Finite Group Databasebeta

← #23775545

Subgroups — #23775545

Order 10112.

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#19099265C211yesmaximal, characteristic, complemented
2D4×C22⋊D79C211yesmaximal, characteristic, complemented
3#19098926C211yesmaximal, characteristic, complemented
4#19098886C211yesmaximal, characteristic, complemented
5#19098882C211yesmaximal, characteristic, complemented
6#19098865C211yesmaximal, characteristic, complemented
7#19098813C211yesmaximal, characteristic, complemented
8#19098797C211yesmaximal, characteristic, complemented
9#19098756C211yesmaximal, characteristic, complemented
10#19098695C211yesmaximal, characteristic, complemented
11#19098675C211yesmaximal, characteristic, complemented
12#19098631C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic, complemented
14C2×#14579082C211yesmaximal, characteristic, complemented
15#447×C79C211yesmaximal, characteristic, complemented
16C22×C22⋊D79—21no—
17C2×D4×D79C2211yescharacteristic
18C2×#11929609C2211yescharacteristic, complemented
19C2×#11929607C2211yescharacteristic, complemented
20C22×C79⋊C8C2211yescharacteristic, complemented
21#14579157C2211yescharacteristic
22#14579154—21no—
23#14579152C2211yescharacteristic, complemented
24#14579145—21no—
25#14579135C2211yescharacteristic
26#14579133—21no—
27#14579133—21no—
28#14579132C2211yescharacteristic
29#14579132C2211yescharacteristic, complemented
30#14579130—21no—
31#14579129—21no—
32D4×Dic79—21no—
33D4×Dic79C2211yescharacteristic
34D4×Dic79C2211yescharacteristic, complemented
35C4×C22⋊D79C2211yescharacteristic
36#14579119C2211yescharacteristic, complemented
37C2×C4⋊Dic79C2211yescharacteristic, complemented
38#14579094C2211yescharacteristic, complemented
39#14579093C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42#14579083C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic, complemented
44#14579082C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic, complemented
48#14579082C2211yescharacteristic, complemented
49#14579081C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51#14579071C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C2×D8×C79C2211yescharacteristic
54C2×D8×C79C2211yescharacteristic, complemented
55#121×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×D316C2311yescharacteristic
61C2×C22⋊D79—21no—
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—
72C22×Dic79—21no—
73C22×Dic79—21no—
74C2×C4×D79C2311yescharacteristic
75#11929609—41no—
76#11929607—41no—
77C2×C79⋊C8—41no—
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C4⋊Dic79—21no—
81C4⋊Dic79—21no—
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4D411yescharacteristic
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79D411yescharacteristic
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4D411yescharacteristic
95C4×Dic79—21no—
96C4×Dic79C2311yescharacteristic
97C24×C79—21no—
98C2×D4×C79—22no—
99C2×D4×C79—21no—
100C2×D4×C79—21no—
101C2×D4×C79—41no—
102C2×D4×C79C2311yescharacteristic
103C2×D4×C79C2311yescharacteristic
104C2×D4×C79C2311yescharacteristic
105C22×C4×C79C2311yescharacteristic
106D8×C79—22no—
107D8×C79—41no—
108C2×C8×C79C2311yescharacteristic
109C2×C8×C79C2311yescharacteristic
110C4⋊C4×C79C2311yescharacteristic
111C22⋊C4×C79—21no—
112C23×C79—21no—
113C23×C79—21no—
114C23×C79—21no—
115C23×C79—42no—
116C23×C79—42no—
117C23×C79—81no—
118C23×C79C2×D411yescharacteristic
119C22×D79—21no—
120C22×D79—42no—
121C22×D79—42no—
122C22×D79—81no—
123C22×D79C2×D411yescharacteristic
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—21no—
129D4×C79—42no—
130D4×C79—42no—
131D4×C79#4112yes—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2411yescharacteristic
137C22⋊D79—22no—
138C22⋊D79—42no—
139C22⋊D79—42no—
140C22⋊D79—42no—
141C22⋊D79—42no—
142C22⋊D79—81no—
143C22⋊D79—81no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—42no—
148C2×Dic79—81no—
149C2×Dic79—81no—
150C2×Dic79C2×D411yescharacteristic
151C2×Dic79C2×D411yescharacteristic
152C2×Dic79C2×D411yescharacteristic
153D316—21no—
154D316—21no—
155C4×D79—21no—
156C4×D79—21no—
157C8×C79—21no—
158C8×C79—21no—
159C79⋊C8—21no—
160C79⋊C8—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—22no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79—84no—
173C22×C79AGL(1,ℤ/8)12yes—
174C22×C79C22×D411yescharacteristic
175C2×D79—21no—
176C2×D79—21no—
177C2×D79—21no—
178C2×D79—41no—
179C2×D79—41no—
180C2×D79—41no—
181C2×D79—84no—
182C4×C79—21no—
183C4×C79—41no—
184C4×C79C2×#4111yescharacteristic
185C4×C79H(5,𝔽2)11yescharacteristic
186Dic79—21no—
187Dic79—21no—
188Dic79—21no—
189Dic79—41no—
190Dic79—41no—
191Dic79—41no—
192C2×C79—22no—
193C2×C79—42no—
194C2×C79—81no—
195C2×C79—81no—
196C2×C79#54611yescharacteristic
197C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C79#57611yescharacteristic
199D79—41no—
200D79—81no—
201#3318—791nomaximal, Sylow
202C79#331811yescharacteristic, complemented, Sylow
203#553—791no—
204D42—791no—
205#490—791no—
206#482—791no—
207#481—791no—
208#478—791no—
209#469—791no—
210#466—791no—
211#459—791no—
212#447—791no—
213#447D7911yescharacteristic, complemented
214#442—791no—
215#435—791no—
216#418—791no—
217C2×#102—791no—
218C22×D4—791no—
219C22×D4—1581no—
220C22×D4C2×D7911yescharacteristic
221C2×D8—791no—
222C2×D8C2×D7911yescharacteristic
223C2×D8C2×D7911yescharacteristic, complemented
224C2×M16—791no—
225C22×C8—791no—
226#127—791no—
227#126—1581no—
228#125—791no—
229#123—1581no—
230#121—791no—
231#121—791no—
232#121—791no—
233#121—1581no—
234#121—1581no—
235#121C2×D7911yescharacteristic, complemented
236#120—1581no—
237#120—1581no—
238C4×D4—791no—
239C4×D4—791no—
240C4×D4—791no—
241C4×D4—1581no—
242#117—791no—
243C2×C4⋊C4—791no—
244#107—791no—
245#106—791no—
246#106—791no—
247C4⋊C8—791no—
248#102—791no—
249#102—791no—
250#102—791no—
251#102—791no—
252#102—791no—
253#102—791no—
254#102—791no—
255#102—791no—
256#102C2×D7911yescharacteristic
257#102C2×D7911yescharacteristic, complemented
258C22⋊C8—791no—
259C22⋊C8C2×D7911yescharacteristic, complemented
260#97—791no—
261C24—21no—
262C24—1581no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—3164no—
268C2×D4—3161no—
269C2×D4—791no—
270C2×D4—791no—
271C2×D4—1581no—
272C2×D4—1581no—
273C2×D4—1581no—
274C2×D4—1581no—
275C2×D4—1581no—
276C2×D4—1582no—
277C2×D4—1581no—
278C2×D4C22×D7911yescharacteristic
279C2×D4C22×D7911yescharacteristic
280C2×D4C22×D7911yescharacteristic
281C22×C4—791no—
282C22×C4—1581no—
283C22×C4—1581no—
284C22×C4—1581no—
285C22×C4C22×D7911yescharacteristic
286D8—22no—
287D8—41no—
288D8—3161no—
289M16—3161no—
290C2×C8—3161no—
291C2×C8—791no—
292C2×C8—791no—
293C2×C8C22×D7911yescharacteristic
294C2×C8C22×D7911yescharacteristic
295C4⋊C4—791no—
296C4⋊C4—791no—
297C4⋊C4—791no—
298C4⋊C4—791no—
299C4⋊C4—1581no—
300C4⋊C4—1581no—
301C4⋊C4—1581no—
302C4⋊C4C22×D7911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—791no—
305C22⋊C4—791no—
306C22⋊C4—1581no—
307C22⋊C4—1581no—
308C22⋊C4—1581no—
309C22⋊C4—1581no—
310C22⋊C4—1581no—
311C22⋊C4—1581no—
312C42—791no—
313C42—1581no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—81no—
320C23—3162no—
321C23—3162no—
322C23—791no—
323C23—6321no—
324C23—1581no—
325C23D4×D7911yescharacteristic
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—42no—
332D4—42no—
333D4—3162no—
334D4—3162no—
335D4—3162no—
336D4—3162no—
337D4—6321no—
338D4—6321no—
339D4—1582no—
340D4—1581no—
341D4—1581no—
342D4#1192962312yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—3162no—
347C2×C4—791no—
348C2×C4—791no—
349C2×C4—791no—
350C2×C4—6321no—
351C2×C4—6321no—
352C2×C4—1581no—
353C2×C4—1581no—
354C2×C4—1581no—
355C2×C4—1581no—
356C2×C4—1581no—
357C2×C4D4×D7911yescharacteristic
358C2×C4C23×D7911yescharacteristic
359C8—21no—
360C8—21no—
361C8—1581no—
362C8—1581no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—84no—
375C22—3161no—
376C22—3161no—
377C22—3161no—
378C22—6324no—
379C22—1581no—
380C22—1581no—
381C22—1581no—
382C22#1457918512yes—
383C22C2×D4×D7911yescharacteristic
384C4—21no—
385C4—41no—
386C4—3161no—
387C4—3161no—
388C4—3161no—
389C4—1581no—
390C4—1581no—
391C4—1581no—
392C4C2×#1192962311yescharacteristic
393C4#1457920611yescharacteristic
394C2—22no—
395C2—42no—
396C2—81no—
397C2—81no—
398C2—3161no—
399C2—6321no—
400C2#1909920011yescharacteristic
401C2C2×#1457918511yescharacteristic
402C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#447×C79C2
socleC22×C79C22×D4
hypercenter#447D79
hypocenterC79#3318
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #19099265C2semidirect
2. D4×C22⋊D79C2semidirect
3. #19098926C2semidirect
4. #19098886C2semidirect
5. #19098882C2semidirect
6. #19098865C2semidirect
7. #19098813C2semidirect
8. #19098797C2semidirect
9. #19098756C2semidirect
10. #19098695C2semidirect
11. #19098675C2semidirect
12. #19098631C2semidirect
13. #19098566C2semidirect
14. C2×#14579082C2semidirect
15. #447×C79C2semidirect
18. C2×#11929609C22semidirect
19. C2×#11929607C22semidirect
20. C22×C79⋊C8C22semidirect
23. #14579152C22semidirect
29. #14579132C22semidirect
34. D4×Dic79C22semidirect
36. #14579119C22semidirect
37. C2×C4⋊Dic79C22semidirect
38. #14579094C22semidirect
39. #14579093C22semidirect
40. #14579093C22semidirect
41. Dic79⋊C8C22semidirect
42. #14579083C22semidirect
43. #14579083C22semidirect
46. #14579082C22semidirect
47. #14579082C22semidirect
48. #14579082C22semidirect
49. #14579081C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. #14579071C22semidirect
54. C2×D8×C79C22semidirect
55. #121×C79C22semidirect
57. #102×C79C22semidirect
58. C22⋊C8×C79C22semidirect
202. C79#3318semidirect
213. #447D79semidirect
223. C2×D8C2×D79semidirect
235. #121C2×D79semidirect
257. #102C2×D79semidirect
259. C22⋊C8C2×D79semidirect