Finite Group Databasebeta

← #18071771

Subgroups — #18071771

Order 4864.

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

normal subgroups only

This group has 410 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#14570667C211yesmaximal, characteristic
2#14565178C211yesmaximal, characteristic
3#14565113C212yesmaximal
4#14561457C212yesmaximal
5C19×#1272C211yesmaximal, characteristic
6C2×#10597390—21no—
7C2×#10597274—22no—
8C2×#10597265—21no—
9C2×#10597292—21no—
10#11926474—21no—
11#11926465—22no—
12#11926442C2212yes—
13#11926429—22no—
14#11926414C2211yescharacteristic
15#11926307—22no—
16#11926299C2211yescharacteristic
17C19×#391C2211yescharacteristic
18C19×#336C2212yes—
19C22×Q8×C19D411yescharacteristic
20C22×Dic38—21no—
21C22×C8×C19—22no—
22C2×C4⋊C4×C19D411yescharacteristic
23C2×C42×C19C2311yescharacteristic
24#10597390—42no—
25#10597390—42no—
26C2×C4⋊Dic19—21no—
27C2×C4⋊Dic19—22no—
28C2×C4⋊Dic19—21no—
29C2×C4⋊Dic19D412yes—
30C2×C4⋊Dic19D412yes—
31C2×Dic19⋊C4—22no—
32C2×Dic19⋊C4—22no—
33C2×C4×Dic19—21no—
34C22×C19⋊C8—21no—
35C19×#95—22no—
36#10597292—42no—
37C19⋊#95—21no—
38C19⋊#95—22no—
39C19⋊#95—22no—
40#10597274—44no—
41#10597265—42no—
42C2×Q8×C19—21no—
43C2×Q8×C19—41no—
44C2×Q8×C19—41no—
45C2×Q8×C19SD1612yes—
46C22×C4×C19—21no—
47C22×C4×C19—21no—
48C22×C4×C19C2×D411yescharacteristic
49C22×C4×C19C2×D412yes—
50C22×Dic19—22no—
51C22×Dic19—22no—
52C22×Dic19—41no—
53C2×Dic38—42no—
54C2×Dic38—81no—
55C2×Dic38—81no—
56C2×C8×C19—24no—
57C2×C8×C19—42no—
58C2×C8×C19—42no—
59C4⋊C4×C19—41no—
60C42×C19—41no—
61C4⋊Dic19—22no—
62C4⋊Dic19—42no—
63C4⋊Dic19—41no—
64C4⋊Dic19—41no—
65C4⋊Dic19—42no—
66C4⋊Dic19—42no—
67C4⋊Dic19—81no—
68C4⋊Dic19SD1614yes—
69Dic19⋊C4—44no—
70Dic19⋊C4—42no—
71Dic19⋊C4—42no—
72C4×Dic19—42no—
73C2×C19⋊C8—22no—
74C2×C19⋊C8—41no—
75C2×C19⋊C8—41no—
76#7817—191nomaximal, Sylow
77C23×C19#12011yescharacteristic
78Q8×C19—42no—
79Q8×C19—81no—
80C2×C4×C19—21no—
81C2×C4×C19—22no—
82C2×C4×C19—21no—
83C2×C4×C19—22no—
84C2×C4×C19—22no—
85C2×C4×C19—41no—
86C2×C4×C19—41no—
87C2×C4×C19—41no—
88C2×C4×C19—42no—
89C2×C4×C19C2×SD1611yescharacteristic
90C2×C4×C19C2×SD1612yes—
91C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
92C2×C4×C19#13712yes—
93C2×Dic19—24no—
94C2×Dic19—42no—
95C2×Dic19—42no—
96C2×Dic19—42no—
97C2×Dic19—42no—
98C2×Dic19—42no—
99C2×Dic19—82no—
100C2×Dic19—81no—
101Dic38—84no—
102C8×C19—44no—
103C19⋊C8—42no—
104#2734—191no—
105#2096—191no—
106#2084—192no—
107#1272D1911yescharacteristic
108#1271—192no—
109C22×C19#44812yes—
110C22×C19#45011yescharacteristic
111C22×C19#45311yescharacteristic
112C22×C19#45612yes—
113C22×C19#45811yescharacteristic
114C4×C19—22no—
115C4×C19—22no—
116C4×C19—21no—
117C4×C19—21no—
118C4×C19—42no—
119C4×C19—81no—
120Dic19—44no—
121Dic19—82no—
122Dic19—161no—
123C2×C4⋊Q8—381no—
124C2×#106—382no—
125C2×#106—381no—
126C2×#103—381no—
127#398—381no—
128#395—382no—
129#391C2×D1911yescharacteristic
130#389—192no—
131#387—382no—
132#384—191no—
133#340—382no—
134#336—191no—
135#336C2×D1912yes—
136C2×C19#161112yes—
137C2×C19#161311yescharacteristic
138C2×C19#162311yescharacteristic
139C2×C19#165112yes—
140C2×C19#166011yescharacteristic
141C22×Q8—381no—
142C22×Q8D7611yescharacteristic
143C22×C8—22no—
144C22×C8—381no—
145C4⋊Q8—762no—
146C4⋊Q8—762no—
147C2×C4⋊C4—192no—
148C2×C4⋊C4—192no—
149C2×C4⋊C4—382no—
150C2×C4⋊C4—382no—
151C2×C4⋊C4—381no—
152C2×C4⋊C4—382no—
153C2×C4⋊C4—381no—
154C2×C4⋊C4D7611yescharacteristic
155C2×C42—381no—
156C2×C42C22×D1911yescharacteristic
157#106—762no—
158#106—764no—
159#103—762no—
160#95—22no—
161#95—381no—
162#95—382no—
163#95—382no—
164C19#781711yescharacteristic, complemented, Sylow
165C2×Q8—21no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—762no—
169C2×Q8—1521no—
170C2×Q8—1521no—
171C2×Q8#6451612yes—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—382no—
175C22×C4—382no—
176C22×C4—761no—
177C22×C4C2×D7611yescharacteristic
178C22×C4D4×D1912yes—
179C2×C8—24no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—382no—
183C2×C8—761no—
184C2×C8—761no—
185C4⋊C4—41no—
186C4⋊C4—194no—
187C4⋊C4—382no—
188C4⋊C4—762no—
189C4⋊C4—764no—
190C4⋊C4—761no—
191C4⋊C4—761no—
192C4⋊C4—762no—
193C4⋊C4—762no—
194C4⋊C4—762no—
195C4⋊C4—762no—
196C4⋊C4—1521no—
197C42—41no—
198C42—762no—
199C23#1059732811yescharacteristic
200Q8—42no—
201Q8—81no—
202Q8—1524no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—384no—
213C2×C4—762no—
214C2×C4—762no—
215C2×C4—762no—
216C2×C4—762no—
217C2×C4—762no—
218C2×C4—1522no—
219C2×C4—1521no—
220C2×C4C2×#6451611yescharacteristic
221C2×C4#1059735411yescharacteristic
222C2×C4SD16×D1912yes—
223C2×C4#1059736412yes—
224C8—44no—
225C8—762no—
226C22#1192668412yes—
227C22#1192669711yescharacteristic
228C22#1192671411yescharacteristic
229C22#1192672812yes—
230C22#1192673511yescharacteristic
231C4—22no—
232C4—22no—
233C4—21no—
234C4—21no—
235C4—42no—
236C4—81no—
237C4—3041no—
238C4—764no—
239C4—1522no—
240C2#1456264412yes—
241C2#1456265711yescharacteristic
242C2#1456271411yescharacteristic
243C2#1456290112yes—
244C2#1456294711yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1272C2
socle, prime radicalC23×C19#120
hypercenter#1272D19
hypocenterC19#7817
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
164. C19#7817semidirect

Maximal subgroups

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

subgroupindex
#145706672
#145651782
#145651132
#145614572
C19×#12722
#781719