Finite Group Databasebeta

← #18083200

Subgroups — #18083200

Order 4864.

502 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 81 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#14573579C212yesmaximal
2#14563710C211yesmaximal, characteristic
3#14562168C212yesmaximal
4#14561543C211yesmaximal, characteristic
5C19×#2817C211yesmaximal, characteristic
6C2×#10597372C2211yescharacteristic
7#11926882—24no—
8#11926877—22no—
9#11926872—22no—
10#11926584—22no—
11#11926553—22no—
12#11926508C2212yes—
13#11926407C2211yescharacteristic
14#11926310—22no—
15#11926281—24no—
16C2×C19×C22⋊Q8C2212yes—
17C19×#400—22no—
18C19×#397—22no—
19C19×#395—22no—
20C19×#381C2211yescharacteristic
21C22×Q8×C19D412yes—
22C23×C4×C19C2311yescharacteristic
23C19×C22⋊Q8—22no—
24C19×C22⋊Q8—22no—
25C19×C22⋊Q8—22no—
26C19×C22⋊Q8—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19D412yes—
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19D412yes—
32C2×C22⋊Dic19—21no—
33C2×C22⋊Dic19—21no—
34#10597372—22no—
35#10597372—22no—
36C2×C4⋊Dic19D412yes—
37C2×C4×Dic19—21no—
38C2×#64520—22no—
39C19×#95—24no—
40C19×#95—22no—
41C19×#95—22no—
42#10597292—24no—
43#10597292—24no—
44C19⋊#95—22no—
45C22⋊(C19⋊C8)—22no—
46C22⋊(C19⋊C8)D414yes—
47#10597265—24no—
48#10597264—24no—
49C24×C19C2×D411yescharacteristic
50C2×Q8×C19—22no—
51C2×Q8×C19—22no—
52C2×Q8×C19—44no—
53C22×C4×C19—22no—
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—42no—
57C22×C4×C19C2×D411yescharacteristic
58C22×C4×C19C2×D412yes—
59C22×C4×C19C2×D412yes—
60C22×C4×C19#4111yescharacteristic
61C22×Dic19—22no—
62C22×Dic19—41no—
63C4⋊C4×C19—22no—
64C4⋊C4×C19—22no—
65C4⋊C4×C19—42no—
66C4⋊C4×C19—42no—
67C4⋊C4×C19—82no—
68C22⋊C4×C19—42no—
69C22⋊C4×C19—42no—
70C22⋊C4×C19—42no—
71C22⋊Dic19—41no—
72C22⋊Dic19—41no—
73C22⋊Dic19—42no—
74C4⋊Dic19—22no—
75C4⋊Dic19—22no—
76C4×Dic19—42no—
77#64520—44no—
78C2×C19⋊C8—24no—
79#9985—191nomaximal, Sylow
80C23×C19—22no—
81C23×C19—42no—
82C23×C19#12011yescharacteristic
83C23×C19#12111yescharacteristic
84C23×C19#12711yescharacteristic
85Q8×C19—44no—
86Q8×C19—82no—
87C2×C4×C19—24no—
88C2×C4×C19—41no—
89C2×C4×C19—42no—
90C2×C4×C19—41no—
91C2×C4×C19—44no—
92C2×C4×C19—44no—
93C2×C4×C19—42no—
94C2×C4×C19—42no—
95C2×C4×C19—42no—
96C2×C4×C19—44no—
97C2×C4×C19#12012yes—
98C2×C4×C19#12112yes—
99C2×Dic19—42no—
100C2×Dic19—82no—
101C2×Dic19—81no—
102C2×Dic19—82no—
103C19⋊C8—44no—
104#3095—192no—
105#2817D1911yescharacteristic
106#1820—191no—
107#1511—192no—
108#1306—191no—
109C22×C19—22no—
110C22×C19—22no—
111C22×C19—22no—
112C22×C19—21no—
113C22×C19—21no—
114C22×C19—82no—
115C22×C19#39211yescharacteristic
116C22×C19#45812yes—
117C4×C19—22no—
118C4×C19—22no—
119C4×C19—82no—
120C4×C19—82no—
121C4×C19—82no—
122Dic19—82no—
123Dic19—161no—
124C2×C22⋊Q8C2×D1912yes—
125C2×#117—191no—
126#485—384no—
127#484—382no—
128#483—382no—
129#428—382no—
130#419—382no—
131#407—192no—
132#400—22no—
133#397—22no—
134#395—22no—
135#381—191no—
136#381C2×D1911yescharacteristic
137#342—382no—
138#328—384no—
139C2×C19—22no—
140C2×C19—41no—
141C2×C19—41no—
142C2×C19#200912yes—
143C2×C19#202211yescharacteristic
144C22×Q8C22⋊D1912yes—
145C23×C4C22×D1911yescharacteristic
146C2×M16—382no—
147C22⋊Q8—22no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151#117—382no—
152#117—382no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—192no—
156C2×C4⋊C4C22⋊D1912yes—
157C2×C22⋊C4—22no—
158C2×C22⋊C4—381no—
159C2×C22⋊C4—381no—
160C2×C22⋊C4C22⋊D1912yes—
161C2×C42—381no—
162#107—384no—
163#106—384no—
164#103—384no—
165#103—384no—
166C22⋊C8—194no—
167C22⋊C8—382no—
168#95—24no—
169#95—22no—
170#95—22no—
171#95—382no—
172C19#998511yescharacteristic, complemented, Sylow
173C24C2×C22⋊D1911yescharacteristic
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—44no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—42no—
181C22×C4—382no—
182C22×C4—761no—
183C22×C4D4×D1911yescharacteristic
184C22×C4D4×D1912yes—
185C22×C4#6454311yescharacteristic
186C22×C4C2×C22⋊D1912yes—
187M16—764no—
188C2×C8—384no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—82no—
194C4⋊C4—382no—
195C4⋊C4—382no—
196C22⋊C4—42no—
197C22⋊C4—42no—
198C22⋊C4—42no—
199C22⋊C4—761no—
200C22⋊C4—761no—
201C22⋊C4—762no—
202C42—762no—
203C23—22no—
204C23—42no—
205C23#1059738411yescharacteristic
206C23#1059738611yescharacteristic
207C23#1059739911yescharacteristic
208Q8—44no—
209Q8—82no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—44no—
215C2×C4—44no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—44no—
220C2×C4—762no—
221C2×C4—1521no—
222C2×C4—1522no—
223C2×C4—1522no—
224C2×C4#1059738312yes—
225C2×C4#1059738512yes—
226C8—764no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—21no—
232C22—82no—
233C22#1192645211yescharacteristic
234C22#1192673412yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—82no—
239C4—82no—
240C4—3041no—
241C4—1522no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2#1456469512yes—
246C2#1456476411yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2817C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#2817D19
hypocenterC19#9985
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2817

Complements

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

NH ≅ G/Ntype
172. C19#9985semidirect

Maximal subgroups

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

subgroupindex
#145735792
#145637102
#145621682
#145615432
C19×#28172
#998519