Finite Group Databasebeta

← #21457957

Subgroups — #21457957

Order 7808.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840465C211yesmaximal, characteristic, complemented
2D4×D244C211yesmaximal, characteristic, complemented
3#16840128C211yesmaximal, characteristic, complemented
4#16840089C211yesmaximal, characteristic, complemented
5#16840082C211yesmaximal, characteristic, complemented
6#16840016C211yesmaximal, characteristic, complemented
7#16839999C211yesmaximal, characteristic, complemented
8#16839958C211yesmaximal, characteristic, complemented
9#16839897C211yesmaximal, characteristic, complemented
10#16839897C211yesmaximal, characteristic, complemented
11#16839872C211yesmaximal, characteristic, complemented
12#16839832C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#478C211yesmaximal, characteristic, complemented
16C22×D244—21no—
17C2×D4×D61C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19C2×D488C2211yescharacteristic, complemented
20C2×D488C2211yescharacteristic, complemented
21C2×#11758199C2211yescharacteristic
22C2×#11758189C2211yescharacteristic, complemented
23C2×C8×D61C2211yescharacteristic, complemented
24#14519774C2211yescharacteristic
25#14519772—21no—
26#14519762—21no—
27#14519752—21no—
28#14519752C2211yescharacteristic
29#14519752C2211yescharacteristic
30#14519752C2211yescharacteristic, complemented
31#14519752C2211yescharacteristic, complemented
32#14519751—21no—
33#14519747—21no—
34#14519747—21no—
35C4×D244C2211yescharacteristic
36C4×D244C2211yescharacteristic, complemented
37#14519739—21no—
38#14519735C2211yescharacteristic, complemented
39C4⋊C4×D61C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519699C2211yescharacteristic, complemented
42#14519699C2211yescharacteristic, complemented
43#14519698C2211yescharacteristic
44#14519697C2211yescharacteristic, complemented
45#14519697C2211yescharacteristic, complemented
46#14519697C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49#14519689C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51#14519688C2211yescharacteristic, complemented
52#125×C61C2211yescharacteristic, complemented
53C4×D4×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56C4⋊C8×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C23×D61—21no—
60C23×D61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65D4×D61—22no—
66D4×D61—22no—
67D4×D61—41no—
68D4×D61—41no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—44no—
76C2×D244D411yescharacteristic
77C2×D244C2311yescharacteristic
78C2×D244C2311yescharacteristic
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61C2311yescharacteristic
83C2×C4×D61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61C2311yescharacteristic
89C4⋊C4×C61C2311yescharacteristic
90C4⋊C4×C61C2311yescharacteristic
91C22⋊C4×C61—21no—
92C42×C61C2311yescharacteristic
93#11758199—22no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198D411yescharacteristic
101#11758198D411yescharacteristic
102C4⋊Dic61D411yescharacteristic
103C4⋊Dic61C2311yescharacteristic
104#11758196—21no—
105C4×Dic61—21no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108D488—41no—
109D488—41no—
110#11758189—41no—
111C8×D61—41no—
112C23×C61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61—81no—
121C22×D61—81no—
122C22×D61C2×D411yescharacteristic
123C22×D61C2×D411yescharacteristic
124D4×C61—21no—
125D4×C61#4112yes—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—42no—
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2411yescharacteristic
133C22⋊D61—42no—
134C22⋊D61—42no—
135C2×Dic61—21no—
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138D244—22no—
139D244—21no—
140D244—21no—
141D244—21no—
142D244—21no—
143D244—21no—
144D244—21no—
145D244—42no—
146D244—42no—
147D244—42no—
148D244—42no—
149D244—81no—
150D244—81no—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—81no—
156C4×D61—81no—
157C8×C61—21no—
158C8×C61—21no—
159#92418—21no—
160#92418—21no—
161C22×C61—22no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C22×D411yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—84no—
180C2×D61—84no—
181C2×D61AGL(1,ℤ/8)12yes—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61C2×#4111yescharacteristic
188C4×C61H(5,𝔽2)11yescharacteristic
189Dic61—21no—
190Dic61—21no—
191Dic61—41no—
192#3318—611nomaximal, Sylow
193C2×C61—42no—
194C2×C61#54611yescharacteristic
195C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C61#57611yescharacteristic
197D61—22no—
198D61—41no—
199D61—81no—
200D61—81no—
201D61—81no—
202#553—611no—
203D42—611no—
204#490—611no—
205#482—611no—
206#481—611no—
207#478D6111yescharacteristic, complemented
208#469—611no—
209#466—611no—
210#459—611no—
211#447—611no—
212#447—611no—
213#442—611no—
214#435—611no—
215#418—611no—
216C2×#102—611no—
217C61#331811yescharacteristic, complemented, Sylow
218C22×D4—611no—
219C22×D4—611no—
220C22×D4—1221no—
221C2×D8—611no—
222C2×D8—611no—
223C2×D8—611no—
224C2×M16—611no—
225C22×C8—611no—
226#127—611no—
227#126—1221no—
228#125C2×D6111yescharacteristic, complemented
229#123—1221no—
230#121—611no—
231#121—611no—
232#121—611no—
233#121—611no—
234#121—1221no—
235#121—1221no—
236#120—1221no—
237#120—1221no—
238C4×D4—611no—
239C4×D4—611no—
240C4×D4—1221no—
241C4×D4C2×D6111yescharacteristic
242#117—611no—
243C2×C4⋊C4—611no—
244#107C2×D6111yescharacteristic, complemented
245#106—611no—
246#106C2×D6111yescharacteristic, complemented
247C4⋊C8C2×D6111yescharacteristic, complemented
248#102—611no—
249#102—611no—
250#102—611no—
251#102—611no—
252#102—611no—
253#102—611no—
254#102—611no—
255#102—611no—
256#102C2×D6111yescharacteristic
257#102C2×D6111yescharacteristic
258C22⋊C8—611no—
259C22⋊C8—611no—
260#97—611no—
261C24—1221no—
262C24—1221no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4—611no—
266C2×D4—611no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1222no—
274C2×D4—1222no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—2444no—
278C2×D4—2441no—
279C2×D4—2441no—
280C2×D4C22×D6111yescharacteristic
281C22×C4—21no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—1221no—
285C22×C4—1221no—
286D8—1222no—
287D8—2441no—
288D8—2441no—
289M16—2441no—
290C2×C8—611no—
291C2×C8—611no—
292C2×C8—2441no—
293C2×C8C22×D6111yescharacteristic
294C2×C8C22×D6111yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—611no—
298C4⋊C4—611no—
299C4⋊C4—1221no—
300C4⋊C4C22×D6111yescharacteristic
301C4⋊C4C22×D6111yescharacteristic
302C4⋊C4C22×D6111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—611no—
305C22⋊C4—611no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C42—1221no—
313C42C22×D6111yescharacteristic
314C23—21no—
315C23—611no—
316C23—611no—
317C23—1221no—
318C23—1221no—
319C23—1221no—
320C23—4881no—
321C23—4881no—
322C23—2442no—
323C23—2442no—
324C23—2442no—
325C23—2442no—
326D4—21no—
327D4—1222no—
328D4—1221no—
329D4—1221no—
330D4—1221no—
331D4—1221no—
332D4—1221no—
333D4—1221no—
334D4—4881no—
335D4—4881no—
336D4—2442no—
337D4—2442no—
338D4—2442no—
339D4—2442no—
340D4—2442no—
341D4—2442no—
342D4#1175822612yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—4881no—
355C2×C4—4881no—
356C2×C4D4×D6111yescharacteristic
357C2×C4D4×D6111yescharacteristic
358C2×C4C23×D6111yescharacteristic
359C8—21no—
360C8—21no—
361C8—1221no—
362C8—1221no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—612no—
367C22—1221no—
368C22—1221no—
369C22—1221no—
370C22—1221no—
371C22—1221no—
372C22—4884no—
373C22—4884no—
374C22—2441no—
375C22—2441no—
376C22—2441no—
377C22—2441no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22C2×D4×D6111yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—1221no—
390C4—1221no—
391C4—2441no—
392C4C2×#1175822611yescharacteristic
393C4#1451982311yescharacteristic
394C2—42no—
395C2—1222no—
396C2—4881no—
397C2—4881no—
398C2—4881no—
399C2—2441no—
400C2#1684040311yescharacteristic
401C2AGL(1,ℤ/8)×D6111yescharacteristic
402C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#478C2
socleC22×C61C22×D4
hypercenter#478D61
hypocenterC61#3318
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #16840465C2semidirect
2. D4×D244C2semidirect
3. #16840128C2semidirect
4. #16840089C2semidirect
5. #16840082C2semidirect
6. #16840016C2semidirect
7. #16839999C2semidirect
8. #16839958C2semidirect
9. #16839897C2semidirect
10. #16839897C2semidirect
11. #16839872C2semidirect
12. #16839832C2semidirect
13. #16839765C2semidirect
14. #102×D61C2semidirect
15. C61×#478C2semidirect
19. C2×D488C22semidirect
20. C2×D488C22semidirect
22. C2×#11758189C22semidirect
23. C2×C8×D61C22semidirect
30. #14519752C22semidirect
31. #14519752C22semidirect
36. C4×D244C22semidirect
38. #14519735C22semidirect
39. C4⋊C4×D61C22semidirect
40. #14519708C22semidirect
41. #14519699C22semidirect
42. #14519699C22semidirect
44. #14519697C22semidirect
45. #14519697C22semidirect
46. #14519697C22semidirect
47. #14519697C22semidirect
48. #14519697C22semidirect
49. #14519689C22semidirect
50. #14519689C22semidirect
51. #14519688C22semidirect
52. #125×C61C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. C4⋊C8×C61C22semidirect
207. #478D61semidirect
217. C61#3318semidirect
228. #125C2×D61semidirect
244. #107C2×D61semidirect
246. #106C2×D61semidirect
247. C4⋊C8C2×D61semidirect