Finite Group Databasebeta

← #21457298

Subgroups — #21457298

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
4#16840397C211yesmaximal, characteristic, complemented
5#16840012C211yesmaximal, characteristic, complemented
6#16839988C211yesmaximal, characteristic, complemented
7#16839974C211yesmaximal, characteristic, complemented
8#16839954C211yesmaximal, characteristic, complemented
9#16839911C211yesmaximal, characteristic, complemented
10#16839906C211yesmaximal, characteristic, complemented
11#16839894C211yesmaximal, characteristic, complemented
12#16839894C211yesmaximal, characteristic, complemented
13#16839875C211yesmaximal, characteristic, complemented
14#16839835C211yesmaximal, characteristic, complemented
15C61×#496C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic, complemented
17C2×D4×D61—21no—
18C2×D4×D61C2211yescharacteristic
19C2×D4×D61C2211yescharacteristic, complemented
20C2×D4×D61C2211yescharacteristic, complemented
21#14519804—24no—
22C2×#11758201C2211yescharacteristic, complemented
23C2×D488C2211yescharacteristic
24C2×#11758199C2211yescharacteristic
25C2×#11758199C2211yescharacteristic, complemented
26C2×#11758199C2211yescharacteristic, complemented
27D8×D61—24no—
28C2×#11758189C2211yescharacteristic, complemented
29C2×C8×D61C2211yescharacteristic, complemented
30#14519759—21no—
31#14519753C2211yescharacteristic, complemented
32#14519750—21no—
33#14519748—21no—
34#14519748C2211yescharacteristic
35#14519748C2211yescharacteristic, complemented
36#14519748C2211yescharacteristic, complemented
37#14519747—21no—
38#14519745—21no—
39#14519745—21no—
40C4×D244C2211yescharacteristic
41C4×D244C2211yescharacteristic, complemented
42C4×D244C2211yescharacteristic, complemented
43C22⋊C4×D61—21no—
44#14519709C2211yescharacteristic, complemented
45C4⋊#92418C2211yescharacteristic, complemented
46#14519701C2211yescharacteristic, complemented
47#14519699C2211yescharacteristic, complemented
48#14519699C2211yescharacteristic, complemented
49#14519698C2211yescharacteristic, complemented
50#14519698C2211yescharacteristic, complemented
51#14519698C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53#14519689C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×SD16×C61C2211yescharacteristic, complemented
56C2×D8×C61C2211yescharacteristic, complemented
57C2×D8×C61C2211yescharacteristic, complemented
58#127×C61C2211yescharacteristic, complemented
59#124×C61C2211yescharacteristic, complemented
60#97×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63C23×D61—21no—
64C2×Q8×C61C2311yescharacteristic
65C2×D4×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61C2311yescharacteristic
68C2×D4×C61C2311yescharacteristic
69C2×D4×C61C2311yescharacteristic
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76#11758226—22no—
77#11758226—41no—
78D4×D61—22no—
79D4×D61—22no—
80D4×D61—22no—
81D4×D61—41no—
82D4×D61—41no—
83D4×D61—41no—
84D4×D61—44no—
85C2×D244—21no—
86C2×D244D411yescharacteristic
87C2×D244C2311yescharacteristic
88C2×D244C2311yescharacteristic
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61C2311yescharacteristic
93C2×C4×D61C2311yescharacteristic
94SD16×C61—22no—
95SD16×C61—41no—
96D8×C61—22no—
97D8×C61—41no—
98C2×C8×C61C2311yescharacteristic
99C2×C8×C61C2311yescharacteristic
100C22⋊C4×C61—21no—
101C22⋊C4×C61—21no—
102C42×C61C2311yescharacteristic
103C22⋊Dic61—21no—
104C22⋊Dic61—21no—
105C22⋊Dic61—21no—
106#11758201—22no—
107#11758199—22no—
108#11758199—22no—
109#11758199—22no—
110#11758198—21no—
111#11758198—21no—
112#11758198—21no—
113#11758198D411yescharacteristic
114#11758198D411yescharacteristic
115C4⋊Dic61D411yescharacteristic
116C4⋊Dic61C2311yescharacteristic
117C4⋊Dic61C2311yescharacteristic
118#11758196—21no—
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121D488D414yescomplemented
122#11758189—22no—
123C8×D61—22no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—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×C61—21no—
146D4×C61—21no—
147D4×C61—21no—
148D4×C61—42no—
149D4×C61—81no—
150C2×C4×C61—21no—
151C2×C4×C61C2×D411yescharacteristic
152C2×C4×C61C2×D411yescharacteristic
153C2×C4×C61C2411yescharacteristic
154C22⋊D61—42no—
155C22⋊D61—42no—
156C22⋊D61—42no—
157C22⋊D61—42no—
158C22⋊D61—42no—
159C22⋊D61—81no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61C2×D411yescharacteristic
163C2×Dic61C2×D411yescharacteristic
164D244—22no—
165D244—21no—
166D244—21no—
167D244—42no—
168D244C2×D412yes—
169D244C2×D412yescomplemented
170C4×D61—21no—
171C4×D61—21no—
172C4×D61—21no—
173C4×D61—21no—
174C4×D61—42no—
175C4×D61—42no—
176C4×D61—81no—
177C8×C61—21no—
178C8×C61C2×D412yescomplemented
179#92418—21no—
180#92418—21no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61C22×D411yescharacteristic
191C2×D61—21no—
192C2×D61—21no—
193C2×D61—21no—
194C2×D61—22no—
195C2×D61—22no—
196C2×D61—21no—
197C2×D61—21no—
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×C61C22×D411yescharacteristic
210C4×C61H(5,𝔽2)11yescharacteristic
211Dic61—21no—
212Dic61—21no—
213Dic61—41no—
214Dic61—41no—
215#3264—611nomaximal, Sylow
216C2×C61—81no—
217C2×C61—81no—
218C2×C61—81no—
219C2×C61D4211yescharacteristic
220C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
221C2×C61#57611yescharacteristic
222D61—22no—
223D61—41no—
224D61—42no—
225D61—42no—
226C2×AGL(1,ℤ/8)—611no—
227C22×D8—611no—
228#546—611no—
229D42—611no—
230#496D6111yescharacteristic, complemented
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#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×SD16C2×D6111yescharacteristic, complemented
250C2×SD16C2×D6111yescharacteristic, complemented
251C2×D8—611no—
252C2×D8—611no—
253C2×D8—611no—
254C2×D8—611no—
255C2×D8—1224no—
256C2×D8C2×D6111yescharacteristic, complemented
257C2×D8C2×D6111yescharacteristic, complemented
258C2×M16—611no—
259C22×C8—611no—
260#127C2×D6111yescharacteristic, complemented
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×D4—611no—
275C2×C22⋊C4—1221no—
276#106—611no—
277C4⋊C8—611no—
278#103—611no—
279#102—611no—
280#102—611no—
281#102—611no—
282#102—611no—
283#102—611no—
284C22⋊C8—611no—
285C22⋊C8—611no—
286#97C2×D6111yescharacteristic, complemented
287C24—1221no—
288C24—1221no—
289C24—1221no—
290#41—1222no—
291#41—2441no—
292C2×Q8C22×D6111yescharacteristic
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—611no—
296C2×D4—611no—
297C2×D4—611no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—1222no—
303C2×D4—1222no—
304C2×D4—1222no—
305C2×D4—1221no—
306C2×D4—1221no—
307C2×D4—1221no—
308C2×D4—2441no—
309C2×D4—2441no—
310C2×D4—2441no—
311C2×D4—2444no—
312C2×D4C22×D6111yescharacteristic
313C2×D4C22×D6111yescharacteristic
314C2×D4C22×D6111yescharacteristic
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320SD16—22no—
321SD16—41no—
322SD16—1222no—
323D8—22no—
324D8—41no—
325D8—614no—
326D8—1222no—
327D8—1222no—
328D8—1222no—
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—611no—
338C4⋊C4—1221no—
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—21no—
353C23—611no—
354C23—611no—
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—21no—
372D4—21no—
373D4—21no—
374D4—42no—
375D4—81no—
376D4—612no—
377D4—612no—
378D4—1222no—
379D4—1221no—
380D4—1221no—
381D4—4881no—
382D4—2442no—
383D4—2442no—
384D4—2442no—
385D4—2442no—
386D4—2442no—
387D4—2442no—
388C2×C4—21no—
389C2×C4—611no—
390C2×C4—611no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—4881no—
398C2×C4—2442no—
399C2×C4—2442no—
400C2×C4D4×D6111yescharacteristic
401C2×C4D4×D6111yescharacteristic
402C2×C4C23×D6111yescharacteristic
403C8—21no—
404C8—1221no—
405C8—1221no—
406C8D4×D6112yescomplemented
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—612no—
417C22—1221no—
418C22—1221no—
419C22—1221no—
420C22—1221no—
421C22—1221no—
422C22—1222no—
423C22—1222no—
424C22—4884no—
425C22—4884no—
426C22—4884no—
427C22—2441no—
428C22—2441no—
429C22—2441no—
430C22—2441no—
431C22C2×D4×D6111yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—1221no—
436C4—1221no—
437C4—2441no—
438C4—2441no—
439C4C2×D4×D6111yescharacteristic
440C4#1451982211yescharacteristic
441C2—81no—
442C2—81no—
443C2—81no—
444C2—1222no—
445C2—2441no—
446C2—2442no—
447C2—2442no—
448C2#1684039711yescharacteristic
449C2AGL(1,ℤ/8)×D6111yescharacteristic
450C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3264
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. C2×D8×D61C2semidirect
3. #16840405C2semidirect
4. #16840397C2semidirect
5. #16840012C2semidirect
6. #16839988C2semidirect
7. #16839974C2semidirect
8. #16839954C2semidirect
9. #16839911C2semidirect
10. #16839906C2semidirect
11. #16839894C2semidirect
12. #16839894C2semidirect
13. #16839875C2semidirect
14. #16839835C2semidirect
15. C61×#496C2semidirect
16. C2×#11758226C22semidirect
19. C2×D4×D61C22semidirect
20. C2×D4×D61C22semidirect
22. C2×#11758201C22semidirect
25. C2×#11758199C22semidirect
26. C2×#11758199C22semidirect
28. C2×#11758189C22semidirect
29. C2×C8×D61C22semidirect
31. #14519753C22semidirect
35. #14519748C22semidirect
36. #14519748C22semidirect
41. C4×D244C22semidirect
42. C4×D244C22semidirect
44. #14519709C22semidirect
45. C4⋊#92418C22semidirect
46. #14519701C22semidirect
47. #14519699C22semidirect
48. #14519699C22semidirect
49. #14519698C22semidirect
50. #14519698C22semidirect
51. #14519698C22semidirect
52. #14519689C22semidirect
53. #14519689C22semidirect
54. C2×SD16×C61C22semidirect
55. C2×SD16×C61C22semidirect
56. C2×D8×C61C22semidirect
57. C2×D8×C61C22semidirect
58. #127×C61C22semidirect
59. #124×C61C22semidirect
60. #97×C61C22semidirect
121. D488D4semidirect
169. D244C2×D4semidirect
178. C8×C61C2×D4semidirect
205. C2×D61AGL(1,ℤ/8)semidirect
230. #496D61semidirect
241. C61#3264semidirect
249. C2×SD16C2×D61semidirect
250. C2×SD16C2×D61semidirect
256. C2×D8C2×D61semidirect
257. C2×D8C2×D61semidirect
260. #127C2×D61semidirect
261. #124C2×D61semidirect
286. #97C2×D61semidirect
406. C8D4×D61semidirect