Finite Group Databasebeta

← #21457436

Subgroups — #21457436

Order 7808.

556 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519805C211yesmaximal, characteristic, complemented
2C2×#14519801C211yesmaximal, characteristic, complemented
3#16840430C211yesmaximal, characteristic, complemented
4#16840396C211yesmaximal, characteristic, complemented
5#16840137C211yesmaximal, characteristic, complemented
6#16840016C211yesmaximal, characteristic, complemented
7#16839961C211yesmaximal, characteristic, complemented
8#16839956C211yesmaximal, characteristic, complemented
9#16839908C211yesmaximal, characteristic, complemented
10#16839905C211yesmaximal, characteristic, complemented
11#16839897C211yesmaximal, characteristic, complemented
12#16839895C211yesmaximal, characteristic, complemented
13#16839849C211yesmaximal, characteristic, complemented
14#16839838C211yesmaximal, characteristic, complemented
15C61×#469C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic, complemented
17C2×#11758224C2211yescharacteristic, complemented
18C22×D244C2211yescharacteristic
19C2×D4×D61—21no—
20C2×D4×D61C2211yescharacteristic
21#14519805—24no—
22#14519801—24no—
23C2×#11758190C2211yescharacteristic
24C2×#11758190C2211yescharacteristic, complemented
25C2×#11758200C2211yescharacteristic, complemented
26C2×D488C2211yescharacteristic
27C2×D488C2211yescharacteristic, complemented
28C2×#11758199C2211yescharacteristic
29C2×#11758199C2211yescharacteristic, complemented
30C2×#11758199C2211yescharacteristic, complemented
31C2×#11758189C2211yescharacteristic, complemented
32#14519773—21no—
33#14519773C2211yescharacteristic
34#14519773C2211yescharacteristic, complemented
35#14519752C2211yescharacteristic
36#14519752C2211yescharacteristic, complemented
37#14519750—21no—
38#14519750—21no—
39#14519749—21no—
40#14519747—21no—
41#14519745—21no—
42#14519742C2211yescharacteristic, complemented
43#14519739C2211yescharacteristic
44C4×C22⋊D61C2211yescharacteristic
45#14519737—21no—
46#14519706C2211yescharacteristic, complemented
47#14519700C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic, complemented
50#14519697C2211yescharacteristic, complemented
51C22⋊#92418C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53C8×Dic61C2211yescharacteristic, complemented
54C2×D8×C61C2211yescharacteristic, complemented
55C2×M16×C61C2211yescharacteristic, complemented
56#121×C61C2211yescharacteristic
57#121×C61C2211yescharacteristic, complemented
58#106×C61C2211yescharacteristic, complemented
59#102×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63C2×D4×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61D411yescharacteristic
76C22×Dic61—21no—
77#11758224—22no—
78#11758224—41no—
79D4×D61—22no—
80D4×D61—41no—
81D4×D61—44no—
82#11758222—22no—
83#11758222—41no—
84C2×D244—22no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—41no—
89C2×D244C2311yescharacteristic
90C2×D244C2311yescharacteristic
91C2×D244C2311yescharacteristic
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61C2311yescharacteristic
95C2×Dic122C2311yescharacteristic
96D8×C61—22no—
97M16×C61—22no—
98C2×C8×C61C2311yescharacteristic
99C2×C8×C61C2311yescharacteristic
100C4⋊C4×C61C2311yescharacteristic
101C4⋊C4×C61C2311yescharacteristic
102C22⋊C4×C61—21no—
103C22⋊C4×C61—21no—
104C22⋊Dic61D411yescharacteristic
105#11758200—22no—
106#11758199—22no—
107#11758199—41no—
108#11758199—41no—
109#11758198—21no—
110#11758198—21no—
111#11758198—21no—
112#11758198D411yescharacteristic
113#11758196—21no—
114#11758196D411yescharacteristic
115C4×Dic61—21no—
116C4×Dic61C2311yescharacteristic
117C2×#92418C2311yescharacteristic
118C2×#92418C2311yescharacteristic
119D488—22no—
120D488—22no—
121#11758190—22no—
122#11758190D414yescomplemented
123#11758189—22no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61C2×D411yescharacteristic
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—42no—
133C22×D61—42no—
134C22×D61—81no—
135C22×D61—81no—
136C22×D61C2×D411yescharacteristic
137D4×C61—21no—
138D4×C61—21no—
139D4×C61—21no—
140D4×C61—21no—
141D4×C61—42no—
142D4×C61—81no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61C2×D411yescharacteristic
148C2×C4×C61C2411yescharacteristic
149C22⋊D61—22no—
150C22⋊D61—42no—
151C22⋊D61—42no—
152C22⋊D61—42no—
153C22⋊D61—42no—
154C22⋊D61—42no—
155C22⋊D61—81no—
156C22⋊D61—81no—
157C2×Dic61—21no—
158C2×Dic61—42no—
159C2×Dic61C2×D411yescharacteristic
160C2×Dic61C2×D411yescharacteristic
161C2×Dic61C2×D411yescharacteristic
162D244—21no—
163D244—21no—
164D244—21no—
165D244—21no—
166D244—21no—
167D244—42no—
168D244—42no—
169D244—81no—
170D244C2×D412yes—
171C4×D61—21no—
172C4×D61—21no—
173C4×D61—42no—
174C4×D61—42no—
175Dic122—21no—
176Dic122C2×D412yescomplemented
177C8×C61—21no—
178C8×C61C2×D412yescomplemented
179#92418—21no—
180#92418—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
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—22no—
193C2×D61—21no—
194C2×D61—21no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—84no—
204C2×D61—84no—
205C4×C61—21no—
206C4×C61—41no—
207C4×C61—41no—
208C4×C61C22×D411yescharacteristic
209C4×C61H(5,𝔽2)11yescharacteristic
210Dic61—22no—
211Dic61—21no—
212Dic61—21no—
213Dic61AGL(1,ℤ/8)12yescomplemented
214#3274—611nomaximal, Sylow
215C2×C61—41no—
216C2×C61—81no—
217C2×C61—81no—
218C2×C61D4211yescharacteristic
219C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C61#57611yescharacteristic
221D61—41no—
222D61—42no—
223D61—81no—
224D61—81no—
225C2×AGL(1,ℤ/8)—611no—
226C2×AGL(1,ℤ/8)—611no—
227#550—611no—
228D42—611no—
229#493—611no—
230#469—611no—
231#469D6111yescharacteristic, complemented
232#460—611no—
233#459—611no—
234#449—611no—
235#449—611no—
236#447—611no—
237#447—611no—
238C4×SD16—611no—
239#436—611no—
240C61#327411yescharacteristic, complemented, Sylow
241C2×#41—611no—
242C2×#41—611no—
243C22×D4—611no—
244C22×D4—611no—
245C22×D4—1221no—
246AGL(1,ℤ/8)—1224no—
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×D8C2×D6111yescharacteristic, complemented
257C2×M16—611no—
258C2×M16C2×D6111yescharacteristic, complemented
259#127—611no—
260#127—611no—
261#127—1221no—
262#121—611no—
263#121—611no—
264#121—1221no—
265#121—1221no—
266#121—1221no—
267#121C2×D6111yescharacteristic
268#121C2×D6111yescharacteristic, complemented
269#120—1221no—
270#120—1221no—
271C4×Q8—611no—
272C4×D4—611no—
273C4×D4—611no—
274C4×D4—1221no—
275#106C2×D6111yescharacteristic, complemented
276C4⋊C8—611no—
277#103—611no—
278#102—611no—
279#102—611no—
280#102—611no—
281#102C2×D6111yescharacteristic, complemented
282#102C2×D6111yescharacteristic, complemented
283C22⋊C8—611no—
284C22⋊C8—611no—
285C4×C8—611no—
286C24—1221no—
287C24—1221no—
288#41—1222no—
289#41—1222no—
290#41—2441no—
291#41—2441no—
292C2×Q8—611no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—611no—
296C2×D4—611no—
297C2×D4—611no—
298C2×D4—611no—
299C2×D4—1222no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—1221no—
303C2×D4—1221no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4—1221no—
307C2×D4—1222no—
308C2×D4—1221no—
309C2×D4—1221no—
310C2×D4—1221no—
311C2×D4—2441no—
312C2×D4—2441no—
313C2×D4—2444no—
314C2×D4C22×D6111yescharacteristic
315C2×D4C22×D6111yescharacteristic
316C22×C4—611no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4C22×D6111yescharacteristic
321SD16—614no—
322SD16—1222no—
323SD16—1222no—
324D8—22no—
325D8—1222no—
326D8—1222no—
327D8—1222no—
328D8—2441no—
329D8—2441no—
330M16—22no—
331M16—1222no—
332C2×C8—611no—
333C2×C8—611no—
334C2×C8C22×D6111yescharacteristic
335C2×C8C22×D6111yescharacteristic
336C4⋊C4—611no—
337C4⋊C4—1221no—
338C4⋊C4C22×D6111yescharacteristic
339C4⋊C4C22×D6111yescharacteristic
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—611no—
343C22⋊C4—611no—
344C22⋊C4—1221no—
345C22⋊C4—1221no—
346C22⋊C4—1221no—
347C42—611no—
348C42—1221no—
349C23—21no—
350C23—21no—
351C23—611no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23—4881no—
356C23—4881no—
357C23—2442no—
358C23—2442no—
359C23—2442no—
360C23—2442no—
361C23D4×D6111yescharacteristic
362Q8—612no—
363Q8—1221no—
364D4—21no—
365D4—21no—
366D4—21no—
367D4—21no—
368D4—42no—
369D4—81no—
370D4—612no—
371D4—1222no—
372D4—1221no—
373D4—1221no—
374D4—1221no—
375D4—1221no—
376D4—1221no—
377D4—4881no—
378D4—4881no—
379D4—4881no—
380D4—2442no—
381D4—2442no—
382D4—2442no—
383D4—2442no—
384D4—2442no—
385D4—2442no—
386D4—2442no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—611no—
392C2×C4—611no—
393C2×C4—611no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—2442no—
398C2×C4—2442no—
399C2×C4—2442no—
400C2×C4D4×D6111yescharacteristic
401C2×C4C23×D6111yescharacteristic
402C8—21no—
403C8—1221no—
404C8—1221no—
405C8D4×D6112yescomplemented
406C22—21no—
407C22—21no—
408C22—21no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—1221no—
416C22—1221no—
417C22—1221no—
418C22—1222no—
419C22—4884no—
420C22—4884no—
421C22—2441no—
422C22—2441no—
423C22—2441no—
424C22—2441no—
425C22—2441no—
426C22—2441no—
427C22—2441no—
428C22—2441no—
429C22C2×D4×D6111yescharacteristic
430C4—21no—
431C4—41no—
432C4—41no—
433C4—612no—
434C4—1221no—
435C4—1221no—
436C4—1222no—
437C4C2×D4×D6111yescharacteristic
438C4#1451982311yescharacteristic
439C2—41no—
440C2—81no—
441C2—81no—
442C2—4881no—
443C2—4881no—
444C2—2441no—
445C2—2442no—
446C2#1684039611yescharacteristic
447C2AGL(1,ℤ/8)×D6111yescharacteristic
448C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#469C2
socleC22×C61C22×D4
hypercenter#469D61
hypocenterC61#3274
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#14519805C2semidirect
2. C2×#14519801C2semidirect
3. #16840430C2semidirect
4. #16840396C2semidirect
5. #16840137C2semidirect
6. #16840016C2semidirect
7. #16839961C2semidirect
8. #16839956C2semidirect
9. #16839908C2semidirect
10. #16839905C2semidirect
11. #16839897C2semidirect
12. #16839895C2semidirect
13. #16839849C2semidirect
14. #16839838C2semidirect
15. C61×#469C2semidirect
16. C2×#11758222C22semidirect
17. C2×#11758224C22semidirect
24. C2×#11758190C22semidirect
25. C2×#11758200C22semidirect
27. C2×D488C22semidirect
29. C2×#11758199C22semidirect
30. C2×#11758199C22semidirect
31. C2×#11758189C22semidirect
34. #14519773C22semidirect
36. #14519752C22semidirect
42. #14519742C22semidirect
46. #14519706C22semidirect
47. #14519700C22semidirect
49. #14519697C22semidirect
50. #14519697C22semidirect
51. C22⋊#92418C22semidirect
52. #14519689C22semidirect
53. C8×Dic61C22semidirect
54. C2×D8×C61C22semidirect
55. C2×M16×C61C22semidirect
57. #121×C61C22semidirect
58. #106×C61C22semidirect
59. #102×C61C22semidirect
60. #102×C61C22semidirect
122. #11758190D4semidirect
176. Dic122C2×D4semidirect
178. C8×C61C2×D4semidirect
213. Dic61AGL(1,ℤ/8)semidirect
231. #469D61semidirect
240. C61#3274semidirect
256. C2×D8C2×D61semidirect
258. C2×M16C2×D61semidirect
268. #121C2×D61semidirect
275. #106C2×D61semidirect
281. #102C2×D61semidirect
282. #102C2×D61semidirect
405. C8D4×D61semidirect