Finite Group Databasebeta

← #18080374

Subgroups — #18080374

Order 4864.

518 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 107 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#14566238C211yesmaximal, characteristic
2#14563734C212yesmaximal
3#14561965C211yesmaximal, characteristic
4#14561487C212yesmaximal
5C19×#2484C211yesmaximal, characteristic
6#11926508C2212yes—
7#11926430—24no—
8#11926407—21no—
9#11926404—21no—
10C4×C22⋊Dic19C2212yes—
11#11926303—24no—
12#11926270—22no—
13C2×C19×#117C2211yescharacteristic
14C22×C4⋊C4×C19C2211yescharacteristic
15C19×#400C412yescomplemented
16C19×#398C412yescomplemented
17C19×#387—22no—
18C19×#385—21no—
19C19×#381—21no—
20C19×#381C2211yescharacteristic
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C19×#117—22no—
25C19×#117—22no—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19C2×C411yescharacteristic
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19C2×C412yes—
32C2×C4⋊C4×C19D412yes—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—21no—
35C2×C42×C19—21no—
36C2×C22⋊Dic19—22no—
37C2×C4⋊Dic19—22no—
38C2×C4×Dic19D414yes—
39C2×#64520—22no—
40C19×#95—22no—
41C19×#95—22no—
42C19×#95—22no—
43C19×#95—21no—
44C19×#95C2×C412yes—
45C19⋊#95—22no—
46C19⋊#95—24no—
47C19⋊#95—22no—
48C22⋊(C19⋊C8)—22no—
49C22⋊(C19⋊C8)—22no—
50C24×C19C2×D411yescharacteristic
51C22×C4×C19—21no—
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—22no—
58C22×C4×C19—42no—
59C22×C4×C19—42no—
60C22×C4×C19—42no—
61C22×C4×C19C22⋊C412yes—
62C22×C4×C19C22⋊C412yes—
63C22×C4×C19C22×C411yescharacteristic
64C22×C4×C19C2×D412yes—
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19#4112yes—
67C22×Dic19—24no—
68C4⋊C4×C19—24no—
69C4⋊C4×C19—24no—
70C4⋊C4×C19—22no—
71C4⋊C4×C19—22no—
72C4⋊C4×C19—44no—
73C22⋊C4×C19—42no—
74C22⋊C4×C19—41no—
75C22⋊C4×C19—41no—
76C42×C19—42no—
77C22⋊Dic19—44no—
78C4⋊Dic19—82no—
79C4×Dic19—44no—
80#64520—44no—
81C2×C19⋊C8—42no—
82#9482—191nomaximal, Sylow
83C23×C19—22no—
84C23×C19—22no—
85C23×C19—41no—
86C23×C19C2×C22⋊C411yescharacteristic
87C23×C19#12011yescharacteristic
88C23×C19#12311yescharacteristic
89C2×C4×C19—24no—
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19—22no—
94C2×C4×C19—41no—
95C2×C4×C19—41no—
96C2×C4×C19—42no—
97C2×C4×C19—42no—
98C2×C4×C19—42no—
99C2×C4×C19—42no—
100C2×C4×C19—42no—
101C2×C4×C19—42no—
102C2×C4×C19—42no—
103C2×C4×C19—42no—
104C2×C4×C19—41no—
105C2×C4×C19—41no—
106C2×C4×C19—42no—
107C2×C4×C19—42no—
108C2×C4×C19—81no—
109C2×C4×C19C4×D412yes—
110C2×C4×C19#12112yes—
111C2×Dic19—44no—
112C2×Dic19—44no—
113C2×Dic19—44no—
114C19⋊C8—82no—
115#2484D1911yescharacteristic
116#2313—191no—
117#1826—192no—
118#1463—191no—
119#1284—192no—
120C22×C19—21no—
121C22×C19—21no—
122C22×C19—21no—
123C22×C19—21no—
124C22×C19—21no—
125C22×C19—21no—
126C22×C19—21no—
127C22×C19—44no—
128C22×C19#38611yescharacteristic
129C22×C19#42112yes—
130C22×C19#45812yes—
131C4×C19—22no—
132C4×C19—22no—
133C4×C19—42no—
134C4×C19—42no—
135C4×C19—82no—
136C4×C19—81no—
137C4×C19—81no—
138Dic19—84no—
139C2×#117C2×D1911yescharacteristic
140C22×C4⋊C4C2×D1911yescharacteristic
141#407—192no—
142#400Dic1912yescomplemented
143#398Dic1912yescomplemented
144#387—22no—
145#387—384no—
146#385—21no—
147#381—21no—
148#381—381no—
149#381C2×D1911yescharacteristic
150#380—381no—
151C4×C22⋊C4—192no—
152#339—384no—
153#324—382no—
154C2×C19—22no—
155C2×C19—22no—
156C2×C19—41no—
157C2×C19#189011yescharacteristic
158C2×C19#189711yescharacteristic
159C2×C19#191211yescharacteristic
160C23×C4C22⋊D1911yescharacteristic
161C23×C4C22⋊D1911yescharacteristic
162C23×C4C22×D1911yescharacteristic
163C2×M16—382no—
164#117—22no—
165#117—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—382no—
170C2×C4⋊C4C2×Dic1911yescharacteristic
171C2×C4⋊C4C2×Dic1911yescharacteristic
172C2×C4⋊C4C2×Dic1912yes—
173C2×C4⋊C4C22⋊D1912yes—
174C2×C22⋊C4—21no—
175C2×C22⋊C4—21no—
176C2×C22⋊C4—382no—
177C2×C42—21no—
178C2×C42—194no—
179C22⋊C8—382no—
180C22⋊C8—382no—
181#95—22no—
182#95—22no—
183#95—22no—
184#95—21no—
185#95—382no—
186#95—384no—
187#95—382no—
188#95C2×Dic1912yes—
189C19#948211yescharacteristic, complemented, Sylow
190C24C2×C22⋊D1911yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—384no—
202C22×C4C22⋊Dic1912yes—
203C22×C4C22⋊Dic1912yes—
204C22×C4D4×D1912yes—
205C22×C4#6454312yes—
206C22×C4C22×Dic1911yescharacteristic
207C22×C4C2×C22⋊D1911yescharacteristic
208M16—764no—
209C2×C8—762no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—44no—
215C4⋊C4—1522no—
216C22⋊C4—42no—
217C22⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—764no—
220C42—42no—
221C42—764no—
222C23—22no—
223C23—22no—
224C23—41no—
225C23#1059738111yescharacteristic
226C23#1059738311yescharacteristic
227C23C2×C22⋊Dic1911yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—764no—
249C2×C4—764no—
250C2×C4—764no—
251C2×C4D4×Dic1912yes—
252C2×C4#1059738512yes—
253C8—1522no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22#1192642411yescharacteristic
263C22#1192656112yes—
264C22#1192673312yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—82no—
270C4—81no—
271C4—81no—
272C4—1524no—
273C2—22no—
274C2—22no—
275C2—41no—
276C2#1456404911yescharacteristic
277C2#1456408411yescharacteristic
278C2#1456417311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2484C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2484D19
hypocenterC19#9482
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
15. C19×#400C4semidirect
16. C19×#398C4semidirect
142. #400Dic19semidirect
143. #398Dic19semidirect
189. C19#9482semidirect

Maximal subgroups

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

subgroupindex
#145662382
#145637342
#145619652
#145614872
C19×#24842
#948219