Finite Group Databasebeta

← #18085433

Subgroups — #18085433

Order 4864.

806 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 89 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#14567294C212yesmaximal, complemented
2#14563558C211yesmaximal, characteristic, complemented
3#14562151C212yesmaximal, complemented
4#14561520C211yesmaximal, characteristic, complemented
5C19×#3192C211yesmaximal, characteristic
6C23×Dic38C2211yescharacteristic
7C2×#10597382—22no—
8C2×#10597281—22no—
9#11926508C2211yescharacteristic
10#11926456—24no—
11#11926449—22no—
12#11926424—24no—
13C4×C22⋊Dic19C2212yes—
14#11926278—24no—
15C2×C19×#121C2212yes—
16C19×#481—22no—
17C19×#469—22no—
18C19×#447—22no—
19C19×#407C2211yescharacteristic
20C22×D4×C19—22no—
21C22×D4×C19D412yes—
22C23×C4×C19C2311yescharacteristic
23C23×Dic19D412yes—
24C22×Dic38—22no—
25C22×Dic38—21no—
26C22×Dic38—22no—
27C22×Dic38—21no—
28C22×Dic38—44no—
29C2×D8×C19—22no—
30C2×M16×C19D412yes—
31C19×#121—22no—
32C19×#121—22no—
33C19×#121—22no—
34C19×#121—22no—
35C2×C4⋊C4×C19D412yes—
36C2×C22⋊C4×C19—22no—
37C2×C22⋊Dic19—28no—
38C2×C22⋊Dic19—22no—
39#10597382—48no—
40C2×C4×Dic19—22no—
41C2×#64520—21no—
42C19×#106—22no—
43C19×#102—24no—
44C19×C22⋊C8—22no—
45C19⋊#95—28no—
46C19⋊#95D414yes—
47C22⋊(C19⋊C8)—22no—
48#10597281—44no—
49C24×C19—22no—
50C24×C19C2×D411yescharacteristic
51C2×D4×C19—22no—
52C2×D4×C19—22no—
53C2×D4×C19—44no—
54C2×D4×C19—48no—
55C2×D4×C19—42no—
56C2×D4×C19—42no—
57C22×C4×C19—22no—
58C22×C4×C19—42no—
59C22×C4×C19C2×D412yes—
60C22×C4×C19C2×D412yes—
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19#4111yescharacteristic
63C22×Dic19—24no—
64C22×Dic19—22no—
65C22×Dic19—24no—
66C22×Dic19—44no—
67C2×Dic38—28no—
68C2×Dic38—24no—
69C2×Dic38—48no—
70C2×Dic38—44no—
71C2×Dic38—42no—
72C2×Dic38—44no—
73C2×Dic38—41no—
74C2×Dic38—42no—
75C2×Dic38—41no—
76D8×C19—82no—
77M16×C19—42no—
78C2×C8×C19—22no—
79C4⋊C4×C19—22no—
80C4⋊C4×C19—22no—
81C22⋊C4×C19—42no—
82C22⋊C4×C19—42no—
83C22⋊Dic19—416no—
84C22⋊Dic19—44no—
85C4×Dic19—44no—
86#64520—42no—
87C2×C19⋊C8—41no—
88#10327—191nomaximal, Sylow
89C23×C19—24no—
90C23×C19—41no—
91C23×C19—44no—
92C23×C19—44no—
93C23×C19—42no—
94C23×C19—44no—
95C23×C19#12012yes—
96C23×C19#12111yescharacteristic
97D4×C19—44no—
98D4×C19—82no—
99D4×C19—84no—
100D4×C19—84no—
101C2×C4×C19—22no—
102C2×C4×C19—24no—
103C2×C4×C19—42no—
104C2×C4×C19—41no—
105C2×C4×C19—44no—
106C2×C4×C19—42no—
107C2×C4×C19#12011yescharacteristic
108C2×C4×C19#12112yes—
109C2×C4×C19#12711yescharacteristic
110C2×Dic19—28no—
111C2×Dic19—24no—
112C2×Dic19—44no—
113C2×Dic19—42no—
114C2×Dic19—42no—
115C2×Dic19—44no—
116C2×Dic19—44no—
117C2×Dic19—44no—
118Dic38—44no—
119Dic38—48no—
120Dic38—44no—
121C8×C19—42no—
122C19⋊C8—81no—
123#3192D1911yescharacteristic
124#2436—192no—
125#1784—191no—
126#1507—192no—
127#1297—191no—
128C22×C19—22no—
129C22×C19—22no—
130C22×C19—22no—
131C22×C19—21no—
132C22×C19—44no—
133C22×C19—88no—
134C22×C19—82no—
135C22×C19—82no—
136C22×C19—82no—
137C22×C19#39211yescharacteristic
138C22×C19#45414yes—
139C4×C19—21no—
140C4×C19—22no—
141C4×C19—82no—
142C4×C19B(4,𝔽2)12yes—
143Dic19—44no—
144Dic19—84no—
145C23×Q8—191no—
146C2×#124—382no—
147C2×#121C2×D1912yes—
148#481—22no—
149#469—22no—
150#447—22no—
151C2×#101—382no—
152#407—191no—
153#407C2×D1911yescharacteristic
154#393—384no—
155#391—382no—
156#386—384no—
157C4×C22⋊C4—192no—
158#327—384no—
159C2×C19—24no—
160C2×C19—41no—
161C2×C19—162no—
162C2×C19#200312yes—
163C2×C19#202111yescharacteristic
164C22×Q8—382no—
165C22×Q8—381no—
166C22×Q8—382no—
167C22×Q8—381no—
168C22×Q8—764no—
169C22×D4—22no—
170C22×D4C22⋊D1912yes—
171C23×C4—192no—
172C23×C4C22×D1911yescharacteristic
173C2×D8—22no—
174C2×M16—381no—
175C2×M16C22⋊D1912yes—
176#124—768no—
177#121—22no—
178#121—22no—
179#121—22no—
180#121—22no—
181C2×C4⋊C4C22⋊D1912yes—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—388no—
184C2×C22⋊C4—382no—
185C2×C42—382no—
186#106—22no—
187#102—24no—
188#101—764no—
189C22⋊C8—22no—
190C22⋊C8—382no—
191#95—194no—
192#95—388no—
193C19#1032711yescharacteristic, complemented, Sylow
194C24—22no—
195C24D4×D1911yescharacteristic
196C2×Q8—384no—
197C2×Q8—388no—
198C2×Q8—764no—
199C2×Q8—762no—
200C2×Q8—768no—
201C2×Q8—764no—
202C2×Q8—762no—
203C2×Q8—761no—
204C2×Q8—761no—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—44no—
208C2×D4—48no—
209C2×D4—42no—
210C2×D4—42no—
211C22×C4—22no—
212C22×C4—42no—
213C22×C4—384no—
214C22×C4—382no—
215C22×C4—384no—
216C22×C4—764no—
217C22×C4D4×D1912yes—
218C22×C4#6454311yescharacteristic
219C22×C4C2×C22⋊D1912yes—
220C22×C4C2×C22⋊D1911yescharacteristic
221D8—82no—
222M16—42no—
223M16—762no—
224C2×C8—22no—
225C2×C8—761no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C22⋊C4—42no—
229C22⋊C4—42no—
230C22⋊C4—7616no—
231C22⋊C4—764no—
232C42—764no—
233C23—24no—
234C23—41no—
235C23—44no—
236C23—44no—
237C23—42no—
238C23—44no—
239C23#1059738312yes—
240C23#1059738411yescharacteristic
241Q8—764no—
242Q8—768no—
243Q8—764no—
244D4—44no—
245D4—82no—
246D4—84no—
247D4—84no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—44no—
253C2×C4—42no—
254C2×C4—388no—
255C2×C4—384no—
256C2×C4—764no—
257C2×C4—762no—
258C2×C4—762no—
259C2×C4—764no—
260C2×C4—764no—
261C2×C4—764no—
262C2×C4#1059738512yes—
263C2×C4#1059738611yescharacteristic
264C2×C4#1059739911yescharacteristic
265C8—42no—
266C8—1521no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—21no—
271C22—44no—
272C22—88no—
273C22—82no—
274C22—82no—
275C22—82no—
276C22#1192645211yescharacteristic
277C22#1192671514yes—
278C4—21no—
279C4—22no—
280C4—82no—
281C4—764no—
282C4—1524no—
283C4#1192673112yes—
284C2—24no—
285C2—41no—
286C2—162no—
287C2#1456465412yes—
288C2#1456475911yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3192C2
socleC22×C19#392
hypercenter#3192D19
hypocenterC19#10327
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3192

Complements

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

NH ≅ G/Ntype
1. #14567294C2semidirect
2. #14563558C2semidirect
3. #14562151C2semidirect
4. #14561520C2semidirect
193. C19#10327semidirect

Maximal subgroups

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

subgroupindex
#145672942
#145635582
#145621512
#145615202
C19×#31922
#1032719