Finite Group Databasebeta

← #21458043

Subgroups — #21458043

Order 7808.

448 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840483C211yesmaximal, characteristic, complemented
2D4×C22⋊D61C211yesmaximal, characteristic
3#16840107C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840085C211yesmaximal, characteristic, complemented
6#16840040C211yesmaximal, characteristic, complemented
7#16840010C211yesmaximal, characteristic, complemented
8#16840005C211yesmaximal, characteristic, complemented
9#16839960C211yesmaximal, characteristic, complemented
10#16839911C211yesmaximal, characteristic, complemented
11SD16×Dic61C211yesmaximal, characteristic, complemented
12#16839837C211yesmaximal, characteristic, complemented
13#16839767C211yesmaximal, characteristic, complemented
14#16839765C211yesmaximal, characteristic, complemented
15C61×#450C211yesmaximal, characteristic, complemented
16C22×C22⋊D61—21no—
17C2×D4×D61C2211yescharacteristic
18C2×#11758201C2211yescharacteristic, complemented
19C2×#11758194C2211yescharacteristic, complemented
20C2×#11758189C2211yescharacteristic, complemented
21#14519776C2211yescharacteristic, complemented
22#14519773C2211yescharacteristic
23#14519772—21no—
24#14519770—21no—
25#14519763—21no—
26#14519753C2211yescharacteristic, complemented
27#14519751C2211yescharacteristic
28#14519749—21no—
29#14519748C2211yescharacteristic
30#14519746—21no—
31#14519745—21no—
32Q8×Dic61C2211yescharacteristic, complemented
33#14519742—21no—
34D4×Dic61C2211yescharacteristic
35C4×C22⋊D61C2211yescharacteristic
36#14519736C2211yescharacteristic, complemented
37#14519735C2211yescharacteristic, complemented
38#14519711C2211yescharacteristic, complemented
39#14519710C2211yescharacteristic, complemented
40#14519709C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519701C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic, complemented
48#14519698C2211yescharacteristic, complemented
49#14519697C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic, complemented
55C22⋊Q8×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic, complemented
59C24×C61—21no—
60C23×D61—21no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—22no—
63C2×D4×C61—21no—
64C2×D4×C61—41no—
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
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×D244C2311yescharacteristic
79C2×C4×D61C2311yescharacteristic
80C2×Dic122—21no—
81SD16×C61—22no—
82SD16×C61—41no—
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C4⋊C4×C61—21no—
86C4⋊C4×C61C2311yescharacteristic
87C22⋊C4×C61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61D411yescharacteristic
92#11758201—41no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198D411yescharacteristic
97C4⋊Dic61—21no—
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61—21no—
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—42no—
115C23×C61—42no—
116C23×C61—81no—
117C23×C61C2×D411yescharacteristic
118C22×D61—21no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—81no—
122C22×D61C2×D411yescharacteristic
123Q8×C61—21no—
124Q8×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—42no—
129D4×C61#4112yes—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2411yescharacteristic
136C22⋊D61—22no—
137C22⋊D61—42no—
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—42no—
141C22⋊D61—81no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—42no—
146C2×Dic61C2×D411yescharacteristic
147C2×Dic61C2×D411yescharacteristic
148C2×Dic61C2×D411yescharacteristic
149D244—21no—
150D244—21no—
151C4×D61—21no—
152C4×D61—21no—
153Dic122—42no—
154C8×C61—21no—
155C8×C61—21no—
156#92418—21no—
157#92418—21no—
158C22×C61—22no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—84no—
168C22×C61C22×D411yescharacteristic
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—84no—
176C4×C61—21no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61C2×#4111yescharacteristic
180C4×C61H(5,𝔽2)11yescharacteristic
181Dic61—21no—
182Dic61—21no—
183Dic61—41no—
184Dic61—41no—
185Dic61—41no—
186Dic61AGL(1,ℤ/8)12yes—
187#3324—611nomaximal, Sylow
188C2×C61—42no—
189C2×C61—41no—
190C2×C61—81no—
191C2×C61#54611yescharacteristic
192C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C61#57711yescharacteristic
194D61—41no—
195D61—81no—
196#556—611no—
197D42—611no—
198#486—611no—
199#482—611no—
200#482—611no—
201#474—611no—
202#468—611no—
203#468—611no—
204#460—611no—
205#450—611no—
206#450D6111yescharacteristic, complemented
207C4×SD16—611no—
208#436—611no—
209#418—611no—
210#418—611no—
211C61#332411yescharacteristic, complemented, Sylow
212C22×D4—611no—
213C22×D4—1221no—
214C22×D4C2×D6111yescharacteristic
215C2×SD16—611no—
216C2×SD16C2×D6111yescharacteristic
217C2×SD16C2×D6111yescharacteristic, complemented
218C2×M16—611no—
219C2×M16—611no—
220C4⋊Q8—611no—
221#127—611no—
222#126—1221no—
223#126—1221no—
224#124—1221no—
225C22⋊Q8—611no—
226C22⋊Q8C2×D6111yescharacteristic, complemented
227#121—611no—
228#121—611no—
229#121—1221no—
230#120—1221no—
231#120—1221no—
232C4×Q8—611no—
233C4×Q8—1221no—
234C4×D4—611no—
235C4×D4—611no—
236#117—611no—
237#117—611no—
238#107—611no—
239#107—611no—
240#106—611no—
241C4⋊C8—611no—
242#103—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102C2×D6111yescharacteristic
251#102C2×D6111yescharacteristic, complemented
252C22⋊C8—611no—
253C22⋊C8C2×D6111yescharacteristic, complemented
254C4×C8—611no—
255C24—21no—
256C24—1221no—
257C2×Q8—1221no—
258C2×Q8C22×D6111yescharacteristic
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4—1222no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—2441no—
271C2×D4—2444no—
272C2×D4C22×D6111yescharacteristic
273C2×D4C22×D6111yescharacteristic
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4C22×D6111yescharacteristic
277SD16—22no—
278SD16—41no—
279SD16—2441no—
280M16—2441no—
281M16—2441no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8C22×D6111yescharacteristic
285C2×C8C22×D6111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—611no—
288C4⋊C4—611no—
289C4⋊C4—611no—
290C4⋊C4—611no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4C22×D6111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—611no—
297C22⋊C4—611no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C42—611no—
305C42—1221no—
306C42—1221no—
307C42—1221no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—611no—
314C23—1221no—
315C23—4881no—
316C23—2442no—
317C23—2442no—
318C23D4×D6111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—2442no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—1222no—
327D4—1221no—
328D4—1221no—
329D4—4881no—
330D4—2442no—
331D4—2442no—
332D4—2442no—
333D4—2442no—
334D4#1175822412yes—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—611no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—2442no—
348C2×C4D4×D6111yescharacteristic
349C2×C4C23×D6111yescharacteristic
350C8—21no—
351C8—21no—
352C8—1221no—
353C8—1221no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—84no—
364C22—1221no—
365C22—1221no—
366C22—1221no—
367C22—4884no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22C2×D4×D6111yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—612no—
376C4—1221no—
377C4—1221no—
378C4—2441no—
379C4—2441no—
380C4—2441no—
381C4C2×#1175822411yescharacteristic
382C4#1451982211yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—4881no—
387C2—2441no—
388C2#1684039911yescharacteristic
389C2AGL(1,ℤ/8)×D6111yescharacteristic
390C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3324
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #16840483C2semidirect
3. #16840107C2semidirect
4. #16840087C2semidirect
5. #16840085C2semidirect
6. #16840040C2semidirect
7. #16840010C2semidirect
8. #16840005C2semidirect
9. #16839960C2semidirect
10. #16839911C2semidirect
11. SD16×Dic61C2semidirect
12. #16839837C2semidirect
13. #16839767C2semidirect
14. #16839765C2semidirect
15. C61×#450C2semidirect
18. C2×#11758201C22semidirect
19. C2×#11758194C22semidirect
20. C2×#11758189C22semidirect
21. #14519776C22semidirect
26. #14519753C22semidirect
32. Q8×Dic61C22semidirect
36. #14519736C22semidirect
37. #14519735C22semidirect
38. #14519711C22semidirect
39. #14519710C22semidirect
40. #14519709C22semidirect
41. #14519706C22semidirect
42. #14519701C22semidirect
43. #14519699C22semidirect
44. #14519699C22semidirect
47. #14519698C22semidirect
48. #14519698C22semidirect
49. #14519697C22semidirect
50. #14519689C22semidirect
51. C8×Dic61C22semidirect
54. C2×SD16×C61C22semidirect
55. C22⋊Q8×C61C22semidirect
57. #102×C61C22semidirect
58. C22⋊C8×C61C22semidirect
206. #450D61semidirect
211. C61#3324semidirect
217. C2×SD16C2×D61semidirect
226. C22⋊Q8C2×D61semidirect
251. #102C2×D61semidirect
253. C22⋊C8C2×D61semidirect