Finite Group Databasebeta

← #18080353

Subgroups — #18080353

Order 4864.

610 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 111 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#14567922C211yesmaximal, characteristic
2#14563735C212yesmaximal
3#14561965C211yesmaximal, characteristic
4#14561488C212yesmaximal
5C19×#2274C211yesmaximal, characteristic
6C2×#10597372C2211yescharacteristic
7#11926508C2212yes—
8#11926483C412yescomplemented
9#11926474C412yescomplemented
10#11926425—22no—
11#11926417—21no—
12#11926407—21no—
13#11926407C2211yescharacteristic
14#11926304—24no—
15#11926270—22no—
16C2×C19×#117—21no—
17C22×C4⋊C4×C19C2211yescharacteristic
18C4×C4⋊C4×C19—24no—
19C4×C22⋊C4×C19—21no—
20C4×C22⋊C4×C19C2212yes—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C19×#117—28no—
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×C42×C19—22no—
33C2×C42×C19D414yes—
34C2×C22⋊Dic19—21no—
35C2×C22⋊Dic19—21no—
36#10597372—22no—
37#10597372—22no—
38C2×C4⋊Dic19C2×C411yescharacteristic
39C2×C4⋊Dic19C2×C411yescharacteristic
40C2×Dic19⋊C4—22no—
41C2×C4×Dic19—21no—
42C2×#64520—22no—
43C19×#95—22no—
44C19×#95—22no—
45C19⋊#95—22no—
46C19⋊#95—22no—
47C19⋊#95—22no—
48C19⋊#95—21no—
49C19⋊#95C2×C412yes—
50C22⋊(C19⋊C8)—22no—
51C22⋊(C19⋊C8)—22no—
52C24×C19C2×D411yescharacteristic
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—24no—
56C22×C4×C19—24no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—42no—
60C22×C4×C19—42no—
61C22×C4×C19C22⋊C412yes—
62C22×C4×C19C22⋊C412yes—
63C22×C4×C19C22×C411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×C4×C19C2×D412yes—
66C22×C4×C19#4112yes—
67C22×Dic19—22no—
68C22×Dic19—21no—
69C22×Dic19—21no—
70C4⋊C4×C19—28no—
71C4⋊C4×C19—24no—
72C4⋊C4×C19—24no—
73C22⋊C4×C19—28no—
74C42×C19—28no—
75C42×C19—44no—
76C42×C19—82no—
77C22⋊Dic19—42no—
78C22⋊Dic19—41no—
79C22⋊Dic19—41no—
80C4⋊Dic19—22no—
81C4⋊Dic19—22no—
82Dic19⋊C4—44no—
83C4×Dic19—42no—
84#64520—44no—
85C2×C19⋊C8—42no—
86#9478—191nomaximal, Sylow
87C23×C19—22no—
88C23×C19—22no—
89C23×C19—41no—
90C23×C19C2×C22⋊C411yescharacteristic
91C23×C19#12011yescharacteristic
92C23×C19#12311yescharacteristic
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—24no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—24no—
99C2×C4×C19—28no—
100C2×C4×C19—22no—
101C2×C4×C19—41no—
102C2×C4×C19—41no—
103C2×C4×C19—42no—
104C2×C4×C19—44no—
105C2×C4×C19—44no—
106C2×C4×C19—42no—
107C2×C4×C19—42no—
108C2×C4×C19—81no—
109C2×C4×C19#10414yes—
110C2×C4×C19C4×D412yes—
111C2×C4×C19#12112yes—
112C2×Dic19—42no—
113C2×Dic19—42no—
114C2×Dic19—42no—
115C2×Dic19—41no—
116C2×Dic19—41no—
117C2×Dic19—42no—
118C2×Dic19—42no—
119C19⋊C8—82no—
120#2484—191no—
121#2274D1911yescharacteristic
122#1826—192no—
123#1463—191no—
124#1284—192no—
125C22×C19—21no—
126C22×C19—21no—
127C22×C19—21no—
128C22×C19—21no—
129C22×C19—21no—
130C22×C19—21no—
131C22×C19—21no—
132C22×C19—44no—
133C22×C19#38611yescharacteristic
134C22×C19C2×#10412yes—
135C22×C19#45812yes—
136C4×C19—22no—
137C4×C19—22no—
138C4×C19—24no—
139C4×C19—48no—
140C4×C19—42no—
141Dic19—82no—
142Dic19—81no—
143Dic19—81no—
144C2×#117—21no—
145C2×#117—191no—
146C22×C4⋊C4C2×D1911yescharacteristic
147#407—192no—
148#400—192no—
149#398—192no—
150#387—382no—
151#385—381no—
152#381—191no—
153#381—381no—
154C4×C4⋊C4—24no—
155C4×C22⋊C4—21no—
156C4×C22⋊C4C2×D1912yes—
157#339—384no—
158#324—382no—
159C2×C19—22no—
160C2×C19—22no—
161C2×C19—41no—
162C2×C19#189011yescharacteristic
163C2×C19#189611yescharacteristic
164C2×C19#191211yescharacteristic
165C23×C4C22⋊D1911yescharacteristic
166C23×C4C22⋊D1911yescharacteristic
167C23×C4C22×D1911yescharacteristic
168C2×M16—382no—
169#117—28no—
170#117—382no—
171#117—382no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—191no—
176C2×C4⋊C4—191no—
177C2×C4⋊C4—382no—
178C2×C4⋊C4C4×D1912yes—
179C2×C4⋊C4D7612yes—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—381no—
182C2×C22⋊C4—381no—
183C2×C42—22no—
184C2×C42—22no—
185C2×C42—381no—
186C2×C42C22⋊D1914yes—
187C22⋊C8—382no—
188C22⋊C8—382no—
189#95—22no—
190#95—22no—
191#95—192no—
192#95—382no—
193#95—382no—
194#95—382no—
195#95—381no—
196C19#947811yescharacteristic, complemented, Sylow
197C24C2×C22⋊D1911yescharacteristic
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—24no—
201C22×C4—24no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—382no—
207C22×C4—381no—
208C22×C4—381no—
209C22×C4(C2×D19)⋊C412yes—
210C22×C4(C2×D19)⋊C412yes—
211C22×C4C2×C4×D1911yescharacteristic
212C22×C4C2×D7611yescharacteristic
213C22×C4#6454112yes—
214C22×C4C2×C22⋊D1912yes—
215M16—764no—
216C2×C8—762no—
217C4⋊C4—28no—
218C4⋊C4—24no—
219C4⋊C4—24no—
220C4⋊C4—382no—
221C4⋊C4—382no—
222C4⋊C4—764no—
223C22⋊C4—28no—
224C22⋊C4—762no—
225C22⋊C4—761no—
226C22⋊C4—761no—
227C42—28no—
228C42—44no—
229C42—82no—
230C42—762no—
231C23—22no—
232C23—22no—
233C23—41no—
234C23C2×(C2×D19)⋊C411yescharacteristic
235C23#1059737511yescharacteristic
236C23#1059739911yescharacteristic
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—24no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—24no—
243C2×C4—28no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—44no—
249C2×C4—44no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—81no—
253C2×C4—762no—
254C2×C4—762no—
255C2×C4—762no—
256C2×C4—762no—
257C2×C4—762no—
258C2×C4—761no—
259C2×C4—761no—
260C2×C4#1059726214yes—
261C2×C4C4×C22⋊D1912yes—
262C2×C4#1059737612yes—
263C8—1522no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22#1192642311yescharacteristic
273C22C2×#1059726212yes—
274C22#1192673412yes—
275C4—22no—
276C4—22no—
277C4—24no—
278C4—48no—
279C4—42no—
280C4—1522no—
281C4—1521no—
282C4—1521no—
283C2—22no—
284C2—22no—
285C2—41no—
286C2#1456404811yescharacteristic
287C2#1456407811yescharacteristic
288C2#1456417211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2274C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2274D19
hypocenterC19#9478
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2274

Complements

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

NH ≅ G/Ntype
8. #11926483C4semidirect
9. #11926474C4semidirect
196. C19#9478semidirect

Maximal subgroups

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

subgroupindex
#145679222
#145637352
#145619652
#145614882
C19×#22742
#947819