Finite Group Databasebeta

← #18075184

Subgroups — #18075184

Order 4864.

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

normal subgroups only

This group has 778 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#14563715C212yesmaximal
2#14561965C212yesmaximal
3#14561965C212yesmaximal
4C22×C19×#125C211yesmaximal, characteristic
5#11926508C2214yes—
6#11926313—24no—
7#11926270—24no—
8#11926270—24no—
9C2×C19×#125—24no—
10C2×C19×#125—24no—
11C2×C19×#125—24no—
12C22×C4⋊C4×C19C411yescharacteristic
13C22×C4⋊C4×C19C411yescharacteristic
14C22×C4⋊C4×C19C411yescharacteristic
15C22×C4⋊C4×C19C2211yescharacteristic
16C22×C4⋊C4×C19C2211yescharacteristic
17C22×C4⋊C4×C19C2211yescharacteristic
18C22×C42×C19C411yescharacteristic
19C23×C4×C19C2×C411yescharacteristic
20C23×C4×C19C2×C411yescharacteristic
21C23×C4×C19C2×C411yescharacteristic
22C23×C4×C19C2×C411yescharacteristic
23C23×C4×C19C2×C411yescharacteristic
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C19×#125—232no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—22no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19—22no—
34C2×C4⋊C4×C19—22no—
35C2×C4⋊C4×C19—22no—
36C2×C4⋊C4×C19—22no—
37C2×C4⋊C4×C19—22no—
38C2×C4⋊C4×C19—22no—
39C2×C4⋊C4×C19—22no—
40C2×C4⋊C4×C19—22no—
41C2×C4⋊C4×C19—22no—
42C2×C4⋊C4×C19D414yes—
43C2×C4⋊C4×C19D414yes—
44C2×C4⋊C4×C19D414yes—
45C2×C42×C19—22no—
46C2×C42×C19—22no—
47C2×C42×C19—22no—
48C2×#64520—24no—
49C22⋊(C19⋊C8)—24no—
50C22⋊(C19⋊C8)—24no—
51C24×C19C22×C411yescharacteristic
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—24no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—42no—
66C22×C4×C19—42no—
67C22×C4×C19—42no—
68C22×C4×C19—42no—
69C22×C4×C19—42no—
70C22×C4×C19—42no—
71C22×C4×C19C22⋊C412yes—
72C22×C4×C19C22⋊C412yes—
73C22×C4×C19C22⋊C412yes—
74C22×C4×C19C22⋊C412yes—
75C22×C4×C19C22⋊C412yes—
76C22×C4×C19C22⋊C412yes—
77C22×C4×C19C2×D412yes—
78C22×C4×C19C2×D412yes—
79C22×C4×C19C2×D412yes—
80C4⋊C4×C19—28no—
81C4⋊C4×C19—28no—
82C4⋊C4×C19—28no—
83C4⋊C4×C19—28no—
84C4⋊C4×C19—28no—
85C4⋊C4×C19—28no—
86C42×C19—28no—
87#64520—48no—
88C2×C19⋊C8—44no—
89#8554—191nomaximal, Sylow
90C23×C19—22no—
91C23×C19—22no—
92C23×C19—22no—
93C23×C19C2×C22⋊C411yescharacteristic
94C23×C19C2×C22⋊C411yescharacteristic
95C23×C19C2×C22⋊C411yescharacteristic
96C2×C4×C19—24no—
97C2×C4×C19—24no—
98C2×C4×C19—22no—
99C2×C4×C19—24no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—22no—
103C2×C4×C19—22no—
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19—24no—
107C2×C4×C19—42no—
108C2×C4×C19—42no—
109C2×C4×C19—42no—
110C2×C4×C19—42no—
111C2×C4×C19—42no—
112C2×C4×C19—42no—
113C2×C4×C19—42no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19#10114yes—
124C2×C4×C19#12014yes—
125C19⋊C8—84no—
126C22×#125D1911yescharacteristic
127#1821—192no—
128#1463—192no—
129#1463—192no—
130C22×C19—28no—
131C22×C19—21no—
132C22×C19—21no—
133C22×C19—21no—
134C22×C19—21no—
135C22×C19—21no—
136C22×C19—21no—
137C22×C19#37911yescharacteristic
138C22×C19#41012yes—
139C22×C19C2×#10112yes—
140C22×C19#41312yes—
141C4×C19—24no—
142C4×C19—24no—
143C4×C19—42no—
144C4×C19—42no—
145C4×C19—42no—
146C4×C19—42no—
147C4×C19—42no—
148C2×#125—24no—
149C2×#125—24no—
150C2×#125—24no—
151C22×C4⋊C4Dic1911yescharacteristic
152C22×C4⋊C4Dic1911yescharacteristic
153C22×C4⋊C4Dic1911yescharacteristic
154C22×C4⋊C4C2×D1911yescharacteristic
155C22×C4⋊C4C2×D1911yescharacteristic
156C22×C4⋊C4C2×D1911yescharacteristic
157C22×C42Dic1911yescharacteristic
158#407—194no—
159#343—384no—
160#324—384no—
161#324—384no—
162C2×C19—22no—
163C2×C19—22no—
164C2×C19—22no—
165C2×C19#178211yescharacteristic
166C2×C19#178411yescharacteristic
167C2×C19#178511yescharacteristic
168C23×C4C2×Dic1911yescharacteristic
169C23×C4C2×Dic1911yescharacteristic
170C23×C4C2×Dic1911yescharacteristic
171C23×C4C2×Dic1911yescharacteristic
172C23×C4C2×Dic1911yescharacteristic
173C23×C4C2×Dic1911yescharacteristic
174C23×C4C22×D1911yescharacteristic
175C2×M16—384no—
176#125—232no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4C22⋊D1914yes—
193C2×C4⋊C4C22⋊D1914yes—
194C2×C4⋊C4C22⋊D1914yes—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42—22no—
198C22⋊C8—384no—
199C22⋊C8—384no—
200C19#855411yescharacteristic, complemented, Sylow
201C24C22×Dic1911yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—24no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4C22⋊Dic1912yes—
222C22×C4C22⋊Dic1912yes—
223C22×C4C22⋊Dic1912yes—
224C22×C4C22⋊Dic1912yes—
225C22×C4C22⋊Dic1912yes—
226C22×C4C22⋊Dic1912yes—
227C22×C4C2×C22⋊D1912yes—
228C22×C4C2×C22⋊D1912yes—
229C22×C4C2×C22⋊D1912yes—
230M16—768no—
231C2×C8—764no—
232C4⋊C4—28no—
233C4⋊C4—28no—
234C4⋊C4—28no—
235C4⋊C4—28no—
236C4⋊C4—28no—
237C4⋊C4—28no—
238C42—28no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23C2×C22⋊Dic1911yescharacteristic
243C23C2×C22⋊Dic1911yescharacteristic
244C23C2×C22⋊Dic1911yescharacteristic
245C2×C4—24no—
246C2×C4—24no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4#1059729314yes—
273C2×C4#1059739914yes—
274C8—1524no—
275C22—28no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22#1192640011yescharacteristic
283C22#1192651812yes—
284C22C2×#1059729312yes—
285C22#1192652812yes—
286C4—24no—
287C4—24no—
288C4—42no—
289C4—42no—
290C4—42no—
291C4—42no—
292C4—42no—
293C2—22no—
294C2—22no—
295C2—22no—
296C2#1456355311yescharacteristic
297C2#1456355911yescharacteristic
298C2#1456356311yescharacteristic
subgroupG/H
centerC22#11926400
commutator, prime radicalC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC22×C19×#125C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenterC22×#125D19
hypocenterC19#8554
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
200. C19#8554semidirect

Maximal subgroups

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

subgroupindex
#145637152
#145619652
C22×C19×#1252
#855419