Finite Group Databasebeta

← #14567281

Subgroups — #14567281

Order 2432.

1088 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 161 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
1C22×D4×D19C211yesmaximal, characteristic
2C2×#10597331C212yesmaximal, complemented
3C2×#10597342C211yesmaximal, characteristic, complemented
4#11926462C211yesmaximal, characteristic, complemented
5#11926461C211yesmaximal, characteristic, complemented
6#11926458C211yesmaximal, characteristic, complemented
7#11926444C212yesmaximal, complemented
8#11926399C212yesmaximal, complemented
9#11926399C212yesmaximal, complemented
10#11926391C211yesmaximal, characteristic, complemented
11C19×#394C211yesmaximal, characteristic, complemented
12C24×D19C2212yes—
13C22×D4×C19C2211yescharacteristic
14C22×C22⋊D19C2212yes—
15C2×D4×D19—28no—
16C2×D4×D19—24no—
17C22×D76C2211yescharacteristic
18C22×C4×D19C2211yescharacteristic
19C22×Dic38C2211yescharacteristic, complemented
20C2×C4⋊C4×C19C2211yescharacteristic, complemented
21C2×C22⋊C4×C19C2212yescomplemented
22C2×C22⋊C4×C19C2212yescomplemented
23C2×C22⋊Dic19C2212yescomplemented
24C2×C22⋊Dic19C2212yescomplemented
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×(C2×D19)⋊C4C2211yescharacteristic
27C2×(C2×D19)⋊C4C2212yes—
28C2×(C2×D19)⋊C4C2212yescomplemented
29C2×(C2×D19)⋊C4C2212yescomplemented
30C2×(C2×D19)⋊C4C2212yescomplemented
31C2×(C2×D19)⋊C4C2212yescomplemented
32C2×Dic19⋊C4C2211yescharacteristic, complemented
33C2×Dic19⋊C4C2211yescharacteristic, complemented
34C2×C4×Dic19C2212yescomplemented
35#10597342—24no—
36#10597331—28no—
37C19×#95C2211yescharacteristic, complemented
38C19⋊#95C2211yescharacteristic, complemented
39C24×C19C2312yes—
40C23×D19—24no—
41C23×D19—24no—
42C23×D19—24no—
43C23×D19—24no—
44C23×D19—24no—
45C23×D19—42no—
46C23×D19—42no—
47C23×D19C2312yes—
48C23×D19C2311yescharacteristic
49C2×D4×C19—24no—
50C2×D4×C19—22no—
51C22×C4×C19C2311yescharacteristic
52C22×C4×C19C2311yescharacteristic
53C22×C4×C19C2312yes—
54C22×C4×C19C2311yescharacteristic
55C2×C22⋊D19—24no—
56C2×C22⋊D19—24no—
57C2×C22⋊D19D418yes—
58C22×Dic19C2311yescharacteristic
59C22×Dic19C2312yes—
60C22×Dic19C2311yescharacteristic
61C22×Dic19C2311yescharacteristic
62D4×D19—232no—
63C2×D76—24no—
64C2×D76—22no—
65C2×C4×D19—24no—
66C2×C4×D19D414yes—
67C2×Dic38—24no—
68C2×Dic38—22no—
69C4⋊C4×C19—22no—
70C22⋊C4×C19—24no—
71C22⋊C4×C19—42no—
72C22⋊Dic19—24no—
73C22⋊Dic19—42no—
74(C2×D19)⋊C4—24no—
75(C2×D19)⋊C4—24no—
76(C2×D19)⋊C4—22no—
77(C2×D19)⋊C4—22no—
78(C2×D19)⋊C4—24no—
79(C2×D19)⋊C4—42no—
80(C2×D19)⋊C4—42no—
81Dic19⋊C4—22no—
82Dic19⋊C4—22no—
83C4×Dic19—24no—
84C23×C19—22no—
85C23×C19—22no—
86C23×C19—22no—
87C23×C19—22no—
88C23×C19—22no—
89C23×C19—22no—
90C23×C19C2×D414yes—
91C23×C19C2411yescharacteristic
92C22×D19—22no—
93C22×D19—21no—
94C22×D19—21no—
95C22×D19—216no—
96C22×D19—22no—
97C22×D19—22no—
98C22×D19—22no—
99C22×D19—22no—
100C22×D19—22no—
101C22×D19—22no—
102C22×D19—48no—
103C22×D19—48no—
104C22×D19—48no—
105C22×D19—48no—
106C22×D19—48no—
107C22×D19—48no—
108C22×D19C2×D414yes—
109C22×D19C2×D412yes—
110C22×D19#4114yes—
111D4×C19—28no—
112C2×C4×C19—22no—
113C2×C4×C19—22no—
114C2×C4×C19—21no—
115C2×C4×C19—22no—
116C2×C4×C19—21no—
117C2×C4×C19—22no—
118C2×C4×C19—21no—
119C2×C4×C19—22no—
120C2×C4×C19—21no—
121C2×C4×C19C2×D412yes—
122C22⋊D19—216no—
123C2×Dic19—22no—
124C2×Dic19—21no—
125C2×Dic19—21no—
126C2×Dic19—22no—
127C2×Dic19—22no—
128C2×Dic19—21no—
129C2×Dic19—22no—
130C2×Dic19—21no—
131C2×Dic19C2×D414yes—
132C2×Dic19C2×D412yes—
133D76—28no—
134C4×D19—28no—
135Dic38—44no—
136#2435—191nomaximal, Sylow
137C22×C19—24no—
138C22×C19—24no—
139C22×C19—24no—
140C22×C19—42no—
141C22×C19—42no—
142C22×C19—42no—
143C22×C19—42no—
144C22×C19C22×D411yescharacteristic
145C22×C19C22×D412yes—
146C22×C19C2×#4112yes—
147C22×C19H(5,𝔽2)11yescharacteristic
148C22×C19H(5,𝔽2)11yescharacteristic
149C2×D19—22no—
150C2×D19—22no—
151C2×D19—24no—
152C2×D19—24no—
153C2×D19—24no—
154C2×D19—24no—
155C2×D19—24no—
156C2×D19—432no—
157C2×D19—42no—
158C2×D19—42no—
159C2×D19—42no—
160C2×D19—42no—
161C2×D19#12414yescomplemented
162C4×C19—22no—
163C4×C19—41no—
164C4×C19—41no—
165C4×C19—42no—
166Dic19—41no—
167Dic19—41no—
168Dic19—42no—
169Dic19#12014yes—
170C23×D4—191no—
171C2×#124—192no—
172C2×C22⋊Q8—191no—
173#394—191no—
174#394—191no—
175#394—191no—
176#394D1911yescharacteristic, complemented
177#390—192no—
178#379—192no—
179#379—192no—
180C4×C22⋊C4—191no—
181C2×C19—44no—
182C2×C19C2×#12011yescharacteristic
183C2×C19C2×#12411yescharacteristic
184C2×C19#53511yescharacteristic
185C2×C19#54612yes—
186C2×C19#54612yes—
187D19—24no—
188D19—44no—
189C25—192no—
190C22×Q8—191no—
191C22×D4—192no—
192C22×D4—191no—
193C22×D4—384no—
194C22×D4—388no—
195C22×D4C2×D1911yescharacteristic
196C23×C4—191no—
197#124—388no—
198C22⋊Q8—384no—
199C2×C4⋊C4—191no—
200C2×C4⋊C4—191no—
201C2×C4⋊C4C2×D1911yescharacteristic, complemented
202C2×C22⋊C4—192no—
203C2×C22⋊C4—191no—
204C2×C22⋊C4—191no—
205C2×C22⋊C4—192no—
206C2×C22⋊C4—192no—
207C2×C22⋊C4—192no—
208C2×C22⋊C4—192no—
209C2×C22⋊C4—192no—
210C2×C22⋊C4—192no—
211C2×C22⋊C4C2×D1912yescomplemented
212C2×C22⋊C4C2×D1912yescomplemented
213C2×C42—192no—
214#95—191no—
215#95C2×D1911yescharacteristic, complemented
216C19#243511yescharacteristic, complemented, Sylow
217C24—191no—
218C24—192no—
219C24—384no—
220C24—384no—
221C24—384no—
222C24—384no—
223C24—384no—
224C24—762no—
225C24—762no—
226C24C22×D1912yes—
227C2×Q8—382no—
228C2×Q8—384no—
229C2×D4—24no—
230C2×D4—22no—
231C2×D4—198no—
232C2×D4—384no—
233C2×D4—384no—
234C2×D4—384no—
235C2×D4—3832no—
236C2×D4—382no—
237C22×C4—191no—
238C22×C4—194no—
239C22×C4—192no—
240C22×C4—191no—
241C22×C4—191no—
242C22×C4—384no—
243C22×C4C22×D1912yes—
244C22×C4C22×D1911yescharacteristic
245C22×C4C22×D1911yescharacteristic
246C22×C4C22×D1911yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—382no—
249C4⋊C4—382no—
250C22⋊C4—24no—
251C22⋊C4—42no—
252C22⋊C4—384no—
253C22⋊C4—382no—
254C22⋊C4—382no—
255C22⋊C4—384no—
256C22⋊C4—384no—
257C22⋊C4—384no—
258C22⋊C4—762no—
259C22⋊C4—762no—
260C22⋊C4—762no—
261C42—384no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—192no—
269C23—194no—
270C23—194no—
271C23—3816no—
272C23—382no—
273C23—381no—
274C23—381no—
275C23—382no—
276C23—382no—
277C23—382no—
278C23—382no—
279C23—382no—
280C23—382no—
281C23—768no—
282C23—768no—
283C23—768no—
284C23—768no—
285C23—768no—
286C23—768no—
287C23D4×D1914yes—
288C23C23×D1911yescharacteristic
289Q8—764no—
290D4—28no—
291D4—388no—
292D4—3816no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—194no—
303C2×C4—192no—
304C2×C4—388no—
305C2×C4—382no—
306C2×C4—382no—
307C2×C4—381no—
308C2×C4—381no—
309C2×C4—381no—
310C2×C4—382no—
311C2×C4—381no—
312C2×C4—382no—
313C2×C4D4×D1912yes—
314C22—24no—
315C22—24no—
316C22—24no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—194no—
322C22—382no—
323C22—384no—
324C22—384no—
325C22—382no—
326C22—384no—
327C22—384no—
328C22—384no—
329C22—7632no—
330C22—762no—
331C22—762no—
332C22—762no—
333C22—762no—
334C22C2×D4×D1911yescharacteristic
335C22C2×D4×D1912yes—
336C22#1059743011yescharacteristic
337C22#41×D1912yes—
338C22#1059743511yescharacteristic
339C4—22no—
340C4—41no—
341C4—42no—
342C4—41no—
343C4—194no—
344C4—761no—
345C4—762no—
346C4—761no—
347C2—44no—
348C2—384no—
349C2—764no—
350C2#120×D1911yescharacteristic
351C2#124×D1911yescharacteristic
352C2#1192711011yescharacteristic
353C2#1192718312yes—
354C2#1192718612yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
prime radicalC22×D4×D19C2
hypercenter#394D19
hypocenterC19#2435
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#10597331C2semidirect
3. C2×#10597342C2semidirect
4. #11926462C2semidirect
5. #11926461C2semidirect
6. #11926458C2semidirect
7. #11926444C2semidirect
8. #11926399C2semidirect
9. #11926399C2semidirect
10. #11926391C2semidirect
11. C19×#394C2semidirect
19. C22×Dic38C22semidirect
20. C2×C4⋊C4×C19C22semidirect
21. C2×C22⋊C4×C19C22semidirect
22. C2×C22⋊C4×C19C22semidirect
23. C2×C22⋊Dic19C22semidirect
24. C2×C22⋊Dic19C22semidirect
28. C2×(C2×D19)⋊C4C22semidirect
29. C2×(C2×D19)⋊C4C22semidirect
30. C2×(C2×D19)⋊C4C22semidirect
31. C2×(C2×D19)⋊C4C22semidirect
32. C2×Dic19⋊C4C22semidirect
33. C2×Dic19⋊C4C22semidirect
34. C2×C4×Dic19C22semidirect
37. C19×#95C22semidirect
38. C19⋊#95C22semidirect
161. C2×D19#124semidirect
176. #394D19semidirect
201. C2×C4⋊C4C2×D19semidirect
211. C2×C22⋊C4C2×D19semidirect
212. C2×C22⋊C4C2×D19semidirect
215. #95C2×D19semidirect
216. C19#2435semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D192
C2×#105973312
C2×#105973422
#119264622
#119264612
#119264582
#119264442
#119263992
#119263912
C19×#3942
#243519