Finite Group Databasebeta

← #18071383

Subgroups — #18071383

Order 4864.

424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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#14571623C211yesmaximal, characteristic
2#14564969C212yesmaximal
3#14564734C211yesmaximal, characteristic
4#14561459C212yesmaximal
5C19×#1272C211yesmaximal, characteristic
6C22×#64528—21no—
7C2×#10597315C2211yescharacteristic
8C2×#10597274—22no—
9C2×#10597267—21no—
10#11926483—21no—
11#11926476—22no—
12#11926451—21no—
13#11926442C2212yes—
14#11926431—22no—
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
24C2×#64528—42no—
25C2×#64528—42no—
26C2×#64528—42no—
27C2×C4⋊Dic19—22no—
28C2×C4⋊Dic19—21no—
29C2×C4⋊Dic19—21no—
30C2×C4⋊Dic19D412yes—
31C2×C4⋊Dic19D412yes—
32C2×Dic19⋊C4—22no—
33C2×C4×Dic19—21no—
34C22×C19⋊C8—21no—
35#10597315—42no—
36C19×#95—22no—
37C19⋊#95—21no—
38C19⋊#95—22no—
39C19⋊#95—22no—
40C19⋊#95—22no—
41#10597274—44no—
42#10597267—42no—
43C2×Q8×C19—21no—
44C2×Q8×C19—41no—
45C2×Q8×C19—41no—
46C2×Q8×C19SD1612yes—
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19C2×D411yescharacteristic
50C22×C4×C19C2×D412yes—
51C22×Dic19—22no—
52C22×Dic19—22no—
53C22×Dic19—41no—
54C2×Dic38—22no—
55C2×Dic38—41no—
56C2×Dic38—41no—
57C2×Dic38—41no—
58C2×Dic38—41no—
59C2×Dic38—41no—
60C2×C8×C19—24no—
61C2×C8×C19—42no—
62C2×C8×C19—42no—
63C4⋊C4×C19—41no—
64C42×C19—41no—
65#64528—48no—
66C4⋊Dic19—24no—
67C4⋊Dic19—22no—
68C4⋊Dic19—22no—
69C4⋊Dic19—42no—
70C4⋊Dic19—42no—
71C4⋊Dic19—81no—
72C4⋊Dic19—81no—
73Dic19⋊C4—42no—
74Dic19⋊C4—42no—
75C4×Dic19—81no—
76C2×C19⋊C8—22no—
77C2×C19⋊C8—41no—
78C2×C19⋊C8—41no—
79#7760—191nomaximal, Sylow
80C23×C19#12011yescharacteristic
81Q8×C19—42no—
82Q8×C19—81no—
83C2×C4×C19—21no—
84C2×C4×C19—22no—
85C2×C4×C19—21no—
86C2×C4×C19—22no—
87C2×C4×C19—22no—
88C2×C4×C19—41no—
89C2×C4×C19—41no—
90C2×C4×C19—41no—
91C2×C4×C19—42no—
92C2×C4×C19C2×SD1611yescharacteristic
93C2×C4×C19#13512yes—
94C2×C4×C19#13711yescharacteristic
95C2×C4×C19#13712yes—
96C2×Dic19—42no—
97C2×Dic19—42no—
98C2×Dic19—42no—
99C2×Dic19—42no—
100C2×Dic19—42no—
101C2×Dic19—42no—
102C2×Dic19—42no—
103C2×Dic19—81no—
104C2×Dic19—81no—
105Dic38—42no—
106Dic38—42no—
107Dic38—81no—
108Dic38—81no—
109C8×C19—44no—
110C19⋊C8—42no—
111#2809—191no—
112#2058—192no—
113#2016—191no—
114#1272D1911yescharacteristic
115#1271—192no—
116C22×C19#44811yescharacteristic
117C22×C19#45212yes—
118C22×C19#45311yescharacteristic
119C22×C19#45612yes—
120C22×C19B(4,𝔽2)11yescharacteristic
121C4×C19—21no—
122C4×C19—21no—
123C4×C19—22no—
124C4×C19—22no—
125C4×C19—42no—
126C4×C19—81no—
127Dic19—82no—
128Dic19—82no—
129Dic19—82no—
130C22×Q16—381no—
131C2×C4⋊Q8—191no—
132C2×#106—382no—
133C2×#103—381no—
134#400—381no—
135#398—382no—
136#391—381no—
137#391C2×D1911yescharacteristic
138#389—192no—
139#387—382no—
140#340—382no—
141#336—191no—
142#336C2×D1912yes—
143C2×C19#159611yescharacteristic
144C2×C19#160312yes—
145C2×C19#163411yescharacteristic
146C2×C19#165312yes—
147C2×C19#166011yescharacteristic
148C22×Q8—381no—
149C22×Q8D7611yescharacteristic
150C2×Q16—762no—
151C2×Q16—762no—
152C2×Q16—762no—
153C22×C8—22no—
154C22×C8—381no—
155C4⋊Q8—762no—
156C2×C4⋊C4—192no—
157C2×C4⋊C4—192no—
158C2×C4⋊C4—382no—
159C2×C4⋊C4—382no—
160C2×C4⋊C4—381no—
161C2×C4⋊C4—381no—
162C2×C4⋊C4D7611yescharacteristic
163C2×C42—381no—
164C2×C42C22×D1911yescharacteristic
165#106—764no—
166#103—762no—
167#95—22no—
168#95—381no—
169#95—382no—
170#95—382no—
171#95—382no—
172C19#776011yescharacteristic, complemented, Sylow
173C2×Q8—21no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—382no—
177C2×Q8—761no—
178C2×Q8—761no—
179C2×Q8—761no—
180C2×Q8—761no—
181C2×Q8—761no—
182C2×Q8#6451612yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—382no—
186C22×C4—382no—
187C22×C4—761no—
188C22×C4C2×D7611yescharacteristic
189C22×C4D4×D1912yes—
190Q16—768no—
191C2×C8—24no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—382no—
195C2×C8—761no—
196C2×C8—761no—
197C4⋊C4—41no—
198C4⋊C4—384no—
199C4⋊C4—382no—
200C4⋊C4—382no—
201C4⋊C4—762no—
202C4⋊C4—762no—
203C4⋊C4—762no—
204C4⋊C4—762no—
205C4⋊C4—1521no—
206C4⋊C4—1521no—
207C42—41no—
208C42—1521no—
209C23#1059732811yescharacteristic
210Q8—42no—
211Q8—81no—
212Q8—762no—
213Q8—762no—
214Q8—1521no—
215Q8—1521no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—762no—
226C2×C4—762no—
227C2×C4—762no—
228C2×C4—762no—
229C2×C4—762no—
230C2×C4—762no—
231C2×C4—762no—
232C2×C4—1521no—
233C2×C4—1521no—
234C2×C4C2×#6451611yescharacteristic
235C2×C4#1059735511yescharacteristic
236C2×C4#1059736212yes—
237C2×C4#1059736412yes—
238C8—44no—
239C8—762no—
240C22#1192668511yescharacteristic
241C22#1192670912yes—
242C22#1192671411yescharacteristic
243C22#1192672812yes—
244C22#1192673211yescharacteristic
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—42no—
250C4—81no—
251C4—1522no—
252C4—1522no—
253C4—1522no—
254C2#1456256011yescharacteristic
255C2#1456260112yes—
256C2#1456278111yescharacteristic
257C2#1456291412yes—
258C2#1456294711yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1272C2
socle, prime radicalC23×C19#120
hypercenter#1272D19
hypocenterC19#7760
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
172. C19#7760semidirect

Maximal subgroups

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

subgroupindex
#145716232
#145649692
#145647342
#145614592
C19×#12722
#776019