×#537C411yescharacteristic, complemented
8C2×C19×#104—21no—
9C19×#390C2211yescharacteristic
10C19×#343C411yescharacteristic, complemented
11C2×#41×C19—21no—
12C22×D4×C19D411yescharacteristic
13C19×AGL(1,ℤ/8)—42no—
14C19×AGL(1,ℤ/8)—41no—
15C19×AGL(1,ℤ/8)—41no—
16C2×SD16×C19—41no—
17C2×D8×C19—41no—
18C2×M16×C19—21no—
19C19×C22⋊Q8—41no—
20C19×#121—41no—
21C19×#121—41no—
22C2×C4⋊C4×C19C2×C411yescharacteristic
23C2×C22⋊C4×C19—41no—
24C2×C42×C19D411yescharacteristic
25C2×C22⋊Dic19—41no—
26C22×C19⋊C8—41no—
27C19×#104—42no—
28#10597291—22no—
29#10597291—41no—
30C24×C19—21no—
31#41×C19—41no—
32#41×C19—41no—
33#41×C19—41no—
34#41×C19—41no—
35C2×Q8×C19—21no—
36C2×D4×C19—21no—
37C2×D4×C19—21no—
38C2×D4×C19—41no—
39C2×D4×C19—41no—
40C2×D4×C19—41no—
41C2×D4×C19—41no—
42C2×D4×C19D811yescharacteristic
43C2×D4×C19SD1611yescharacteristic
44C22×C4×C19—21no—
45C22×C4×C19—21no—
46C22×C4×C19—41no—
47C22×C4×C19C22⋊C411yescharacteristic
48C22×Dic19—81no—
49SD16×C19—42no—
50SD16×C19—42no—
51D8×C19—42no—
52D8×C19—42no—
53M16×C19—22no—
54M16×C19—41no—
55C2×C8×C19—41no—
56C4⋊C4×C19—41no—
57C4⋊C4×C19—41no—
58C22⋊C4×C19—42no—
59C22⋊C4×C19—81no—
60C22⋊C4×C19—81no—
61C42×C19—41no—
62C22⋊Dic19—42no—
63C22⋊Dic19—81no—
64C2×C19⋊C8—42no—
65C2×C19⋊C8—81no—
66C2×C19⋊C8—81no—
67#7408—191nomaximal, Sylow
68C23×C19—21no—
69C23×C19—21no—
70C23×C19—41no—
71C23×C19—41no—
72C23×C19—41no—
73C23×C19—81no—
74C23×C19—81no—
75C23×C19#9911yescharacteristic
76Q8×C19—41no—
77Q8×C19—41no—
78D4×C19—41no—
79D4×C19—41no—
80D4×C19—41no—
81D4×C19—41no—
82D4×C19—81no—
83D4×C19—81no—
84D4×C19—81no—
85D4×C19—161no—
86C2×C4×C19—21no—
87C2×C4×C19—21no—
88C2×C4×C19—21no—
89C2×C4×C19—21no—
90C2×C4×C19—41no—
91C2×C4×C19—41no—
92C2×C4×C19—41no—
93C2×C4×C19—41no—
94C2×C4×C19—81no—
95C2×C4×C19—81no—
96C2×C4×C19—81no—
97C2×C4×C19#10211yescharacteristic
98C2×C4×C19#10411yescharacteristic
99C2×Dic19—82no—
100C2×Dic19—161no—
101C2×Dic19—161no—
102C8×C19—42no—
103C19⋊C8—82no—
104#2006D1911yescharacteristic
105#1393—191no—
106#1270—191no—
107C22×C19—21no—
108C22×C19—21no—
109C22×C19—41no—
110C22×C19—41no—
111C22×C19—81no—
112C22×C19—81no—
113C22×C19—81no—
114C22×C19—81no—
115C22×C19—81no—
116C22×C19—81no—
117C22×C19—81no—
118C22×C19—161no—
119C22×C19#32711yescharacteristic
120C22×C19AΣL(1,𝔽16)11yescharacteristic
121C22×C19#35311yescharacteristic
122C4×C19—21no—
123C4×C19—21no—
124C4×C19—41no—
125C4×C19—41no—
126C4×C19—81no—
127C4×C19—81no—
128Dic19—162no—
129C2×AGL(1,ℤ/8)—21no—
130#537Dic1911yescharacteristic, complemented
131C2×#104—21no—
132C2×#99—381no—
133#390C2×D1911yescharacteristic
134#343Dic1911yescharacteristic, complemented
135#336—381no—
136C2×C19—21no—
137C2×C19—21no—
138C2×C19—81no—
139C2×C19—81no—
140C2×C19—161no—
141C2×C19#134311yescharacteristic
142C2×C19#140211yescharacteristic
143C2×C19#140411yescharacteristic
144C2×#41—21no—
145C22×D4C22⋊D1911yescharacteristic
146AGL(1,ℤ/8)—42no—
147AGL(1,ℤ/8)—41no—
148AGL(1,ℤ/8)—41no—
149C2×SD16—41no—
150C2×D8—41no—
151C2×M16—21no—
152C22×C8—761no—
153C22⋊Q8—41no—
154#121—41no—
155#121—41no—
156C2×C4⋊C4C2×Dic1911yescharacteristic
157C2×C22⋊C4—41no—
158C2×C22⋊C4—761no—
159C2×C42C22⋊D1911yescharacteristic
160#104—42no—
161#99—382no—
162#99—761no—
163C19#740811yescharacteristic, complemented, Sylow
164C24—21no—
165#41—41no—
166#41—41no—
167#41—41no—
168#41—41no—
169C2×Q8—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—41no—
173C2×D4—41no—
174C2×D4—41no—
175C2×D4—41no—
176C2×D4#6452511yescharacteristic
177C2×D4#6452611yescharacteristic
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—1521no—
182C22×C4C22⋊Dic1911yescharacteristic
183SD16—42no—
184SD16—42no—
185D8—42no—
186D8—42no—
187M16—22no—
188M16—41no—
189C2×C8—41no—
190C2×C8—762no—
191C2×C8—1521no—
192C2×C8—1521no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C22⋊C4—42no—
196C22⋊C4—81no—
197C22⋊C4—81no—
198C22⋊C4—762no—
199C22⋊C4—1521no—
200C42—41no—
201C23—21no—
202C23—21no—
203C23—41no—
204C23—41no—
205C23—41no—
206C23—81no—
207C23—81no—
208C23#1059729111yescharacteristic
209Q8—41no—
210Q8—41no—
211D4—41no—
212D4—41no—
213D4—41no—
214D4—41no—
215D4—81no—
216D4—81no—
217D4—81no—
218D4—161no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—81no—
230C2×C4—3041no—
231C2×C4—3041no—
232C2×C4—1522no—
233C2×C4#1059728911yescharacteristic
234C2×C4#1059729411yescharacteristic
235C8—42no—
236C8—1522no—
237C22—21no—
238C22—21no—
239C22—41no—
240C22—41no—
241C22—81no—
242C22—81no—
243C22—81no—
244C22—81no—
245C22—81no—
246C22—81no—
247C22—81no—
248C22—161no—
249C22#1192627811yescharacteristic
250C22#1192633111yescharacteristic
251C22#1192633711yescharacteristic
252C4—21no—
253C4—21no—
254C4—41no—
255C4—41no—
256C4—81no—
257C4—81no—
258C4—3042no—
259C2—21no—
260C2—21no—
261C2—81no—
262C2—81no—
263C2—161no—
264C2#1456163211yescharacteristic
265C2#1456178011yescharacteristic
266C2#1456178611yescharacteristic
subgroupG/H
centerC22#11926331
commutatorC2×C4⋊C4×C19C2×C4
Frattini#390C2×D19
Fitting, prime radicalC19×#2006C2
socleC22×C19AΣL(1,𝔽16)
cosocleC19×#390C22
hypercenter#2006D19
hypocenterC19#7408
LCSG ▷ C2×C4⋊C4×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #2006

Complements

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

NH ≅ G/Ntype
1. #14561760C2semidirect
2. #14561456C2semidirect
7. C19×#537C4semidirect
10. C19×#343C4semidirect
130. #537Dic19semidirect
134. #343Dic19semidirect
163. C19#7408semidirect

Maximal subgroups

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

subgroupindex
#145617602
#145614562
C19×#20062
#740819