Finite Group Databasebeta

← #18080371

Subgroups — #18080371

Order 4864.

518 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 99 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#14567922C211yesmaximal, characteristic
2#14566238C211yesmaximal, characteristic
3#14563732C212yesmaximal
4#14561489C212yesmaximal
5C19×#1463C211yesmaximal, characteristic
6C2×#10597372C2211yescharacteristic
7#11926483C412yescomplemented
8#11926474C412yescomplemented
9#11926430—24no—
10#11926425—22no—
11#11926417—21no—
12#11926407—21no—
13#11926407—21no—
14#11926407C2211yescharacteristic
15#11926404—21no—
16C4×C22⋊Dic19C2212yes—
17#11926305—24no—
18C22×C4⋊C4×C19C2211yescharacteristic
19C19×#407C2212yes—
20C19×#324—22no—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C2×M16×C19—22no—
25C2×C4⋊C4×C19—22no—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19C2×C412yes—
28C2×C4⋊C4×C19D412yes—
29C2×C22⋊Dic19—22no—
30C2×C22⋊Dic19—21no—
31C2×C22⋊Dic19—21no—
32#10597372—22no—
33#10597372—22no—
34C2×C4⋊Dic19—22no—
35C2×C4⋊Dic19C2×C411yescharacteristic
36C2×C4⋊Dic19C2×C411yescharacteristic
37C2×Dic19⋊C4—22no—
38C2×C4×Dic19—21no—
39C2×C4×Dic19D414yes—
40C19×C22⋊C8—22no—
41C19×C22⋊C8—22no—
42C19⋊#95—22no—
43C19⋊#95—24no—
44C19⋊#95—22no—
45C19⋊#95—22no—
46C19⋊#95—22no—
47C19⋊#95—22no—
48C19⋊#95—21no—
49C19⋊#95C2×C412yes—
50C24×C19C2×D411yescharacteristic
51C22×C4×C19—21no—
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—42no—
56C22×C4×C19—42no—
57C22×C4×C19—42no—
58C22×C4×C19C22⋊C412yes—
59C22×C4×C19C22⋊C412yes—
60C22×C4×C19C22×C411yescharacteristic
61C22×C4×C19C2×D412yes—
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19#4112yes—
64C22×Dic19—22no—
65C22×Dic19—21no—
66C22×Dic19—21no—
67C22×Dic19—24no—
68M16×C19—44no—
69C2×C8×C19—42no—
70C4⋊C4×C19—24no—
71C4⋊C4×C19—24no—
72C22⋊Dic19—44no—
73C22⋊Dic19—42no—
74C22⋊Dic19—41no—
75C22⋊Dic19—41no—
76C4⋊Dic19—22no—
77C4⋊Dic19—22no—
78C4⋊Dic19—82no—
79Dic19⋊C4—44no—
80C4×Dic19—42no—
81C4×Dic19—44no—
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—81no—
102C2×C4×C19C4×D412yes—
103C2×C4×C19#12112yes—
104C2×Dic19—42no—
105C2×Dic19—44no—
106C2×Dic19—42no—
107C2×Dic19—44no—
108C2×Dic19—42no—
109C2×Dic19—41no—
110C2×Dic19—41no—
111C2×Dic19—42no—
112C2×Dic19—42no—
113C2×Dic19—44no—
114C8×C19—82no—
115#2484—191no—
116#2313—191no—
117#1826—192no—
118#1463D1911yescharacteristic
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—
135Dic19—84no—
136Dic19—82no—
137Dic19—81no—
138Dic19—81no—
139C2×#117—191no—
140C22×C4⋊C4C2×D1911yescharacteristic
141#407C2×D1912yes—
142#400—192no—
143#398—192no—
144#387—384no—
145#387—382no—
146#385—381no—
147#381—191no—
148#381—381no—
149#381—381no—
150#380—381no—
151C4×C22⋊C4—192no—
152#339—384no—
153#324—22no—
154C2×C19—22no—
155C2×C19—22no—
156C2×C19—41no—
157C2×C19#189011yescharacteristic
158C2×C19#189711yescharacteristic
159C2×C19#191211yescharacteristic
160C23×C4D7611yescharacteristic
161C23×C4D7611yescharacteristic
162C23×C4C22×D1911yescharacteristic
163C2×M16—22no—
164#117—382no—
165#117—382no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—191no—
169C2×C4⋊C4—191no—
170C2×C4⋊C4—382no—
171C2×C4⋊C4—382no—
172C2×C4⋊C4C4×D1912yes—
173C2×C4⋊C4C22⋊D1912yes—
174C2×C22⋊C4—381no—
175C2×C22⋊C4—382no—
176C2×C22⋊C4—381no—
177C2×C42—194no—
178C2×C42—381no—
179C22⋊C8—22no—
180C22⋊C8—22no—
181#95—192no—
182#95—382no—
183#95—384no—
184#95—382no—
185#95—382no—
186#95—382no—
187#95—382no—
188#95—381no—
189C19#948211yescharacteristic, complemented, Sylow
190C24C2×D7611yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—384no—
199C22×C4—382no—
200C22×C4—381no—
201C22×C4—381no—
202C22×C4(C2×D19)⋊C412yes—
203C22×C4(C2×D19)⋊C412yes—
204C22×C4C2×C4×D1911yescharacteristic
205C22×C4D4×D1912yes—
206C22×C4#6454312yes—
207C22×C4C2×C22⋊D1911yescharacteristic
208M16—44no—
209C2×C8—42no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—382no—
213C4⋊C4—382no—
214C4⋊C4—764no—
215C4⋊C4—1522no—
216C22⋊C4—764no—
217C22⋊C4—762no—
218C22⋊C4—761no—
219C22⋊C4—761no—
220C42—764no—
221C42—762no—
222C23—22no—
223C23—22no—
224C23—41no—
225C23#1059732811yescharacteristic
226C23#1059733211yescharacteristic
227C23C2×(C2×D19)⋊C411yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—81no—
241C2×C4—762no—
242C2×C4—764no—
243C2×C4—764no—
244C2×C4—762no—
245C2×C4—762no—
246C2×C4—762no—
247C2×C4—762no—
248C2×C4—761no—
249C2×C4—761no—
250C2×C4—764no—
251C2×C4(C22⋊D19)⋊C412yes—
252C2×C4#1059738512yes—
253C8—82no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22#1192642111yescharacteristic
263C22#1192656012yes—
264C22#1192673512yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—1524no—
270C4—1522no—
271C4—1521no—
272C4—1521no—
273C2—22no—
274C2—22no—
275C2—41no—
276C2#1456404611yescharacteristic
277C2#1456408111yescharacteristic
278C2#1456417011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1463C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#1463D19
hypocenterC19#9482
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
7. #11926483C4semidirect
8. #11926474C4semidirect
189. C19#9482semidirect

Maximal subgroups

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

subgroupindex
#145679222
#145662382
#145637322
#145614892
C19×#14632
#948219