Finite Group Databasebeta

← #21457305

Subgroups — #21457305

Order 7808.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519804C211yesmaximal, characteristic, complemented
2C2×D8×D61C211yesmaximal, characteristic, complemented
3#16840405C211yesmaximal, characteristic, complemented
4D4×D244C211yesmaximal, characteristic, complemented
5#16840152C211yesmaximal, characteristic, complemented
6#16840014C211yesmaximal, characteristic, complemented
7#16839994C211yesmaximal, characteristic, complemented
8#16839958C211yesmaximal, characteristic, complemented
9#16839911C211yesmaximal, characteristic, complemented
10#16839910C211yesmaximal, characteristic, complemented
11#16839897C211yesmaximal, characteristic, complemented
12#16839894C211yesmaximal, characteristic, complemented
13#16839872C211yesmaximal, characteristic, complemented
14#16839832C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic, complemented
17C22×D244—21no—
18C2×D4×D61C2211yescharacteristic
19C2×D4×D61C2211yescharacteristic, complemented
20C2×D4×D61C2211yescharacteristic, complemented
21#14519804—24no—
22C2×#11758201C2211yescharacteristic, complemented
23C2×#11758201C2211yescharacteristic, complemented
24C2×D488C2211yescharacteristic, complemented
25C2×D488C2211yescharacteristic, complemented
26C2×#11758199C2211yescharacteristic
27C2×#11758199C2211yescharacteristic, complemented
28C2×#11758199C2211yescharacteristic, complemented
29D8×D61—24no—
30C2×#11758189C2211yescharacteristic, complemented
31C2×C8×D61C2211yescharacteristic, complemented
32#14519774C2211yescharacteristic, complemented
33#14519759—21no—
34#14519753C2211yescharacteristic, complemented
35#14519752C2211yescharacteristic
36#14519752C2211yescharacteristic, complemented
37#14519751—21no—
38#14519750—21no—
39#14519748C2211yescharacteristic, complemented
40#14519747—21no—
41#14519747—21no—
42#14519747—21no—
43C4×D244C2211yescharacteristic
44C4×D244C2211yescharacteristic, complemented
45C22⋊C4×D61—21no—
46#14519708C2211yescharacteristic, complemented
47#14519699C2211yescharacteristic, complemented
48#14519699C2211yescharacteristic, complemented
49#14519698C2211yescharacteristic, complemented
50#14519697C2211yescharacteristic, complemented
51#14519689C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53#14519688C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×D8×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic, complemented
57C4×D4×C61C2211yescharacteristic, complemented
58C4⋊C8×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63C23×D61—21no—
64C2×Q8×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C22×C4×C61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72#11758226—22no—
73#11758226—41no—
74D4×D61—22no—
75D4×D61—22no—
76D4×D61—22no—
77D4×D61—41no—
78D4×D61—41no—
79D4×D61—41no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—44no—
86C2×D244D411yescharacteristic
87C2×D244C2311yescharacteristic
88C2×D244C2311yescharacteristic
89C2×D244C2311yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61C2311yescharacteristic
93C2×C4×D61C2311yescharacteristic
94SD16×C61—22no—
95D8×C61—22no—
96C2×C8×C61C2311yescharacteristic
97C2×C8×C61C2311yescharacteristic
98C4⋊C4×C61C2311yescharacteristic
99C22⋊C4×C61—21no—
100C22⋊C4×C61—21no—
101C22⋊C4×C61—21no—
102C42×C61C2311yescharacteristic
103C22⋊Dic61—21no—
104#11758201—22no—
105#11758201—41no—
106#11758199—22no—
107#11758199—41no—
108#11758199D414yescomplemented
109#11758198—21no—
110#11758198—21no—
111#11758198—21no—
112#11758198—21no—
113#11758198D411yescharacteristic
114#11758198D411yescharacteristic
115C4⋊Dic61D411yescharacteristic
116C4⋊Dic61C2311yescharacteristic
117#11758196—21no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120D488—22no—
121D488—22no—
122#11758189—22no—
123C8×D61—22no—
124C23×C61—21no—
125C23×C61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—42no—
133C22×D61—42no—
134C22×D61—42no—
135C22×D61—81no—
136C22×D61—81no—
137C22×D61—81no—
138C22×D61C2×D411yescharacteristic
139C22×D61C2×D411yescharacteristic
140Q8×C61—21no—
141Q8×C61—21no—
142D4×C61—21no—
143D4×C61—21no—
144D4×C61—21no—
145D4×C61C2×D412yes—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—42no—
149C2×C4×C61C2×D411yescharacteristic
150C2×C4×C61C2×D411yescharacteristic
151C2×C4×C61C2411yescharacteristic
152C22⋊D61—42no—
153C22⋊D61—42no—
154C22⋊D61—42no—
155C22⋊D61—81no—
156C2×Dic61—21no—
157C2×Dic61C2×D411yescharacteristic
158C2×Dic61C2×D411yescharacteristic
159D244—22no—
160D244—21no—
161D244—21no—
162D244—21no—
163D244—21no—
164D244—21no—
165D244—42no—
166D244—42no—
167D244—42no—
168D244—42no—
169D244—81no—
170D244C2×D412yescomplemented
171C4×D61—21no—
172C4×D61—21no—
173C4×D61—21no—
174C4×D61—21no—
175C4×D61—42no—
176C4×D61—81no—
177C8×C61—21no—
178C8×C61—21no—
179#92418—21no—
180#92418C2×D412yescomplemented
181C22×C61—22no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61C22×D411yescharacteristic
188C2×D61—21no—
189C2×D61—21no—
190C2×D61—21no—
191C2×D61—22no—
192C2×D61—21no—
193C2×D61—21no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—84no—
203C2×D61—84no—
204C2×D61—84no—
205C2×D61AGL(1,ℤ/8)12yescomplemented
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—41no—
209C4×C61—41no—
210C4×C61C22×D411yescharacteristic
211C4×C61H(5,𝔽2)11yescharacteristic
212Dic61—21no—
213Dic61—21no—
214Dic61—41no—
215#3264—611nomaximal, Sylow
216C2×C61—42no—
217C2×C61—81no—
218C2×C61D4211yescharacteristic
219C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C61#57611yescharacteristic
221D61—22no—
222D61—41no—
223D61—42no—
224D61—81no—
225D61—81no—
226C2×AGL(1,ℤ/8)—611no—
227C22×D8—611no—
228#546—611no—
229D42—611no—
230#496—611no—
231#469—611no—
232#465—611no—
233#463D6111yescharacteristic, complemented
234#459—611no—
235#450—611no—
236#449—611no—
237#447—611no—
238#447—611no—
239#442—611no—
240#435—611no—
241C61#326411yescharacteristic, complemented, Sylow
242C2×#41—611no—
243C22×D4—611no—
244C22×D4—611no—
245C22×D4—611no—
246C22×D4—1221no—
247AGL(1,ℤ/8)—1224no—
248C2×SD16—611no—
249C2×SD16—611no—
250C2×SD16C2×D6111yescharacteristic, complemented
251C2×D8—611no—
252C2×D8—611no—
253C2×D8—611no—
254C2×D8—611no—
255C2×D8—611no—
256C2×D8—1224no—
257C2×D8C2×D6111yescharacteristic
258C2×M16—611no—
259C22×C8—611no—
260#127—611no—
261#124C2×D6111yescharacteristic, complemented
262#123—1221no—
263C22⋊Q8—611no—
264#121—611no—
265#121—611no—
266#121—611no—
267#121—1221no—
268#121—1221no—
269#120—1221no—
270#120—1221no—
271#120—1221no—
272C4×D4—611no—
273C4×D4—611no—
274C4×D4C2×D6111yescharacteristic, complemented
275C2×C22⋊C4—1221no—
276#106—611no—
277C4⋊C8C2×D6111yescharacteristic, complemented
278#103C2×D6111yescharacteristic, complemented
279#102—611no—
280#102—611no—
281#102—611no—
282#102—611no—
283#102C2×D6111yescharacteristic, complemented
284C22⋊C8—611no—
285C22⋊C8—611no—
286#97—611no—
287C24—1221no—
288C24—1221no—
289C24—1221no—
290#41—1222no—
291#41—2441no—
292C2×Q8C22×D6111yescharacteristic
293C2×D4—611no—
294C2×D4—611no—
295C2×D4—611no—
296C2×D4—611no—
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—1221no—
303C2×D4—1222no—
304C2×D4—1222no—
305C2×D4—1222no—
306C2×D4—1221no—
307C2×D4—1221no—
308C2×D4—1221no—
309C2×D4—2444no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C2×D4C22×D6111yescharacteristic
314C2×D4C22×D6111yescharacteristic
315C22×C4—21no—
316C22×C4—611no—
317C22×C4—611no—
318C22×C4—1221no—
319C22×C4—1221no—
320SD16—22no—
321SD16—1222no—
322SD16—2441no—
323D8—22no—
324D8—614no—
325D8—1222no—
326D8—1222no—
327D8—1222no—
328D8—2441no—
329M16—1222no—
330C2×C8—611no—
331C2×C8—611no—
332C2×C8—1222no—
333C2×C8C22×D6111yescharacteristic
334C2×C8C22×D6111yescharacteristic
335C4⋊C4—611no—
336C4⋊C4—611no—
337C4⋊C4—1221no—
338C4⋊C4C22×D6111yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—611no—
343C22⋊C4—611no—
344C22⋊C4—1221no—
345C22⋊C4—1221no—
346C22⋊C4—1221no—
347C22⋊C4—1221no—
348C22⋊C4—1221no—
349C42C22×D6111yescharacteristic
350C23—21no—
351C23—21no—
352C23—611no—
353C23—611no—
354C23—1221no—
355C23—1221no—
356C23—1221no—
357C23—4881no—
358C23—4881no—
359C23—4881no—
360C23—2442no—
361C23—2442no—
362C23—2442no—
363C23—2442no—
364C23—2442no—
365C23—2442no—
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—612no—
372D4—1222no—
373D4—1221no—
374D4—1221no—
375D4—1221no—
376D4—1221no—
377D4—1221no—
378D4—4881no—
379D4—4881no—
380D4—2442no—
381D4—2442no—
382D4—2442no—
383D4—2442no—
384D4—2442no—
385D4—2442no—
386D4—2442no—
387D4D4×D6112yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—611no—
392C2×C4—611no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—4881no—
399C2×C4—2442no—
400C2×C4D4×D6111yescharacteristic
401C2×C4D4×D6111yescharacteristic
402C2×C4C23×D6111yescharacteristic
403C8—21no—
404C8—21no—
405C8—612no—
406C8—1221no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—612no—
414C22—1221no—
415C22—1221no—
416C22—1221no—
417C22—1221no—
418C22—1221no—
419C22—1222no—
420C22—4884no—
421C22—4884no—
422C22—4884no—
423C22—2441no—
424C22—2441no—
425C22—2441no—
426C22—2441no—
427C22—2441no—
428C22—2441no—
429C22—2441no—
430C22—2441no—
431C22C2×D4×D6111yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—1221no—
437C4—1221no—
438C4—2441no—
439C4C2×D4×D6111yescharacteristic
440C4#1451982311yescharacteristic
441C2—42no—
442C2—81no—
443C2—1222no—
444C2—4881no—
445C2—4881no—
446C2—2441no—
447C2—2442no—
448C2#1684039611yescharacteristic
449C2AGL(1,ℤ/8)×D6111yescharacteristic
450C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3264
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. C2×D8×D61C2semidirect
3. #16840405C2semidirect
4. D4×D244C2semidirect
5. #16840152C2semidirect
6. #16840014C2semidirect
7. #16839994C2semidirect
8. #16839958C2semidirect
9. #16839911C2semidirect
10. #16839910C2semidirect
11. #16839897C2semidirect
12. #16839894C2semidirect
13. #16839872C2semidirect
14. #16839832C2semidirect
15. C61×#463C2semidirect
16. C2×#11758226C22semidirect
19. C2×D4×D61C22semidirect
20. C2×D4×D61C22semidirect
22. C2×#11758201C22semidirect
23. C2×#11758201C22semidirect
24. C2×D488C22semidirect
25. C2×D488C22semidirect
27. C2×#11758199C22semidirect
28. C2×#11758199C22semidirect
30. C2×#11758189C22semidirect
31. C2×C8×D61C22semidirect
32. #14519774C22semidirect
34. #14519753C22semidirect
36. #14519752C22semidirect
39. #14519748C22semidirect
44. C4×D244C22semidirect
46. #14519708C22semidirect
47. #14519699C22semidirect
48. #14519699C22semidirect
49. #14519698C22semidirect
50. #14519697C22semidirect
51. #14519689C22semidirect
52. #14519689C22semidirect
53. #14519688C22semidirect
54. C2×SD16×C61C22semidirect
56. #124×C61C22semidirect
57. C4×D4×C61C22semidirect
58. C4⋊C8×C61C22semidirect
59. #103×C61C22semidirect
60. #102×C61C22semidirect
108. #11758199D4semidirect
170. D244C2×D4semidirect
180. #92418C2×D4semidirect
205. C2×D61AGL(1,ℤ/8)semidirect
233. #463D61semidirect
241. C61#3264semidirect
250. C2×SD16C2×D61semidirect
261. #124C2×D61semidirect
274. C4×D4C2×D61semidirect
277. C4⋊C8C2×D61semidirect
278. #103C2×D61semidirect
283. #102C2×D61semidirect