Finite Group Databasebeta

← #18087047

Subgroups — #18087047

Order 4864.

382 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 97 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#14571910C211yesmaximal, characteristic
2#14563803C212yesmaximal
3#14563768C211yesmaximal, characteristic
4#14561517C212yesmaximal
5C19×#1295C211yesmaximal, characteristic
6C2×#10597275—22no—
7C2×#10597274—22no—
8C2×#10597260C2211yescharacteristic
9#11926478—22no—
10#11926477—22no—
11#11926476—22no—
12#11926414C2211yescharacteristic
13#11926410C2212yes—
14#11926306—22no—
15C2×C19×#97C2212yes—
16C19×#382C2211yescharacteristic
17C22×C8×C19—22no—
18C2×C4⋊C4×C19D412yes—
19C2×C42×C19C2311yescharacteristic
20C2×C4⋊Dic19—21no—
21C2×C4⋊Dic19—22no—
22C2×C4⋊Dic19—22no—
23C2×C4⋊Dic19D412yes—
24C2×C4⋊Dic19D412yes—
25C2×Dic19⋊C4—22no—
26C2×Dic19⋊C4—22no—
27C22×C19⋊C8—21no—
28C19×#97—22no—
29C19×#97Q814yes—
30C19×#95—22no—
31C19⋊#95—22no—
32C19⋊#95—22no—
33C19⋊#95—22no—
34#10597275—44no—
35#10597274—44no—
36#10597260—21no—
37#10597260Q812yes—
38C22×C4×C19—22no—
39C22×C4×C19C2×D411yescharacteristic
40C22×C4×C19C2×D412yes—
41C22×Dic19—22no—
42C22×Dic19—22no—
43C22×Dic19—41no—
44C2×C8×C19—24no—
45C2×C8×C19—24no—
46C2×C8×C19—24no—
47C4⋊C4×C19—42no—
48C42×C19C2×Q812yes—
49C42×C19C2×Q811yescharacteristic
50C42×C19#4111yescharacteristic
51C4⋊Dic19—42no—
52C4⋊Dic19—42no—
53C4⋊Dic19—42no—
54C4⋊Dic19—42no—
55C4⋊Dic19—42no—
56C4⋊Dic19—82no—
57Dic19⋊C4—82no—
58Dic19⋊C4—82no—
59C2×C19⋊C8—22no—
60C2×C19⋊C8—41no—
61C2×C19⋊C8—41no—
62#10585—191nomaximal, Sylow
63C23×C19#12011yescharacteristic
64C2×C4×C19—22no—
65C2×C4×C19—21no—
66C2×C4×C19—21no—
67C2×C4×C19—22no—
68C2×C4×C19—42no—
69C2×C4×C19—42no—
70C2×C4×C19—42no—
71C2×C4×C19C22⋊Q812yes—
72C2×C4×C19C22⋊Q811yescharacteristic
73C2×C4×C19C4⋊Q811yescharacteristic
74C2×C4×C19C4⋊Q812yes—
75C2×Dic19—42no—
76C2×Dic19—42no—
77C2×Dic19—42no—
78C2×Dic19—42no—
79C2×Dic19—42no—
80C2×Dic19—42no—
81C2×Dic19—82no—
82C2×Dic19—81no—
83C8×C19—28no—
84C19⋊C8—42no—
85#2845—191no—
86#1847—192no—
87#1836—191no—
88#1295—192no—
89#1295D1911yescharacteristic
90C22×C19#39511yescharacteristic
91C22×C19#45312yes—
92C22×C19#45411yescharacteristic
93C22×C19#45511yescharacteristic
94C22×C19#45612yes—
95C4×C19—22no—
96C4×C19—22no—
97C4×C19—21no—
98C4×C19—21no—
99C4×C19—82no—
100Dic19—82no—
101Dic19—82no—
102Dic19—161no—
103C2×#107—382no—
104C2×#106—382no—
105C2×#97—191no—
106C2×#97C2×D1912yes—
107#398—382no—
108#398—382no—
109#398—382no—
110#384—191no—
111#382—192no—
112#382C2×D1911yescharacteristic
113#340—382no—
114C2×C19#165611yescharacteristic
115C2×C19#166112yes—
116C2×C19#166311yescharacteristic
117C2×C19#206012yes—
118C2×C19#206111yescharacteristic
119C22×C8—22no—
120C22×C8—381no—
121C2×C4⋊C4—192no—
122C2×C4⋊C4—192no—
123C2×C4⋊C4—381no—
124C2×C4⋊C4—382no—
125C2×C4⋊C4—382no—
126C2×C4⋊C4—382no—
127C2×C4⋊C4—382no—
128C2×C4⋊C4D7612yes—
129C2×C42C22×D1911yescharacteristic
130#107—764no—
131#106—764no—
132#97—22no—
133#97—192no—
134#97—381no—
135#97Dic3814yes—
136#95—22no—
137#95—382no—
138#95—382no—
139#95—382no—
140C19#1058511yescharacteristic, complemented, Sylow
141C22×C4—22no—
142C22×C4—382no—
143C22×C4—382no—
144C22×C4—761no—
145C22×C4C2×D7611yescharacteristic
146C22×C4D4×D1912yes—
147C2×C8—24no—
148C2×C8—24no—
149C2×C8—24no—
150C2×C8—382no—
151C2×C8—761no—
152C2×C8—761no—
153C4⋊C4—42no—
154C4⋊C4—762no—
155C4⋊C4—762no—
156C4⋊C4—762no—
157C4⋊C4—762no—
158C4⋊C4—762no—
159C4⋊C4—1522no—
160C4⋊C4—1522no—
161C4⋊C4—1522no—
162C42C2×Dic3812yes—
163C42#6454311yescharacteristic
164C42Q8×D1911yescharacteristic
165C23#1059732811yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—762no—
174C2×C4—762no—
175C2×C4—762no—
176C2×C4—762no—
177C2×C4—762no—
178C2×C4—762no—
179C2×C4—1522no—
180C2×C4—1521no—
181C2×C4#1059731511yescharacteristic
182C2×C4#1059732412yes—
183C2×C4#1059733412yes—
184C2×C4#1059734311yescharacteristic
185C8—28no—
186C8—762no—
187C22#1192646511yescharacteristic
188C22#1192671312yes—
189C22#1192671911yescharacteristic
190C22#1192672411yescharacteristic
191C22#1192672812yes—
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—82no—
197C4—3041no—
198C4—1522no—
199C4—1522no—
200C2#1456293011yescharacteristic
201C2#1456295512yes—
202C2#1456296411yescharacteristic
203C2#1456497912yes—
204C2#1456498611yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1295C2
socle, prime radicalC23×C19#120
hypercenter#1295D19
hypocenterC19#10585
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
140. C19#10585semidirect

Maximal subgroups

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

subgroupindex
#145719102
#145638032
#145637682
#145615172
C19×#12952
#1058519