Finite Group Databasebeta

← #18071769

Subgroups — #18071769

Order 4864.

410 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 95 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#14565178C211yesmaximal, characteristic
2#14565111C212yesmaximal
3#14561461C211yesmaximal, characteristic
4#14561458C212yesmaximal
5C19×#2734C211yesmaximal, characteristic
6C2×#10597265—21no—
7C2×#10597265—22no—
8C2×#10597292—21no—
9#11926414C2211yescharacteristic
10#11926306—22no—
11#11926299C2211yescharacteristic
12#11926299C2212yes—
13C2×C19×C4⋊Q8—21no—
14C19×#398—21no—
15C19×#395—22no—
16C19×#391C2211yescharacteristic
17C19×#389C2212yes—
18C19×#387—22no—
19C22×Q8×C19—21no—
20C22×Q8×C19D411yescharacteristic
21C19×C4⋊Q8—42no—
22C19×C4⋊Q8—42no—
23C2×C4⋊C4×C19—22no—
24C2×C4⋊C4×C19—22no—
25C2×C4⋊C4×C19—21no—
26C2×C4⋊C4×C19D412yes—
27C2×C4⋊C4×C19D412yes—
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C42×C19—21no—
30C2×C42×C19C2311yescharacteristic
31C2×C4⋊Dic19—21no—
32C2×C4⋊Dic19—22no—
33C22×C19⋊C8—21no—
34C22×C19⋊C8—22no—
35C19×#95—21no—
36C19×#95—22no—
37C19×#95—22no—
38C19×#95—22no—
39#10597292—42no—
40#10597265—42no—
41#10597265—44no—
42C2×Q8×C19—21no—
43C2×Q8×C19—42no—
44C2×Q8×C19—41no—
45C2×Q8×C19—41no—
46C2×Q8×C19—81no—
47C2×Q8×C19—81no—
48C2×Q8×C19SD1612yes—
49C22×C4×C19—22no—
50C22×C4×C19—21no—
51C22×C4×C19—22no—
52C22×C4×C19—21no—
53C22×C4×C19C2×D411yescharacteristic
54C22×C4×C19C2×D412yes—
55C22×Dic19—41no—
56C4⋊C4×C19—22no—
57C4⋊C4×C19—42no—
58C4⋊C4×C19—41no—
59C4⋊C4×C19—44no—
60C4⋊C4×C19—42no—
61C4⋊C4×C19—42no—
62C4⋊C4×C19—81no—
63C4⋊C4×C19SD1614yes—
64C42×C19—41no—
65C42×C19—42no—
66C4⋊Dic19—41no—
67C4⋊Dic19—41no—
68C4⋊Dic19—42no—
69C4⋊Dic19—42no—
70C2×C19⋊C8—22no—
71C2×C19⋊C8—24no—
72C2×C19⋊C8—42no—
73C2×C19⋊C8—41no—
74C2×C19⋊C8—42no—
75C2×C19⋊C8—41no—
76#7817—191nomaximal, Sylow
77C23×C19#12011yescharacteristic
78Q8×C19—42no—
79Q8×C19—81no—
80Q8×C19—84no—
81C2×C4×C19—21no—
82C2×C4×C19—22no—
83C2×C4×C19—22no—
84C2×C4×C19—21no—
85C2×C4×C19—24no—
86C2×C4×C19—22no—
87C2×C4×C19—42no—
88C2×C4×C19—41no—
89C2×C4×C19—42no—
90C2×C4×C19—41no—
91C2×C4×C19—42no—
92C2×C4×C19—41no—
93C2×C4×C19—42no—
94C2×C4×C19—42no—
95C2×C4×C19—42no—
96C2×C4×C19C2×SD1611yescharacteristic
97C2×C4×C19C2×SD1612yes—
98C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
99C2×C4×C19#13712yes—
100C2×Dic19—82no—
101C2×Dic19—81no—
102C19⋊C8—44no—
103C19⋊C8—42no—
104#2734D1911yescharacteristic
105#2096—191no—
106#2084—192no—
107#1272—191no—
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—44no—
120C4×C19—82no—
121C4×C19—81no—
122Dic19—161no—
123C2×C4⋊Q8—21no—
124C2×#106—382no—
125C2×#106—381no—
126C2×#103—381no—
127#398—21no—
128#395—22no—
129#391C2×D1911yescharacteristic
130#389C2×D1912yes—
131#387—22no—
132#384—191no—
133#340—382no—
134#336—192no—
135#336—191no—
136C2×C19#161112yes—
137C2×C19#161311yescharacteristic
138C2×C19#162311yescharacteristic
139C2×C19#165112yes—
140C2×C19#166011yescharacteristic
141C22×Q8—21no—
142C22×Q8C22⋊D1911yescharacteristic
143C22×C8—382no—
144C22×C8—381no—
145C4⋊Q8—42no—
146C4⋊Q8—42no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—382no—
151C2×C4⋊C4—381no—
152C2×C4⋊C4C22⋊D1912yes—
153C2×C4⋊C4C22⋊D1912yes—
154C2×C4⋊C4C22⋊D1911yescharacteristic
155C2×C42—21no—
156C2×C42C22×D1911yescharacteristic
157#106—762no—
158#106—764no—
159#103—762no—
160#95—21no—
161#95—22no—
162#95—22no—
163#95—22no—
164C19#781711yescharacteristic, complemented, Sylow
165C2×Q8—21no—
166C2×Q8—42no—
167C2×Q8—41no—
168C2×Q8—41no—
169C2×Q8—81no—
170C2×Q8—81no—
171C2×Q8#6452612yes—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—761no—
177C22×C4C2×C22⋊D1911yescharacteristic
178C22×C4C2×C22⋊D1912yes—
179C2×C8—382no—
180C2×C8—384no—
181C2×C8—762no—
182C2×C8—761no—
183C2×C8—761no—
184C2×C8—762no—
185C4⋊C4—22no—
186C4⋊C4—41no—
187C4⋊C4—42no—
188C4⋊C4—44no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—81no—
192C4⋊C4—761no—
193C4⋊C4—761no—
194C4⋊C4—762no—
195C4⋊C4—762no—
196C4⋊C4#6452714yes—
197C42—41no—
198C42—42no—
199C23#1059739911yescharacteristic
200Q8—42no—
201Q8—81no—
202Q8—84no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—24no—
208C2×C4—22no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—1522no—
219C2×C4—1521no—
220C2×C4#1059737811yescharacteristic
221C2×C4C2×#6452611yescharacteristic
222C2×C4C2×#6452712yes—
223C2×C4#1059738812yes—
224C8—764no—
225C8—762no—
226C22#1192668312yes—
227C22#1192669511yescharacteristic
228C22#1192671211yescharacteristic
229C22#1192672712yes—
230C22#1192673411yescharacteristic
231C4—22no—
232C4—22no—
233C4—21no—
234C4—21no—
235C4—44no—
236C4—42no—
237C4—82no—
238C4—81no—
239C4—3041no—
240C2#1456264312yes—
241C2#1456265511yescharacteristic
242C2#1456271311yescharacteristic
243C2#1456289812yes—
244C2#1456294611yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2734C2
socle, prime radicalC23×C19#120
hypercenter#2734D19
hypocenterC19#7817
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2734

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
#145651782
#145651112
#145614612
#145614582
C19×#27342
#781719