Finite Group Databasebeta

← #18087043

Subgroups — #18087043

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#14563804C212yesmaximal
2#14563768C211yesmaximal, characteristic
3#14561516C211yesmaximal, characteristic
4#14561516C212yesmaximal
5C19×#2845C211yesmaximal, characteristic
6C2×#10597264—22no—
7C2×#10597265—22no—
8C2×#10597260C2211yescharacteristic
9C2×#10597260C2212yes—
10#11926414C2211yescharacteristic
11#11926306—22no—
12C19×#398—22no—
13C19×#398—22no—
14C19×#398—22no—
15C19×#382C2211yescharacteristic
16C19×#382C2212yes—
17C2×C4⋊C4×C19—22no—
18C2×C4⋊C4×C19—22no—
19C2×C4⋊C4×C19—22no—
20C2×C4⋊C4×C19D412yes—
21C2×C4⋊C4×C19D412yes—
22C2×C4⋊C4×C19D412yes—
23C2×C42×C19C2311yescharacteristic
24C2×C4⋊Dic19—21no—
25C2×C4⋊Dic19—22no—
26C22×C19⋊C8—22no—
27C22×C19⋊C8—21no—
28C19×#95—22no—
29C19×#95—22no—
30C19×#95—22no—
31C19×#95—22no—
32#10597265—44no—
33#10597264—44no—
34#10597260—22no—
35#10597260—21no—
36#10597260Q814yes—
37#10597260Q812yes—
38C22×C4×C19—22no—
39C22×C4×C19—22no—
40C22×C4×C19—22no—
41C22×C4×C19C2×D412yes—
42C22×C4×C19C2×D411yescharacteristic
43C22×Dic19—41no—
44C4⋊C4×C19—42no—
45C4⋊C4×C19—42no—
46C4⋊C4×C19—42no—
47C4⋊C4×C19—82no—
48C4⋊C4×C19—82no—
49C4⋊C4×C19—82no—
50C42×C19C2×Q812yes—
51C42×C19C2×Q811yescharacteristic
52C42×C19#4111yescharacteristic
53C4⋊Dic19—42no—
54C4⋊Dic19—42no—
55C4⋊Dic19—42no—
56C2×C19⋊C8—24no—
57C2×C19⋊C8—24no—
58C2×C19⋊C8—24no—
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×C19—42no—
72C2×C4×C19—42no—
73C2×C4×C19—42no—
74C2×C4×C19—42no—
75C2×C4×C19—42no—
76C2×C4×C19—42no—
77C2×C4×C19C22⋊Q812yes—
78C2×C4×C19C22⋊Q811yescharacteristic
79C2×C4×C19C4⋊Q812yes—
80C2×C4×C19C4⋊Q811yescharacteristic
81C2×Dic19—82no—
82C2×Dic19—81no—
83C19⋊C8—28no—
84C19⋊C8—42no—
85#2845D1911yescharacteristic
86#1847—192no—
87#1836—191no—
88#1295—191no—
89#1295—192no—
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—
100C4×C19—82no—
101C4×C19—82no—
102Dic19—161no—
103C2×#107—382no—
104C2×#106—382no—
105C2×#97—191no—
106C2×#97—192no—
107#398—22no—
108#398—22no—
109#398—22no—
110#384—191no—
111#382C2×D1911yescharacteristic
112#382C2×D1912yes—
113#340—382no—
114C2×C19#165611yescharacteristic
115C2×C19#166112yes—
116C2×C19#166311yescharacteristic
117C2×C19#206012yes—
118C2×C19#206111yescharacteristic
119C22×C8—382no—
120C22×C8—381no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—381no—
125C2×C4⋊C4—382no—
126C2×C4⋊C4C22⋊D1912yes—
127C2×C4⋊C4C22⋊D1912yes—
128C2×C4⋊C4C22⋊D1912yes—
129C2×C42C22×D1911yescharacteristic
130#107—764no—
131#106—764no—
132#97—194no—
133#97—192no—
134#97—382no—
135#97—381no—
136#95—22no—
137#95—22no—
138#95—22no—
139#95—22no—
140C19#1058511yescharacteristic, complemented, Sylow
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—761no—
145C22×C4C2×C22⋊D1912yes—
146C22×C4C2×C22⋊D1911yescharacteristic
147C2×C8—384no—
148C2×C8—384no—
149C2×C8—384no—
150C2×C8—382no—
151C2×C8—761no—
152C2×C8—761no—
153C4⋊C4—42no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—82no—
157C4⋊C4—82no—
158C4⋊C4—82no—
159C4⋊C4—762no—
160C4⋊C4—762no—
161C4⋊C4—762no—
162C42Q8×D1911yescharacteristic
163C42Q8×D1912yes—
164C42#6454511yescharacteristic
165C23#1059739911yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—1522no—
180C2×C4—1521no—
181C2×C4#1059739012yes—
182C2×C4#1059739011yescharacteristic
183C2×C4#1059739212yes—
184C2×C4#1059739211yescharacteristic
185C8—388no—
186C8—762no—
187C22#1192646311yescharacteristic
188C22#1192671212yes—
189C22#1192671711yescharacteristic
190C22#1192672211yescharacteristic
191C22#1192672712yes—
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—82no—
197C4—82no—
198C4—82no—
199C4—3041no—
200C2#1456292811yescharacteristic
201C2#1456295212yes—
202C2#1456296311yescharacteristic
203C2#1456497712yes—
204C2#1456498211yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2845C2
socle, prime radicalC23×C19#120
hypercenter#2845D19
hypocenterC19#10585
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2845

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
#145638042
#145637682
#145615162
C19×#28452
#1058519