Finite Group Databasebeta

← #14572938

Subgroups — #14572938

Order 2432.

764 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#10597430C211yesmaximal, characteristic, complemented
2C2×#10597396C211yesmaximal, characteristic, complemented
3#11927122C211yesmaximal, characteristic, complemented
4#11926703C212yesmaximal, complemented
5#11926693C212yesmaximal, complemented
6#11926686C212yesmaximal, complemented
7#11926676C212yesmaximal, complemented
8#11926546C211yesmaximal, characteristic, complemented
9C2×#10597289C211yesmaximal, characteristic, complemented
10#11926512C211yesmaximal, characteristic, complemented
11C2×C19×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
12C2×#41×C19C2211yescharacteristic, complemented
13C22×D4×C19C2211yescharacteristic
14C22×C22⋊D19—22no—
15#10597430—24no—
16#10597430—24no—
17C2×#64543—21no—
18C2×#64543C2212yes—
19C2×D4×D19—21no—
20C2×D4×D19C2212yes—
21C2×#64541C2211yescharacteristic
22C2×#64541C2211yescharacteristic
23C19×AGL(1,ℤ/8)—24no—
24C2×SD16×C19C2212yescomplemented
25C2×D8×C19C2212yescomplemented
26C2×M16×C19C2211yescharacteristic, complemented
27#10597396—24no—
28#10597392C2212yescomplemented
29C2×#64528C2211yescharacteristic, complemented
30C2×#64527C2211yescharacteristic, complemented
31#10597385—22no—
32#10597384C2212yescomplemented
33C2×#64526C2211yescharacteristic, complemented
34C2×#64525C2211yescharacteristic, complemented
35#10597376—21no—
36C2×C4⋊Dic19C2211yescharacteristic, complemented
37#10597370—21no—
38C22×C19⋊C8C2211yescharacteristic, complemented
39#10597289C2212yescomplemented
40#10597289C2212yescomplemented
41#10597278C2212yescomplemented
42(C2×D19)⋊C8C2212yescomplemented
43(C2×D19)⋊C8C2212yescomplemented
44#10597273C2212yescomplemented
45C24×C19—21no—
46C23×D19—22no—
47#41×C19—22no—
48#41×C19—22no—
49C2×Q8×C19C2311yescharacteristic
50C2×D4×C19—21no—
51C2×D4×C19—21no—
52C2×D4×C19—22no—
53C2×D4×C19D414yescomplemented
54C2×D4×C19C2311yescharacteristic
55C2×D4×C19C2312yes—
56C22×C4×C19—21no—
57C22×C4×C19C2311yescharacteristic
58C2×C22⋊D19—216no—
59C2×C22⋊D19—21no—
60C2×C22⋊D19—22no—
61C2×C22⋊D19—22no—
62C2×C22⋊D19—22no—
63C2×C22⋊D19D412yes—
64C22×Dic19—22no—
65C22×Dic19—21no—
66#64543—28no—
67#64543—24no—
68#64543—24no—
69D4×D19—28no—
70D4×D19—24no—
71D4×D19—24no—
72#64541—22no—
73#64541—22no—
74#64541—22no—
75#64541D414yescomplemented
76C2×D76D411yescharacteristic
77C2×D76C2311yescharacteristic
78C2×C4×D19—21no—
79C2×C4×D19C2312yes—
80C2×Dic38D411yescharacteristic
81C2×Dic38C2311yescharacteristic
82SD16×C19—24no—
83D8×C19—24no—
84M16×C19—22no—
85C2×C8×C19C2312yes—
86C22⋊Dic19—22no—
87#64528—22no—
88#64527—22no—
89#64526—22no—
90#64525—22no—
91(C2×D19)⋊C4—22no—
92C4⋊Dic19—21no—
93C4⋊Dic19C2312yes—
94Dic19⋊C4—22no—
95C2×C19⋊C8—22no—
96C2×C19⋊C8C2311yescharacteristic
97C2×C19⋊C8C2311yescharacteristic
98C23×C19—22no—
99C23×C19—24no—
100C23×C19—21no—
101C23×C19—81no—
102C23×C19—81no—
103C23×C19C2×D411yescharacteristic
104C22×D19—21no—
105C22×D19—28no—
106C22×D19—82no—
107C22×D19—82no—
108C22×D19C2×D412yes—
109Q8×C19—21no—
110Q8×C19—21no—
111D4×C19—24no—
112D4×C19—22no—
113D4×C19—21no—
114D4×C19—21no—
115D4×C19—42no—
116D4×C19C2×D414yes—
117C2×C4×C19—21no—
118C2×C4×C19—42no—
119C2×C4×C19C2×D411yescharacteristic
120C2×C4×C19C2×D412yes—
121C2×C4×C19C2×D412yes—
122C2×C4×C19C2411yescharacteristic
123C22⋊D19—28no—
124C22⋊D19—28no—
125C22⋊D19—24no—
126C22⋊D19—24no—
127C22⋊D19—82no—
128C2×Dic19—28no—
129C2×Dic19—21no—
130C2×Dic19—22no—
131C2×Dic19—81no—
132C2×Dic19C2×D412yes—
133D76—22no—
134D76—21no—
135D76C2×D412yes—
136C4×D19—24no—
137C4×D19—22no—
138C4×D19—22no—
139Dic38—22no—
140Dic38—21no—
141Dic38C2×D412yes—
142C8×C19—22no—
143C19⋊C8—21no—
144C19⋊C8—21no—
145#3012—191nomaximal, Sylow
146C22×C19—21no—
147C22×C19—21no—
148C22×C19—24no—
149C22×C19—42no—
150C22×C19—42no—
151C22×C19—41no—
152C22×C19—41no—
153C22×C19—41no—
154C22×C19—84no—
155C22×C19#12012yes—
156C22×C19C22×D411yescharacteristic
157C2×D19—22no—
158C2×D19—22no—
159C2×D19—22no—
160C2×D19—22no—
161C2×D19—41no—
162C2×D19—41no—
163C2×D19—88no—
164C4×C19—41no—
165C4×C19#12012yes—
166C4×C19C22×D411yescharacteristic
167C4×C19C22×D411yescharacteristic
168Dic19—22no—
169Dic19—22no—
170Dic19—42no—
171C2×H(5,𝔽2)—191no—
172C2×AGL(1,ℤ/8)D1911yescharacteristic, complemented
173C2×#135—191no—
174#537—191no—
175#452—192no—
176#450—192no—
177#449—192no—
178#447—192no—
179#417—191no—
180C2×#102—191no—
181#408—191no—
182C2×C19—22no—
183C2×C19—44no—
184C2×C19—81no—
185C2×C19C2×#12011yescharacteristic
186C2×C19#57611yescharacteristic
187C2×C19#57711yescharacteristic
188D19—42no—
189D19—42no—
190H(5,𝔽2)—384no—
191H(5,𝔽2)—384no—
192C2×#41—191no—
193C2×#41—192no—
194C2×#41—191no—
195C2×#41—381no—
196C2×#41C2×D1911yescharacteristic, complemented
197C22×D4—192no—
198C22×D4—381no—
199C22×D4—382no—
200C22×D4C2×D1911yescharacteristic
201AGL(1,ℤ/8)—24no—
202#135—384no—
203C2×Q16—191no—
204C2×SD16—191no—
205C2×SD16—191no—
206C2×SD16C2×D1912yescomplemented
207C2×D8—191no—
208C2×D8C2×D1912yescomplemented
209C2×M16C2×D1911yescharacteristic, complemented
210C22×C8—191no—
211C22⋊Q8—192no—
212C22⋊Q8—381no—
213#121—192no—
214#121—381no—
215#121—382no—
216C2×C4⋊C4—191no—
217#103—192no—
218#102—192no—
219#102—192no—
220#102—192no—
221C22⋊C8—192no—
222C22⋊C8—192no—
223C19#301211yescharacteristic, complemented, Sylow
224C24—21no—
225C24—382no—
226#41—22no—
227#41—22no—
228#41—194no—
229#41—384no—
230#41—388no—
231#41—384no—
232#41—382no—
233#41—382no—
234#41—382no—
235C2×Q8—191no—
236C2×Q8—191no—
237C2×Q8C22×D1911yescharacteristic
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—22no—
241C2×D4—192no—
242C2×D4—191no—
243C2×D4—191no—
244C2×D4—382no—
245C2×D4—384no—
246C2×D4—388no—
247C2×D4—382no—
248C2×D4—3816no—
249C2×D4—381no—
250C2×D4—384no—
251C2×D4—382no—
252C2×D4C22⋊D1914yescomplemented
253C2×D4C22×D1911yescharacteristic
254C2×D4C22×D1912yes—
255C22×C4—21no—
256C22×C4—192no—
257C22×C4—382no—
258C22×C4—381no—
259C22×C4—381no—
260C22×C4C22×D1911yescharacteristic
261Q16—382no—
262SD16—24no—
263SD16—382no—
264SD16—382no—
265D8—24no—
266D8—382no—
267M16—22no—
268C2×C8—191no—
269C2×C8—191no—
270C2×C8—382no—
271C2×C8C22×D1912yes—
272C4⋊C4—192no—
273C4⋊C4—382no—
274C4⋊C4—381no—
275C22⋊C4—382no—
276C22⋊C4—382no—
277C23—22no—
278C23—24no—
279C23—21no—
280C23—81no—
281C23—81no—
282C23—192no—
283C23—388no—
284C23—381no—
285C23—1522no—
286C23—1522no—
287C23D4×D1911yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—192no—
291Q8—382no—
292Q8—381no—
293D4—24no—
294D4—22no—
295D4—21no—
296D4—21no—
297D4—42no—
298D4—192no—
299D4—388no—
300D4—388no—
301D4—384no—
302D4—384no—
303D4—382no—
304D4—381no—
305D4—1522no—
306D4C2×C22⋊D1914yes—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—192no—
310C2×C4—388no—
311C2×C4—381no—
312C2×C4—384no—
313C2×C4—382no—
314C2×C4—382no—
315C2×C4—382no—
316C2×C4—1521no—
317C2×C4D4×D1911yescharacteristic
318C2×C4D4×D1912yes—
319C2×C4C2×C22⋊D1912yes—
320C2×C4C23×D1911yescharacteristic
321C8—22no—
322C8—381no—
323C8—381no—
324C22—21no—
325C22—21no—
326C22—24no—
327C22—42no—
328C22—42no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—84no—
333C22—382no—
334C22—382no—
335C22—382no—
336C22—382no—
337C22—761no—
338C22—761no—
339C22—1528no—
340C22#1059738312yes—
341C22C2×D4×D1911yescharacteristic
342C4—41no—
343C4—382no—
344C4—382no—
345C4—762no—
346C4#1059738312yes—
347C4C2×D4×D1911yescharacteristic
348C4C22×C22⋊D1911yescharacteristic
349C2—22no—
350C2—44no—
351C2—81no—
352C2—762no—
353C2—762no—
354C2C2×#1059738311yescharacteristic
355C2#1192734811yescharacteristic
356C2#1192735411yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×AGL(1,ℤ/8)C2
socleC22×C19C22×D4
hypercenterC2×AGL(1,ℤ/8)D19
hypocenterC19#3012
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#10597430C2semidirect
2. C2×#10597396C2semidirect
3. #11927122C2semidirect
4. #11926703C2semidirect
5. #11926693C2semidirect
6. #11926686C2semidirect
7. #11926676C2semidirect
8. #11926546C2semidirect
9. C2×#10597289C2semidirect
10. #11926512C2semidirect
11. C2×C19×AGL(1,ℤ/8)C2semidirect
12. C2×#41×C19C22semidirect
24. C2×SD16×C19C22semidirect
25. C2×D8×C19C22semidirect
26. C2×M16×C19C22semidirect
28. #10597392C22semidirect
29. C2×#64528C22semidirect
30. C2×#64527C22semidirect
32. #10597384C22semidirect
33. C2×#64526C22semidirect
34. C2×#64525C22semidirect
36. C2×C4⋊Dic19C22semidirect
38. C22×C19⋊C8C22semidirect
39. #10597289C22semidirect
40. #10597289C22semidirect
41. #10597278C22semidirect
42. (C2×D19)⋊C8C22semidirect
43. (C2×D19)⋊C8C22semidirect
44. #10597273C22semidirect
53. C2×D4×C19D4semidirect
75. #64541D4semidirect
172. C2×AGL(1,ℤ/8)D19semidirect
196. C2×#41C2×D19semidirect
206. C2×SD16C2×D19semidirect
208. C2×D8C2×D19semidirect
209. C2×M16C2×D19semidirect
223. C19#3012semidirect
252. C2×D4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105974302
C2×#105973962
#119271222
#119267032
#119266932
#119266862
#119266762
#119265462
C2×#105972892
#119265122
C2×C19×AGL(1,ℤ/8)2
#301219