Finite Group Databasebeta

← #18075139

Subgroups — #18075139

Order 4864.

718 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 131 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#14563718C211yesmaximal, characteristic, complemented
2#14563706C211yesmaximal, characteristic, complemented
3#14561983C214yesmaximal, complemented
4C19×#3491C211yesmaximal, characteristic
5#11926508C2212yes—
6C2×C22⋊(C19⋊C8)C2212yes—
7#11926313—22no—
8#11926299—22no—
9#11926270—24no—
10#11926268—24no—
11C19×#552—24no—
12C19×#551—24no—
13C19×#543C411yescharacteristic
14C19×#539—22no—
15C19×#534C411yescharacteristic
16C19×#529—22no—
17C2×C19×#123C2212yes—
18C19×#518C412yes—
19C2×C19×#117C2211yescharacteristic
20C22×D4×C19C2×C412yes—
21C23×C4×C19C2311yescharacteristic
22C19×#126—24no—
23C19×#126—24no—
24C19×#125—22no—
25C19×#125—24no—
26C19×#124—22no—
27C19×#123—24no—
28C19×#123—22no—
29C19×#123—22no—
30C19×#123—22no—
31C19×#123—24no—
32C19×C22⋊Q8—24no—
33C19×C22⋊Q8—22no—
34C19×C22⋊Q8—24no—
35C19×#121—22no—
36C19×#120—22no—
37C4×Q8×C19—22no—
38C4×D4×C19—22no—
39C4×D4×C19—24no—
40C4×D4×C19—24no—
41C19×#117—24no—
42C19×#117—22no—
43C19×#117—24no—
44C2×C4⋊C4×C19D412yes—
45C2×C4⋊C4×C19D414yes—
46C2×C22⋊C4×C19—22no—
47C2×C22⋊C4×C19C2×C411yescharacteristic
48C2×C22⋊C4×C19C2×C411yescharacteristic
49C2×C22⋊C4×C19C2×C412yes—
50C2×C22⋊C4×C19D414yes—
51C2×C42×C19D412yes—
52C2×#64520—22no—
53C22×C19⋊C8—22no—
54C22⋊(C19⋊C8)—24no—
55C22⋊(C19⋊C8)—24no—
56C24×C19C22⋊C412yes—
57C24×C19C22×C411yescharacteristic
58C2×Q8×C19—22no—
59C2×D4×C19—22no—
60C2×D4×C19—22no—
61C2×D4×C19—22no—
62C2×D4×C19—44no—
63C22×C4×C19—24no—
64C22×C4×C19—42no—
65C22×C4×C19C22⋊C412yes—
66C22×C4×C19C22⋊C412yes—
67C22×C4×C19C22⋊C414yes—
68C22×C4×C19C22⋊C412yes—
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19C2×D414yes—
72C4⋊C4×C19—24no—
73C4⋊C4×C19—24no—
74C4⋊C4×C19—22no—
75C4⋊C4×C19—22no—
76C4⋊C4×C19—24no—
77C4⋊C4×C19—24no—
78C4⋊C4×C19—24no—
79C22⋊C4×C19—24no—
80C22⋊C4×C19—24no—
81C22⋊C4×C19—22no—
82C22⋊C4×C19—22no—
83C22⋊C4×C19—22no—
84C22⋊C4×C19—22no—
85C22⋊C4×C19—24no—
86C22⋊C4×C19—24no—
87C42×C19—24no—
88C42×C19—22no—
89C42×C19—22no—
90#64520—44no—
91C2×C19⋊C8—44no—
92C2×C19⋊C8—42no—
93C2×C19⋊C8—42no—
94#8540—191nomaximal, Sylow
95C23×C19—22no—
96C23×C19—22no—
97C23×C19—42no—
98C23×C19—42no—
99C23×C19—44no—
100C23×C19C2×C22⋊C412yes—
101C23×C19C2×C22⋊C411yescharacteristic
102Q8×C19—82no—
103D4×C19—44no—
104D4×C19—44no—
105D4×C19—82no—
106C2×C4×C19—22no—
107C2×C4×C19—22no—
108C2×C4×C19—22no—
109C2×C4×C19—22no—
110C2×C4×C19—22no—
111C2×C4×C19—24no—
112C2×C4×C19—44no—
113C2×C4×C19—42no—
114C2×C4×C19—44no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19—84no—
118C2×C4×C19#12012yes—
119C2×C4×C19#12012yes—
120C19⋊C8—82no—
121C19⋊C8—82no—
122#3491D1911yescharacteristic
123#1822—191no—
124#1818—191no—
125#1468—194no—
126C22×C19—22no—
127C22×C19—22no—
128C22×C19—24no—
129C22×C19—42no—
130C22×C19—44no—
131C22×C19—82no—
132C22×C19—162no—
133C22×C19#37911yescharacteristic
134C22×C19#41012yes—
135C4×C19—22no—
136C4×C19—22no—
137C4×C19—42no—
138C4×C19—42no—
139C4×C19—44no—
140C4×C19—42no—
141#552—24no—
142#551—24no—
143#543Dic1911yescharacteristic
144#539—22no—
145#534Dic1911yescharacteristic
146#529—22no—
147C2×#123C2×D1912yes—
148#518Dic1912yes—
149C2×#117C2×D1911yescharacteristic
150#407—192no—
151C2×C22⋊C8—192no—
152#343—382no—
153#336—382no—
154#324—384no—
155#323—384no—
156C2×C19—22no—
157C2×C19—42no—
158C2×C19—82no—
159C2×C19#178211yescharacteristic
160C2×C19#179112yes—
161C22×D4C2×Dic1912yes—
162C23×C4C22×D1911yescharacteristic
163C2×M16—382no—
164C22×C8—382no—
165#126—24no—
166#126—24no—
167#125—22no—
168#125—24no—
169#124—22no—
170#123—24no—
171#123—22no—
172#123—22no—
173#123—22no—
174#123—24no—
175C22⋊Q8—24no—
176C22⋊Q8—22no—
177C22⋊Q8—24no—
178#121—22no—
179#120—22no—
180C4×Q8—22no—
181C4×D4—22no—
182C4×D4—24no—
183C4×D4—24no—
184#117—24no—
185#117—22no—
186#117—24no—
187C2×C4⋊C4C22⋊D1912yes—
188C2×C4⋊C4C22⋊D1914yes—
189C2×C22⋊C4—22no—
190C2×C22⋊C4C2×Dic1911yescharacteristic
191C2×C22⋊C4C2×Dic1911yescharacteristic
192C2×C22⋊C4C2×Dic1912yes—
193C2×C22⋊C4C22⋊D1914yes—
194C2×C42C22⋊D1912yes—
195C22⋊C8—384no—
196C22⋊C8—384no—
197C19#854011yescharacteristic, complemented, Sylow
198C24C22⋊Dic1912yes—
199C24C22×Dic1911yescharacteristic
200C2×Q8—22no—
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—44no—
205C22×C4—24no—
206C22×C4—42no—
207C22×C4C22⋊Dic1912yes—
208C22×C4C22⋊Dic1912yes—
209C22×C4C22⋊Dic1914yes—
210C22×C4C22⋊Dic1912yes—
211C22×C4C2×C22⋊D1911yescharacteristic
212C22×C4C2×C22⋊D1911yescharacteristic
213C22×C4C2×C22⋊D1914yes—
214M16—764no—
215C2×C8—764no—
216C2×C8—762no—
217C2×C8—762no—
218C4⋊C4—24no—
219C4⋊C4—24no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—24no—
223C4⋊C4—24no—
224C4⋊C4—24no—
225C22⋊C4—24no—
226C22⋊C4—24no—
227C22⋊C4—22no—
228C22⋊C4—22no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—24no—
232C22⋊C4—24no—
233C42—24no—
234C42—22no—
235C42—22no—
236C23—22no—
237C23—22no—
238C23—42no—
239C23—42no—
240C23—44no—
241C23C2×C22⋊Dic1912yes—
242C23C2×C22⋊Dic1911yescharacteristic
243Q8—82no—
244D4—44no—
245D4—44no—
246D4—82no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—44no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—84no—
259C2×C4#1059739912yes—
260C2×C4#1059739912yes—
261C8—1522no—
262C8—1522no—
263C22—22no—
264C22—24no—
265C22—22no—
266C22—44no—
267C22—42no—
268C22—82no—
269C22—162no—
270C22#1192640011yescharacteristic
271C22#1192651812yes—
272C4—22no—
273C4—22no—
274C4—42no—
275C4—44no—
276C4—42no—
277C4—42no—
278C2—22no—
279C2—42no—
280C2—82no—
281C2#1456355311yescharacteristic
282C2#1456358612yes—
subgroupG/H
centerC22#11926400
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3491C2
socleC22×C19#379
prime radicalC19×#534C4
cosocleC23×C4×C19C23
hypercenter#3491D19
hypocenterC19#8540
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3491

Complements

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

NH ≅ G/Ntype
1. #14563718C2semidirect
2. #14563706C2semidirect
3. #14561983C2semidirect
197. C19#8540semidirect

Maximal subgroups

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

subgroupindex
#145637182
#145637062
#145619832
C19×#34912
#854019