Finite Group Databasebeta

← #21458057

Subgroups — #21458057

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#16840475C211yesmaximal, characteristic, complemented
2D4×C22⋊D61C211yesmaximal, characteristic, complemented
3#16840107C211yesmaximal, characteristic, complemented
4#16840086C211yesmaximal, characteristic, complemented
5#16840085C211yesmaximal, characteristic, complemented
6#16840050C211yesmaximal, characteristic, complemented
7#16840015C211yesmaximal, characteristic, complemented
8#16840014C211yesmaximal, characteristic, complemented
9#16839956C211yesmaximal, characteristic, complemented
10#16839897C211yesmaximal, characteristic, complemented
11#16839896C211yesmaximal, characteristic, complemented
12#16839842C211yesmaximal, characteristic, complemented
13#16839838C211yesmaximal, characteristic, complemented
14#16839765C211yesmaximal, characteristic, complemented
15C61×#418C211yesmaximal, characteristic, complemented
16C22×C22⋊D61—21no—
17C2×D4×D61C2211yescharacteristic
18C2×D488C2211yescharacteristic, complemented
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic, complemented
21C2×#11758189C2211yescharacteristic, complemented
22#14519776C2211yescharacteristic, complemented
23#14519773C2211yescharacteristic
24#14519765—21no—
25#14519763—21no—
26#14519752C2211yescharacteristic, complemented
27#14519751C2211yescharacteristic
28#14519751C2211yescharacteristic, complemented
29#14519750—21no—
30#14519749—21no—
31#14519748C2211yescharacteristic
32#14519746—21no—
33#14519745—21no—
34D4×Dic61C2211yescharacteristic
35#14519739C2211yescharacteristic, complemented
36C4×C22⋊D61C2211yescharacteristic
37#14519735C2211yescharacteristic, complemented
38#14519734—21no—
39#14519710C2211yescharacteristic, complemented
40#14519709C2211yescharacteristic, complemented
41#14519708C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic, complemented
54#117×C61C2211yescharacteristic, complemented
55#102×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic, complemented
59C24×C61—21no—
60C23×D61—21no—
61C2×D4×C61—22no—
62C2×D4×C61—21no—
63C2×D4×C61—41no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—44no—
74C2×C22⋊D61D411yescharacteristic
75C22×Dic61—21no—
76D4×D61—22no—
77D4×D61—41no—
78C2×D244—21no—
79C2×D244C2311yescharacteristic
80C2×D244C2311yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61C2311yescharacteristic
83C2×Dic122—21no—
84M16×C61—41no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C42×C61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61D411yescharacteristic
94#11758199—22no—
95#11758199—41no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198D411yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103C4⋊Dic61C2311yescharacteristic
104#11758196—21no—
105#11758196D411yescharacteristic
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110D488—41no—
111#11758189—41no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—42no—
115C23×C61—42no—
116C23×C61—81no—
117C23×C61C2×D411yescharacteristic
118C22×D61—21no—
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—42no—
128D4×C61#4112yes—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—22no—
136C22⋊D61—42no—
137C22⋊D61—42no—
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—81no—
141C22⋊D61—81no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—42no—
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147C2×Dic61C2×D411yescharacteristic
148D244—21no—
149D244—21no—
150D244—21no—
151D244—21no—
152D244—81no—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—42no—
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—84no—
171C22×C61C22×D411yescharacteristic
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—84no—
182C4×C61—21no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61C2×#4111yescharacteristic
186C4×C61H(5,𝔽2)11yescharacteristic
187Dic61—21no—
188Dic61—21no—
189Dic61—41no—
190Dic61—41no—
191Dic61AGL(1,ℤ/8)12yes—
192#3325—611nomaximal, Sylow
193C2×C61—42no—
194C2×C61—41no—
195C2×C61—81no—
196C2×C61#54611yescharacteristic
197C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C61#57611yescharacteristic
199D61—41no—
200D61—81no—
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#447—611no—
213C4×D8—611no—
214#436—611no—
215#418—611no—
216#418D6111yescharacteristic, complemented
217C61#332511yescharacteristic, complemented, Sylow
218C22×D4—611no—
219C22×D4—1221no—
220C22×D4C2×D6111yescharacteristic
221C2×D8—611no—
222C2×D8—611no—
223C2×D8—611no—
224C2×M16—611no—
225C2×M16C2×D6111yescharacteristic, complemented
226C4⋊Q8—611no—
227#127—611no—
228#124—1221no—
229#124—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—611no—
241#117—611no—
242#117—1221no—
243#117C2×D6111yescharacteristic, complemented
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#102C2×D6111yescharacteristic
255#102C2×D6111yescharacteristic
256#102C2×D6111yescharacteristic, complemented
257#102C2×D6111yescharacteristic, complemented
258C22⋊C8—611no—
259C22⋊C8—611no—
260C4×C8—611no—
261C24—21no—
262C24—1221no—
263C2×Q8—1221no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—611no—
268C2×D4—611no—
269C2×D4—611no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1222no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—2441no—
279C2×D4—2444no—
280C2×D4C22×D6111yescharacteristic
281C2×D4C22×D6111yescharacteristic
282C22×C4—611no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4C22×D6111yescharacteristic
286D8—1222no—
287D8—2441no—
288D8—2441no—
289M16—41no—
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—1221no—
299C4⋊C4C22×D6111yescharacteristic
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—21no—
312C42—611no—
313C42—1221no—
314C23—21no—
315C23—21no—
316C23—42no—
317C23—42no—
318C23—81no—
319C23—611no—
320C23—1221no—
321C23—1221no—
322C23—4881no—
323C23—2442no—
324C23—2442no—
325C23D4×D6111yescharacteristic
326Q8—4881no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—1222no—
332D4—1221no—
333D4—1221no—
334D4—1221no—
335D4—1221no—
336D4—4881no—
337D4—4881no—
338D4—4881no—
339D4—2442no—
340D4—2442no—
341D4—2442no—
342D4—2442no—
343D4#1175822212yes—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—611no—
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—84no—
373C22—1221no—
374C22—1221no—
375C22—1221no—
376C22—4884no—
377C22—2441no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22C2×D4×D6111yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—612no—
388C4—1221no—
389C4—1221no—
390C4—2441no—
391C4—2441no—
392C4C2×#1175822211yescharacteristic
393C4#1451982211yescharacteristic
394C2—41no—
395C2—42no—
396C2—81no—
397C2—4881no—
398C2—4881no—
399C2—2441no—
400C2#1684040211yescharacteristic
401C2AGL(1,ℤ/8)×D6111yescharacteristic
402C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#418C2
socleC22×C61C22×D4
hypercenter#418D61
hypocenterC61#3325
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #16840475C2semidirect
2. D4×C22⋊D61C2semidirect
3. #16840107C2semidirect
4. #16840086C2semidirect
5. #16840085C2semidirect
6. #16840050C2semidirect
7. #16840015C2semidirect
8. #16840014C2semidirect
9. #16839956C2semidirect
10. #16839897C2semidirect
11. #16839896C2semidirect
12. #16839842C2semidirect
13. #16839838C2semidirect
14. #16839765C2semidirect
15. C61×#418C2semidirect
18. C2×D488C22semidirect
20. C2×#11758199C22semidirect
21. C2×#11758189C22semidirect
22. #14519776C22semidirect
26. #14519752C22semidirect
28. #14519751C22semidirect
35. #14519739C22semidirect
37. #14519735C22semidirect
39. #14519710C22semidirect
40. #14519709C22semidirect
41. #14519708C22semidirect
42. #14519706C22semidirect
43. #14519699C22semidirect
44. #14519699C22semidirect
46. #14519698C22semidirect
47. #14519697C22semidirect
48. #14519697C22semidirect
49. C22⋊#92418C22semidirect
50. #14519689C22semidirect
51. C8×Dic61C22semidirect
53. C2×M16×C61C22semidirect
54. #117×C61C22semidirect
57. #102×C61C22semidirect
58. #102×C61C22semidirect
216. #418D61semidirect
217. C61#3325semidirect
225. C2×M16C2×D61semidirect
243. #117C2×D61semidirect
256. #102C2×D61semidirect
257. #102C2×D61semidirect