Finite Group Databasebeta

← #18080281

Subgroups — #18080281

Order 4864.

610 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 99 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#14568102C211yesmaximal, characteristic
2#14566238C211yesmaximal, characteristic, complemented
3#14562165C212yesmaximal
4#14561489C212yesmaximal, complemented
5C19×#1821C211yesmaximal, characteristic, complemented
6C2×#10597375—21no—
7C2×#10597375—21no—
8C2×#10597376C2211yescharacteristic
9#11926479—22no—
10#11926445C412yescomplemented
11#11926430—24no—
12#11926413C412yescomplemented
13#11926407C2212yes—
14#11926404—21no—
15C4×C22⋊Dic19—21no—
16C4×C22⋊Dic19C2211yescharacteristic
17#11926279—24no—
18C22×C4⋊C4×C19C2211yescharacteristic
19C19×#407C2212yes—
20C19×#343—22no—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—21no—
25C22×D76C2×C411yescharacteristic
26C2×M16×C19—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19C2×C412yes—
30C2×C4⋊C4×C19D412yes—
31C2×C22⋊Dic19—21no—
32C2×C22⋊Dic19—22no—
33#10597376—22no—
34#10597376—22no—
35#10597375—44no—
36#10597375—44no—
37C2×(C2×D19)⋊C4—22no—
38C2×(C2×D19)⋊C4—22no—
39C2×(C2×D19)⋊C4—21no—
40C2×C4⋊Dic19—22no—
41C2×C4⋊Dic19C2×C411yescharacteristic
42C2×Dic19⋊C4—22no—
43C2×Dic19⋊C4—22no—
44C2×C4×Dic19—22no—
45C2×C4×Dic19C2×C412yes—
46C19×C22⋊C8—22no—
47C19×C22⋊C8—22no—
48C19⋊#95—22no—
49C19⋊#95—22no—
50C19⋊#95—21no—
51C19⋊#95—22no—
52C19⋊#95D414yes—
53C24×C19C2×D411yescharacteristic
54C23×D19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—42no—
60C22×C4×C19—42no—
61C22×C4×C19—42no—
62C22×C4×C19C22⋊C412yes—
63C22×C4×C19C22⋊C412yes—
64C22×C4×C19C22×C411yescharacteristic
65C22×C4×C19C2×D412yes—
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19#4112yes—
68C2×C22⋊D19—42no—
69C2×C22⋊D19—42no—
70C2×C22⋊D19—41no—
71C2×C22⋊D19—41no—
72C22×Dic19—22no—
73C22×Dic19—21no—
74C22×Dic19—24no—
75C2×D76—22no—
76C2×D76—42no—
77M16×C19—44no—
78C2×C8×C19—42no—
79C4⋊C4×C19—24no—
80C4⋊C4×C19—24no—
81C22⋊Dic19—24no—
82C22⋊Dic19—44no—
83(C2×D19)⋊C4—44no—
84(C2×D19)⋊C4—44no—
85(C2×D19)⋊C4—42no—
86C4⋊Dic19—22no—
87C4⋊Dic19—82no—
88Dic19⋊C4—44no—
89Dic19⋊C4—44no—
90C4×Dic19—42no—
91C4×Dic19—82no—
92#9464—191nomaximal, Sylow
93C23×C19—22no—
94C23×C19—22no—
95C23×C19—41no—
96C23×C19C2×C22⋊C411yescharacteristic
97C23×C19#12011yescharacteristic
98C23×C19#12311yescharacteristic
99C22×D19—41no—
100C22×D19—41no—
101C22×D19—42no—
102C22×D19—41no—
103C22×D19—42no—
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19—22no—
107C2×C4×C19—22no—
108C2×C4×C19—42no—
109C2×C4×C19—42no—
110C2×C4×C19—42no—
111C2×C4×C19—42no—
112C2×C4×C19—42no—
113C2×C4×C19—42no—
114C2×C4×C19—81no—
115C2×C4×C19—81no—
116C2×C4×C19C4×D412yes—
117C2×C4×C19#12112yes—
118C22⋊D19—82no—
119C22⋊D19—82no—
120C2×Dic19—24no—
121C2×Dic19—42no—
122C2×Dic19—42no—
123C2×Dic19—41no—
124C2×Dic19—41no—
125C2×Dic19—44no—
126C2×Dic19—44no—
127C2×Dic19—41no—
128C2×Dic19—44no—
129D76—82no—
130C8×C19—82no—
131#2501—191no—
132#2313—191no—
133#1821D1911yescharacteristic, complemented
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#38611yescharacteristic
145C22×C19#41012yes—
146C22×C19#45312yes—
147C2×D19—82no—
148C2×D19—82no—
149C2×D19—81no—
150C2×D19—81no—
151C2×D19—81no—
152C4×C19—22no—
153C4×C19—22no—
154C4×C19—42no—
155C4×C19—42no—
156Dic19—44no—
157Dic19—84no—
158Dic19—81no—
159C2×#123—381no—
160C2×#123—381no—
161C2×#121—191no—
162C22×C4⋊C4C2×D1911yescharacteristic
163#407C2×D1912yes—
164#399—382no—
165#390—192no—
166#387—384no—
167#384—192no—
168#381—192no—
169#380—381no—
170C4×C22⋊C4—191no—
171C4×C22⋊C4—381no—
172#343—22no—
173#327—384no—
174C2×C19—22no—
175C2×C19—22no—
176C2×C19—41no—
177C2×C19#188711yescharacteristic
178C2×C19#189911yescharacteristic
179C2×C19#191211yescharacteristic
180D19—161no—
181C22×D4—191no—
182C22×D4—381no—
183C23×C4D7611yescharacteristic
184C23×C4D7611yescharacteristic
185C23×C4C22×D1911yescharacteristic
186C2×M16—22no—
187#123—764no—
188#123—764no—
189#121—382no—
190#121—382no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—191no—
194C2×C4⋊C4—382no—
195C2×C4⋊C4—382no—
196C2×C4⋊C4—382no—
197C2×C4⋊C4C4×D1912yes—
198C2×C4⋊C4C22⋊D1912yes—
199C2×C22⋊C4—381no—
200C2×C22⋊C4—382no—
201C2×C22⋊C4—382no—
202C2×C22⋊C4—382no—
203C2×C22⋊C4—381no—
204C2×C42—192no—
205C2×C42—382no—
206C22⋊C8—22no—
207C22⋊C8—22no—
208#95—194no—
209#95—382no—
210#95—382no—
211#95—382no—
212#95—381no—
213C19#946411yescharacteristic, complemented, Sylow
214C24—381no—
215C24C2×D7611yescharacteristic
216C2×D4—382no—
217C2×D4—762no—
218C2×D4—762no—
219C2×D4—762no—
220C2×D4—761no—
221C2×D4—761no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—382no—
230C22×C4—384no—
231C22×C4—381no—
232C22×C4(C2×D19)⋊C412yes—
233C22×C4(C2×D19)⋊C412yes—
234C22×C4C2×C4×D1911yescharacteristic
235C22×C4D4×D1912yes—
236C22×C4#6454312yes—
237C22×C4C2×C22⋊D1911yescharacteristic
238M16—44no—
239C2×C8—42no—
240C4⋊C4—24no—
241C4⋊C4—24no—
242C4⋊C4—382no—
243C4⋊C4—764no—
244C4⋊C4—764no—
245C4⋊C4—1522no—
246C22⋊C4—384no—
247C22⋊C4—764no—
248C22⋊C4—764no—
249C22⋊C4—764no—
250C22⋊C4—762no—
251C42—762no—
252C42—1522no—
253C23—22no—
254C23—22no—
255C23—41no—
256C23—761no—
257C23—761no—
258C23—762no—
259C23—761no—
260C23—762no—
261C23#1059732811yescharacteristic
262C23#1059733211yescharacteristic
263C23C2×(C2×D19)⋊C411yescharacteristic
264D4—1522no—
265D4—1522no—
266D4—1522no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—384no—
280C2×C4—762no—
281C2×C4—762no—
282C2×C4—764no—
283C2×C4—761no—
284C2×C4—761no—
285C2×C4—764no—
286C2×C4—761no—
287C2×C4—764no—
288C2×C4(C22⋊D19)⋊C412yes—
289C2×C4#1059738512yes—
290C8—82no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—44no—
299C22—1522no—
300C22—1522no—
301C22—1521no—
302C22—1521no—
303C22—1521no—
304C22#1192642111yescharacteristic
305C22#1192651712yes—
306C22#1192671412yes—
307C4—22no—
308C4—22no—
309C4—42no—
310C4—42no—
311C4—764no—
312C4—1524no—
313C4—1521no—
314C2—22no—
315C2—22no—
316C2—41no—
317C2—3041no—
318C2#1456403111yescharacteristic
319C2#1456409111yescharacteristic
320C2#1456417011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1821C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1821D19
hypocenterC19#9464
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
2. #14566238C2semidirect
4. #14561489C2semidirect
5. C19×#1821C2semidirect
10. #11926445C4semidirect
12. #11926413C4semidirect
133. #1821D19semidirect
213. C19#9464semidirect

Maximal subgroups

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

subgroupindex
#145681022
#145662382
#145621652
#145614892
C19×#18212
#946419