Finite Group Databasebeta

← #23775624

Subgroups — #23775624

Order 10112.

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#19099284C211yesmaximal, characteristic, complemented
2D4×C22⋊D79C211yesmaximal, characteristic
3#19098908C211yesmaximal, characteristic, complemented
4#19098888C211yesmaximal, characteristic, complemented
5#19098886C211yesmaximal, characteristic, complemented
6#19098841C211yesmaximal, characteristic, complemented
7#19098811C211yesmaximal, characteristic, complemented
8#19098806C211yesmaximal, characteristic, complemented
9#19098761C211yesmaximal, characteristic, complemented
10#19098712C211yesmaximal, characteristic, complemented
11SD16×Dic79C211yesmaximal, characteristic, complemented
12#19098638C211yesmaximal, characteristic, complemented
13#19098568C211yesmaximal, characteristic, complemented
14#19098566C211yesmaximal, characteristic, complemented
15#450×C79C211yesmaximal, characteristic, complemented
16C22×C22⋊D79—21no—
17C2×D4×D79C2211yescharacteristic
18C2×#11929611C2211yescharacteristic, complemented
19C2×#11929608C2211yescharacteristic, complemented
20C2×#11929607C2211yescharacteristic, complemented
21#14579160C2211yescharacteristic, complemented
22#14579157C2211yescharacteristic
23#14579156—21no—
24#14579154—21no—
25#14579147—21no—
26#14579137C2211yescharacteristic, complemented
27#14579135C2211yescharacteristic
28#14579133—21no—
29#14579132C2211yescharacteristic
30#14579130—21no—
31#14579129—21no—
32Q8×Dic79C2211yescharacteristic, complemented
33#14579126—21no—
34D4×Dic79C2211yescharacteristic
35C4×C22⋊D79C2211yescharacteristic
36#14579120C2211yescharacteristic, complemented
37#14579119C2211yescharacteristic, complemented
38#14579095C2211yescharacteristic, complemented
39#14579094C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic, complemented
48#14579082C2211yescharacteristic, complemented
49#14579081C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic, complemented
55C22⋊Q8×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×Dic158—21no—
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—44no—
68C2×C22⋊D79D411yescharacteristic
69D4×D79—22no—
70D4×D79—41no—
71C22×Dic79—21no—
72C2×C4×D79C2311yescharacteristic
73#11929611—41no—
74#11929608—41no—
75#11929607—41no—
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C4⋊Dic79—21no—
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4D411yescharacteristic
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79D411yescharacteristic
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4D411yescharacteristic
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79—21no—
96C4×Dic79C2311yescharacteristic
97C24×C79—21no—
98C2×Q8×C79C2311yescharacteristic
99C2×D4×C79—22no—
100C2×D4×C79—21no—
101C2×D4×C79—41no—
102C2×D4×C79C2311yescharacteristic
103C2×D4×C79C2311yescharacteristic
104C22×C4×C79C2311yescharacteristic
105SD16×C79—22no—
106SD16×C79—41no—
107C2×C8×C79C2311yescharacteristic
108C2×C8×C79C2311yescharacteristic
109C4⋊C4×C79—21no—
110C4⋊C4×C79C2311yescharacteristic
111C22⋊C4×C79—21no—
112C23×C79—21no—
113C23×C79—21no—
114C23×C79—42no—
115C23×C79—42no—
116C23×C79—81no—
117C23×C79C2×D411yescharacteristic
118C22×D79—21no—
119C22×D79—42no—
120C22×D79—42no—
121C22×D79—81no—
122C22×D79C2×D411yescharacteristic
123Q8×C79—21no—
124Q8×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—42no—
129D4×C79#4112yes—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2411yescharacteristic
136C22⋊D79—22no—
137C22⋊D79—42no—
138C22⋊D79—42no—
139C22⋊D79—42no—
140C22⋊D79—42no—
141C22⋊D79—81no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—42no—
146C2×Dic79C2×D411yescharacteristic
147C2×Dic79C2×D411yescharacteristic
148C2×Dic79C2×D411yescharacteristic
149D316—21no—
150D316—21no—
151C4×D79—21no—
152C4×D79—21no—
153Dic158—42no—
154C8×C79—21no—
155C8×C79—21no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C22×C79—22no—
159C22×C79—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—84no—
168C22×C79C22×D411yescharacteristic
169C2×D79—21no—
170C2×D79—21no—
171C2×D79—21no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—84no—
176C4×C79—21no—
177C4×C79—41no—
178C4×C79—41no—
179C4×C79C2×#4111yescharacteristic
180C4×C79H(5,𝔽2)11yescharacteristic
181Dic79—21no—
182Dic79—21no—
183Dic79—41no—
184Dic79—41no—
185Dic79—41no—
186Dic79AGL(1,ℤ/8)12yes—
187C2×C79—42no—
188C2×C79—41no—
189C2×C79—81no—
190C2×C79#54611yescharacteristic
191C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C79#57711yescharacteristic
193D79—41no—
194D79—81no—
195#3324—791nomaximal, Sylow
196C79#332411yescharacteristic, complemented, Sylow
197#556—791no—
198D42—791no—
199#486—791no—
200#482—791no—
201#482—791no—
202#474—791no—
203#468—791no—
204#468—791no—
205#460—791no—
206#450—791no—
207#450D7911yescharacteristic, complemented
208C4×SD16—791no—
209#436—791no—
210#418—791no—
211#418—791no—
212C22×D4—791no—
213C22×D4—1581no—
214C22×D4C2×D7911yescharacteristic
215C2×SD16—791no—
216C2×SD16C2×D7911yescharacteristic
217C2×SD16C2×D7911yescharacteristic, complemented
218C2×M16—791no—
219C2×M16—791no—
220C4⋊Q8—791no—
221#127—791no—
222#126—1581no—
223#126—1581no—
224#124—1581no—
225C22⋊Q8—791no—
226C22⋊Q8C2×D7911yescharacteristic, complemented
227#121—791no—
228#121—791no—
229#121—1581no—
230#120—1581no—
231#120—1581no—
232C4×Q8—791no—
233C4×Q8—1581no—
234C4×D4—791no—
235C4×D4—791no—
236#117—791no—
237#117—791no—
238#107—791no—
239#107—791no—
240#106—791no—
241C4⋊C8—791no—
242#103—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102C2×D7911yescharacteristic
251#102C2×D7911yescharacteristic, complemented
252C22⋊C8—791no—
253C22⋊C8C2×D7911yescharacteristic, complemented
254C4×C8—791no—
255C24—21no—
256C24—1581no—
257C2×Q8—1581no—
258C2×Q8C22×D7911yescharacteristic
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—3164no—
263C2×D4—3161no—
264C2×D4—791no—
265C2×D4—791no—
266C2×D4—1581no—
267C2×D4—1581no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4—1582no—
272C2×D4C22×D7911yescharacteristic
273C2×D4C22×D7911yescharacteristic
274C22×C4—791no—
275C22×C4—1581no—
276C22×C4C22×D7911yescharacteristic
277SD16—22no—
278SD16—41no—
279SD16—3161no—
280M16—3161no—
281M16—3161no—
282C2×C8—791no—
283C2×C8—791no—
284C2×C8C22×D7911yescharacteristic
285C2×C8C22×D7911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—791no—
288C4⋊C4—791no—
289C4⋊C4—791no—
290C4⋊C4—791no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4C22×D7911yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—791no—
297C22⋊C4—791no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C42—791no—
305C42—1581no—
306C42—1581no—
307C42—1581no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—3162no—
314C23—3162no—
315C23—791no—
316C23—6321no—
317C23—1581no—
318C23D4×D7911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—3162no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—3162no—
327D4—3162no—
328D4—3162no—
329D4—3162no—
330D4—6321no—
331D4—1582no—
332D4—1581no—
333D4—1581no—
334D4#1192962312yes—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—3162no—
340C2×C4—791no—
341C2×C4—791no—
342C2×C4—791no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4—1581no—
348C2×C4D4×D7911yescharacteristic
349C2×C4C23×D7911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1581no—
353C8—1581no—
354C22—21no—
355C22—22no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—84no—
364C22—3161no—
365C22—3161no—
366C22—3161no—
367C22—6324no—
368C22—1581no—
369C22—1581no—
370C22—1581no—
371C22C2×D4×D7911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—3161no—
376C4—3161no—
377C4—3161no—
378C4—792no—
379C4—1581no—
380C4—1581no—
381C4C2×#1192962311yescharacteristic
382C4#1457920611yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—3161no—
387C2—6321no—
388C2#1909920011yescharacteristic
389C2AGL(1,ℤ/8)×D7911yescharacteristic
390C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#450×C79C2
socleC22×C79C22×D4
prime radicalD4×C22⋊D79C2
hypercenter#450D79
hypocenterC79#3324
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #19099284C2semidirect
3. #19098908C2semidirect
4. #19098888C2semidirect
5. #19098886C2semidirect
6. #19098841C2semidirect
7. #19098811C2semidirect
8. #19098806C2semidirect
9. #19098761C2semidirect
10. #19098712C2semidirect
11. SD16×Dic79C2semidirect
12. #19098638C2semidirect
13. #19098568C2semidirect
14. #19098566C2semidirect
15. #450×C79C2semidirect
18. C2×#11929611C22semidirect
19. C2×#11929608C22semidirect
20. C2×#11929607C22semidirect
21. #14579160C22semidirect
26. #14579137C22semidirect
32. Q8×Dic79C22semidirect
36. #14579120C22semidirect
37. #14579119C22semidirect
38. #14579095C22semidirect
39. #14579094C22semidirect
40. #14579093C22semidirect
41. Dic79⋊C8C22semidirect
42. #14579085C22semidirect
43. #14579083C22semidirect
44. #14579083C22semidirect
47. #14579082C22semidirect
48. #14579082C22semidirect
49. #14579081C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. C8×Dic79C22semidirect
54. C2×SD16×C79C22semidirect
55. C22⋊Q8×C79C22semidirect
57. #102×C79C22semidirect
58. C22⋊C8×C79C22semidirect
196. C79#3324semidirect
207. #450D79semidirect
217. C2×SD16C2×D79semidirect
226. C22⋊Q8C2×D79semidirect
251. #102C2×D79semidirect
253. C22⋊C8C2×D79semidirect