Finite Group Databasebeta

← #21458054

Subgroups — #21458054

Order 7808.

460 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#16840476C211yesmaximal, characteristic, complemented
2D4×C22⋊D61C211yesmaximal, characteristic, complemented
3#16840107C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840084C211yesmaximal, characteristic, complemented
6#16840050C211yesmaximal, characteristic, complemented
7#16840013C211yesmaximal, characteristic, complemented
8#16840012C211yesmaximal, characteristic, complemented
9#16839955C211yesmaximal, characteristic, complemented
10#16839894C211yesmaximal, characteristic, complemented
11D8×Dic61C211yesmaximal, characteristic, complemented
12#16839837C211yesmaximal, characteristic, complemented
13#16839767C211yesmaximal, characteristic, complemented
14#16839765C211yesmaximal, characteristic, complemented
15C61×#447C211yesmaximal, characteristic, complemented
16C22×C22⋊D61—21no—
17C2×D4×D61C2211yescharacteristic
18C2×#11758199C2211yescharacteristic, complemented
19C2×#11758194C2211yescharacteristic, complemented
20C2×#11758189C2211yescharacteristic, complemented
21#14519776C2211yescharacteristic, complemented
22#14519773C2211yescharacteristic
23#14519764—21no—
24#14519763—21no—
25#14519751C2211yescharacteristic
26#14519749—21no—
27#14519749—21no—
28#14519748C2211yescharacteristic
29#14519748C2211yescharacteristic, complemented
30#14519746—21no—
31#14519745—21no—
32D4×Dic61C2211yescharacteristic
33D4×Dic61C2211yescharacteristic, complemented
34C4×C22⋊D61C2211yescharacteristic
35#14519736C2211yescharacteristic, complemented
36#14519735C2211yescharacteristic, complemented
37#14519733—21no—
38#14519711C2211yescharacteristic, complemented
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519699C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic, complemented
44#14519698C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic, complemented
48#14519698C2211yescharacteristic, complemented
49#14519697C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C2×D8×C61C2211yescharacteristic
54C2×D8×C61C2211yescharacteristic, complemented
55#121×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic, complemented
59C24×C61—21no—
60C23×D61—21no—
61C2×D4×C61—22no—
62C2×D4×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61—41no—
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C2×D4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
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⋊D61—44no—
76C2×C22⋊D61D411yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79D4×D61—22no—
80D4×D61—41no—
81C2×D244C2311yescharacteristic
82C2×C4×D61C2311yescharacteristic
83C2×Dic122—21no—
84D8×C61—22no—
85D8×C61—41no—
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95C22⋊Dic61D411yescharacteristic
96#11758199—41no—
97#11758198—21no—
98#11758198—21no—
99#11758198D411yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196D411yescharacteristic
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108#11758194—41no—
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111#11758189—41no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—42no—
116C23×C61—42no—
117C23×C61—81no—
118C23×C61C2×D411yescharacteristic
119C22×D61—21no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—81no—
123C22×D61C2×D411yescharacteristic
124D4×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129D4×C61—42no—
130D4×C61—81no—
131D4×C61#4112yes—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2411yescharacteristic
137C22⋊D61—22no—
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—42no—
141C22⋊D61—42no—
142C22⋊D61—81no—
143C22⋊D61—81no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61C2×D411yescharacteristic
150C2×Dic61C2×D411yescharacteristic
151C2×Dic61C2×D411yescharacteristic
152D244—21no—
153D244—21no—
154C4×D61—21no—
155C4×D61—21no—
156Dic122—81no—
157C8×C61—21no—
158C8×C61—21no—
159#92418—21no—
160#92418—21no—
161C22×C61—22no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—84no—
174C22×C61C22×D411yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—84no—
182C4×C61—21no—
183C4×C61—41no—
184C4×C61C2×#4111yescharacteristic
185C4×C61H(5,𝔽2)11yescharacteristic
186Dic61—21no—
187Dic61—21no—
188Dic61—41no—
189Dic61—41no—
190Dic61—41no—
191Dic61AGL(1,ℤ/8)12yes—
192#3325—611nomaximal, Sylow
193C2×C61—42no—
194C2×C61—41no—
195C2×C61—81no—
196C2×C61—81no—
197C2×C61#54611yescharacteristic
198C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
199C2×C61#57611yescharacteristic
200D61—41no—
201D61—81no—
202#555—611no—
203D42—611no—
204#486—611no—
205#482—611no—
206#482—611no—
207#476—611no—
208#469—611no—
209#469—611no—
210#459—611no—
211#447—611no—
212#447D6111yescharacteristic, complemented
213C4×D8—611no—
214#436—611no—
215#418—611no—
216#418—611no—
217C61#332511yescharacteristic, complemented, Sylow
218C22×D4—611no—
219C22×D4—1221no—
220C22×D4C2×D6111yescharacteristic
221C2×D8—611no—
222C2×D8C2×D6111yescharacteristic
223C2×D8C2×D6111yescharacteristic, complemented
224C2×M16—611no—
225C2×M16—611no—
226C4⋊Q8—611no—
227#127—611no—
228#124—1221no—
229#124—1221no—
230#121—611no—
231#121—611no—
232#121—611no—
233#121—1221no—
234#121—1221no—
235#121C2×D6111yescharacteristic, complemented
236#120—1221no—
237#120—1221no—
238C4×D4—611no—
239C4×D4—611no—
240C4×D4—611no—
241#117—611no—
242#117—611no—
243#117—1221no—
244#107—611no—
245#106—611no—
246#106—611no—
247C4⋊C8—611no—
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, complemented
258C22⋊C8—611no—
259C22⋊C8C2×D6111yescharacteristic, complemented
260C4×C8—611no—
261C24—21no—
262C24—1221no—
263C2×Q8—1221no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—611no—
269C2×D4—611no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1222no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—2441no—
278C2×D4—2444no—
279C2×D4C22×D6111yescharacteristic
280C2×D4C22×D6111yescharacteristic
281C2×D4C22×D6111yescharacteristic
282C22×C4—611no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4C22×D6111yescharacteristic
286D8—22no—
287D8—41no—
288D8—2441no—
289M16—2441no—
290M16—2441no—
291C2×C8—611no—
292C2×C8—611no—
293C2×C8C22×D6111yescharacteristic
294C2×C8C22×D6111yescharacteristic
295C4⋊C4—611no—
296C4⋊C4—611no—
297C4⋊C4—611no—
298C4⋊C4—611no—
299C4⋊C4—1221no—
300C4⋊C4C22×D6111yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—611no—
303C22⋊C4—611no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C42—611no—
312C42—1221no—
313C42—1221no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—81no—
320C23—611no—
321C23—1221no—
322C23—4881no—
323C23—2442no—
324C23—2442no—
325C23D4×D6111yescharacteristic
326Q8—4881no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—1222no—
335D4—1221no—
336D4—1221no—
337D4—4881no—
338D4—4881no—
339D4—2442no—
340D4—2442no—
341D4—2442no—
342D4—2442no—
343D4#1175822412yes—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4D4×D6111yescharacteristic
358C2×C4C23×D6111yescharacteristic
359C8—21no—
360C8—21no—
361C8—1221no—
362C8—1221no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—84no—
376C22—1221no—
377C22—1221no—
378C22—1221no—
379C22—4884no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22C2×D4×D6111yescharacteristic
384C4—21no—
385C4—41no—
386C4—612no—
387C4—1221no—
388C4—1221no—
389C4—2441no—
390C4—2441no—
391C4—2441no—
392C4C2×#1175822411yescharacteristic
393C4#1451982211yescharacteristic
394C2—41no—
395C2—42no—
396C2—81no—
397C2—81no—
398C2—4881no—
399C2—2441no—
400C2#1684039911yescharacteristic
401C2AGL(1,ℤ/8)×D6111yescharacteristic
402C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#447C2
socleC22×C61C22×D4
hypercenter#447D61
hypocenterC61#3325
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #16840476C2semidirect
2. D4×C22⋊D61C2semidirect
3. #16840107C2semidirect
4. #16840087C2semidirect
5. #16840084C2semidirect
6. #16840050C2semidirect
7. #16840013C2semidirect
8. #16840012C2semidirect
9. #16839955C2semidirect
10. #16839894C2semidirect
11. D8×Dic61C2semidirect
12. #16839837C2semidirect
13. #16839767C2semidirect
14. #16839765C2semidirect
15. C61×#447C2semidirect
18. C2×#11758199C22semidirect
19. C2×#11758194C22semidirect
20. C2×#11758189C22semidirect
21. #14519776C22semidirect
29. #14519748C22semidirect
33. D4×Dic61C22semidirect
35. #14519736C22semidirect
36. #14519735C22semidirect
38. #14519711C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519699C22semidirect
43. #14519699C22semidirect
46. #14519698C22semidirect
47. #14519698C22semidirect
48. #14519698C22semidirect
49. #14519697C22semidirect
50. #14519689C22semidirect
51. C8×Dic61C22semidirect
54. C2×D8×C61C22semidirect
55. #121×C61C22semidirect
57. #102×C61C22semidirect
58. C22⋊C8×C61C22semidirect
212. #447D61semidirect
217. C61#3325semidirect
223. C2×D8C2×D61semidirect
235. #121C2×D61semidirect
257. #102C2×D61semidirect
259. C22⋊C8C2×D61semidirect