Finite Group Databasebeta

← #18080478

Subgroups — #18080478

Order 4864.

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

normal subgroups only

This group has 880 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#14566991C211yesmaximal, characteristic
2#14563555C212yesmaximal, complemented
3#14561973C211yesmaximal, characteristic, complemented
4#14561540C212yesmaximal, complemented
5C19×#2973C211yesmaximal, characteristic, complemented
6C23×D76C2211yescharacteristic
7C2×#10597376—21no—
8C2×#10597383C412yes—
9C2×#10597280—24no—
10#11926508C2212yes—
11#11926461—21no—
12#11926453—21no—
13#11926446—21no—
14#11926404C2211yescharacteristic
15#11926399C412yes—
16#11926270—21no—
17#11926268—21no—
18C2×C4×D4×C19C2211yescharacteristic
19C19×#435—24no—
20C19×#432—21no—
21C19×#407C2212yes—
22C2×C19×C22⋊C8—21no—
23C24×D19C2×C412yes—
24C22×D4×C19C2×C411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C22×C22⋊D19—22no—
28C22×D76—21no—
29C22×D76—22no—
30C22×D76—21no—
31C22×D76—22no—
32C22×D76—44no—
33C2×M16×C19D414yescomplemented
34C22×C8×C19—22no—
35C4×D4×C19—22no—
36C4×D4×C19—22no—
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C22⋊C4×C19C2×C411yescharacteristic
39C2×C22⋊C4×C19D411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×C22⋊Dic19C2×C412yes—
42#10597383—44no—
43#10597376—44no—
44C2×(C2×D19)⋊C4—22no—
45C2×(C2×D19)⋊C4—22no—
46C2×(C2×D19)⋊C4—22no—
47C2×C4⋊Dic19—21no—
48C2×#64520—22no—
49C19×C4⋊C8—22no—
50C19×C22⋊C8—22no—
51C19×C22⋊C8—22no—
52C19×C22⋊C8—22no—
53C19×#97—22no—
54C19⋊#95—21no—
55C22⋊(C19⋊C8)—22no—
56C22⋊(C19⋊C8)—22no—
57#10597280—48no—
58C24×C19C22⋊C411yescharacteristic
59C24×C19C22×C411yescharacteristic
60C23×D19—22no—
61C23×D19—24no—
62C23×D19—44no—
63C23×D19—42no—
64C23×D19—42no—
65C23×D19—82no—
66C2×D4×C19—22no—
67C2×D4×C19—22no—
68C2×D4×C19—41no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—42no—
72C22×C4×C19—42no—
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D412yes—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19#4112yes—
80C2×C22⋊D19—44no—
81C2×C22⋊D19—44no—
82C2×C22⋊D19—82no—
83C22×Dic19—22no—
84C2×D76—24no—
85C2×D76—28no—
86C2×D76—44no—
87C2×D76—42no—
88C2×D76—44no—
89C2×D76—48no—
90C2×D76—41no—
91C2×D76—42no—
92C2×D76—41no—
93M16×C19—44no—
94C2×C8×C19—24no—
95C2×C8×C19—82no—
96C4⋊C4×C19—22no—
97C22⋊C4×C19—22no—
98C22⋊C4×C19—22no—
99C42×C19—21no—
100C42×C19—21no—
101C22⋊Dic19—42no—
102(C2×D19)⋊C4—44no—
103(C2×D19)⋊C4—44no—
104(C2×D19)⋊C4—82no—
105C4⋊Dic19—42no—
106#64520—44no—
107C2×C19⋊C8—42no—
108#9503—191nomaximal, Sylow
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—21no—
112C23×C19—21no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19—41no—
116C23×C19—41no—
117C23×C19#10012yescomplemented
118C23×C19C2×C22⋊C411yescharacteristic
119C23×C19C4×D412yes—
120C22×D19—24no—
121C22×D19—28no—
122C22×D19—42no—
123C22×D19—42no—
124C22×D19—44no—
125C22×D19—42no—
126C22×D19—42no—
127C22×D19—42no—
128C22×D19—42no—
129C22×D19—88no—
130C22×D19—88no—
131C22×D19—84no—
132C22×D19—84no—
133D4×C19—44no—
134C2×C4×C19—24no—
135C2×C4×C19—22no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—41no—
142C2×C4×C19—42no—
143C2×C4×C19—42no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—81no—
147C2×C4×C19#12011yescharacteristic
148C2×C4×C19#12112yes—
149C2×C4×C19#12311yescharacteristic
150C22⋊D19—88no—
151C2×Dic19—42no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154D76—48no—
155D76—44no—
156D76—44no—
157C8×C19—44no—
158C19⋊C8—82no—
159#2973D1911yescharacteristic, complemented
160#2408—191no—
161#1783—192no—
162#1465—191no—
163#1305—192no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—22no—
167C22×C19—22no—
168C22×C19—22no—
169C22×C19—22no—
170C22×C19—42no—
171C22×C19—42no—
172C22×C19—42no—
173C22×C19—41no—
174C22×C19—41no—
175C22×C19—81no—
176C22×C19#38611yescharacteristic
177C22×C19C2×#10011yescharacteristic
178C22×C19#41311yescharacteristic
179C2×D19—44no—
180C2×D19—44no—
181C2×D19—44no—
182C2×D19—82no—
183C2×D19—82no—
184C2×D19—88no—
185C2×D19—82no—
186C2×D19—82no—
187C2×D19—88no—
188C4×C19—22no—
189C4×C19—21no—
190C4×C19—41no—
191C4×C19—41no—
192C4×C19—41no—
193C4×C19B(4,𝔽2)12yes—
194Dic19—82no—
195C23×D4—191no—
196C2×#121—381no—
197C2×#120—192no—
198C2×C4×D4C2×D1911yescharacteristic
199#435—24no—
200#432—21no—
201C2×#100—384no—
202#407—192no—
203#407C2×D1912yes—
204C2×C22⋊C8—21no—
205#394—381no—
206#392—381no—
207#390—381no—
208#380—191no—
209#379—192no—
210#324—381no—
211#323—381no—
212C2×C19—21no—
213C2×C19—21no—
214C2×C19—42no—
215C2×C19—42no—
216C2×C19#188911yescharacteristic
217C2×C19#190011yescharacteristic
218C2×C19#191411yescharacteristic
219D19—84no—
220C25—192no—
221C22×D4—382no—
222C22×D4—381no—
223C22×D4—382no—
224C22×D4—381no—
225C22×D4—382no—
226C22×D4—764no—
227C22×D4C4×D1911yescharacteristic
228C23×C4C22⋊D1911yescharacteristic
229C23×C4C22×D1911yescharacteristic
230C2×M16—382no—
231C2×M16C22⋊D1914yescomplemented
232C22×C8—22no—
233#121—764no—
234#120—764no—
235C4×D4—22no—
236C4×D4—22no—
237C2×C4⋊C4—381no—
238C2×C4⋊C4D7611yescharacteristic
239C2×C22⋊C4—192no—
240C2×C22⋊C4—382no—
241C2×C22⋊C4—382no—
242C2×C22⋊C4—382no—
243C2×C22⋊C4C4×D1911yescharacteristic
244C2×C22⋊C4D7611yescharacteristic
245C2×C42C22⋊D1911yescharacteristic
246C4⋊C8—22no—
247#100—768no—
248C22⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251C22⋊C8—382no—
252C22⋊C8—382no—
253#97—22no—
254#95—381no—
255C19#950311yescharacteristic, complemented, Sylow
256C24—382no—
257C24—384no—
258C24—762no—
259C24—762no—
260C24—764no—
261C24—1522no—
262C24(C2×D19)⋊C411yescharacteristic
263C24C2×C4×D1911yescharacteristic
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—41no—
267C2×D4—388no—
268C2×D4—384no—
269C2×D4—762no—
270C2×D4—764no—
271C2×D4—764no—
272C2×D4—768no—
273C2×D4—764no—
274C2×D4—764no—
275C2×D4—762no—
276C2×D4—761no—
277C2×D4—761no—
278C2×D4—1522no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—382no—
284C22×C4(C2×D19)⋊C411yescharacteristic
285C22×C4(C2×D19)⋊C411yescharacteristic
286C22×C4(C2×D19)⋊C411yescharacteristic
287C22×C4C2×D7611yescharacteristic
288C22×C4#6454112yes—
289C22×C4C2×C22⋊D1912yes—
290C22×C4C2×C22⋊D1911yescharacteristic
291M16—44no—
292M16—764no—
293C2×C8—24no—
294C2×C8—82no—
295C2×C8—762no—
296C4⋊C4—22no—
297C4⋊C4—762no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—764no—
301C22⋊C4—764no—
302C22⋊C4—762no—
303C22⋊C4—1522no—
304C42—21no—
305C42—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—384no—
315C23—388no—
316C23—762no—
317C23—762no—
318C23—764no—
319C23—762no—
320C23—762no—
321C23—762no—
322C23—762no—
323C23—1524no—
324C23—1524no—
325C23—1528no—
326C23—1528no—
327C23#1059728012yescomplemented
328C23C2×(C2×D19)⋊C411yescharacteristic
329C23C4×C22⋊D1912yes—
330D4—44no—
331D4—768no—
332D4—764no—
333D4—764no—
334D4—1528no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—762no—
349C2×C4—762no—
350C2×C4—762no—
351C2×C4#1059737511yescharacteristic
352C2×C4#1059737612yes—
353C2×C4#1059739911yescharacteristic
354C8—44no—
355C8—1522no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—41no—
366C22—41no—
367C22—81no—
368C22—764no—
369C22—764no—
370C22—764no—
371C22—1522no—
372C22—1522no—
373C22—1528no—
374C22—1528no—
375C22—1522no—
376C22—1522no—
377C22#1192642311yescharacteristic
378C22C2×#1059728011yescharacteristic
379C22#1192652611yescharacteristic
380C4—22no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—1522no—
386C4#1192673112yes—
387C2—21no—
388C2—21no—
389C2—42no—
390C2—42no—
391C2—1524no—
392C2#1456404311yescharacteristic
393C2#1456409811yescharacteristic
394C2#1456418211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2973C2
socleC22×C19#386
prime radical#14566991C2
cosocleC23×C4×C19C23
hypercenter#2973D19
hypocenterC19#9503
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #14563555C2semidirect
3. #14561973C2semidirect
4. #14561540C2semidirect
5. C19×#2973C2semidirect
33. C2×M16×C19D4semidirect
117. C23×C19#100semidirect
159. #2973D19semidirect
231. C2×M16C22⋊D19semidirect
255. C19#9503semidirect
327. C23#10597280semidirect

Maximal subgroups

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

subgroupindex
#145669912
#145635552
#145619732
#145615402
C19×#29732
#950319