Finite Group Databasebeta

← #14566140

Subgroups — #14566140

Order 2432.

1224 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D19C211yesmaximal, characteristic, complemented
2C2×#10597383C211yesmaximal, characteristic
3C2×D4×Dic19C211yesmaximal, characteristic, complemented
4C2×(C22⋊D19)⋊C4C212yesmaximal, complemented
5#11926420C212yesmaximal, complemented
6#11926418C212yesmaximal, complemented
7#11926417C211yesmaximal, characteristic, complemented
8#11926399C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic19C211yesmaximal, characteristic, complemented
10#11926391C212yesmaximal, complemented
11C19×#386C211yesmaximal, characteristic, complemented
12C24×D19C2211yescharacteristic
13C22×D4×C19C2211yescharacteristic
14C23×C4×C19C2211yescharacteristic
15C22×C22⋊D19C2212yes—
16C23×Dic19C2211yescharacteristic
17C23×Dic19C2211yescharacteristic, complemented
18C22×C4×D19—24no—
19C22×C4×D19—28no—
20C22×C4×D19C2212yes—
21C22×C4×D19C2212yes—
22C2×C22⋊C4×C19C2211yescharacteristic
23C2×C22⋊C4×C19C2212yescomplemented
24C2×C22⋊Dic19C2211yescharacteristic
25C2×C22⋊Dic19C2211yescharacteristic
26C2×C22⋊Dic19C2211yescharacteristic, complemented
27#10597383C418yescomplemented
28D4×Dic19—24no—
29C2×(C2×D19)⋊C4C2212yes—
30C2×(C2×D19)⋊C4C2212yes—
31C2×(C2×D19)⋊C4C2212yes—
32C2×C4⋊Dic19C2211yescharacteristic, complemented
33C2×Dic19⋊C4C2212yescomplemented
34C2×C4×Dic19C2211yescharacteristic, complemented
35C2×C4×Dic19C2212yescomplemented
36(C22⋊D19)⋊C4—28no—
37C19×#95C2212yescomplemented
38C19⋊#95C2212yescomplemented
39C19⋊#95C2212yescomplemented
40C24×C19C2311yescharacteristic
41C24×C19C2311yescharacteristic
42C23×D19—22no—
43C23×D19—22no—
44C23×D19—24no—
45C23×D19—24no—
46C23×D19C2×C414yescomplemented
47C23×D19C2312yes—
48C2×D4×C19—22no—
49C2×D4×C19—22no—
50C2×D4×C19C2×C414yescomplemented
51C22×C4×C19—22no—
52C22×C4×C19—24no—
53C22×C4×C19C2312yes—
54C22×C4×C19C2311yescharacteristic
55C22×C4×C19C2312yes—
56C2×C22⋊D19—24no—
57C2×C22⋊D19—24no—
58C2×C22⋊D19C2×C418yescomplemented
59C22×Dic19—24no—
60C22×Dic19—22no—
61C22×Dic19—24no—
62C22×Dic19D414yescomplemented
63C22×Dic19C2311yescharacteristic
64C22×Dic19C2311yescharacteristic
65C22×Dic19C2312yes—
66C22×Dic19C2311yescharacteristic
67C22×Dic19C2311yescharacteristic
68C2×C4×D19—232no—
69C2×C4×D19—24no—
70C2×C4×D19—24no—
71C2×C4×D19—24no—
72C2×C4×D19—24no—
73C2×C4×D19—24no—
74C2×C4×D19D418yescomplemented
75C22⋊C4×C19—22no—
76C22⋊C4×C19—24no—
77C22⋊Dic19—22no—
78C22⋊Dic19—22no—
79C22⋊Dic19C2×C414yescomplemented
80(C2×D19)⋊C4—24no—
81(C2×D19)⋊C4—24no—
82(C2×D19)⋊C4C2×C418yescomplemented
83C4⋊Dic19—22no—
84Dic19⋊C4—24no—
85C4×Dic19—22no—
86C4×Dic19—24no—
87C23×C19—22no—
88C23×C19—22no—
89C23×C19—21no—
90C23×C19—22no—
91C23×C19—22no—
92C23×C19—21no—
93C23×C19C22×C412yes—
94C23×C19C22×C412yescomplemented
95C23×C19C2×D412yes—
96C23×C19#4112yes—
97C23×C19C2411yescharacteristic
98C22×D19—28no—
99C22×D19—216no—
100C22×D19—28no—
101C22×D19—28no—
102C22×D19—22no—
103C22×D19—22no—
104C22×D19—22no—
105C22×D19—22no—
106C22×D19—216no—
107C22×D19C22×C414yes—
108C22×D19C2×D414yes—
109C22×D19#4114yes—
110D4×C19—28no—
111C2×C4×C19—28no—
112C2×C4×C19—21no—
113C2×C4×C19—22no—
114C2×C4×C19—22no—
115C2×C4×C19—21no—
116C2×C4×C19—22no—
117C2×C4×C19—22no—
118C2×C4×C19—22no—
119C2×C4×C19C22×C412yescomplemented
120C2×C4×C19C2×D414yes—
121C22⋊D19—216no—
122C2×Dic19—22no—
123C2×Dic19—22no—
124C2×Dic19—22no—
125C2×Dic19—28no—
126C2×Dic19—21no—
127C2×Dic19—22no—
128C2×Dic19—21no—
129C2×Dic19—22no—
130C2×Dic19—44no—
131C2×Dic19C22×C414yescomplemented
132C2×Dic19C2×D412yes—
133C2×Dic19C2×D412yes—
134C2×Dic19C2×D414yes—
135C4×D19—216no—
136C4×D19—216no—
137C4×#120—191nomaximal, Sylow
138C22×C19—24no—
139C22×C19—22no—
140C22×C19—22no—
141C22×C19—24no—
142C22×C19—24no—
143C22×C19—22no—
144C22×C19—41no—
145C22×C19—41no—
146C22×C19—42no—
147C22×C19C4×D414yescomplemented
148C22×C19C23×C411yescharacteristic
149C22×C19C22×D412yes—
150C22×C19C22×D411yescharacteristic
151C22×C19C2×#4111yescharacteristic
152C22×C19C2×#4112yes—
153C2×D19—232no—
154C2×D19—24no—
155C2×D19—24no—
156C2×D19—24no—
157C2×D19—24no—
158C2×D19—24no—
159C2×D19—24no—
160C2×D19C4×D418yescomplemented
161C4×C19—22no—
162C4×C19—24no—
163C4×C19—42no—
164Dic19—24no—
165Dic19—22no—
166Dic19—41no—
167Dic19—41no—
168Dic19#12014yescomplemented
169C24×C4—191no—
170C2×#120—191no—
171C2×C4×D4—191no—
172C2×C4×D4—192no—
173#386—192no—
174#386D1911yescharacteristic, complemented
175#385—191no—
176#385—192no—
177#379—191no—
178C4×C22⋊C4—191no—
179C4×C22⋊C4—192no—
180C2×C19—24no—
181C2×C19—42no—
182C2×C19C2×C4×D412yes—
183C2×C19C2×C4×D411yescharacteristic
184C2×C19C2×#12011yescharacteristic
185C2×C19#52511yescharacteristic
186C2×C19#52512yes—
187D19—28no—
188C25—191no—
189C22×D4—192no—
190C22×D4C2×D1911yescharacteristic
191C23×C4—191no—
192C23×C4—192no—
193C23×C4—191no—
194C23×C4—192no—
195C23×C4—384no—
196C23×C4—388no—
197C23×C4C2×D1911yescharacteristic
198#120—198no—
199C4×D4—388no—
200C4×D4—384no—
201C2×C4⋊C4—192no—
202C2×C4⋊C4—191no—
203C2×C22⋊C4—191no—
204C2×C22⋊C4—192no—
205C2×C22⋊C4—191no—
206C2×C22⋊C4—191no—
207C2×C22⋊C4—192no—
208C2×C22⋊C4—192no—
209C2×C22⋊C4C2×D1911yescharacteristic
210C2×C22⋊C4C2×D1912yescomplemented
211C2×C42—192no—
212C2×C42—191no—
213#95—192no—
214#95—192no—
215#95C2×D1912yescomplemented
216C19C4×#12011yescharacteristic, complemented, Sylow
217C24—192no—
218C24—194no—
219C24—384no—
220C24—384no—
221C24—382no—
222C24—382no—
223C24C22×D1911yescharacteristic
224C24C22×D1911yescharacteristic
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—198no—
228C2×D4—384no—
229C2×D4—384no—
230C2×D4C4×D1914yescomplemented
231C22×C4—22no—
232C22×C4—24no—
233C22×C4—191no—
234C22×C4—194no—
235C22×C4—192no—
236C22×C4—191no—
237C22×C4—198no—
238C22×C4—191no—
239C22×C4—191no—
240C22×C4—384no—
241C22×C4—384no—
242C22×C4—384no—
243C22×C4—384no—
244C22×C4—3832no—
245C22×C4—384no—
246C22×C4—384no—
247C22×C4—382no—
248C22×C4—384no—
249C22×C4C22×D1912yes—
250C22×C4C22×D1911yescharacteristic
251C22×C4C22×D1912yes—
252C4⋊C4—382no—
253C4⋊C4—384no—
254C22⋊C4—22no—
255C22⋊C4—24no—
256C22⋊C4—194no—
257C22⋊C4—198no—
258C22⋊C4—384no—
259C22⋊C4—384no—
260C22⋊C4—382no—
261C22⋊C4—382no—
262C42—382no—
263C42—384no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—21no—
268C23—21no—
269C23—22no—
270C23—194no—
271C23—194no—
272C23—194no—
273C23—3816no—
274C23—388no—
275C23—388no—
276C23—3816no—
277C23—382no—
278C23—382no—
279C23—382no—
280C23—382no—
281C23—388no—
282C23C2×C4×D1912yes—
283C23C2×C4×D1912yescomplemented
284C23D4×D1912yes—
285C23#6454312yes—
286C23C23×D1911yescharacteristic
287D4—28no—
288D4—3816no—
289C2×C4—28no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—192no—
298C2×C4—194no—
299C2×C4—194no—
300C2×C4—192no—
301C2×C4—3816no—
302C2×C4—3816no—
303C2×C4—388no—
304C2×C4—382no—
305C2×C4—382no—
306C2×C4—382no—
307C2×C4—381no—
308C2×C4—381no—
309C2×C4—382no—
310C2×C4—382no—
311C2×C4—764no—
312C2×C4C2×C4×D1912yescomplemented
313C2×C4D4×D1914yes—
314C22—22no—
315C22—24no—
316C22—24no—
317C22—22no—
318C22—24no—
319C22—22no—
320C22—41no—
321C22—42no—
322C22—41no—
323C22—198no—
324C22—3832no—
325C22—384no—
326C22—384no—
327C22—384no—
328C22—384no—
329C22—384no—
330C22—384no—
331C22(C22⋊D19)⋊C414yescomplemented
332C22C22×C4×D1911yescharacteristic
333C22C2×D4×D1911yescharacteristic
334C22C2×D4×D1912yes—
335C22C2×#6454311yescharacteristic
336C22#41×D1912yes—
337C4—22no—
338C4—24no—
339C4—42no—
340C4—194no—
341C4—384no—
342C4—382no—
343C4—761no—
344C4—761no—
345C2—24no—
346C2—42no—
347C2—388no—
348C2C4×D4×D1912yes—
349C2C2×(C22⋊D19)⋊C411yescharacteristic
350C2#120×D1911yescharacteristic
351C2#1192705211yescharacteristic
352C2#1192705412yes—
subgroupG/H
center, FrattiniC23C23×D19
commutatorC22×C19C23×C4
FittingC19×#386C2
socle, cosocleC23×C19C24
prime radicalC2×#10597383C2
hypercenter#386D19
hypocenterC19C4×#120
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C23×C4×D19C2semidirect
3. C2×D4×Dic19C2semidirect
4. C2×(C22⋊D19)⋊C4C2semidirect
5. #11926420C2semidirect
6. #11926418C2semidirect
7. #11926417C2semidirect
8. #11926399C2semidirect
9. C22⋊C4×Dic19C2semidirect
10. #11926391C2semidirect
11. C19×#386C2semidirect
17. C23×Dic19C22semidirect
23. C2×C22⋊C4×C19C22semidirect
26. C2×C22⋊Dic19C22semidirect
27. #10597383C4semidirect
32. C2×C4⋊Dic19C22semidirect
33. C2×Dic19⋊C4C22semidirect
34. C2×C4×Dic19C22semidirect
35. C2×C4×Dic19C22semidirect
37. C19×#95C22semidirect
38. C19⋊#95C22semidirect
39. C19⋊#95C22semidirect
46. C23×D19C2×C4semidirect
50. C2×D4×C19C2×C4semidirect
58. C2×C22⋊D19C2×C4semidirect
62. C22×Dic19D4semidirect
74. C2×C4×D19D4semidirect
79. C22⋊Dic19C2×C4semidirect
82. (C2×D19)⋊C4C2×C4semidirect
94. C23×C19C22×C4semidirect
119. C2×C4×C19C22×C4semidirect
131. C2×Dic19C22×C4semidirect
147. C22×C19C4×D4semidirect
160. C2×D19C4×D4semidirect
168. Dic19#120semidirect
174. #386D19semidirect
210. C2×C22⋊C4C2×D19semidirect
215. #95C2×D19semidirect
216. C19C4×#120semidirect
230. C2×D4C4×D19semidirect
283. C23C2×C4×D19semidirect
312. C2×C4C2×C4×D19semidirect
331. C22(C22⋊D19)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D192
C2×#105973832
C2×D4×Dic192
C2×(C22⋊D19)⋊C42
#119264202
#119264182
#119264172
#119263992
C22⋊C4×Dic192
#119263912
C19×#3862
C4×#12019