Finite Group Databasebeta

← #14577026

Subgroups — #14577026

Order 2432.

1040 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927167C212yesmaximal, complemented
2#11927166C212yesmaximal, complemented
3#11927155C211yesmaximal, characteristic, complemented
4#11927150C211yesmaximal, characteristic, complemented
5#11927149C211yesmaximal, characteristic, complemented
6#11927142C214yesmaximal, complemented
7#11927133C214yesmaximal, complemented
8#11927100C211yesmaximal, characteristic, complemented
9#11927095C211yesmaximal, characteristic, complemented
10#11927079C214yesmaximal, complemented
11#11927077C214yesmaximal, complemented
12#11927057C212yesmaximal, complemented
13C4×#64545C212yesmaximal, complemented
14#117×D19C211yesmaximal, characteristic, complemented
15C19×#541C211yesmaximal, characteristic, complemented
16C2×#64545C2212yes—
17C22×C4×D19C2211yescharacteristic
18C19×C4⋊Q8C2211yescharacteristic, complemented
19C19×#126C2214yes—
20C19×#125C2214yescomplemented
21C19×#125C2211yescharacteristic, complemented
22C19×C22⋊Q8C2212yes—
23C4×Q8×C19C2212yescomplemented
24C19×#117C2211yescharacteristic
25#10597393C2212yescomplemented
26#10597392C2212yes—
27Q8×Dic19C2212yescomplemented
28#10597376C2212yes—
29#10597372C2211yescharacteristic
30#10597344C2214yes—
31#10597344C2214yescomplemented
32#10597343C2214yescomplemented
33#10597342C2214yes—
34#10597342C2214yescomplemented
35#10597341C2212yes—
36#10597341C2214yes—
37#10597341C2214yes—
38#10597340C2214yes—
39#10597340C2214yes—
40#10597340C2214yescomplemented
41#10597340C2214yescomplemented
42#10597339C2214yes—
43#10597339C2214yes—
44#10597339C2214yescomplemented
45#10597339C2212yescomplemented
46#10597338C2212yes—
47#10597338C2212yes—
48#10597338C2214yescomplemented
49C4⋊C4×D19C2212yes—
50#10597335C2214yescomplemented
51#10597334C2212yescomplemented
52#10597333C2214yescomplemented
53#10597331C2214yes—
54#10597330C2214yes—
55#10597329C2214yes—
56#10597328C2214yes—
57(C22⋊D19)⋊C4C2214yes—
58C22⋊C4×D19C2212yes—
59#10597323C2212yes—
60#10597322C2214yescomplemented
61#10597321C2214yes—
62#10597320C2211yescharacteristic, complemented
63C4×D76C2214yes—
64C4×D76C2212yescomplemented
65#10597318C2211yescharacteristic
66#10597318C2211yescharacteristic
67C42×D19C2211yescharacteristic
68C42×D19C2211yescharacteristic
69C42×D19C2214yescomplemented
70#10597316C2211yescharacteristic, complemented
71C23×D19C2311yescharacteristic
72C2×Q8×C19C2312yes—
73C22×C4×C19C2311yescharacteristic
74C2×C22⋊D19C2314yes—
75C22×Dic19C2311yescharacteristic
76#64545—28no—
77C2×D76C2312yes—
78C2×D76C2314yes—
79C2×D76C2314yes—
80C2×D76C2314yes—
81C2×C4×D19—24no—
82C2×C4×D19C2311yescharacteristic
83C2×C4×D19C2311yescharacteristic
84C2×C4×D19C2311yescharacteristic
85C2×C4×D19C2314yes—
86C2×C4×D19C2312yes—
87C2×C4×D19C2312yes—
88C2×C4×D19C2314yes—
89C2×C4×D19C2314yes—
90C2×C4×D19C2311yescharacteristic
91C2×Dic38C2314yes—
92C4⋊C4×C19C2312yes—
93C4⋊C4×C19C2312yes—
94C4⋊C4×C19C2314yes—
95C4⋊C4×C19C2314yes—
96C4⋊C4×C19C2314yes—
97C4⋊C4×C19C2314yes—
98C22⋊C4×C19C2312yes—
99C22⋊C4×C19C2314yes—
100C42×C19C2311yescharacteristic
101C42×C19C2311yescharacteristic
102C42×C19C2314yes—
103C22⋊Dic19C2312yes—
104(C2×D19)⋊C4C2314yes—
105(C2×D19)⋊C4C2314yes—
106(C2×D19)⋊C4C2314yes—
107(C2×D19)⋊C4C2314yes—
108(C2×D19)⋊C4C2312yes—
109(C2×D19)⋊C4C2312yes—
110(C2×D19)⋊C4C2314yes—
111(C2×D19)⋊C4C2314yes—
112(C2×D19)⋊C4C2314yes—
113(C2×D19)⋊C4C2314yes—
114C4⋊Dic19C2312yes—
115C4⋊Dic19C2314yes—
116C4⋊Dic19C2312yes—
117Dic19⋊C4C2314yes—
118Dic19⋊C4C2314yes—
119Dic19⋊C4C2312yes—
120Dic19⋊C4C2312yes—
121Dic19⋊C4C2314yes—
122C4×Dic19C2311yescharacteristic
123C4×Dic19C2314yes—
124C4×Dic19C2311yescharacteristic
125C4×Dic19C2312yes—
126C4×Dic19C2312yes—
127C4×Dic19C2314yes—
128C23×C19C2411yescharacteristic
129C22×D19—22no—
130C22×D19—42no—
131C22×D19C2411yescharacteristic
132C22×D19C2414yes—
133C22×D19C2411yescharacteristic
134Q8×C19—24no—
135C2×C4×C19—22no—
136C2×C4×C19C2412yes—
137C2×C4×C19C2414yes—
138C2×C4×C19C2412yes—
139C2×C4×C19C2414yes—
140C2×C4×C19C2411yescharacteristic
141C2×C4×C19C2411yescharacteristic
142C22⋊D19—44no—
143C2×Dic19—22no—
144C2×Dic19C2412yes—
145C2×Dic19C2414yes—
146C2×Dic19C2412yes—
147C2×Dic19C2411yescharacteristic
148C2×Dic19C2411yescharacteristic
149D76—28no—
150D76—24no—
151D76—44no—
152D76—44no—
153C4×D19—22no—
154C4×D19—22no—
155C4×D19—22no—
156C4×D19—28no—
157C4×D19—42no—
158C4×D19—44no—
159C4×D19—44no—
160C4×D19—42no—
161C4×D19#4114yes—
162Dic38—44no—
163#3455—191nomaximal, Sylow
164C22×C19—21no—
165C22×C19—22no—
166C22×C19C2511yescharacteristic
167C2×D19—22no—
168C2×D19—21no—
169C2×D19—24no—
170C2×D19—24no—
171C2×D19—24no—
172C2×D19—22no—
173C2×D19—44no—
174C2×D19C2×#4112yes—
175C4×C19—21no—
176C4×C19—24no—
177C4×C19—24no—
178C4×C19—22no—
179C4×C19—22no—
180C4×C19C2×#4112yes—
181Dic19—21no—
182Dic19—22no—
183Dic19—24no—
184Dic19—22no—
185Dic19C2×#4112yes—
186#542—192no—
187#542—192no—
188#541—191no—
189#541D1911yescharacteristic, complemented
190#540—191no—
191#540—191no—
192#539—194no—
193#538—194no—
194#533—191no—
195#532—191no—
196#529—194no—
197#529—194no—
198#525—192no—
199C4×#41—192no—
200C2×#117—191no—
201C2×C19—41no—
202C2×C19C22×#4111yescharacteristic
203C2×C19#58512yes—
204D19—22no—
205D19—44no—
206D19—41no—
207C2×#41—192no—
208C23×C4—191no—
209C4⋊Q8—192no—
210C4⋊Q8C2×D1911yescharacteristic, complemented
211#127—191no—
212#126—194no—
213#126—194no—
214#126—194no—
215#126C2×D1914yes—
216#125—194no—
217#125—191no—
218#125C2×D1914yescomplemented
219#125C2×D1911yescharacteristic, complemented
220#124—192no—
221#124—194no—
222#124—194no—
223#123—194no—
224#123—194no—
225#123—194no—
226#123—194no—
227#123—194no—
228C22⋊Q8—192no—
229C22⋊Q8—194no—
230C22⋊Q8—194no—
231C22⋊Q8—194no—
232C22⋊Q8C2×D1912yes—
233#121—192no—
234#121—192no—
235#121—194no—
236#121—194no—
237#121—194no—
238#120—194no—
239C4×Q8—192no—
240C4×Q8—194no—
241C4×Q8C2×D1912yescomplemented
242C4×D4—194no—
243C4×D4—192no—
244C4×D4—194no—
245C4×D4—194no—
246C4×D4—194no—
247C4×D4—194no—
248C4×D4—192no—
249#117—191no—
250#117—192no—
251#117—192no—
252#117—194no—
253#117—192no—
254#117—191no—
255#117—191no—
256#117C2×D1911yescharacteristic
257C2×C4⋊C4—192no—
258C2×C22⋊C4—192no—
259C2×C42—191no—
260C2×C42—191no—
261C2×C42—194no—
262C19#345511yescharacteristic, complemented, Sylow
263C24—191no—
264#41—388no—
265C2×Q8—194no—
266C2×Q8C22×D1912yes—
267C2×D4—194no—
268C2×D4—194no—
269C2×D4—192no—
270C2×D4—194no—
271C2×D4—194no—
272C22×C4—191no—
273C22×C4—191no—
274C22×C4—194no—
275C22×C4—191no—
276C22×C4—191no—
277C22×C4—191no—
278C22×C4—192no—
279C22×C4—192no—
280C22×C4—194no—
281C22×C4—194no—
282C22×C4—384no—
283C22×C4C22×D1911yescharacteristic
284C4⋊C4—192no—
285C4⋊C4—192no—
286C4⋊C4—194no—
287C4⋊C4—194no—
288C4⋊C4—194no—
289C4⋊C4—192no—
290C4⋊C4—192no—
291C4⋊C4—194no—
292C4⋊C4C22×D1912yes—
293C4⋊C4C22×D1912yes—
294C4⋊C4C22×D1914yes—
295C4⋊C4C22×D1914yes—
296C4⋊C4C22×D1914yes—
297C4⋊C4C22×D1914yes—
298C22⋊C4—192no—
299C22⋊C4—192no—
300C22⋊C4—192no—
301C22⋊C4—194no—
302C22⋊C4—194no—
303C22⋊C4—194no—
304C22⋊C4—194no—
305C22⋊C4—194no—
306C22⋊C4—194no—
307C22⋊C4—194no—
308C22⋊C4—194no—
309C22⋊C4C22×D1912yes—
310C22⋊C4C22×D1914yes—
311C42—192no—
312C42—192no—
313C42—194no—
314C42—191no—
315C42—191no—
316C42—194no—
317C42C22×D1911yescharacteristic
318C42C22×D1911yescharacteristic
319C42C22×D1914yes—
320C23—191no—
321C23—191no—
322C23—194no—
323C23—382no—
324C23—762no—
325C23C23×D1911yescharacteristic
326Q8—24no—
327Q8—764no—
328D4—388no—
329D4—384no—
330D4—764no—
331D4—764no—
332D4—764no—
333C2×C4—22no—
334C2×C4—191no—
335C2×C4—194no—
336C2×C4—192no—
337C2×C4—192no—
338C2×C4—194no—
339C2×C4—191no—
340C2×C4—382no—
341C2×C4—388no—
342C2×C4—382no—
343C2×C4—382no—
344C2×C4—382no—
345C2×C4—762no—
346C2×C4—764no—
347C2×C4—762no—
348C2×C4—764no—
349C2×C4C23×D1912yes—
350C2×C4C23×D1914yes—
351C2×C4C23×D1914yes—
352C2×C4C23×D1912yes—
353C2×C4C23×D1911yescharacteristic
354C2×C4C23×D1911yescharacteristic
355C22—21no—
356C22—22no—
357C22—192no—
358C22—382no—
359C22—381no—
360C22—384no—
361C22—384no—
362C22—384no—
363C22—382no—
364C22—764no—
365C22C24×D1911yescharacteristic
366C4—21no—
367C4—24no—
368C4—22no—
369C4—22no—
370C4—24no—
371C4—192no—
372C4—381no—
373C4—382no—
374C4—384no—
375C4—382no—
376C4#41×D1912yes—
377C2—41no—
378C2—382no—
379C2—761no—
380C2—764no—
381C2C2×#41×D1911yescharacteristic
382C2#1192738112yes—
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#541C2
hypercenter#541D19
hypocenterC19#3455
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #541

Complements

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

NH ≅ G/Ntype
1. #11927167C2semidirect
2. #11927166C2semidirect
3. #11927155C2semidirect
4. #11927150C2semidirect
5. #11927149C2semidirect
6. #11927142C2semidirect
7. #11927133C2semidirect
8. #11927100C2semidirect
9. #11927095C2semidirect
10. #11927079C2semidirect
11. #11927077C2semidirect
12. #11927057C2semidirect
13. C4×#64545C2semidirect
14. #117×D19C2semidirect
15. C19×#541C2semidirect
18. C19×C4⋊Q8C22semidirect
20. C19×#125C22semidirect
21. C19×#125C22semidirect
23. C4×Q8×C19C22semidirect
25. #10597393C22semidirect
27. Q8×Dic19C22semidirect
31. #10597344C22semidirect
32. #10597343C22semidirect
34. #10597342C22semidirect
40. #10597340C22semidirect
41. #10597340C22semidirect
44. #10597339C22semidirect
45. #10597339C22semidirect
48. #10597338C22semidirect
50. #10597335C22semidirect
51. #10597334C22semidirect
52. #10597333C22semidirect
60. #10597322C22semidirect
62. #10597320C22semidirect
64. C4×D76C22semidirect
69. C42×D19C22semidirect
70. #10597316C22semidirect
189. #541D19semidirect
210. C4⋊Q8C2×D19semidirect
218. #125C2×D19semidirect
219. #125C2×D19semidirect
241. C4×Q8C2×D19semidirect
262. C19#3455semidirect

Maximal subgroups

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

subgroupindex
#119271672
#119271662
#119271552
#119271502
#119271492
#119271422
#119271332
#119271002
#119270952
#119270792
#119270772
#119270572
C4×#645452
#117×D192
C19×#5412
#345519