Finite Group Databasebeta

← #21457962

Subgroups — #21457962

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#16840458C211yesmaximal, characteristic, complemented
2D4×D244C211yesmaximal, characteristic, complemented
3#16840127C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840081C211yesmaximal, characteristic, complemented
6#16840063C211yesmaximal, characteristic, complemented
7#16840015C211yesmaximal, characteristic, complemented
8#16839998C211yesmaximal, characteristic, complemented
9#16839958C211yesmaximal, characteristic, complemented
10#16839898C211yesmaximal, characteristic, complemented
11#16839898C211yesmaximal, characteristic, complemented
12#16839875C211yesmaximal, characteristic, complemented
13#16839768C211yesmaximal, characteristic, complemented
14C2×#14519699C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C2×D4×D61—21no—
19C2×D488C2211yescharacteristic
20C2×D488C2211yescharacteristic, complemented
21C2×D488C2211yescharacteristic, complemented
22#14519774C2211yescharacteristic
23#14519772—21no—
24#14519769C2211yescharacteristic, complemented
25#14519759—21no—
26#14519752—21no—
27#14519751C2211yescharacteristic
28#14519751C2211yescharacteristic
29#14519751C2211yescharacteristic, complemented
30#14519751C2211yescharacteristic, complemented
31#14519749—21no—
32#14519747—21no—
33#14519747—21no—
34C4×D244C2211yescharacteristic
35C4×D244C2211yescharacteristic, complemented
36#14519737—21no—
37#14519736C2211yescharacteristic, complemented
38C2×C4⋊Dic61C2211yescharacteristic, complemented
39#14519711C2211yescharacteristic, complemented
40#14519709C2211yescharacteristic, complemented
41#14519709C2211yescharacteristic, complemented
42#14519699C2211yescharacteristic
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic, complemented
47#14519699C2211yescharacteristic, complemented
48#14519699C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic, complemented
50#14519699C2211yescharacteristic, complemented
51#14519699C2211yescharacteristic, complemented
52C2×M16×C61C2211yescharacteristic, complemented
53C22×C8×C61C2211yescharacteristic, complemented
54C4×D4×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic, complemented
56C22⋊C8×C61C2211yescharacteristic, complemented
57C22⋊C8×C61C2211yescharacteristic, complemented
58#97×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61—21no—
61C2×D4×C61D411yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C22×Dic61—21no—
69D4×D61—44no—
70C2×D244—22no—
71C2×D244—22no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244C2311yescharacteristic
79C2×D244C2311yescharacteristic
80C2×D244C2311yescharacteristic
81C2×D244C2311yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84M16×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C2×C8×C61C2311yescharacteristic
89C2×C8×C61C2311yescharacteristic
90C4⋊C4×C61D411yescharacteristic
91C22⋊C4×C61D411yescharacteristic
92C22⋊C4×C61D411yescharacteristic
93C42×C61C2311yescharacteristic
94C22⋊Dic61—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61C2311yescharacteristic
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105C4⋊Dic61C2311yescharacteristic
106#11758196—21no—
107#11758196—21no—
108C4×Dic61—21no—
109D488—22no—
110D488—41no—
111D488—41no—
112C23×C61C2×D411yescharacteristic
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—81no—
123C22×D61—81no—
124D4×C61—22no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2411yescharacteristic
134C22⋊D61—42no—
135C22⋊D61—42no—
136C22⋊D61—42no—
137C22⋊D61—81no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—81no—
143D244—21no—
144D244—21no—
145D244—21no—
146D244—21no—
147D244—21no—
148D244—21no—
149D244—21no—
150D244—42no—
151D244—42no—
152D244—42no—
153D244—81no—
154D244#4112yes—
155C4×D61—42no—
156C4×D61—81no—
157C8×C61—21no—
158C8×C61—21no—
159C8×C61—21no—
160C8×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61AGL(1,ℤ/8)12yes—
167C22×C61C22×D411yescharacteristic
168C2×D61—22no—
169C2×D61—41no—
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—41no—
180C2×D61—84no—
181C2×D61—84no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61C2×#4111yescharacteristic
187C4×C61H(5,𝔽2)11yescharacteristic
188Dic61—41no—
189Dic61—41no—
190Dic61—41no—
191Dic61—41no—
192#3318—611nomaximal, Sylow
193C2×C61—22no—
194C2×C61—41no—
195C2×C61#54611yescharacteristic
196C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C61#57611yescharacteristic
198D61—42no—
199D61—81no—
200D61—81no—
201D61—81no—
202#553—611no—
203D42—611no—
204#490—611no—
205#482—611no—
206#481—611no—
207#478—611no—
208#469—611no—
209#466—611no—
210#459—611no—
211#447—611no—
212#447—611no—
213#442—611no—
214#435D6111yescharacteristic, complemented
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×M16C2×D6111yescharacteristic, complemented
225C22×C8C2×D6111yescharacteristic, complemented
226#127—611no—
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
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#102—611no—
257#102—611no—
258C22⋊C8C2×D6111yescharacteristic, complemented
259C22⋊C8C2×D6111yescharacteristic, complemented
260#97C2×D6111yescharacteristic, complemented
261C24—1221no—
262C24—1221no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4—611no—
266C2×D4—611no—
267C2×D4—1222no—
268C2×D4—1222no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—2441no—
278C2×D4—2441no—
279C2×D4—2444no—
280C2×D4D24411yescharacteristic
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4C22×D6111yescharacteristic
285C22×C4C22×D6111yescharacteristic
286D8—1222no—
287D8—2441no—
288D8—2441no—
289M16—41no—
290C2×C8—41no—
291C2×C8C22×D6111yescharacteristic
292C2×C8C22×D6111yescharacteristic
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⋊C4D24411yescharacteristic
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4D24411yescharacteristic
311C22⋊C4D24411yescharacteristic
312C42—1221no—
313C42C22×D6111yescharacteristic
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—1221no—
318C23—4881no—
319C23—4881no—
320C23—2442no—
321C23—2442no—
322C23—2442no—
323C23—2442no—
324C23C2×D24411yescharacteristic
325C23C2×D24411yescharacteristic
326D4—22no—
327D4—612no—
328D4—1221no—
329D4—1221no—
330D4—1221no—
331D4—1221no—
332D4—1221no—
333D4—1221no—
334D4—1221no—
335D4—4881no—
336D4—4881no—
337D4—2442no—
338D4—2442no—
339D4—2442no—
340D4—2442no—
341D4—2442no—
342D4—2442no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—4881no—
352C2×C4—4881no—
353C2×C4—2442no—
354C2×C4C2×D24411yescharacteristic
355C2×C4C2×D24411yescharacteristic
356C2×C4C2×D24411yescharacteristic
357C2×C4C2×D24411yescharacteristic
358C2×C4C23×D6111yescharacteristic
359C8—21no—
360C8—21no—
361C8—21no—
362C8—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—1222no—
369C22—4884no—
370C22—4884no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22—2441no—
375C22—2441no—
376C22—2441no—
377C22—2441no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22#1451980512yes—
383C22C22×D24411yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—2441no—
389C4—2441no—
390C4—2441no—
391C4—2441no—
392C4#41×D6111yescharacteristic
393C4#1451982211yescharacteristic
394C2—22no—
395C2—41no—
396C2—4881no—
397C2—4881no—
398C2—4881no—
399C2—2442no—
400C2#1684040711yescharacteristic
401C2C2×#1451980511yescharacteristic
402C2#1684056711yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3318
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #16840458C2semidirect
2. D4×D244C2semidirect
3. #16840127C2semidirect
4. #16840087C2semidirect
5. #16840081C2semidirect
6. #16840063C2semidirect
7. #16840015C2semidirect
8. #16839998C2semidirect
9. #16839958C2semidirect
10. #16839898C2semidirect
11. #16839898C2semidirect
12. #16839875C2semidirect
13. #16839768C2semidirect
14. C2×#14519699C2semidirect
15. C61×#435C2semidirect
20. C2×D488C22semidirect
21. C2×D488C22semidirect
24. #14519769C22semidirect
29. #14519751C22semidirect
30. #14519751C22semidirect
35. C4×D244C22semidirect
37. #14519736C22semidirect
38. C2×C4⋊Dic61C22semidirect
39. #14519711C22semidirect
40. #14519709C22semidirect
41. #14519709C22semidirect
45. #14519699C22semidirect
46. #14519699C22semidirect
47. #14519699C22semidirect
48. #14519699C22semidirect
49. #14519699C22semidirect
50. #14519699C22semidirect
51. #14519699C22semidirect
52. C2×M16×C61C22semidirect
53. C22×C8×C61C22semidirect
55. C4⋊C8×C61C22semidirect
56. C22⋊C8×C61C22semidirect
57. C22⋊C8×C61C22semidirect
58. #97×C61C22semidirect
214. #435D61semidirect
217. C61#3318semidirect
224. C2×M16C2×D61semidirect
225. C22×C8C2×D61semidirect
247. C4⋊C8C2×D61semidirect
258. C22⋊C8C2×D61semidirect
259. C22⋊C8C2×D61semidirect
260. #97C2×D61semidirect