Finite Group Databasebeta

← #21457301

Subgroups — #21457301

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×#14519801C211yesmaximal, characteristic, complemented
2C2×D8×D61C211yesmaximal, characteristic, complemented
3#16840407C211yesmaximal, characteristic, complemented
4D4×D244C211yesmaximal, characteristic, complemented
5#16840151C211yesmaximal, characteristic, complemented
6#16840016C211yesmaximal, characteristic, complemented
7#16839992C211yesmaximal, characteristic, complemented
8#16839977C211yesmaximal, characteristic, complemented
9#16839957C211yesmaximal, characteristic, complemented
10#16839914C211yesmaximal, characteristic, complemented
11#16839908C211yesmaximal, characteristic, complemented
12#16839897C211yesmaximal, characteristic, complemented
13#16839897C211yesmaximal, characteristic, complemented
14#16839835C211yesmaximal, characteristic, complemented
15C61×#442C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic, complemented
17C22×D244—21no—
18C2×D4×D61C2211yescharacteristic
19C2×D4×D61C2211yescharacteristic, complemented
20C2×D4×D61C2211yescharacteristic, complemented
21#14519801—24no—
22C2×#11758190C2211yescharacteristic, complemented
23C2×#11758190C2211yescharacteristic, complemented
24C2×#11758200C2211yescharacteristic, complemented
25C2×D488C2211yescharacteristic, complemented
26C2×D488C2211yescharacteristic, complemented
27C2×#11758199C2211yescharacteristic
28C2×#11758199C2211yescharacteristic, complemented
29C2×#11758199C2211yescharacteristic, complemented
30D8×D61—24no—
31C2×#11758189C2211yescharacteristic, complemented
32C2×C8×D61C2211yescharacteristic, complemented
33#14519774C2211yescharacteristic, complemented
34#14519765C2211yescharacteristic, complemented
35#14519761—21no—
36#14519757C2211yescharacteristic, complemented
37#14519752C2211yescharacteristic
38#14519752C2211yescharacteristic, complemented
39#14519752C2211yescharacteristic, complemented
40#14519751—21no—
41#14519751—21no—
42#14519747—21no—
43#14519747—21no—
44#14519747—21no—
45C4×D244C2211yescharacteristic
46C2×#11758198—21no—
47C4⋊#92418C2211yescharacteristic, complemented
48#14519700C2211yescharacteristic, complemented
49#14519697C2211yescharacteristic, complemented
50#14519697C2211yescharacteristic, complemented
51#14519697C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53#14519689C2211yescharacteristic, complemented
54C2×D8×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic, complemented
56C4×D4×C61C2211yescharacteristic, complemented
57#106×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic, complemented
59#102×C61C2211yescharacteristic, complemented
60#97×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63C23×D61—21no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C22×Dic61—21no—
73#11758224—22no—
74#11758224—41no—
75D4×D61—22no—
76D4×D61—22no—
77D4×D61—22no—
78D4×D61—41no—
79D4×D61—41no—
80D4×D61—41no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—44no—
87C2×D244D411yescharacteristic
88C2×D244C2311yescharacteristic
89C2×D244C2311yescharacteristic
90C2×D244C2311yescharacteristic
91C2×C4×D61C2311yescharacteristic
92C2×C4×D61C2311yescharacteristic
93C2×Dic122C2311yescharacteristic
94D8×C61D414yescomplemented
95C2×C8×C61C2311yescharacteristic
96C2×C8×C61C2311yescharacteristic
97C4⋊C4×C61C2311yescharacteristic
98C4⋊C4×C61C2311yescharacteristic
99C22⋊C4×C61—21no—
100C22⋊C4×C61—21no—
101C42×C61C2311yescharacteristic
102#11758200—22no—
103#11758199—22no—
104#11758199—22no—
105#11758199—22no—
106#11758198—21no—
107#11758198—21no—
108#11758198—21no—
109#11758198—21no—
110#11758198—21no—
111#11758198—21no—
112#11758198D411yescharacteristic
113#11758198D411yescharacteristic
114C4⋊Dic61—21no—
115C4⋊Dic61D411yescharacteristic
116C2×#92418C2311yescharacteristic
117C2×#92418C2311yescharacteristic
118D488—22no—
119D488—41no—
120#11758190—22no—
121#11758190—41no—
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
140D4×C61—21no—
141D4×C61—21no—
142D4×C61C2×D412yes—
143D4×C61C2×D412yescomplemented
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—42no—
147C2×C4×C61—81no—
148C2×C4×C61C2×D411yescharacteristic
149C2×C4×C61C2×D411yescharacteristic
150C2×C4×C61C2411yescharacteristic
151C22⋊D61—42no—
152C22⋊D61—42no—
153C22⋊D61—42no—
154C22⋊D61—42no—
155C2×Dic61—21no—
156C2×Dic61—42no—
157C2×Dic61C2×D411yescharacteristic
158C2×Dic61C2×D411yescharacteristic
159D244—22no—
160D244—21no—
161D244—21no—
162D244—21no—
163D244—21no—
164D244—21no—
165D244—21no—
166D244—42no—
167D244—42no—
168D244—42no—
169D244—81no—
170D244—81no—
171C4×D61—21no—
172C4×D61—21no—
173C4×D61—21no—
174C4×D61—21no—
175Dic122—21no—
176Dic122—21no—
177C8×C61—21no—
178C8×C61C2×D412yescomplemented
179#92418—21no—
180#92418—21no—
181C22×C61—22no—
182C22×C61—22no—
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—21no—
192C2×D61—21no—
193C2×D61—41no—
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—42no—
218C2×C61D4211yescharacteristic
219C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C61#57611yescharacteristic
221D61—22no—
222D61—41no—
223D61—81no—
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#463—611no—
234#459—611no—
235#450—611no—
236#449—611no—
237#447—611no—
238#447—611no—
239#442D6111yescharacteristic, complemented
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×SD16—611no—
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#124—611no—
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×D4C2×D6111yescharacteristic, complemented
274C4×D4C2×D6111yescharacteristic, complemented
275C2×C22⋊C4—1221no—
276#106C2×D6111yescharacteristic, complemented
277C4⋊C8—611no—
278#103—611no—
279#102—611no—
280#102—611no—
281#102—611no—
282#102C2×D6111yescharacteristic, complemented
283#102C2×D6111yescharacteristic, complemented
284C22⋊C8—611no—
285C22⋊C8—611no—
286#97C2×D6111yescharacteristic, complemented
287C24—1221no—
288C24—1221no—
289C24—1221no—
290#41—1222no—
291#41—2441no—
292C2×Q8—611no—
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—21no—
317C22×C4—611no—
318C22×C4—611no—
319C22×C4—1221no—
320SD16—1222no—
321SD16—1222no—
322SD16—2441no—
323D8—1222no—
324D8—1222no—
325D8—1222no—
326D8—1222no—
327D8—2441no—
328D8D24414yescomplemented
329M16—1222no—
330C2×C8—611no—
331C2×C8—611no—
332C2×C8—1222no—
333C2×C8C22×D6111yescharacteristic
334C2×C8C22×D6111yescharacteristic
335C4⋊C4—611no—
336C4⋊C4—1221no—
337C4⋊C4C22×D6111yescharacteristic
338C4⋊C4C22×D6111yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—611no—
342C22⋊C4—611no—
343C22⋊C4—1221no—
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—1221no—
367Q8—1221no—
368D4—21no—
369D4—21no—
370D4—1222no—
371D4—1221no—
372D4—1221no—
373D4—1221no—
374D4—1221no—
375D4—1221no—
376D4—1221no—
377D4—4881no—
378D4—4881no—
379D4—2442no—
380D4—2442no—
381D4—2442no—
382D4—2442no—
383D4—2442no—
384D4—2442no—
385D4—2442no—
386D4C2×D24412yes—
387D4C2×D24412yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—81no—
392C2×C4—611no—
393C2×C4—611no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—2442no—
400C2×C4D4×D6111yescharacteristic
401C2×C4D4×D6111yescharacteristic
402C2×C4C23×D6111yescharacteristic
403C8—21no—
404C8—1221no—
405C8—1221no—
406C8C2×D24412yescomplemented
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—612no—
414C22—1221no—
415C22—1221no—
416C22—1221no—
417C22—1221no—
418C22—1221no—
419C22—4884no—
420C22—4884no—
421C22—4884no—
422C22—2441no—
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—
439C4C22×D24411yescharacteristic
440C4#1451982311yescharacteristic
441C2—42no—
442C2—42no—
443C2—1222no—
444C2—4881no—
445C2—4881no—
446C2—4881no—
447C2—2441no—
448C2D4×D24411yescharacteristic
449C2AGL(1,ℤ/8)×D6111yescharacteristic
450C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#442C2
socleC22×C61C22×D4
hypercenter#442D61
hypocenterC61#3264
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#14519801C2semidirect
2. C2×D8×D61C2semidirect
3. #16840407C2semidirect
4. D4×D244C2semidirect
5. #16840151C2semidirect
6. #16840016C2semidirect
7. #16839992C2semidirect
8. #16839977C2semidirect
9. #16839957C2semidirect
10. #16839914C2semidirect
11. #16839908C2semidirect
12. #16839897C2semidirect
13. #16839897C2semidirect
14. #16839835C2semidirect
15. C61×#442C2semidirect
16. C2×#11758224C22semidirect
19. C2×D4×D61C22semidirect
20. C2×D4×D61C22semidirect
22. C2×#11758190C22semidirect
23. C2×#11758190C22semidirect
24. C2×#11758200C22semidirect
25. C2×D488C22semidirect
26. C2×D488C22semidirect
28. C2×#11758199C22semidirect
29. C2×#11758199C22semidirect
31. C2×#11758189C22semidirect
32. C2×C8×D61C22semidirect
33. #14519774C22semidirect
34. #14519765C22semidirect
36. #14519757C22semidirect
38. #14519752C22semidirect
39. #14519752C22semidirect
47. C4⋊#92418C22semidirect
48. #14519700C22semidirect
49. #14519697C22semidirect
50. #14519697C22semidirect
51. #14519697C22semidirect
52. #14519689C22semidirect
53. #14519689C22semidirect
55. C4×D4×C61C22semidirect
56. C4×D4×C61C22semidirect
57. #106×C61C22semidirect
58. #102×C61C22semidirect
59. #102×C61C22semidirect
60. #97×C61C22semidirect
94. D8×C61D4semidirect
143. D4×C61C2×D4semidirect
178. C8×C61C2×D4semidirect
205. C2×D61AGL(1,ℤ/8)semidirect
239. #442D61semidirect
241. C61#3264semidirect
273. C4×D4C2×D61semidirect
274. C4×D4C2×D61semidirect
276. #106C2×D61semidirect
282. #102C2×D61semidirect
283. #102C2×D61semidirect
286. #97C2×D61semidirect
328. D8D244semidirect
387. D4C2×D244semidirect
406. C8C2×D244semidirect