Finite Group Databasebeta

← #18080284

Subgroups — #18080284

Order 4864.

610 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 107 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#14566238C211yesmaximal, characteristic, complemented
2#14563715C211yesmaximal, characteristic, complemented
3#14562164C212yesmaximal
4#14561488C212yesmaximal, complemented
5C19×#2501C211yesmaximal, characteristic
6#11926508C2212yes—
7#11926430—24no—
8#11926407C2212yes—
9#11926404—21no—
10C4×C22⋊Dic19—21no—
11#11926313—22no—
12#11926278—24no—
13C2×C19×#123—21no—
14C2×C19×#123—21no—
15C2×C19×#121C2211yescharacteristic
16C22×C4⋊C4×C19C2211yescharacteristic
17C19×#399—22no—
18C19×#390C412yescomplemented
19C19×#384C412yescomplemented
20C4×C22⋊C4×C19C2211yescharacteristic
21C22×D4×C19—21no—
22C22×D4×C19C2×C411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C19×#123—44no—
27C19×#123—44no—
28C19×#121—22no—
29C19×#121—22no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19—22no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19C2×C412yes—
36C2×C4⋊C4×C19D412yes—
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—22no—
39C2×C22⋊C4×C19—22no—
40C2×C22⋊C4×C19—21no—
41C2×C42×C19C2×C412yes—
42C2×C22⋊Dic19—22no—
43C2×C4⋊Dic19—22no—
44C2×C4×Dic19—22no—
45C2×#64520—22no—
46C19×#95—21no—
47C19⋊#95—22no—
48C19⋊#95—22no—
49C19⋊#95—22no—
50C19⋊#95D414yes—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—22no—
53C24×C19—21no—
54C24×C19C2×D411yescharacteristic
55C2×D4×C19—22no—
56C2×D4×C19—42no—
57C2×D4×C19—42no—
58C2×D4×C19—42no—
59C2×D4×C19—41no—
60C2×D4×C19—41no—
61C22×C4×C19—22no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—42no—
68C22×C4×C19—42no—
69C22×C4×C19—42no—
70C22×C4×C19C22⋊C412yes—
71C22×C4×C19C22⋊C412yes—
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19C2×D412yes—
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19#4112yes—
76C22×Dic19—24no—
77C4⋊C4×C19—24no—
78C4⋊C4×C19—24no—
79C4⋊C4×C19—22no—
80C4⋊C4×C19—44no—
81C4⋊C4×C19—44no—
82C22⋊C4×C19—24no—
83C22⋊C4×C19—44no—
84C22⋊C4×C19—44no—
85C22⋊C4×C19—42no—
86C42×C19—42no—
87C22⋊Dic19—44no—
88C4⋊Dic19—82no—
89C4×Dic19—82no—
90#64520—44no—
91C2×C19⋊C8—42no—
92#9464—191nomaximal, Sylow
93C23×C19—22no—
94C23×C19—22no—
95C23×C19—41no—
96C23×C19—41no—
97C23×C19—41no—
98C23×C19—42no—
99C23×C19—41no—
100C23×C19—42no—
101C23×C19C2×C22⋊C411yescharacteristic
102C23×C19#12011yescharacteristic
103C23×C19#12311yescharacteristic
104D4×C19—82no—
105D4×C19—82no—
106D4×C19—82no—
107C2×C4×C19—22no—
108C2×C4×C19—22no—
109C2×C4×C19—24no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
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—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—81no—
124C2×C4×C19—81no—
125C2×C4×C19C4×D412yes—
126C2×C4×C19#12112yes—
127C2×Dic19—44no—
128C2×Dic19—44no—
129C2×Dic19—44no—
130C19⋊C8—82no—
131#2501D1911yescharacteristic
132#2313—191no—
133#1821—191no—
134#1510—192no—
135#1284—192no—
136C22×C19—21no—
137C22×C19—21no—
138C22×C19—21no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—21no—
142C22×C19—21no—
143C22×C19—44no—
144C22×C19—82no—
145C22×C19—82no—
146C22×C19—81no—
147C22×C19—81no—
148C22×C19—81no—
149C22×C19#38611yescharacteristic
150C22×C19#41012yes—
151C22×C19#45312yes—
152C4×C19—22no—
153C4×C19—22no—
154C4×C19—44no—
155C4×C19—42no—
156C4×C19—42no—
157C4×C19—81no—
158Dic19—84no—
159C2×#123—21no—
160C2×#123—21no—
161C2×#121C2×D1911yescharacteristic
162C22×C4⋊C4C2×D1911yescharacteristic
163#407—192no—
164#399—22no—
165#390Dic1912yescomplemented
166#387—384no—
167#384Dic1912yescomplemented
168#381—192no—
169#380—381no—
170C4×C22⋊C4—381no—
171C4×C22⋊C4C2×D1911yescharacteristic
172#343—382no—
173#327—384no—
174C2×C19—22no—
175C2×C19—22no—
176C2×C19—41no—
177C2×C19—161no—
178C2×C19#188711yescharacteristic
179C2×C19#189911yescharacteristic
180C2×C19#191211yescharacteristic
181C22×D4—21no—
182C22×D4C2×Dic1911yescharacteristic
183C23×C4C22⋊D1911yescharacteristic
184C23×C4C22⋊D1911yescharacteristic
185C23×C4C22×D1911yescharacteristic
186C2×M16—382no—
187#123—44no—
188#123—44no—
189#121—22no—
190#121—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—382no—
196C2×C4⋊C4C2×Dic1911yescharacteristic
197C2×C4⋊C4C2×Dic1912yes—
198C2×C4⋊C4C22⋊D1912yes—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—382no—
204C2×C42—382no—
205C2×C42C2×Dic1912yes—
206C22⋊C8—382no—
207C22⋊C8—382no—
208#95—21no—
209#95—194no—
210#95—382no—
211#95—382no—
212#95—382no—
213C19#946411yescharacteristic, complemented, Sylow
214C24—21no—
215C24C2×C22⋊D1911yescharacteristic
216C2×D4—22no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—42no—
220C2×D4—41no—
221C2×D4—41no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—384no—
232C22×C4C22⋊Dic1912yes—
233C22×C4C22⋊Dic1912yes—
234C22×C4D4×D1912yes—
235C22×C4#6454312yes—
236C22×C4C22×Dic1911yescharacteristic
237C22×C4C2×C22⋊D1911yescharacteristic
238M16—764no—
239C2×C8—762no—
240C4⋊C4—24no—
241C4⋊C4—24no—
242C4⋊C4—22no—
243C4⋊C4—44no—
244C4⋊C4—44no—
245C4⋊C4—1522no—
246C22⋊C4—24no—
247C22⋊C4—44no—
248C22⋊C4—44no—
249C22⋊C4—42no—
250C22⋊C4—764no—
251C42—42no—
252C42—1522no—
253C23—22no—
254C23—22no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—42no—
259C23—41no—
260C23—42no—
261C23#1059738111yescharacteristic
262C23#1059738311yescharacteristic
263C23C2×C22⋊Dic1911yescharacteristic
264D4—82no—
265D4—82no—
266D4—82no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—764no—
286C2×C4—764no—
287C2×C4—764no—
288C2×C4D4×Dic1912yes—
289C2×C4#1059738512yes—
290C8—1522no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—44no—
299C22—82no—
300C22—82no—
301C22—81no—
302C22—81no—
303C22—81no—
304C22#1192642411yescharacteristic
305C22#1192651812yes—
306C22#1192671112yes—
307C4—22no—
308C4—22no—
309C4—44no—
310C4—42no—
311C4—42no—
312C4—81no—
313C4—1524no—
314C2—22no—
315C2—22no—
316C2—41no—
317C2—161no—
318C2#1456403411yescharacteristic
319C2#1456409411yescharacteristic
320C2#1456417311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2501C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#2501D19
hypocenterC19#9464
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2501

Complements

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

NH ≅ G/Ntype
1. #14566238C2semidirect
2. #14563715C2semidirect
4. #14561488C2semidirect
18. C19×#390C4semidirect
19. C19×#384C4semidirect
165. #390Dic19semidirect
167. #384Dic19semidirect
213. C19#9464semidirect

Maximal subgroups

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

subgroupindex
#145662382
#145637152
#145621642
#145614882
C19×#25012
#946419