Finite Group Databasebeta

← #21455082

Subgroups — #21455082

Order 7808.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519822C211yesmaximal, characteristic, complemented
2C2×#14519801C211yesmaximal, characteristic, complemented
3C2×D8×D61C211yesmaximal, characteristic, complemented
4#16840328C211yesmaximal, characteristic, complemented
5#16839909C211yesmaximal, characteristic, complemented
6#16839908C211yesmaximal, characteristic, complemented
7#16839905C211yesmaximal, characteristic, complemented
8#16839904C211yesmaximal, characteristic, complemented
9#16839897C211yesmaximal, characteristic, complemented
10#16839896C211yesmaximal, characteristic, complemented
11#16839894C211yesmaximal, characteristic, complemented
12#16839765C211yesmaximal, characteristic, complemented
13#16839755C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#447C211yesmaximal, characteristic, complemented
16#14519822—24no—
17#14519822—24no—
18C2×#11758222C2211yescharacteristic
19C2×#11758222C2211yescharacteristic, complemented
20C2×#11758224—21no—
21C2×#11758224C2211yescharacteristic
22C2×#11758224C2211yescharacteristic, complemented
23C22×C22⋊D61—21no—
24C22×C22⋊D61—21no—
25C2×D4×D61—21no—
26C2×D4×D61C2211yescharacteristic
27C2×D4×D61C2211yescharacteristic, complemented
28C2×D4×D61C2211yescharacteristic, complemented
29#14519801—24no—
30C2×#11758190C2211yescharacteristic, complemented
31C2×#11758200C2211yescharacteristic, complemented
32C2×D488C2211yescharacteristic, complemented
33C2×#11758199C2211yescharacteristic, complemented
34C2×#11758199C2211yescharacteristic, complemented
35C2×#11758199C2211yescharacteristic, complemented
36D8×D61—24no—
37C2×#11758189C2211yescharacteristic, complemented
38C2×C8×D61C2211yescharacteristic, complemented
39#14519773—21no—
40#14519763—21no—
41#14519752C2211yescharacteristic, complemented
42#14519751C2211yescharacteristic, complemented
43#14519748C2211yescharacteristic, complemented
44#14519747—21no—
45#14519745—21no—
46#14519735C2211yescharacteristic, complemented
47#14519702C2211yescharacteristic, complemented
48#14519700C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic, complemented
50#14519698C2211yescharacteristic, complemented
51#14519698C2211yescharacteristic, complemented
52#14519697C2211yescharacteristic, complemented
53C22⋊#92418C2211yescharacteristic, complemented
54#14519689C2211yescharacteristic, complemented
55#14519689C2211yescharacteristic, complemented
56C22×D4×C61C2211yescharacteristic, complemented
57C2×D8×C61C2211yescharacteristic, complemented
58C2×D8×C61C2211yescharacteristic, complemented
59#121×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61#102×C61C2211yescharacteristic, complemented
62C22⋊C8×C61C2211yescharacteristic, complemented
63C24×C61—21no—
64C23×D61—21no—
65C23×D61—21no—
66C23×D61—21no—
67C2×D4×C61—22no—
68C2×D4×C61—22no—
69C2×D4×C61—21no—
70C2×D4×C61—21no—
71C2×D4×C61C2311yescharacteristic
72C2×D4×C61C2311yescharacteristic
73C2×D4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C2×C22⋊D61—28no—
76C2×C22⋊D61—28no—
77C2×C22⋊D61—21no—
78C2×C22⋊D61—21no—
79C2×C22⋊D61—21no—
80C2×C22⋊D61—21no—
81C2×C22⋊D61—21no—
82C2×C22⋊D61—21no—
83C2×C22⋊D61—21no—
84C2×C22⋊D61—21no—
85C2×C22⋊D61D411yescharacteristic
86C2×C22⋊D61D411yescharacteristic
87C22×Dic61—21no—
88C22×Dic61—21no—
89#11758224—28no—
90#11758224—22no—
91#11758224—22no—
92#11758224—22no—
93#11758224D414yescomplemented
94D4×D61—28no—
95D4×D61—22no—
96D4×D61—22no—
97D4×D61—22no—
98D4×D61—22no—
99D4×D61—22no—
100D4×D61D414yescomplemented
101#11758222—22no—
102#11758222—22no—
103#11758222—22no—
104#11758222—22no—
105C2×D244—21no—
106C2×D244D411yescharacteristic
107C2×D244C2311yescharacteristic
108C2×D244C2311yescharacteristic
109C2×C4×D61—21no—
110C2×C4×D61C2311yescharacteristic
111C2×C4×D61C2311yescharacteristic
112C2×Dic122D411yescharacteristic
113C2×Dic122C2311yescharacteristic
114D8×C61—22no—
115D8×C61—22no—
116C2×C8×C61C2311yescharacteristic
117C2×C8×C61C2311yescharacteristic
118C4⋊C4×C61C2311yescharacteristic
119C22⋊C4×C61—21no—
120C22⋊Dic61—21no—
121#11758200—22no—
122#11758199—22no—
123#11758199—22no—
124#11758199—22no—
125#11758198—21no—
126#11758198—21no—
127#11758198—21no—
128C4⋊Dic61C2311yescharacteristic
129C4×Dic61—21no—
130C2×#92418C2311yescharacteristic
131C2×#92418C2311yescharacteristic
132D488—22no—
133#11758190—22no—
134#11758189—22no—
135C8×D61—22no—
136C23×C61—24no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—81no—
141C23×C61—81no—
142C23×C61C2×D411yescharacteristic
143C22×D61—21no—
144C22×D61—24no—
145C22×D61—24no—
146C22×D61—21no—
147C22×D61—42no—
148C22×D61—81no—
149C22×D61—81no—
150C22×D61—81no—
151C22×D61—81no—
152C22×D61—81no—
153C22×D61—81no—
154C22×D61C2×D411yescharacteristic
155C22×D61C2×D411yescharacteristic
156D4×C61—24no—
157D4×C61—21no—
158D4×C61—21no—
159D4×C61—21no—
160D4×C61—21no—
161D4×C61—81no—
162D4×C61C2×D412yes—
163D4×C61C2×D412yes—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61C2×D411yescharacteristic
168C2×C4×C61C2411yescharacteristic
169C22⋊D61—24no—
170C22⋊D61—24no—
171C22⋊D61—24no—
172C22⋊D61—22no—
173C22⋊D61—24no—
174C22⋊D61—22no—
175C22⋊D61—24no—
176C22⋊D61—42no—
177C22⋊D61—81no—
178C22⋊D61—81no—
179C2×Dic61—24no—
180C2×Dic61—21no—
181C2×Dic61—24no—
182C2×Dic61—21no—
183C2×Dic61C2×D411yescharacteristic
184C2×Dic61C2×D411yescharacteristic
185D244—22no—
186D244—21no—
187D244—21no—
188D244—21no—
189D244—81no—
190D244C2×D412yes—
191C4×D61—24no—
192C4×D61—21no—
193C4×D61—21no—
194C4×D61C2×D412yes—
195C4×D61C2×D412yes—
196Dic122—21no—
197Dic122—22no—
198Dic122C2×D412yes—
199C8×C61—21no—
200C8×C61—21no—
201#92418—21no—
202#92418—21no—
203C22×C61—22no—
204C22×C61—22no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61—84no—
216C22×C61C22×D411yescharacteristic
217C2×D61—21no—
218C2×D61—21no—
219C2×D61—21no—
220C2×D61—22no—
221C2×D61—21no—
222C2×D61—21no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61—41no—
228C2×D61—84no—
229C2×D61—84no—
230C2×D61—84no—
231C2×D61#12012yes—
232C4×C61—21no—
233C4×C61—41no—
234C4×C61C22×D411yescharacteristic
235C4×C61C22×D411yescharacteristic
236Dic61—21no—
237Dic61—22no—
238Dic61—41no—
239Dic61#12012yes—
240#3008—611nomaximal, Sylow
241C2×C61—42no—
242C2×C61—42no—
243C2×C61—41no—
244C2×C61—81no—
245C2×C61C2×#12011yescharacteristic
246C2×C61#57611yescharacteristic
247C2×C61#57611yescharacteristic
248D61—22no—
249D61—41no—
250D61—42no—
251D61—81no—
252C2×H(5,𝔽2)—611no—
253C2×AGL(1,ℤ/8)—611no—
254C22×D8—611no—
255#535—611no—
256#449—611no—
257#449—611no—
258#449—611no—
259#449—611no—
260#447—611no—
261#447—611no—
262#447—611no—
263#447D6111yescharacteristic, complemented
264#418—611no—
265#416—611no—
266#408—611no—
267C61#300811yescharacteristic, complemented, Sylow
268H(5,𝔽2)—1224no—
269H(5,𝔽2)—1224no—
270C2×#41—611no—
271C2×#41—611no—
272C2×#41—611no—
273C2×#41—611no—
274C2×#41—1221no—
275C22×D4—611no—
276C22×D4—611no—
277C22×D4—611no—
278C22×D4—1221no—
279C22×D4—1221no—
280C22×D4—1221no—
281C22×D4C2×D6111yescharacteristic, complemented
282AGL(1,ℤ/8)—1224no—
283C2×SD16—611no—
284C2×SD16—611no—
285C2×D8—611no—
286C2×D8—611no—
287C2×D8—611no—
288C2×D8—611no—
289C2×D8—1224no—
290C2×D8C2×D6111yescharacteristic, complemented
291C2×D8C2×D6111yescharacteristic, complemented
292C2×M16—611no—
293C22×C8—611no—
294#127—1221no—
295#124—1221no—
296#121—611no—
297#121—611no—
298#121—611no—
299#121C2×D6111yescharacteristic, complemented
300#120—1221no—
301#120—1221no—
302#117—611no—
303#103—611no—
304#103—611no—
305#102—611no—
306#102—611no—
307#102—611no—
308#102—611no—
309#102C2×D6111yescharacteristic, complemented
310#102C2×D6111yescharacteristic, complemented
311C22⋊C8—611no—
312C22⋊C8—611no—
313C22⋊C8—611no—
314C22⋊C8C2×D6111yescharacteristic, complemented
315C24—21no—
316C24—1221no—
317C24—1221no—
318C24—1221no—
319#41—614no—
320#41—1222no—
321#41—1222no—
322#41—1222no—
323#41—1222no—
324#41—1222no—
325#41—1222no—
326#41—1228no—
327#41—1222no—
328C2×Q8—611no—
329C2×Q8—611no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—614no—
335C2×D4—611no—
336C2×D4—611no—
337C2×D4—611no—
338C2×D4—611no—
339C2×D4—611no—
340C2×D4—1221no—
341C2×D4—1222no—
342C2×D4—1222no—
343C2×D4—1222no—
344C2×D4—1221no—
345C2×D4—1221no—
346C2×D4—1221no—
347C2×D4—1222no—
348C2×D4—1228no—
349C2×D4—1221no—
350C2×D4—1221no—
351C2×D4—1228no—
352C2×D4—1228no—
353C2×D4—1221no—
354C2×D4—1222no—
355C2×D4—1221no—
356C2×D4—1221no—
357C2×D4C22×D6111yescharacteristic
358C2×D4C22×D6111yescharacteristic
359C2×D4C22×D6111yescharacteristic
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—1221no—
363C22×C4—1221no—
364C22×C4—1221no—
365C22×C4C22×D6111yescharacteristic
366SD16—1222no—
367SD16—1222no—
368D8—22no—
369D8—22no—
370D8—1222no—
371D8—1222no—
372D8—1222no—
373D8—1222no—
374M16—1222no—
375C2×C8—611no—
376C2×C8—611no—
377C2×C8—1222no—
378C2×C8C22×D6111yescharacteristic
379C2×C8C22×D6111yescharacteristic
380C4⋊C4—611no—
381C4⋊C4C22×D6111yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—1221no—
384C22⋊C4—1221no—
385C22⋊C4—1221no—
386C22⋊C4—1221no—
387C42—1221no—
388C23—24no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—81no—
393C23—81no—
394C23—611no—
395C23—611no—
396C23—1224no—
397C23—1224no—
398C23—1221no—
399C23—1221no—
400C23—4881no—
401C23—4881no—
402C23—4881no—
403C23—4881no—
404C23—4881no—
405C23—4881no—
406C23—2442no—
407C23D4×D6111yescharacteristic
408Q8—612no—
409Q8—1222no—
410Q8—1221no—
411D4—24no—
412D4—21no—
413D4—21no—
414D4—21no—
415D4—21no—
416D4—81no—
417D4—612no—
418D4—1222no—
419D4—1222no—
420D4—1224no—
421D4—1222no—
422D4—1224no—
423D4—1224no—
424D4—1224no—
425D4—1224no—
426D4—1221no—
427D4—1221no—
428D4—1221no—
429D4—4881no—
430D4—4881no—
431D4—4881no—
432D4—2442no—
433D4D4×D6112yes—
434D4D4×D6112yes—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—611no—
439C2×C4—612no—
440C2×C4—612no—
441C2×C4—611no—
442C2×C4—1224no—
443C2×C4—1224no—
444C2×C4—1224no—
445C2×C4—1221no—
446C2×C4—1221no—
447C2×C4—1221no—
448C2×C4—1221no—
449C2×C4D4×D6111yescharacteristic
450C2×C4C23×D6111yescharacteristic
451C8—21no—
452C8—21no—
453C8—1221no—
454C8—1221no—
455C22—21no—
456C22—22no—
457C22—22no—
458C22—21no—
459C22—21no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—84no—
468C22—612no—
469C22—1221no—
470C22—1221no—
471C22—1222no—
472C22—1221no—
473C22—1221no—
474C22—1221no—
475C22—4884no—
476C22—4884no—
477C22—4884no—
478C22—2441no—
479C22—2441no—
480C22—2441no—
481C22—2441no—
482C22—2441no—
483C22C2×D4×D6111yescharacteristic
484C4—21no—
485C4—41no—
486C4—612no—
487C4—1221no—
488C4—1222no—
489C4—2441no—
490C4C2×D4×D6111yescharacteristic
491C4C2×D4×D6111yescharacteristic
492C2—41no—
493C2—42no—
494C2—42no—
495C2—81no—
496C2—1222no—
497C2—4881no—
498C2—2441no—
499C2—2442no—
500C2#120×D6111yescharacteristic
501C2#1684056311yescharacteristic
502C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#447C2
socleC22×C61C22×D4
hypercenter#447D61
hypocenterC61#3008
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#14519822C2semidirect
2. C2×#14519801C2semidirect
3. C2×D8×D61C2semidirect
4. #16840328C2semidirect
5. #16839909C2semidirect
6. #16839908C2semidirect
7. #16839905C2semidirect
8. #16839904C2semidirect
9. #16839897C2semidirect
10. #16839896C2semidirect
11. #16839894C2semidirect
12. #16839765C2semidirect
13. #16839755C2semidirect
14. #16839727C2semidirect
15. C61×#447C2semidirect
19. C2×#11758222C22semidirect
22. C2×#11758224C22semidirect
27. C2×D4×D61C22semidirect
28. C2×D4×D61C22semidirect
30. C2×#11758190C22semidirect
31. C2×#11758200C22semidirect
32. C2×D488C22semidirect
33. C2×#11758199C22semidirect
34. C2×#11758199C22semidirect
35. C2×#11758199C22semidirect
37. C2×#11758189C22semidirect
38. C2×C8×D61C22semidirect
41. #14519752C22semidirect
42. #14519751C22semidirect
43. #14519748C22semidirect
46. #14519735C22semidirect
47. #14519702C22semidirect
48. #14519700C22semidirect
49. #14519699C22semidirect
50. #14519698C22semidirect
51. #14519698C22semidirect
52. #14519697C22semidirect
53. C22⋊#92418C22semidirect
54. #14519689C22semidirect
55. #14519689C22semidirect
56. C22×D4×C61C22semidirect
57. C2×D8×C61C22semidirect
58. C2×D8×C61C22semidirect
59. #121×C61C22semidirect
60. #102×C61C22semidirect
61. #102×C61C22semidirect
62. C22⋊C8×C61C22semidirect
93. #11758224D4semidirect
100. D4×D61D4semidirect
263. #447D61semidirect
267. C61#3008semidirect
281. C22×D4C2×D61semidirect
290. C2×D8C2×D61semidirect
291. C2×D8C2×D61semidirect
299. #121C2×D61semidirect
309. #102C2×D61semidirect
310. #102C2×D61semidirect
314. C22⋊C8C2×D61semidirect