Finite Group Databasebeta

← #14572941

Subgroups — #14572941

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×#10597435C211yesmaximal, characteristic, complemented
2C2×#10597354C211yesmaximal, characteristic, complemented
3C2×#10597396C211yesmaximal, characteristic, complemented
4#11927125C211yesmaximal, characteristic, complemented
5#11926709C212yesmaximal, complemented
6#11926696C212yesmaximal, complemented
7#11926692C212yesmaximal, complemented
8#11926679C212yesmaximal, complemented
9C2×#10597266C211yesmaximal, characteristic, complemented
10#11926512C211yesmaximal, characteristic, complemented
11C19×#417C211yesmaximal, characteristic, complemented
12C2×#41×C19C2211yescharacteristic
13#10597435—24no—
14#10597435—24no—
15C2×#64545C2212yes—
16C2×D4×D19—22no—
17C2×D4×D19C2212yes—
18C2×#64541—21no—
19C2×#64541C2211yescharacteristic
20C2×#64541C2211yescharacteristic, complemented
21C22×D76—21no—
22C22×D76C2211yescharacteristic
23C2×M16×C19C2211yescharacteristic, complemented
24C2×C4⋊C4×C19C2211yescharacteristic, complemented
25#10597396—24no—
26C2×#64528C2211yescharacteristic, complemented
27C2×#64527C2211yescharacteristic, complemented
28C2×#64526C2211yescharacteristic, complemented
29C2×#64525C2211yescharacteristic, complemented
30#10597376—22no—
31C22×C19⋊C8C2211yescharacteristic, complemented
32#10597354—24no—
33C2×D152C2212yescomplemented
34C2×#64516C2212yescomplemented
35#10597343—21no—
36#10597343C2212yescomplemented
37#10597341—21no—
38#10597341C2212yescomplemented
39C19×#103C2212yescomplemented
40C19×#102C2212yescomplemented
41(C2×D19)⋊C8C2212yescomplemented
42(C2×D19)⋊C8C2212yescomplemented
43#10597266C2212yescomplemented
44#10597266C2212yescomplemented
45C23×D19—21no—
46C23×D19—22no—
47#41×C19—22no—
48#41×C19D414yescomplemented
49C2×Q8×C19C2311yescharacteristic
50C2×D4×C19—21no—
51C2×D4×C19C2311yescharacteristic
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19C2311yescharacteristic
55C2×C22⋊D19—21no—
56C2×C22⋊D19—22no—
57C2×C22⋊D19D412yes—
58#64545—24no—
59#64545—24no—
60D4×D19—216no—
61D4×D19—24no—
62D4×D19—24no—
63#64541—28no—
64#64541—22no—
65#64541—22no—
66#64541—22no—
67#64541—22no—
68C2×D76—28no—
69C2×D76—22no—
70C2×D76—21no—
71C2×D76—22no—
72C2×D76—22no—
73C2×D76D411yescharacteristic
74C2×D76D414yescomplemented
75C2×D76C2311yescharacteristic
76C2×D76C2312yes—
77C2×C4×D19—22no—
78C2×C4×D19—21no—
79C2×C4×D19C2312yes—
80C2×Dic38D411yescharacteristic
81C2×Dic38C2311yescharacteristic
82M16×C19—22no—
83C2×C8×C19C2312yes—
84C4⋊C4×C19—21no—
85C4⋊C4×C19C2312yes—
86#64528—22no—
87#64527—22no—
88#64526—22no—
89#64525—22no—
90(C2×D19)⋊C4—22no—
91(C2×D19)⋊C4—22no—
92C4⋊Dic19—22no—
93C2×C19⋊C8—22no—
94C2×C19⋊C8C2311yescharacteristic
95C2×C19⋊C8C2311yescharacteristic
96D152—24no—
97#64516—24no—
98C23×C19—21no—
99C23×C19C2×D411yescharacteristic
100C22×D19—22no—
101C22×D19—28no—
102C22×D19—24no—
103C22×D19—21no—
104C22×D19—82no—
105C22×D19—82no—
106C22×D19—81no—
107C22×D19—81no—
108C22×D19C2×D412yes—
109Q8×C19—21no—
110Q8×C19C2×D412yes—
111D4×C19—24no—
112D4×C19—21no—
113D4×C19C2×D412yes—
114C2×C4×C19—21no—
115C2×C4×C19—24no—
116C2×C4×C19—22no—
117C2×C4×C19—81no—
118C2×C4×C19C2×D412yes—
119C2×C4×C19C2×D411yescharacteristic
120C2×C4×C19C2×D412yes—
121C2×C4×C19C2411yescharacteristic
122C22⋊D19—28no—
123C22⋊D19—24no—
124C22⋊D19—42no—
125C2×Dic19—21no—
126C2×Dic19C2×D412yes—
127D76—28no—
128D76—22no—
129D76—24no—
130D76—22no—
131D76—21no—
132D76—21no—
133D76—82no—
134D76C2×D414yes—
135C4×D19—28no—
136C4×D19—22no—
137C4×D19—22no—
138C4×D19—42no—
139Dic38—22no—
140Dic38—21no—
141Dic38—21no—
142C8×C19—22no—
143C19⋊C8—21no—
144C19⋊C8—21no—
145#3012—191nomaximal, Sylow
146C22×C19—21no—
147C22×C19—21no—
148C22×C19—22no—
149C22×C19—41no—
150C22×C19—41no—
151C22×C19#12012yes—
152C22×C19C22×D411yescharacteristic
153C2×D19—22no—
154C2×D19—24no—
155C2×D19—22no—
156C2×D19—22no—
157C2×D19—42no—
158C2×D19—42no—
159C2×D19—41no—
160C2×D19—41no—
161C2×D19—41no—
162C2×D19—84no—
163C2×D19—88no—
164C4×C19—22no—
165C4×C19—42no—
166C4×C19#12012yes—
167C4×C19C22×D411yescharacteristic
168C4×C19C22×D411yescharacteristic
169Dic19—22no—
170Dic19—41no—
171C2×H(5,𝔽2)—191no—
172C2×AGL(1,ℤ/8)—191no—
173C2×#135—191no—
174#537—191no—
175#452—192no—
176#450—192no—
177#449—192no—
178#447—192no—
179#417D1911yescharacteristic, complemented
180C2×#102—191no—
181#408—191no—
182C2×C19—22no—
183C2×C19—42no—
184C2×C19C2×#12011yescharacteristic
185C2×C19#57611yescharacteristic
186C2×C19#57711yescharacteristic
187D19—42no—
188D19—44no—
189D19—81no—
190H(5,𝔽2)—384no—
191H(5,𝔽2)—384no—
192C2×#41—191no—
193C2×#41—192no—
194C2×#41—191no—
195C2×#41—381no—
196C2×#41C2×D1911yescharacteristic
197C22×D4—192no—
198C22×D4—191no—
199C22×D4—381no—
200C22×D4—382no—
201AGL(1,ℤ/8)—384no—
202#135—384no—
203C2×Q16—191no—
204C2×SD16—191no—
205C2×SD16—191no—
206C2×SD16—192no—
207C2×D8—191no—
208C2×D8—192no—
209C2×M16C2×D1911yescharacteristic, complemented
210C22×C8—191no—
211C22⋊Q8—192no—
212C22⋊Q8—381no—
213#121—192no—
214#121—381no—
215#121—382no—
216C2×C4⋊C4C2×D1911yescharacteristic, complemented
217#103C2×D1912yescomplemented
218#102—192no—
219#102—192no—
220#102C2×D1912yescomplemented
221C22⋊C8—192no—
222C22⋊C8—192no—
223C19#301211yescharacteristic, complemented, Sylow
224C24—382no—
225C24—381no—
226#41—22no—
227#41—388no—
228#41—384no—
229#41—384no—
230#41—382no—
231#41—382no—
232#41—382no—
233#41—382no—
234#41D7614yescomplemented
235C2×Q8—191no—
236C2×Q8—191no—
237C2×Q8C22×D1911yescharacteristic
238C2×D4—21no—
239C2×D4—192no—
240C2×D4—194no—
241C2×D4—191no—
242C2×D4—192no—
243C2×D4—191no—
244C2×D4—382no—
245C2×D4—388no—
246C2×D4—382no—
247C2×D4—382no—
248C2×D4—384no—
249C2×D4—3816no—
250C2×D4—384no—
251C2×D4—381no—
252C2×D4—382no—
253C2×D4—381no—
254C2×D4C22×D1911yescharacteristic
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—192no—
258C22×C4—382no—
259C22×C4—381no—
260C22×C4C22×D1911yescharacteristic
261Q16—382no—
262SD16—384no—
263SD16—382no—
264SD16—382no—
265D8—384no—
266D8—382no—
267M16—22no—
268C2×C8—191no—
269C2×C8—191no—
270C2×C8—382no—
271C2×C8C22×D1912yes—
272C4⋊C4—21no—
273C4⋊C4—382no—
274C4⋊C4C22×D1912yes—
275C22⋊C4—382no—
276C22⋊C4—382no—
277C23—21no—
278C23—192no—
279C23—388no—
280C23—382no—
281C23—384no—
282C23—381no—
283C23—1521no—
284C23—1521no—
285C23—1522no—
286C23—1522no—
287C23D4×D1911yescharacteristic
288Q8—21no—
289Q8—382no—
290Q8—381no—
291Q8—381no—
292Q8C2×D7612yes—
293D4—24no—
294D4—21no—
295D4—194no—
296D4—388no—
297D4—388no—
298D4—384no—
299D4—382no—
300D4—381no—
301D4—381no—
302D4—384no—
303D4—382no—
304D4—762no—
305D4—1522no—
306D4C2×D7612yes—
307C2×C4—21no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—81no—
311C2×C4—192no—
312C2×C4—388no—
313C2×C4—382no—
314C2×C4—382no—
315C2×C4—381no—
316C2×C4—762no—
317C2×C4C2×D7612yes—
318C2×C4D4×D1912yes—
319C2×C4D4×D1911yescharacteristic
320C2×C4C23×D1911yescharacteristic
321C8—22no—
322C8—381no—
323C8—381no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—41no—
328C22—41no—
329C22—382no—
330C22—382no—
331C22—384no—
332C22—382no—
333C22—762no—
334C22—762no—
335C22—761no—
336C22—761no—
337C22—761no—
338C22—1524no—
339C22—1528no—
340C22#1059732812yes—
341C22C2×D4×D1911yescharacteristic
342C4—22no—
343C4—42no—
344C4—382no—
345C4—761no—
346C4#1059732812yes—
347C4C22×D7611yescharacteristic
348C4C2×D4×D1911yescharacteristic
349C2—22no—
350C2—42no—
351C2—762no—
352C2—764no—
353C2—1521no—
354C2C2×#1059732811yescharacteristic
355C2#1192734811yescharacteristic
356C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#417C2
socleC22×C19C22×D4
hypercenter#417D19
hypocenterC19#3012
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#10597435C2semidirect
2. C2×#10597354C2semidirect
3. C2×#10597396C2semidirect
4. #11927125C2semidirect
5. #11926709C2semidirect
6. #11926696C2semidirect
7. #11926692C2semidirect
8. #11926679C2semidirect
9. C2×#10597266C2semidirect
10. #11926512C2semidirect
11. C19×#417C2semidirect
20. C2×#64541C22semidirect
23. C2×M16×C19C22semidirect
24. C2×C4⋊C4×C19C22semidirect
26. C2×#64528C22semidirect
27. C2×#64527C22semidirect
28. C2×#64526C22semidirect
29. C2×#64525C22semidirect
31. C22×C19⋊C8C22semidirect
33. C2×D152C22semidirect
34. C2×#64516C22semidirect
36. #10597343C22semidirect
38. #10597341C22semidirect
39. C19×#103C22semidirect
40. C19×#102C22semidirect
41. (C2×D19)⋊C8C22semidirect
42. (C2×D19)⋊C8C22semidirect
43. #10597266C22semidirect
44. #10597266C22semidirect
48. #41×C19D4semidirect
74. C2×D76D4semidirect
179. #417D19semidirect
209. C2×M16C2×D19semidirect
216. C2×C4⋊C4C2×D19semidirect
217. #103C2×D19semidirect
220. #102C2×D19semidirect
223. C19#3012semidirect
234. #41D76semidirect

Maximal subgroups

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

subgroupindex
C2×#105974352
C2×#105973542
C2×#105973962
#119271252
#119267092
#119266962
#119266922
#119266792
C2×#105972662
#119265122
C19×#4172
#301219