Finite Group Databasebeta

← #21457303

Subgroups — #21457303

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
2C22×#11758199C211yesmaximal, characteristic, complemented
3#16840403C211yesmaximal, characteristic, complemented
4D4×C22⋊D61C211yesmaximal, characteristic, complemented
5#16840148C211yesmaximal, characteristic, complemented
6#16840014C211yesmaximal, characteristic, complemented
7#16839993C211yesmaximal, characteristic, complemented
8#16839979C211yesmaximal, characteristic, complemented
9#16839956C211yesmaximal, characteristic, complemented
10#16839906C211yesmaximal, characteristic, complemented
11#16839898C211yesmaximal, characteristic, complemented
12#16839897C211yesmaximal, characteristic, complemented
13#16839871C211yesmaximal, characteristic, complemented
14#16839830C211yesmaximal, characteristic, complemented
15C61×#450C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic, complemented
17C22×D244C2211yescharacteristic, complemented
18C22×C22⋊D61—21no—
19C2×D4×D61C2211yescharacteristic, complemented
20#14519804—24no—
21C2×#11758201C2211yescharacteristic, complemented
22C2×D488C2211yescharacteristic, complemented
23C2×D488C2211yescharacteristic, complemented
24C2×#11758199—24no—
25C2×#11758199C2211yescharacteristic
26C2×#11758199C2211yescharacteristic
27C2×#11758199C2211yescharacteristic, complemented
28C2×#11758199C2211yescharacteristic, complemented
29C2×#11758189C2211yescharacteristic, complemented
30C22×#92418C2211yescharacteristic, complemented
31#14519773C2211yescharacteristic, complemented
32#14519766C2211yescharacteristic, complemented
33#14519762—21no—
34#14519752—21no—
35#14519752C2211yescharacteristic, complemented
36#14519751C2211yescharacteristic
37#14519749—21no—
38#14519748C2211yescharacteristic, complemented
39#14519747—21no—
40#14519746—21no—
41#14519745—21no—
42D4×Dic61C2211yescharacteristic, complemented
43#14519739C2211yescharacteristic, complemented
44C4×C22⋊D61C2211yescharacteristic
45C22⋊C4×D61—21no—
46#14519708C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519701C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic, complemented
50#14519699C2211yescharacteristic, complemented
51#14519697C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53#14519687C2211yescharacteristic, complemented
54C22×D4×C61C2211yescharacteristic
55C2×SD16×C61C2211yescharacteristic, complemented
56C2×SD16×C61C2211yescharacteristic, complemented
57C22⋊Q8×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic, complemented
59#102×C61C2211yescharacteristic, complemented
60C22⋊C8×C61C2211yescharacteristic, complemented
61C24×C61—21no—
62C23×D61—21no—
63C23×D61—21no—
64C2×Q8×C61C2311yescharacteristic
65C2×D4×C61—22no—
66C2×D4×C61—21no—
67C2×D4×C61—41no—
68C2×D4×C61C2311yescharacteristic
69C2×D4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61—44no—
77C2×C22⋊D61D411yescharacteristic
78C22×Dic61—21no—
79#11758226—22no—
80#11758226—41no—
81D4×D61—22no—
82D4×D61—41no—
83C2×D244—22no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—41no—
88C2×D244C2311yescharacteristic
89C2×D244C2311yescharacteristic
90C2×D244C2311yescharacteristic
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61C2311yescharacteristic
94SD16×C61—22no—
95SD16×C61—41no—
96C2×C8×C61C2311yescharacteristic
97C2×C8×C61C2311yescharacteristic
98C4⋊C4×C61—21no—
99C4⋊C4×C61C2311yescharacteristic
100C22⋊C4×C61—21no—
101C22⋊Dic61—21no—
102C22⋊Dic61—21no—
103C22⋊Dic61D411yescharacteristic
104#11758201—22no—
105#11758199—22no—
106#11758199—22no—
107#11758199—22no—
108#11758199D414yescomplemented
109#11758198—21no—
110#11758198—21no—
111#11758198—21no—
112#11758198—21no—
113#11758198—21no—
114#11758198D411yescharacteristic
115C4⋊Dic61C2311yescharacteristic
116#11758196D411yescharacteristic
117C4×Dic61C2311yescharacteristic
118C2×#92418—22no—
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121D488—22no—
122D488—41no—
123#11758189—22no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—42no—
127C23×C61—42no—
128C23×C61—81no—
129C23×C61C2×D411yescharacteristic
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—42no—
134C22×D61—42no—
135C22×D61—42no—
136C22×D61—42no—
137C22×D61—81no—
138C22×D61—81no—
139C22×D61C2×D411yescharacteristic
140Q8×C61—21no—
141Q8×C61—21no—
142D4×C61—21no—
143D4×C61—21no—
144D4×C61—21no—
145D4×C61—42no—
146D4×C61C2×D412yes—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61C2×D411yescharacteristic
152C2×C4×C61C2411yescharacteristic
153C22⋊D61—22no—
154C22⋊D61—42no—
155C22⋊D61—42no—
156C22⋊D61—42no—
157C22⋊D61—42no—
158C22⋊D61—81no—
159C2×Dic61—21no—
160C2×Dic61—42no—
161C2×Dic61C2×D411yescharacteristic
162C2×Dic61C2×D411yescharacteristic
163C2×Dic61C2×D411yescharacteristic
164D244—21no—
165D244—21no—
166D244—21no—
167D244—21no—
168D244—21no—
169D244—42no—
170D244—42no—
171D244—81no—
172D244C2×D412yescomplemented
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—21no—
182C22×C61—21no—
183C22×C61—22no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—84no—
190C22×C61AGL(1,ℤ/8)12yescomplemented
191C22×C61C22×D411yescharacteristic
192C2×D61—21no—
193C2×D61—22no—
194C2×D61—21no—
195C2×D61—21no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—84no—
205C2×D61—84no—
206C4×C61—21no—
207C4×C61—41no—
208C4×C61—41no—
209C4×C61C22×D411yescharacteristic
210C4×C61H(5,𝔽2)11yescharacteristic
211Dic61—21no—
212Dic61—21no—
213Dic61—21no—
214Dic61—41no—
215#3264—611nomaximal, Sylow
216C2×C61—22no—
217C2×C61—42no—
218C2×C61—81no—
219C2×C61D4211yescharacteristic
220C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
221C2×C61#57611yescharacteristic
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#463—611no—
234#459—611no—
235#450D6111yescharacteristic, complemented
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—1221no—
246C22×D4C2×D6111yescharacteristic
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—611no—
256C2×D8—611no—
257C2×D8—1224no—
258C2×M16—611no—
259C22×C8—611no—
260#127—611no—
261#124—611no—
262#123—1221no—
263C22⋊Q8C2×D6111yescharacteristic, complemented
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#102C2×D6111yescharacteristic, complemented
283#102C2×D6111yescharacteristic, complemented
284C22⋊C8—611no—
285C22⋊C8C2×D6111yescharacteristic, complemented
286#97—611no—
287C24—21no—
288C24—1221no—
289C24—1221no—
290#41—1222no—
291#41—2441no—
292C2×Q8C22×D6111yescharacteristic
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—611no—
297C2×D4—611no—
298C2×D4—611no—
299C2×D4—611no—
300C2×D4—1222no—
301C2×D4—1221no—
302C2×D4—1221no—
303C2×D4—1221no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4—1222no—
307C2×D4—1221no—
308C2×D4—1221no—
309C2×D4—1221no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2444no—
313C2×D4C22×D6111yescharacteristic
314C2×D4C22×D6111yescharacteristic
315C22×C4—611no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4C22×D6111yescharacteristic
320SD16—22no—
321SD16—41no—
322SD16—1222no—
323D8—614no—
324D8—1222no—
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—21no—
336C4⋊C4—611no—
337C4⋊C4—611no—
338C4⋊C4C22×D6111yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—611no—
341C22⋊C4—611no—
342C22⋊C4—1221no—
343C22⋊C4—1221no—
344C22⋊C4—1221no—
345C22⋊C4—1221no—
346C22⋊C4—1221no—
347C22⋊C4—1221no—
348C22⋊C4—1221no—
349C42—611no—
350C23—21no—
351C23—21no—
352C23—42no—
353C23—42no—
354C23—81no—
355C23—611no—
356C23—1221no—
357C23—1221no—
358C23—1221no—
359C23—4881no—
360C23—4881no—
361C23—2442no—
362C23—2442no—
363C23—2442no—
364C23—2442no—
365C23D4×D6111yescharacteristic
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—42no—
372D4—612no—
373D4—1222no—
374D4—1221no—
375D4—1221no—
376D4—1221no—
377D4—1221no—
378D4—1221no—
379D4—4881no—
380D4—4881no—
381D4—2442no—
382D4—2442no—
383D4—2442no—
384D4—2442no—
385D4—2442no—
386D4—2442no—
387D4D4×D6112yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—611no—
393C2×C4—611no—
394C2×C4—611no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—4881no—
399C2×C4—2442no—
400C2×C4—2442no—
401C2×C4D4×D6111yescharacteristic
402C2×C4C23×D6111yescharacteristic
403C8—21no—
404C8—21no—
405C8—612no—
406C8—1221no—
407C22—21no—
408C22—21no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—84no—
416C22—1221no—
417C22—1221no—
418C22—1221no—
419C22—1222no—
420C22—4884no—
421C22—4884no—
422C22—2441no—
423C22—2441no—
424C22—2441no—
425C22—2441no—
426C22—2441no—
427C22—2441no—
428C22—2441no—
429C22—2441no—
430C22#1451980412yescomplemented
431C22C2×D4×D6111yescharacteristic
432C4—21no—
433C4—41no—
434C4—41no—
435C4—1221no—
436C4—1221no—
437C4—1221no—
438C4—2441no—
439C4C2×D4×D6111yescharacteristic
440C4#1451982211yescharacteristic
441C2—22no—
442C2—42no—
443C2—81no—
444C2—4881no—
445C2—4881no—
446C2—2441no—
447C2—2442no—
448C2#1684039411yescharacteristic
449C2C2×#1451980411yescharacteristic
450C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3264
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. C22×#11758199C2semidirect
3. #16840403C2semidirect
4. D4×C22⋊D61C2semidirect
5. #16840148C2semidirect
6. #16840014C2semidirect
7. #16839993C2semidirect
8. #16839979C2semidirect
9. #16839956C2semidirect
10. #16839906C2semidirect
11. #16839898C2semidirect
12. #16839897C2semidirect
13. #16839871C2semidirect
14. #16839830C2semidirect
15. C61×#450C2semidirect
16. C2×#11758226C22semidirect
17. C22×D244C22semidirect
19. C2×D4×D61C22semidirect
21. C2×#11758201C22semidirect
22. C2×D488C22semidirect
23. C2×D488C22semidirect
27. C2×#11758199C22semidirect
28. C2×#11758199C22semidirect
29. C2×#11758189C22semidirect
30. C22×#92418C22semidirect
31. #14519773C22semidirect
32. #14519766C22semidirect
35. #14519752C22semidirect
38. #14519748C22semidirect
42. D4×Dic61C22semidirect
43. #14519739C22semidirect
46. #14519708C22semidirect
47. #14519706C22semidirect
48. #14519701C22semidirect
49. #14519699C22semidirect
50. #14519699C22semidirect
51. #14519697C22semidirect
52. #14519689C22semidirect
53. #14519687C22semidirect
55. C2×SD16×C61C22semidirect
56. C2×SD16×C61C22semidirect
57. C22⋊Q8×C61C22semidirect
58. #102×C61C22semidirect
59. #102×C61C22semidirect
60. C22⋊C8×C61C22semidirect
108. #11758199D4semidirect
172. D244C2×D4semidirect
180. #92418C2×D4semidirect
190. C22×C61AGL(1,ℤ/8)semidirect
235. #450D61semidirect
241. C61#3264semidirect
249. C2×SD16C2×D61semidirect
250. C2×SD16C2×D61semidirect
263. C22⋊Q8C2×D61semidirect
282. #102C2×D61semidirect
283. #102C2×D61semidirect
285. C22⋊C8C2×D61semidirect
430. C22#14519804semidirect