Finite Group Databasebeta

← #14577394

Subgroups — #14577394

Order 2432.

1660 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597430C211yesmaximal, characteristic, complemented
2#11927193C214yesmaximal, complemented
3#11927188C214yesmaximal, complemented
4#11927182C214yesmaximal, complemented
5D4×C22⋊D19C214yesmaximal, complemented
6#11927122C212yesmaximal, complemented
7#11927103C214yesmaximal, complemented
8#11927090C212yesmaximal, complemented
9C2×#10597385C214yesmaximal, complemented
10C2×D4×Dic19C211yesmaximal, characteristic, complemented
11C2×C19×H(5,𝔽2)C211yesmaximal, characteristic, complemented
12C19×H(5,𝔽2)—28no—
13C2×#41×C19C2212yescomplemented
14C2×#41×C19C2214yescomplemented
15C22×D4×C19C2211yescharacteristic
16C22×D4×C19C2214yescomplemented
17C22×D4×C19C2214yescomplemented
18C22×C22⋊D19C2214yescomplemented
19C22×C22⋊D19C2214yescomplemented
20C23×Dic19C2212yescomplemented
21#10597430—28no—
22C2×#64543C2214yescomplemented
23C2×D4×D19C2214yescomplemented
24C2×#64541C2212yescomplemented
25#10597399C2218yescomplemented
26C2×C22⋊Dic19C2212yescomplemented
27C2×C22⋊Dic19C2214yescomplemented
28#10597393C2212yescomplemented
29#10597392C2214yescomplemented
30#10597390C2212yescomplemented
31#10597386C2212yescomplemented
32#10597385C2214yescomplemented
33#10597385C2214yescomplemented
34#10597385C2218yescomplemented
35#10597385C2218yescomplemented
36#10597385C2218yescomplemented
37#10597384C2214yescomplemented
38#10597383C2218yescomplemented
39#10597382C2212yescomplemented
40#10597381C2218yescomplemented
41D4×Dic19C2214yescomplemented
42D4×Dic19C2214yescomplemented
43#10597376C2214yescomplemented
44#10597375C2218yescomplemented
45C4×C22⋊D19C2214yescomplemented
46C4×C22⋊D19C2214yescomplemented
47C2×(C2×D19)⋊C4C2214yescomplemented
48C2×C4⋊Dic19C2211yescharacteristic, complemented
49#10597370C2214yescomplemented
50C2×Dic19⋊C4C2214yescomplemented
51C2×C4×Dic19C2211yescharacteristic, complemented
52C24×C19C2314yes—
53C24×C19C2312yes—
54C23×D19C2314yes—
55#41×C19—216no—
56#41×C19—28no—
57C2×Q8×C19C2312yes—
58C2×D4×C19—216no—
59C2×D4×C19—216no—
60C2×D4×C19D418yescomplemented
61C2×D4×C19C2318yes—
62C2×D4×C19C2312yes—
63C2×D4×C19C2314yes—
64C2×D4×C19C2314yes—
65C22×C4×C19C2314yes—
66C22×C4×C19C2314yes—
67C22×C4×C19C2311yescharacteristic
68C2×C22⋊D19—216no—
69C2×C22⋊D19—48no—
70C2×C22⋊D19C2314yes—
71C2×C22⋊D19C2314yes—
72C2×C22⋊D19C2318yes—
73C2×C22⋊D19C2318yes—
74C2×C22⋊D19C2314yes—
75C22×Dic19—44no—
76C22×Dic19C2314yes—
77C22×Dic19C2314yes—
78C22×Dic19C2311yescharacteristic
79C22×Dic19C2314yes—
80C22×Dic19C2311yescharacteristic
81C22×Dic19C2312yes—
82#64543—216no—
83D4×D19—216no—
84#64541—28no—
85C2×D76C2312yes—
86C2×C4×D19C2314yes—
87C2×Dic38C2312yes—
88C22⋊Dic19C2318yes—
89C22⋊Dic19C2314yes—
90C22⋊Dic19C2318yes—
91C22⋊Dic19C2314yes—
92(C2×D19)⋊C4C2318yes—
93(C2×D19)⋊C4C2314yes—
94(C2×D19)⋊C4C2314yes—
95C4⋊Dic19C2314yes—
96Dic19⋊C4C2314yes—
97Dic19⋊C4C2318yes—
98Dic19⋊C4C2314yes—
99C4×Dic19C2312yes—
100C4×Dic19C2312yes—
101C23×C19—28no—
102C23×C19—42no—
103C23×C19—42no—
104C23×C19—44no—
105C23×C19—44no—
106C23×C19C2×D418yescomplemented
107C23×C19C2414yes—
108C23×C19C2414yes—
109C23×C19C2411yescharacteristic
110C22×D19—28no—
111C22×D19—44no—
112C22×D19—44no—
113C22×D19C2414yes—
114Q8×C19—24no—
115D4×C19—216no—
116D4×C19—28no—
117D4×C19—24no—
118D4×C19C2×D4116yescomplemented
119C2×C4×C19—28no—
120C2×C4×C19—28no—
121C2×C4×C19C2×D414yescomplemented
122C2×C4×C19C2414yes—
123C2×C4×C19C2412yes—
124C22⋊D19—28no—
125C22⋊D19—216no—
126C22⋊D19—28no—
127C22⋊D19—48no—
128C22⋊D19—44no—
129C2×Dic19—28no—
130C2×Dic19—22no—
131C2×Dic19—28no—
132C2×Dic19—44no—
133C2×Dic19—42no—
134C2×Dic19—41no—
135C2×Dic19C2412yes—
136C2×Dic19C2411yescharacteristic
137C2×Dic19C2414yes—
138C2×Dic19C2414yes—
139C2×Dic19C2411yescharacteristic
140D76—24no—
141C4×D19—28no—
142Dic38—24no—
143#3496—191nomaximal, Sylow
144C22×C19—21no—
145C22×C19—24no—
146C22×C19—21no—
147C22×C19—24no—
148C22×C19—24no—
149C22×C19—24no—
150C22×C19—24no—
151C22×C19—48no—
152C22×C19—88no—
153C22×C19C22×D418yes—
154C22×C19C22×D412yes—
155C22×C19C2511yescharacteristic
156C2×D19—24no—
157C2×D19—24no—
158C2×D19—24no—
159C2×D19—88no—
160C4×C19—24no—
161C4×C19C22×D414yes—
162Dic19—24no—
163Dic19—21no—
164Dic19—24no—
165Dic19—22no—
166Dic19H(5,𝔽2)12yescomplemented
167C2×H(5,𝔽2)—191no—
168C2×H(5,𝔽2)D1911yescharacteristic, complemented
169#547—194no—
170#546—194no—
171#546—194no—
172D42—194no—
173#537—192no—
174#534—194no—
175#532—192no—
176C2×#121—194no—
177C2×C4×D4—191no—
178C2×C19—28no—
179C2×C19—22no—
180C2×C19—44no—
181C2×C19C23×D411yescharacteristic
182C2×C19C2×H(5,𝔽2)11yescharacteristic
183C2×C19#58511yescharacteristic
184D19—44no—
185H(5,𝔽2)—28no—
186H(5,𝔽2)—388no—
187C2×#41—194no—
188C2×#41—192no—
189C2×#41C2×D1912yescomplemented
190C2×#41C2×D1914yescomplemented
191C22×D4—194no—
192C22×D4—194no—
193C22×D4—194no—
194C22×D4C2×D1911yescharacteristic
195C22×D4C2×D1914yescomplemented
196C22×D4C2×D1914yescomplemented
197C23×C4—192no—
198C4⋊Q8—192no—
199#127—192no—
200#124—192no—
201#124—192no—
202#123—198no—
203#123—198no—
204C22⋊Q8—194no—
205C22⋊Q8—194no—
206#121—194no—
207#121—194no—
208#121—198no—
209#121—198no—
210#121—198no—
211#121—194no—
212#121—194no—
213#120—198no—
214#120—198no—
215C4×D4—194no—
216C4×D4—194no—
217C4×D4—194no—
218C4×D4—194no—
219C2×C4⋊C4—191no—
220C2×C4⋊C4—194no—
221C2×C22⋊C4—192no—
222C2×C22⋊C4—194no—
223C2×C22⋊C4—194no—
224C2×C42—191no—
225C19#349611yescharacteristic, complemented, Sylow
226C24—194no—
227C24C22×D1914yes—
228C24C22×D1912yes—
229#41—216no—
230#41—28no—
231#41—3816no—
232#41—388no—
233C2×Q8—192no—
234C2×Q8C22×D1912yes—
235C2×D4—216no—
236C2×D4—216no—
237C2×D4—194no—
238C2×D4—198no—
239C2×D4—194no—
240C2×D4—194no—
241C2×D4—198no—
242C2×D4—192no—
243C2×D4—3816no—
244C2×D4—3816no—
245C2×D4—768no—
246C2×D4C22⋊D1918yescomplemented
247C2×D4C22×D1918yes—
248C2×D4C22×D1914yes—
249C2×D4C22×D1912yes—
250C2×D4C22×D1914yes—
251C22×C4—191no—
252C22×C4—194no—
253C22×C4—194no—
254C22×C4—191no—
255C22×C4—194no—
256C22×C4—192no—
257C22×C4—194no—
258C22×C4—764no—
259C22×C4C22×D1914yes—
260C22×C4C22×D1914yes—
261C22×C4C22×D1911yescharacteristic
262C4⋊C4—194no—
263C4⋊C4—198no—
264C4⋊C4—194no—
265C4⋊C4—194no—
266C22⋊C4—194no—
267C22⋊C4—198no—
268C22⋊C4—198no—
269C22⋊C4—194no—
270C22⋊C4—194no—
271C22⋊C4—198no—
272C22⋊C4—194no—
273C42—192no—
274C42—192no—
275C23—28no—
276C23—42no—
277C23—42no—
278C23—44no—
279C23—44no—
280C23—194no—
281C23—388no—
282C23—764no—
283C23—764no—
284C23C2×C22⋊D1918yescomplemented
285C23C23×D1914yes—
286C23C23×D1914yes—
287C23C23×D1911yescharacteristic
288Q8—24no—
289Q8—384no—
290D4—216no—
291D4—28no—
292D4—24no—
293D4—388no—
294D4—3816no—
295D4—388no—
296D4—384no—
297D4—768no—
298D4—764no—
299D4C2×C22⋊D19116yescomplemented
300C2×C4—28no—
301C2×C4—28no—
302C2×C4—191no—
303C2×C4—192no—
304C2×C4—191no—
305C2×C4—194no—
306C2×C4—194no—
307C2×C4—382no—
308C2×C4—388no—
309C2×C4—388no—
310C2×C4—388no—
311C2×C4—764no—
312C2×C4—762no—
313C2×C4—761no—
314C2×C4C2×C22⋊D1914yescomplemented
315C2×C4C23×D1914yes—
316C2×C4C23×D1912yes—
317C22—21no—
318C22—24no—
319C22—21no—
320C22—24no—
321C22—24no—
322C22—24no—
323C22—24no—
324C22—48no—
325C22—88no—
326C22—384no—
327C22—384no—
328C22—384no—
329C22—1528no—
330C22C22×C22⋊D1918yes—
331C22C22×C22⋊D1912yes—
332C22C24×D1911yescharacteristic
333C4—24no—
334C4—192no—
335C4—384no—
336C4—381no—
337C4—384no—
338C4—382no—
339C4C22×C22⋊D1914yes—
340C2—22no—
341C2—28no—
342C2—44no—
343C2—764no—
344C2C23×C22⋊D1911yescharacteristic
345C2H(5,𝔽2)×D1911yescharacteristic
346C2#1192737911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC2×C19×H(5,𝔽2)C2
hypercenterC2×H(5,𝔽2)D19
hypocenterC19#3496
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×#10597430C2semidirect
2. #11927193C2semidirect
3. #11927188C2semidirect
4. #11927182C2semidirect
5. D4×C22⋊D19C2semidirect
6. #11927122C2semidirect
7. #11927103C2semidirect
8. #11927090C2semidirect
9. C2×#10597385C2semidirect
10. C2×D4×Dic19C2semidirect
11. C2×C19×H(5,𝔽2)C2semidirect
13. C2×#41×C19C22semidirect
14. C2×#41×C19C22semidirect
16. C22×D4×C19C22semidirect
17. C22×D4×C19C22semidirect
18. C22×C22⋊D19C22semidirect
19. C22×C22⋊D19C22semidirect
20. C23×Dic19C22semidirect
22. C2×#64543C22semidirect
23. C2×D4×D19C22semidirect
24. C2×#64541C22semidirect
25. #10597399C22semidirect
26. C2×C22⋊Dic19C22semidirect
27. C2×C22⋊Dic19C22semidirect
28. #10597393C22semidirect
29. #10597392C22semidirect
30. #10597390C22semidirect
31. #10597386C22semidirect
32. #10597385C22semidirect
33. #10597385C22semidirect
34. #10597385C22semidirect
35. #10597385C22semidirect
36. #10597385C22semidirect
37. #10597384C22semidirect
38. #10597383C22semidirect
39. #10597382C22semidirect
40. #10597381C22semidirect
41. D4×Dic19C22semidirect
42. D4×Dic19C22semidirect
43. #10597376C22semidirect
44. #10597375C22semidirect
45. C4×C22⋊D19C22semidirect
46. C4×C22⋊D19C22semidirect
47. C2×(C2×D19)⋊C4C22semidirect
48. C2×C4⋊Dic19C22semidirect
49. #10597370C22semidirect
50. C2×Dic19⋊C4C22semidirect
51. C2×C4×Dic19C22semidirect
60. C2×D4×C19D4semidirect
106. C23×C19C2×D4semidirect
118. D4×C19C2×D4semidirect
121. C2×C4×C19C2×D4semidirect
166. Dic19H(5,𝔽2)semidirect
168. C2×H(5,𝔽2)D19semidirect
189. C2×#41C2×D19semidirect
190. C2×#41C2×D19semidirect
195. C22×D4C2×D19semidirect
196. C22×D4C2×D19semidirect
225. C19#3496semidirect
246. C2×D4C22⋊D19semidirect
284. C23C2×C22⋊D19semidirect
299. D4C2×C22⋊D19semidirect
314. C2×C4C2×C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105974302
#119271932
#119271882
#119271822
D4×C22⋊D192
#119271222
#119271032
#119270902
C2×#105973852
C2×D4×Dic192
C2×C19×H(5,𝔽2)2
#349619