Finite Group Databasebeta

← #18071781

Subgroups — #18071781

Order 4864.

434 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 87 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#14565163C211yesmaximal, characteristic
2#14565111C212yesmaximal, complemented
3#14561458C212yesmaximal, complemented
4#14561456C211yesmaximal, characteristic
5C19×#2724C211yesmaximal, characteristic
6C2×#10597264—21no—
7C2×#10597265—22no—
8C2×#10597289—21no—
9#11926414C2211yescharacteristic
10#11926306—22no—
11#11926299C2211yescharacteristic
12#11926299C2212yes—
13C2×C19×#123—21no—
14C19×#398—21no—
15C19×#397—22no—
16C19×#390C2211yescharacteristic
17C19×#389C2212yes—
18C19×#385—22no—
19C22×D4×C19D411yescharacteristic
20C23×C4×C19—21no—
21C19×#123—42no—
22C19×#123—42no—
23C2×C4⋊C4×C19—22no—
24C2×C4⋊C4×C19—21no—
25C2×C4⋊C4×C19D412yes—
26C2×C4⋊C4×C19D412yes—
27C2×C4⋊C4×C19D411yescharacteristic
28C2×C22⋊C4×C19—22no—
29C2×C22⋊C4×C19—21no—
30C2×C22⋊C4×C19—22no—
31C2×C42×C19C2311yescharacteristic
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19—22no—
34C22×C19⋊C8—21no—
35C22×C19⋊C8—22no—
36C19×#95—22no—
37C19×#95—21no—
38C19×#95—22no—
39#10597289—42no—
40#10597265—44no—
41#10597264—42no—
42C24×C19—21no—
43C2×D4×C19—21no—
44C2×D4×C19—41no—
45C2×D4×C19—41no—
46C2×D4×C19SD1612yes—
47C22×C4×C19—21no—
48C22×C4×C19—22no—
49C22×C4×C19—22no—
50C22×C4×C19—42no—
51C22×C4×C19—81no—
52C22×C4×C19—81no—
53C22×C4×C19C2×D411yescharacteristic
54C22×C4×C19C2×D412yes—
55C22×Dic19—41no—
56C4⋊C4×C19—22no—
57C4⋊C4×C19—22no—
58C4⋊C4×C19—42no—
59C4⋊C4×C19—41no—
60C4⋊C4×C19—42no—
61C4⋊C4×C19—42no—
62C4⋊C4×C19—81no—
63C22⋊C4×C19—42no—
64C22⋊C4×C19—44no—
65C22⋊C4×C19—42no—
66C22⋊C4×C19—42no—
67C42×C19—41no—
68C4⋊Dic19—41no—
69C4⋊Dic19—41no—
70C4⋊Dic19—42no—
71C4⋊Dic19—42no—
72C2×C19⋊C8—22no—
73C2×C19⋊C8—24no—
74C2×C19⋊C8—42no—
75C2×C19⋊C8—41no—
76C2×C19⋊C8—42no—
77C2×C19⋊C8—41no—
78#7819—191nomaximal, Sylow
79C23×C19—22no—
80C23×C19—42no—
81C23×C19—41no—
82C23×C19—42no—
83C23×C19—41no—
84C23×C19#12011yescharacteristic
85D4×C19—42no—
86D4×C19—81no—
87C2×C4×C19—21no—
88C2×C4×C19—22no—
89C2×C4×C19—22no—
90C2×C4×C19—21no—
91C2×C4×C19—42no—
92C2×C4×C19—42no—
93C2×C4×C19—42no—
94C2×C4×C19—42no—
95C2×C4×C19—41no—
96C2×C4×C19—42no—
97C2×C4×C19—42no—
98C2×C4×C19—42no—
99C2×C4×C19—84no—
100C2×C4×C19C2×SD1611yescharacteristic
101C2×C4×C19#13512yes—
102C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C19AGL(1,ℤ/8)12yes—
104C2×Dic19—82no—
105C2×Dic19—81no—
106C19⋊C8—44no—
107C19⋊C8—42no—
108#2724D1911yescharacteristic
109#2093—191no—
110#2084—192no—
111#1271—192no—
112#1270—191no—
113C22×C19—42no—
114C22×C19—44no—
115C22×C19—82no—
116C22×C19—81no—
117C22×C19—81no—
118C22×C19#44912yes—
119C22×C19#45011yescharacteristic
120C22×C19#45311yescharacteristic
121C22×C19#45612yes—
122C22×C19#45811yescharacteristic
123C4×C19—22no—
124C4×C19—22no—
125C4×C19—21no—
126C4×C19—21no—
127C4×C19—82no—
128C4×C19—81no—
129C4×C19—82no—
130Dic19—161no—
131C2×#123—21no—
132C2×#107—381no—
133C2×#106—382no—
134C2×#102—381no—
135#398—21no—
136#397—22no—
137#390C2×D1911yescharacteristic
138#389C2×D1912yes—
139#385—22no—
140#384—191no—
141#340—382no—
142#336—192no—
143#336—191no—
144C2×C19—82no—
145C2×C19#160912yes—
146C2×C19#161311yescharacteristic
147C2×C19#162011yescharacteristic
148C2×C19#165412yes—
149C2×C19#166011yescharacteristic
150C22×D4C22⋊D1911yescharacteristic
151C23×C4—21no—
152C22×C8—382no—
153C22×C8—381no—
154#123—42no—
155#123—42no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—382no—
159C2×C4⋊C4—381no—
160C2×C4⋊C4C22⋊D1912yes—
161C2×C4⋊C4C22⋊D1912yes—
162C2×C4⋊C4C22⋊D1911yescharacteristic
163C2×C22⋊C4—22no—
164C2×C22⋊C4—21no—
165C2×C22⋊C4—22no—
166C2×C42C22×D1911yescharacteristic
167#107—762no—
168#106—764no—
169#102—762no—
170#95—22no—
171#95—21no—
172#95—22no—
173C19#781911yescharacteristic, complemented, Sylow
174C24—21no—
175C2×D4—21no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4#6452612yes—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—42no—
183C22×C4—81no—
184C22×C4—81no—
185C22×C4—761no—
186C22×C4C2×C22⋊D1911yescharacteristic
187C22×C4C2×C22⋊D1912yes—
188C2×C8—382no—
189C2×C8—384no—
190C2×C8—762no—
191C2×C8—761no—
192C2×C8—761no—
193C2×C8—762no—
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—81no—
201C4⋊C4—761no—
202C4⋊C4—761no—
203C4⋊C4—762no—
204C4⋊C4—762no—
205C22⋊C4—42no—
206C22⋊C4—44no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C42—41no—
210C23—22no—
211C23—42no—
212C23—41no—
213C23—42no—
214C23—41no—
215C23#1059739911yescharacteristic
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—1522no—
232C2×C4—1521no—
233C2×C4#1059737811yescharacteristic
234C2×C4C2×#6452611yescharacteristic
235C2×C4#1059739512yes—
236C2×C4#1059739612yes—
237C8—764no—
238C8—762no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22#1192668912yes—
245C22#1192669511yescharacteristic
246C22#1192671211yescharacteristic
247C22#1192672712yes—
248C22#1192673411yescharacteristic
249C4—22no—
250C4—22no—
251C4—21no—
252C4—21no—
253C4—82no—
254C4—82no—
255C4—81no—
256C4—3041no—
257C2—82no—
258C2#1456263212yes—
259C2#1456265511yescharacteristic
260C2#1456269411yescharacteristic
261C2#1456291912yes—
262C2#1456294611yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2724C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#2724D19
hypocenterC19#7819
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2724

Complements

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

NH ≅ G/Ntype
2. #14565111C2semidirect
3. #14561458C2semidirect
173. C19#7819semidirect

Maximal subgroups

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

subgroupindex
#145651632
#145651112
#145614582
#145614562
C19×#27242
#781919