Finite Group Databasebeta

← #14577292

Subgroups — #14577292

Order 2432.

1536 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597433C211yesmaximal, characteristic, complemented
2C2×#41×D19C211yesmaximal, characteristic, complemented
3#11927216C211yesmaximal, characteristic, complemented
4#11927215C213yesmaximal, complemented
5#11927213C211yesmaximal, characteristic, complemented
6#11927212C213yesmaximal, complemented
7#11927205C211yesmaximal, characteristic, complemented
8#11927204C213yesmaximal, complemented
9#11927202C213yesmaximal, complemented
10#11927112C213yesmaximal, complemented
11#11927110C213yesmaximal, complemented
12#11927057C213yesmaximal, complemented
13#11927053C213yesmaximal, complemented
14#11927020C211yesmaximal, characteristic, complemented
15C19×#548C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C22×Q8×C19C2211yescharacteristic, complemented
18#41×D19—28no—
19#10597433—28no—
20C2×#64545C2213yes—
21C2×#64545C2211yescharacteristic
22C2×#64545C2211yescharacteristic, complemented
23C2×Q8×D19C2211yescharacteristic
24C2×Q8×D19C2213yescomplemented
25C2×#64543C2213yes—
26C2×D4×D19C2213yes—
27C2×#64541C2213yes—
28C2×#64541C2213yes—
29C2×#64541C2213yescomplemented
30C22×C4×D19C2213yes—
31C19×#124C2213yescomplemented
32C19×C22⋊Q8C2213yescomplemented
33C19×#121C2213yescomplemented
34C4×Q8×C19C2211yescharacteristic, complemented
35C4×D4×C19C2213yescomplemented
36#10597393C2213yescomplemented
37#10597392C2213yescomplemented
38Q8×Dic19C2211yescharacteristic, complemented
39#10597386C2216yescomplemented
40#10597386C2213yescomplemented
41#10597385C2213yescomplemented
42#10597384C2213yescomplemented
43#10597383C2213yes—
44#10597376C2213yescomplemented
45#10597376C2213yescomplemented
46C4×C22⋊D19C2213yescomplemented
47C4×C22⋊D19C2213yescomplemented
48#10597342C2213yescomplemented
49#10597341C2213yescomplemented
50#10597341C2213yescomplemented
51#10597340C2213yes—
52#10597339C2216yescomplemented
53#10597338C2213yes—
54#10597333C2213yescomplemented
55#10597331C2216yescomplemented
56#10597330C2213yescomplemented
57#10597330C2216yescomplemented
58#10597330C2216yescomplemented
59#10597329C2211yescharacteristic
60#10597328C2213yes—
61#10597328C2216yes—
62(C22⋊D19)⋊C4C2216yescomplemented
63#10597324C2213yescomplemented
64#10597320C2213yescomplemented
65C4×D76C2213yescomplemented
66#10597318C2213yes—
67C4×Dic38C2213yescomplemented
68C23×D19C2313yes—
69#41×C19—24no—
70C2×Q8×C19—24no—
71C2×Q8×C19C2313yes—
72C2×Q8×C19C2311yescharacteristic
73C2×D4×C19C2313yes—
74C2×D4×C19C2313yes—
75C22×C4×C19C2313yes—
76C22×C4×C19C2313yes—
77C2×C22⋊D19C2311yescharacteristic
78C2×C22⋊D19C2313yes—
79C2×C22⋊D19C2316yes—
80C2×C22⋊D19C2313yes—
81C2×C22⋊D19C2316yes—
82C2×C22⋊D19C2313yes—
83C22×Dic19C2313yes—
84#64545—24no—
85#64545—24no—
86#64545—212no—
87Q8×D19—212no—
88Q8×D19D418yescomplemented
89#64543—212no—
90D4×D19—212no—
91#64541—212no—
92#64541—212no—
93#64541—212no—
94C2×D76C2313yes—
95C2×D76C2313yes—
96C2×D76C2313yes—
97C2×D76C2316yes—
98C2×D76C2313yes—
99C2×C4×D19—212no—
100C2×C4×D19C2313yes—
101C2×C4×D19C2313yes—
102C2×C4×D19C2311yescharacteristic
103C2×C4×D19C2313yes—
104C2×C4×D19C2316yes—
105C2×C4×D19C2313yes—
106C2×Dic38C2313yes—
107C2×Dic38C2313yes—
108C4⋊C4×C19C2313yes—
109C4⋊C4×C19C2313yes—
110C22⋊C4×C19C2311yescharacteristic
111C22⋊C4×C19C2313yes—
112C22⋊C4×C19C2316yes—
113C42×C19C2313yes—
114C22⋊Dic19C2313yes—
115C22⋊Dic19C2311yescharacteristic
116(C2×D19)⋊C4C2313yes—
117(C2×D19)⋊C4C2316yes—
118(C2×D19)⋊C4C2313yes—
119(C2×D19)⋊C4C2313yes—
120(C2×D19)⋊C4C2313yes—
121(C2×D19)⋊C4C2313yes—
122(C2×D19)⋊C4C2311yescharacteristic
123C4⋊Dic19C2313yes—
124C4⋊Dic19C2311yescharacteristic
125Dic19⋊C4C2313yes—
126Dic19⋊C4C2313yes—
127Dic19⋊C4C2313yes—
128Dic19⋊C4C2311yescharacteristic
129C4×Dic19C2313yes—
130C4×Dic19C2316yes—
131C23×C19C2413yes—
132C23×C19C2411yescharacteristic
133C22×D19—26no—
134C22×D19—43no—
135C22×D19—43no—
136C22×D19C2413yes—
137C22×D19C2413yes—
138C22×D19C2411yescharacteristic
139Q8×C19—26no—
140Q8×C19C2×D414yes—
141D4×C19—26no—
142D4×C19—43no—
143C2×C4×C19—26no—
144C2×C4×C19—26no—
145C2×C4×C19C2413yes—
146C2×C4×C19C2411yescharacteristic
147C2×C4×C19C2413yes—
148C2×C4×C19C2411yescharacteristic
149C2×C4×C19C2413yes—
150C22⋊D19—22no—
151C22⋊D19—26no—
152C22⋊D19—212no—
153C22⋊D19—43no—
154C22⋊D19—46no—
155C22⋊D19—43no—
156C2×Dic19—26no—
157C2×Dic19C2411yescharacteristic
158C2×Dic19C2413yes—
159C2×Dic19C2411yescharacteristic
160C2×Dic19C2411yescharacteristic
161C2×Dic19C2413yes—
162D76—26no—
163D76—26no—
164D76—26no—
165D76—43no—
166D76—46no—
167C4×D19—22no—
168C4×D19—26no—
169C4×D19—26no—
170C4×D19—26no—
171C4×D19—212no—
172C4×D19C2×D4112yes—
173Dic38—26no—
174Dic38C2×D4112yes—
175#3487—191nomaximal, Sylow
176C22×C19—23no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—23no—
180C22×C19—23no—
181C22×C19—21no—
182C22×C19C2511yescharacteristic
183C2×D19—21no—
184C2×D19—21no—
185C2×D19—23no—
186C2×D19—23no—
187C2×D19—23no—
188C2×D19—23no—
189C2×D19—23no—
190C2×D19—23no—
191C2×D19—412no—
192C2×D19C22×D412yes—
193C4×C19—23no—
194C4×C19—21no—
195C4×C19—21no—
196C4×C19—23no—
197C4×C19C22×D416yes—
198Dic19—21no—
199Dic19—21no—
200Dic19—21no—
201Dic19—23no—
202Dic19C22×D416yes—
203C2×2−1+4—191no—
204C22×#41—191no—
205#550—191no—
206#550—193no—
207#550—191no—
208#550—193no—
209#548—191no—
210#548—193no—
211#548—193no—
212#548D1911yescharacteristic, complemented
213#535—193no—
214#535—193no—
215#525—193no—
216#525—193no—
217#519—191no—
218C2×C19—43no—
219C2×C19—41no—
220C2×C19C23×D411yescharacteristic
221C2×C19#58511yescharacteristic
222C2×C19#58511yescharacteristic
223D19—22no—
224D19—43no—
225D19—43no—
2262−1+4—388no—
227C2×#41—193no—
228C2×#41—191no—
229C2×#41—191no—
230C2×#41—193no—
231C2×#41—193no—
232C2×#41—193no—
233C2×#41—193no—
234C2×#41—388no—
235C2×#41C2×D1911yescharacteristic
236C22×Q8—191no—
237C22×Q8—193no—
238C22×Q8C2×D1911yescharacteristic, complemented
239C22×D4—193no—
240C23×C4—193no—
241#127—196no—
242#127—193no—
243#127—193no—
244#124—193no—
245#124—196no—
246#124C2×D1913yescomplemented
247#123—193no—
248#123—191no—
249C22⋊Q8—193no—
250C22⋊Q8—193no—
251C22⋊Q8—193no—
252C22⋊Q8C2×D1913yescomplemented
253#121—193no—
254#121—193no—
255#121—193no—
256#121—193no—
257#121—193no—
258#121—193no—
259#121—193no—
260#121—196no—
261#121—196no—
262#121C2×D1913yescomplemented
263#120—193no—
264#120—196no—
265#120—193no—
266C4×Q8—191no—
267C4×Q8—193no—
268C4×Q8—193no—
269C4×Q8C2×D1911yescharacteristic, complemented
270C4×D4—193no—
271C4×D4—193no—
272C4×D4—196no—
273C4×D4—196no—
274C4×D4—193no—
275C4×D4C2×D1913yescomplemented
276#117—193no—
277#117—193no—
278C19#348711yescharacteristic, complemented, Sylow
279C24—193no—
280#41—24no—
281#41—3812no—
282#41—3812no—
283#41—3812no—
284#41—3812no—
285#41—3812no—
286#41—384no—
287#41—384no—
288C2×Q8—24no—
289C2×Q8—198no—
290C2×Q8—193no—
291C2×Q8—193no—
292C2×Q8—3812no—
293C2×Q8C22×D1913yes—
294C2×Q8C22×D1911yescharacteristic
295C2×D4—191no—
296C2×D4—196no—
297C2×D4—193no—
298C2×D4—193no—
299C2×D4—196no—
300C2×D4—193no—
301C2×D4—193no—
302C2×D4—193no—
303C2×D4—193no—
304C2×D4—196no—
305C2×D4—193no—
306C2×D4—3812no—
307C2×D4C22×D1913yes—
308C2×D4C22×D1913yes—
309C22×C4—193no—
310C22×C4—193no—
311C22×C4—196no—
312C22×C4—193no—
313C22×C4—193no—
314C22×C4—193no—
315C22×C4—191no—
316C22×C4—3812no—
317C22×C4C22×D1913yes—
318C22×C4C22×D1913yes—
319C4⋊C4—193no—
320C4⋊C4—193no—
321C4⋊C4—191no—
322C4⋊C4—193no—
323C4⋊C4—193no—
324C4⋊C4—191no—
325C4⋊C4C22×D1913yes—
326C4⋊C4C22×D1913yes—
327C22⋊C4—191no—
328C22⋊C4—193no—
329C22⋊C4—193no—
330C22⋊C4—191no—
331C22⋊C4—193no—
332C22⋊C4—193no—
333C22⋊C4—196no—
334C22⋊C4—193no—
335C22⋊C4—193no—
336C22⋊C4C22×D1916yes—
337C22⋊C4C22×D1911yescharacteristic
338C22⋊C4C22×D1913yes—
339C42—196no—
340C42—193no—
341C42C22×D1913yes—
342C23—191no—
343C23—193no—
344C23—193no—
345C23—386no—
346C23—763no—
347C23—763no—
348C23C23×D1913yes—
349C23C23×D1911yescharacteristic
350Q8—26no—
351Q8—1912no—
352Q8—386no—
353Q8D4×D1914yes—
354D4—26no—
355D4—43no—
356D4—386no—
357D4—3812no—
358D4—386no—
359D4—382no—
360D4—386no—
361D4—386no—
362D4—766no—
363D4—763no—
364D4—763no—
365D4—763no—
366D4—766no—
367C2×C4—26no—
368C2×C4—26no—
369C2×C4—193no—
370C2×C4—1912no—
371C2×C4—191no—
372C2×C4—193no—
373C2×C4—191no—
374C2×C4—191no—
375C2×C4—386no—
376C2×C4—3812no—
377C2×C4—382no—
378C2×C4—386no—
379C2×C4—386no—
380C2×C4—386no—
381C2×C4C23×D1913yes—
382C2×C4C23×D1911yescharacteristic
383C2×C4C23×D1913yes—
384C2×C4C23×D1911yescharacteristic
385C2×C4C23×D1913yes—
386C22—21no—
387C22—23no—
388C22—21no—
389C22—23no—
390C22—21no—
391C22—23no—
392C22—192no—
393C22—381no—
394C22—381no—
395C22—383no—
396C22—383no—
397C22—383no—
398C22—383no—
399C22—383no—
400C22—383no—
401C22—7612no—
402C22C24×D1911yescharacteristic
403C4—21no—
404C4—23no—
405C4—23no—
406C4—21no—
407C4—196no—
408C4—381no—
409C4—381no—
410C4—381no—
411C4—383no—
412C4C2×D4×D1916yes—
413C2—43no—
414C2—41no—
415C2—382no—
416C2—763no—
417C2—763no—
418C2C22×D4×D1911yescharacteristic
419C2#1192738011yescharacteristic
420C2#1192738111yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#548C2
hypercenter#548D19
hypocenterC19#3487
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#10597433C2semidirect
2. C2×#41×D19C2semidirect
3. #11927216C2semidirect
4. #11927215C2semidirect
5. #11927213C2semidirect
6. #11927212C2semidirect
7. #11927205C2semidirect
8. #11927204C2semidirect
9. #11927202C2semidirect
10. #11927112C2semidirect
11. #11927110C2semidirect
12. #11927057C2semidirect
13. #11927053C2semidirect
14. #11927020C2semidirect
15. C19×#548C2semidirect
17. C22×Q8×C19C22semidirect
22. C2×#64545C22semidirect
24. C2×Q8×D19C22semidirect
29. C2×#64541C22semidirect
31. C19×#124C22semidirect
32. C19×C22⋊Q8C22semidirect
33. C19×#121C22semidirect
34. C4×Q8×C19C22semidirect
35. C4×D4×C19C22semidirect
36. #10597393C22semidirect
37. #10597392C22semidirect
38. Q8×Dic19C22semidirect
39. #10597386C22semidirect
40. #10597386C22semidirect
41. #10597385C22semidirect
42. #10597384C22semidirect
44. #10597376C22semidirect
45. #10597376C22semidirect
46. C4×C22⋊D19C22semidirect
47. C4×C22⋊D19C22semidirect
48. #10597342C22semidirect
49. #10597341C22semidirect
50. #10597341C22semidirect
52. #10597339C22semidirect
54. #10597333C22semidirect
55. #10597331C22semidirect
56. #10597330C22semidirect
57. #10597330C22semidirect
58. #10597330C22semidirect
62. (C22⋊D19)⋊C4C22semidirect
63. #10597324C22semidirect
64. #10597320C22semidirect
65. C4×D76C22semidirect
67. C4×Dic38C22semidirect
88. Q8×D19D4semidirect
212. #548D19semidirect
238. C22×Q8C2×D19semidirect
246. #124C2×D19semidirect
252. C22⋊Q8C2×D19semidirect
262. #121C2×D19semidirect
269. C4×Q8C2×D19semidirect
275. C4×D4C2×D19semidirect
278. C19#3487semidirect

Maximal subgroups

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

subgroupindex
C2×#105974332
C2×#41×D192
#119272162
#119272152
#119272132
#119272122
#119272052
#119272042
#119272022
#119271122
#119271102
#119270572
#119270532
#119270202
C19×#5482
#348719