Finite Group Databasebeta

← #18074606

Subgroups — #18074606

Order 4864.

1516 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564442C211yesmaximal, characteristic, complemented
2#14563635C212yesmaximal, complemented
3C2×#11926288C211yesmaximal, characteristic, complemented
4C2×D4⋊(C19⋊C8)C212yesmaximal, complemented
5C2×D42×C19C211yesmaximal, characteristic
6C2×C4⋊(C19⋊C8)C2212yescomplemented
7C2×#10597289—22no—
8C2×#10597289—22no—
9C2×C4×C19⋊C8C2211yescharacteristic, complemented
10#11926414C2211yescharacteristic, complemented
11#11926306—22no—
12#11926288—22no—
13D4⋊(C19⋊C8)—24no—
14C23×D4×C19—22no—
15D42×C19—22no—
16D42×C19—24no—
17D42×C19C414yescomplemented
18C2×C19×#127C2211yescharacteristic
19C2×C19×#121—22no—
20C2×C19×#120—22no—
21C2×C4×D4×C19C2212yes—
22C25×C19—22no—
23C22×D4×C19—24no—
24C22×D4×C19—28no—
25C22×D4×C19—28no—
26C22×D4×C19—22no—
27C22×D4×C19—44no—
28C22×D4×C19—44no—
29C22×D4×C19—44no—
30C22×D4×C19—44no—
31C22×D4×C19D412yes—
32C22×D4×C19D412yes—
33C23×C4×C19—22no—
34C19×#127—22no—
35C19×#127C2×C412yes—
36C19×#127D412yes—
37C19×#121—28no—
38C19×#121—28no—
39C19×#120—28no—
40C19×#120—28no—
41C4×D4×C19—22no—
42C4×D4×C19—22no—
43C4×D4×C19C2×C414yes—
44C4×D4×C19D414yes—
45C2×C4⋊C4×C19D412yes—
46C2×C22⋊C4×C19—22no—
47C2×C22⋊C4×C19—22no—
48C2×C42×C19C2311yescharacteristic
49C2×C4⋊Dic19—21no—
50C2×C4⋊Dic19—22no—
51C22×C19⋊C8—21no—
52C22×C19⋊C8—22no—
53#10597289—44no—
54#10597289—44no—
55C4⋊(C19⋊C8)—22no—
56C4⋊(C19⋊C8)—22no—
57C4×C19⋊C8—22no—
58C24×C19—22no—
59C24×C19—28no—
60C24×C19—22no—
61C24×C19—48no—
62C24×C19—48no—
63C24×C19—82no—
64C24×C19—82no—
65C2×D4×C19—216no—
66C2×D4×C19—24no—
67C2×D4×C19—22no—
68C2×D4×C19—24no—
69C2×D4×C19—22no—
70C2×D4×C19—22no—
71C2×D4×C19—22no—
72C2×D4×C19—42no—
73C2×D4×C19—42no—
74C2×D4×C19—416no—
75C2×D4×C19—416no—
76C2×D4×C19—416no—
77C2×D4×C19—48no—
78C2×D4×C19—48no—
79C2×D4×C19—416no—
80C2×D4×C19—42no—
81C2×D4×C19—42no—
82C2×D4×C19—42no—
83C2×D4×C19—42no—
84C2×D4×C19C22⋊C414yes—
85C2×D4×C19C22⋊C414yes—
86C2×D4×C19D814yes—
87C2×D4×C19SD1614yes—
88C22×C4×C19—22no—
89C22×C4×C19—24no—
90C22×C4×C19—24no—
91C22×C4×C19—42no—
92C22×C4×C19—42no—
93C22×C4×C19—42no—
94C22×C4×C19—42no—
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19C2×D412yes—
97C22×Dic19—41no—
98C4⋊C4×C19—22no—
99C4⋊C4×C19C22⋊C414yes—
100C22⋊C4×C19—28no—
101C22⋊C4×C19—24no—
102C22⋊C4×C19—24no—
103C42×C19C22×C411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19C2×D412yes—
106C4⋊Dic19—42no—
107C4⋊Dic19—42no—
108C4⋊Dic19—42no—
109C2×C19⋊C8—22no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—42no—
113C2×C19⋊C8—42no—
114C2×C19⋊C8—42no—
115#8443—191nomaximal, Sylow
116C23×C19—24no—
117C23×C19—24no—
118C23×C19—24no—
119C23×C19—24no—
120C23×C19—432no—
121C23×C19—42no—
122C23×C19—42no—
123C23×C19—42no—
124C23×C19—42no—
125C23×C19—44no—
126C23×C19—44no—
127C23×C19—42no—
128C23×C19—42no—
129C23×C19—88no—
130C23×C19—88no—
131C23×C19—88no—
132C23×C19—816no—
133C23×C19#12011yescharacteristic
134D4×C19—24no—
135D4×C19—24no—
136D4×C19—24no—
137D4×C19—44no—
138D4×C19—432no—
139D4×C19—44no—
140D4×C19—44no—
141D4×C19—44no—
142D4×C19—44no—
143D4×C19—82no—
144D4×C19#10218yescomplemented
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—24no—
148C2×C4×C19—42no—
149C2×C4×C19—42no—
150C2×C4×C19—44no—
151C2×C4×C19—44no—
152C2×C4×C19—44no—
153C2×C4×C19—44no—
154C2×C4×C19C2×C22⋊C411yescharacteristic
155C2×C4×C19C2×C22⋊C412yes—
156C2×C4×C19#12011yescharacteristic
157C2×C4×C19#12012yes—
158C2×C4×C19C2×D812yes—
159C2×C4×C19C2×SD1612yes—
160C2×C4×C19AGL(1,ℤ/8)12yes—
161C2×C4×C19AGL(1,ℤ/8)12yes—
162C2×Dic19—82no—
163C2×Dic19—81no—
164C19⋊C8—42no—
165C19⋊C8—82no—
166C2×D42D1911yescharacteristic
167#1957—191no—
168#1802—192no—
169C2×#331—191no—
170C2×D4⋊C8—192no—
171C22×C19—28no—
172C22×C19—44no—
173C22×C19—44no—
174C22×C19—44no—
175C22×C19—44no—
176C22×C19—44no—
177C22×C19—44no—
178C22×C19—44no—
179C22×C19—48no—
180C22×C19—832no—
181C22×C19—82no—
182C22×C19—82no—
183C22×C19—84no—
184C22×C19#37911yescharacteristic
185C22×C19#44712yes—
186C22×C19#45012yes—
187C22×C19#45311yescharacteristic
188C22×C19#45511yescharacteristic
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—44no—
192C4×C19C2×#10212yes—
193C4×C19#41812yes—
194C4×C19#44712yes—
195C4×C19#45012yes—
196Dic19—161no—
197C23×D4—22no—
198D42—22no—
199D42—24no—
200D42Dic1914yescomplemented
201C2×#127C2×D1911yescharacteristic
202C2×#121—22no—
203C2×#120—22no—
204C2×C4×D4C2×D1912yes—
205C2×C4⋊C8—192no—
206C2×#102—382no—
207C2×#102—382no—
208C2×C4×C8—191no—
209#384—191no—
210#340—382no—
211#331—382no—
212D4⋊C8—384no—
213C2×C19—48no—
214C2×C19—84no—
215C2×C19#161911yescharacteristic
216C2×C19#162911yescharacteristic
217C2×C19#163912yes—
218C2×C19#178612yes—
219C2×C19#179211yescharacteristic
220C25—22no—
221C22×D4—24no—
222C22×D4—28no—
223C22×D4—28no—
224C22×D4—22no—
225C22×D4—44no—
226C22×D4—44no—
227C22×D4—44no—
228C22×D4—44no—
229C22×D4C22⋊D1912yes—
230C22×D4C22⋊D1912yes—
231C23×C4—22no—
232C22×C8—381no—
233C22×C8—382no—
234#127—22no—
235#127C2×Dic1912yes—
236#127C22⋊D1912yes—
237#121—28no—
238#121—28no—
239#120—28no—
240#120—28no—
241C4×D4—22no—
242C4×D4—22no—
243C4×D4C2×Dic1914yes—
244C4×D4C22⋊D1914yes—
245C2×C4⋊C4—382no—
246C2×C4⋊C4—381no—
247C2×C4⋊C4C22⋊D1912yes—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C42C22×D1911yescharacteristic
251C4⋊C8—382no—
252C4⋊C8—382no—
253#102—764no—
254#102—764no—
255C4×C8—382no—
256C19#844311yescharacteristic, complemented, Sylow
257C24—22no—
258C24—28no—
259C24—22no—
260C24—48no—
261C24—48no—
262C24—82no—
263C24—82no—
264C2×D4—216no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—24no—
268C2×D4—22no—
269C2×D4—24no—
270C2×D4—22no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—416no—
274C2×D4—416no—
275C2×D4—416no—
276C2×D4—48no—
277C2×D4—48no—
278C2×D4—416no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4#6452514yes—
284C2×D4#6452614yes—
285C2×D4C22⋊Dic1914yes—
286C2×D4C22⋊Dic1914yes—
287C22×C4—22no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—761no—
295C22×C4C2×C22⋊D1911yescharacteristic
296C22×C4C2×C22⋊D1912yes—
297C2×C8—382no—
298C2×C8—761no—
299C2×C8—761no—
300C2×C8—762no—
301C2×C8—762no—
302C2×C8—762no—
303C4⋊C4—22no—
304C4⋊C4—762no—
305C4⋊C4—762no—
306C4⋊C4—762no—
307C4⋊C4C22⋊Dic1914yes—
308C22⋊C4—28no—
309C22⋊C4—24no—
310C22⋊C4—24no—
311C42C22×Dic1911yescharacteristic
312C42C2×C22⋊D1912yes—
313C42C2×C22⋊D1911yescharacteristic
314C23—24no—
315C23—24no—
316C23—24no—
317C23—24no—
318C23—432no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—44no—
324C23—44no—
325C23—42no—
326C23—42no—
327C23—88no—
328C23—88no—
329C23—88no—
330C23—816no—
331C23#1059739911yescharacteristic
332D4—24no—
333D4—24no—
334D4—24no—
335D4—44no—
336D4—432no—
337D4—44no—
338D4—44no—
339D4—44no—
340D4—44no—
341D4—82no—
342D4#1059728918yescomplemented
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—24no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—1522no—
353C2×C4—1521no—
354C2×C4C2×#6452512yes—
355C2×C4#1059737812yes—
356C2×C4#1059737812yes—
357C2×C4C2×#6452612yes—
358C2×C4C2×C22⋊Dic1911yescharacteristic
359C2×C4C2×C22⋊Dic1912yes—
360C2×C4#1059739911yescharacteristic
361C2×C4#1059739912yes—
362C8—762no—
363C8—1522no—
364C22—28no—
365C22—44no—
366C22—44no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22—44no—
371C22—44no—
372C22—48no—
373C22—832no—
374C22—82no—
375C22—82no—
376C22—84no—
377C22#1192640011yescharacteristic
378C22#1192667812yes—
379C22#1192669512yes—
380C22#1192671211yescharacteristic
381C22#1192672211yescharacteristic
382C4—21no—
383C4—21no—
384C4—44no—
385C4—3041no—
386C4C2×#1059728912yes—
387C4#1192654912yes—
388C4#1192667812yes—
389C4#1192669512yes—
390C2—48no—
391C2—84no—
392C2#1456268911yescharacteristic
393C2#1456275111yescharacteristic
394C2#1456281412yes—
395C2#1456356612yes—
396C2#1456358911yescharacteristic
subgroupG/H
centerC23#10597399
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC2×D42×C19C2
socleC23×C19#120
cosocleC2×C42×C19C23
hypercenterC2×D42D19
hypocenterC19#8443
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. #14564442C2semidirect
2. #14563635C2semidirect
3. C2×#11926288C2semidirect
4. C2×D4⋊(C19⋊C8)C2semidirect
6. C2×C4⋊(C19⋊C8)C22semidirect
9. C2×C4×C19⋊C8C22semidirect
10. #11926414C22semidirect
17. D42×C19C4semidirect
144. D4×C19#102semidirect
200. D42Dic19semidirect
256. C19#8443semidirect
342. D4#10597289semidirect

Maximal subgroups

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

subgroupindex
#145644422
#145636352
C2×#119262882
C2×D4⋊(C19⋊C8)2
C2×D42×C192
#844319