Finite Group Databasebeta

← #21457967

Subgroups — #21457967

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#16840462C211yesmaximal, characteristic, complemented
2#16840397C211yesmaximal, characteristic, complemented
3#16840126C211yesmaximal, characteristic, complemented
4#16840084C211yesmaximal, characteristic, complemented
5#16840079C211yesmaximal, characteristic, complemented
6#16840063C211yesmaximal, characteristic, complemented
7#16840012C211yesmaximal, characteristic, complemented
8#16839995C211yesmaximal, characteristic, complemented
9#16839894C211yesmaximal, characteristic, complemented
10#16839894C211yesmaximal, characteristic, complemented
11#16839872C211yesmaximal, characteristic, complemented
12#16839832C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#459C211yesmaximal, characteristic, complemented
16C2×D4×D61—21no—
17C2×D4×D61C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758189C2211yescharacteristic, complemented
21C2×C8×D61C2211yescharacteristic, complemented
22#14519770—21no—
23#14519769C2211yescharacteristic, complemented
24#14519760—21no—
25#14519750—21no—
26#14519748—21no—
27#14519748C2211yescharacteristic
28#14519748C2211yescharacteristic
29#14519748C2211yescharacteristic, complemented
30#14519748C2211yescharacteristic, complemented
31#14519745—21no—
32#14519745—21no—
33C4×D244C2211yescharacteristic
34C4×D244C2211yescharacteristic
35C4×C22⋊D61—21no—
36#14519735C2211yescharacteristic, complemented
37C4⋊C4×D61C2211yescharacteristic, complemented
38#14519711C2211yescharacteristic, complemented
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519699C2211yescharacteristic
42#14519699C2211yescharacteristic
43#14519698C2211yescharacteristic, complemented
44#14519698C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic, complemented
46#14519698C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51#14519688C2211yescharacteristic, complemented
52C2×D8×C61C2211yescharacteristic, complemented
53C2×D8×C61C2211yescharacteristic, complemented
54#127×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic, complemented
56C4⋊C8×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61—21no—
61C2×D4×C61—21no—
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73D4×D61—22no—
74D4×D61—22no—
75D4×D61—41no—
76D4×D61—41no—
77D4×D61—44no—
78C2×D244D411yescharacteristic
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61C2311yescharacteristic
83C2×C4×D61C2311yescharacteristic
84D8×C61—41no—
85D8×C61—41no—
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C42×C61C2311yescharacteristic
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95#11758199—22no—
96#11758198—21no—
97#11758198—21no—
98#11758198D411yescharacteristic
99#11758198D411yescharacteristic
100C4⋊Dic61D411yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103C4⋊Dic61C2311yescharacteristic
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107C4×Dic61—21no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758189—41no—
111C8×D61—41no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—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—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129D4×C61—21no—
130D4×C61—42no—
131D4×C61—81no—
132C2×C4×C61—21no—
133C2×C4×C61—81no—
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2411yescharacteristic
137C22⋊D61—42no—
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—42no—
141C22⋊D61—42no—
142C22⋊D61—81no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61C2×D411yescharacteristic
147C2×Dic61C2×D411yescharacteristic
148D244—22no—
149D244—21no—
150D244#4112yes—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—42no—
156C4×D61—81no—
157C8×C61—21no—
158C8×C61—21no—
159#92418—21no—
160#92418—21no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61C22×D411yescharacteristic
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—22no—
175C2×D61—21no—
176C2×D61—21no—
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×C61C2×#4111yescharacteristic
186C4×C61H(5,𝔽2)11yescharacteristic
187Dic61—21no—
188Dic61—21no—
189Dic61—41no—
190Dic61—41no—
191Dic61—41no—
192#3318—611nomaximal, Sylow
193C2×C61—81no—
194C2×C61—81no—
195C2×C61—81no—
196C2×C61#54611yescharacteristic
197C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C61#57611yescharacteristic
199D61—22no—
200D61—41no—
201D61—42no—
202#553—611no—
203D42—611no—
204#490—611no—
205#482—611no—
206#481—611no—
207#478—611no—
208#469—611no—
209#466—611no—
210#459D6111yescharacteristic, complemented
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×D8C2×D6111yescharacteristic, complemented
223C2×D8C2×D6111yescharacteristic, complemented
224C2×M16—611no—
225C22×C8—611no—
226#127C2×D6111yescharacteristic
227#126—1221no—
228#125—611no—
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, complemented
242#117—611no—
243C2×C4⋊C4—611no—
244#107—611no—
245#106—611no—
246#106—611no—
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, complemented
257#102C2×D6111yescharacteristic, complemented
258C22⋊C8—611no—
259C22⋊C8—611no—
260#97—611no—
261C24—1221no—
262C24—1221no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—611no—
266C2×D4—611no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1222no—
270C2×D4—1222no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—2441no—
276C2×D4—2441no—
277C2×D4—2444no—
278C2×D4C22×D6111yescharacteristic
279C2×D4C22×D6111yescharacteristic
280C2×D4C22×D6111yescharacteristic
281C22×C4—21no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—1221no—
285C22×C4—1221no—
286D8—41no—
287D8—41no—
288D8—1222no—
289M16—2441no—
290C2×C8—611no—
291C2×C8—611no—
292C2×C8—2441no—
293C2×C8C22×D6111yescharacteristic
294C2×C8C22×D6111yescharacteristic
295C4⋊C4—611no—
296C4⋊C4—611no—
297C4⋊C4—611no—
298C4⋊C4—611no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
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—21no—
316C23—21no—
317C23—611no—
318C23—611no—
319C23—1221no—
320C23—4881no—
321C23—4881no—
322C23—2442no—
323C23—2442no—
324C23—2442no—
325C23—2442no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—612no—
335D4—1222no—
336D4—1221no—
337D4—4881no—
338D4—2442no—
339D4—2442no—
340D4—2442no—
341D4—2442no—
342D4—2442no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—4881no—
355C2×C4—2442no—
356C2×C4D4×D6111yescharacteristic
357C2×C4D4×D6111yescharacteristic
358C2×C4C23×D6111yescharacteristic
359C8—21no—
360C8—21no—
361C8—1221no—
362C8—1221no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—612no—
373C22—1221no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—1221no—
378C22—1222no—
379C22—4884no—
380C22—4884no—
381C22—2441no—
382C22—2441no—
383C22C2×D4×D6111yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—1221no—
388C4—1221no—
389C4—2441no—
390C4—2441no—
391C4—2441no—
392C4#41×D6111yescharacteristic
393C4#1451982211yescharacteristic
394C2—81no—
395C2—81no—
396C2—81no—
397C2—1222no—
398C2—2441no—
399C2—2442no—
400C2#1684040911yescharacteristic
401C2AGL(1,ℤ/8)×D6111yescharacteristic
402C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3318
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16840462C2semidirect
2. #16840397C2semidirect
3. #16840126C2semidirect
4. #16840084C2semidirect
5. #16840079C2semidirect
6. #16840063C2semidirect
7. #16840012C2semidirect
8. #16839995C2semidirect
9. #16839894C2semidirect
10. #16839894C2semidirect
11. #16839872C2semidirect
12. #16839832C2semidirect
13. #16839765C2semidirect
14. #102×D61C2semidirect
15. C61×#459C2semidirect
20. C2×#11758189C22semidirect
21. C2×C8×D61C22semidirect
23. #14519769C22semidirect
29. #14519748C22semidirect
30. #14519748C22semidirect
36. #14519735C22semidirect
37. C4⋊C4×D61C22semidirect
38. #14519711C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
43. #14519698C22semidirect
44. #14519698C22semidirect
45. #14519698C22semidirect
46. #14519698C22semidirect
47. #14519698C22semidirect
49. #14519689C22semidirect
50. #14519689C22semidirect
51. #14519688C22semidirect
52. C2×D8×C61C22semidirect
53. C2×D8×C61C22semidirect
55. C4×D4×C61C22semidirect
56. C4⋊C8×C61C22semidirect
57. #102×C61C22semidirect
58. #102×C61C22semidirect
210. #459D61semidirect
217. C61#3318semidirect
222. C2×D8C2×D61semidirect
223. C2×D8C2×D61semidirect
241. C4×D4C2×D61semidirect
247. C4⋊C8C2×D61semidirect
256. #102C2×D61semidirect
257. #102C2×D61semidirect