Finite Group Databasebeta

← #14571916

Subgroups — #14571916

Order 2432.

1224 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D19C211yesmaximal, characteristic, complemented
2C2×#10597330C212yesmaximal, complemented
3C2×#10597385C211yesmaximal, characteristic, complemented
4C2×#10597328C211yesmaximal, characteristic, complemented
5C2×#10597383C211yesmaximal, characteristic, complemented
6#11926423C211yesmaximal, characteristic, complemented
7#11926422C212yesmaximal, complemented
8#11926420C212yesmaximal, complemented
9#11926403C212yesmaximal, complemented
10#11926402C211yesmaximal, characteristic, complemented
11C19×#386C211yesmaximal, characteristic, complemented
12C24×D19C2211yescharacteristic
13C22×D4×C19C2211yescharacteristic
14C23×C4×C19C2211yescharacteristic
15C22×C22⋊D19C2212yes—
16C22×C22⋊D19C2211yescharacteristic
17C22×C22⋊D19C2211yescharacteristic, complemented
18C23×Dic19C2211yescharacteristic
19C22×D76C2212yes—
20C22×C4×D19—24no—
21C22×C4×D19—28no—
22C22×C4×D19C2212yes—
23C22×C4×D19C2212yes—
24C2×C22⋊C4×C19C2211yescharacteristic
25C2×C22⋊C4×C19C2212yescomplemented
26C2×C22⋊Dic19C2211yescharacteristic
27C2×C22⋊Dic19C2211yescharacteristic, complemented
28#10597385—24no—
29#10597383—24no—
30C2×(C2×D19)⋊C4C2212yes—
31C2×(C2×D19)⋊C4C2212yes—
32C2×(C2×D19)⋊C4C2211yescharacteristic, complemented
33C2×(C2×D19)⋊C4C2212yescomplemented
34C2×Dic19⋊C4C2212yescomplemented
35C2×Dic19⋊C4C2211yescharacteristic, complemented
36#10597330—28no—
37#10597328—24no—
38C19×#95C2212yescomplemented
39C19⋊#95C2212yescomplemented
40C19⋊#95C2212yescomplemented
41C24×C19C2311yescharacteristic
42C24×C19C2311yescharacteristic
43C23×D19—22no—
44C23×D19—22no—
45C23×D19—24no—
46C23×D19—24no—
47C23×D19D414yescomplemented
48C23×D19C2311yescharacteristic
49C23×D19C2312yes—
50C2×D4×C19—22no—
51C2×D4×C19—22no—
52C2×D4×C19—22no—
53C22×C4×C19—22no—
54C22×C4×C19—24no—
55C22×C4×C19C2312yes—
56C22×C4×C19C2311yescharacteristic
57C22×C4×C19C2312yes—
58C2×C22⋊D19—22no—
59C2×C22⋊D19—22no—
60C2×C22⋊D19—22no—
61C2×C22⋊D19—24no—
62C2×C22⋊D19—24no—
63C2×C22⋊D19—24no—
64C2×C22⋊D19—22no—
65C2×C22⋊D19—24no—
66C22×Dic19—24no—
67C22×Dic19D414yescomplemented
68C22×Dic19C2312yes—
69C22×Dic19C2311yescharacteristic
70C22×Dic19C2311yescharacteristic
71C22×Dic19C2311yescharacteristic
72C2×D76—24no—
73C2×D76—24no—
74C2×D76—24no—
75C2×C4×D19—232no—
76C2×C4×D19—24no—
77C2×C4×D19—24no—
78C2×C4×D19—24no—
79C2×C4×D19—24no—
80C2×C4×D19—24no—
81C2×C4×D19D418yescomplemented
82C22⋊C4×C19—22no—
83C22⋊C4×C19—24no—
84C22⋊Dic19—22no—
85C22⋊Dic19—22no—
86(C2×D19)⋊C4—24no—
87(C2×D19)⋊C4—24no—
88(C2×D19)⋊C4—24no—
89(C2×D19)⋊C4—22no—
90Dic19⋊C4—22no—
91Dic19⋊C4—24no—
92C23×C19—22no—
93C23×C19—22no—
94C23×C19—21no—
95C23×C19—22no—
96C23×C19—21no—
97C23×C19—22no—
98C23×C19—21no—
99C23×C19C2×D412yes—
100C23×C19C2×D412yes—
101C23×C19#4112yes—
102C23×C19C2411yescharacteristic
103C22×D19—28no—
104C22×D19—216no—
105C22×D19—28no—
106C22×D19—28no—
107C22×D19—22no—
108C22×D19—22no—
109C22×D19—22no—
110C22×D19—22no—
111C22×D19—216no—
112C22×D19—22no—
113C22×D19—21no—
114C22×D19—21no—
115C22×D19—22no—
116C22×D19—21no—
117C22×D19C2×D414yes—
118C22×D19C2×D414yes—
119C22×D19#4114yes—
120D4×C19—44no—
121C2×C4×C19—28no—
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19—21no—
125C2×C4×C19—22no—
126C2×C4×C19—21no—
127C2×C4×C19—22no—
128C2×C4×C19—22no—
129C2×C4×C19—21no—
130C2×C4×C19C2×D414yes—
131C22⋊D19—44no—
132C22⋊D19—48no—
133C22⋊D19—44no—
134C2×Dic19—22no—
135C2×Dic19—28no—
136C2×Dic19—22no—
137C2×Dic19—21no—
138C2×Dic19—21no—
139C2×Dic19—22no—
140C2×Dic19—21no—
141C2×Dic19—22no—
142C2×Dic19C2×D412yes—
143C2×Dic19C2×D412yes—
144C2×Dic19C2×D414yes—
145D76—48no—
146C4×D19—216no—
147C4×D19—216no—
148#2847—191nomaximal, Sylow
149C22×C19—22no—
150C22×C19—24no—
151C22×C19—22no—
152C22×C19—24no—
153C22×C19—41no—
154C22×C19—42no—
155C22×C19—41no—
156C22×C19—41no—
157C22×C19—42no—
158C22×C19#12114yescomplemented
159C22×C19C22×D412yes—
160C22×C19C22×D411yescharacteristic
161C22×C19C22×D411yescharacteristic
162C22×C19C2×#4111yescharacteristic
163C22×C19C2×#4112yes—
164C2×D19—232no—
165C2×D19—24no—
166C2×D19—24no—
167C2×D19—24no—
168C2×D19—24no—
169C2×D19—24no—
170C2×D19—24no—
171C2×D19—41no—
172C2×D19—42no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—42no—
176C2×D19#12118yescomplemented
177C4×C19—24no—
178C4×C19—42no—
179C4×C19—41no—
180Dic19—22no—
181Dic19—42no—
182Dic19—41no—
183Dic19#12014yescomplemented
184C24×C4—191no—
185C2×#121—191no—
186C2×#121—192no—
187C2×#120—191no—
188C2×#120—191no—
189#386—191no—
190#386—192no—
191#386—192no—
192#386D1911yescharacteristic, complemented
193#380—191no—
194#380—192no—
195C2×C19—24no—
196C2×C19—81no—
197C2×C19C2×#12011yescharacteristic
198C2×C19C2×#12112yes—
199C2×C19C2×#12111yescharacteristic
200C2×C19#52511yescharacteristic
201C2×C19#52512yes—
202D19—28no—
203D19—81no—
204C25—191no—
205C22×D4—192no—
206C22×D4—191no—
207C22×D4—191no—
208C22×D4—192no—
209C22×D4C2×D1911yescharacteristic
210C23×C4—191no—
211C23×C4—192no—
212C23×C4—192no—
213C23×C4—384no—
214C23×C4—388no—
215C23×C4C2×D1911yescharacteristic
216#121—388no—
217#121—384no—
218#120—384no—
219#120—384no—
220C2×C4⋊C4—192no—
221C2×C4⋊C4—191no—
222C2×C22⋊C4—191no—
223C2×C22⋊C4—191no—
224C2×C22⋊C4—192no—
225C2×C22⋊C4—192no—
226C2×C22⋊C4—191no—
227C2×C22⋊C4—192no—
228C2×C22⋊C4C2×D1911yescharacteristic
229C2×C22⋊C4C2×D1912yescomplemented
230#95—192no—
231#95—192no—
232#95C2×D1912yescomplemented
233C19#284711yescharacteristic, complemented, Sylow
234C24—192no—
235C24—194no—
236C24—191no—
237C24—384no—
238C24—384no—
239C24—382no—
240C24—382no—
241C24C22×D1911yescharacteristic
242C24C22×D1911yescharacteristic
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—384no—
247C2×D4—384no—
248C2×D4—384no—
249C2×D4—384no—
250C2×D4—382no—
251C2×D4—384no—
252C2×D4—384no—
253C2×D4—384no—
254C2×D4—382no—
255C2×D4—382no—
256C2×D4—382no—
257C22×C4—22no—
258C22×C4—24no—
259C22×C4—191no—
260C22×C4—194no—
261C22×C4—191no—
262C22×C4—198no—
263C22×C4—191no—
264C22×C4—192no—
265C22×C4—384no—
266C22×C4—384no—
267C22×C4—384no—
268C22×C4—384no—
269C22×C4—3832no—
270C22×C4—384no—
271C22×C4—384no—
272C22×C4C22×D1912yes—
273C22×C4C22×D1911yescharacteristic
274C22×C4C22×D1912yes—
275C4⋊C4—384no—
276C4⋊C4—382no—
277C22⋊C4—22no—
278C22⋊C4—24no—
279C22⋊C4—382no—
280C22⋊C4—384no—
281C22⋊C4—384no—
282C22⋊C4—382no—
283C22⋊C4—382no—
284C22⋊C4—384no—
285C23—22no—
286C23—22no—
287C23—21no—
288C23—22no—
289C23—21no—
290C23—21no—
291C23—22no—
292C23—194no—
293C23—194no—
294C23—194no—
295C23—3816no—
296C23—388no—
297C23—388no—
298C23—3816no—
299C23—382no—
300C23—382no—
301C23—382no—
302C23—382no—
303C23—388no—
304C23—381no—
305C23—381no—
306C23—382no—
307C23—381no—
308C23—382no—
309C23#6454112yes—
310C23D4×D1912yes—
311C23D4×D1912yes—
312C23C23×D1911yescharacteristic
313D4—44no—
314D4—768no—
315D4—764no—
316D4—768no—
317D4—764no—
318C2×C4—28no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—192no—
328C2×C4—194no—
329C2×C4—192no—
330C2×C4—3816no—
331C2×C4—3816no—
332C2×C4—388no—
333C2×C4—382no—
334C2×C4—381no—
335C2×C4—382no—
336C2×C4—381no—
337C2×C4—382no—
338C2×C4—381no—
339C2×C4—382no—
340C2×C4D4×D1914yes—
341C22—22no—
342C22—24no—
343C22—22no—
344C22—24no—
345C22—41no—
346C22—42no—
347C22—41no—
348C22—42no—
349C22—41no—
350C22—198no—
351C22—3832no—
352C22—384no—
353C22—384no—
354C22—384no—
355C22—384no—
356C22—384no—
357C22—384no—
358C22—761no—
359C22—762no—
360C22—761no—
361C22—762no—
362C22—761no—
363C22#1059733014yescomplemented
364C22C2×#6454111yescharacteristic
365C22C2×D4×D1911yescharacteristic
366C22C2×D4×D1912yes—
367C22C2×D4×D1911yescharacteristic
368C22#41×D1912yes—
369C4—24no—
370C4—42no—
371C4—41no—
372C4—194no—
373C4—382no—
374C4—762no—
375C4—761no—
376C2—24no—
377C2—81no—
378C2—388no—
379C2—1521no—
380C2#120×D1911yescharacteristic
381C2#121×D1912yes—
382C2C2×#1059733011yescharacteristic
383C2#1192705211yescharacteristic
384C2#1192705312yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#386C2
hypercenter#386D19
hypocenterC19#2847
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C23×C4×D19C2semidirect
2. C2×#10597330C2semidirect
3. C2×#10597385C2semidirect
4. C2×#10597328C2semidirect
5. C2×#10597383C2semidirect
6. #11926423C2semidirect
7. #11926422C2semidirect
8. #11926420C2semidirect
9. #11926403C2semidirect
10. #11926402C2semidirect
11. C19×#386C2semidirect
17. C22×C22⋊D19C22semidirect
25. C2×C22⋊C4×C19C22semidirect
27. C2×C22⋊Dic19C22semidirect
32. C2×(C2×D19)⋊C4C22semidirect
33. C2×(C2×D19)⋊C4C22semidirect
34. C2×Dic19⋊C4C22semidirect
35. C2×Dic19⋊C4C22semidirect
38. C19×#95C22semidirect
39. C19⋊#95C22semidirect
40. C19⋊#95C22semidirect
47. C23×D19D4semidirect
67. C22×Dic19D4semidirect
81. C2×C4×D19D4semidirect
158. C22×C19#121semidirect
176. C2×D19#121semidirect
183. Dic19#120semidirect
192. #386D19semidirect
229. C2×C22⋊C4C2×D19semidirect
232. #95C2×D19semidirect
233. C19#2847semidirect
363. C22#10597330semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D192
C2×#105973302
C2×#105973852
C2×#105973282
C2×#105973832
#119264232
#119264222
#119264202
#119264032
#119264022
C19×#3862
#284719