Finite Group Databasebeta

← #18080263

Subgroups — #18080263

Order 4864.

512 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 103 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#14568116C211yesmaximal, characteristic
2#14563715C211yesmaximal, characteristic
3#14562167C212yesmaximal
4#14561487C212yesmaximal
5C19×#2313C211yesmaximal, characteristic
6C2×#10597370C2211yescharacteristic
7#11926508C2212yes—
8#11926482—22no—
9#11926449C412yescomplemented
10#11926409C412yescomplemented
11#11926407—21no—
12#11926407—21no—
13C4×C22⋊Dic19C2211yescharacteristic
14#11926313—22no—
15#11926280—24no—
16C22×C4⋊C4×C19C2211yescharacteristic
17C19×#387—24no—
18C19×#381C2212yes—
19C19×#380—21no—
20C4×C22⋊C4×C19—21no—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×Dic38C2×C411yescharacteristic
25C2×C4⋊C4×C19—22no—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19C2×C412yes—
29C2×C4⋊C4×C19D412yes—
30C2×C22⋊C4×C19—22no—
31C2×C42×C19—22no—
32C2×C22⋊Dic19—21no—
33C2×C22⋊Dic19—21no—
34C2×C4⋊Dic19C2×C411yescharacteristic
35#10597370—22no—
36#10597370—22no—
37C2×Dic19⋊C4—21no—
38C2×C4×Dic19C2×C412yes—
39C2×#64520—22no—
40C19×#95—22no—
41C19×#95—22no—
42C19×#95—22no—
43C19×#95D414yes—
44C19⋊#95—22no—
45C19⋊#95—22no—
46C19⋊#95—22no—
47C19⋊#95—22no—
48C19⋊#95—21no—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)—22no—
51C24×C19C2×D411yescharacteristic
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—24no—
57C22×C4×C19—42no—
58C22×C4×C19—42no—
59C22×C4×C19—42no—
60C22×C4×C19C22⋊C412yes—
61C22×C4×C19C22⋊C412yes—
62C22×C4×C19C22×C411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D412yes—
65C22×C4×C19#4112yes—
66C22×Dic19—21no—
67C22×Dic19—22no—
68C22×Dic19—21no—
69C2×Dic38—22no—
70C2×Dic38—42no—
71C4⋊C4×C19—24no—
72C4⋊C4×C19—24no—
73C4⋊C4×C19—82no—
74C22⋊C4×C19—44no—
75C42×C19—82no—
76C22⋊Dic19—42no—
77C22⋊Dic19—41no—
78C22⋊Dic19—41no—
79C4⋊Dic19—22no—
80Dic19⋊C4—42no—
81C4×Dic19—42no—
82#64520—44no—
83C2×C19⋊C8—42no—
84#9460—191nomaximal, Sylow
85C23×C19—22no—
86C23×C19—22no—
87C23×C19—41no—
88C23×C19C2×C22⋊C411yescharacteristic
89C23×C19#12011yescharacteristic
90C23×C19#12311yescharacteristic
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—42no—
96C2×C4×C19—42no—
97C2×C4×C19—42no—
98C2×C4×C19—42no—
99C2×C4×C19—42no—
100C2×C4×C19—42no—
101C2×C4×C19—44no—
102C2×C4×C19—44no—
103C2×C4×C19—44no—
104C2×C4×C19—81no—
105C2×C4×C19—81no—
106C2×C4×C19C4×D412yes—
107C2×C4×C19#12112yes—
108C2×Dic19—42no—
109C2×Dic19—42no—
110C2×Dic19—42no—
111C2×Dic19—41no—
112C2×Dic19—41no—
113C2×Dic19—42no—
114C2×Dic19—42no—
115Dic38—82no—
116C19⋊C8—82no—
117#2503—191no—
118#2313D1911yescharacteristic
119#1821—191no—
120#1511—192no—
121#1284—192no—
122C22×C19—21no—
123C22×C19—21no—
124C22×C19—21no—
125C22×C19—21no—
126C22×C19—21no—
127C22×C19—21no—
128C22×C19—21no—
129C22×C19—44no—
130C22×C19#38611yescharacteristic
131C22×C19#41012yes—
132C22×C19#45512yes—
133C4×C19—22no—
134C4×C19—22no—
135C4×C19—42no—
136C4×C19—42no—
137C4×C19—84no—
138Dic19—82no—
139Dic19—81no—
140Dic19—81no—
141C2×C22⋊Q8—191no—
142C22×C4⋊C4C2×D1911yescharacteristic
143#407—192no—
144#400—382no—
145#391—192no—
146#387—24no—
147#382—192no—
148#381—381no—
149#381—381no—
150#381C2×D1912yes—
151#380—21no—
152C4×C22⋊C4—21no—
153C4×C22⋊C4—191no—
154#343—382no—
155#328—384no—
156C2×C19—22no—
157C2×C19—22no—
158C2×C19—41no—
159C2×C19#188511yescharacteristic
160C2×C19#189911yescharacteristic
161C2×C19#191211yescharacteristic
162C22×Q8—191no—
163C23×C4C22⋊D1911yescharacteristic
164C23×C4C22⋊D1911yescharacteristic
165C23×C4C22×D1911yescharacteristic
166C2×M16—382no—
167C22⋊Q8—382no—
168C22⋊Q8—382no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—191no—
173C2×C4⋊C4—381no—
174C2×C4⋊C4C4×D1912yes—
175C2×C4⋊C4D7612yes—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—381no—
178C2×C22⋊C4—381no—
179C2×C42—22no—
180C2×C42—192no—
181C22⋊C8—382no—
182C22⋊C8—382no—
183#95—22no—
184#95—22no—
185#95—22no—
186#95—382no—
187#95—382no—
188#95—382no—
189#95—382no—
190#95—381no—
191#95C22⋊D1914yes—
192C19#946011yescharacteristic, complemented, Sylow
193C24C2×C22⋊D1911yescharacteristic
194C2×Q8—382no—
195C2×Q8—762no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—24no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—382no—
205C22×C4—381no—
206C22×C4—381no—
207C22×C4(C2×D19)⋊C412yes—
208C22×C4(C2×D19)⋊C412yes—
209C22×C4C2×C4×D1911yescharacteristic
210C22×C4C2×D7611yescharacteristic
211C22×C4#6454112yes—
212C22×C4C2×C22⋊D1912yes—
213M16—764no—
214C2×C8—762no—
215C4⋊C4—24no—
216C4⋊C4—24no—
217C4⋊C4—82no—
218C4⋊C4—382no—
219C4⋊C4—762no—
220C22⋊C4—44no—
221C22⋊C4—762no—
222C22⋊C4—761no—
223C22⋊C4—761no—
224C42—82no—
225C42—762no—
226C23—22no—
227C23—22no—
228C23—41no—
229C23C2×(C2×D19)⋊C411yescharacteristic
230C23#1059737511yescharacteristic
231C23#1059739911yescharacteristic
232Q8—1522no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—44no—
245C2×C4—44no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—762no—
249C2×C4—762no—
250C2×C4—762no—
251C2×C4—761no—
252C2×C4—761no—
253C2×C4—762no—
254C2×C4—762no—
255C2×C4C4×C22⋊D1912yes—
256C2×C4#1059737612yes—
257C8—1522no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—44no—
266C22#1192642311yescharacteristic
267C22#1192651712yes—
268C22#1192672212yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—84no—
274C4—1522no—
275C4—1521no—
276C4—1521no—
277C2—22no—
278C2—22no—
279C2—41no—
280C2#1456402311yescharacteristic
281C2#1456409311yescharacteristic
282C2#1456417211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2313C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2313D19
hypocenterC19#9460
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
9. #11926449C4semidirect
10. #11926409C4semidirect
192. C19#9460semidirect

Maximal subgroups

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

subgroupindex
#145681162
#145637152
#145621672
#145614872
C19×#23132
#946019