Finite Group Databasebeta

← #18083203

Subgroups — #18083203

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#14573584C212yesmaximal
2#14571672C211yesmaximal, characteristic
3#14563710C211yesmaximal, characteristic
4#14562169C212yesmaximal
5C19×#1306C211yesmaximal, characteristic
6C2×#10597370C2212yes—
7C2×#10597372C2211yescharacteristic
8#11926886—24no—
9#11926880—22no—
10#11926875—22no—
11#11926586—22no—
12#11926554—22no—
13#11926484—22no—
14#11926469—22no—
15#11926465—22no—
16#11926407C2211yescharacteristic
17#11926310—22no—
18#11926282—24no—
19C19×#407C2212yes—
20C19×#381C2211yescharacteristic
21C23×C4×C19C2311yescharacteristic
22C22×Dic38D412yes—
23C2×M16×C19—22no—
24C2×C22⋊C4×C19D412yes—
25C2×C22⋊Dic19—22no—
26C2×C22⋊Dic19—21no—
27C2×C22⋊Dic19—21no—
28#10597372—22no—
29#10597372—22no—
30C2×C4⋊Dic19—22no—
31C2×C4⋊Dic19D412yes—
32C2×C4⋊Dic19D412yes—
33#10597370—22no—
34#10597370—22no—
35#10597370—22no—
36#10597370—22no—
37C2×Dic19⋊C4—22no—
38C2×C4×Dic19—21no—
39C19×C22⋊C8—22no—
40C19×C22⋊C8D414yes—
41C19×#95—22no—
42C19⋊#95—24no—
43C19⋊#95—22no—
44C19⋊#95—22no—
45#10597275—24no—
46#10597274—24no—
47#10597273—24no—
48#10597273—24no—
49C24×C19C2×D411yescharacteristic
50C22×C4×C19—22no—
51C22×C4×C19—42no—
52C22×C4×C19C2×D412yes—
53C22×C4×C19C2×D412yes—
54C22×C4×C19C2×D411yescharacteristic
55C22×C4×C19#4111yescharacteristic
56C22×Dic19—22no—
57C22×Dic19—22no—
58C22×Dic19—22no—
59C22×Dic19—41no—
60C2×Dic38—22no—
61C2×Dic38—22no—
62C2×Dic38—44no—
63M16×C19—44no—
64C2×C8×C19—24no—
65C22⋊C4×C19—42no—
66C22⋊Dic19—41no—
67C22⋊Dic19—42no—
68C22⋊Dic19—42no—
69C22⋊Dic19—41no—
70C22⋊Dic19—42no—
71C4⋊Dic19—22no—
72C4⋊Dic19—22no—
73C4⋊Dic19—22no—
74C4⋊Dic19—22no—
75C4⋊Dic19—82no—
76Dic19⋊C4—42no—
77Dic19⋊C4—42no—
78C4×Dic19—42no—
79#9985—191nomaximal, Sylow
80C23×C19—22no—
81C23×C19—42no—
82C23×C19#12011yescharacteristic
83C23×C19#12111yescharacteristic
84C23×C19#12711yescharacteristic
85C2×C4×C19—24no—
86C2×C4×C19—42no—
87C2×C4×C19—41no—
88C2×C4×C19—41no—
89C2×C4×C19—44no—
90C2×C4×C19—42no—
91C2×C4×C19#12012yes—
92C2×C4×C19#12112yes—
93C2×Dic19—44no—
94C2×Dic19—42no—
95C2×Dic19—42no—
96C2×Dic19—42no—
97C2×Dic19—44no—
98C2×Dic19—82no—
99C2×Dic19—81no—
100C2×Dic19—82no—
101Dic38—44no—
102Dic38—82no—
103C8×C19—44no—
104#3095—192no—
105#2817—191no—
106#1820—191no—
107#1511—192no—
108#1306D1911yescharacteristic
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—
120Dic19—82no—
121Dic19—82no—
122Dic19—82no—
123Dic19—161no—
124C2×C22⋊Q8—192no—
125C2×#117—191no—
126#485—384no—
127#484—382no—
128#483—382no—
129#428—382no—
130#419—382no—
131#407C2×D1912yes—
132#400—382no—
133#397—382no—
134#395—382no—
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×Q8—192no—
145C23×C4C22×D1911yescharacteristic
146C2×M16—22no—
147C22⋊Q8—382no—
148C22⋊Q8—382no—
149C22⋊Q8—382no—
150C22⋊Q8—382no—
151#117—382no—
152#117—382no—
153C2×C4⋊C4—192no—
154C2×C4⋊C4—192no—
155C2×C4⋊C4—382no—
156C2×C4⋊C4—382no—
157C2×C22⋊C4—381no—
158C2×C22⋊C4—382no—
159C2×C22⋊C4—381no—
160C2×C22⋊C4D7612yes—
161C2×C42—381no—
162#107—384no—
163#106—384no—
164#103—384no—
165#103—384no—
166C22⋊C8—22no—
167C22⋊C8D7614yes—
168#95—22no—
169#95—384no—
170#95—382no—
171#95—382no—
172C19#998511yescharacteristic, complemented, Sylow
173C24C2×D7611yescharacteristic
174C2×Q8—382no—
175C2×Q8—382no—
176C2×Q8—764no—
177C22×C4—22no—
178C22×C4—42no—
179C22×C4—382no—
180C22×C4—382no—
181C22×C4—382no—
182C22×C4—761no—
183C22×C4C2×D7612yes—
184C22×C4D4×D1912yes—
185C22×C4D4×D1911yescharacteristic
186C22×C4#6454511yescharacteristic
187M16—44no—
188C2×C8—24no—
189C4⋊C4—382no—
190C4⋊C4—382no—
191C4⋊C4—382no—
192C4⋊C4—382no—
193C4⋊C4—762no—
194C4⋊C4—762no—
195C4⋊C4—1522no—
196C22⋊C4—42no—
197C22⋊C4—761no—
198C22⋊C4—762no—
199C22⋊C4—761no—
200C22⋊C4—762no—
201C22⋊C4—762no—
202C42—762no—
203C23—22no—
204C23—42no—
205C23#1059732011yescharacteristic
206C23#1059732811yescharacteristic
207C23#1059734111yescharacteristic
208Q8—764no—
209Q8—1522no—
210C2×C4—24no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—764no—
217C2×C4—762no—
218C2×C4—762no—
219C2×C4—762no—
220C2×C4—764no—
221C2×C4—1521no—
222C2×C4—1522no—
223C2×C4—1522no—
224C2×C4#1059732812yes—
225C2×C4#1059734112yes—
226C8—44no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—21no—
232C22—82no—
233C22#1192645411yescharacteristic
234C22#1192673512yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—3041no—
239C4—1522no—
240C4—1522no—
241C4—1522no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2#1456469812yes—
246C2#1456476711yescharacteristic
subgroupG/H
centerC22#11926454
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1306C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#1306D19
hypocenterC19#9985
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

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
#145735842
#145716722
#145637102
#145621692
C19×#13062
#998519