Finite Group Databasebeta

← #18075152

Subgroups — #18075152

Order 4864.

1222 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1222 conjugacy classes of subgroups — too many to draw. Only its 147 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#14563709C214yesmaximal, complemented
2#14563550C212yesmaximal
3C22×C19×#124C211yesmaximal, characteristic
4C2×#10597291—24no—
5#11926400C2214yes—
6#11926311—28no—
7C23×Q8×C19C411yescharacteristic, complemented
8C23×D4×C19C2211yescharacteristic
9C2×C19×#124—24no—
10C2×C19×#124—28no—
11C22×C22⋊C4×C19C412yescomplemented
12C22×C22⋊C4×C19C2212yes—
13C22×C42×C19C411yescharacteristic, complemented
14C25×C19C2×C411yescharacteristic
15C25×C19C2311yescharacteristic
16C22×Q8×C19—24no—
17C22×Q8×C19—22no—
18C22×Q8×C19—44no—
19C22×D4×C19—24no—
20C22×D4×C19—44no—
21C22×D4×C19D414yes—
22C23×C4×C19C2×C411yescharacteristic
23C23×C4×C19C2×C412yes—
24C23×C4×C19C2×C412yes—
25C19×#124—232no—
26C2×C22⋊C4×C19—24no—
27C2×C22⋊C4×C19—24no—
28C2×C22⋊C4×C19—24no—
29C2×C22⋊C4×C19—24no—
30C2×C22⋊C4×C19—24no—
31C2×C22⋊C4×C19D418yes—
32C2×C42×C19—24no—
33C2×C42×C19—22no—
34C2×C22⋊Dic19—28no—
35C2×C22⋊Dic19—24no—
36#10597291—48no—
37C24×C19—22no—
38C24×C19—42no—
39C24×C19—42no—
40C24×C19—44no—
41C24×C19—44no—
42C24×C19C22⋊C412yes—
43C24×C19C22×C411yescharacteristic
44C24×C19C2×D412yes—
45C24×C19C2×D414yes—
46C2×Q8×C19—28no—
47C2×Q8×C19—416no—
48C2×Q8×C19—44no—
49C2×Q8×C19—44no—
50C2×D4×C19—28no—
51C2×D4×C19—28no—
52C2×D4×C19—44no—
53C2×D4×C19—416no—
54C22×C4×C19—22no—
55C22×C4×C19—24no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19—22no—
59C22×C4×C19—22no—
60C22×C4×C19—44no—
61C22×C4×C19—44no—
62C22×C4×C19C22⋊C412yes—
63C22×C4×C19C22⋊C414yes—
64C22×C4×C19C22⋊C414yes—
65C22×Dic19—44no—
66C22⋊C4×C19—216no—
67C22⋊C4×C19—216no—
68C42×C19—28no—
69C22⋊Dic19—416no—
70C22⋊Dic19—48no—
71#8544—191nomaximal, Sylow
72C23×C19—22no—
73C23×C19—24no—
74C23×C19—24no—
75C23×C19—28no—
76C23×C19—22no—
77C23×C19—24no—
78C23×C19—44no—
79C23×C19—44no—
80C23×C19—44no—
81C23×C19—44no—
82C23×C19—44no—
83C23×C19—44no—
84C23×C19—44no—
85C23×C19—88no—
86C23×C19—88no—
87C23×C19C2×C22⋊C411yescharacteristic
88C23×C19C2×C22⋊C412yes—
89C23×C19#12014yes—
90Q8×C19—416no—
91D4×C19—416no—
92C2×C4×C19—28no—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—24no—
96C2×C4×C19—24no—
97C2×C4×C19—44no—
98C2×C4×C19—44no—
99C2×C4×C19—44no—
100C2×C4×C19—44no—
101C2×C4×C19—44no—
102C2×C4×C19—44no—
103C2×C4×C19#9914yes—
104C2×Dic19—84no—
105C2×Dic19—88no—
106C22×#124D1911yescharacteristic
107#1819—194no—
108#1781—192no—
109C22×C19—28no—
110C22×C19—22no—
111C22×C19—22no—
112C22×C19—22no—
113C22×C19—24no—
114C22×C19—28no—
115C22×C19—42no—
116C22×C19—44no—
117C22×C19—84no—
118C22×C19—88no—
119C22×C19—84no—
120C22×C19—88no—
121C22×C19#37911yescharacteristic
122C22×C19C2×#9912yes—
123C22×C19#41014yes—
124C4×C19—24no—
125C4×C19—44no—
126C4×C19—44no—
127Dic19—164no—
128C23×Q8Dic1911yescharacteristic, complemented
129C23×D4C2×D1911yescharacteristic
130C2×#124—24no—
131C2×#124—28no—
132C22×C22⋊C4Dic1912yescomplemented
133C22×C22⋊C4C2×D1912yes—
134C22×C42Dic1911yescharacteristic, complemented
135C2×#99—384no—
136#379—194no—
137#342—388no—
138C2×C19—22no—
139C2×C19—24no—
140C2×C19—44no—
141C2×C19—82no—
142C2×C19#178111yescharacteristic
143C2×C19#178212yes—
144C25C2×Dic1911yescharacteristic
145C25C22×D1911yescharacteristic
146C22×Q8—24no—
147C22×Q8—22no—
148C22×Q8—44no—
149C22×D4—24no—
150C22×D4—44no—
151C22×D4C22⋊D1914yes—
152C23×C4C2×Dic1911yescharacteristic
153C23×C4C2×Dic1912yes—
154C23×C4C2×Dic1912yes—
155#124—232no—
156C2×C22⋊C4—24no—
157C2×C22⋊C4—24no—
158C2×C22⋊C4—24no—
159C2×C22⋊C4—24no—
160C2×C22⋊C4—24no—
161C2×C22⋊C4—388no—
162C2×C22⋊C4—384no—
163C2×C22⋊C4C22⋊D1918yes—
164C2×C42—24no—
165C2×C42—22no—
166#99—768no—
167C19#854411yescharacteristic, complemented, Sylow
168C24—22no—
169C24—42no—
170C24—42no—
171C24—44no—
172C24—44no—
173C24C22⋊Dic1912yes—
174C24C22×Dic1911yescharacteristic
175C24C2×C22⋊D1912yes—
176C24C2×C22⋊D1914yes—
177C2×Q8—28no—
178C2×Q8—416no—
179C2×Q8—44no—
180C2×Q8—44no—
181C2×D4—28no—
182C2×D4—28no—
183C2×D4—44no—
184C2×D4—416no—
185C22×C4—22no—
186C22×C4—24no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—44no—
192C22×C4—44no—
193C22×C4—764no—
194C22×C4C22⋊Dic1912yes—
195C22×C4C22⋊Dic1914yes—
196C22×C4C22⋊Dic1914yes—
197C22⋊C4—216no—
198C22⋊C4—216no—
199C22⋊C4—768no—
200C22⋊C4—7616no—
201C42—28no—
202C23—22no—
203C23—24no—
204C23—24no—
205C23—28no—
206C23—22no—
207C23—24no—
208C23—44no—
209C23—44no—
210C23—44no—
211C23—44no—
212C23—44no—
213C23—44no—
214C23—44no—
215C23—88no—
216C23—88no—
217C23C2×C22⋊Dic1911yescharacteristic
218C23C2×C22⋊Dic1912yes—
219C23#1059739914yes—
220Q8—416no—
221D4—416no—
222C2×C4—28no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—24no—
226C2×C4—24no—
227C2×C4—44no—
228C2×C4—44no—
229C2×C4—44no—
230C2×C4—44no—
231C2×C4—44no—
232C2×C4—44no—
233C2×C4—1524no—
234C2×C4—1528no—
235C2×C4#1059729114yes—
236C22—28no—
237C22—22no—
238C22—22no—
239C22—22no—
240C22—24no—
241C22—28no—
242C22—42no—
243C22—44no—
244C22—84no—
245C22—88no—
246C22—84no—
247C22—88no—
248C22#1192640011yescharacteristic
249C22C2×#1059729112yes—
250C22#1192651814yes—
251C4—24no—
252C4—44no—
253C4—44no—
254C4—3044no—
255C2—22no—
256C2—24no—
257C2—44no—
258C2—82no—
259C2#1456355011yescharacteristic
260C2#1456355312yes—
subgroupG/H
centerC22#11926400
commutatorC24×C19C22×C4
FrattiniC25C22×D19
FittingC22×C19×#124C2
socleC22×C19#379
prime radicalC23×D4×C19C22
cosocleC25×C19C23
hypercenterC22×#124D19
hypocenterC19#8544
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. #14563709C2semidirect
7. C23×Q8×C19C4semidirect
11. C22×C22⋊C4×C19C4semidirect
13. C22×C42×C19C4semidirect
128. C23×Q8Dic19semidirect
132. C22×C22⋊C4Dic19semidirect
134. C22×C42Dic19semidirect
167. C19#8544semidirect

Maximal subgroups

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

subgroupindex
#145637092
#145635502
C22×C19×#1242
#854419