Finite Group Databasebeta

← #21455084

Subgroups — #21455084

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×#14519823C211yesmaximal, characteristic, complemented
2C2×#14519804C211yesmaximal, characteristic, complemented
3C2×D8×D61C211yesmaximal, characteristic, complemented
4#16840328C211yesmaximal, characteristic, complemented
5#16839910C211yesmaximal, characteristic, complemented
6#16839907C211yesmaximal, characteristic, complemented
7#16839906C211yesmaximal, characteristic, complemented
8#16839898C211yesmaximal, characteristic, complemented
9#16839897C211yesmaximal, characteristic, complemented
10#16839895C211yesmaximal, characteristic, complemented
11#16839894C211yesmaximal, characteristic, complemented
12#16839765C211yesmaximal, characteristic, complemented
13#16839757C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic, complemented
16#14519823—24no—
17#14519823—24no—
18C2×#11758226C2211yescharacteristic
19C2×#11758226C2211yescharacteristic, complemented
20C2×#11758222—21no—
21C2×#11758222C2211yescharacteristic
22C22×D244—21no—
23C22×D244C2211yescharacteristic, complemented
24C2×D4×D61—21no—
25C2×D4×D61—21no—
26C2×D4×D61C2211yescharacteristic
27C2×D4×D61C2211yescharacteristic, complemented
28C2×D4×D61C2211yescharacteristic, complemented
29#14519804—24no—
30C2×#11758201C2211yescharacteristic, complemented
31C2×D488C2211yescharacteristic, 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#14519701C2211yescharacteristic, complemented
48#14519699C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic, complemented
50#14519698C2211yescharacteristic, complemented
51#14519697C2211yescharacteristic, complemented
52#14519697C2211yescharacteristic, complemented
53C22⋊#92418C2211yescharacteristic, complemented
54#14519689C2211yescharacteristic, complemented
55#14519689C2211yescharacteristic, complemented
56C2×#41×C61C2211yescharacteristic, complemented
57C2×SD16×C61C2211yescharacteristic, complemented
58C2×D8×C61C2211yescharacteristic, complemented
59#121×C61C2211yescharacteristic, complemented
60#103×C61C2211yescharacteristic, complemented
61#102×C61C2211yescharacteristic, complemented
62C22⋊C8×C61C2211yescharacteristic, complemented
63C23×D61—21no—
64C23×D61—21no—
65C23×D61—21no—
66C23×D61—21no—
67#41×C61—22no—
68#41×C61—22no—
69C2×Q8×C61C2311yescharacteristic
70C2×D4×C61—21no—
71C2×D4×C61—21no—
72C2×D4×C61C2311yescharacteristic
73C2×D4×C61C2311yescharacteristic
74C22×C4×C61—21no—
75C22×C4×C61C2311yescharacteristic
76C2×C22⋊D61—21no—
77C2×C22⋊D61—21no—
78C2×C22⋊D61—21no—
79C2×C22⋊D61—21no—
80C2×C22⋊D61—21no—
81C2×C22⋊D61D411yescharacteristic
82C2×C22⋊D61D411yescharacteristic
83#11758226—22no—
84#11758226—22no—
85#11758226—22no—
86#11758226D414yescomplemented
87D4×D61—28no—
88D4×D61—28no—
89D4×D61—22no—
90D4×D61—22no—
91D4×D61—22no—
92D4×D61—22no—
93D4×D61—22no—
94D4×D61D414yescomplemented
95#11758222—28no—
96#11758222—22no—
97#11758222—22no—
98C2×D244—28no—
99C2×D244—21no—
100C2×D244—21no—
101C2×D244—21no—
102C2×D244—22no—
103C2×D244—22no—
104C2×D244—21no—
105C2×D244D411yescharacteristic
106C2×D244C2311yescharacteristic
107C2×D244C2311yescharacteristic
108C2×D244C2311yescharacteristic
109C2×C4×D61—21no—
110C2×C4×D61—21no—
111C2×C4×D61C2311yescharacteristic
112C2×C4×D61C2311yescharacteristic
113C2×Dic122D411yescharacteristic
114SD16×C61—22no—
115D8×C61—22no—
116C2×C8×C61C2311yescharacteristic
117C2×C8×C61C2311yescharacteristic
118C4⋊C4×C61C2311yescharacteristic
119C22⋊C4×C61—21no—
120C22⋊Dic61—21no—
121#11758201—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—
133D488—22no—
134#11758189—22no—
135C8×D61—22no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61C2×D411yescharacteristic
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—24no—
142C22×D61—24no—
143C22×D61—24no—
144C22×D61—21no—
145C22×D61—42no—
146C22×D61—81no—
147C22×D61—81no—
148C22×D61—81no—
149C22×D61—81no—
150C22×D61—81no—
151C22×D61—81no—
152C22×D61—81no—
153C22×D61—81no—
154C22×D61C2×D411yescharacteristic
155C22×D61C2×D411yescharacteristic
156Q8×C61—21no—
157Q8×C61C2×D412yes—
158D4×C61—24no—
159D4×C61—21no—
160D4×C61—21no—
161D4×C61—21no—
162D4×C61—81no—
163D4×C61C2×D412yes—
164C2×C4×C61—24no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61C2×D411yescharacteristic
170C2×C4×C61C2411yescharacteristic
171C22⋊D61—24no—
172C22⋊D61—22no—
173C22⋊D61—22no—
174C22⋊D61—24no—
175C22⋊D61—42no—
176C22⋊D61—81no—
177C22⋊D61—81no—
178C2×Dic61—21no—
179C2×Dic61C2×D411yescharacteristic
180C2×Dic61C2×D411yescharacteristic
181D244—24no—
182D244—24no—
183D244—22no—
184D244—24no—
185D244—21no—
186D244—21no—
187D244—21no—
188D244—21no—
189D244—81no—
190D244C2×D412yes—
191D244C2×D412yes—
192C4×D61—24no—
193C4×D61—21no—
194C4×D61—21no—
195C4×D61—24no—
196C4×D61C2×D412yes—
197C4×D61C2×D412yes—
198Dic122—22no—
199C8×C61—21no—
200C8×C61—21no—
201#92418—21no—
202#92418—21no—
203C22×C61—21no—
204C22×C61—22no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61C22×D411yescharacteristic
213C2×D61—21no—
214C2×D61—21no—
215C2×D61—21no—
216C2×D61—22no—
217C2×D61—22no—
218C2×D61—21no—
219C2×D61—21no—
220C2×D61—41no—
221C2×D61—41no—
222C2×D61—41no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61—84no—
228C2×D61—84no—
229C2×D61—84no—
230C2×D61—84no—
231C2×D61#12012yes—
232C4×C61—21no—
233C4×C61—22no—
234C4×C61—41no—
235C4×C61C22×D411yescharacteristic
236C4×C61C22×D411yescharacteristic
237Dic61—21no—
238Dic61—41no—
239Dic61#12012yes—
240#3008—611nomaximal, Sylow
241C2×C61—41no—
242C2×C61—42no—
243C2×C61—81no—
244C2×C61C2×#12011yescharacteristic
245C2×C61#57611yescharacteristic
246C2×C61#57611yescharacteristic
247D61—22no—
248D61—41no—
249D61—42no—
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#449D6111yescharacteristic, complemented
260#447—611no—
261#447—611no—
262#447—611no—
263#447—611no—
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—1221no—
274C2×#41C2×D6111yescharacteristic, complemented
275C22×D4—611no—
276C22×D4—611no—
277C22×D4—611no—
278C22×D4—611no—
279C22×D4—1221no—
280C22×D4—1221no—
281C22×D4—1221no—
282AGL(1,ℤ/8)—1224no—
283C2×SD16—611no—
284C2×SD16C2×D6111yescharacteristic, complemented
285C2×D8—611no—
286C2×D8—611no—
287C2×D8—611no—
288C2×D8—611no—
289C2×D8—611no—
290C2×D8—1224no—
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#103C2×D6111yescharacteristic, complemented
305#102—611no—
306#102—611no—
307#102—611no—
308#102—611no—
309#102—611no—
310#102C2×D6111yescharacteristic, complemented
311C22⋊C8—611no—
312C22⋊C8—611no—
313C22⋊C8—611no—
314C22⋊C8C2×D6111yescharacteristic, complemented
315C24—1221no—
316C24—1221no—
317C24—1221no—
318C24—1221no—
319#41—22no—
320#41—22no—
321#41—614no—
322#41—1222no—
323#41—1222no—
324#41—1228no—
325#41—1222no—
326#41—1222no—
327#41—1222no—
328C2×Q8—611no—
329C2×Q8C22×D6111yescharacteristic
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—614no—
333C2×D4—611no—
334C2×D4—611no—
335C2×D4—611no—
336C2×D4—611no—
337C2×D4—611no—
338C2×D4—611no—
339C2×D4—1222no—
340C2×D4—1222no—
341C2×D4—1221no—
342C2×D4—1221no—
343C2×D4—1228no—
344C2×D4—1221no—
345C2×D4—1222no—
346C2×D4—1222no—
347C2×D4—1222no—
348C2×D4—1221no—
349C2×D4—1221no—
350C2×D4—1221no—
351C2×D4—1222no—
352C2×D4—1228no—
353C2×D4—1228no—
354C2×D4—1222no—
355C2×D4—1221no—
356C2×D4—1221no—
357C2×D4—1221no—
358C2×D4C22×D6111yescharacteristic
359C2×D4C22×D6111yescharacteristic
360C22×C4—21no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—1221no—
364C22×C4—1221no—
365C22×C4C22×D6111yescharacteristic
366SD16—22no—
367SD16—1222no—
368D8—22no—
369D8—1222no—
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—21no—
389C23—21no—
390C23—611no—
391C23—611no—
392C23—1224no—
393C23—1224no—
394C23—1224no—
395C23—1221no—
396C23—1221no—
397C23—1221no—
398C23—4881no—
399C23—4881no—
400C23—4881no—
401C23—4881no—
402C23—4881no—
403C23—4881no—
404C23—4881no—
405C23—4881no—
406C23—2442no—
407C23D4×D6111yescharacteristic
408Q8—21no—
409Q8—1222no—
410Q8D4×D6112yes—
411D4—24no—
412D4—21no—
413D4—21no—
414D4—21no—
415D4—81no—
416D4—612no—
417D4—612no—
418D4—1222no—
419D4—1224no—
420D4—1224no—
421D4—1224no—
422D4—1222no—
423D4—1224no—
424D4—1222no—
425D4—1224no—
426D4—1221no—
427D4—1221no—
428D4—1221no—
429D4—1221no—
430D4—4881no—
431D4—4881no—
432D4—4881no—
433D4—2442no—
434D4D4×D6112yes—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—611no—
441C2×C4—612no—
442C2×C4—612no—
443C2×C4—611no—
444C2×C4—1224no—
445C2×C4—1224no—
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—21no—
458C22—21no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—612no—
465C22—1221no—
466C22—1221no—
467C22—1222no—
468C22—1222no—
469C22—1221no—
470C22—1221no—
471C22—1221no—
472C22—4884no—
473C22—4884no—
474C22—4884no—
475C22—4884no—
476C22—2441no—
477C22—2441no—
478C22—2441no—
479C22—2441no—
480C22—2441no—
481C22—2441no—
482C22—2441no—
483C22C2×D4×D6111yescharacteristic
484C4—21no—
485C4—22no—
486C4—41no—
487C4—612no—
488C4—1221no—
489C4—2441no—
490C4C2×D4×D6111yescharacteristic
491C4C2×D4×D6111yescharacteristic
492C2—41no—
493C2—42no—
494C2—81no—
495C2—1222no—
496C2—4881no—
497C2—2441no—
498C2—2442no—
499C2—2442no—
500C2#120×D6111yescharacteristic
501C2#1684056411yescharacteristic
502C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#449C2
socleC22×C61C22×D4
hypercenter#449D61
hypocenterC61#3008
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#14519823C2semidirect
2. C2×#14519804C2semidirect
3. C2×D8×D61C2semidirect
4. #16840328C2semidirect
5. #16839910C2semidirect
6. #16839907C2semidirect
7. #16839906C2semidirect
8. #16839898C2semidirect
9. #16839897C2semidirect
10. #16839895C2semidirect
11. #16839894C2semidirect
12. #16839765C2semidirect
13. #16839757C2semidirect
14. #16839727C2semidirect
15. C61×#449C2semidirect
19. C2×#11758226C22semidirect
23. C22×D244C22semidirect
27. C2×D4×D61C22semidirect
28. C2×D4×D61C22semidirect
30. C2×#11758201C22semidirect
31. C2×D488C22semidirect
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. #14519701C22semidirect
48. #14519699C22semidirect
49. #14519699C22semidirect
50. #14519698C22semidirect
51. #14519697C22semidirect
52. #14519697C22semidirect
53. C22⋊#92418C22semidirect
54. #14519689C22semidirect
55. #14519689C22semidirect
56. C2×#41×C61C22semidirect
57. C2×SD16×C61C22semidirect
58. C2×D8×C61C22semidirect
59. #121×C61C22semidirect
60. #103×C61C22semidirect
61. #102×C61C22semidirect
62. C22⋊C8×C61C22semidirect
86. #11758226D4semidirect
94. D4×D61D4semidirect
259. #449D61semidirect
267. C61#3008semidirect
274. C2×#41C2×D61semidirect
284. C2×SD16C2×D61semidirect
291. C2×D8C2×D61semidirect
299. #121C2×D61semidirect
304. #103C2×D61semidirect
310. #102C2×D61semidirect
314. C22⋊C8C2×D61semidirect