Finite Group Databasebeta

← #18080369

Subgroups — #18080369

Order 4864.

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

normal subgroups only

This group has 614 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#14566233C211yesmaximal, characteristic
2#14563734C212yesmaximal, complemented
3#14561962C211yesmaximal, characteristic
4#14561487C212yesmaximal, complemented
5C19×#2482C211yesmaximal, characteristic
6#11926508C2212yes—
7#11926437—24no—
8#11926404—21no—
9#11926400—21no—
10C4×C22⋊Dic19C2212yes—
11#11926303—24no—
12#11926268—22no—
13C2×C19×#117C2211yescharacteristic
14C22×C22⋊C4×C19C2211yescharacteristic
15C19×#399C412yescomplemented
16C19×#397C412yescomplemented
17C19×#388—22no—
18C19×#385—21no—
19C19×#381C2211yescharacteristic
20C19×#379—21no—
21C25×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C19×#117—22no—
25C19×#117—22no—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19C2×C411yescharacteristic
28C2×C4⋊C4×C19C2×C411yescharacteristic
29C2×C22⋊C4×C19—22no—
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19—22no—
32C2×C22⋊C4×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19C2×C412yes—
36C2×C22⋊C4×C19D412yes—
37C2×C42×C19—21no—
38C2×C22⋊Dic19—22no—
39C2×C22⋊Dic19—22no—
40C2×C22⋊Dic19—22no—
41C2×C4⋊Dic19—22no—
42C2×C4×Dic19D414yes—
43C2×#64520—22no—
44C19×#95—22no—
45C19×#95—21no—
46C19×#95C2×C412yes—
47C19⋊#95—22no—
48C19⋊#95—22no—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)—22no—
51C24×C19—21no—
52C24×C19—21no—
53C24×C19—42no—
54C24×C19—42no—
55C24×C19—81no—
56C24×C19C22⋊C412yes—
57C24×C19C2×D411yescharacteristic
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—22no—
63C22×C4×C19—42no—
64C22×C4×C19—81no—
65C22×C4×C19C22⋊C412yes—
66C22×C4×C19C22×C411yescharacteristic
67C22×C4×C19C2×D412yes—
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19#4112yes—
70C22×Dic19—24no—
71C4⋊C4×C19—22no—
72C4⋊C4×C19—22no—
73C4⋊C4×C19—82no—
74C22⋊C4×C19—24no—
75C22⋊C4×C19—24no—
76C22⋊C4×C19—42no—
77C22⋊C4×C19—44no—
78C22⋊C4×C19—41no—
79C22⋊C4×C19—41no—
80C22⋊C4×C19—82no—
81C42×C19—42no—
82C22⋊Dic19—44no—
83C22⋊Dic19—82no—
84C22⋊Dic19—82no—
85C4⋊Dic19—82no—
86C4×Dic19—44no—
87#64520—44no—
88C2×C19⋊C8—42no—
89#9481—191nomaximal, Sylow
90C23×C19—22no—
91C23×C19—22no—
92C23×C19—22no—
93C23×C19—22no—
94C23×C19—22no—
95C23×C19—41no—
96C23×C19—42no—
97C23×C19—42no—
98C23×C19—42no—
99C23×C19—42no—
100C23×C19—42no—
101C23×C19—42no—
102C23×C19—81no—
103C23×C19—81no—
104C23×C19—88no—
105C23×C19C2×C22⋊C411yescharacteristic
106C23×C19#12011yescharacteristic
107C23×C19#12311yescharacteristic
108C2×C4×C19—24no—
109C2×C4×C19—22no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
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—41no—
119C2×C4×C19—41no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19—81no—
123C2×C4×C19C4×D412yes—
124C2×C4×C19#12112yes—
125C2×Dic19—44no—
126C2×Dic19—44no—
127C2×Dic19—44no—
128C19⋊C8—82no—
129#2482D1911yescharacteristic
130#2312—191no—
131#1826—192no—
132#1462—191no—
133#1284—192no—
134C22×C19—21no—
135C22×C19—21no—
136C22×C19—21no—
137C22×C19—21no—
138C22×C19—21no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—44no—
142C22×C19—44no—
143C22×C19—42no—
144C22×C19—42no—
145C22×C19—42no—
146C22×C19—82no—
147C22×C19—84no—
148C22×C19—84no—
149C22×C19#38611yescharacteristic
150C22×C19#42112yes—
151C22×C19#45812yes—
152C4×C19—22no—
153C4×C19—22no—
154C4×C19—42no—
155C4×C19—82no—
156C4×C19—81no—
157C4×C19—81no—
158Dic19—84no—
159C2×#117C2×D1911yescharacteristic
160C22×C22⋊C4C2×D1911yescharacteristic
161#407—192no—
162#399Dic1912yescomplemented
163#397Dic1912yescomplemented
164#388—22no—
165#388—384no—
166#385—21no—
167#381C2×D1911yescharacteristic
168#380—381no—
169#379—21no—
170#379—381no—
171C4×C22⋊C4—192no—
172#339—384no—
173#323—382no—
174C2×C19—22no—
175C2×C19—22no—
176C2×C19—41no—
177C2×C19—82no—
178C2×C19#189011yescharacteristic
179C2×C19#189711yescharacteristic
180C2×C19#191111yescharacteristic
181C25C22⋊D1911yescharacteristic
182C23×C4C22⋊D1911yescharacteristic
183C23×C4C22×D1911yescharacteristic
184C2×M16—382no—
185#117—22no—
186#117—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—382no—
189C2×C4⋊C4C2×Dic1911yescharacteristic
190C2×C4⋊C4C2×Dic1911yescharacteristic
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—382no—
198C2×C22⋊C4—382no—
199C2×C22⋊C4—382no—
200C2×C22⋊C4C2×Dic1912yes—
201C2×C22⋊C4C22⋊D1912yes—
202C2×C42—21no—
203C2×C42—194no—
204C22⋊C8—382no—
205C22⋊C8—382no—
206#95—22no—
207#95—21no—
208#95—382no—
209#95—382no—
210#95C2×Dic1912yes—
211C19#948111yescharacteristic, complemented, Sylow
212C24—21no—
213C24—21no—
214C24—42no—
215C24—42no—
216C24—81no—
217C24C22⋊Dic1912yes—
218C24C2×C22⋊D1911yescharacteristic
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—42no—
225C22×C4—81no—
226C22×C4—384no—
227C22×C4C22⋊Dic1912yes—
228C22×C4D4×D1912yes—
229C22×C4#6454312yes—
230C22×C4C22×Dic1911yescharacteristic
231C22×C4C2×C22⋊D1911yescharacteristic
232M16—764no—
233C2×C8—762no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—82no—
237C4⋊C4—1522no—
238C22⋊C4—24no—
239C22⋊C4—24no—
240C22⋊C4—42no—
241C22⋊C4—44no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—82no—
245C22⋊C4—764no—
246C22⋊C4—1522no—
247C22⋊C4—1522no—
248C42—42no—
249C42—764no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—41no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—81no—
263C23—81no—
264C23—88no—
265C23#1059738111yescharacteristic
266C23#1059738311yescharacteristic
267C23C2×C22⋊Dic1911yescharacteristic
268C2×C4—24no—
269C2×C4—22no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
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—81no—
283C2×C4—764no—
284C2×C4—764no—
285C2×C4—764no—
286C2×C4D4×Dic1912yes—
287C2×C4#1059738512yes—
288C8—1522no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—44no—
297C22—44no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—82no—
302C22—84no—
303C22—84no—
304C22#1192642411yescharacteristic
305C22#1192656112yes—
306C22#1192673312yes—
307C4—22no—
308C4—22no—
309C4—42no—
310C4—82no—
311C4—81no—
312C4—81no—
313C4—1524no—
314C2—22no—
315C2—22no—
316C2—41no—
317C2—82no—
318C2#1456404911yescharacteristic
319C2#1456408411yescharacteristic
320C2#1456416811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2482C2
socleC22×C19#386
prime radicalC25×C19D4
cosocleC23×C4×C19C23
hypercenter#2482D19
hypocenterC19#9481
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
2. #14563734C2semidirect
4. #14561487C2semidirect
15. C19×#399C4semidirect
16. C19×#397C4semidirect
162. #399Dic19semidirect
163. #397Dic19semidirect
211. C19#9481semidirect

Maximal subgroups

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

subgroupindex
#145662332
#145637342
#145619622
#145614872
C19×#24822
#948119