Finite Group Databasebeta

← #14572891

Subgroups — #14572891

Order 2432.

754 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D19C211yesmaximal, characteristic
2C2×#10597388C211yesmaximal, characteristic, complemented
3C2×#10597392C211yesmaximal, characteristic, complemented
4#11926705C212yesmaximal, complemented
5#11926703C212yesmaximal, complemented
6#11926698C212yesmaximal, complemented
7#11926693C212yesmaximal, complemented
8#11926546C211yesmaximal, characteristic, complemented
9#11926545C211yesmaximal, characteristic, complemented
10#11926507C211yesmaximal, characteristic, complemented
11C2×C19×#137C211yesmaximal, characteristic, complemented
12C2×#41×C19C2211yescharacteristic
13C22×Q8×C19C2211yescharacteristic, complemented
14#41×D19—24no—
15#41×D19—24no—
16C2×#64545C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic
18C2×#64543—21no—
19C2×#64543C2211yescharacteristic
20C2×D4×D19—21no—
21C2×D4×D19C2211yescharacteristic
22C2×#64541—21no—
23C2×#64541C2211yescharacteristic
24C22×C4×D19—21no—
25C22×C4×D19C2211yescharacteristic
26C19×#137—24no—
27C2×Q16×C19C2212yescomplemented
28C2×SD16×C19C2212yescomplemented
29C2×M16×C19C2211yescharacteristic, complemented
30#10597392—21no—
31#10597392—21no—
32#10597392C2212yes—
33#10597392C2212yescomplemented
34C2×#64528C2212yescomplemented
35#10597388—24no—
36C2×#64527C2212yescomplemented
37C2×(C2×D19)⋊C4—21no—
38C2×C4⋊Dic19C2211yescharacteristic, complemented
39C2×Dic19⋊C4—21no—
40C2×#64520C2211yescharacteristic, complemented
41#10597292C2212yescomplemented
42#10597289C2212yescomplemented
43#10597278C2212yescomplemented
44(C2×D19)⋊C8C2212yes—
45(C2×D19)⋊C8C2212yescomplemented
46#10597273C2212yescomplemented
47C23×D19—21no—
48C23×D19D411yescharacteristic
49#41×C19—22no—
50#41×C19D414yes—
51C2×Q8×C19—21no—
52C2×Q8×C19—22no—
53C2×Q8×C19—22no—
54C2×Q8×C19C2312yes—
55C2×Q8×C19C2311yescharacteristic
56C2×D4×C19—21no—
57C2×D4×C19C2311yescharacteristic
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19C2311yescharacteristic
61C2×C22⋊D19—21no—
62C2×C22⋊D19—21no—
63C2×C22⋊D19—21no—
64C22×Dic19—21no—
65C22×Dic19—21no—
66C22×Dic19D411yescharacteristic
67#64545—22no—
68#64545—22no—
69Q8×D19—22no—
70Q8×D19—22no—
71#64543—28no—
72#64543—22no—
73#64543—22no—
74D4×D19—28no—
75D4×D19—22no—
76D4×D19—22no—
77#64541—28no—
78#64541—22no—
79#64541D414yes—
80C2×D76—21no—
81C2×D76C2311yescharacteristic
82C2×C4×D19—28no—
83C2×C4×D19—21no—
84C2×C4×D19—21no—
85C2×C4×D19—22no—
86C2×C4×D19—22no—
87C2×C4×D19—21no—
88C2×C4×D19D411yescharacteristic
89C2×C4×D19D411yescharacteristic
90C2×C4×D19C2311yescharacteristic
91C2×C4×D19C2311yescharacteristic
92C2×Dic38—21no—
93C2×Dic38C2311yescharacteristic
94Q16×C19—24no—
95SD16×C19—24no—
96M16×C19—22no—
97C2×C8×C19C2312yes—
98#64528—24no—
99#64527—24no—
100(C2×D19)⋊C4—22no—
101(C2×D19)⋊C4—22no—
102C4⋊Dic19—21no—
103C4⋊Dic19C2312yes—
104Dic19⋊C4—22no—
105Dic19⋊C4—22no—
106#64520—22no—
107C2×C19⋊C8C2312yes—
108C23×C19—21no—
109C23×C19C2×D411yescharacteristic
110C22×D19—24no—
111C22×D19—22no—
112C22×D19—21no—
113C22×D19—22no—
114C22×D19—41no—
115C22×D19—42no—
116C22×D19—42no—
117C22×D19C2×D411yescharacteristic
118C22×D19C2×D411yescharacteristic
119Q8×C19—21no—
120Q8×C19—22no—
121Q8×C19—22no—
122Q8×C19—42no—
123Q8×C19C2×D412yes—
124D4×C19—24no—
125D4×C19—21no—
126D4×C19C2×D412yes—
127C2×C4×C19—21no—
128C2×C4×C19—24no—
129C2×C4×C19—22no—
130C2×C4×C19—42no—
131C2×C4×C19C2×D411yescharacteristic
132C2×C4×C19C2×D412yes—
133C2×C4×C19C2×D412yes—
134C2×C4×C19C2411yescharacteristic
135C22⋊D19—24no—
136C22⋊D19—24no—
137C22⋊D19—24no—
138C2×Dic19—24no—
139C2×Dic19—22no—
140C2×Dic19—21no—
141C2×Dic19—22no—
142C2×Dic19—42no—
143C2×Dic19C2×D411yescharacteristic
144C2×Dic19C2×D411yescharacteristic
145D76—24no—
146D76—21no—
147D76C2×D412yes—
148C4×D19—24no—
149C4×D19—24no—
150C4×D19—22no—
151C4×D19—24no—
152C4×D19—22no—
153C4×D19—21no—
154C4×D19—21no—
155C4×D19—21no—
156C4×D19—21no—
157Dic38—24no—
158Dic38—21no—
159Dic38C2×D412yes—
160C8×C19—22no—
161C19⋊C8—22no—
162#3007—191nomaximal, Sylow
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—22no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19#12012yes—
169C22×C19C22×D411yescharacteristic
170C2×D19—21no—
171C2×D19—21no—
172C2×D19—21no—
173C2×D19—22no—
174C2×D19—21no—
175C2×D19—21no—
176C2×D19—44no—
177C2×D19—48no—
178C2×D19—41no—
179C2×D19—41no—
180C2×D19#13712yescomplemented
181C4×C19—22no—
182C4×C19—42no—
183C4×C19#12012yes—
184C4×C19C22×D411yescharacteristic
185C4×C19C22×D411yescharacteristic
186Dic19—21no—
187Dic19—22no—
188Dic19—21no—
189Dic19—42no—
190C22×#41—191no—
191C2×#137—191no—
192C2×#137D1911yescharacteristic, complemented
193C2×C22⋊Q8—191no—
194#452—192no—
195#452—192no—
196#451—192no—
197#450—192no—
198#417—191no—
199#417—191no—
200#407—191no—
201C2×C19—22no—
202C2×C19—42no—
203C2×C19C2×#12011yescharacteristic
204C2×C19C2×#13711yescharacteristic
205C2×C19#57511yescharacteristic
206D19—22no—
207D19—41no—
208D19—42no—
209C2×#41—191no—
210C2×#41—191no—
211C2×#41—191no—
212C2×#41—381no—
213C2×#41—381no—
214C2×#41—384no—
215C2×#41—384no—
216C2×#41C2×D1911yescharacteristic
217C22×Q8—191no—
218C22×Q8C2×D1911yescharacteristic, complemented
219C22×D4—191no—
220C22×D4—381no—
221C23×C4—191no—
222C23×C4—381no—
223#137—24no—
224#137—384no—
225C2×Q16—192no—
226C2×Q16C2×D1912yescomplemented
227C2×SD16—192no—
228C2×SD16C2×D1912yescomplemented
229C2×M16—191no—
230C2×M16C2×D1911yescharacteristic, complemented
231C22⋊Q8—192no—
232C22⋊Q8—192no—
233C22⋊Q8—381no—
234C22⋊Q8—381no—
235C2×C4⋊C4—191no—
236C2×C4⋊C4—381no—
237C2×C22⋊C4—381no—
238#103—192no—
239#103—192no—
240#102—192no—
241#102—192no—
242C22⋊C8—192no—
243C22⋊C8—192no—
244C19#300711yescharacteristic, complemented, Sylow
245C24—191no—
246C24—381no—
247#41—22no—
248#41—194no—
249#41—388no—
250#41—382no—
251#41—388no—
252#41—382no—
253#41—382no—
254#41—382no—
255#41—382no—
256#41C22⋊D1914yes—
257C2×Q8—21no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—191no—
261C2×Q8—381no—
262C2×Q8—382no—
263C2×Q8—382no—
264C2×Q8C22×D1912yes—
265C2×Q8C22×D1911yescharacteristic
266C2×D4—21no—
267C2×D4—191no—
268C2×D4—381no—
269C2×D4—381no—
270C2×D4—382no—
271C2×D4—388no—
272C2×D4—381no—
273C2×D4—381no—
274C2×D4—382no—
275C2×D4C22×D1911yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—191no—
279C22×C4—191no—
280C22×C4—191no—
281C22×C4—191no—
282C22×C4—191no—
283C22×C4—381no—
284C22×C4—381no—
285C22×C4—388no—
286C22×C4—381no—
287C22×C4—382no—
288C22×C4—381no—
289C22×C4—382no—
290C22×C4—381no—
291C22×C4C22×D1911yescharacteristic
292Q16—24no—
293Q16—384no—
294SD16—24no—
295SD16—384no—
296M16—22no—
297M16—382no—
298C2×C8—192no—
299C2×C8C22×D1912yes—
300C4⋊C4—192no—
301C4⋊C4—382no—
302C4⋊C4—382no—
303C4⋊C4—381no—
304C22⋊C4—382no—
305C22⋊C4—382no—
306C23—21no—
307C23—191no—
308C23—191no—
309C23—382no—
310C23—384no—
311C23—382no—
312C23—381no—
313C23—761no—
314C23—762no—
315C23—762no—
316C23D4×D1911yescharacteristic
317Q8—21no—
318Q8—22no—
319Q8—22no—
320Q8—42no—
321Q8—192no—
322Q8—384no—
323Q8—381no—
324Q8C2×C22⋊D1912yes—
325D4—24no—
326D4—21no—
327D4—192no—
328D4—384no—
329D4—384no—
330D4—384no—
331D4—384no—
332D4—381no—
333D4C2×C22⋊D1912yes—
334C2×C4—21no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—42no—
338C2×C4—191no—
339C2×C4—191no—
340C2×C4—384no—
341C2×C4—384no—
342C2×C4—384no—
343C2×C4—382no—
344C2×C4—381no—
345C2×C4—382no—
346C2×C4—382no—
347C2×C4—384no—
348C2×C4—381no—
349C2×C4—381no—
350C2×C4—381no—
351C2×C4—381no—
352C2×C4—382no—
353C2×C4—762no—
354C2×C4D4×D1911yescharacteristic
355C2×C4D4×D1912yes—
356C2×C4C2×C22⋊D1912yes—
357C2×C4C23×D1911yescharacteristic
358C8—22no—
359C8—382no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—41no—
364C22—41no—
365C22—192no—
366C22—381no—
367C22—381no—
368C22—381no—
369C22—381no—
370C22—382no—
371C22—381no—
372C22—764no—
373C22—768no—
374C22—761no—
375C22—761no—
376C22#1059738312yes—
377C22C2×D4×D1911yescharacteristic
378C4—22no—
379C4—42no—
380C4—381no—
381C4—381no—
382C4—382no—
383C4—762no—
384C4#1059738312yes—
385C4C2×D4×D1911yescharacteristic
386C4C22×C22⋊D1911yescharacteristic
387C2—22no—
388C2—42no—
389C2—382no—
390C2—761no—
391C2—762no—
392C2C2×#1059738311yescharacteristic
393C2#137×D1911yescharacteristic
394C2#1192734311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×#137C2
socleC22×C19C22×D4
prime radicalC2×#41×D19C2
hypercenterC2×#137D19
hypocenterC19#3007
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#10597388C2semidirect
3. C2×#10597392C2semidirect
4. #11926705C2semidirect
5. #11926703C2semidirect
6. #11926698C2semidirect
7. #11926693C2semidirect
8. #11926546C2semidirect
9. #11926545C2semidirect
10. #11926507C2semidirect
11. C2×C19×#137C2semidirect
13. C22×Q8×C19C22semidirect
27. C2×Q16×C19C22semidirect
28. C2×SD16×C19C22semidirect
29. C2×M16×C19C22semidirect
33. #10597392C22semidirect
34. C2×#64528C22semidirect
36. C2×#64527C22semidirect
38. C2×C4⋊Dic19C22semidirect
40. C2×#64520C22semidirect
41. #10597292C22semidirect
42. #10597289C22semidirect
43. #10597278C22semidirect
45. (C2×D19)⋊C8C22semidirect
46. #10597273C22semidirect
180. C2×D19#137semidirect
192. C2×#137D19semidirect
218. C22×Q8C2×D19semidirect
226. C2×Q16C2×D19semidirect
228. C2×SD16C2×D19semidirect
230. C2×M16C2×D19semidirect
244. C19#3007semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D192
C2×#105973882
C2×#105973922
#119267052
#119267032
#119266982
#119266932
#119265462
#119265452
#119265072
C2×C19×#1372
#300719